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| author | hardythe1 | 2015-04-07 15:58:05 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-04-07 15:58:05 +0530 |
| commit | c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131 (patch) | |
| tree | 725a7d43dc1687edf95bc36d39bebc3000f1de8f /_Power_Electronics | |
| parent | 62aa228e2519ac7b7f1aef53001f2f2e988a6eb1 (diff) | |
| download | Python-Textbook-Companions-c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131.tar.gz Python-Textbook-Companions-c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131.tar.bz2 Python-Textbook-Companions-c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131.zip | |
added books
Diffstat (limited to '_Power_Electronics')
80 files changed, 49095 insertions, 0 deletions
diff --git a/_Power_Electronics/Chapter10.ipynb b/_Power_Electronics/Chapter10.ipynb new file mode 100755 index 00000000..cbc3cb90 --- /dev/null +++ b/_Power_Electronics/Chapter10.ipynb @@ -0,0 +1,228 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10 : Cycloconverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.2, Page No 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=10.0\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/math.sqrt(2))*math.sqrt((1/math.pi)*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2))\n",
+ "I_or=V_or/R \n",
+ "I_s=I_or\n",
+ "pf=(I_or**2*R)/(V_s*I_s) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p current=%.2f A\" %I_or)\n",
+ "print(\"rms value of o/p current for each convertor=%.2f A\" %(I_or/math.sqrt(2)))\n",
+ "print(\"rms value of o/p current for each thyristor=%.3f A\" %(I_or/2))\n",
+ "print(\"i/p pf=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p current=22.67 A\n",
+ "rms value of o/p current for each convertor=16.03 A\n",
+ "rms value of o/p current for each thyristor=11.333 A\n",
+ "i/p pf=0.9855\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.4, Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=3\n",
+ "V_or=r*(V_ph*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=155.424 V\n",
+ "rms o/p current=62.17 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=7730.11 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.5 Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "V_l=V_ph*math.sqrt(3)\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=6\n",
+ "V_or=r*(V_l*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=310.85 V\n",
+ "rms o/p current=124.34 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=30920.44 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.7, Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=400.0\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "m=6\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.0012\n",
+ "I=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or1=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx1=V_or1-3*w*L*I/math.pi\n",
+ "V_rms1=V_omx1/math.sqrt(2) \n",
+ "a2=30.0\n",
+ "V_or2=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx2=V_or2-3*w*L*I/math.pi\n",
+ "V_rms2=V_omx2/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=0deg\")\n",
+ "a1=0\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)\n",
+ "print(\"for firing angle=30deg\")\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=0deg\n",
+ "rms value of load voltage=-369.12 V\n",
+ "for firing angle=30deg\n",
+ "rms value of load voltage=-369.12 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter10_1.ipynb b/_Power_Electronics/Chapter10_1.ipynb new file mode 100755 index 00000000..cbc3cb90 --- /dev/null +++ b/_Power_Electronics/Chapter10_1.ipynb @@ -0,0 +1,228 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10 : Cycloconverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.2, Page No 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=10.0\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/math.sqrt(2))*math.sqrt((1/math.pi)*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2))\n",
+ "I_or=V_or/R \n",
+ "I_s=I_or\n",
+ "pf=(I_or**2*R)/(V_s*I_s) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p current=%.2f A\" %I_or)\n",
+ "print(\"rms value of o/p current for each convertor=%.2f A\" %(I_or/math.sqrt(2)))\n",
+ "print(\"rms value of o/p current for each thyristor=%.3f A\" %(I_or/2))\n",
+ "print(\"i/p pf=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p current=22.67 A\n",
+ "rms value of o/p current for each convertor=16.03 A\n",
+ "rms value of o/p current for each thyristor=11.333 A\n",
+ "i/p pf=0.9855\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.4, Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=3\n",
+ "V_or=r*(V_ph*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=155.424 V\n",
+ "rms o/p current=62.17 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=7730.11 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.5 Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "V_l=V_ph*math.sqrt(3)\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=6\n",
+ "V_or=r*(V_l*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=310.85 V\n",
+ "rms o/p current=124.34 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=30920.44 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.7, Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=400.0\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "m=6\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.0012\n",
+ "I=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or1=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx1=V_or1-3*w*L*I/math.pi\n",
+ "V_rms1=V_omx1/math.sqrt(2) \n",
+ "a2=30.0\n",
+ "V_or2=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx2=V_or2-3*w*L*I/math.pi\n",
+ "V_rms2=V_omx2/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=0deg\")\n",
+ "a1=0\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)\n",
+ "print(\"for firing angle=30deg\")\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=0deg\n",
+ "rms value of load voltage=-369.12 V\n",
+ "for firing angle=30deg\n",
+ "rms value of load voltage=-369.12 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter10_2.ipynb b/_Power_Electronics/Chapter10_2.ipynb new file mode 100755 index 00000000..cbc3cb90 --- /dev/null +++ b/_Power_Electronics/Chapter10_2.ipynb @@ -0,0 +1,228 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10 : Cycloconverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.2, Page No 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=10.0\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/math.sqrt(2))*math.sqrt((1/math.pi)*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2))\n",
+ "I_or=V_or/R \n",
+ "I_s=I_or\n",
+ "pf=(I_or**2*R)/(V_s*I_s) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p current=%.2f A\" %I_or)\n",
+ "print(\"rms value of o/p current for each convertor=%.2f A\" %(I_or/math.sqrt(2)))\n",
+ "print(\"rms value of o/p current for each thyristor=%.3f A\" %(I_or/2))\n",
+ "print(\"i/p pf=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p current=22.67 A\n",
+ "rms value of o/p current for each convertor=16.03 A\n",
+ "rms value of o/p current for each thyristor=11.333 A\n",
+ "i/p pf=0.9855\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.4, Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=3\n",
+ "V_or=r*(V_ph*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=155.424 V\n",
+ "rms o/p current=62.17 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=7730.11 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.5 Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "V_l=V_ph*math.sqrt(3)\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=6\n",
+ "V_or=r*(V_l*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=310.85 V\n",
+ "rms o/p current=124.34 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=30920.44 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.7, Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=400.0\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "m=6\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.0012\n",
+ "I=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or1=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx1=V_or1-3*w*L*I/math.pi\n",
+ "V_rms1=V_omx1/math.sqrt(2) \n",
+ "a2=30.0\n",
+ "V_or2=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx2=V_or2-3*w*L*I/math.pi\n",
+ "V_rms2=V_omx2/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=0deg\")\n",
+ "a1=0\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)\n",
+ "print(\"for firing angle=30deg\")\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=0deg\n",
+ "rms value of load voltage=-369.12 V\n",
+ "for firing angle=30deg\n",
+ "rms value of load voltage=-369.12 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter10_3.ipynb b/_Power_Electronics/Chapter10_3.ipynb new file mode 100755 index 00000000..cbc3cb90 --- /dev/null +++ b/_Power_Electronics/Chapter10_3.ipynb @@ -0,0 +1,228 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10 : Cycloconverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.2, Page No 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=10.0\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/math.sqrt(2))*math.sqrt((1/math.pi)*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2))\n",
+ "I_or=V_or/R \n",
+ "I_s=I_or\n",
+ "pf=(I_or**2*R)/(V_s*I_s) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p current=%.2f A\" %I_or)\n",
+ "print(\"rms value of o/p current for each convertor=%.2f A\" %(I_or/math.sqrt(2)))\n",
+ "print(\"rms value of o/p current for each thyristor=%.3f A\" %(I_or/2))\n",
+ "print(\"i/p pf=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p current=22.67 A\n",
+ "rms value of o/p current for each convertor=16.03 A\n",
+ "rms value of o/p current for each thyristor=11.333 A\n",
+ "i/p pf=0.9855\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.4, Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=3\n",
+ "V_or=r*(V_ph*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=155.424 V\n",
+ "rms o/p current=62.17 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=7730.11 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.5 Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "V_l=V_ph*math.sqrt(3)\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=6\n",
+ "V_or=r*(V_l*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=310.85 V\n",
+ "rms o/p current=124.34 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=30920.44 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.7, Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=400.0\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "m=6\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.0012\n",
+ "I=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or1=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx1=V_or1-3*w*L*I/math.pi\n",
+ "V_rms1=V_omx1/math.sqrt(2) \n",
+ "a2=30.0\n",
+ "V_or2=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx2=V_or2-3*w*L*I/math.pi\n",
+ "V_rms2=V_omx2/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=0deg\")\n",
+ "a1=0\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)\n",
+ "print(\"for firing angle=30deg\")\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=0deg\n",
+ "rms value of load voltage=-369.12 V\n",
+ "for firing angle=30deg\n",
+ "rms value of load voltage=-369.12 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter10_4.ipynb b/_Power_Electronics/Chapter10_4.ipynb new file mode 100755 index 00000000..cbc3cb90 --- /dev/null +++ b/_Power_Electronics/Chapter10_4.ipynb @@ -0,0 +1,228 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10 : Cycloconverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.2, Page No 594"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=10.0\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/math.sqrt(2))*math.sqrt((1/math.pi)*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2))\n",
+ "I_or=V_or/R \n",
+ "I_s=I_or\n",
+ "pf=(I_or**2*R)/(V_s*I_s) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p current=%.2f A\" %I_or)\n",
+ "print(\"rms value of o/p current for each convertor=%.2f A\" %(I_or/math.sqrt(2)))\n",
+ "print(\"rms value of o/p current for each thyristor=%.3f A\" %(I_or/2))\n",
+ "print(\"i/p pf=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p current=22.67 A\n",
+ "rms value of o/p current for each convertor=16.03 A\n",
+ "rms value of o/p current for each thyristor=11.333 A\n",
+ "i/p pf=0.9855\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.4, Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=3\n",
+ "V_or=r*(V_ph*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=155.424 V\n",
+ "rms o/p current=62.17 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=7730.11 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.5 Page No 604"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_ph=V_s/2\n",
+ "V_l=V_ph*math.sqrt(3)\n",
+ "a=160.0\n",
+ "\n",
+ "#Calculations\n",
+ "r=math.cos(math.radians(180-a))\n",
+ "m=6\n",
+ "V_or=r*(V_l*(m/math.pi)*math.sin(math.pi/m)) \n",
+ "R=2\n",
+ "X_L=1.5\n",
+ "th=math.degrees(math.atan(X_L/R))\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_or/Z \n",
+ "P=I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms o/p current=%.2f A\" %I_or)\n",
+ "print(\"phase angle of o/p current=%.2f deg\" %-th)\n",
+ "print(\"o/p power=%.2f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms o/p voltage=310.85 V\n",
+ "rms o/p current=124.34 A\n",
+ "phase angle of o/p current=-36.87 deg\n",
+ "o/p power=30920.44 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 10.7, Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=400.0\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "m=6\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.0012\n",
+ "I=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or1=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx1=V_or1-3*w*L*I/math.pi\n",
+ "V_rms1=V_omx1/math.sqrt(2) \n",
+ "a2=30.0\n",
+ "V_or2=(V_ml*(m/math.pi)*math.sin(math.pi/m))*math.cos(math.radians(a))\n",
+ "V_omx2=V_or2-3*w*L*I/math.pi\n",
+ "V_rms2=V_omx2/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=0deg\")\n",
+ "a1=0\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)\n",
+ "print(\"for firing angle=30deg\")\n",
+ "print(\"rms value of load voltage=%.2f V\" %V_rms2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=0deg\n",
+ "rms value of load voltage=-369.12 V\n",
+ "for firing angle=30deg\n",
+ "rms value of load voltage=-369.12 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter11.ipynb b/_Power_Electronics/Chapter11.ipynb new file mode 100755 index 00000000..d2317d28 --- /dev/null +++ b/_Power_Electronics/Chapter11.ipynb @@ -0,0 +1,299 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Some Applications"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page No 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=11000.0\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "I_d=300\n",
+ "R_d=1\n",
+ "g=20 #g=gamma\n",
+ "a=math.degrees(math.acos(math.cos(math.radians(g))+math.pi/(3*V_ml)*I_d*R_d)) \n",
+ "L_s=.01\n",
+ "V_d=(3/math.pi)*((V_ml*math.cos(math.radians(a)))-w*L_s*I_d) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"rectifier o/p voltage=%.1f V\" %V_d)\n",
+ "print(\"dc link voltage=%.3f V\" %(2*V_d/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=16.283 deg\n",
+ "rectifier o/p voltage=13359.3 V\n",
+ "dc link voltage=26.719 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 623"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_d=(200.0+200)*10**3\n",
+ "P=1000.0*10**6\n",
+ "\n",
+ "#Calculations\n",
+ "I_d=P/V_d\n",
+ " #each thristor conducts for 120deg for a periodicity of 360deg\n",
+ "a=0\n",
+ "V_d=200.0*10**3\n",
+ "V_ml=V_d*math.pi/(3*math.cos(math.radians(a)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms current rating of thyristor=%.2f A\" %(I_d*math.sqrt(120/360)))\n",
+ "print(\"peak reverse voltage across each thyristor=%.2f kV\" %(V_ml/2/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms current rating of thyristor=0.00 A\n",
+ "peak reverse voltage across each thyristor=104.72 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page No 627"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_m=230.0\n",
+ "V_s=230/math.sqrt(2)\n",
+ "pf=0.8\n",
+ "P=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_m=P/(V_s*pf)\n",
+ "I_Tr=I_m/math.sqrt(2)\n",
+ "I_TA=2*I_m/math.pi\n",
+ "fos=2 #factor of safety\n",
+ "PIV=V_m*math.sqrt(2)\n",
+ "I_Tr=I_m/(2)\n",
+ "I_TA=I_m/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of thyristor current=%.2f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of thyristor=%.2f V\" %PIV)\n",
+ "print(\"rms value of diode current=%.3f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of diode current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of diode=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of thyristor current=15.37 A\n",
+ "avg value of thyristor current=9.786 A\n",
+ "voltage rating of thyristor=325.27 V\n",
+ "rms value of diode current=15.372 A\n",
+ "avg value of diode current=9.786 A\n",
+ "voltage rating of diode=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=200.0\n",
+ "I=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "R_L=V/I \n",
+ "I_h=.005 #holding current\n",
+ "R2=V/I_h \n",
+ "t_c=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C=t_c*fos/(R_L*math.log(2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of load resistance=%.0f ohm\" %R_L)\n",
+ "print(\"value of R2=%.0f kilo-ohm\" %(R2/1000))\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of load resistance=20 ohm\n",
+ "value of R2=40 kilo-ohm\n",
+ "value of C=2.885 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "u_r=10\n",
+ "f=10000.0 #Hz\n",
+ "p=4.0*10**-8 #ohm-m\n",
+ "\n",
+ "#Calculations\n",
+ "dl=(1/(2*math.pi))*math.sqrt(p*10**7/(u_r*f)) \n",
+ "l=0.12 #length of cylinder\n",
+ "t=20.0 #no of turns\n",
+ "I=100.0\n",
+ "H=t*I/l\n",
+ "P_s=2*math.pi*H**2*math.sqrt(u_r*f*p*10**-7) \n",
+ "d=.02 #diameter\n",
+ "P_v=4*H**2*p/(d*dl) \n",
+ "\n",
+ "#Results\n",
+ "print(\"depth of heat of penetration=%.5f mm\" %(dl*1000))\n",
+ "print(\"heat generated per unit cylinder surface area=%.3f W/m**2\" %P_s)\n",
+ "print(\"heat generated per unit cylinder volume=%.0f W/m**3\" %P_v)\n",
+ " #answer of P_v varies as given in book as value of d is not taken as in formulae. "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depth of heat of penetration=0.31831 mm\n",
+ "heat generated per unit cylinder surface area=34906.585 W/m**2\n",
+ "heat generated per unit cylinder volume=6981317 W/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=3000.0\n",
+ "\n",
+ "#Calculations\n",
+ "t_qmin=30.0*10**-6\n",
+ "f_r=f/(1-2*t_qmin*f)\n",
+ "R=0.06\n",
+ "L=20.0*10**-6\n",
+ "C=1/(L*((2*math.pi*f_r)**2+(R/(2*L))**2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"required capacitor size=%.4f F\" %(C*10**6))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required capacitor size=94.2215 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter11_1.ipynb b/_Power_Electronics/Chapter11_1.ipynb new file mode 100755 index 00000000..d2317d28 --- /dev/null +++ b/_Power_Electronics/Chapter11_1.ipynb @@ -0,0 +1,299 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Some Applications"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page No 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=11000.0\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "I_d=300\n",
+ "R_d=1\n",
+ "g=20 #g=gamma\n",
+ "a=math.degrees(math.acos(math.cos(math.radians(g))+math.pi/(3*V_ml)*I_d*R_d)) \n",
+ "L_s=.01\n",
+ "V_d=(3/math.pi)*((V_ml*math.cos(math.radians(a)))-w*L_s*I_d) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"rectifier o/p voltage=%.1f V\" %V_d)\n",
+ "print(\"dc link voltage=%.3f V\" %(2*V_d/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=16.283 deg\n",
+ "rectifier o/p voltage=13359.3 V\n",
+ "dc link voltage=26.719 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 623"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_d=(200.0+200)*10**3\n",
+ "P=1000.0*10**6\n",
+ "\n",
+ "#Calculations\n",
+ "I_d=P/V_d\n",
+ " #each thristor conducts for 120deg for a periodicity of 360deg\n",
+ "a=0\n",
+ "V_d=200.0*10**3\n",
+ "V_ml=V_d*math.pi/(3*math.cos(math.radians(a)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms current rating of thyristor=%.2f A\" %(I_d*math.sqrt(120/360)))\n",
+ "print(\"peak reverse voltage across each thyristor=%.2f kV\" %(V_ml/2/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms current rating of thyristor=0.00 A\n",
+ "peak reverse voltage across each thyristor=104.72 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page No 627"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_m=230.0\n",
+ "V_s=230/math.sqrt(2)\n",
+ "pf=0.8\n",
+ "P=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_m=P/(V_s*pf)\n",
+ "I_Tr=I_m/math.sqrt(2)\n",
+ "I_TA=2*I_m/math.pi\n",
+ "fos=2 #factor of safety\n",
+ "PIV=V_m*math.sqrt(2)\n",
+ "I_Tr=I_m/(2)\n",
+ "I_TA=I_m/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of thyristor current=%.2f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of thyristor=%.2f V\" %PIV)\n",
+ "print(\"rms value of diode current=%.3f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of diode current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of diode=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of thyristor current=15.37 A\n",
+ "avg value of thyristor current=9.786 A\n",
+ "voltage rating of thyristor=325.27 V\n",
+ "rms value of diode current=15.372 A\n",
+ "avg value of diode current=9.786 A\n",
+ "voltage rating of diode=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=200.0\n",
+ "I=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "R_L=V/I \n",
+ "I_h=.005 #holding current\n",
+ "R2=V/I_h \n",
+ "t_c=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C=t_c*fos/(R_L*math.log(2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of load resistance=%.0f ohm\" %R_L)\n",
+ "print(\"value of R2=%.0f kilo-ohm\" %(R2/1000))\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of load resistance=20 ohm\n",
+ "value of R2=40 kilo-ohm\n",
+ "value of C=2.885 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "u_r=10\n",
+ "f=10000.0 #Hz\n",
+ "p=4.0*10**-8 #ohm-m\n",
+ "\n",
+ "#Calculations\n",
+ "dl=(1/(2*math.pi))*math.sqrt(p*10**7/(u_r*f)) \n",
+ "l=0.12 #length of cylinder\n",
+ "t=20.0 #no of turns\n",
+ "I=100.0\n",
+ "H=t*I/l\n",
+ "P_s=2*math.pi*H**2*math.sqrt(u_r*f*p*10**-7) \n",
+ "d=.02 #diameter\n",
+ "P_v=4*H**2*p/(d*dl) \n",
+ "\n",
+ "#Results\n",
+ "print(\"depth of heat of penetration=%.5f mm\" %(dl*1000))\n",
+ "print(\"heat generated per unit cylinder surface area=%.3f W/m**2\" %P_s)\n",
+ "print(\"heat generated per unit cylinder volume=%.0f W/m**3\" %P_v)\n",
+ " #answer of P_v varies as given in book as value of d is not taken as in formulae. "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depth of heat of penetration=0.31831 mm\n",
+ "heat generated per unit cylinder surface area=34906.585 W/m**2\n",
+ "heat generated per unit cylinder volume=6981317 W/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=3000.0\n",
+ "\n",
+ "#Calculations\n",
+ "t_qmin=30.0*10**-6\n",
+ "f_r=f/(1-2*t_qmin*f)\n",
+ "R=0.06\n",
+ "L=20.0*10**-6\n",
+ "C=1/(L*((2*math.pi*f_r)**2+(R/(2*L))**2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"required capacitor size=%.4f F\" %(C*10**6))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required capacitor size=94.2215 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter11_2.ipynb b/_Power_Electronics/Chapter11_2.ipynb new file mode 100755 index 00000000..d2317d28 --- /dev/null +++ b/_Power_Electronics/Chapter11_2.ipynb @@ -0,0 +1,299 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Some Applications"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page No 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=11000.0\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "I_d=300\n",
+ "R_d=1\n",
+ "g=20 #g=gamma\n",
+ "a=math.degrees(math.acos(math.cos(math.radians(g))+math.pi/(3*V_ml)*I_d*R_d)) \n",
+ "L_s=.01\n",
+ "V_d=(3/math.pi)*((V_ml*math.cos(math.radians(a)))-w*L_s*I_d) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"rectifier o/p voltage=%.1f V\" %V_d)\n",
+ "print(\"dc link voltage=%.3f V\" %(2*V_d/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=16.283 deg\n",
+ "rectifier o/p voltage=13359.3 V\n",
+ "dc link voltage=26.719 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 623"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_d=(200.0+200)*10**3\n",
+ "P=1000.0*10**6\n",
+ "\n",
+ "#Calculations\n",
+ "I_d=P/V_d\n",
+ " #each thristor conducts for 120deg for a periodicity of 360deg\n",
+ "a=0\n",
+ "V_d=200.0*10**3\n",
+ "V_ml=V_d*math.pi/(3*math.cos(math.radians(a)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms current rating of thyristor=%.2f A\" %(I_d*math.sqrt(120/360)))\n",
+ "print(\"peak reverse voltage across each thyristor=%.2f kV\" %(V_ml/2/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms current rating of thyristor=0.00 A\n",
+ "peak reverse voltage across each thyristor=104.72 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page No 627"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_m=230.0\n",
+ "V_s=230/math.sqrt(2)\n",
+ "pf=0.8\n",
+ "P=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_m=P/(V_s*pf)\n",
+ "I_Tr=I_m/math.sqrt(2)\n",
+ "I_TA=2*I_m/math.pi\n",
+ "fos=2 #factor of safety\n",
+ "PIV=V_m*math.sqrt(2)\n",
+ "I_Tr=I_m/(2)\n",
+ "I_TA=I_m/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of thyristor current=%.2f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of thyristor=%.2f V\" %PIV)\n",
+ "print(\"rms value of diode current=%.3f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of diode current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of diode=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of thyristor current=15.37 A\n",
+ "avg value of thyristor current=9.786 A\n",
+ "voltage rating of thyristor=325.27 V\n",
+ "rms value of diode current=15.372 A\n",
+ "avg value of diode current=9.786 A\n",
+ "voltage rating of diode=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=200.0\n",
+ "I=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "R_L=V/I \n",
+ "I_h=.005 #holding current\n",
+ "R2=V/I_h \n",
+ "t_c=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C=t_c*fos/(R_L*math.log(2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of load resistance=%.0f ohm\" %R_L)\n",
+ "print(\"value of R2=%.0f kilo-ohm\" %(R2/1000))\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of load resistance=20 ohm\n",
+ "value of R2=40 kilo-ohm\n",
+ "value of C=2.885 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "u_r=10\n",
+ "f=10000.0 #Hz\n",
+ "p=4.0*10**-8 #ohm-m\n",
+ "\n",
+ "#Calculations\n",
+ "dl=(1/(2*math.pi))*math.sqrt(p*10**7/(u_r*f)) \n",
+ "l=0.12 #length of cylinder\n",
+ "t=20.0 #no of turns\n",
+ "I=100.0\n",
+ "H=t*I/l\n",
+ "P_s=2*math.pi*H**2*math.sqrt(u_r*f*p*10**-7) \n",
+ "d=.02 #diameter\n",
+ "P_v=4*H**2*p/(d*dl) \n",
+ "\n",
+ "#Results\n",
+ "print(\"depth of heat of penetration=%.5f mm\" %(dl*1000))\n",
+ "print(\"heat generated per unit cylinder surface area=%.3f W/m**2\" %P_s)\n",
+ "print(\"heat generated per unit cylinder volume=%.0f W/m**3\" %P_v)\n",
+ " #answer of P_v varies as given in book as value of d is not taken as in formulae. "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depth of heat of penetration=0.31831 mm\n",
+ "heat generated per unit cylinder surface area=34906.585 W/m**2\n",
+ "heat generated per unit cylinder volume=6981317 W/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=3000.0\n",
+ "\n",
+ "#Calculations\n",
+ "t_qmin=30.0*10**-6\n",
+ "f_r=f/(1-2*t_qmin*f)\n",
+ "R=0.06\n",
+ "L=20.0*10**-6\n",
+ "C=1/(L*((2*math.pi*f_r)**2+(R/(2*L))**2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"required capacitor size=%.4f F\" %(C*10**6))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required capacitor size=94.2215 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter11_3.ipynb b/_Power_Electronics/Chapter11_3.ipynb new file mode 100755 index 00000000..d2317d28 --- /dev/null +++ b/_Power_Electronics/Chapter11_3.ipynb @@ -0,0 +1,299 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Some Applications"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page No 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=11000.0\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "I_d=300\n",
+ "R_d=1\n",
+ "g=20 #g=gamma\n",
+ "a=math.degrees(math.acos(math.cos(math.radians(g))+math.pi/(3*V_ml)*I_d*R_d)) \n",
+ "L_s=.01\n",
+ "V_d=(3/math.pi)*((V_ml*math.cos(math.radians(a)))-w*L_s*I_d) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"rectifier o/p voltage=%.1f V\" %V_d)\n",
+ "print(\"dc link voltage=%.3f V\" %(2*V_d/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=16.283 deg\n",
+ "rectifier o/p voltage=13359.3 V\n",
+ "dc link voltage=26.719 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 623"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_d=(200.0+200)*10**3\n",
+ "P=1000.0*10**6\n",
+ "\n",
+ "#Calculations\n",
+ "I_d=P/V_d\n",
+ " #each thristor conducts for 120deg for a periodicity of 360deg\n",
+ "a=0\n",
+ "V_d=200.0*10**3\n",
+ "V_ml=V_d*math.pi/(3*math.cos(math.radians(a)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms current rating of thyristor=%.2f A\" %(I_d*math.sqrt(120/360)))\n",
+ "print(\"peak reverse voltage across each thyristor=%.2f kV\" %(V_ml/2/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms current rating of thyristor=0.00 A\n",
+ "peak reverse voltage across each thyristor=104.72 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page No 627"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_m=230.0\n",
+ "V_s=230/math.sqrt(2)\n",
+ "pf=0.8\n",
+ "P=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_m=P/(V_s*pf)\n",
+ "I_Tr=I_m/math.sqrt(2)\n",
+ "I_TA=2*I_m/math.pi\n",
+ "fos=2 #factor of safety\n",
+ "PIV=V_m*math.sqrt(2)\n",
+ "I_Tr=I_m/(2)\n",
+ "I_TA=I_m/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of thyristor current=%.2f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of thyristor=%.2f V\" %PIV)\n",
+ "print(\"rms value of diode current=%.3f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of diode current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of diode=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of thyristor current=15.37 A\n",
+ "avg value of thyristor current=9.786 A\n",
+ "voltage rating of thyristor=325.27 V\n",
+ "rms value of diode current=15.372 A\n",
+ "avg value of diode current=9.786 A\n",
+ "voltage rating of diode=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=200.0\n",
+ "I=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "R_L=V/I \n",
+ "I_h=.005 #holding current\n",
+ "R2=V/I_h \n",
+ "t_c=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C=t_c*fos/(R_L*math.log(2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of load resistance=%.0f ohm\" %R_L)\n",
+ "print(\"value of R2=%.0f kilo-ohm\" %(R2/1000))\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of load resistance=20 ohm\n",
+ "value of R2=40 kilo-ohm\n",
+ "value of C=2.885 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "u_r=10\n",
+ "f=10000.0 #Hz\n",
+ "p=4.0*10**-8 #ohm-m\n",
+ "\n",
+ "#Calculations\n",
+ "dl=(1/(2*math.pi))*math.sqrt(p*10**7/(u_r*f)) \n",
+ "l=0.12 #length of cylinder\n",
+ "t=20.0 #no of turns\n",
+ "I=100.0\n",
+ "H=t*I/l\n",
+ "P_s=2*math.pi*H**2*math.sqrt(u_r*f*p*10**-7) \n",
+ "d=.02 #diameter\n",
+ "P_v=4*H**2*p/(d*dl) \n",
+ "\n",
+ "#Results\n",
+ "print(\"depth of heat of penetration=%.5f mm\" %(dl*1000))\n",
+ "print(\"heat generated per unit cylinder surface area=%.3f W/m**2\" %P_s)\n",
+ "print(\"heat generated per unit cylinder volume=%.0f W/m**3\" %P_v)\n",
+ " #answer of P_v varies as given in book as value of d is not taken as in formulae. "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depth of heat of penetration=0.31831 mm\n",
+ "heat generated per unit cylinder surface area=34906.585 W/m**2\n",
+ "heat generated per unit cylinder volume=6981317 W/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=3000.0\n",
+ "\n",
+ "#Calculations\n",
+ "t_qmin=30.0*10**-6\n",
+ "f_r=f/(1-2*t_qmin*f)\n",
+ "R=0.06\n",
+ "L=20.0*10**-6\n",
+ "C=1/(L*((2*math.pi*f_r)**2+(R/(2*L))**2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"required capacitor size=%.4f F\" %(C*10**6))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required capacitor size=94.2215 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter11_4.ipynb b/_Power_Electronics/Chapter11_4.ipynb new file mode 100755 index 00000000..d2317d28 --- /dev/null +++ b/_Power_Electronics/Chapter11_4.ipynb @@ -0,0 +1,299 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11 : Some Applications"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page No 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=11000.0\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "I_d=300\n",
+ "R_d=1\n",
+ "g=20 #g=gamma\n",
+ "a=math.degrees(math.acos(math.cos(math.radians(g))+math.pi/(3*V_ml)*I_d*R_d)) \n",
+ "L_s=.01\n",
+ "V_d=(3/math.pi)*((V_ml*math.cos(math.radians(a)))-w*L_s*I_d) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"rectifier o/p voltage=%.1f V\" %V_d)\n",
+ "print(\"dc link voltage=%.3f V\" %(2*V_d/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=16.283 deg\n",
+ "rectifier o/p voltage=13359.3 V\n",
+ "dc link voltage=26.719 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page No 623"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_d=(200.0+200)*10**3\n",
+ "P=1000.0*10**6\n",
+ "\n",
+ "#Calculations\n",
+ "I_d=P/V_d\n",
+ " #each thristor conducts for 120deg for a periodicity of 360deg\n",
+ "a=0\n",
+ "V_d=200.0*10**3\n",
+ "V_ml=V_d*math.pi/(3*math.cos(math.radians(a)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms current rating of thyristor=%.2f A\" %(I_d*math.sqrt(120/360)))\n",
+ "print(\"peak reverse voltage across each thyristor=%.2f kV\" %(V_ml/2/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms current rating of thyristor=0.00 A\n",
+ "peak reverse voltage across each thyristor=104.72 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page No 627"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_m=230.0\n",
+ "V_s=230/math.sqrt(2)\n",
+ "pf=0.8\n",
+ "P=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_m=P/(V_s*pf)\n",
+ "I_Tr=I_m/math.sqrt(2)\n",
+ "I_TA=2*I_m/math.pi\n",
+ "fos=2 #factor of safety\n",
+ "PIV=V_m*math.sqrt(2)\n",
+ "I_Tr=I_m/(2)\n",
+ "I_TA=I_m/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of thyristor current=%.2f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of thyristor=%.2f V\" %PIV)\n",
+ "print(\"rms value of diode current=%.3f A\" %(fos*I_Tr))\n",
+ "print(\"avg value of diode current=%.3f A\" %(fos*I_TA))\n",
+ "print(\"voltage rating of diode=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of thyristor current=15.37 A\n",
+ "avg value of thyristor current=9.786 A\n",
+ "voltage rating of thyristor=325.27 V\n",
+ "rms value of diode current=15.372 A\n",
+ "avg value of diode current=9.786 A\n",
+ "voltage rating of diode=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page No 629"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=200.0\n",
+ "I=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "R_L=V/I \n",
+ "I_h=.005 #holding current\n",
+ "R2=V/I_h \n",
+ "t_c=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C=t_c*fos/(R_L*math.log(2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of load resistance=%.0f ohm\" %R_L)\n",
+ "print(\"value of R2=%.0f kilo-ohm\" %(R2/1000))\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of load resistance=20 ohm\n",
+ "value of R2=40 kilo-ohm\n",
+ "value of C=2.885 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "u_r=10\n",
+ "f=10000.0 #Hz\n",
+ "p=4.0*10**-8 #ohm-m\n",
+ "\n",
+ "#Calculations\n",
+ "dl=(1/(2*math.pi))*math.sqrt(p*10**7/(u_r*f)) \n",
+ "l=0.12 #length of cylinder\n",
+ "t=20.0 #no of turns\n",
+ "I=100.0\n",
+ "H=t*I/l\n",
+ "P_s=2*math.pi*H**2*math.sqrt(u_r*f*p*10**-7) \n",
+ "d=.02 #diameter\n",
+ "P_v=4*H**2*p/(d*dl) \n",
+ "\n",
+ "#Results\n",
+ "print(\"depth of heat of penetration=%.5f mm\" %(dl*1000))\n",
+ "print(\"heat generated per unit cylinder surface area=%.3f W/m**2\" %P_s)\n",
+ "print(\"heat generated per unit cylinder volume=%.0f W/m**3\" %P_v)\n",
+ " #answer of P_v varies as given in book as value of d is not taken as in formulae. "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "depth of heat of penetration=0.31831 mm\n",
+ "heat generated per unit cylinder surface area=34906.585 W/m**2\n",
+ "heat generated per unit cylinder volume=6981317 W/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page No 646"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=3000.0\n",
+ "\n",
+ "#Calculations\n",
+ "t_qmin=30.0*10**-6\n",
+ "f_r=f/(1-2*t_qmin*f)\n",
+ "R=0.06\n",
+ "L=20.0*10**-6\n",
+ "C=1/(L*((2*math.pi*f_r)**2+(R/(2*L))**2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"required capacitor size=%.4f F\" %(C*10**6))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "required capacitor size=94.2215 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter12.ipynb b/_Power_Electronics/Chapter12.ipynb new file mode 100755 index 00000000..f8605d69 --- /dev/null +++ b/_Power_Electronics/Chapter12.ipynb @@ -0,0 +1,1997 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12 : Electic Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, Page No 658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=15.0 #Nm\n",
+ "K_m=0.5 #V-s/rad\n",
+ "I_a=T_e/K_m\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "E_a=K_m*w_m\n",
+ "r_a=0.7\n",
+ "V_t=E_a+I_a*r_a\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "I_Tr=I_a*math.sqrt((180-a)/360) \n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "I_fdr=I_a*math.sqrt((180+a)/360) \n",
+ "print(\"rms value of freewheeling diode current=%.3f A\" %I_fdr)\n",
+ "pf=V_t*I_a/(V_s*I_Tr) \n",
+ "\n",
+ "#Results \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=65.349 deg\n",
+ "rms value of thyristor current=16.930 A\n",
+ "rms value of freewheeling diode current=24.766 A\n",
+ "input power factor=0.5652\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, Page No 660"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 661"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=250\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "k=0.03 #Nm/A**2\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r=.2 #r_a+r_s\n",
+ "V_t=V_m/math.pi*(1+math.cos(math.radians(a)))\n",
+ "I_a=V_t/(k*w_m+r) \n",
+ "print(\"motor armature current=%.2f A\" %I_a)\n",
+ "T_e=k*I_a**2 \n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n",
+ "I_sr=I_a*math.sqrt((180-a)/180)\n",
+ "pf=(V_t*I_a)/(V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor armature current=57.82 A\n",
+ "motor torque=100.285 Nm\n",
+ "input power factor=0.92\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, Page No 663"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(I_f*K_a) \n",
+ "print(\"rated armature current=%.2f A\" %I_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.2\n",
+ "V_t=K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "E_a=V_t\n",
+ "w_mo=E_a/(K_a*I_f)\n",
+ "N=60*w_mo/(2*math.pi)\n",
+ "reg=((N-n_m)/n_m)*100 \n",
+ "print(\"speed regulation at full load=%.2f\" %reg)\n",
+ "I_ar=I_a\n",
+ "pf=(V_t*I_a)/(V_s*I_ar) \n",
+ "print(\"input power factor of armature convertor=%.4f\" %pf)\n",
+ "I_fr=I_f\n",
+ "I_sr=math.sqrt(I_fr**2+I_ar**2)\n",
+ "VA=I_sr*V_s\n",
+ "P=V_t*I_a+V_f*I_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor of drive=%.4f\" %(P/VA))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rated armature current=59.01 A\n",
+ "firing angle delay=57.63 deg\n",
+ "speed regulation at full load=6.52\n",
+ "input power factor of armature convertor=0.4821\n",
+ "input power factor of drive=0.5093\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) \n",
+ "print(\"delay angle of field converter=%.0f deg\" %a1)\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "I_a=T_e/(I_f*K_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.1\n",
+ "I_a=50.0\n",
+ "V_t=-K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay of armature converter=%.3f deg\" %a)\n",
+ "print(\"power fed back to ac supply=%.0f W\" %(-V_t*I_a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle of field converter=58 deg\n",
+ "firing angle delay of armature converter=119.260 deg\n",
+ "power fed back to ac supply=8801 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=10.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "T=5.0\n",
+ "I_a=T/K_m\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n",
+ "a=45\n",
+ "n_m=1000\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=(V_t-K_m*w_m)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"torque developed=%.3f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=1254.22 rpm\n",
+ "torque developed=8.586 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, Page No 666"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1000.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=60.0\n",
+ "r_a=.1\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=230\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for 600rpm speed\")\n",
+ "n_m=600.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) \n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"for -500rpm speed\")\n",
+ "n_m=-500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_a=I_a/2\n",
+ "a=150\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.3f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 600rpm speed\n",
+ "firing angle=49.530 deg\n",
+ "for -500rpm speed\n",
+ "firing angle=119.19 deg\n",
+ "motor speed=-852.011 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.5\n",
+ "T_e=50.0\n",
+ "I_a=T_e/K_m\n",
+ "r_a=0.9\n",
+ "a=45.0\n",
+ "V_s=415.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=2854.42 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_t=600\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=80.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for firing angle=45deg and speed=1200rpm\")\n",
+ "a=45.0\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(2/3) \n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(1/3)))\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_a*(1/3))\n",
+ "pf=(3/(2*math.pi)*(1+math.cos(math.radians(a)))) \n",
+ "print(\"input power factor=%.3f\" %pf)\n",
+ "\n",
+ "print(\"for firing angle=90deg and speed=700rpm\")\n",
+ "a=90\n",
+ "n_m=700\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(90/180) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(90.0/360)))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_a*(1/3))\n",
+ "pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a)) \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=45deg and speed=1200rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=0.000 A\n",
+ "\n",
+ "input power factor=0.815\n",
+ "for firing angle=90deg and speed=700rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=195.558 A\n",
+ "\n",
+ "input power factor=0.5513\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10 Page No 676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=21.0\n",
+ "r_a=.1\n",
+ "V_d=2.0\n",
+ "K_m=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"speed of motor=%.1f rpm\" %N)\n",
+ "\n",
+ "N=2000\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=210\n",
+ "V_t=K_m*w_m+I_a*r_a+V_d\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_sr=I_a*math.sqrt(2.0/3.0)\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"supply power factor=%.3f\" %pf)\n",
+ "\n",
+ "I_a=21\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "n=w_m*60/(2*math.pi)\n",
+ "reg=(n-N)/N*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"speed regulation(percent)=%.2f\" %reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of motor=2767.6 rpm\n",
+ "firing angle=48.48 deg\n",
+ "supply power factor=0.633\n",
+ "speed regulation(percent)=5.64\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11, Page No 677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=230.0\n",
+ "V_l=V_t*math.pi/(3*math.sqrt(2))\n",
+ "V_ph=V_l/math.sqrt(3)\n",
+ "V_in=400 #per phase voltage input\n",
+ "\n",
+ "#Calculations\n",
+ "N1=1500.0\n",
+ "I_a1=20.0\n",
+ "r_a1=.6\n",
+ "E_a1=V_t-I_a1*r_a1\n",
+ "n1=1000.0\n",
+ "E_a2=E_a1/1500.0*1000.0\n",
+ "V_t1=E_a1+I_a1*r_a1\n",
+ "a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))\n",
+ "I_a2=.5*I_a1\n",
+ "n2=-900.0\n",
+ "V_t2=n2*E_a2/N1+I_a2*r_a1\n",
+ "a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer phase turns ratio=%.3f\" %(V_in/V_ph))\n",
+ "print(\"for motor running at 1000rpm at rated torque\")\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"for motor running at -900rpm at half of rated torque\")\n",
+ "print(\"firing angle delay=%.3f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer phase turns ratio=4.068\n",
+ "for motor running at 1000rpm at rated torque\n",
+ "firing angle delay=0.00 deg\n",
+ "for motor running at -900rpm at half of rated torque\n",
+ "firing angle delay=110.674 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12, Page No 678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=400\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_f=3*V_ml/math.pi\n",
+ "R_f=300.0\n",
+ "I_f=V_f/R_f\n",
+ "T_e=60.0\n",
+ "k=1.1\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(k*I_f)\n",
+ "N1=1000.0\n",
+ "w_m1=2*math.pi*N1/60\n",
+ "r_a1=.3\n",
+ "V_t1=k*I_f*w_m1+I_a*r_a1\n",
+ "a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))\n",
+ "N2=3000\n",
+ "w_m2=2*math.pi*N/60\n",
+ "a2=0\n",
+ "V_t2=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "I_f2=(V_t2-I_a*r_a)/(w_m2*k)\n",
+ "V_f2=I_f2*R_f\n",
+ "a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle=%.3f deg\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=48.477 deg\n",
+ "firing angle=48.477 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ " #after calculating\n",
+ " #t=w_m/6000-math.pi/360\n",
+ "\n",
+ "N=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "t=w_m/6000-math.pi/360 \n",
+ "\n",
+ "#Results\n",
+ "print(\"time reqd=%.2f s\" %t)\n",
+ " #printing mistake in the answer in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time reqd=0.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=1.0 #supposition\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))\n",
+ "I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))\n",
+ "I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))\n",
+ "per3=I_s3/I_s1*100 \n",
+ "print(\"percent of 3rd harmonic current in fundamental=%.2f\" %per3)\n",
+ "per5=I_s5/I_s1*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"percent of 5th harmonic current in fundamental=%.2f\" %per5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percent of 3rd harmonic current in fundamental=0.00\n",
+ "percent of 5th harmonic current in fundamental=-20.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15, Page No 680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=60.0\n",
+ "I_TA=I_a/3 \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"avg thyristor current=%.0f A\" %I_TA)\n",
+ "I_Tr=I_a/math.sqrt(3) \n",
+ "print(\"rms thyristor current=%.3f A\" %I_Tr)\n",
+ "V_s=400\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_sr=I_a*math.sqrt(2.0/3)\n",
+ "a=150\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"power factor of ac source=%.3f\" %pf)\n",
+ "\n",
+ "r_a=0.5\n",
+ "K_m=2.4\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Speed of motor=%.2f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg thyristor current=20 A\n",
+ "rms thyristor current=34.641 A\n",
+ "power factor of ac source=-0.827\n",
+ "Speed of motor=-1980.76 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16, Page No 685"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=300.0\n",
+ "V_s=600.0\n",
+ "a=0.6\n",
+ "V_t=a*V_s\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"input power from source=%.0f kW\" %(P/1000))\n",
+ "R_eq=V_s/(a*I_a) \n",
+ "print(\"equivalent input resistance=%.3f ohm\" %R_eq)\n",
+ "k=.004\n",
+ "R=.04+.06\n",
+ "w_m=(a*V_s-I_a*R)/(k*I_a)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ "T_e=k*I_a**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.0f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "input power from source=108 kW\n",
+ "equivalent input resistance=3.333 ohm\n",
+ "motor speed=2626.1 rpm\n",
+ "motor torque=360 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.17, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=10.0\n",
+ "T_off=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_s=230.0\n",
+ "V_t=a*V_s\n",
+ "r_a=3\n",
+ "K_m=.5\n",
+ "N=1500\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=(V_t-K_m*w_m)/r_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor load current=%.3f A\" %I_a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor load current=4.487 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "w_m=0 \n",
+ "print(\"lower limit of speed control=%.0f rpm\" %w_m)\n",
+ "I_a=25.0\n",
+ "r_a=.2\n",
+ "V_s=220\n",
+ "K_m=0.08\n",
+ "\n",
+ "#Calculations\n",
+ "a=(K_m*w_m+I_a*r_a)/V_s \n",
+ "print(\"lower limit of duty cycle=%.3f\" %a)\n",
+ "a=1 \n",
+ "print(\"upper limit of duty cycle=%.0f\" %a)\n",
+ "w_m=(a*V_s-I_a*r_a)/K_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"upper limit of speed control=%.1f rpm\" %w_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lower limit of speed control=0 rpm\n",
+ "lower limit of duty cycle=0.023\n",
+ "upper limit of duty cycle=1\n",
+ "upper limit of speed control=2687.5 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21, Page No 691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.6\n",
+ "V_s=400.0\n",
+ "V_t=(1-a)*V_s\n",
+ "I_a=300.0\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations \n",
+ "print(\"power returned=%.0f kW\" %(P/1000))\n",
+ "r_a=.2\n",
+ "K_m=1.2\n",
+ "R_eq=(1-a)*V_s/I_a+r_a \n",
+ "print(\"equivalent load resistance=%.4f ohm\" %R_eq)\n",
+ "w_mn=I_a*r_a/K_m\n",
+ "N=w_mn*60/(2*math.pi) \n",
+ "print(\"min braking speed=%.2f rpm\" %N)\n",
+ "w_mx=(V_s+I_a*r_a)/K_m\n",
+ "N=w_mx*60/(2*math.pi) \n",
+ "print(\"max braking speed=%.1f rpm\" %N)\n",
+ "w_m=(V_t+I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"max braking speed=%.1f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power returned=48 kW\n",
+ "equivalent load resistance=0.7333 ohm\n",
+ "min braking speed=477.46 rpm\n",
+ "max braking speed=3660.6 rpm\n",
+ "max braking speed=1750.7 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22, Page No 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "N=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when speed=1455rpm\")\n",
+ "n=1455.0\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)\n",
+ "print(\"when speed=1350rpm\")\n",
+ "n=1350\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when speed=1455rpm\n",
+ "I_2mx/I_2r=0.000\n",
+ "when speed=1350rpm\n",
+ "I_2mx/I_2r=0.000\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24, Page No 705"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=400.0\n",
+ "r1=0.6\n",
+ "r2=0.4\n",
+ "s=1.0\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"at starting in normal conditions\")\n",
+ "I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"current=%.2f A\" %I_n)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s) \n",
+ "print(\"\\nTorque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.0f A\" %I_d)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"pf=%.2f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_ed=(3/w_s)*I_d**2*(r2/s) \n",
+ "print(\"Torque developed=%.3f Nm\" %T_ed)\n",
+ "print(\"at max torque conditions\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)\n",
+ "I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"current=%.3f A\" %I_n)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s_mn) \n",
+ "print(\"Torque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.3f A\" %I_d)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"\\npf=%.3f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_d**2*(r2/s_mn) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"Torque developed=%.3f Nm\" %T_en)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at starting in normal conditions\n",
+ "current=119.31 A\n",
+ "pf=0.2983\n",
+ "\n",
+ "Torque developed=108.75 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=106 A\n",
+ "pf=0.53\n",
+ "Torque developed=171.673 Nm\n",
+ "at max torque conditions\n",
+ "current=79.829 A\n",
+ "pf=0.7695\n",
+ "Torque developed=396.26 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=71.199 A\n",
+ "\n",
+ "pf=0.822\n",
+ "Torque developed=330.883 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.25, Page No 709"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x1=1.0\n",
+ "X_m=50.0\n",
+ "X_e=x1*X_m/(x1+X_m)\n",
+ "V=231.0\n",
+ "V_e=V*X_m/(x1+X_m)\n",
+ "x2=1.0\n",
+ "r2=.4\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "s_m=r2/(x2+X_e) \n",
+ "print(\"slip at max torque=%.2f\" %s_m)\n",
+ "s_mT=r2/(x2+X_m) \n",
+ "print(\"slip at max torque=%.5f\" %s_mT)\n",
+ "f1=50.0\n",
+ "w_s=4*math.pi*f1/4\n",
+ "print(\"for constant voltage input\")\n",
+ "T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2) \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*V_e**2/(2*(x2+X_e)) \n",
+ "print(\"maximum torque developed=%.2f Nm\" %T_em)\n",
+ "print(\"for constant current input\")\n",
+ "I1=28\n",
+ "T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2 \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m)) \n",
+ "print(\"maximum torque developed=%.3f Nm\" %T_em)\n",
+ "s=s_mT\n",
+ "i=1\n",
+ "I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))\n",
+ "I_m=math.fabs(I_m)\n",
+ "V1=math.sqrt(3)*I_m*X_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"supply voltage reqd=%.1f V\" %V1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip at max torque=0.20\n",
+ "slip at max torque=0.00784\n",
+ "for constant voltage input\n",
+ "starting torque=95.988 Nm\n",
+ "maximum torque developed=247.31 Nm\n",
+ "for constant current input\n",
+ "starting torque=5.756 Nm\n",
+ "maximum torque developed=366.993 Nm\n",
+ "supply voltage reqd=1236.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.27, Page No 718"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "T_e=450.0\n",
+ "N=1440.0\n",
+ "n=1000.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "n1=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n1/60\n",
+ "w_m=2*math.pi*n/60\n",
+ "a=.8\n",
+ "I_d=T_L*w_s/(2.339*a*V1)\n",
+ "k=0\n",
+ "R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k)) \n",
+ "print(\"value of chopper resistance=%.4f ohm\" %R)\n",
+ "n=1320.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "I_d=T_L*w_s/(2.339*a*V1) \n",
+ "print(\"Inductor current=%.3f A\" %I_d)\n",
+ "w_m=2*math.pi*n/60\n",
+ "k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.4f\" %k)\n",
+ "s=(n1-n)/n1\n",
+ "V_d=2.339*s*a*V1 \n",
+ "print(\"Rectifed o/p voltage=%.3f V\" %V_d)\n",
+ "P=V_d*I_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "Pr=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "r1=0.015\n",
+ "Ps=3*I1**2*r1\n",
+ "Po=T_L*w_m\n",
+ "Pi=Po+Ps+Pr+P\n",
+ "eff=Po/Pi*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Efficiency(in percent)=%.2f\" %eff)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of chopper resistance=2.0132 ohm\n",
+ "Inductor current=130.902 A\n",
+ "value of duty cycle=0.7934\n",
+ "Rectifed o/p voltage=54.449 V\n",
+ "Efficiency(in percent)=88.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.28, Page No 720"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ph=V/math.sqrt(3)\n",
+ "N_s=1000.0\n",
+ "N=800.0\n",
+ "a=.7\n",
+ "I_d=110\n",
+ "R=2.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.3f\" %k)\n",
+ "P=I_d**2*R*(1-k)\n",
+ "I1=a*I_d*math.sqrt(2/3)\n",
+ "r1=0.1\n",
+ "r2=0.08\n",
+ "Pr=3*I1**2*(r1+r2)\n",
+ "P_o=20000\n",
+ "P_i=P_o+Pr+P\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"Efficiency=%.2f\" %eff)\n",
+ "I11=math.sqrt(6)/math.pi*a*I_d\n",
+ "th=43\n",
+ "P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))\n",
+ "pf=P_ip/(math.sqrt(3)*V*I11) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of duty cycle=0.656\n",
+ "Efficiency=70.62\n",
+ "Input power factor=0.7314\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.29, Page No 724"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "N=1000.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "N_s=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "a=0.8\n",
+ "V_d=2.339*a*s*V1 \n",
+ "print(\"rectified voltage=%.2f V\" %V_d)\n",
+ "T=450.0\n",
+ "N1=1200.0\n",
+ "T_L=T*(N/N1)**2\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "I_d=w_s*T_L/(2.339*a*V1) \n",
+ "print(\"inductor current=%.2f A\" %I_d)\n",
+ "a_T=-.4\n",
+ "a1=math.degrees(math.acos(s*a/a_T))\n",
+ "print(\"delay angle of inverter=%.2f deg\" %a1)\n",
+ "\n",
+ "P_s=V_d*I_d\n",
+ "P_o=T_L*w_m\n",
+ "R_d=0.01\n",
+ "P_i=I_d**2*R_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "r1=0.015\n",
+ "P_rol=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "P_sol=3*I1**2*r1\n",
+ "P_i=P_o+P_rol+P_sol+P_i\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"\\nefficiency=%.2f\" %eff)\n",
+ "w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectified voltage=151.25 V\n",
+ "inductor current=108.18 A\n",
+ "delay angle of inverter=131.81 deg\n",
+ "\n",
+ "efficiency=99.64\n",
+ "motor speed=996.4 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.30, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=0.7\n",
+ "V_dt=1.5\n",
+ "V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd\n",
+ "V1=415.0\n",
+ "a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=70.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.31, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=.7\n",
+ "V_dt=1.5\n",
+ "a=0\n",
+ "u=18 #overlap angle in case of rectifier\n",
+ "V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd\n",
+ "V1=415\n",
+ "V_ml=math.sqrt(2)*V1\n",
+ "u=4 #overlap anglein the inverter\n",
+ " #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)\n",
+ " #V_dc=V_d\n",
+ " #after solving % (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425\n",
+ "a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=71.25 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.32, Page No 727"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V1=415.0\n",
+ "a_T=s*E2/V1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage ratio of the transformer=%.2f\" %a_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage ratio of the transformer=0.34\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.33, Page No 733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=6.0\n",
+ "N_s=600.0\n",
+ "f1=P*N_s/120.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=f1*V/f \n",
+ "print(\"supply freq=%.0f Hz\" %V_t)\n",
+ "T=340.0\n",
+ "N=1000.0\n",
+ "T_L=T*(N_s/N)**2\n",
+ "w_s=2*math.pi*N_s/60\n",
+ "P=T_L*w_s\n",
+ "I_a=P/(math.sqrt(3)*V_t) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "Z_s=2\n",
+ "X_s=f1/f*math.fabs(Z_s)\n",
+ "V_t=V_t/math.sqrt(3)\n",
+ "Ef=math.sqrt(V_t**2+(I_a*X_s)**2)\n",
+ "print(\"excitation voltage=%.2f V\" %(math.sqrt(3)*Ef))\n",
+ "dl=math.degrees(math.atan(I_a*X_s/V_t))\n",
+ "print(\"load angle=%.2f deg\" %dl)\n",
+ "T_em=(3/w_s)*(Ef*V_t/X_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pull out torque=%.2f Nm\" %T_em)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "supply freq=240 Hz\n",
+ "armature current=18.50 A\n",
+ "excitation voltage=243.06 V\n",
+ "load angle=9.10 deg\n",
+ "pull out torque=773.69 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.34, Page No 736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=4.0\n",
+ "f=50.0\n",
+ "w_s=4*math.pi*f/P\n",
+ "X_d=8.0\n",
+ "X_q=2.0\n",
+ "T_e=80.0\n",
+ "V=400.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=V/math.sqrt(3)\n",
+ "dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d)))) \n",
+ "print(\"load angle=%.3f deg\" %dl)\n",
+ "I_d=V_t*math.cos(math.radians(dl))/X_d\n",
+ "I_q=V_t*math.sin(math.radians(dl))/X_q\n",
+ "I_a=math.sqrt(I_d**2+I_q**2) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "pf=T_e*w_s/(math.sqrt(3)*V*I_a) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load angle=0.000 deg\n",
+ "armature current=28.87 A\n",
+ "input power factor=0.6283\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.35, Page No 737"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=3.0\n",
+ "K_m=1.2\n",
+ "I_a=T_e/K_m\n",
+ "r_a=2.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)\n",
+ "w_m=E_a/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=640.96 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.36, Page No 738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1360.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=163.45\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.2578 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.37, Page No 740"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=2100.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=227.66\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=1.94 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.38, Page No 742"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=840.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=75.0\n",
+ "V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=10.5922 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.39, Page No 743"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1400.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "a1=212\n",
+ "V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.257 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.40, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=600.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=13.568 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.41, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r1=.6\n",
+ "r2=.4\n",
+ "s=0.04\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "Z=(r1+r2/s)+(x1+x2)\n",
+ "V=400.0\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "N=1500\n",
+ "w_s=2*math.pi*N/60\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n",
+ "N_r=N*(1-s)\n",
+ "\n",
+ "f=45\n",
+ "N_s1=120*f/4\n",
+ "w_s=2*math.pi*N_s1/60\n",
+ "s1=(N_s1-N_r)/N_s1\n",
+ "Z=(r1+r2/s1)+(x1+x2)*f/50.0\n",
+ "V=360\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s1 \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source current=0.000 A \n",
+ "and with 29.0 deg phase\n",
+ "motor torque=160.46 Nm\n",
+ "source current=-0.000 A \n",
+ "and with 142.9 deg phase\n",
+ "motor torque=-2598.45 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter12_1.ipynb b/_Power_Electronics/Chapter12_1.ipynb new file mode 100755 index 00000000..f8605d69 --- /dev/null +++ b/_Power_Electronics/Chapter12_1.ipynb @@ -0,0 +1,1997 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12 : Electic Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, Page No 658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=15.0 #Nm\n",
+ "K_m=0.5 #V-s/rad\n",
+ "I_a=T_e/K_m\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "E_a=K_m*w_m\n",
+ "r_a=0.7\n",
+ "V_t=E_a+I_a*r_a\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "I_Tr=I_a*math.sqrt((180-a)/360) \n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "I_fdr=I_a*math.sqrt((180+a)/360) \n",
+ "print(\"rms value of freewheeling diode current=%.3f A\" %I_fdr)\n",
+ "pf=V_t*I_a/(V_s*I_Tr) \n",
+ "\n",
+ "#Results \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=65.349 deg\n",
+ "rms value of thyristor current=16.930 A\n",
+ "rms value of freewheeling diode current=24.766 A\n",
+ "input power factor=0.5652\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, Page No 660"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 661"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=250\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "k=0.03 #Nm/A**2\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r=.2 #r_a+r_s\n",
+ "V_t=V_m/math.pi*(1+math.cos(math.radians(a)))\n",
+ "I_a=V_t/(k*w_m+r) \n",
+ "print(\"motor armature current=%.2f A\" %I_a)\n",
+ "T_e=k*I_a**2 \n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n",
+ "I_sr=I_a*math.sqrt((180-a)/180)\n",
+ "pf=(V_t*I_a)/(V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor armature current=57.82 A\n",
+ "motor torque=100.285 Nm\n",
+ "input power factor=0.92\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, Page No 663"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(I_f*K_a) \n",
+ "print(\"rated armature current=%.2f A\" %I_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.2\n",
+ "V_t=K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "E_a=V_t\n",
+ "w_mo=E_a/(K_a*I_f)\n",
+ "N=60*w_mo/(2*math.pi)\n",
+ "reg=((N-n_m)/n_m)*100 \n",
+ "print(\"speed regulation at full load=%.2f\" %reg)\n",
+ "I_ar=I_a\n",
+ "pf=(V_t*I_a)/(V_s*I_ar) \n",
+ "print(\"input power factor of armature convertor=%.4f\" %pf)\n",
+ "I_fr=I_f\n",
+ "I_sr=math.sqrt(I_fr**2+I_ar**2)\n",
+ "VA=I_sr*V_s\n",
+ "P=V_t*I_a+V_f*I_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor of drive=%.4f\" %(P/VA))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rated armature current=59.01 A\n",
+ "firing angle delay=57.63 deg\n",
+ "speed regulation at full load=6.52\n",
+ "input power factor of armature convertor=0.4821\n",
+ "input power factor of drive=0.5093\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) \n",
+ "print(\"delay angle of field converter=%.0f deg\" %a1)\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "I_a=T_e/(I_f*K_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.1\n",
+ "I_a=50.0\n",
+ "V_t=-K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay of armature converter=%.3f deg\" %a)\n",
+ "print(\"power fed back to ac supply=%.0f W\" %(-V_t*I_a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle of field converter=58 deg\n",
+ "firing angle delay of armature converter=119.260 deg\n",
+ "power fed back to ac supply=8801 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=10.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "T=5.0\n",
+ "I_a=T/K_m\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n",
+ "a=45\n",
+ "n_m=1000\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=(V_t-K_m*w_m)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"torque developed=%.3f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=1254.22 rpm\n",
+ "torque developed=8.586 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, Page No 666"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1000.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=60.0\n",
+ "r_a=.1\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=230\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for 600rpm speed\")\n",
+ "n_m=600.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) \n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"for -500rpm speed\")\n",
+ "n_m=-500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_a=I_a/2\n",
+ "a=150\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.3f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 600rpm speed\n",
+ "firing angle=49.530 deg\n",
+ "for -500rpm speed\n",
+ "firing angle=119.19 deg\n",
+ "motor speed=-852.011 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.5\n",
+ "T_e=50.0\n",
+ "I_a=T_e/K_m\n",
+ "r_a=0.9\n",
+ "a=45.0\n",
+ "V_s=415.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=2854.42 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_t=600\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=80.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for firing angle=45deg and speed=1200rpm\")\n",
+ "a=45.0\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(2/3) \n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(1/3)))\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_a*(1/3))\n",
+ "pf=(3/(2*math.pi)*(1+math.cos(math.radians(a)))) \n",
+ "print(\"input power factor=%.3f\" %pf)\n",
+ "\n",
+ "print(\"for firing angle=90deg and speed=700rpm\")\n",
+ "a=90\n",
+ "n_m=700\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(90/180) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(90.0/360)))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_a*(1/3))\n",
+ "pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a)) \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=45deg and speed=1200rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=0.000 A\n",
+ "\n",
+ "input power factor=0.815\n",
+ "for firing angle=90deg and speed=700rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=195.558 A\n",
+ "\n",
+ "input power factor=0.5513\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10 Page No 676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=21.0\n",
+ "r_a=.1\n",
+ "V_d=2.0\n",
+ "K_m=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"speed of motor=%.1f rpm\" %N)\n",
+ "\n",
+ "N=2000\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=210\n",
+ "V_t=K_m*w_m+I_a*r_a+V_d\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_sr=I_a*math.sqrt(2.0/3.0)\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"supply power factor=%.3f\" %pf)\n",
+ "\n",
+ "I_a=21\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "n=w_m*60/(2*math.pi)\n",
+ "reg=(n-N)/N*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"speed regulation(percent)=%.2f\" %reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of motor=2767.6 rpm\n",
+ "firing angle=48.48 deg\n",
+ "supply power factor=0.633\n",
+ "speed regulation(percent)=5.64\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11, Page No 677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=230.0\n",
+ "V_l=V_t*math.pi/(3*math.sqrt(2))\n",
+ "V_ph=V_l/math.sqrt(3)\n",
+ "V_in=400 #per phase voltage input\n",
+ "\n",
+ "#Calculations\n",
+ "N1=1500.0\n",
+ "I_a1=20.0\n",
+ "r_a1=.6\n",
+ "E_a1=V_t-I_a1*r_a1\n",
+ "n1=1000.0\n",
+ "E_a2=E_a1/1500.0*1000.0\n",
+ "V_t1=E_a1+I_a1*r_a1\n",
+ "a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))\n",
+ "I_a2=.5*I_a1\n",
+ "n2=-900.0\n",
+ "V_t2=n2*E_a2/N1+I_a2*r_a1\n",
+ "a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer phase turns ratio=%.3f\" %(V_in/V_ph))\n",
+ "print(\"for motor running at 1000rpm at rated torque\")\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"for motor running at -900rpm at half of rated torque\")\n",
+ "print(\"firing angle delay=%.3f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer phase turns ratio=4.068\n",
+ "for motor running at 1000rpm at rated torque\n",
+ "firing angle delay=0.00 deg\n",
+ "for motor running at -900rpm at half of rated torque\n",
+ "firing angle delay=110.674 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12, Page No 678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=400\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_f=3*V_ml/math.pi\n",
+ "R_f=300.0\n",
+ "I_f=V_f/R_f\n",
+ "T_e=60.0\n",
+ "k=1.1\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(k*I_f)\n",
+ "N1=1000.0\n",
+ "w_m1=2*math.pi*N1/60\n",
+ "r_a1=.3\n",
+ "V_t1=k*I_f*w_m1+I_a*r_a1\n",
+ "a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))\n",
+ "N2=3000\n",
+ "w_m2=2*math.pi*N/60\n",
+ "a2=0\n",
+ "V_t2=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "I_f2=(V_t2-I_a*r_a)/(w_m2*k)\n",
+ "V_f2=I_f2*R_f\n",
+ "a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle=%.3f deg\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=48.477 deg\n",
+ "firing angle=48.477 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ " #after calculating\n",
+ " #t=w_m/6000-math.pi/360\n",
+ "\n",
+ "N=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "t=w_m/6000-math.pi/360 \n",
+ "\n",
+ "#Results\n",
+ "print(\"time reqd=%.2f s\" %t)\n",
+ " #printing mistake in the answer in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time reqd=0.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=1.0 #supposition\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))\n",
+ "I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))\n",
+ "I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))\n",
+ "per3=I_s3/I_s1*100 \n",
+ "print(\"percent of 3rd harmonic current in fundamental=%.2f\" %per3)\n",
+ "per5=I_s5/I_s1*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"percent of 5th harmonic current in fundamental=%.2f\" %per5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percent of 3rd harmonic current in fundamental=0.00\n",
+ "percent of 5th harmonic current in fundamental=-20.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15, Page No 680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=60.0\n",
+ "I_TA=I_a/3 \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"avg thyristor current=%.0f A\" %I_TA)\n",
+ "I_Tr=I_a/math.sqrt(3) \n",
+ "print(\"rms thyristor current=%.3f A\" %I_Tr)\n",
+ "V_s=400\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_sr=I_a*math.sqrt(2.0/3)\n",
+ "a=150\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"power factor of ac source=%.3f\" %pf)\n",
+ "\n",
+ "r_a=0.5\n",
+ "K_m=2.4\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Speed of motor=%.2f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg thyristor current=20 A\n",
+ "rms thyristor current=34.641 A\n",
+ "power factor of ac source=-0.827\n",
+ "Speed of motor=-1980.76 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16, Page No 685"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=300.0\n",
+ "V_s=600.0\n",
+ "a=0.6\n",
+ "V_t=a*V_s\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"input power from source=%.0f kW\" %(P/1000))\n",
+ "R_eq=V_s/(a*I_a) \n",
+ "print(\"equivalent input resistance=%.3f ohm\" %R_eq)\n",
+ "k=.004\n",
+ "R=.04+.06\n",
+ "w_m=(a*V_s-I_a*R)/(k*I_a)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ "T_e=k*I_a**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.0f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "input power from source=108 kW\n",
+ "equivalent input resistance=3.333 ohm\n",
+ "motor speed=2626.1 rpm\n",
+ "motor torque=360 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.17, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=10.0\n",
+ "T_off=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_s=230.0\n",
+ "V_t=a*V_s\n",
+ "r_a=3\n",
+ "K_m=.5\n",
+ "N=1500\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=(V_t-K_m*w_m)/r_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor load current=%.3f A\" %I_a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor load current=4.487 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "w_m=0 \n",
+ "print(\"lower limit of speed control=%.0f rpm\" %w_m)\n",
+ "I_a=25.0\n",
+ "r_a=.2\n",
+ "V_s=220\n",
+ "K_m=0.08\n",
+ "\n",
+ "#Calculations\n",
+ "a=(K_m*w_m+I_a*r_a)/V_s \n",
+ "print(\"lower limit of duty cycle=%.3f\" %a)\n",
+ "a=1 \n",
+ "print(\"upper limit of duty cycle=%.0f\" %a)\n",
+ "w_m=(a*V_s-I_a*r_a)/K_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"upper limit of speed control=%.1f rpm\" %w_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lower limit of speed control=0 rpm\n",
+ "lower limit of duty cycle=0.023\n",
+ "upper limit of duty cycle=1\n",
+ "upper limit of speed control=2687.5 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21, Page No 691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.6\n",
+ "V_s=400.0\n",
+ "V_t=(1-a)*V_s\n",
+ "I_a=300.0\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations \n",
+ "print(\"power returned=%.0f kW\" %(P/1000))\n",
+ "r_a=.2\n",
+ "K_m=1.2\n",
+ "R_eq=(1-a)*V_s/I_a+r_a \n",
+ "print(\"equivalent load resistance=%.4f ohm\" %R_eq)\n",
+ "w_mn=I_a*r_a/K_m\n",
+ "N=w_mn*60/(2*math.pi) \n",
+ "print(\"min braking speed=%.2f rpm\" %N)\n",
+ "w_mx=(V_s+I_a*r_a)/K_m\n",
+ "N=w_mx*60/(2*math.pi) \n",
+ "print(\"max braking speed=%.1f rpm\" %N)\n",
+ "w_m=(V_t+I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"max braking speed=%.1f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power returned=48 kW\n",
+ "equivalent load resistance=0.7333 ohm\n",
+ "min braking speed=477.46 rpm\n",
+ "max braking speed=3660.6 rpm\n",
+ "max braking speed=1750.7 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22, Page No 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "N=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when speed=1455rpm\")\n",
+ "n=1455.0\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)\n",
+ "print(\"when speed=1350rpm\")\n",
+ "n=1350\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when speed=1455rpm\n",
+ "I_2mx/I_2r=0.000\n",
+ "when speed=1350rpm\n",
+ "I_2mx/I_2r=0.000\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24, Page No 705"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=400.0\n",
+ "r1=0.6\n",
+ "r2=0.4\n",
+ "s=1.0\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"at starting in normal conditions\")\n",
+ "I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"current=%.2f A\" %I_n)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s) \n",
+ "print(\"\\nTorque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.0f A\" %I_d)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"pf=%.2f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_ed=(3/w_s)*I_d**2*(r2/s) \n",
+ "print(\"Torque developed=%.3f Nm\" %T_ed)\n",
+ "print(\"at max torque conditions\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)\n",
+ "I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"current=%.3f A\" %I_n)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s_mn) \n",
+ "print(\"Torque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.3f A\" %I_d)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"\\npf=%.3f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_d**2*(r2/s_mn) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"Torque developed=%.3f Nm\" %T_en)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at starting in normal conditions\n",
+ "current=119.31 A\n",
+ "pf=0.2983\n",
+ "\n",
+ "Torque developed=108.75 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=106 A\n",
+ "pf=0.53\n",
+ "Torque developed=171.673 Nm\n",
+ "at max torque conditions\n",
+ "current=79.829 A\n",
+ "pf=0.7695\n",
+ "Torque developed=396.26 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=71.199 A\n",
+ "\n",
+ "pf=0.822\n",
+ "Torque developed=330.883 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.25, Page No 709"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x1=1.0\n",
+ "X_m=50.0\n",
+ "X_e=x1*X_m/(x1+X_m)\n",
+ "V=231.0\n",
+ "V_e=V*X_m/(x1+X_m)\n",
+ "x2=1.0\n",
+ "r2=.4\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "s_m=r2/(x2+X_e) \n",
+ "print(\"slip at max torque=%.2f\" %s_m)\n",
+ "s_mT=r2/(x2+X_m) \n",
+ "print(\"slip at max torque=%.5f\" %s_mT)\n",
+ "f1=50.0\n",
+ "w_s=4*math.pi*f1/4\n",
+ "print(\"for constant voltage input\")\n",
+ "T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2) \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*V_e**2/(2*(x2+X_e)) \n",
+ "print(\"maximum torque developed=%.2f Nm\" %T_em)\n",
+ "print(\"for constant current input\")\n",
+ "I1=28\n",
+ "T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2 \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m)) \n",
+ "print(\"maximum torque developed=%.3f Nm\" %T_em)\n",
+ "s=s_mT\n",
+ "i=1\n",
+ "I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))\n",
+ "I_m=math.fabs(I_m)\n",
+ "V1=math.sqrt(3)*I_m*X_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"supply voltage reqd=%.1f V\" %V1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip at max torque=0.20\n",
+ "slip at max torque=0.00784\n",
+ "for constant voltage input\n",
+ "starting torque=95.988 Nm\n",
+ "maximum torque developed=247.31 Nm\n",
+ "for constant current input\n",
+ "starting torque=5.756 Nm\n",
+ "maximum torque developed=366.993 Nm\n",
+ "supply voltage reqd=1236.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.27, Page No 718"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "T_e=450.0\n",
+ "N=1440.0\n",
+ "n=1000.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "n1=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n1/60\n",
+ "w_m=2*math.pi*n/60\n",
+ "a=.8\n",
+ "I_d=T_L*w_s/(2.339*a*V1)\n",
+ "k=0\n",
+ "R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k)) \n",
+ "print(\"value of chopper resistance=%.4f ohm\" %R)\n",
+ "n=1320.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "I_d=T_L*w_s/(2.339*a*V1) \n",
+ "print(\"Inductor current=%.3f A\" %I_d)\n",
+ "w_m=2*math.pi*n/60\n",
+ "k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.4f\" %k)\n",
+ "s=(n1-n)/n1\n",
+ "V_d=2.339*s*a*V1 \n",
+ "print(\"Rectifed o/p voltage=%.3f V\" %V_d)\n",
+ "P=V_d*I_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "Pr=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "r1=0.015\n",
+ "Ps=3*I1**2*r1\n",
+ "Po=T_L*w_m\n",
+ "Pi=Po+Ps+Pr+P\n",
+ "eff=Po/Pi*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Efficiency(in percent)=%.2f\" %eff)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of chopper resistance=2.0132 ohm\n",
+ "Inductor current=130.902 A\n",
+ "value of duty cycle=0.7934\n",
+ "Rectifed o/p voltage=54.449 V\n",
+ "Efficiency(in percent)=88.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.28, Page No 720"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ph=V/math.sqrt(3)\n",
+ "N_s=1000.0\n",
+ "N=800.0\n",
+ "a=.7\n",
+ "I_d=110\n",
+ "R=2.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.3f\" %k)\n",
+ "P=I_d**2*R*(1-k)\n",
+ "I1=a*I_d*math.sqrt(2/3)\n",
+ "r1=0.1\n",
+ "r2=0.08\n",
+ "Pr=3*I1**2*(r1+r2)\n",
+ "P_o=20000\n",
+ "P_i=P_o+Pr+P\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"Efficiency=%.2f\" %eff)\n",
+ "I11=math.sqrt(6)/math.pi*a*I_d\n",
+ "th=43\n",
+ "P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))\n",
+ "pf=P_ip/(math.sqrt(3)*V*I11) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of duty cycle=0.656\n",
+ "Efficiency=70.62\n",
+ "Input power factor=0.7314\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.29, Page No 724"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "N=1000.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "N_s=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "a=0.8\n",
+ "V_d=2.339*a*s*V1 \n",
+ "print(\"rectified voltage=%.2f V\" %V_d)\n",
+ "T=450.0\n",
+ "N1=1200.0\n",
+ "T_L=T*(N/N1)**2\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "I_d=w_s*T_L/(2.339*a*V1) \n",
+ "print(\"inductor current=%.2f A\" %I_d)\n",
+ "a_T=-.4\n",
+ "a1=math.degrees(math.acos(s*a/a_T))\n",
+ "print(\"delay angle of inverter=%.2f deg\" %a1)\n",
+ "\n",
+ "P_s=V_d*I_d\n",
+ "P_o=T_L*w_m\n",
+ "R_d=0.01\n",
+ "P_i=I_d**2*R_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "r1=0.015\n",
+ "P_rol=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "P_sol=3*I1**2*r1\n",
+ "P_i=P_o+P_rol+P_sol+P_i\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"\\nefficiency=%.2f\" %eff)\n",
+ "w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectified voltage=151.25 V\n",
+ "inductor current=108.18 A\n",
+ "delay angle of inverter=131.81 deg\n",
+ "\n",
+ "efficiency=99.64\n",
+ "motor speed=996.4 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.30, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=0.7\n",
+ "V_dt=1.5\n",
+ "V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd\n",
+ "V1=415.0\n",
+ "a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=70.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.31, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=.7\n",
+ "V_dt=1.5\n",
+ "a=0\n",
+ "u=18 #overlap angle in case of rectifier\n",
+ "V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd\n",
+ "V1=415\n",
+ "V_ml=math.sqrt(2)*V1\n",
+ "u=4 #overlap anglein the inverter\n",
+ " #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)\n",
+ " #V_dc=V_d\n",
+ " #after solving % (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425\n",
+ "a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=71.25 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.32, Page No 727"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V1=415.0\n",
+ "a_T=s*E2/V1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage ratio of the transformer=%.2f\" %a_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage ratio of the transformer=0.34\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.33, Page No 733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=6.0\n",
+ "N_s=600.0\n",
+ "f1=P*N_s/120.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=f1*V/f \n",
+ "print(\"supply freq=%.0f Hz\" %V_t)\n",
+ "T=340.0\n",
+ "N=1000.0\n",
+ "T_L=T*(N_s/N)**2\n",
+ "w_s=2*math.pi*N_s/60\n",
+ "P=T_L*w_s\n",
+ "I_a=P/(math.sqrt(3)*V_t) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "Z_s=2\n",
+ "X_s=f1/f*math.fabs(Z_s)\n",
+ "V_t=V_t/math.sqrt(3)\n",
+ "Ef=math.sqrt(V_t**2+(I_a*X_s)**2)\n",
+ "print(\"excitation voltage=%.2f V\" %(math.sqrt(3)*Ef))\n",
+ "dl=math.degrees(math.atan(I_a*X_s/V_t))\n",
+ "print(\"load angle=%.2f deg\" %dl)\n",
+ "T_em=(3/w_s)*(Ef*V_t/X_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pull out torque=%.2f Nm\" %T_em)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "supply freq=240 Hz\n",
+ "armature current=18.50 A\n",
+ "excitation voltage=243.06 V\n",
+ "load angle=9.10 deg\n",
+ "pull out torque=773.69 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.34, Page No 736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=4.0\n",
+ "f=50.0\n",
+ "w_s=4*math.pi*f/P\n",
+ "X_d=8.0\n",
+ "X_q=2.0\n",
+ "T_e=80.0\n",
+ "V=400.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=V/math.sqrt(3)\n",
+ "dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d)))) \n",
+ "print(\"load angle=%.3f deg\" %dl)\n",
+ "I_d=V_t*math.cos(math.radians(dl))/X_d\n",
+ "I_q=V_t*math.sin(math.radians(dl))/X_q\n",
+ "I_a=math.sqrt(I_d**2+I_q**2) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "pf=T_e*w_s/(math.sqrt(3)*V*I_a) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load angle=0.000 deg\n",
+ "armature current=28.87 A\n",
+ "input power factor=0.6283\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.35, Page No 737"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=3.0\n",
+ "K_m=1.2\n",
+ "I_a=T_e/K_m\n",
+ "r_a=2.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)\n",
+ "w_m=E_a/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=640.96 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.36, Page No 738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1360.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=163.45\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.2578 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.37, Page No 740"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=2100.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=227.66\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=1.94 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.38, Page No 742"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=840.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=75.0\n",
+ "V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=10.5922 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.39, Page No 743"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1400.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "a1=212\n",
+ "V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.257 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.40, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=600.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=13.568 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.41, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r1=.6\n",
+ "r2=.4\n",
+ "s=0.04\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "Z=(r1+r2/s)+(x1+x2)\n",
+ "V=400.0\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "N=1500\n",
+ "w_s=2*math.pi*N/60\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n",
+ "N_r=N*(1-s)\n",
+ "\n",
+ "f=45\n",
+ "N_s1=120*f/4\n",
+ "w_s=2*math.pi*N_s1/60\n",
+ "s1=(N_s1-N_r)/N_s1\n",
+ "Z=(r1+r2/s1)+(x1+x2)*f/50.0\n",
+ "V=360\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s1 \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source current=0.000 A \n",
+ "and with 29.0 deg phase\n",
+ "motor torque=160.46 Nm\n",
+ "source current=-0.000 A \n",
+ "and with 142.9 deg phase\n",
+ "motor torque=-2598.45 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter12_2.ipynb b/_Power_Electronics/Chapter12_2.ipynb new file mode 100755 index 00000000..f8605d69 --- /dev/null +++ b/_Power_Electronics/Chapter12_2.ipynb @@ -0,0 +1,1997 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12 : Electic Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, Page No 658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=15.0 #Nm\n",
+ "K_m=0.5 #V-s/rad\n",
+ "I_a=T_e/K_m\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "E_a=K_m*w_m\n",
+ "r_a=0.7\n",
+ "V_t=E_a+I_a*r_a\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "I_Tr=I_a*math.sqrt((180-a)/360) \n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "I_fdr=I_a*math.sqrt((180+a)/360) \n",
+ "print(\"rms value of freewheeling diode current=%.3f A\" %I_fdr)\n",
+ "pf=V_t*I_a/(V_s*I_Tr) \n",
+ "\n",
+ "#Results \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=65.349 deg\n",
+ "rms value of thyristor current=16.930 A\n",
+ "rms value of freewheeling diode current=24.766 A\n",
+ "input power factor=0.5652\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, Page No 660"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 661"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=250\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "k=0.03 #Nm/A**2\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r=.2 #r_a+r_s\n",
+ "V_t=V_m/math.pi*(1+math.cos(math.radians(a)))\n",
+ "I_a=V_t/(k*w_m+r) \n",
+ "print(\"motor armature current=%.2f A\" %I_a)\n",
+ "T_e=k*I_a**2 \n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n",
+ "I_sr=I_a*math.sqrt((180-a)/180)\n",
+ "pf=(V_t*I_a)/(V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor armature current=57.82 A\n",
+ "motor torque=100.285 Nm\n",
+ "input power factor=0.92\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, Page No 663"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(I_f*K_a) \n",
+ "print(\"rated armature current=%.2f A\" %I_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.2\n",
+ "V_t=K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "E_a=V_t\n",
+ "w_mo=E_a/(K_a*I_f)\n",
+ "N=60*w_mo/(2*math.pi)\n",
+ "reg=((N-n_m)/n_m)*100 \n",
+ "print(\"speed regulation at full load=%.2f\" %reg)\n",
+ "I_ar=I_a\n",
+ "pf=(V_t*I_a)/(V_s*I_ar) \n",
+ "print(\"input power factor of armature convertor=%.4f\" %pf)\n",
+ "I_fr=I_f\n",
+ "I_sr=math.sqrt(I_fr**2+I_ar**2)\n",
+ "VA=I_sr*V_s\n",
+ "P=V_t*I_a+V_f*I_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor of drive=%.4f\" %(P/VA))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rated armature current=59.01 A\n",
+ "firing angle delay=57.63 deg\n",
+ "speed regulation at full load=6.52\n",
+ "input power factor of armature convertor=0.4821\n",
+ "input power factor of drive=0.5093\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) \n",
+ "print(\"delay angle of field converter=%.0f deg\" %a1)\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "I_a=T_e/(I_f*K_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.1\n",
+ "I_a=50.0\n",
+ "V_t=-K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay of armature converter=%.3f deg\" %a)\n",
+ "print(\"power fed back to ac supply=%.0f W\" %(-V_t*I_a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle of field converter=58 deg\n",
+ "firing angle delay of armature converter=119.260 deg\n",
+ "power fed back to ac supply=8801 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=10.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "T=5.0\n",
+ "I_a=T/K_m\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n",
+ "a=45\n",
+ "n_m=1000\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=(V_t-K_m*w_m)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"torque developed=%.3f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=1254.22 rpm\n",
+ "torque developed=8.586 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, Page No 666"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1000.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=60.0\n",
+ "r_a=.1\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=230\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for 600rpm speed\")\n",
+ "n_m=600.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) \n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"for -500rpm speed\")\n",
+ "n_m=-500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_a=I_a/2\n",
+ "a=150\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.3f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 600rpm speed\n",
+ "firing angle=49.530 deg\n",
+ "for -500rpm speed\n",
+ "firing angle=119.19 deg\n",
+ "motor speed=-852.011 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.5\n",
+ "T_e=50.0\n",
+ "I_a=T_e/K_m\n",
+ "r_a=0.9\n",
+ "a=45.0\n",
+ "V_s=415.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=2854.42 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_t=600\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=80.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for firing angle=45deg and speed=1200rpm\")\n",
+ "a=45.0\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(2/3) \n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(1/3)))\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_a*(1/3))\n",
+ "pf=(3/(2*math.pi)*(1+math.cos(math.radians(a)))) \n",
+ "print(\"input power factor=%.3f\" %pf)\n",
+ "\n",
+ "print(\"for firing angle=90deg and speed=700rpm\")\n",
+ "a=90\n",
+ "n_m=700\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(90/180) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(90.0/360)))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_a*(1/3))\n",
+ "pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a)) \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=45deg and speed=1200rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=0.000 A\n",
+ "\n",
+ "input power factor=0.815\n",
+ "for firing angle=90deg and speed=700rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=195.558 A\n",
+ "\n",
+ "input power factor=0.5513\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10 Page No 676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=21.0\n",
+ "r_a=.1\n",
+ "V_d=2.0\n",
+ "K_m=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"speed of motor=%.1f rpm\" %N)\n",
+ "\n",
+ "N=2000\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=210\n",
+ "V_t=K_m*w_m+I_a*r_a+V_d\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_sr=I_a*math.sqrt(2.0/3.0)\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"supply power factor=%.3f\" %pf)\n",
+ "\n",
+ "I_a=21\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "n=w_m*60/(2*math.pi)\n",
+ "reg=(n-N)/N*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"speed regulation(percent)=%.2f\" %reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of motor=2767.6 rpm\n",
+ "firing angle=48.48 deg\n",
+ "supply power factor=0.633\n",
+ "speed regulation(percent)=5.64\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11, Page No 677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=230.0\n",
+ "V_l=V_t*math.pi/(3*math.sqrt(2))\n",
+ "V_ph=V_l/math.sqrt(3)\n",
+ "V_in=400 #per phase voltage input\n",
+ "\n",
+ "#Calculations\n",
+ "N1=1500.0\n",
+ "I_a1=20.0\n",
+ "r_a1=.6\n",
+ "E_a1=V_t-I_a1*r_a1\n",
+ "n1=1000.0\n",
+ "E_a2=E_a1/1500.0*1000.0\n",
+ "V_t1=E_a1+I_a1*r_a1\n",
+ "a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))\n",
+ "I_a2=.5*I_a1\n",
+ "n2=-900.0\n",
+ "V_t2=n2*E_a2/N1+I_a2*r_a1\n",
+ "a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer phase turns ratio=%.3f\" %(V_in/V_ph))\n",
+ "print(\"for motor running at 1000rpm at rated torque\")\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"for motor running at -900rpm at half of rated torque\")\n",
+ "print(\"firing angle delay=%.3f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer phase turns ratio=4.068\n",
+ "for motor running at 1000rpm at rated torque\n",
+ "firing angle delay=0.00 deg\n",
+ "for motor running at -900rpm at half of rated torque\n",
+ "firing angle delay=110.674 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12, Page No 678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=400\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_f=3*V_ml/math.pi\n",
+ "R_f=300.0\n",
+ "I_f=V_f/R_f\n",
+ "T_e=60.0\n",
+ "k=1.1\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(k*I_f)\n",
+ "N1=1000.0\n",
+ "w_m1=2*math.pi*N1/60\n",
+ "r_a1=.3\n",
+ "V_t1=k*I_f*w_m1+I_a*r_a1\n",
+ "a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))\n",
+ "N2=3000\n",
+ "w_m2=2*math.pi*N/60\n",
+ "a2=0\n",
+ "V_t2=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "I_f2=(V_t2-I_a*r_a)/(w_m2*k)\n",
+ "V_f2=I_f2*R_f\n",
+ "a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle=%.3f deg\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=48.477 deg\n",
+ "firing angle=48.477 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ " #after calculating\n",
+ " #t=w_m/6000-math.pi/360\n",
+ "\n",
+ "N=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "t=w_m/6000-math.pi/360 \n",
+ "\n",
+ "#Results\n",
+ "print(\"time reqd=%.2f s\" %t)\n",
+ " #printing mistake in the answer in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time reqd=0.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=1.0 #supposition\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))\n",
+ "I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))\n",
+ "I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))\n",
+ "per3=I_s3/I_s1*100 \n",
+ "print(\"percent of 3rd harmonic current in fundamental=%.2f\" %per3)\n",
+ "per5=I_s5/I_s1*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"percent of 5th harmonic current in fundamental=%.2f\" %per5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percent of 3rd harmonic current in fundamental=0.00\n",
+ "percent of 5th harmonic current in fundamental=-20.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15, Page No 680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=60.0\n",
+ "I_TA=I_a/3 \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"avg thyristor current=%.0f A\" %I_TA)\n",
+ "I_Tr=I_a/math.sqrt(3) \n",
+ "print(\"rms thyristor current=%.3f A\" %I_Tr)\n",
+ "V_s=400\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_sr=I_a*math.sqrt(2.0/3)\n",
+ "a=150\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"power factor of ac source=%.3f\" %pf)\n",
+ "\n",
+ "r_a=0.5\n",
+ "K_m=2.4\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Speed of motor=%.2f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg thyristor current=20 A\n",
+ "rms thyristor current=34.641 A\n",
+ "power factor of ac source=-0.827\n",
+ "Speed of motor=-1980.76 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16, Page No 685"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=300.0\n",
+ "V_s=600.0\n",
+ "a=0.6\n",
+ "V_t=a*V_s\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"input power from source=%.0f kW\" %(P/1000))\n",
+ "R_eq=V_s/(a*I_a) \n",
+ "print(\"equivalent input resistance=%.3f ohm\" %R_eq)\n",
+ "k=.004\n",
+ "R=.04+.06\n",
+ "w_m=(a*V_s-I_a*R)/(k*I_a)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ "T_e=k*I_a**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.0f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "input power from source=108 kW\n",
+ "equivalent input resistance=3.333 ohm\n",
+ "motor speed=2626.1 rpm\n",
+ "motor torque=360 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.17, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=10.0\n",
+ "T_off=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_s=230.0\n",
+ "V_t=a*V_s\n",
+ "r_a=3\n",
+ "K_m=.5\n",
+ "N=1500\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=(V_t-K_m*w_m)/r_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor load current=%.3f A\" %I_a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor load current=4.487 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "w_m=0 \n",
+ "print(\"lower limit of speed control=%.0f rpm\" %w_m)\n",
+ "I_a=25.0\n",
+ "r_a=.2\n",
+ "V_s=220\n",
+ "K_m=0.08\n",
+ "\n",
+ "#Calculations\n",
+ "a=(K_m*w_m+I_a*r_a)/V_s \n",
+ "print(\"lower limit of duty cycle=%.3f\" %a)\n",
+ "a=1 \n",
+ "print(\"upper limit of duty cycle=%.0f\" %a)\n",
+ "w_m=(a*V_s-I_a*r_a)/K_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"upper limit of speed control=%.1f rpm\" %w_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lower limit of speed control=0 rpm\n",
+ "lower limit of duty cycle=0.023\n",
+ "upper limit of duty cycle=1\n",
+ "upper limit of speed control=2687.5 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21, Page No 691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.6\n",
+ "V_s=400.0\n",
+ "V_t=(1-a)*V_s\n",
+ "I_a=300.0\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations \n",
+ "print(\"power returned=%.0f kW\" %(P/1000))\n",
+ "r_a=.2\n",
+ "K_m=1.2\n",
+ "R_eq=(1-a)*V_s/I_a+r_a \n",
+ "print(\"equivalent load resistance=%.4f ohm\" %R_eq)\n",
+ "w_mn=I_a*r_a/K_m\n",
+ "N=w_mn*60/(2*math.pi) \n",
+ "print(\"min braking speed=%.2f rpm\" %N)\n",
+ "w_mx=(V_s+I_a*r_a)/K_m\n",
+ "N=w_mx*60/(2*math.pi) \n",
+ "print(\"max braking speed=%.1f rpm\" %N)\n",
+ "w_m=(V_t+I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"max braking speed=%.1f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power returned=48 kW\n",
+ "equivalent load resistance=0.7333 ohm\n",
+ "min braking speed=477.46 rpm\n",
+ "max braking speed=3660.6 rpm\n",
+ "max braking speed=1750.7 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22, Page No 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "N=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when speed=1455rpm\")\n",
+ "n=1455.0\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)\n",
+ "print(\"when speed=1350rpm\")\n",
+ "n=1350\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when speed=1455rpm\n",
+ "I_2mx/I_2r=0.000\n",
+ "when speed=1350rpm\n",
+ "I_2mx/I_2r=0.000\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24, Page No 705"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=400.0\n",
+ "r1=0.6\n",
+ "r2=0.4\n",
+ "s=1.0\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"at starting in normal conditions\")\n",
+ "I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"current=%.2f A\" %I_n)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s) \n",
+ "print(\"\\nTorque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.0f A\" %I_d)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"pf=%.2f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_ed=(3/w_s)*I_d**2*(r2/s) \n",
+ "print(\"Torque developed=%.3f Nm\" %T_ed)\n",
+ "print(\"at max torque conditions\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)\n",
+ "I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"current=%.3f A\" %I_n)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s_mn) \n",
+ "print(\"Torque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.3f A\" %I_d)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"\\npf=%.3f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_d**2*(r2/s_mn) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"Torque developed=%.3f Nm\" %T_en)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at starting in normal conditions\n",
+ "current=119.31 A\n",
+ "pf=0.2983\n",
+ "\n",
+ "Torque developed=108.75 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=106 A\n",
+ "pf=0.53\n",
+ "Torque developed=171.673 Nm\n",
+ "at max torque conditions\n",
+ "current=79.829 A\n",
+ "pf=0.7695\n",
+ "Torque developed=396.26 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=71.199 A\n",
+ "\n",
+ "pf=0.822\n",
+ "Torque developed=330.883 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.25, Page No 709"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x1=1.0\n",
+ "X_m=50.0\n",
+ "X_e=x1*X_m/(x1+X_m)\n",
+ "V=231.0\n",
+ "V_e=V*X_m/(x1+X_m)\n",
+ "x2=1.0\n",
+ "r2=.4\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "s_m=r2/(x2+X_e) \n",
+ "print(\"slip at max torque=%.2f\" %s_m)\n",
+ "s_mT=r2/(x2+X_m) \n",
+ "print(\"slip at max torque=%.5f\" %s_mT)\n",
+ "f1=50.0\n",
+ "w_s=4*math.pi*f1/4\n",
+ "print(\"for constant voltage input\")\n",
+ "T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2) \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*V_e**2/(2*(x2+X_e)) \n",
+ "print(\"maximum torque developed=%.2f Nm\" %T_em)\n",
+ "print(\"for constant current input\")\n",
+ "I1=28\n",
+ "T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2 \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m)) \n",
+ "print(\"maximum torque developed=%.3f Nm\" %T_em)\n",
+ "s=s_mT\n",
+ "i=1\n",
+ "I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))\n",
+ "I_m=math.fabs(I_m)\n",
+ "V1=math.sqrt(3)*I_m*X_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"supply voltage reqd=%.1f V\" %V1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip at max torque=0.20\n",
+ "slip at max torque=0.00784\n",
+ "for constant voltage input\n",
+ "starting torque=95.988 Nm\n",
+ "maximum torque developed=247.31 Nm\n",
+ "for constant current input\n",
+ "starting torque=5.756 Nm\n",
+ "maximum torque developed=366.993 Nm\n",
+ "supply voltage reqd=1236.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.27, Page No 718"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "T_e=450.0\n",
+ "N=1440.0\n",
+ "n=1000.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "n1=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n1/60\n",
+ "w_m=2*math.pi*n/60\n",
+ "a=.8\n",
+ "I_d=T_L*w_s/(2.339*a*V1)\n",
+ "k=0\n",
+ "R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k)) \n",
+ "print(\"value of chopper resistance=%.4f ohm\" %R)\n",
+ "n=1320.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "I_d=T_L*w_s/(2.339*a*V1) \n",
+ "print(\"Inductor current=%.3f A\" %I_d)\n",
+ "w_m=2*math.pi*n/60\n",
+ "k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.4f\" %k)\n",
+ "s=(n1-n)/n1\n",
+ "V_d=2.339*s*a*V1 \n",
+ "print(\"Rectifed o/p voltage=%.3f V\" %V_d)\n",
+ "P=V_d*I_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "Pr=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "r1=0.015\n",
+ "Ps=3*I1**2*r1\n",
+ "Po=T_L*w_m\n",
+ "Pi=Po+Ps+Pr+P\n",
+ "eff=Po/Pi*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Efficiency(in percent)=%.2f\" %eff)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of chopper resistance=2.0132 ohm\n",
+ "Inductor current=130.902 A\n",
+ "value of duty cycle=0.7934\n",
+ "Rectifed o/p voltage=54.449 V\n",
+ "Efficiency(in percent)=88.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.28, Page No 720"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ph=V/math.sqrt(3)\n",
+ "N_s=1000.0\n",
+ "N=800.0\n",
+ "a=.7\n",
+ "I_d=110\n",
+ "R=2.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.3f\" %k)\n",
+ "P=I_d**2*R*(1-k)\n",
+ "I1=a*I_d*math.sqrt(2/3)\n",
+ "r1=0.1\n",
+ "r2=0.08\n",
+ "Pr=3*I1**2*(r1+r2)\n",
+ "P_o=20000\n",
+ "P_i=P_o+Pr+P\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"Efficiency=%.2f\" %eff)\n",
+ "I11=math.sqrt(6)/math.pi*a*I_d\n",
+ "th=43\n",
+ "P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))\n",
+ "pf=P_ip/(math.sqrt(3)*V*I11) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of duty cycle=0.656\n",
+ "Efficiency=70.62\n",
+ "Input power factor=0.7314\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.29, Page No 724"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "N=1000.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "N_s=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "a=0.8\n",
+ "V_d=2.339*a*s*V1 \n",
+ "print(\"rectified voltage=%.2f V\" %V_d)\n",
+ "T=450.0\n",
+ "N1=1200.0\n",
+ "T_L=T*(N/N1)**2\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "I_d=w_s*T_L/(2.339*a*V1) \n",
+ "print(\"inductor current=%.2f A\" %I_d)\n",
+ "a_T=-.4\n",
+ "a1=math.degrees(math.acos(s*a/a_T))\n",
+ "print(\"delay angle of inverter=%.2f deg\" %a1)\n",
+ "\n",
+ "P_s=V_d*I_d\n",
+ "P_o=T_L*w_m\n",
+ "R_d=0.01\n",
+ "P_i=I_d**2*R_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "r1=0.015\n",
+ "P_rol=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "P_sol=3*I1**2*r1\n",
+ "P_i=P_o+P_rol+P_sol+P_i\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"\\nefficiency=%.2f\" %eff)\n",
+ "w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectified voltage=151.25 V\n",
+ "inductor current=108.18 A\n",
+ "delay angle of inverter=131.81 deg\n",
+ "\n",
+ "efficiency=99.64\n",
+ "motor speed=996.4 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.30, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=0.7\n",
+ "V_dt=1.5\n",
+ "V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd\n",
+ "V1=415.0\n",
+ "a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=70.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.31, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=.7\n",
+ "V_dt=1.5\n",
+ "a=0\n",
+ "u=18 #overlap angle in case of rectifier\n",
+ "V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd\n",
+ "V1=415\n",
+ "V_ml=math.sqrt(2)*V1\n",
+ "u=4 #overlap anglein the inverter\n",
+ " #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)\n",
+ " #V_dc=V_d\n",
+ " #after solving % (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425\n",
+ "a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=71.25 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.32, Page No 727"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V1=415.0\n",
+ "a_T=s*E2/V1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage ratio of the transformer=%.2f\" %a_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage ratio of the transformer=0.34\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.33, Page No 733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=6.0\n",
+ "N_s=600.0\n",
+ "f1=P*N_s/120.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=f1*V/f \n",
+ "print(\"supply freq=%.0f Hz\" %V_t)\n",
+ "T=340.0\n",
+ "N=1000.0\n",
+ "T_L=T*(N_s/N)**2\n",
+ "w_s=2*math.pi*N_s/60\n",
+ "P=T_L*w_s\n",
+ "I_a=P/(math.sqrt(3)*V_t) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "Z_s=2\n",
+ "X_s=f1/f*math.fabs(Z_s)\n",
+ "V_t=V_t/math.sqrt(3)\n",
+ "Ef=math.sqrt(V_t**2+(I_a*X_s)**2)\n",
+ "print(\"excitation voltage=%.2f V\" %(math.sqrt(3)*Ef))\n",
+ "dl=math.degrees(math.atan(I_a*X_s/V_t))\n",
+ "print(\"load angle=%.2f deg\" %dl)\n",
+ "T_em=(3/w_s)*(Ef*V_t/X_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pull out torque=%.2f Nm\" %T_em)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "supply freq=240 Hz\n",
+ "armature current=18.50 A\n",
+ "excitation voltage=243.06 V\n",
+ "load angle=9.10 deg\n",
+ "pull out torque=773.69 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.34, Page No 736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=4.0\n",
+ "f=50.0\n",
+ "w_s=4*math.pi*f/P\n",
+ "X_d=8.0\n",
+ "X_q=2.0\n",
+ "T_e=80.0\n",
+ "V=400.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=V/math.sqrt(3)\n",
+ "dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d)))) \n",
+ "print(\"load angle=%.3f deg\" %dl)\n",
+ "I_d=V_t*math.cos(math.radians(dl))/X_d\n",
+ "I_q=V_t*math.sin(math.radians(dl))/X_q\n",
+ "I_a=math.sqrt(I_d**2+I_q**2) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "pf=T_e*w_s/(math.sqrt(3)*V*I_a) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load angle=0.000 deg\n",
+ "armature current=28.87 A\n",
+ "input power factor=0.6283\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.35, Page No 737"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=3.0\n",
+ "K_m=1.2\n",
+ "I_a=T_e/K_m\n",
+ "r_a=2.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)\n",
+ "w_m=E_a/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=640.96 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.36, Page No 738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1360.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=163.45\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.2578 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.37, Page No 740"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=2100.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=227.66\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=1.94 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.38, Page No 742"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=840.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=75.0\n",
+ "V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=10.5922 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.39, Page No 743"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1400.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "a1=212\n",
+ "V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.257 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.40, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=600.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=13.568 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.41, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r1=.6\n",
+ "r2=.4\n",
+ "s=0.04\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "Z=(r1+r2/s)+(x1+x2)\n",
+ "V=400.0\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "N=1500\n",
+ "w_s=2*math.pi*N/60\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n",
+ "N_r=N*(1-s)\n",
+ "\n",
+ "f=45\n",
+ "N_s1=120*f/4\n",
+ "w_s=2*math.pi*N_s1/60\n",
+ "s1=(N_s1-N_r)/N_s1\n",
+ "Z=(r1+r2/s1)+(x1+x2)*f/50.0\n",
+ "V=360\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s1 \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source current=0.000 A \n",
+ "and with 29.0 deg phase\n",
+ "motor torque=160.46 Nm\n",
+ "source current=-0.000 A \n",
+ "and with 142.9 deg phase\n",
+ "motor torque=-2598.45 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter12_3.ipynb b/_Power_Electronics/Chapter12_3.ipynb new file mode 100755 index 00000000..f8605d69 --- /dev/null +++ b/_Power_Electronics/Chapter12_3.ipynb @@ -0,0 +1,1997 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12 : Electic Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, Page No 658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=15.0 #Nm\n",
+ "K_m=0.5 #V-s/rad\n",
+ "I_a=T_e/K_m\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "E_a=K_m*w_m\n",
+ "r_a=0.7\n",
+ "V_t=E_a+I_a*r_a\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "I_Tr=I_a*math.sqrt((180-a)/360) \n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "I_fdr=I_a*math.sqrt((180+a)/360) \n",
+ "print(\"rms value of freewheeling diode current=%.3f A\" %I_fdr)\n",
+ "pf=V_t*I_a/(V_s*I_Tr) \n",
+ "\n",
+ "#Results \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=65.349 deg\n",
+ "rms value of thyristor current=16.930 A\n",
+ "rms value of freewheeling diode current=24.766 A\n",
+ "input power factor=0.5652\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, Page No 660"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 661"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=250\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "k=0.03 #Nm/A**2\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r=.2 #r_a+r_s\n",
+ "V_t=V_m/math.pi*(1+math.cos(math.radians(a)))\n",
+ "I_a=V_t/(k*w_m+r) \n",
+ "print(\"motor armature current=%.2f A\" %I_a)\n",
+ "T_e=k*I_a**2 \n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n",
+ "I_sr=I_a*math.sqrt((180-a)/180)\n",
+ "pf=(V_t*I_a)/(V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor armature current=57.82 A\n",
+ "motor torque=100.285 Nm\n",
+ "input power factor=0.92\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, Page No 663"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(I_f*K_a) \n",
+ "print(\"rated armature current=%.2f A\" %I_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.2\n",
+ "V_t=K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "E_a=V_t\n",
+ "w_mo=E_a/(K_a*I_f)\n",
+ "N=60*w_mo/(2*math.pi)\n",
+ "reg=((N-n_m)/n_m)*100 \n",
+ "print(\"speed regulation at full load=%.2f\" %reg)\n",
+ "I_ar=I_a\n",
+ "pf=(V_t*I_a)/(V_s*I_ar) \n",
+ "print(\"input power factor of armature convertor=%.4f\" %pf)\n",
+ "I_fr=I_f\n",
+ "I_sr=math.sqrt(I_fr**2+I_ar**2)\n",
+ "VA=I_sr*V_s\n",
+ "P=V_t*I_a+V_f*I_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor of drive=%.4f\" %(P/VA))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rated armature current=59.01 A\n",
+ "firing angle delay=57.63 deg\n",
+ "speed regulation at full load=6.52\n",
+ "input power factor of armature convertor=0.4821\n",
+ "input power factor of drive=0.5093\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) \n",
+ "print(\"delay angle of field converter=%.0f deg\" %a1)\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "I_a=T_e/(I_f*K_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.1\n",
+ "I_a=50.0\n",
+ "V_t=-K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay of armature converter=%.3f deg\" %a)\n",
+ "print(\"power fed back to ac supply=%.0f W\" %(-V_t*I_a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle of field converter=58 deg\n",
+ "firing angle delay of armature converter=119.260 deg\n",
+ "power fed back to ac supply=8801 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=10.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "T=5.0\n",
+ "I_a=T/K_m\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n",
+ "a=45\n",
+ "n_m=1000\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=(V_t-K_m*w_m)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"torque developed=%.3f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=1254.22 rpm\n",
+ "torque developed=8.586 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, Page No 666"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1000.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=60.0\n",
+ "r_a=.1\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=230\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for 600rpm speed\")\n",
+ "n_m=600.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) \n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"for -500rpm speed\")\n",
+ "n_m=-500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_a=I_a/2\n",
+ "a=150\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.3f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 600rpm speed\n",
+ "firing angle=49.530 deg\n",
+ "for -500rpm speed\n",
+ "firing angle=119.19 deg\n",
+ "motor speed=-852.011 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.5\n",
+ "T_e=50.0\n",
+ "I_a=T_e/K_m\n",
+ "r_a=0.9\n",
+ "a=45.0\n",
+ "V_s=415.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=2854.42 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_t=600\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=80.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for firing angle=45deg and speed=1200rpm\")\n",
+ "a=45.0\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(2/3) \n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(1/3)))\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_a*(1/3))\n",
+ "pf=(3/(2*math.pi)*(1+math.cos(math.radians(a)))) \n",
+ "print(\"input power factor=%.3f\" %pf)\n",
+ "\n",
+ "print(\"for firing angle=90deg and speed=700rpm\")\n",
+ "a=90\n",
+ "n_m=700\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(90/180) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(90.0/360)))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_a*(1/3))\n",
+ "pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a)) \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=45deg and speed=1200rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=0.000 A\n",
+ "\n",
+ "input power factor=0.815\n",
+ "for firing angle=90deg and speed=700rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=195.558 A\n",
+ "\n",
+ "input power factor=0.5513\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10 Page No 676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=21.0\n",
+ "r_a=.1\n",
+ "V_d=2.0\n",
+ "K_m=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"speed of motor=%.1f rpm\" %N)\n",
+ "\n",
+ "N=2000\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=210\n",
+ "V_t=K_m*w_m+I_a*r_a+V_d\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_sr=I_a*math.sqrt(2.0/3.0)\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"supply power factor=%.3f\" %pf)\n",
+ "\n",
+ "I_a=21\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "n=w_m*60/(2*math.pi)\n",
+ "reg=(n-N)/N*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"speed regulation(percent)=%.2f\" %reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of motor=2767.6 rpm\n",
+ "firing angle=48.48 deg\n",
+ "supply power factor=0.633\n",
+ "speed regulation(percent)=5.64\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11, Page No 677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=230.0\n",
+ "V_l=V_t*math.pi/(3*math.sqrt(2))\n",
+ "V_ph=V_l/math.sqrt(3)\n",
+ "V_in=400 #per phase voltage input\n",
+ "\n",
+ "#Calculations\n",
+ "N1=1500.0\n",
+ "I_a1=20.0\n",
+ "r_a1=.6\n",
+ "E_a1=V_t-I_a1*r_a1\n",
+ "n1=1000.0\n",
+ "E_a2=E_a1/1500.0*1000.0\n",
+ "V_t1=E_a1+I_a1*r_a1\n",
+ "a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))\n",
+ "I_a2=.5*I_a1\n",
+ "n2=-900.0\n",
+ "V_t2=n2*E_a2/N1+I_a2*r_a1\n",
+ "a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer phase turns ratio=%.3f\" %(V_in/V_ph))\n",
+ "print(\"for motor running at 1000rpm at rated torque\")\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"for motor running at -900rpm at half of rated torque\")\n",
+ "print(\"firing angle delay=%.3f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer phase turns ratio=4.068\n",
+ "for motor running at 1000rpm at rated torque\n",
+ "firing angle delay=0.00 deg\n",
+ "for motor running at -900rpm at half of rated torque\n",
+ "firing angle delay=110.674 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12, Page No 678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=400\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_f=3*V_ml/math.pi\n",
+ "R_f=300.0\n",
+ "I_f=V_f/R_f\n",
+ "T_e=60.0\n",
+ "k=1.1\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(k*I_f)\n",
+ "N1=1000.0\n",
+ "w_m1=2*math.pi*N1/60\n",
+ "r_a1=.3\n",
+ "V_t1=k*I_f*w_m1+I_a*r_a1\n",
+ "a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))\n",
+ "N2=3000\n",
+ "w_m2=2*math.pi*N/60\n",
+ "a2=0\n",
+ "V_t2=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "I_f2=(V_t2-I_a*r_a)/(w_m2*k)\n",
+ "V_f2=I_f2*R_f\n",
+ "a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle=%.3f deg\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=48.477 deg\n",
+ "firing angle=48.477 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ " #after calculating\n",
+ " #t=w_m/6000-math.pi/360\n",
+ "\n",
+ "N=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "t=w_m/6000-math.pi/360 \n",
+ "\n",
+ "#Results\n",
+ "print(\"time reqd=%.2f s\" %t)\n",
+ " #printing mistake in the answer in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time reqd=0.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=1.0 #supposition\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))\n",
+ "I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))\n",
+ "I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))\n",
+ "per3=I_s3/I_s1*100 \n",
+ "print(\"percent of 3rd harmonic current in fundamental=%.2f\" %per3)\n",
+ "per5=I_s5/I_s1*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"percent of 5th harmonic current in fundamental=%.2f\" %per5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percent of 3rd harmonic current in fundamental=0.00\n",
+ "percent of 5th harmonic current in fundamental=-20.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15, Page No 680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=60.0\n",
+ "I_TA=I_a/3 \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"avg thyristor current=%.0f A\" %I_TA)\n",
+ "I_Tr=I_a/math.sqrt(3) \n",
+ "print(\"rms thyristor current=%.3f A\" %I_Tr)\n",
+ "V_s=400\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_sr=I_a*math.sqrt(2.0/3)\n",
+ "a=150\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"power factor of ac source=%.3f\" %pf)\n",
+ "\n",
+ "r_a=0.5\n",
+ "K_m=2.4\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Speed of motor=%.2f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg thyristor current=20 A\n",
+ "rms thyristor current=34.641 A\n",
+ "power factor of ac source=-0.827\n",
+ "Speed of motor=-1980.76 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16, Page No 685"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=300.0\n",
+ "V_s=600.0\n",
+ "a=0.6\n",
+ "V_t=a*V_s\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"input power from source=%.0f kW\" %(P/1000))\n",
+ "R_eq=V_s/(a*I_a) \n",
+ "print(\"equivalent input resistance=%.3f ohm\" %R_eq)\n",
+ "k=.004\n",
+ "R=.04+.06\n",
+ "w_m=(a*V_s-I_a*R)/(k*I_a)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ "T_e=k*I_a**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.0f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "input power from source=108 kW\n",
+ "equivalent input resistance=3.333 ohm\n",
+ "motor speed=2626.1 rpm\n",
+ "motor torque=360 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.17, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=10.0\n",
+ "T_off=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_s=230.0\n",
+ "V_t=a*V_s\n",
+ "r_a=3\n",
+ "K_m=.5\n",
+ "N=1500\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=(V_t-K_m*w_m)/r_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor load current=%.3f A\" %I_a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor load current=4.487 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "w_m=0 \n",
+ "print(\"lower limit of speed control=%.0f rpm\" %w_m)\n",
+ "I_a=25.0\n",
+ "r_a=.2\n",
+ "V_s=220\n",
+ "K_m=0.08\n",
+ "\n",
+ "#Calculations\n",
+ "a=(K_m*w_m+I_a*r_a)/V_s \n",
+ "print(\"lower limit of duty cycle=%.3f\" %a)\n",
+ "a=1 \n",
+ "print(\"upper limit of duty cycle=%.0f\" %a)\n",
+ "w_m=(a*V_s-I_a*r_a)/K_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"upper limit of speed control=%.1f rpm\" %w_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lower limit of speed control=0 rpm\n",
+ "lower limit of duty cycle=0.023\n",
+ "upper limit of duty cycle=1\n",
+ "upper limit of speed control=2687.5 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21, Page No 691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.6\n",
+ "V_s=400.0\n",
+ "V_t=(1-a)*V_s\n",
+ "I_a=300.0\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations \n",
+ "print(\"power returned=%.0f kW\" %(P/1000))\n",
+ "r_a=.2\n",
+ "K_m=1.2\n",
+ "R_eq=(1-a)*V_s/I_a+r_a \n",
+ "print(\"equivalent load resistance=%.4f ohm\" %R_eq)\n",
+ "w_mn=I_a*r_a/K_m\n",
+ "N=w_mn*60/(2*math.pi) \n",
+ "print(\"min braking speed=%.2f rpm\" %N)\n",
+ "w_mx=(V_s+I_a*r_a)/K_m\n",
+ "N=w_mx*60/(2*math.pi) \n",
+ "print(\"max braking speed=%.1f rpm\" %N)\n",
+ "w_m=(V_t+I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"max braking speed=%.1f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power returned=48 kW\n",
+ "equivalent load resistance=0.7333 ohm\n",
+ "min braking speed=477.46 rpm\n",
+ "max braking speed=3660.6 rpm\n",
+ "max braking speed=1750.7 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22, Page No 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "N=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when speed=1455rpm\")\n",
+ "n=1455.0\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)\n",
+ "print(\"when speed=1350rpm\")\n",
+ "n=1350\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when speed=1455rpm\n",
+ "I_2mx/I_2r=0.000\n",
+ "when speed=1350rpm\n",
+ "I_2mx/I_2r=0.000\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24, Page No 705"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=400.0\n",
+ "r1=0.6\n",
+ "r2=0.4\n",
+ "s=1.0\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"at starting in normal conditions\")\n",
+ "I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"current=%.2f A\" %I_n)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s) \n",
+ "print(\"\\nTorque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.0f A\" %I_d)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"pf=%.2f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_ed=(3/w_s)*I_d**2*(r2/s) \n",
+ "print(\"Torque developed=%.3f Nm\" %T_ed)\n",
+ "print(\"at max torque conditions\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)\n",
+ "I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"current=%.3f A\" %I_n)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s_mn) \n",
+ "print(\"Torque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.3f A\" %I_d)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"\\npf=%.3f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_d**2*(r2/s_mn) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"Torque developed=%.3f Nm\" %T_en)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at starting in normal conditions\n",
+ "current=119.31 A\n",
+ "pf=0.2983\n",
+ "\n",
+ "Torque developed=108.75 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=106 A\n",
+ "pf=0.53\n",
+ "Torque developed=171.673 Nm\n",
+ "at max torque conditions\n",
+ "current=79.829 A\n",
+ "pf=0.7695\n",
+ "Torque developed=396.26 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=71.199 A\n",
+ "\n",
+ "pf=0.822\n",
+ "Torque developed=330.883 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.25, Page No 709"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x1=1.0\n",
+ "X_m=50.0\n",
+ "X_e=x1*X_m/(x1+X_m)\n",
+ "V=231.0\n",
+ "V_e=V*X_m/(x1+X_m)\n",
+ "x2=1.0\n",
+ "r2=.4\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "s_m=r2/(x2+X_e) \n",
+ "print(\"slip at max torque=%.2f\" %s_m)\n",
+ "s_mT=r2/(x2+X_m) \n",
+ "print(\"slip at max torque=%.5f\" %s_mT)\n",
+ "f1=50.0\n",
+ "w_s=4*math.pi*f1/4\n",
+ "print(\"for constant voltage input\")\n",
+ "T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2) \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*V_e**2/(2*(x2+X_e)) \n",
+ "print(\"maximum torque developed=%.2f Nm\" %T_em)\n",
+ "print(\"for constant current input\")\n",
+ "I1=28\n",
+ "T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2 \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m)) \n",
+ "print(\"maximum torque developed=%.3f Nm\" %T_em)\n",
+ "s=s_mT\n",
+ "i=1\n",
+ "I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))\n",
+ "I_m=math.fabs(I_m)\n",
+ "V1=math.sqrt(3)*I_m*X_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"supply voltage reqd=%.1f V\" %V1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip at max torque=0.20\n",
+ "slip at max torque=0.00784\n",
+ "for constant voltage input\n",
+ "starting torque=95.988 Nm\n",
+ "maximum torque developed=247.31 Nm\n",
+ "for constant current input\n",
+ "starting torque=5.756 Nm\n",
+ "maximum torque developed=366.993 Nm\n",
+ "supply voltage reqd=1236.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.27, Page No 718"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "T_e=450.0\n",
+ "N=1440.0\n",
+ "n=1000.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "n1=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n1/60\n",
+ "w_m=2*math.pi*n/60\n",
+ "a=.8\n",
+ "I_d=T_L*w_s/(2.339*a*V1)\n",
+ "k=0\n",
+ "R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k)) \n",
+ "print(\"value of chopper resistance=%.4f ohm\" %R)\n",
+ "n=1320.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "I_d=T_L*w_s/(2.339*a*V1) \n",
+ "print(\"Inductor current=%.3f A\" %I_d)\n",
+ "w_m=2*math.pi*n/60\n",
+ "k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.4f\" %k)\n",
+ "s=(n1-n)/n1\n",
+ "V_d=2.339*s*a*V1 \n",
+ "print(\"Rectifed o/p voltage=%.3f V\" %V_d)\n",
+ "P=V_d*I_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "Pr=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "r1=0.015\n",
+ "Ps=3*I1**2*r1\n",
+ "Po=T_L*w_m\n",
+ "Pi=Po+Ps+Pr+P\n",
+ "eff=Po/Pi*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Efficiency(in percent)=%.2f\" %eff)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of chopper resistance=2.0132 ohm\n",
+ "Inductor current=130.902 A\n",
+ "value of duty cycle=0.7934\n",
+ "Rectifed o/p voltage=54.449 V\n",
+ "Efficiency(in percent)=88.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.28, Page No 720"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ph=V/math.sqrt(3)\n",
+ "N_s=1000.0\n",
+ "N=800.0\n",
+ "a=.7\n",
+ "I_d=110\n",
+ "R=2.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.3f\" %k)\n",
+ "P=I_d**2*R*(1-k)\n",
+ "I1=a*I_d*math.sqrt(2/3)\n",
+ "r1=0.1\n",
+ "r2=0.08\n",
+ "Pr=3*I1**2*(r1+r2)\n",
+ "P_o=20000\n",
+ "P_i=P_o+Pr+P\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"Efficiency=%.2f\" %eff)\n",
+ "I11=math.sqrt(6)/math.pi*a*I_d\n",
+ "th=43\n",
+ "P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))\n",
+ "pf=P_ip/(math.sqrt(3)*V*I11) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of duty cycle=0.656\n",
+ "Efficiency=70.62\n",
+ "Input power factor=0.7314\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.29, Page No 724"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "N=1000.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "N_s=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "a=0.8\n",
+ "V_d=2.339*a*s*V1 \n",
+ "print(\"rectified voltage=%.2f V\" %V_d)\n",
+ "T=450.0\n",
+ "N1=1200.0\n",
+ "T_L=T*(N/N1)**2\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "I_d=w_s*T_L/(2.339*a*V1) \n",
+ "print(\"inductor current=%.2f A\" %I_d)\n",
+ "a_T=-.4\n",
+ "a1=math.degrees(math.acos(s*a/a_T))\n",
+ "print(\"delay angle of inverter=%.2f deg\" %a1)\n",
+ "\n",
+ "P_s=V_d*I_d\n",
+ "P_o=T_L*w_m\n",
+ "R_d=0.01\n",
+ "P_i=I_d**2*R_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "r1=0.015\n",
+ "P_rol=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "P_sol=3*I1**2*r1\n",
+ "P_i=P_o+P_rol+P_sol+P_i\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"\\nefficiency=%.2f\" %eff)\n",
+ "w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectified voltage=151.25 V\n",
+ "inductor current=108.18 A\n",
+ "delay angle of inverter=131.81 deg\n",
+ "\n",
+ "efficiency=99.64\n",
+ "motor speed=996.4 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.30, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=0.7\n",
+ "V_dt=1.5\n",
+ "V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd\n",
+ "V1=415.0\n",
+ "a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=70.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.31, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=.7\n",
+ "V_dt=1.5\n",
+ "a=0\n",
+ "u=18 #overlap angle in case of rectifier\n",
+ "V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd\n",
+ "V1=415\n",
+ "V_ml=math.sqrt(2)*V1\n",
+ "u=4 #overlap anglein the inverter\n",
+ " #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)\n",
+ " #V_dc=V_d\n",
+ " #after solving % (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425\n",
+ "a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=71.25 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.32, Page No 727"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V1=415.0\n",
+ "a_T=s*E2/V1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage ratio of the transformer=%.2f\" %a_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage ratio of the transformer=0.34\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.33, Page No 733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=6.0\n",
+ "N_s=600.0\n",
+ "f1=P*N_s/120.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=f1*V/f \n",
+ "print(\"supply freq=%.0f Hz\" %V_t)\n",
+ "T=340.0\n",
+ "N=1000.0\n",
+ "T_L=T*(N_s/N)**2\n",
+ "w_s=2*math.pi*N_s/60\n",
+ "P=T_L*w_s\n",
+ "I_a=P/(math.sqrt(3)*V_t) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "Z_s=2\n",
+ "X_s=f1/f*math.fabs(Z_s)\n",
+ "V_t=V_t/math.sqrt(3)\n",
+ "Ef=math.sqrt(V_t**2+(I_a*X_s)**2)\n",
+ "print(\"excitation voltage=%.2f V\" %(math.sqrt(3)*Ef))\n",
+ "dl=math.degrees(math.atan(I_a*X_s/V_t))\n",
+ "print(\"load angle=%.2f deg\" %dl)\n",
+ "T_em=(3/w_s)*(Ef*V_t/X_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pull out torque=%.2f Nm\" %T_em)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "supply freq=240 Hz\n",
+ "armature current=18.50 A\n",
+ "excitation voltage=243.06 V\n",
+ "load angle=9.10 deg\n",
+ "pull out torque=773.69 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.34, Page No 736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=4.0\n",
+ "f=50.0\n",
+ "w_s=4*math.pi*f/P\n",
+ "X_d=8.0\n",
+ "X_q=2.0\n",
+ "T_e=80.0\n",
+ "V=400.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=V/math.sqrt(3)\n",
+ "dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d)))) \n",
+ "print(\"load angle=%.3f deg\" %dl)\n",
+ "I_d=V_t*math.cos(math.radians(dl))/X_d\n",
+ "I_q=V_t*math.sin(math.radians(dl))/X_q\n",
+ "I_a=math.sqrt(I_d**2+I_q**2) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "pf=T_e*w_s/(math.sqrt(3)*V*I_a) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load angle=0.000 deg\n",
+ "armature current=28.87 A\n",
+ "input power factor=0.6283\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.35, Page No 737"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=3.0\n",
+ "K_m=1.2\n",
+ "I_a=T_e/K_m\n",
+ "r_a=2.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)\n",
+ "w_m=E_a/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=640.96 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.36, Page No 738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1360.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=163.45\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.2578 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.37, Page No 740"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=2100.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=227.66\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=1.94 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.38, Page No 742"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=840.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=75.0\n",
+ "V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=10.5922 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.39, Page No 743"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1400.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "a1=212\n",
+ "V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.257 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.40, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=600.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=13.568 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.41, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r1=.6\n",
+ "r2=.4\n",
+ "s=0.04\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "Z=(r1+r2/s)+(x1+x2)\n",
+ "V=400.0\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "N=1500\n",
+ "w_s=2*math.pi*N/60\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n",
+ "N_r=N*(1-s)\n",
+ "\n",
+ "f=45\n",
+ "N_s1=120*f/4\n",
+ "w_s=2*math.pi*N_s1/60\n",
+ "s1=(N_s1-N_r)/N_s1\n",
+ "Z=(r1+r2/s1)+(x1+x2)*f/50.0\n",
+ "V=360\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s1 \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source current=0.000 A \n",
+ "and with 29.0 deg phase\n",
+ "motor torque=160.46 Nm\n",
+ "source current=-0.000 A \n",
+ "and with 142.9 deg phase\n",
+ "motor torque=-2598.45 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter12_4.ipynb b/_Power_Electronics/Chapter12_4.ipynb new file mode 100755 index 00000000..f8605d69 --- /dev/null +++ b/_Power_Electronics/Chapter12_4.ipynb @@ -0,0 +1,1997 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12 : Electic Drives"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, Page No 658"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=15.0 #Nm\n",
+ "K_m=0.5 #V-s/rad\n",
+ "I_a=T_e/K_m\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "E_a=K_m*w_m\n",
+ "r_a=0.7\n",
+ "V_t=E_a+I_a*r_a\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(2*math.pi*V_t/V_m-1))\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "I_Tr=I_a*math.sqrt((180-a)/360) \n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "I_fdr=I_a*math.sqrt((180+a)/360) \n",
+ "print(\"rms value of freewheeling diode current=%.3f A\" %I_fdr)\n",
+ "pf=V_t*I_a/(V_s*I_Tr) \n",
+ "\n",
+ "#Results \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=65.349 deg\n",
+ "rms value of thyristor current=16.930 A\n",
+ "rms value of freewheeling diode current=24.766 A\n",
+ "input power factor=0.5652\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, Page No 660"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 661"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=250\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "k=0.03 #Nm/A**2\n",
+ "n_m=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r=.2 #r_a+r_s\n",
+ "V_t=V_m/math.pi*(1+math.cos(math.radians(a)))\n",
+ "I_a=V_t/(k*w_m+r) \n",
+ "print(\"motor armature current=%.2f A\" %I_a)\n",
+ "T_e=k*I_a**2 \n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n",
+ "I_sr=I_a*math.sqrt((180-a)/180)\n",
+ "pf=(V_t*I_a)/(V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor armature current=57.82 A\n",
+ "motor torque=100.285 Nm\n",
+ "input power factor=0.92\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, Page No 663"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(I_f*K_a) \n",
+ "print(\"rated armature current=%.2f A\" %I_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.2\n",
+ "V_t=K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "E_a=V_t\n",
+ "w_mo=E_a/(K_a*I_f)\n",
+ "N=60*w_mo/(2*math.pi)\n",
+ "reg=((N-n_m)/n_m)*100 \n",
+ "print(\"speed regulation at full load=%.2f\" %reg)\n",
+ "I_ar=I_a\n",
+ "pf=(V_t*I_a)/(V_s*I_ar) \n",
+ "print(\"input power factor of armature convertor=%.4f\" %pf)\n",
+ "I_fr=I_f\n",
+ "I_sr=math.sqrt(I_fr**2+I_ar**2)\n",
+ "VA=I_sr*V_s\n",
+ "P=V_t*I_a+V_f*I_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor of drive=%.4f\" %(P/VA))\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rated armature current=59.01 A\n",
+ "firing angle delay=57.63 deg\n",
+ "speed regulation at full load=6.52\n",
+ "input power factor of armature convertor=0.4821\n",
+ "input power factor of drive=0.5093\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 664"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_f=2*V_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos(V_t*math.pi/(2*V_m))) \n",
+ "print(\"delay angle of field converter=%.0f deg\" %a1)\n",
+ "r_f=200.0\n",
+ "I_f=V_f/r_f\n",
+ "T_e=85.0\n",
+ "K_a=0.8\n",
+ "I_a=T_e/(I_f*K_a)\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "r_a=0.1\n",
+ "I_a=50.0\n",
+ "V_t=-K_a*I_f*w_m+I_a*r_a\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(2*V_m)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay of armature converter=%.3f deg\" %a)\n",
+ "print(\"power fed back to ac supply=%.0f W\" %(-V_t*I_a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle of field converter=58 deg\n",
+ "firing angle delay of armature converter=119.260 deg\n",
+ "power fed back to ac supply=8801 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 665"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=10.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "T=5.0\n",
+ "I_a=T/K_m\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30.0\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n",
+ "a=45\n",
+ "n_m=1000\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=(V_t-K_m*w_m)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"torque developed=%.3f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=1254.22 rpm\n",
+ "torque developed=8.586 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, Page No 666"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=220.0\n",
+ "n_m=1000.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=60.0\n",
+ "r_a=.1\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=230\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for 600rpm speed\")\n",
+ "n_m=600.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m))) \n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"for -500rpm speed\")\n",
+ "n_m=-500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "a=math.degrees(math.acos((K_m*w_m+I_a*r_a)*math.pi/(2*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_a=I_a/2\n",
+ "a=150\n",
+ "V_t=2*V_m*math.cos(math.radians(a))/math.pi\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.3f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 600rpm speed\n",
+ "firing angle=49.530 deg\n",
+ "for -500rpm speed\n",
+ "firing angle=119.19 deg\n",
+ "motor speed=-852.011 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.5\n",
+ "T_e=50.0\n",
+ "I_a=T_e/K_m\n",
+ "r_a=0.9\n",
+ "a=45.0\n",
+ "V_s=415.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "w_m=((3*V_ml*(1+math.cos(math.radians(a)))/(2*math.pi))-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=2854.42 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9 Page No 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_t=600\n",
+ "n_m=1500.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=80.0\n",
+ "r_a=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "K_m=(V_t-I_a*r_a)/(w_m)\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "print(\"for firing angle=45deg and speed=1200rpm\")\n",
+ "a=45.0\n",
+ "n_m=1200.0\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(2/3) \n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(1/3)))\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_a*(1/3))\n",
+ "pf=(3/(2*math.pi)*(1+math.cos(math.radians(a)))) \n",
+ "print(\"input power factor=%.3f\" %pf)\n",
+ "\n",
+ "print(\"for firing angle=90deg and speed=700rpm\")\n",
+ "a=90\n",
+ "n_m=700\n",
+ "w_m=2*math.pi*n_m/60\n",
+ "I_a=(3*V_m*(1+math.cos(math.radians(a)))/(2*math.pi)-K_m*w_m)/r_a\n",
+ "I_sr=I_a*math.sqrt(90/180) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of source current=%.3f A\" %I_sr)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_a*math.sqrt(90.0/360)))\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_a*(1/3))\n",
+ "pf=(math.sqrt(6)/(2*math.pi)*(1+math.cos(math.radians(a))))*math.sqrt(180/(180-a)) \n",
+ "print(\"input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=45deg and speed=1200rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=0.000 A\n",
+ "\n",
+ "input power factor=0.815\n",
+ "for firing angle=90deg and speed=700rpm\n",
+ "rms value of source current=0.000 A\n",
+ "rms value of thyristor current=195.558 A\n",
+ "\n",
+ "input power factor=0.5513\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10 Page No 676"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=30\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "I_a=21.0\n",
+ "r_a=.1\n",
+ "V_d=2.0\n",
+ "K_m=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"speed of motor=%.1f rpm\" %N)\n",
+ "\n",
+ "N=2000\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=210\n",
+ "V_t=K_m*w_m+I_a*r_a+V_d\n",
+ "a=math.degrees(math.acos(V_t*math.pi/(3*V_m)))\n",
+ "print(\"firing angle=%.2f deg\" %a)\n",
+ "I_sr=I_a*math.sqrt(2.0/3.0)\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"supply power factor=%.3f\" %pf)\n",
+ "\n",
+ "I_a=21\n",
+ "w_m=(V_t-I_a*r_a-V_d)/K_m\n",
+ "n=w_m*60/(2*math.pi)\n",
+ "reg=(n-N)/N*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"speed regulation(percent)=%.2f\" %reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "speed of motor=2767.6 rpm\n",
+ "firing angle=48.48 deg\n",
+ "supply power factor=0.633\n",
+ "speed regulation(percent)=5.64\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.11, Page No 677"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=230.0\n",
+ "V_l=V_t*math.pi/(3*math.sqrt(2))\n",
+ "V_ph=V_l/math.sqrt(3)\n",
+ "V_in=400 #per phase voltage input\n",
+ "\n",
+ "#Calculations\n",
+ "N1=1500.0\n",
+ "I_a1=20.0\n",
+ "r_a1=.6\n",
+ "E_a1=V_t-I_a1*r_a1\n",
+ "n1=1000.0\n",
+ "E_a2=E_a1/1500.0*1000.0\n",
+ "V_t1=E_a1+I_a1*r_a1\n",
+ "a1=math.degrees(math.acos(V_t1*math.pi/(3*math.sqrt(2.0)*V_l)))\n",
+ "I_a2=.5*I_a1\n",
+ "n2=-900.0\n",
+ "V_t2=n2*E_a2/N1+I_a2*r_a1\n",
+ "a2=math.degrees(math.acos(V_t2*math.pi/(3*math.sqrt(2)*V_l))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer phase turns ratio=%.3f\" %(V_in/V_ph))\n",
+ "print(\"for motor running at 1000rpm at rated torque\")\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"for motor running at -900rpm at half of rated torque\")\n",
+ "print(\"firing angle delay=%.3f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer phase turns ratio=4.068\n",
+ "for motor running at 1000rpm at rated torque\n",
+ "firing angle delay=0.00 deg\n",
+ "for motor running at -900rpm at half of rated torque\n",
+ "firing angle delay=110.674 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.12, Page No 678"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=400\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_f=3*V_ml/math.pi\n",
+ "R_f=300.0\n",
+ "I_f=V_f/R_f\n",
+ "T_e=60.0\n",
+ "k=1.1\n",
+ "\n",
+ "#Calculations\n",
+ "I_a=T_e/(k*I_f)\n",
+ "N1=1000.0\n",
+ "w_m1=2*math.pi*N1/60\n",
+ "r_a1=.3\n",
+ "V_t1=k*I_f*w_m1+I_a*r_a1\n",
+ "a1=math.degrees(math.acos(V_f*math.pi/(3*V_ml)))\n",
+ "N2=3000\n",
+ "w_m2=2*math.pi*N/60\n",
+ "a2=0\n",
+ "V_t2=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "I_f2=(V_t2-I_a*r_a)/(w_m2*k)\n",
+ "V_f2=I_f2*R_f\n",
+ "a2=math.degrees(math.acos(V_f2*math.pi/(3*V_ml)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle=%.3f deg\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=48.477 deg\n",
+ "firing angle=48.477 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.13, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ " #after calculating\n",
+ " #t=w_m/6000-math.pi/360\n",
+ "\n",
+ "N=1000.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "t=w_m/6000-math.pi/360 \n",
+ "\n",
+ "#Results\n",
+ "print(\"time reqd=%.2f s\" %t)\n",
+ " #printing mistake in the answer in book"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time reqd=0.01 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.14, Page No 679"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=1.0 #supposition\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_s1=2*math.sqrt(2)/math.pi*I_a*math.sin(math.radians(a))\n",
+ "I_s3=2*math.sqrt(2)/(3*math.pi)*I_a*math.sin(math.radians(3*a))\n",
+ "I_s5=2*math.sqrt(2)/(5*math.pi)*I_a*math.sin(math.radians(5*a))\n",
+ "per3=I_s3/I_s1*100 \n",
+ "print(\"percent of 3rd harmonic current in fundamental=%.2f\" %per3)\n",
+ "per5=I_s5/I_s1*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"percent of 5th harmonic current in fundamental=%.2f\" %per5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "percent of 3rd harmonic current in fundamental=0.00\n",
+ "percent of 5th harmonic current in fundamental=-20.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.15, Page No 680"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=60.0\n",
+ "I_TA=I_a/3 \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"avg thyristor current=%.0f A\" %I_TA)\n",
+ "I_Tr=I_a/math.sqrt(3) \n",
+ "print(\"rms thyristor current=%.3f A\" %I_Tr)\n",
+ "V_s=400\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_sr=I_a*math.sqrt(2.0/3)\n",
+ "a=150\n",
+ "V_t=3*V_m*math.cos(math.radians(a))/math.pi\n",
+ "pf=V_t*I_a/(math.sqrt(3)*V_s*I_sr) \n",
+ "print(\"power factor of ac source=%.3f\" %pf)\n",
+ "\n",
+ "r_a=0.5\n",
+ "K_m=2.4\n",
+ "w_m=(V_t-I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Speed of motor=%.2f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg thyristor current=20 A\n",
+ "rms thyristor current=34.641 A\n",
+ "power factor of ac source=-0.827\n",
+ "Speed of motor=-1980.76 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.16, Page No 685"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=300.0\n",
+ "V_s=600.0\n",
+ "a=0.6\n",
+ "V_t=a*V_s\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations\n",
+ "print(\"input power from source=%.0f kW\" %(P/1000))\n",
+ "R_eq=V_s/(a*I_a) \n",
+ "print(\"equivalent input resistance=%.3f ohm\" %R_eq)\n",
+ "k=.004\n",
+ "R=.04+.06\n",
+ "w_m=(a*V_s-I_a*R)/(k*I_a)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ "T_e=k*I_a**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.0f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "input power from source=108 kW\n",
+ "equivalent input resistance=3.333 ohm\n",
+ "motor speed=2626.1 rpm\n",
+ "motor torque=360 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.17, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=10.0\n",
+ "T_off=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_s=230.0\n",
+ "V_t=a*V_s\n",
+ "r_a=3\n",
+ "K_m=.5\n",
+ "N=1500\n",
+ "w_m=2*math.pi*N/60\n",
+ "I_a=(V_t-K_m*w_m)/r_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor load current=%.3f A\" %I_a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor load current=4.487 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.18, Page No 686"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "w_m=0 \n",
+ "print(\"lower limit of speed control=%.0f rpm\" %w_m)\n",
+ "I_a=25.0\n",
+ "r_a=.2\n",
+ "V_s=220\n",
+ "K_m=0.08\n",
+ "\n",
+ "#Calculations\n",
+ "a=(K_m*w_m+I_a*r_a)/V_s \n",
+ "print(\"lower limit of duty cycle=%.3f\" %a)\n",
+ "a=1 \n",
+ "print(\"upper limit of duty cycle=%.0f\" %a)\n",
+ "w_m=(a*V_s-I_a*r_a)/K_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"upper limit of speed control=%.1f rpm\" %w_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lower limit of speed control=0 rpm\n",
+ "lower limit of duty cycle=0.023\n",
+ "upper limit of duty cycle=1\n",
+ "upper limit of speed control=2687.5 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.21, Page No 691"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.6\n",
+ "V_s=400.0\n",
+ "V_t=(1-a)*V_s\n",
+ "I_a=300.0\n",
+ "P=V_t*I_a \n",
+ "\n",
+ "#Calculations \n",
+ "print(\"power returned=%.0f kW\" %(P/1000))\n",
+ "r_a=.2\n",
+ "K_m=1.2\n",
+ "R_eq=(1-a)*V_s/I_a+r_a \n",
+ "print(\"equivalent load resistance=%.4f ohm\" %R_eq)\n",
+ "w_mn=I_a*r_a/K_m\n",
+ "N=w_mn*60/(2*math.pi) \n",
+ "print(\"min braking speed=%.2f rpm\" %N)\n",
+ "w_mx=(V_s+I_a*r_a)/K_m\n",
+ "N=w_mx*60/(2*math.pi) \n",
+ "print(\"max braking speed=%.1f rpm\" %N)\n",
+ "w_m=(V_t+I_a*r_a)/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"max braking speed=%.1f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power returned=48 kW\n",
+ "equivalent load resistance=0.7333 ohm\n",
+ "min braking speed=477.46 rpm\n",
+ "max braking speed=3660.6 rpm\n",
+ "max braking speed=1750.7 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.22, Page No 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "N=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when speed=1455rpm\")\n",
+ "n=1455.0\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)\n",
+ "print(\"when speed=1350rpm\")\n",
+ "n=1350\n",
+ "s1=(N-n)/N\n",
+ "r=math.sqrt(1/3)*(2/3)/(math.sqrt(s1)*(1-s1)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"I_2mx/I_2r=%.3f\" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when speed=1455rpm\n",
+ "I_2mx/I_2r=0.000\n",
+ "when speed=1350rpm\n",
+ "I_2mx/I_2r=0.000\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.24, Page No 705"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=400.0\n",
+ "r1=0.6\n",
+ "r2=0.4\n",
+ "s=1.0\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"at starting in normal conditions\")\n",
+ "I_n=V1/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"current=%.2f A\" %I_n)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s) \n",
+ "print(\"\\nTorque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.0f A\" %I_d)\n",
+ "pf=(r1+r2)/math.sqrt((r1+r2/s)**2+((x1+x2)/2)**2) \n",
+ "print(\"pf=%.2f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_ed=(3/w_s)*I_d**2*(r2/s) \n",
+ "print(\"Torque developed=%.3f Nm\" %T_ed)\n",
+ "print(\"at max torque conditions\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2))**2)\n",
+ "I_n=V1/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"current=%.3f A\" %I_n)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+(x1+x2)**2) \n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_n**2*(r2/s_mn) \n",
+ "print(\"Torque developed=%.2f Nm\" %T_en)\n",
+ "print(\"motor is operated with DOL starting\")\n",
+ "s_mn=r2/math.sqrt((r1)**2+((x1+x2)/2)**2)\n",
+ "I_d=V1/2/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"current=%.3f A\" %I_d)\n",
+ "pf=(r1+r2/s_mn)/math.sqrt((r1+r2/s_mn)**2+((x1+x2)/2)**2) \n",
+ "print(\"\\npf=%.3f\" %pf)\n",
+ "f1=25\n",
+ "w_s=4*math.pi*f1/4\n",
+ "T_en=(3/w_s)*I_d**2*(r2/s_mn) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"Torque developed=%.3f Nm\" %T_en)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at starting in normal conditions\n",
+ "current=119.31 A\n",
+ "pf=0.2983\n",
+ "\n",
+ "Torque developed=108.75 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=106 A\n",
+ "pf=0.53\n",
+ "Torque developed=171.673 Nm\n",
+ "at max torque conditions\n",
+ "current=79.829 A\n",
+ "pf=0.7695\n",
+ "Torque developed=396.26 Nm\n",
+ "motor is operated with DOL starting\n",
+ "current=71.199 A\n",
+ "\n",
+ "pf=0.822\n",
+ "Torque developed=330.883 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.25, Page No 709"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x1=1.0\n",
+ "X_m=50.0\n",
+ "X_e=x1*X_m/(x1+X_m)\n",
+ "V=231.0\n",
+ "V_e=V*X_m/(x1+X_m)\n",
+ "x2=1.0\n",
+ "r2=.4\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "s_m=r2/(x2+X_e) \n",
+ "print(\"slip at max torque=%.2f\" %s_m)\n",
+ "s_mT=r2/(x2+X_m) \n",
+ "print(\"slip at max torque=%.5f\" %s_mT)\n",
+ "f1=50.0\n",
+ "w_s=4*math.pi*f1/4\n",
+ "print(\"for constant voltage input\")\n",
+ "T_est=(3/w_s)*(V_e/math.sqrt(r2**2+(x2+X_e)**2))**2*(r2) \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*V_e**2/(2*(x2+X_e)) \n",
+ "print(\"maximum torque developed=%.2f Nm\" %T_em)\n",
+ "print(\"for constant current input\")\n",
+ "I1=28\n",
+ "T_est=(3/w_s)*(I1*X_m)**2/(r2**2+(x2+X_m)**2)*r2 \n",
+ "print(\"starting torque=%.3f Nm\" %T_est)\n",
+ "T_em=(3/w_s)*(I1*X_m)**2/(2*(x2+X_m)) \n",
+ "print(\"maximum torque developed=%.3f Nm\" %T_em)\n",
+ "s=s_mT\n",
+ "i=1\n",
+ "I_m=I1*(r2/s+i*x2)/(r2/s+i*(x2+X_m))\n",
+ "I_m=math.fabs(I_m)\n",
+ "V1=math.sqrt(3)*I_m*X_m \n",
+ "\n",
+ "#Results\n",
+ "print(\"supply voltage reqd=%.1f V\" %V1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "slip at max torque=0.20\n",
+ "slip at max torque=0.00784\n",
+ "for constant voltage input\n",
+ "starting torque=95.988 Nm\n",
+ "maximum torque developed=247.31 Nm\n",
+ "for constant current input\n",
+ "starting torque=5.756 Nm\n",
+ "maximum torque developed=366.993 Nm\n",
+ "supply voltage reqd=1236.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.27, Page No 718"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "T_e=450.0\n",
+ "N=1440.0\n",
+ "n=1000.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "n1=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_s=2*math.pi*n1/60\n",
+ "w_m=2*math.pi*n/60\n",
+ "a=.8\n",
+ "I_d=T_L*w_s/(2.339*a*V1)\n",
+ "k=0\n",
+ "R=(1-w_m/w_s)*(2.339*a*V1)/(I_d*(1-k)) \n",
+ "print(\"value of chopper resistance=%.4f ohm\" %R)\n",
+ "n=1320.0\n",
+ "T_L=T_e*(n/N)**2\n",
+ "I_d=T_L*w_s/(2.339*a*V1) \n",
+ "print(\"Inductor current=%.3f A\" %I_d)\n",
+ "w_m=2*math.pi*n/60\n",
+ "k=1-((1-w_m/w_s)*(2.339*a*V1)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.4f\" %k)\n",
+ "s=(n1-n)/n1\n",
+ "V_d=2.339*s*a*V1 \n",
+ "print(\"Rectifed o/p voltage=%.3f V\" %V_d)\n",
+ "P=V_d*I_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "Pr=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "r1=0.015\n",
+ "Ps=3*I1**2*r1\n",
+ "Po=T_L*w_m\n",
+ "Pi=Po+Ps+Pr+P\n",
+ "eff=Po/Pi*100 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Efficiency(in percent)=%.2f\" %eff)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of chopper resistance=2.0132 ohm\n",
+ "Inductor current=130.902 A\n",
+ "value of duty cycle=0.7934\n",
+ "Rectifed o/p voltage=54.449 V\n",
+ "Efficiency(in percent)=88.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.28, Page No 720"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ph=V/math.sqrt(3)\n",
+ "N_s=1000.0\n",
+ "N=800.0\n",
+ "a=.7\n",
+ "I_d=110\n",
+ "R=2.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=1-((1-N/N_s)*(2.339*a*V_ph)/(I_d*R)) \n",
+ "print(\"value of duty cycle=%.3f\" %k)\n",
+ "P=I_d**2*R*(1-k)\n",
+ "I1=a*I_d*math.sqrt(2/3)\n",
+ "r1=0.1\n",
+ "r2=0.08\n",
+ "Pr=3*I1**2*(r1+r2)\n",
+ "P_o=20000\n",
+ "P_i=P_o+Pr+P\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"Efficiency=%.2f\" %eff)\n",
+ "I11=math.sqrt(6)/math.pi*a*I_d\n",
+ "th=43\n",
+ "P_ip=math.sqrt(3)*V*I11*math.cos(math.radians(th))\n",
+ "pf=P_ip/(math.sqrt(3)*V*I11) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Input power factor=%.4f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of duty cycle=0.656\n",
+ "Efficiency=70.62\n",
+ "Input power factor=0.7314\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.29, Page No 724"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=420.0\n",
+ "V1=V/math.sqrt(3)\n",
+ "N=1000.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "N_s=1500.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "a=0.8\n",
+ "V_d=2.339*a*s*V1 \n",
+ "print(\"rectified voltage=%.2f V\" %V_d)\n",
+ "T=450.0\n",
+ "N1=1200.0\n",
+ "T_L=T*(N/N1)**2\n",
+ "f1=50\n",
+ "w_s=4*math.pi*f1/4\n",
+ "I_d=w_s*T_L/(2.339*a*V1) \n",
+ "print(\"inductor current=%.2f A\" %I_d)\n",
+ "a_T=-.4\n",
+ "a1=math.degrees(math.acos(s*a/a_T))\n",
+ "print(\"delay angle of inverter=%.2f deg\" %a1)\n",
+ "\n",
+ "P_s=V_d*I_d\n",
+ "P_o=T_L*w_m\n",
+ "R_d=0.01\n",
+ "P_i=I_d**2*R_d\n",
+ "I2=math.sqrt(2/3)*I_d\n",
+ "r2=0.02\n",
+ "r1=0.015\n",
+ "P_rol=3*I2**2*r2\n",
+ "I1=a*I2\n",
+ "P_sol=3*I1**2*r1\n",
+ "P_i=P_o+P_rol+P_sol+P_i\n",
+ "eff=P_o/P_i*100 \n",
+ "print(\"\\nefficiency=%.2f\" %eff)\n",
+ "w_m=w_s*(1+(-a_T/a)*math.cos(math.radians(a1))-w_s*R_d*T_L/(2.339*a*V1)**2)\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results \n",
+ "print(\"motor speed=%.1f rpm\" %N)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectified voltage=151.25 V\n",
+ "inductor current=108.18 A\n",
+ "delay angle of inverter=131.81 deg\n",
+ "\n",
+ "efficiency=99.64\n",
+ "motor speed=996.4 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.30, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=0.7\n",
+ "V_dt=1.5\n",
+ "V_d=3*math.sqrt(6)*s*E2/math.pi-2*V_dd\n",
+ "V1=415.0\n",
+ "a=math.degrees(math.acos((3*math.sqrt(2)*E2/math.pi)**-1*(-V_d+2*V_dt)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=70.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.31, Page No 726"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V/math.sqrt(3)\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V_dd=.7\n",
+ "V_dt=1.5\n",
+ "a=0\n",
+ "u=18 #overlap angle in case of rectifier\n",
+ "V_d=3*math.sqrt(6)*s*E2*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dd\n",
+ "V1=415\n",
+ "V_ml=math.sqrt(2)*V1\n",
+ "u=4 #overlap anglein the inverter\n",
+ " #V_dc=-(3*V_ml*(math.cos(math.radians(a))+math.cos(math.radians(a+u)))/(2*math.pi)-2*V_dt)\n",
+ " #V_dc=V_d\n",
+ " #after solving % (1+math.cos(math.radians(u)))*math.cos(math.radians(a))-math.sin(math.radians(u))*math.sin(math.radians(a))=-.6425\n",
+ "a=math.degrees(math.acos(-.6425/(math.sqrt((1+math.cos(math.radians(u)))**2+math.sin(math.radians(u))**2))))-math.degrees(math.asin(math.sin(math.radians(a))/(1+math.cos(math.radians(u)))))\n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle advance=%.2f deg\" %(180-a))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle advance=71.25 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.32, Page No 727"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=700.0\n",
+ "E2=V\n",
+ "N_s=1500.0\n",
+ "N=1200.0\n",
+ "\n",
+ "#Calculations\n",
+ "s=(N_s-N)/N_s\n",
+ "V1=415.0\n",
+ "a_T=s*E2/V1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage ratio of the transformer=%.2f\" %a_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage ratio of the transformer=0.34\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.33, Page No 733"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=6.0\n",
+ "N_s=600.0\n",
+ "f1=P*N_s/120.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=f1*V/f \n",
+ "print(\"supply freq=%.0f Hz\" %V_t)\n",
+ "T=340.0\n",
+ "N=1000.0\n",
+ "T_L=T*(N_s/N)**2\n",
+ "w_s=2*math.pi*N_s/60\n",
+ "P=T_L*w_s\n",
+ "I_a=P/(math.sqrt(3)*V_t) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "Z_s=2\n",
+ "X_s=f1/f*math.fabs(Z_s)\n",
+ "V_t=V_t/math.sqrt(3)\n",
+ "Ef=math.sqrt(V_t**2+(I_a*X_s)**2)\n",
+ "print(\"excitation voltage=%.2f V\" %(math.sqrt(3)*Ef))\n",
+ "dl=math.degrees(math.atan(I_a*X_s/V_t))\n",
+ "print(\"load angle=%.2f deg\" %dl)\n",
+ "T_em=(3/w_s)*(Ef*V_t/X_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pull out torque=%.2f Nm\" %T_em)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "supply freq=240 Hz\n",
+ "armature current=18.50 A\n",
+ "excitation voltage=243.06 V\n",
+ "load angle=9.10 deg\n",
+ "pull out torque=773.69 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.34, Page No 736"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=4.0\n",
+ "f=50.0\n",
+ "w_s=4*math.pi*f/P\n",
+ "X_d=8.0\n",
+ "X_q=2.0\n",
+ "T_e=80.0\n",
+ "V=400.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=V/math.sqrt(3)\n",
+ "dl=(1/2)*math.degrees(math.asin(T_e*w_s/((3/2)*(V_t)**2*(1/X_q-1/X_d)))) \n",
+ "print(\"load angle=%.3f deg\" %dl)\n",
+ "I_d=V_t*math.cos(math.radians(dl))/X_d\n",
+ "I_q=V_t*math.sin(math.radians(dl))/X_q\n",
+ "I_a=math.sqrt(I_d**2+I_q**2) \n",
+ "print(\"armature current=%.2f A\" %I_a)\n",
+ "pf=T_e*w_s/(math.sqrt(3)*V*I_a) \n",
+ "\n",
+ "#Results\n",
+ "print(\"input power factor=%.4f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load angle=0.000 deg\n",
+ "armature current=28.87 A\n",
+ "input power factor=0.6283\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.35, Page No 737"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_e=3.0\n",
+ "K_m=1.2\n",
+ "I_a=T_e/K_m\n",
+ "r_a=2.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "E_a=(0.263*math.sqrt(2)*V-I_a*r_a)/(1-55/180)\n",
+ "w_m=E_a/K_m\n",
+ "N=w_m*60/(2*math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor speed=%.2f rpm\" %N)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor speed=640.96 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.36, Page No 738"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1360.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=163.45\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.2578 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.37, Page No 740"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=2100.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ " #after calculations V_t % calculated\n",
+ "V_t=227.66\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=1.94 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.38, Page No 742"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=840.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=75.0\n",
+ "V_t=math.sqrt(2)*V/math.pi*(1+math.cos(math.radians(a)))\n",
+ "r_a=4\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.4f Nm\" %T_e)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=10.5922 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.39, Page No 743"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=1400.0\n",
+ "\n",
+ "#Calculations\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "a1=212\n",
+ "V_t=math.sqrt(2)*V/math.pi*(math.cos(math.radians(a))-math.cos(math.radians(a1)))+E_a*(180+a-a1)/180\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=5.257 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.40, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "K_m=1.0\n",
+ "N=600.0\n",
+ "w_m=2*math.pi*N/60\n",
+ "E_a=K_m*w_m\n",
+ "V=230.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_t=2*math.sqrt(2)*V/math.pi*(math.cos(math.radians(a)))\n",
+ "r_a=3\n",
+ "I_a=(V_t-E_a)/r_a\n",
+ "T_e=K_m*I_a \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"motor torque=%.3f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "motor torque=13.568 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.41, Page No 745"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r1=.6\n",
+ "r2=.4\n",
+ "s=0.04\n",
+ "x1=1.6\n",
+ "x2=1.6\n",
+ "Z=(r1+r2/s)+(x1+x2)\n",
+ "V=400.0\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "N=1500\n",
+ "w_s=2*math.pi*N/60\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n",
+ "N_r=N*(1-s)\n",
+ "\n",
+ "f=45\n",
+ "N_s1=120*f/4\n",
+ "w_s=2*math.pi*N_s1/60\n",
+ "s1=(N_s1-N_r)/N_s1\n",
+ "Z=(r1+r2/s1)+(x1+x2)*f/50.0\n",
+ "V=360\n",
+ "I1=V/Z \n",
+ "print(\"source current=%.3f A \" %math.degrees(math.atan(I1.imag/I1.real)))\n",
+ "print(\"and with %.1f deg phase\" %math.fabs(I1))\n",
+ "I2=V/Z\n",
+ "T_e=(3/w_s)*abs(I2)**2*r2/s1 \n",
+ "print(\"motor torque=%.2f Nm\" %T_e)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source current=0.000 A \n",
+ "and with 29.0 deg phase\n",
+ "motor torque=160.46 Nm\n",
+ "source current=-0.000 A \n",
+ "and with 142.9 deg phase\n",
+ "motor torque=-2598.45 Nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter13.ipynb b/_Power_Electronics/Chapter13.ipynb new file mode 100755 index 00000000..62d2a926 --- /dev/null +++ b/_Power_Electronics/Chapter13.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Power Factor Improvement"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1, Page No 754"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=250.0\n",
+ "R_l=5.0\n",
+ "I_l=20.0\n",
+ "V_l1=math.sqrt(V_s**2-(R_l*I_l)**2)\n",
+ "reg2=(V_s-V_l1)/V_s*100 \n",
+ "pf1=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "P_l1=V_l1*I_l*pf1 #load power\n",
+ "P_r1=V_s*I_l*pf1 #max powwible system rating\n",
+ "utf1=P_l1*100/P_r1 \n",
+ "pf2=0.5\n",
+ " #(.5*V_l)**2+(.866*V_l+R_l*I_l)**2=V_s**2\n",
+ " #after solving\n",
+ "V_l2=158.35 \n",
+ "reg2=(V_s-V_l2)/V_s*100 \n",
+ "P_l2=V_l2*I_l*pf2 #load power\n",
+ "P_r2=V_s*I_l #max powwible system rating\n",
+ "utf2=P_l2*100/P_r2 \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for pf=1\")\n",
+ "print(\"load voltage=%.2f V\" %V_l1)\n",
+ "print(\"voltage regulation=%.2f\" %reg1)\n",
+ "print(\"system utilisation factor=%.3f\" %utf1)\n",
+ "print(\"energy consumed(in units)=%.1f\" %(P_l1/1000))\n",
+ "print(\"for pf=.5\")\n",
+ "print(\"load voltage=%.2f V\" %V_l2)\n",
+ "print(\"voltage regulation=%.2f\" %reg2)\n",
+ "print(\"system utilisation factor=%.3f\" %utf2)\n",
+ "print(\"energy consumed(in units)=%.2f\" %(P_l2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "NameError",
+ "evalue": "name 'reg1' is not defined",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-ffdbe43fd921>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"for pf=1\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"load voltage=%.2f V\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mV_l1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"voltage regulation=%.2f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mreg1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"system utilisation factor=%.3f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mutf1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"energy consumed(in units)=%.1f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP_l1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'reg1' is not defined"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for pf=1\n",
+ "load voltage=229.13 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2, Page No 756"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "I_m1=2\n",
+ "pf1=.3\n",
+ "\n",
+ "#Calculations\n",
+ "I_c1=I_m1*math.sin(math.radians(math.degrees(math.acos(pf1))))\n",
+ "C1=I_c1/(2*math.pi*f*V_s) \n",
+ "I_m2=5\n",
+ "pf2=.5\n",
+ "I_c2=I_m2*math.sin(math.radians(math.degrees(math.acos(pf2))))\n",
+ "C2=I_c2/(2*math.pi*f*V_s) \n",
+ "I_m3=10\n",
+ "pf3=.7\n",
+ "I_c3=I_m3*math.sin(math.radians(math.degrees(math.acos(pf3))))\n",
+ "C3=I_c3/(2*math.pi*f*V_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"at no load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C1*10**6))\n",
+ "print(\"at half full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C2*10**6))\n",
+ "print(\"at full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C3*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at no load\n",
+ "value of capacitance=26.404 uF\n",
+ "at half full load\n",
+ "value of capacitance=59.927 uF\n",
+ "at full load\n",
+ "value of capacitance=98.834 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3 Page No 764"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_c=10.0\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "C=I_c/(2*math.pi*f*V_s) \n",
+ "I_l=10\n",
+ "L=V_s/(2*math.pi*f*I_l) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of capacitance=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of inductor=%.3f mH\" %(L*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitance=138.396 uF\n",
+ "value of inductor=73.211 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4, Page No 765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "I_L=10.0\n",
+ "X_L=V_s/I_L\n",
+ "I_f1=6.0\n",
+ " #B=2*a-math.sin(2*a)\n",
+ "B=2*math.pi-I_f1*math.pi*X_L/V_s\n",
+ "a=0\n",
+ "i=1.0\n",
+ "for a in range(1,360):\n",
+ " b=2*a*math.pi/180-math.sin(math.radians(2*a)) \n",
+ " if math.fabs(B-b)<=0.001 : #by hit and trial\n",
+ " i=2\n",
+ " break\n",
+ "print(\"firing angle of TCR = %.1f deg\" %a)\n",
+ " #(a-.01)*180/math.pi)\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle of TCR = 359.0 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=.01\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for firing angle=90deg\")\n",
+ "a=90*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.0f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=120deg\")\n",
+ "a=120*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=150deg\")\n",
+ "a=150*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.2f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=170deg\")\n",
+ "a=170*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ "print(\"for firing angle=175deg\")\n",
+ "a=175*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.2f H\" %L_eff)\n",
+ "print(\"for firing angle=180deg\")\n",
+ "a=180*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ " #random value at firing angle =180 is equivalent to infinity as in answer in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=90deg\n",
+ "effective inductance=10 mH\n",
+ "for firing angle=120deg\n",
+ "effective inductance=25.575 mH\n",
+ "for firing angle=150deg\n",
+ "effective inductance=173.40 mH\n",
+ "for firing angle=170deg\n",
+ "effective inductance=4.459 H\n",
+ "for firing angle=175deg\n",
+ "effective inductance=35.51 H\n",
+ "for firing angle=180deg\n",
+ "effective inductance=-128265253940037.750 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Q=100.0*10**3\n",
+ "V_s=11.0*10**3\n",
+ "\n",
+ "#Calculations\n",
+ "f=50.0\n",
+ "L=V_s**2/(2*math.pi*f*Q) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.4f H\" %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "effective inductance=3.8515 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter13_1.ipynb b/_Power_Electronics/Chapter13_1.ipynb new file mode 100755 index 00000000..62d2a926 --- /dev/null +++ b/_Power_Electronics/Chapter13_1.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Power Factor Improvement"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1, Page No 754"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=250.0\n",
+ "R_l=5.0\n",
+ "I_l=20.0\n",
+ "V_l1=math.sqrt(V_s**2-(R_l*I_l)**2)\n",
+ "reg2=(V_s-V_l1)/V_s*100 \n",
+ "pf1=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "P_l1=V_l1*I_l*pf1 #load power\n",
+ "P_r1=V_s*I_l*pf1 #max powwible system rating\n",
+ "utf1=P_l1*100/P_r1 \n",
+ "pf2=0.5\n",
+ " #(.5*V_l)**2+(.866*V_l+R_l*I_l)**2=V_s**2\n",
+ " #after solving\n",
+ "V_l2=158.35 \n",
+ "reg2=(V_s-V_l2)/V_s*100 \n",
+ "P_l2=V_l2*I_l*pf2 #load power\n",
+ "P_r2=V_s*I_l #max powwible system rating\n",
+ "utf2=P_l2*100/P_r2 \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for pf=1\")\n",
+ "print(\"load voltage=%.2f V\" %V_l1)\n",
+ "print(\"voltage regulation=%.2f\" %reg1)\n",
+ "print(\"system utilisation factor=%.3f\" %utf1)\n",
+ "print(\"energy consumed(in units)=%.1f\" %(P_l1/1000))\n",
+ "print(\"for pf=.5\")\n",
+ "print(\"load voltage=%.2f V\" %V_l2)\n",
+ "print(\"voltage regulation=%.2f\" %reg2)\n",
+ "print(\"system utilisation factor=%.3f\" %utf2)\n",
+ "print(\"energy consumed(in units)=%.2f\" %(P_l2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "NameError",
+ "evalue": "name 'reg1' is not defined",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-ffdbe43fd921>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"for pf=1\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"load voltage=%.2f V\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mV_l1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"voltage regulation=%.2f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mreg1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"system utilisation factor=%.3f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mutf1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"energy consumed(in units)=%.1f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP_l1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'reg1' is not defined"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for pf=1\n",
+ "load voltage=229.13 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2, Page No 756"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "I_m1=2\n",
+ "pf1=.3\n",
+ "\n",
+ "#Calculations\n",
+ "I_c1=I_m1*math.sin(math.radians(math.degrees(math.acos(pf1))))\n",
+ "C1=I_c1/(2*math.pi*f*V_s) \n",
+ "I_m2=5\n",
+ "pf2=.5\n",
+ "I_c2=I_m2*math.sin(math.radians(math.degrees(math.acos(pf2))))\n",
+ "C2=I_c2/(2*math.pi*f*V_s) \n",
+ "I_m3=10\n",
+ "pf3=.7\n",
+ "I_c3=I_m3*math.sin(math.radians(math.degrees(math.acos(pf3))))\n",
+ "C3=I_c3/(2*math.pi*f*V_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"at no load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C1*10**6))\n",
+ "print(\"at half full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C2*10**6))\n",
+ "print(\"at full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C3*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at no load\n",
+ "value of capacitance=26.404 uF\n",
+ "at half full load\n",
+ "value of capacitance=59.927 uF\n",
+ "at full load\n",
+ "value of capacitance=98.834 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3 Page No 764"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_c=10.0\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "C=I_c/(2*math.pi*f*V_s) \n",
+ "I_l=10\n",
+ "L=V_s/(2*math.pi*f*I_l) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of capacitance=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of inductor=%.3f mH\" %(L*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitance=138.396 uF\n",
+ "value of inductor=73.211 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4, Page No 765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "I_L=10.0\n",
+ "X_L=V_s/I_L\n",
+ "I_f1=6.0\n",
+ " #B=2*a-math.sin(2*a)\n",
+ "B=2*math.pi-I_f1*math.pi*X_L/V_s\n",
+ "a=0\n",
+ "i=1.0\n",
+ "for a in range(1,360):\n",
+ " b=2*a*math.pi/180-math.sin(math.radians(2*a)) \n",
+ " if math.fabs(B-b)<=0.001 : #by hit and trial\n",
+ " i=2\n",
+ " break\n",
+ "print(\"firing angle of TCR = %.1f deg\" %a)\n",
+ " #(a-.01)*180/math.pi)\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle of TCR = 359.0 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=.01\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for firing angle=90deg\")\n",
+ "a=90*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.0f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=120deg\")\n",
+ "a=120*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=150deg\")\n",
+ "a=150*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.2f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=170deg\")\n",
+ "a=170*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ "print(\"for firing angle=175deg\")\n",
+ "a=175*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.2f H\" %L_eff)\n",
+ "print(\"for firing angle=180deg\")\n",
+ "a=180*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ " #random value at firing angle =180 is equivalent to infinity as in answer in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=90deg\n",
+ "effective inductance=10 mH\n",
+ "for firing angle=120deg\n",
+ "effective inductance=25.575 mH\n",
+ "for firing angle=150deg\n",
+ "effective inductance=173.40 mH\n",
+ "for firing angle=170deg\n",
+ "effective inductance=4.459 H\n",
+ "for firing angle=175deg\n",
+ "effective inductance=35.51 H\n",
+ "for firing angle=180deg\n",
+ "effective inductance=-128265253940037.750 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Q=100.0*10**3\n",
+ "V_s=11.0*10**3\n",
+ "\n",
+ "#Calculations\n",
+ "f=50.0\n",
+ "L=V_s**2/(2*math.pi*f*Q) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.4f H\" %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "effective inductance=3.8515 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter13_2.ipynb b/_Power_Electronics/Chapter13_2.ipynb new file mode 100755 index 00000000..62d2a926 --- /dev/null +++ b/_Power_Electronics/Chapter13_2.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Power Factor Improvement"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1, Page No 754"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=250.0\n",
+ "R_l=5.0\n",
+ "I_l=20.0\n",
+ "V_l1=math.sqrt(V_s**2-(R_l*I_l)**2)\n",
+ "reg2=(V_s-V_l1)/V_s*100 \n",
+ "pf1=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "P_l1=V_l1*I_l*pf1 #load power\n",
+ "P_r1=V_s*I_l*pf1 #max powwible system rating\n",
+ "utf1=P_l1*100/P_r1 \n",
+ "pf2=0.5\n",
+ " #(.5*V_l)**2+(.866*V_l+R_l*I_l)**2=V_s**2\n",
+ " #after solving\n",
+ "V_l2=158.35 \n",
+ "reg2=(V_s-V_l2)/V_s*100 \n",
+ "P_l2=V_l2*I_l*pf2 #load power\n",
+ "P_r2=V_s*I_l #max powwible system rating\n",
+ "utf2=P_l2*100/P_r2 \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for pf=1\")\n",
+ "print(\"load voltage=%.2f V\" %V_l1)\n",
+ "print(\"voltage regulation=%.2f\" %reg1)\n",
+ "print(\"system utilisation factor=%.3f\" %utf1)\n",
+ "print(\"energy consumed(in units)=%.1f\" %(P_l1/1000))\n",
+ "print(\"for pf=.5\")\n",
+ "print(\"load voltage=%.2f V\" %V_l2)\n",
+ "print(\"voltage regulation=%.2f\" %reg2)\n",
+ "print(\"system utilisation factor=%.3f\" %utf2)\n",
+ "print(\"energy consumed(in units)=%.2f\" %(P_l2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "NameError",
+ "evalue": "name 'reg1' is not defined",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-ffdbe43fd921>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"for pf=1\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"load voltage=%.2f V\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mV_l1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"voltage regulation=%.2f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mreg1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"system utilisation factor=%.3f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mutf1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"energy consumed(in units)=%.1f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP_l1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'reg1' is not defined"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for pf=1\n",
+ "load voltage=229.13 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2, Page No 756"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "I_m1=2\n",
+ "pf1=.3\n",
+ "\n",
+ "#Calculations\n",
+ "I_c1=I_m1*math.sin(math.radians(math.degrees(math.acos(pf1))))\n",
+ "C1=I_c1/(2*math.pi*f*V_s) \n",
+ "I_m2=5\n",
+ "pf2=.5\n",
+ "I_c2=I_m2*math.sin(math.radians(math.degrees(math.acos(pf2))))\n",
+ "C2=I_c2/(2*math.pi*f*V_s) \n",
+ "I_m3=10\n",
+ "pf3=.7\n",
+ "I_c3=I_m3*math.sin(math.radians(math.degrees(math.acos(pf3))))\n",
+ "C3=I_c3/(2*math.pi*f*V_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"at no load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C1*10**6))\n",
+ "print(\"at half full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C2*10**6))\n",
+ "print(\"at full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C3*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at no load\n",
+ "value of capacitance=26.404 uF\n",
+ "at half full load\n",
+ "value of capacitance=59.927 uF\n",
+ "at full load\n",
+ "value of capacitance=98.834 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3 Page No 764"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_c=10.0\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "C=I_c/(2*math.pi*f*V_s) \n",
+ "I_l=10\n",
+ "L=V_s/(2*math.pi*f*I_l) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of capacitance=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of inductor=%.3f mH\" %(L*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitance=138.396 uF\n",
+ "value of inductor=73.211 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4, Page No 765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "I_L=10.0\n",
+ "X_L=V_s/I_L\n",
+ "I_f1=6.0\n",
+ " #B=2*a-math.sin(2*a)\n",
+ "B=2*math.pi-I_f1*math.pi*X_L/V_s\n",
+ "a=0\n",
+ "i=1.0\n",
+ "for a in range(1,360):\n",
+ " b=2*a*math.pi/180-math.sin(math.radians(2*a)) \n",
+ " if math.fabs(B-b)<=0.001 : #by hit and trial\n",
+ " i=2\n",
+ " break\n",
+ "print(\"firing angle of TCR = %.1f deg\" %a)\n",
+ " #(a-.01)*180/math.pi)\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle of TCR = 359.0 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=.01\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for firing angle=90deg\")\n",
+ "a=90*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.0f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=120deg\")\n",
+ "a=120*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=150deg\")\n",
+ "a=150*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.2f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=170deg\")\n",
+ "a=170*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ "print(\"for firing angle=175deg\")\n",
+ "a=175*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.2f H\" %L_eff)\n",
+ "print(\"for firing angle=180deg\")\n",
+ "a=180*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ " #random value at firing angle =180 is equivalent to infinity as in answer in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=90deg\n",
+ "effective inductance=10 mH\n",
+ "for firing angle=120deg\n",
+ "effective inductance=25.575 mH\n",
+ "for firing angle=150deg\n",
+ "effective inductance=173.40 mH\n",
+ "for firing angle=170deg\n",
+ "effective inductance=4.459 H\n",
+ "for firing angle=175deg\n",
+ "effective inductance=35.51 H\n",
+ "for firing angle=180deg\n",
+ "effective inductance=-128265253940037.750 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Q=100.0*10**3\n",
+ "V_s=11.0*10**3\n",
+ "\n",
+ "#Calculations\n",
+ "f=50.0\n",
+ "L=V_s**2/(2*math.pi*f*Q) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.4f H\" %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "effective inductance=3.8515 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter13_3.ipynb b/_Power_Electronics/Chapter13_3.ipynb new file mode 100755 index 00000000..62d2a926 --- /dev/null +++ b/_Power_Electronics/Chapter13_3.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Power Factor Improvement"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1, Page No 754"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=250.0\n",
+ "R_l=5.0\n",
+ "I_l=20.0\n",
+ "V_l1=math.sqrt(V_s**2-(R_l*I_l)**2)\n",
+ "reg2=(V_s-V_l1)/V_s*100 \n",
+ "pf1=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "P_l1=V_l1*I_l*pf1 #load power\n",
+ "P_r1=V_s*I_l*pf1 #max powwible system rating\n",
+ "utf1=P_l1*100/P_r1 \n",
+ "pf2=0.5\n",
+ " #(.5*V_l)**2+(.866*V_l+R_l*I_l)**2=V_s**2\n",
+ " #after solving\n",
+ "V_l2=158.35 \n",
+ "reg2=(V_s-V_l2)/V_s*100 \n",
+ "P_l2=V_l2*I_l*pf2 #load power\n",
+ "P_r2=V_s*I_l #max powwible system rating\n",
+ "utf2=P_l2*100/P_r2 \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for pf=1\")\n",
+ "print(\"load voltage=%.2f V\" %V_l1)\n",
+ "print(\"voltage regulation=%.2f\" %reg1)\n",
+ "print(\"system utilisation factor=%.3f\" %utf1)\n",
+ "print(\"energy consumed(in units)=%.1f\" %(P_l1/1000))\n",
+ "print(\"for pf=.5\")\n",
+ "print(\"load voltage=%.2f V\" %V_l2)\n",
+ "print(\"voltage regulation=%.2f\" %reg2)\n",
+ "print(\"system utilisation factor=%.3f\" %utf2)\n",
+ "print(\"energy consumed(in units)=%.2f\" %(P_l2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "NameError",
+ "evalue": "name 'reg1' is not defined",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-ffdbe43fd921>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"for pf=1\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"load voltage=%.2f V\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mV_l1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"voltage regulation=%.2f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mreg1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"system utilisation factor=%.3f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mutf1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"energy consumed(in units)=%.1f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP_l1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'reg1' is not defined"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for pf=1\n",
+ "load voltage=229.13 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2, Page No 756"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "I_m1=2\n",
+ "pf1=.3\n",
+ "\n",
+ "#Calculations\n",
+ "I_c1=I_m1*math.sin(math.radians(math.degrees(math.acos(pf1))))\n",
+ "C1=I_c1/(2*math.pi*f*V_s) \n",
+ "I_m2=5\n",
+ "pf2=.5\n",
+ "I_c2=I_m2*math.sin(math.radians(math.degrees(math.acos(pf2))))\n",
+ "C2=I_c2/(2*math.pi*f*V_s) \n",
+ "I_m3=10\n",
+ "pf3=.7\n",
+ "I_c3=I_m3*math.sin(math.radians(math.degrees(math.acos(pf3))))\n",
+ "C3=I_c3/(2*math.pi*f*V_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"at no load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C1*10**6))\n",
+ "print(\"at half full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C2*10**6))\n",
+ "print(\"at full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C3*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at no load\n",
+ "value of capacitance=26.404 uF\n",
+ "at half full load\n",
+ "value of capacitance=59.927 uF\n",
+ "at full load\n",
+ "value of capacitance=98.834 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3 Page No 764"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_c=10.0\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "C=I_c/(2*math.pi*f*V_s) \n",
+ "I_l=10\n",
+ "L=V_s/(2*math.pi*f*I_l) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of capacitance=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of inductor=%.3f mH\" %(L*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitance=138.396 uF\n",
+ "value of inductor=73.211 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4, Page No 765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "I_L=10.0\n",
+ "X_L=V_s/I_L\n",
+ "I_f1=6.0\n",
+ " #B=2*a-math.sin(2*a)\n",
+ "B=2*math.pi-I_f1*math.pi*X_L/V_s\n",
+ "a=0\n",
+ "i=1.0\n",
+ "for a in range(1,360):\n",
+ " b=2*a*math.pi/180-math.sin(math.radians(2*a)) \n",
+ " if math.fabs(B-b)<=0.001 : #by hit and trial\n",
+ " i=2\n",
+ " break\n",
+ "print(\"firing angle of TCR = %.1f deg\" %a)\n",
+ " #(a-.01)*180/math.pi)\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle of TCR = 359.0 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=.01\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for firing angle=90deg\")\n",
+ "a=90*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.0f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=120deg\")\n",
+ "a=120*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=150deg\")\n",
+ "a=150*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.2f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=170deg\")\n",
+ "a=170*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ "print(\"for firing angle=175deg\")\n",
+ "a=175*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.2f H\" %L_eff)\n",
+ "print(\"for firing angle=180deg\")\n",
+ "a=180*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ " #random value at firing angle =180 is equivalent to infinity as in answer in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=90deg\n",
+ "effective inductance=10 mH\n",
+ "for firing angle=120deg\n",
+ "effective inductance=25.575 mH\n",
+ "for firing angle=150deg\n",
+ "effective inductance=173.40 mH\n",
+ "for firing angle=170deg\n",
+ "effective inductance=4.459 H\n",
+ "for firing angle=175deg\n",
+ "effective inductance=35.51 H\n",
+ "for firing angle=180deg\n",
+ "effective inductance=-128265253940037.750 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Q=100.0*10**3\n",
+ "V_s=11.0*10**3\n",
+ "\n",
+ "#Calculations\n",
+ "f=50.0\n",
+ "L=V_s**2/(2*math.pi*f*Q) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.4f H\" %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "effective inductance=3.8515 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter13_4.ipynb b/_Power_Electronics/Chapter13_4.ipynb new file mode 100755 index 00000000..62d2a926 --- /dev/null +++ b/_Power_Electronics/Chapter13_4.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13 : Power Factor Improvement"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.1, Page No 754"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=250.0\n",
+ "R_l=5.0\n",
+ "I_l=20.0\n",
+ "V_l1=math.sqrt(V_s**2-(R_l*I_l)**2)\n",
+ "reg2=(V_s-V_l1)/V_s*100 \n",
+ "pf1=1.0\n",
+ "\n",
+ "#Calculations\n",
+ "P_l1=V_l1*I_l*pf1 #load power\n",
+ "P_r1=V_s*I_l*pf1 #max powwible system rating\n",
+ "utf1=P_l1*100/P_r1 \n",
+ "pf2=0.5\n",
+ " #(.5*V_l)**2+(.866*V_l+R_l*I_l)**2=V_s**2\n",
+ " #after solving\n",
+ "V_l2=158.35 \n",
+ "reg2=(V_s-V_l2)/V_s*100 \n",
+ "P_l2=V_l2*I_l*pf2 #load power\n",
+ "P_r2=V_s*I_l #max powwible system rating\n",
+ "utf2=P_l2*100/P_r2 \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for pf=1\")\n",
+ "print(\"load voltage=%.2f V\" %V_l1)\n",
+ "print(\"voltage regulation=%.2f\" %reg1)\n",
+ "print(\"system utilisation factor=%.3f\" %utf1)\n",
+ "print(\"energy consumed(in units)=%.1f\" %(P_l1/1000))\n",
+ "print(\"for pf=.5\")\n",
+ "print(\"load voltage=%.2f V\" %V_l2)\n",
+ "print(\"voltage regulation=%.2f\" %reg2)\n",
+ "print(\"system utilisation factor=%.3f\" %utf2)\n",
+ "print(\"energy consumed(in units)=%.2f\" %(P_l2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "NameError",
+ "evalue": "name 'reg1' is not defined",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-ffdbe43fd921>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 25\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"for pf=1\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"load voltage=%.2f V\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mV_l1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"voltage regulation=%.2f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mreg1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 28\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"system utilisation factor=%.3f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mutf1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 29\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"energy consumed(in units)=%.1f\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP_l1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'reg1' is not defined"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for pf=1\n",
+ "load voltage=229.13 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.2, Page No 756"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "I_m1=2\n",
+ "pf1=.3\n",
+ "\n",
+ "#Calculations\n",
+ "I_c1=I_m1*math.sin(math.radians(math.degrees(math.acos(pf1))))\n",
+ "C1=I_c1/(2*math.pi*f*V_s) \n",
+ "I_m2=5\n",
+ "pf2=.5\n",
+ "I_c2=I_m2*math.sin(math.radians(math.degrees(math.acos(pf2))))\n",
+ "C2=I_c2/(2*math.pi*f*V_s) \n",
+ "I_m3=10\n",
+ "pf3=.7\n",
+ "I_c3=I_m3*math.sin(math.radians(math.degrees(math.acos(pf3))))\n",
+ "C3=I_c3/(2*math.pi*f*V_s) \n",
+ "\n",
+ "#Results\n",
+ "print(\"at no load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C1*10**6))\n",
+ "print(\"at half full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C2*10**6))\n",
+ "print(\"at full load\")\n",
+ "print(\"value of capacitance=%.3f uF\" %(C3*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "at no load\n",
+ "value of capacitance=26.404 uF\n",
+ "at half full load\n",
+ "value of capacitance=59.927 uF\n",
+ "at full load\n",
+ "value of capacitance=98.834 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.3 Page No 764"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_c=10.0\n",
+ "f=50.0\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "C=I_c/(2*math.pi*f*V_s) \n",
+ "I_l=10\n",
+ "L=V_s/(2*math.pi*f*I_l) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of capacitance=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of inductor=%.3f mH\" %(L*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitance=138.396 uF\n",
+ "value of inductor=73.211 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.4, Page No 765"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "I_L=10.0\n",
+ "X_L=V_s/I_L\n",
+ "I_f1=6.0\n",
+ " #B=2*a-math.sin(2*a)\n",
+ "B=2*math.pi-I_f1*math.pi*X_L/V_s\n",
+ "a=0\n",
+ "i=1.0\n",
+ "for a in range(1,360):\n",
+ " b=2*a*math.pi/180-math.sin(math.radians(2*a)) \n",
+ " if math.fabs(B-b)<=0.001 : #by hit and trial\n",
+ " i=2\n",
+ " break\n",
+ "print(\"firing angle of TCR = %.1f deg\" %a)\n",
+ " #(a-.01)*180/math.pi)\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle of TCR = 359.0 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.5 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=.01\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for firing angle=90deg\")\n",
+ "a=90*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.0f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=120deg\")\n",
+ "a=120*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=150deg\")\n",
+ "a=150*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.2f mH\" %(L_eff*1000))\n",
+ "print(\"for firing angle=170deg\")\n",
+ "a=170*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ "print(\"for firing angle=175deg\")\n",
+ "a=175*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.2f H\" %L_eff)\n",
+ "print(\"for firing angle=180deg\")\n",
+ "a=180*math.pi/180\n",
+ "L_eff=math.pi*L/(2*math.pi-2*a+math.sin(2*a)) \n",
+ "print(\"effective inductance=%.3f H\" %L_eff)\n",
+ " #random value at firing angle =180 is equivalent to infinity as in answer in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=90deg\n",
+ "effective inductance=10 mH\n",
+ "for firing angle=120deg\n",
+ "effective inductance=25.575 mH\n",
+ "for firing angle=150deg\n",
+ "effective inductance=173.40 mH\n",
+ "for firing angle=170deg\n",
+ "effective inductance=4.459 H\n",
+ "for firing angle=175deg\n",
+ "effective inductance=35.51 H\n",
+ "for firing angle=180deg\n",
+ "effective inductance=-128265253940037.750 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 13.6 Page No 766"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Q=100.0*10**3\n",
+ "V_s=11.0*10**3\n",
+ "\n",
+ "#Calculations\n",
+ "f=50.0\n",
+ "L=V_s**2/(2*math.pi*f*Q) \n",
+ "\n",
+ "#Results\n",
+ "print(\"effective inductance=%.4f H\" %L)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "effective inductance=3.8515 H\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter14.ipynb b/_Power_Electronics/Chapter14.ipynb new file mode 100755 index 00000000..a9c3a3f1 --- /dev/null +++ b/_Power_Electronics/Chapter14.ipynb @@ -0,0 +1,93 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 : Miscellaneous Topics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1, Page No 777"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a1=0\n",
+ "a2=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for two single phase series semiconvertors\")\n",
+ "V_0=V_m/math.pi*(2+math.cos(math.radians(a1))+math.cos(math.radians(a2))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*(4*math.pi-3*a2*math.pi/180+(3/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=(3+math.cos(math.radians(a2)))/(math.sqrt(2)*math.sqrt(5+3*math.cos(math.radians(a2)))) \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/math.pi)*(3+math.cos(math.radians(a2)))/math.sqrt(4*math.pi-3*a2*math.pi/180) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-(3/4)*a2*math.pi/180)/(5+3*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)\n",
+ "print(\"for two single phase series full convertors\")\n",
+ "a=45.0\n",
+ "V_0=2*V_m/math.pi*(1+math.cos(math.radians(a))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=2*V_s*math.sqrt((1/math.pi)*(math.pi-a2*math.pi/180+(1/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=math.cos(math.radians(a2/2)) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/(math.pi*(math.pi-a2*math.pi/180)))*(1+math.cos(math.radians(a2))) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-a2*math.pi/180)/(4+4*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for two single phase series semiconvertors\n",
+ "avg o/p voltage=383.82 V\n",
+ "rms value of o/p voltage=434.47 V\n",
+ "DF=0.98\n",
+ "PF=0.93\n",
+ "HF=0.62\n",
+ "for two single phase series full convertors\n",
+ "avg o/p voltage=353.50 V\n",
+ "rms value of o/p voltage=398.37 V\n",
+ "DF=0.92\n",
+ "PF=0.89\n",
+ "HF=0.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter14_1.ipynb b/_Power_Electronics/Chapter14_1.ipynb new file mode 100755 index 00000000..a9c3a3f1 --- /dev/null +++ b/_Power_Electronics/Chapter14_1.ipynb @@ -0,0 +1,93 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 : Miscellaneous Topics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1, Page No 777"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a1=0\n",
+ "a2=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for two single phase series semiconvertors\")\n",
+ "V_0=V_m/math.pi*(2+math.cos(math.radians(a1))+math.cos(math.radians(a2))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*(4*math.pi-3*a2*math.pi/180+(3/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=(3+math.cos(math.radians(a2)))/(math.sqrt(2)*math.sqrt(5+3*math.cos(math.radians(a2)))) \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/math.pi)*(3+math.cos(math.radians(a2)))/math.sqrt(4*math.pi-3*a2*math.pi/180) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-(3/4)*a2*math.pi/180)/(5+3*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)\n",
+ "print(\"for two single phase series full convertors\")\n",
+ "a=45.0\n",
+ "V_0=2*V_m/math.pi*(1+math.cos(math.radians(a))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=2*V_s*math.sqrt((1/math.pi)*(math.pi-a2*math.pi/180+(1/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=math.cos(math.radians(a2/2)) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/(math.pi*(math.pi-a2*math.pi/180)))*(1+math.cos(math.radians(a2))) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-a2*math.pi/180)/(4+4*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for two single phase series semiconvertors\n",
+ "avg o/p voltage=383.82 V\n",
+ "rms value of o/p voltage=434.47 V\n",
+ "DF=0.98\n",
+ "PF=0.93\n",
+ "HF=0.62\n",
+ "for two single phase series full convertors\n",
+ "avg o/p voltage=353.50 V\n",
+ "rms value of o/p voltage=398.37 V\n",
+ "DF=0.92\n",
+ "PF=0.89\n",
+ "HF=0.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter14_2.ipynb b/_Power_Electronics/Chapter14_2.ipynb new file mode 100755 index 00000000..a9c3a3f1 --- /dev/null +++ b/_Power_Electronics/Chapter14_2.ipynb @@ -0,0 +1,93 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 : Miscellaneous Topics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1, Page No 777"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a1=0\n",
+ "a2=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for two single phase series semiconvertors\")\n",
+ "V_0=V_m/math.pi*(2+math.cos(math.radians(a1))+math.cos(math.radians(a2))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*(4*math.pi-3*a2*math.pi/180+(3/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=(3+math.cos(math.radians(a2)))/(math.sqrt(2)*math.sqrt(5+3*math.cos(math.radians(a2)))) \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/math.pi)*(3+math.cos(math.radians(a2)))/math.sqrt(4*math.pi-3*a2*math.pi/180) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-(3/4)*a2*math.pi/180)/(5+3*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)\n",
+ "print(\"for two single phase series full convertors\")\n",
+ "a=45.0\n",
+ "V_0=2*V_m/math.pi*(1+math.cos(math.radians(a))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=2*V_s*math.sqrt((1/math.pi)*(math.pi-a2*math.pi/180+(1/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=math.cos(math.radians(a2/2)) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/(math.pi*(math.pi-a2*math.pi/180)))*(1+math.cos(math.radians(a2))) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-a2*math.pi/180)/(4+4*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for two single phase series semiconvertors\n",
+ "avg o/p voltage=383.82 V\n",
+ "rms value of o/p voltage=434.47 V\n",
+ "DF=0.98\n",
+ "PF=0.93\n",
+ "HF=0.62\n",
+ "for two single phase series full convertors\n",
+ "avg o/p voltage=353.50 V\n",
+ "rms value of o/p voltage=398.37 V\n",
+ "DF=0.92\n",
+ "PF=0.89\n",
+ "HF=0.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter14_3.ipynb b/_Power_Electronics/Chapter14_3.ipynb new file mode 100755 index 00000000..a9c3a3f1 --- /dev/null +++ b/_Power_Electronics/Chapter14_3.ipynb @@ -0,0 +1,93 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 : Miscellaneous Topics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1, Page No 777"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a1=0\n",
+ "a2=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for two single phase series semiconvertors\")\n",
+ "V_0=V_m/math.pi*(2+math.cos(math.radians(a1))+math.cos(math.radians(a2))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*(4*math.pi-3*a2*math.pi/180+(3/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=(3+math.cos(math.radians(a2)))/(math.sqrt(2)*math.sqrt(5+3*math.cos(math.radians(a2)))) \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/math.pi)*(3+math.cos(math.radians(a2)))/math.sqrt(4*math.pi-3*a2*math.pi/180) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-(3/4)*a2*math.pi/180)/(5+3*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)\n",
+ "print(\"for two single phase series full convertors\")\n",
+ "a=45.0\n",
+ "V_0=2*V_m/math.pi*(1+math.cos(math.radians(a))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=2*V_s*math.sqrt((1/math.pi)*(math.pi-a2*math.pi/180+(1/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=math.cos(math.radians(a2/2)) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/(math.pi*(math.pi-a2*math.pi/180)))*(1+math.cos(math.radians(a2))) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-a2*math.pi/180)/(4+4*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for two single phase series semiconvertors\n",
+ "avg o/p voltage=383.82 V\n",
+ "rms value of o/p voltage=434.47 V\n",
+ "DF=0.98\n",
+ "PF=0.93\n",
+ "HF=0.62\n",
+ "for two single phase series full convertors\n",
+ "avg o/p voltage=353.50 V\n",
+ "rms value of o/p voltage=398.37 V\n",
+ "DF=0.92\n",
+ "PF=0.89\n",
+ "HF=0.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter14_4.ipynb b/_Power_Electronics/Chapter14_4.ipynb new file mode 100755 index 00000000..a9c3a3f1 --- /dev/null +++ b/_Power_Electronics/Chapter14_4.ipynb @@ -0,0 +1,93 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 14 : Miscellaneous Topics"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 14.1, Page No 777"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a1=0\n",
+ "a2=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"for two single phase series semiconvertors\")\n",
+ "V_0=V_m/math.pi*(2+math.cos(math.radians(a1))+math.cos(math.radians(a2))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*(4*math.pi-3*a2*math.pi/180+(3/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=(3+math.cos(math.radians(a2)))/(math.sqrt(2)*math.sqrt(5+3*math.cos(math.radians(a2)))) \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/math.pi)*(3+math.cos(math.radians(a2)))/math.sqrt(4*math.pi-3*a2*math.pi/180) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-(3/4)*a2*math.pi/180)/(5+3*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)\n",
+ "print(\"for two single phase series full convertors\")\n",
+ "a=45.0\n",
+ "V_0=2*V_m/math.pi*(1+math.cos(math.radians(a))) \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_0)\n",
+ "V_or=2*V_s*math.sqrt((1/math.pi)*(math.pi-a2*math.pi/180+(1/2)*math.sin(math.radians(2*a2)))) \n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "DF=math.cos(math.radians(a2/2)) \n",
+ "\n",
+ "\n",
+ "#Results \n",
+ "print(\"DF=%.2f\" %DF)\n",
+ "PF=math.sqrt(2/(math.pi*(math.pi-a2*math.pi/180)))*(1+math.cos(math.radians(a2))) \n",
+ "print(\"PF=%.2f\" %PF)\n",
+ "HF=math.sqrt((math.pi*(math.pi-a2*math.pi/180)/(4+4*math.cos(math.radians(a2))))-1) \n",
+ "print(\"HF=%.2f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for two single phase series semiconvertors\n",
+ "avg o/p voltage=383.82 V\n",
+ "rms value of o/p voltage=434.47 V\n",
+ "DF=0.98\n",
+ "PF=0.93\n",
+ "HF=0.62\n",
+ "for two single phase series full convertors\n",
+ "avg o/p voltage=353.50 V\n",
+ "rms value of o/p voltage=398.37 V\n",
+ "DF=0.92\n",
+ "PF=0.89\n",
+ "HF=0.29\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter2.ipynb b/_Power_Electronics/Chapter2.ipynb new file mode 100755 index 00000000..1872c9f4 --- /dev/null +++ b/_Power_Electronics/Chapter2.ipynb @@ -0,0 +1,233 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 02 : Power Semiconductor Diodes and Transistors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page No 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=40.0\n",
+ "R_c=10 #ohm\n",
+ "V_cc=130.0 #V\n",
+ "V_B=10.0 #V\n",
+ "V_CES=1.0 #V\n",
+ "V_BES=1.5 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_CS=(V_cc-V_CES)/R_c #A\n",
+ "I_BS=I_CS/B #A\n",
+ "R_B1=(V_B-V_BES)/I_BS\n",
+ "P_T1=V_BES*I_BS+V_CES*I_CS\n",
+ "ODF=5\n",
+ "I_B=ODF*I_BS\n",
+ "R_B2=(V_B-V_BES)/I_B\n",
+ "P_T2=V_BES*I_B+V_CES*I_CS\n",
+ "B_f=I_CS/I_B\n",
+ "\n",
+ "#Results\n",
+ "print(\"value of R_B in saturated state= %.2f ohm\" %R_B1)\n",
+ "print(\"Power loss in transistor=%.2f W\" %P_T1)\n",
+ "print(\"Value of R_B for an overdrive factor 5 = %.2f ohm\" %R_B2)\n",
+ "print(\"Power loss in transistor = %.2f W\" %P_T2)\n",
+ "print(\"Forced current gain=%.0f\" %B_f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of R_B in saturated state= 26.36 ohm\n",
+ "Power loss in transistor=13.38 W\n",
+ "Value of R_B for an overdrive factor 5 = 5.27 ohm\n",
+ "Power loss in transistor = 15.32 W\n",
+ "Forced current gain=8\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page No 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220.0 #V\n",
+ "P_dt=I_CEO*V_CC #instant. power loss during delay time\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "P_d=f*I_CEO*V_CC*t_d #avg power loss during delay time\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "\n",
+ "#Calculations\n",
+ "P_r=f*I_CS*t_r*(V_CC/2-(V_CC-V_CES)/3) #avg power loss during rise time\n",
+ "t_m=V_CC*t_r/(2*(V_CC-V_CES))\n",
+ "P_rm=I_CS*V_CC**2/(4*(V_CC-V_CES)) #instant. power loss during rise time\n",
+ "\n",
+ "#Results\n",
+ "P_on=P_d+P_r \n",
+ "print(\"Avg power loss during turn on = %.2f W\" %P_on)\n",
+ "P_nt=I_CS*V_CES \n",
+ "print(\"Instantaneous power loss during turn on = %.0f W\" %P_nt)\n",
+ "t_n=50*10**-6\n",
+ "P_n=f*I_CS*V_CES*t_n\n",
+ "print(\"Avg power loss during conduction period = %.0f W\" %P_n)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg power loss during turn on = 14.93 W\n",
+ "Instantaneous power loss during turn on = 160 W\n",
+ "Avg power loss during conduction period = 40 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220 #V\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "t_n=50*10**-6 #s\n",
+ "t_0=40*10**-6 #s\n",
+ "t_f=3*10**-6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "P_st=I_CS*V_CES # instant. power loss during t_s\n",
+ "P_s=f*I_CS*V_CES*t_f #avg power loss during t_s\n",
+ "P_f=f*t_f*(I_CS/6)*(V_CC-V_CES) #avg power loss during fall time\n",
+ "P_fm=(I_CS/4)*(V_CC-V_CES) #peak instant power dissipation\n",
+ "P_off=P_s+P_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss during turn off = %.2f W\" %P_off)\n",
+ "P_0t=I_CEO*V_CC\n",
+ "print(\"Instantaneous power loss during t_0 = %.2f W\" %P_0t)\n",
+ "P_0=f*I_CEO*V_CC*t_0 #avg power loss during t_s\n",
+ "P_on=14.9339 #W from previous eg\n",
+ "P_n=40 #W from previous eg\n",
+ "P_T=P_on+P_n+P_off+P_0 \n",
+ "print(\"Total power loss = %.2f W\" %P_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss during turn off = 44.91 W\n",
+ "Instantaneous power loss during t_0 = 0.44 W\n",
+ "Total power loss = 99.93 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page No 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_CS=100.0 \n",
+ "V_CC=200.0 \n",
+ "t_on=40*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "P_on=(I_CS/50)*10**6*t_on*(V_CC*t_on/2-(V_CC*10**6*t_on**2/(40*3))) #energy during turn on\n",
+ "t_off=60*10**-6\n",
+ "P_off=(I_CS*t_off/2-(I_CS/60)*10**6*(t_off**2)/3)*((V_CC/75)*10**6*t_off) #energy during turn off\n",
+ "P_t=P_on+P_off #total energy\n",
+ "P_avg=300.0\n",
+ "f=P_avg/P_t\n",
+ "\n",
+ "#Results\n",
+ "print(\"Allowable switching frequency = %.2f Hz\" %f)\n",
+ "#in book ans is: f=1123.6 Hz. The difference in results due to difference in rounding of of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Allowable switching frequency = 1125.00 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter2_1.ipynb b/_Power_Electronics/Chapter2_1.ipynb new file mode 100755 index 00000000..1872c9f4 --- /dev/null +++ b/_Power_Electronics/Chapter2_1.ipynb @@ -0,0 +1,233 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 02 : Power Semiconductor Diodes and Transistors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page No 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=40.0\n",
+ "R_c=10 #ohm\n",
+ "V_cc=130.0 #V\n",
+ "V_B=10.0 #V\n",
+ "V_CES=1.0 #V\n",
+ "V_BES=1.5 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_CS=(V_cc-V_CES)/R_c #A\n",
+ "I_BS=I_CS/B #A\n",
+ "R_B1=(V_B-V_BES)/I_BS\n",
+ "P_T1=V_BES*I_BS+V_CES*I_CS\n",
+ "ODF=5\n",
+ "I_B=ODF*I_BS\n",
+ "R_B2=(V_B-V_BES)/I_B\n",
+ "P_T2=V_BES*I_B+V_CES*I_CS\n",
+ "B_f=I_CS/I_B\n",
+ "\n",
+ "#Results\n",
+ "print(\"value of R_B in saturated state= %.2f ohm\" %R_B1)\n",
+ "print(\"Power loss in transistor=%.2f W\" %P_T1)\n",
+ "print(\"Value of R_B for an overdrive factor 5 = %.2f ohm\" %R_B2)\n",
+ "print(\"Power loss in transistor = %.2f W\" %P_T2)\n",
+ "print(\"Forced current gain=%.0f\" %B_f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of R_B in saturated state= 26.36 ohm\n",
+ "Power loss in transistor=13.38 W\n",
+ "Value of R_B for an overdrive factor 5 = 5.27 ohm\n",
+ "Power loss in transistor = 15.32 W\n",
+ "Forced current gain=8\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page No 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220.0 #V\n",
+ "P_dt=I_CEO*V_CC #instant. power loss during delay time\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "P_d=f*I_CEO*V_CC*t_d #avg power loss during delay time\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "\n",
+ "#Calculations\n",
+ "P_r=f*I_CS*t_r*(V_CC/2-(V_CC-V_CES)/3) #avg power loss during rise time\n",
+ "t_m=V_CC*t_r/(2*(V_CC-V_CES))\n",
+ "P_rm=I_CS*V_CC**2/(4*(V_CC-V_CES)) #instant. power loss during rise time\n",
+ "\n",
+ "#Results\n",
+ "P_on=P_d+P_r \n",
+ "print(\"Avg power loss during turn on = %.2f W\" %P_on)\n",
+ "P_nt=I_CS*V_CES \n",
+ "print(\"Instantaneous power loss during turn on = %.0f W\" %P_nt)\n",
+ "t_n=50*10**-6\n",
+ "P_n=f*I_CS*V_CES*t_n\n",
+ "print(\"Avg power loss during conduction period = %.0f W\" %P_n)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg power loss during turn on = 14.93 W\n",
+ "Instantaneous power loss during turn on = 160 W\n",
+ "Avg power loss during conduction period = 40 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220 #V\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "t_n=50*10**-6 #s\n",
+ "t_0=40*10**-6 #s\n",
+ "t_f=3*10**-6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "P_st=I_CS*V_CES # instant. power loss during t_s\n",
+ "P_s=f*I_CS*V_CES*t_f #avg power loss during t_s\n",
+ "P_f=f*t_f*(I_CS/6)*(V_CC-V_CES) #avg power loss during fall time\n",
+ "P_fm=(I_CS/4)*(V_CC-V_CES) #peak instant power dissipation\n",
+ "P_off=P_s+P_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss during turn off = %.2f W\" %P_off)\n",
+ "P_0t=I_CEO*V_CC\n",
+ "print(\"Instantaneous power loss during t_0 = %.2f W\" %P_0t)\n",
+ "P_0=f*I_CEO*V_CC*t_0 #avg power loss during t_s\n",
+ "P_on=14.9339 #W from previous eg\n",
+ "P_n=40 #W from previous eg\n",
+ "P_T=P_on+P_n+P_off+P_0 \n",
+ "print(\"Total power loss = %.2f W\" %P_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss during turn off = 44.91 W\n",
+ "Instantaneous power loss during t_0 = 0.44 W\n",
+ "Total power loss = 99.93 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page No 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_CS=100.0 \n",
+ "V_CC=200.0 \n",
+ "t_on=40*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "P_on=(I_CS/50)*10**6*t_on*(V_CC*t_on/2-(V_CC*10**6*t_on**2/(40*3))) #energy during turn on\n",
+ "t_off=60*10**-6\n",
+ "P_off=(I_CS*t_off/2-(I_CS/60)*10**6*(t_off**2)/3)*((V_CC/75)*10**6*t_off) #energy during turn off\n",
+ "P_t=P_on+P_off #total energy\n",
+ "P_avg=300.0\n",
+ "f=P_avg/P_t\n",
+ "\n",
+ "#Results\n",
+ "print(\"Allowable switching frequency = %.2f Hz\" %f)\n",
+ "#in book ans is: f=1123.6 Hz. The difference in results due to difference in rounding of of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Allowable switching frequency = 1125.00 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter2_2.ipynb b/_Power_Electronics/Chapter2_2.ipynb new file mode 100755 index 00000000..1872c9f4 --- /dev/null +++ b/_Power_Electronics/Chapter2_2.ipynb @@ -0,0 +1,233 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 02 : Power Semiconductor Diodes and Transistors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page No 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=40.0\n",
+ "R_c=10 #ohm\n",
+ "V_cc=130.0 #V\n",
+ "V_B=10.0 #V\n",
+ "V_CES=1.0 #V\n",
+ "V_BES=1.5 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_CS=(V_cc-V_CES)/R_c #A\n",
+ "I_BS=I_CS/B #A\n",
+ "R_B1=(V_B-V_BES)/I_BS\n",
+ "P_T1=V_BES*I_BS+V_CES*I_CS\n",
+ "ODF=5\n",
+ "I_B=ODF*I_BS\n",
+ "R_B2=(V_B-V_BES)/I_B\n",
+ "P_T2=V_BES*I_B+V_CES*I_CS\n",
+ "B_f=I_CS/I_B\n",
+ "\n",
+ "#Results\n",
+ "print(\"value of R_B in saturated state= %.2f ohm\" %R_B1)\n",
+ "print(\"Power loss in transistor=%.2f W\" %P_T1)\n",
+ "print(\"Value of R_B for an overdrive factor 5 = %.2f ohm\" %R_B2)\n",
+ "print(\"Power loss in transistor = %.2f W\" %P_T2)\n",
+ "print(\"Forced current gain=%.0f\" %B_f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of R_B in saturated state= 26.36 ohm\n",
+ "Power loss in transistor=13.38 W\n",
+ "Value of R_B for an overdrive factor 5 = 5.27 ohm\n",
+ "Power loss in transistor = 15.32 W\n",
+ "Forced current gain=8\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page No 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220.0 #V\n",
+ "P_dt=I_CEO*V_CC #instant. power loss during delay time\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "P_d=f*I_CEO*V_CC*t_d #avg power loss during delay time\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "\n",
+ "#Calculations\n",
+ "P_r=f*I_CS*t_r*(V_CC/2-(V_CC-V_CES)/3) #avg power loss during rise time\n",
+ "t_m=V_CC*t_r/(2*(V_CC-V_CES))\n",
+ "P_rm=I_CS*V_CC**2/(4*(V_CC-V_CES)) #instant. power loss during rise time\n",
+ "\n",
+ "#Results\n",
+ "P_on=P_d+P_r \n",
+ "print(\"Avg power loss during turn on = %.2f W\" %P_on)\n",
+ "P_nt=I_CS*V_CES \n",
+ "print(\"Instantaneous power loss during turn on = %.0f W\" %P_nt)\n",
+ "t_n=50*10**-6\n",
+ "P_n=f*I_CS*V_CES*t_n\n",
+ "print(\"Avg power loss during conduction period = %.0f W\" %P_n)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg power loss during turn on = 14.93 W\n",
+ "Instantaneous power loss during turn on = 160 W\n",
+ "Avg power loss during conduction period = 40 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220 #V\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "t_n=50*10**-6 #s\n",
+ "t_0=40*10**-6 #s\n",
+ "t_f=3*10**-6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "P_st=I_CS*V_CES # instant. power loss during t_s\n",
+ "P_s=f*I_CS*V_CES*t_f #avg power loss during t_s\n",
+ "P_f=f*t_f*(I_CS/6)*(V_CC-V_CES) #avg power loss during fall time\n",
+ "P_fm=(I_CS/4)*(V_CC-V_CES) #peak instant power dissipation\n",
+ "P_off=P_s+P_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss during turn off = %.2f W\" %P_off)\n",
+ "P_0t=I_CEO*V_CC\n",
+ "print(\"Instantaneous power loss during t_0 = %.2f W\" %P_0t)\n",
+ "P_0=f*I_CEO*V_CC*t_0 #avg power loss during t_s\n",
+ "P_on=14.9339 #W from previous eg\n",
+ "P_n=40 #W from previous eg\n",
+ "P_T=P_on+P_n+P_off+P_0 \n",
+ "print(\"Total power loss = %.2f W\" %P_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss during turn off = 44.91 W\n",
+ "Instantaneous power loss during t_0 = 0.44 W\n",
+ "Total power loss = 99.93 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page No 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_CS=100.0 \n",
+ "V_CC=200.0 \n",
+ "t_on=40*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "P_on=(I_CS/50)*10**6*t_on*(V_CC*t_on/2-(V_CC*10**6*t_on**2/(40*3))) #energy during turn on\n",
+ "t_off=60*10**-6\n",
+ "P_off=(I_CS*t_off/2-(I_CS/60)*10**6*(t_off**2)/3)*((V_CC/75)*10**6*t_off) #energy during turn off\n",
+ "P_t=P_on+P_off #total energy\n",
+ "P_avg=300.0\n",
+ "f=P_avg/P_t\n",
+ "\n",
+ "#Results\n",
+ "print(\"Allowable switching frequency = %.2f Hz\" %f)\n",
+ "#in book ans is: f=1123.6 Hz. The difference in results due to difference in rounding of of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Allowable switching frequency = 1125.00 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter2_3.ipynb b/_Power_Electronics/Chapter2_3.ipynb new file mode 100755 index 00000000..1872c9f4 --- /dev/null +++ b/_Power_Electronics/Chapter2_3.ipynb @@ -0,0 +1,233 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 02 : Power Semiconductor Diodes and Transistors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page No 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=40.0\n",
+ "R_c=10 #ohm\n",
+ "V_cc=130.0 #V\n",
+ "V_B=10.0 #V\n",
+ "V_CES=1.0 #V\n",
+ "V_BES=1.5 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_CS=(V_cc-V_CES)/R_c #A\n",
+ "I_BS=I_CS/B #A\n",
+ "R_B1=(V_B-V_BES)/I_BS\n",
+ "P_T1=V_BES*I_BS+V_CES*I_CS\n",
+ "ODF=5\n",
+ "I_B=ODF*I_BS\n",
+ "R_B2=(V_B-V_BES)/I_B\n",
+ "P_T2=V_BES*I_B+V_CES*I_CS\n",
+ "B_f=I_CS/I_B\n",
+ "\n",
+ "#Results\n",
+ "print(\"value of R_B in saturated state= %.2f ohm\" %R_B1)\n",
+ "print(\"Power loss in transistor=%.2f W\" %P_T1)\n",
+ "print(\"Value of R_B for an overdrive factor 5 = %.2f ohm\" %R_B2)\n",
+ "print(\"Power loss in transistor = %.2f W\" %P_T2)\n",
+ "print(\"Forced current gain=%.0f\" %B_f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of R_B in saturated state= 26.36 ohm\n",
+ "Power loss in transistor=13.38 W\n",
+ "Value of R_B for an overdrive factor 5 = 5.27 ohm\n",
+ "Power loss in transistor = 15.32 W\n",
+ "Forced current gain=8\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page No 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220.0 #V\n",
+ "P_dt=I_CEO*V_CC #instant. power loss during delay time\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "P_d=f*I_CEO*V_CC*t_d #avg power loss during delay time\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "\n",
+ "#Calculations\n",
+ "P_r=f*I_CS*t_r*(V_CC/2-(V_CC-V_CES)/3) #avg power loss during rise time\n",
+ "t_m=V_CC*t_r/(2*(V_CC-V_CES))\n",
+ "P_rm=I_CS*V_CC**2/(4*(V_CC-V_CES)) #instant. power loss during rise time\n",
+ "\n",
+ "#Results\n",
+ "P_on=P_d+P_r \n",
+ "print(\"Avg power loss during turn on = %.2f W\" %P_on)\n",
+ "P_nt=I_CS*V_CES \n",
+ "print(\"Instantaneous power loss during turn on = %.0f W\" %P_nt)\n",
+ "t_n=50*10**-6\n",
+ "P_n=f*I_CS*V_CES*t_n\n",
+ "print(\"Avg power loss during conduction period = %.0f W\" %P_n)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg power loss during turn on = 14.93 W\n",
+ "Instantaneous power loss during turn on = 160 W\n",
+ "Avg power loss during conduction period = 40 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220 #V\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "t_n=50*10**-6 #s\n",
+ "t_0=40*10**-6 #s\n",
+ "t_f=3*10**-6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "P_st=I_CS*V_CES # instant. power loss during t_s\n",
+ "P_s=f*I_CS*V_CES*t_f #avg power loss during t_s\n",
+ "P_f=f*t_f*(I_CS/6)*(V_CC-V_CES) #avg power loss during fall time\n",
+ "P_fm=(I_CS/4)*(V_CC-V_CES) #peak instant power dissipation\n",
+ "P_off=P_s+P_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss during turn off = %.2f W\" %P_off)\n",
+ "P_0t=I_CEO*V_CC\n",
+ "print(\"Instantaneous power loss during t_0 = %.2f W\" %P_0t)\n",
+ "P_0=f*I_CEO*V_CC*t_0 #avg power loss during t_s\n",
+ "P_on=14.9339 #W from previous eg\n",
+ "P_n=40 #W from previous eg\n",
+ "P_T=P_on+P_n+P_off+P_0 \n",
+ "print(\"Total power loss = %.2f W\" %P_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss during turn off = 44.91 W\n",
+ "Instantaneous power loss during t_0 = 0.44 W\n",
+ "Total power loss = 99.93 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page No 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_CS=100.0 \n",
+ "V_CC=200.0 \n",
+ "t_on=40*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "P_on=(I_CS/50)*10**6*t_on*(V_CC*t_on/2-(V_CC*10**6*t_on**2/(40*3))) #energy during turn on\n",
+ "t_off=60*10**-6\n",
+ "P_off=(I_CS*t_off/2-(I_CS/60)*10**6*(t_off**2)/3)*((V_CC/75)*10**6*t_off) #energy during turn off\n",
+ "P_t=P_on+P_off #total energy\n",
+ "P_avg=300.0\n",
+ "f=P_avg/P_t\n",
+ "\n",
+ "#Results\n",
+ "print(\"Allowable switching frequency = %.2f Hz\" %f)\n",
+ "#in book ans is: f=1123.6 Hz. The difference in results due to difference in rounding of of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Allowable switching frequency = 1125.00 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter2_4.ipynb b/_Power_Electronics/Chapter2_4.ipynb new file mode 100755 index 00000000..1872c9f4 --- /dev/null +++ b/_Power_Electronics/Chapter2_4.ipynb @@ -0,0 +1,233 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 02 : Power Semiconductor Diodes and Transistors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.1, Page No 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=40.0\n",
+ "R_c=10 #ohm\n",
+ "V_cc=130.0 #V\n",
+ "V_B=10.0 #V\n",
+ "V_CES=1.0 #V\n",
+ "V_BES=1.5 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_CS=(V_cc-V_CES)/R_c #A\n",
+ "I_BS=I_CS/B #A\n",
+ "R_B1=(V_B-V_BES)/I_BS\n",
+ "P_T1=V_BES*I_BS+V_CES*I_CS\n",
+ "ODF=5\n",
+ "I_B=ODF*I_BS\n",
+ "R_B2=(V_B-V_BES)/I_B\n",
+ "P_T2=V_BES*I_B+V_CES*I_CS\n",
+ "B_f=I_CS/I_B\n",
+ "\n",
+ "#Results\n",
+ "print(\"value of R_B in saturated state= %.2f ohm\" %R_B1)\n",
+ "print(\"Power loss in transistor=%.2f W\" %P_T1)\n",
+ "print(\"Value of R_B for an overdrive factor 5 = %.2f ohm\" %R_B2)\n",
+ "print(\"Power loss in transistor = %.2f W\" %P_T2)\n",
+ "print(\"Forced current gain=%.0f\" %B_f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of R_B in saturated state= 26.36 ohm\n",
+ "Power loss in transistor=13.38 W\n",
+ "Value of R_B for an overdrive factor 5 = 5.27 ohm\n",
+ "Power loss in transistor = 15.32 W\n",
+ "Forced current gain=8\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.2, Page No 24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220.0 #V\n",
+ "P_dt=I_CEO*V_CC #instant. power loss during delay time\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "P_d=f*I_CEO*V_CC*t_d #avg power loss during delay time\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "\n",
+ "#Calculations\n",
+ "P_r=f*I_CS*t_r*(V_CC/2-(V_CC-V_CES)/3) #avg power loss during rise time\n",
+ "t_m=V_CC*t_r/(2*(V_CC-V_CES))\n",
+ "P_rm=I_CS*V_CC**2/(4*(V_CC-V_CES)) #instant. power loss during rise time\n",
+ "\n",
+ "#Results\n",
+ "P_on=P_d+P_r \n",
+ "print(\"Avg power loss during turn on = %.2f W\" %P_on)\n",
+ "P_nt=I_CS*V_CES \n",
+ "print(\"Instantaneous power loss during turn on = %.0f W\" %P_nt)\n",
+ "t_n=50*10**-6\n",
+ "P_n=f*I_CS*V_CES*t_n\n",
+ "print(\"Avg power loss during conduction period = %.0f W\" %P_n)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg power loss during turn on = 14.93 W\n",
+ "Instantaneous power loss during turn on = 160 W\n",
+ "Avg power loss during conduction period = 40 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_CEO=2*10**-3 #A\n",
+ "V_CC=220 #V\n",
+ "t_d=.4*10**-6 #s\n",
+ "f=5000\n",
+ "V_CES=2 #V\n",
+ "t_r=1*10**-6 #s\n",
+ "I_CS=80 #A\n",
+ "t_n=50*10**-6 #s\n",
+ "t_0=40*10**-6 #s\n",
+ "t_f=3*10**-6 #s\n",
+ "\n",
+ "#Calculations\n",
+ "P_st=I_CS*V_CES # instant. power loss during t_s\n",
+ "P_s=f*I_CS*V_CES*t_f #avg power loss during t_s\n",
+ "P_f=f*t_f*(I_CS/6)*(V_CC-V_CES) #avg power loss during fall time\n",
+ "P_fm=(I_CS/4)*(V_CC-V_CES) #peak instant power dissipation\n",
+ "P_off=P_s+P_f\n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss during turn off = %.2f W\" %P_off)\n",
+ "P_0t=I_CEO*V_CC\n",
+ "print(\"Instantaneous power loss during t_0 = %.2f W\" %P_0t)\n",
+ "P_0=f*I_CEO*V_CC*t_0 #avg power loss during t_s\n",
+ "P_on=14.9339 #W from previous eg\n",
+ "P_n=40 #W from previous eg\n",
+ "P_T=P_on+P_n+P_off+P_0 \n",
+ "print(\"Total power loss = %.2f W\" %P_T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss during turn off = 44.91 W\n",
+ "Instantaneous power loss during t_0 = 0.44 W\n",
+ "Total power loss = 99.93 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2.4, Page No 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_CS=100.0 \n",
+ "V_CC=200.0 \n",
+ "t_on=40*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "P_on=(I_CS/50)*10**6*t_on*(V_CC*t_on/2-(V_CC*10**6*t_on**2/(40*3))) #energy during turn on\n",
+ "t_off=60*10**-6\n",
+ "P_off=(I_CS*t_off/2-(I_CS/60)*10**6*(t_off**2)/3)*((V_CC/75)*10**6*t_off) #energy during turn off\n",
+ "P_t=P_on+P_off #total energy\n",
+ "P_avg=300.0\n",
+ "f=P_avg/P_t\n",
+ "\n",
+ "#Results\n",
+ "print(\"Allowable switching frequency = %.2f Hz\" %f)\n",
+ "#in book ans is: f=1123.6 Hz. The difference in results due to difference in rounding of of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Allowable switching frequency = 1125.00 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter3.ipynb b/_Power_Electronics/Chapter3.ipynb new file mode 100755 index 00000000..2e53ef9d --- /dev/null +++ b/_Power_Electronics/Chapter3.ipynb @@ -0,0 +1,1001 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 03 : Diode Circuits and Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page No 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0 #V\n",
+ "V_o=100.0 #V\n",
+ "L=100.0 #uH\n",
+ "C=30.0 #uF\n",
+ "\n",
+ "#Calculations\n",
+ "t_o=math.pi*math.sqrt(L*C)\n",
+ "print(\"conduction time of diode = %.2f us\" %t_o)\n",
+ "#in book solution is t_o=54.77 us. The ans is incorrect as %pi is not muliplied in ans. Formulae mentioned in correct.\n",
+ "I_p=(V_s-V_o)*math.sqrt(C/L)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak current through diode=%.2f A\" %I_p)\n",
+ "v_D=-V_s+V_o \n",
+ "print(\"Voltage across diode = %.2f V\" %v_D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of diode = 172.07 us\n",
+ "Peak current through diode=164.32 A\n",
+ "Voltage across diode = -300.00 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page No 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=10 #ohm\n",
+ "L=0.001 #H\n",
+ "C=5*10**-6 #F\n",
+ "V_s=230 #V\n",
+ "xi=R/(2*L)\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t=math.pi/w_r \n",
+ "\n",
+ "#Results\n",
+ "print('Conduction time of diode=%.3f us'%(t*10**6))\n",
+ "t=0\n",
+ "di=V_s/L\n",
+ "print('Rate of change of current at t=0 is %.2f A/s' %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Conduction time of diode=237.482 us\n",
+ "Rate of change of current at t=0 is 230000.00 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7 Page No 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_or=100 #A\n",
+ "R=1.0 #assumption\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=I_or*2*R\n",
+ "I_o=V_m/(math.pi*R)\n",
+ "q=200 #Ah\n",
+ "t=q/I_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"time required to deliver charge=%.02f hrs\" %t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to deliver charge=3.14 hrs\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page No 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "P=1000 #W\n",
+ "R=V_s**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(2)*V_s/2\n",
+ "P_h=V_or**2/R \n",
+ "print(\"Power delivered to the heater = %.2f W\" %P_h)\n",
+ "V_m=math.sqrt(2)*230\n",
+ "I_m=V_m/R\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak value of diode current = %.2f A\" %I_m)\n",
+ "pf=V_or/V_s\n",
+ "print(\"Input power factor=%.2f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to the heater = 500.00 W\n",
+ "Peak value of diode current = 6.15 A\n",
+ "Input power factor=0.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9 Page No 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "V_m=V_s*math.sqrt(2)\n",
+ "E=150 #V\n",
+ "\n",
+ "#Calculations\n",
+ "theta1=math.degrees(E/(math.sqrt(2)*V_s))\n",
+ "R=8 #ohm\n",
+ "f=50 #Hz\n",
+ "I_o=(1/(2*math.pi*R))*((2*math.sqrt(2)*V_s*math.cos(math.radians(theta1)))-E*(math.pi-2*theta1*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg value of charging current=%.2f A\" %I_o)\n",
+ "P_d=E*I_o\n",
+ "print(\"\\npower delivered to battery=%.2f W\" %P_d)\n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V_s**2+E**2)*(math.pi-2*theta1*math.pi/180)+V_s**2*math.sin(math.radians(2*theta1))-4*V_m*E*math.cos(math.radians(theta1))))\n",
+ "print(\"\\nrms value of the load current=%.2f A\" %I_or)\n",
+ "pf=(E*I_o+I_or**2*R)/(V_s*I_or)\n",
+ "print(\"\\nsupply pf=%.3f\" %pf)\n",
+ "P_dd=I_or**2*R\n",
+ "print(\"\\npower dissipated in the resistor=%.2f W\" %P_dd)\n",
+ "q=1000.00 #Wh\n",
+ "t=q/P_d \n",
+ "print(\"\\ncharging time=%.2f hr\" %t)\n",
+ "n=P_d*100/(P_d+P_dd)\n",
+ "print(\"rectifier efficiency =%.2f \" %n)\n",
+ "PIV=math.sqrt(2)*V_s+E\n",
+ "print(\"PIV of diode=%.2f V\" %PIV)\n",
+ "#solutions have small variations due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg value of charging current=4.97 A\n",
+ "\n",
+ "power delivered to battery=745.11 W\n",
+ "\n",
+ "rms value of the load current=9.29 A\n",
+ "\n",
+ "supply pf=0.672\n",
+ "\n",
+ "power dissipated in the resistor=690.74 W\n",
+ "\n",
+ "charging time=1.34 hr\n",
+ "rectifier efficiency =51.89 \n",
+ "PIV of diode=475.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10 Page No 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "t_rr=40*10**-6 #s reverde recovery time\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*math.sqrt(2)*V_s/math.pi\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "f=50\n",
+ "V_r1=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg1=V_r1*100/V_o*10**3\n",
+ "f=2500\n",
+ "V_r2=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg2=V_r2*100/V_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"when f=50Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage=%.2f x 10^-3\" %v_avg1)\n",
+ "print(\"when f=2500Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage = %.3f\" %v_avg2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when f=50Hz\n",
+ "Percentage reduction in avg o/p voltage=3.95 x 10^-3\n",
+ "when f=2500Hz\n",
+ "Percentage reduction in avg o/p voltage = 9.549\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page No 79 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "R=10.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "print(\"Avg value of o/p voltage = %.2f V\" %V_o)\n",
+ "I_o=V_o/R\n",
+ "print(\"Avg value of o/p current = %.2f A\" %I_o)\n",
+ "I_DA=I_o/2\n",
+ "print(\"Avg value of diode current=%.2f A\" %I_DA)\n",
+ "I_Dr=I_o/math.sqrt(2) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"rms value of o/p current = %.2f A\" %I_o)\n",
+ "print(\"rms value of i/p current = %.2f A\" %I_o)\n",
+ "pf=(V_o/V_s)\n",
+ "print(\"supply pf = %.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg value of o/p voltage = 207.07 V\n",
+ "Avg value of o/p current = 20.71 A\n",
+ "Avg value of diode current=10.35 A\n",
+ "rms value of diode current=14.64 A\n",
+ "rms value of o/p current = 20.71 A\n",
+ "rms value of i/p current = 20.71 A\n",
+ "supply pf = 0.90\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12 Page No 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "R=1000.0 #ohm\n",
+ "R_D=20.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_om=V_m/(R+R_D) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak load current = %.2f A\" %I_om)\n",
+ "I_o=I_om/math.pi\n",
+ "print(\"dc load current = %.2f A\" %I_o)\n",
+ "V_D=I_o*R_D-V_m/math.pi\n",
+ "print(\"dc diode voltage = %.2f V\" %V_D)\n",
+ "V_on=V_m/math.pi\n",
+ "print(\"at no load, load voltage = %.2f V\" %V_on)\n",
+ "V_o1=I_o*R \n",
+ "print(\"at given load, load voltage = %.2f V\" %V_o1)\n",
+ "vr=(V_on-V_o1)*100/V_on \n",
+ "print(\"Voltage regulation(in percent)=%.2f\" %vr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Peak load current = 0.32 A\n",
+ "dc load current = 0.10 A\n",
+ "dc diode voltage = -101.51 V\n",
+ "at no load, load voltage = 103.54 V\n",
+ "at given load, load voltage = 101.51 V\n",
+ "Voltage regulation(in percent)=1.96\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13 Page No 82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_L=6.8 #V\n",
+ "V_smax=20*1.2 #V\n",
+ "V_smin=20*.8 #V\n",
+ "I_Lmax=30*1.5 #mA\n",
+ "I_Lmin=30*0.5 #mA\n",
+ "I_z=1 #mA\n",
+ "\n",
+ "#Calculations\n",
+ "R_smax=(V_smax-V_L)/((I_Lmin+I_z)*10**-3)\n",
+ "print(\"max source resistance = %.2f ohm\" %R_smax)\n",
+ "R_smin=(V_smin-V_L)/((I_Lmax+I_z)*10**-3) \n",
+ "print(\"Min source resistance = %.2f ohm\" %R_smin) #in book solution, error is committed in putting the values in formulea(printing error) but solution is correct\n",
+ "R_Lmax=V_L*1000/I_Lmin\n",
+ "print(\"Max load resistance = %.2f ohm\" %R_Lmax)\n",
+ "R_Lmin=V_L*1000/I_Lmax \n",
+ "V_d=0.6 #V\n",
+ "V_r=V_L-V_d\n",
+ "\n",
+ "#Results\n",
+ "print(\"Min load resistance=%.2f ohm\" %R_Lmin)\n",
+ "print(\"Voltage rating of zener diode=%.2f V\" %V_r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max source resistance = 1075.00 ohm\n",
+ "Min source resistance = 200.00 ohm\n",
+ "Max load resistance = 453.33 ohm\n",
+ "Min load resistance=151.11 ohm\n",
+ "Voltage rating of zener diode=6.20 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14 Page No 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I2=200*10**-6 #A\n",
+ "V_z=20 #V\n",
+ "R_G=500.0 #hm\n",
+ "\n",
+ "#Calculations\n",
+ "R2=(V_z/I2)-R_G\n",
+ "print(\"R2=%.2f kilo-ohm\" %(R2/1000))\n",
+ "\n",
+ "V_v=25 #V\n",
+ "I1=I2\n",
+ "R1=(V_v-V_z)/I1\n",
+ "\n",
+ "#Results\n",
+ "print(\"R1=%.0f kilo-ohm\"%(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2=99.50 kilo-ohm\n",
+ "R1=25 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=2*230 #V\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(math.sqrt(2)*V_s)/math.pi\n",
+ "R=60 #ohm\n",
+ "P_dc=(V_o)**2/R\n",
+ "TUF=0.2865\n",
+ "VA=P_dc/TUF\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"kVA rating of the transformer = %.2f kVA\" %(VA/1000));\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA rating of the transformer = 2.49 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=0.5 #turns ratio\n",
+ "I_o=10.0\n",
+ "V=230.0\n",
+ "V_s=V/tr\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "phi1=0\n",
+ "#displacemnt angle=0 as fundamnetal component of i/p source current in phase with source voltage\n",
+ "DF=math.cos(math.radians(phi1))\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*math.pi/math.pi)\n",
+ "CDF=I_s1/I_o\n",
+ "pf=CDF*DF\n",
+ "HF=math.sqrt((I_s/I_s1)**2-1)\n",
+ "CF=I_o/I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p voltage = %.2f V\" %V_o)\n",
+ "print(\"distortion factor = %.2f\" %DF)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"Current displacent factor=%.2f\" %CDF)\n",
+ "print(\"Harmonic factor = %.2f\" %HF)\n",
+ "print(\"Creast factor = %.2f\" %CF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p voltage = 414.15 V\n",
+ "distortion factor = 1.00\n",
+ "i/p pf=0.90\n",
+ "Current displacent factor=0.90\n",
+ "Harmonic factor = 0.48\n",
+ "Creast factor = 1.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=230.0\n",
+ "R=10.0\n",
+ "V_s=V_o*math.pi/(2*math.sqrt(2))\n",
+ "I_o=V_o/R\n",
+ "I_m=math.sqrt(2)*V_s/R\n",
+ "I_DAV=I_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "#avg value of diode current\n",
+ "I_Dr=I_m/2\n",
+ "PIV=math.sqrt(2)*V_s\n",
+ "I_s=I_m/math.sqrt(2)\n",
+ "TF=V_s*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak diode current=%.2f A\" %I_m)\n",
+ "print(\"I_DAV=%.2f A\" %I_DAV)\n",
+ "print(\"I_Dr=%.2f A\" %I_Dr) #rms value of diode current\n",
+ "print(\"PIV=%.1f V\" %PIV)\n",
+ "print(\"Transformer rating = %.2f kVA\" %(TF/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak diode current=36.13 A\n",
+ "I_DAV=11.50 A\n",
+ "I_Dr=18.06 A\n",
+ "PIV=361.3 V\n",
+ "Transformer rating = 6.53 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.18, Page No 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=5\n",
+ "V=1100.0\n",
+ "R=10.0\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"In case of 3ph-3pulse type\")\n",
+ "V_ph=V/tr\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*math.sqrt(3)*V_mp/(2*math.pi)\n",
+ "print(\"avg o/p voltage=%.1f V\" %V_o)\n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/3) \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3))) \n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "V_or=V_mp*math.sqrt((3/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3)))\n",
+ "P=(V_or**2)/R \n",
+ "print(\"\\npower delivered=%.1f W\" %P)\n",
+ "print(\"in case of 3ph-M6 type\")\n",
+ "V_ph=V_ph/2\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*V_mp/(math.pi) \n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/6) \n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6))) \n",
+ "V_or=V_mp*math.sqrt((6/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6)))\n",
+ "P=(V_or**2)/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"\\navg value of diode current=%.2f A\" %I_D)\n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"\\npower delivered=%.0f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "In case of 3ph-3pulse type\n",
+ "avg o/p voltage=257.3 V\n",
+ "\n",
+ "avg value of diode current=8.577 A\n",
+ "\n",
+ "rms value of diode current=15.10 A\n",
+ "\n",
+ "power delivered=6841.3 W\n",
+ "in case of 3ph-M6 type\n",
+ "avg o/p voltage=148.55 V\n",
+ "\n",
+ "avg value of diode current=2.48 A\n",
+ "\n",
+ "rms value of diode current=6.07 A\n",
+ "\n",
+ "power delivered=2211 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.19, Page No 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=400\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=V_o*math.pi/3\n",
+ "V_s=V_ml/(math.sqrt(2)*math.sqrt(3))\n",
+ "I_m=V_ml/R\n",
+ "I_s=.7804*I_m\n",
+ "tr=3*V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer rating=%.1f VA\" %tr)\n",
+ "I_Dr=.5518*I_m \n",
+ "print(\"\\nrms value of diode current=%.3f A\" %I_Dr)\n",
+ "I_D=I_m/math.pi \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "print(\"\\npeak diode current=%.2f A\" %I_m)\n",
+ "PIV=V_ml \n",
+ "print(\"\\nPIV=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer rating=16770.3 VA\n",
+ "\n",
+ "rms value of diode current=23.114 A\n",
+ "\n",
+ "avg value of diode current=13.333 A\n",
+ "\n",
+ "peak diode current=41.89 A\n",
+ "\n",
+ "PIV=418.88 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.20, Page No 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=230\n",
+ "E=240\n",
+ "R=8\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "V_o=3*V_ml/math.pi\n",
+ "I_o=(V_o-E)/R\n",
+ "P_b=E*I_o \n",
+ "P_d=E*I_o+I_o**2*R \n",
+ "phi1=0\n",
+ "math.cos(math.radians(phi1))\n",
+ "I_s1=2*math.sqrt(3)*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*2*math.pi/(3*math.pi))\n",
+ "CDF=I_s1/I_s \n",
+ "pf=DF*CDF \n",
+ "HF=math.sqrt(CDF**-2-1) \n",
+ "tr=math.sqrt(3)*V_l*I_o*math.sqrt(2/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Power delivered to battery=%.1f W\" %P_b)\n",
+ "print(\"Power delivered to load=%.2f W\" %P_d)\n",
+ "print(\"Displacement factor=%.2f\" %DF)\n",
+ "print(\"Current distortion factor=%.3f\" %CDF)\n",
+ "print(\"i/p pf=%.3f\"%pf)\n",
+ "print(\"Harmonic factor=%.2f\" %HF)\n",
+ "print(\"Tranformer rating=%.2f VA\" %tr)\n",
+ "#answers have small variations from the book due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to battery=2118.3 W\n",
+ "Power delivered to load=2741.48 W\n",
+ "Displacement factor=1.00\n",
+ "Current distortion factor=0.955\n",
+ "i/p pf=0.955\n",
+ "Harmonic factor=0.31\n",
+ "Tranformer rating=0.00 VA\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.21, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50 #Hz\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "R=400.0\n",
+ "RF=0.05\n",
+ "C=(1/(4*f*R))*(1+(1/(math.sqrt(2)*RF)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"capacitor value=%.2f uF\" %(C/10**-6))\n",
+ "V_o=V_m*(1-1/(4*f*R*C))\n",
+ "print(\"o/p voltage with filter=%.2f V\" %V_o)\n",
+ "V_o=2*V_m/math.pi \n",
+ "print(\"o/p voltage without filter=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "capacitor value=189.28 uF\n",
+ "o/p voltage with filter=303.79 V\n",
+ "o/p voltage without filter=207.07 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.22, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50\n",
+ "CRF=0.05\n",
+ "R=300\n",
+ "\n",
+ "#Calculations\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "print(\"L=%.2f H\" %L)\n",
+ "R=30\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nL=%.2f H\" %L)\n",
+ "L=0\n",
+ "CRF=.4715*R/math.sqrt(R**2+(2*2*math.pi*f*L)**2) \n",
+ "print(\"\\nCRF=%.2f\" %CRF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "L=4.48 H\n",
+ "\n",
+ "L=0.45 H\n",
+ "\n",
+ "CRF=0.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.23, Page No 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=50\n",
+ "L_L=10*10**-3\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "\n",
+ "#Calculations\n",
+ "C=10/(2*w*math.sqrt(R**2+(2*w*L_L)**2))\n",
+ "\n",
+ "#Results\n",
+ "print(\"C=%.2f uF\" %(C*10**6))\n",
+ "VRF=0.1\n",
+ "L=(1/(4*w**2*C))*((math.sqrt(2)/(3*VRF))+1)\n",
+ "print(\"\\nL=%.2f mH\" %(L*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C=315.83 uF\n",
+ "\n",
+ "L=45.83 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter3_1.ipynb b/_Power_Electronics/Chapter3_1.ipynb new file mode 100755 index 00000000..2e53ef9d --- /dev/null +++ b/_Power_Electronics/Chapter3_1.ipynb @@ -0,0 +1,1001 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 03 : Diode Circuits and Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page No 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0 #V\n",
+ "V_o=100.0 #V\n",
+ "L=100.0 #uH\n",
+ "C=30.0 #uF\n",
+ "\n",
+ "#Calculations\n",
+ "t_o=math.pi*math.sqrt(L*C)\n",
+ "print(\"conduction time of diode = %.2f us\" %t_o)\n",
+ "#in book solution is t_o=54.77 us. The ans is incorrect as %pi is not muliplied in ans. Formulae mentioned in correct.\n",
+ "I_p=(V_s-V_o)*math.sqrt(C/L)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak current through diode=%.2f A\" %I_p)\n",
+ "v_D=-V_s+V_o \n",
+ "print(\"Voltage across diode = %.2f V\" %v_D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of diode = 172.07 us\n",
+ "Peak current through diode=164.32 A\n",
+ "Voltage across diode = -300.00 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page No 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=10 #ohm\n",
+ "L=0.001 #H\n",
+ "C=5*10**-6 #F\n",
+ "V_s=230 #V\n",
+ "xi=R/(2*L)\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t=math.pi/w_r \n",
+ "\n",
+ "#Results\n",
+ "print('Conduction time of diode=%.3f us'%(t*10**6))\n",
+ "t=0\n",
+ "di=V_s/L\n",
+ "print('Rate of change of current at t=0 is %.2f A/s' %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Conduction time of diode=237.482 us\n",
+ "Rate of change of current at t=0 is 230000.00 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7 Page No 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_or=100 #A\n",
+ "R=1.0 #assumption\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=I_or*2*R\n",
+ "I_o=V_m/(math.pi*R)\n",
+ "q=200 #Ah\n",
+ "t=q/I_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"time required to deliver charge=%.02f hrs\" %t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to deliver charge=3.14 hrs\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page No 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "P=1000 #W\n",
+ "R=V_s**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(2)*V_s/2\n",
+ "P_h=V_or**2/R \n",
+ "print(\"Power delivered to the heater = %.2f W\" %P_h)\n",
+ "V_m=math.sqrt(2)*230\n",
+ "I_m=V_m/R\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak value of diode current = %.2f A\" %I_m)\n",
+ "pf=V_or/V_s\n",
+ "print(\"Input power factor=%.2f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to the heater = 500.00 W\n",
+ "Peak value of diode current = 6.15 A\n",
+ "Input power factor=0.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9 Page No 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "V_m=V_s*math.sqrt(2)\n",
+ "E=150 #V\n",
+ "\n",
+ "#Calculations\n",
+ "theta1=math.degrees(E/(math.sqrt(2)*V_s))\n",
+ "R=8 #ohm\n",
+ "f=50 #Hz\n",
+ "I_o=(1/(2*math.pi*R))*((2*math.sqrt(2)*V_s*math.cos(math.radians(theta1)))-E*(math.pi-2*theta1*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg value of charging current=%.2f A\" %I_o)\n",
+ "P_d=E*I_o\n",
+ "print(\"\\npower delivered to battery=%.2f W\" %P_d)\n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V_s**2+E**2)*(math.pi-2*theta1*math.pi/180)+V_s**2*math.sin(math.radians(2*theta1))-4*V_m*E*math.cos(math.radians(theta1))))\n",
+ "print(\"\\nrms value of the load current=%.2f A\" %I_or)\n",
+ "pf=(E*I_o+I_or**2*R)/(V_s*I_or)\n",
+ "print(\"\\nsupply pf=%.3f\" %pf)\n",
+ "P_dd=I_or**2*R\n",
+ "print(\"\\npower dissipated in the resistor=%.2f W\" %P_dd)\n",
+ "q=1000.00 #Wh\n",
+ "t=q/P_d \n",
+ "print(\"\\ncharging time=%.2f hr\" %t)\n",
+ "n=P_d*100/(P_d+P_dd)\n",
+ "print(\"rectifier efficiency =%.2f \" %n)\n",
+ "PIV=math.sqrt(2)*V_s+E\n",
+ "print(\"PIV of diode=%.2f V\" %PIV)\n",
+ "#solutions have small variations due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg value of charging current=4.97 A\n",
+ "\n",
+ "power delivered to battery=745.11 W\n",
+ "\n",
+ "rms value of the load current=9.29 A\n",
+ "\n",
+ "supply pf=0.672\n",
+ "\n",
+ "power dissipated in the resistor=690.74 W\n",
+ "\n",
+ "charging time=1.34 hr\n",
+ "rectifier efficiency =51.89 \n",
+ "PIV of diode=475.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10 Page No 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "t_rr=40*10**-6 #s reverde recovery time\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*math.sqrt(2)*V_s/math.pi\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "f=50\n",
+ "V_r1=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg1=V_r1*100/V_o*10**3\n",
+ "f=2500\n",
+ "V_r2=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg2=V_r2*100/V_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"when f=50Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage=%.2f x 10^-3\" %v_avg1)\n",
+ "print(\"when f=2500Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage = %.3f\" %v_avg2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when f=50Hz\n",
+ "Percentage reduction in avg o/p voltage=3.95 x 10^-3\n",
+ "when f=2500Hz\n",
+ "Percentage reduction in avg o/p voltage = 9.549\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page No 79 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "R=10.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "print(\"Avg value of o/p voltage = %.2f V\" %V_o)\n",
+ "I_o=V_o/R\n",
+ "print(\"Avg value of o/p current = %.2f A\" %I_o)\n",
+ "I_DA=I_o/2\n",
+ "print(\"Avg value of diode current=%.2f A\" %I_DA)\n",
+ "I_Dr=I_o/math.sqrt(2) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"rms value of o/p current = %.2f A\" %I_o)\n",
+ "print(\"rms value of i/p current = %.2f A\" %I_o)\n",
+ "pf=(V_o/V_s)\n",
+ "print(\"supply pf = %.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg value of o/p voltage = 207.07 V\n",
+ "Avg value of o/p current = 20.71 A\n",
+ "Avg value of diode current=10.35 A\n",
+ "rms value of diode current=14.64 A\n",
+ "rms value of o/p current = 20.71 A\n",
+ "rms value of i/p current = 20.71 A\n",
+ "supply pf = 0.90\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12 Page No 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "R=1000.0 #ohm\n",
+ "R_D=20.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_om=V_m/(R+R_D) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak load current = %.2f A\" %I_om)\n",
+ "I_o=I_om/math.pi\n",
+ "print(\"dc load current = %.2f A\" %I_o)\n",
+ "V_D=I_o*R_D-V_m/math.pi\n",
+ "print(\"dc diode voltage = %.2f V\" %V_D)\n",
+ "V_on=V_m/math.pi\n",
+ "print(\"at no load, load voltage = %.2f V\" %V_on)\n",
+ "V_o1=I_o*R \n",
+ "print(\"at given load, load voltage = %.2f V\" %V_o1)\n",
+ "vr=(V_on-V_o1)*100/V_on \n",
+ "print(\"Voltage regulation(in percent)=%.2f\" %vr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Peak load current = 0.32 A\n",
+ "dc load current = 0.10 A\n",
+ "dc diode voltage = -101.51 V\n",
+ "at no load, load voltage = 103.54 V\n",
+ "at given load, load voltage = 101.51 V\n",
+ "Voltage regulation(in percent)=1.96\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13 Page No 82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_L=6.8 #V\n",
+ "V_smax=20*1.2 #V\n",
+ "V_smin=20*.8 #V\n",
+ "I_Lmax=30*1.5 #mA\n",
+ "I_Lmin=30*0.5 #mA\n",
+ "I_z=1 #mA\n",
+ "\n",
+ "#Calculations\n",
+ "R_smax=(V_smax-V_L)/((I_Lmin+I_z)*10**-3)\n",
+ "print(\"max source resistance = %.2f ohm\" %R_smax)\n",
+ "R_smin=(V_smin-V_L)/((I_Lmax+I_z)*10**-3) \n",
+ "print(\"Min source resistance = %.2f ohm\" %R_smin) #in book solution, error is committed in putting the values in formulea(printing error) but solution is correct\n",
+ "R_Lmax=V_L*1000/I_Lmin\n",
+ "print(\"Max load resistance = %.2f ohm\" %R_Lmax)\n",
+ "R_Lmin=V_L*1000/I_Lmax \n",
+ "V_d=0.6 #V\n",
+ "V_r=V_L-V_d\n",
+ "\n",
+ "#Results\n",
+ "print(\"Min load resistance=%.2f ohm\" %R_Lmin)\n",
+ "print(\"Voltage rating of zener diode=%.2f V\" %V_r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max source resistance = 1075.00 ohm\n",
+ "Min source resistance = 200.00 ohm\n",
+ "Max load resistance = 453.33 ohm\n",
+ "Min load resistance=151.11 ohm\n",
+ "Voltage rating of zener diode=6.20 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14 Page No 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I2=200*10**-6 #A\n",
+ "V_z=20 #V\n",
+ "R_G=500.0 #hm\n",
+ "\n",
+ "#Calculations\n",
+ "R2=(V_z/I2)-R_G\n",
+ "print(\"R2=%.2f kilo-ohm\" %(R2/1000))\n",
+ "\n",
+ "V_v=25 #V\n",
+ "I1=I2\n",
+ "R1=(V_v-V_z)/I1\n",
+ "\n",
+ "#Results\n",
+ "print(\"R1=%.0f kilo-ohm\"%(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2=99.50 kilo-ohm\n",
+ "R1=25 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=2*230 #V\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(math.sqrt(2)*V_s)/math.pi\n",
+ "R=60 #ohm\n",
+ "P_dc=(V_o)**2/R\n",
+ "TUF=0.2865\n",
+ "VA=P_dc/TUF\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"kVA rating of the transformer = %.2f kVA\" %(VA/1000));\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA rating of the transformer = 2.49 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=0.5 #turns ratio\n",
+ "I_o=10.0\n",
+ "V=230.0\n",
+ "V_s=V/tr\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "phi1=0\n",
+ "#displacemnt angle=0 as fundamnetal component of i/p source current in phase with source voltage\n",
+ "DF=math.cos(math.radians(phi1))\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*math.pi/math.pi)\n",
+ "CDF=I_s1/I_o\n",
+ "pf=CDF*DF\n",
+ "HF=math.sqrt((I_s/I_s1)**2-1)\n",
+ "CF=I_o/I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p voltage = %.2f V\" %V_o)\n",
+ "print(\"distortion factor = %.2f\" %DF)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"Current displacent factor=%.2f\" %CDF)\n",
+ "print(\"Harmonic factor = %.2f\" %HF)\n",
+ "print(\"Creast factor = %.2f\" %CF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p voltage = 414.15 V\n",
+ "distortion factor = 1.00\n",
+ "i/p pf=0.90\n",
+ "Current displacent factor=0.90\n",
+ "Harmonic factor = 0.48\n",
+ "Creast factor = 1.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=230.0\n",
+ "R=10.0\n",
+ "V_s=V_o*math.pi/(2*math.sqrt(2))\n",
+ "I_o=V_o/R\n",
+ "I_m=math.sqrt(2)*V_s/R\n",
+ "I_DAV=I_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "#avg value of diode current\n",
+ "I_Dr=I_m/2\n",
+ "PIV=math.sqrt(2)*V_s\n",
+ "I_s=I_m/math.sqrt(2)\n",
+ "TF=V_s*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak diode current=%.2f A\" %I_m)\n",
+ "print(\"I_DAV=%.2f A\" %I_DAV)\n",
+ "print(\"I_Dr=%.2f A\" %I_Dr) #rms value of diode current\n",
+ "print(\"PIV=%.1f V\" %PIV)\n",
+ "print(\"Transformer rating = %.2f kVA\" %(TF/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak diode current=36.13 A\n",
+ "I_DAV=11.50 A\n",
+ "I_Dr=18.06 A\n",
+ "PIV=361.3 V\n",
+ "Transformer rating = 6.53 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.18, Page No 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=5\n",
+ "V=1100.0\n",
+ "R=10.0\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"In case of 3ph-3pulse type\")\n",
+ "V_ph=V/tr\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*math.sqrt(3)*V_mp/(2*math.pi)\n",
+ "print(\"avg o/p voltage=%.1f V\" %V_o)\n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/3) \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3))) \n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "V_or=V_mp*math.sqrt((3/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3)))\n",
+ "P=(V_or**2)/R \n",
+ "print(\"\\npower delivered=%.1f W\" %P)\n",
+ "print(\"in case of 3ph-M6 type\")\n",
+ "V_ph=V_ph/2\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*V_mp/(math.pi) \n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/6) \n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6))) \n",
+ "V_or=V_mp*math.sqrt((6/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6)))\n",
+ "P=(V_or**2)/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"\\navg value of diode current=%.2f A\" %I_D)\n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"\\npower delivered=%.0f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "In case of 3ph-3pulse type\n",
+ "avg o/p voltage=257.3 V\n",
+ "\n",
+ "avg value of diode current=8.577 A\n",
+ "\n",
+ "rms value of diode current=15.10 A\n",
+ "\n",
+ "power delivered=6841.3 W\n",
+ "in case of 3ph-M6 type\n",
+ "avg o/p voltage=148.55 V\n",
+ "\n",
+ "avg value of diode current=2.48 A\n",
+ "\n",
+ "rms value of diode current=6.07 A\n",
+ "\n",
+ "power delivered=2211 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.19, Page No 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=400\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=V_o*math.pi/3\n",
+ "V_s=V_ml/(math.sqrt(2)*math.sqrt(3))\n",
+ "I_m=V_ml/R\n",
+ "I_s=.7804*I_m\n",
+ "tr=3*V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer rating=%.1f VA\" %tr)\n",
+ "I_Dr=.5518*I_m \n",
+ "print(\"\\nrms value of diode current=%.3f A\" %I_Dr)\n",
+ "I_D=I_m/math.pi \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "print(\"\\npeak diode current=%.2f A\" %I_m)\n",
+ "PIV=V_ml \n",
+ "print(\"\\nPIV=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer rating=16770.3 VA\n",
+ "\n",
+ "rms value of diode current=23.114 A\n",
+ "\n",
+ "avg value of diode current=13.333 A\n",
+ "\n",
+ "peak diode current=41.89 A\n",
+ "\n",
+ "PIV=418.88 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.20, Page No 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=230\n",
+ "E=240\n",
+ "R=8\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "V_o=3*V_ml/math.pi\n",
+ "I_o=(V_o-E)/R\n",
+ "P_b=E*I_o \n",
+ "P_d=E*I_o+I_o**2*R \n",
+ "phi1=0\n",
+ "math.cos(math.radians(phi1))\n",
+ "I_s1=2*math.sqrt(3)*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*2*math.pi/(3*math.pi))\n",
+ "CDF=I_s1/I_s \n",
+ "pf=DF*CDF \n",
+ "HF=math.sqrt(CDF**-2-1) \n",
+ "tr=math.sqrt(3)*V_l*I_o*math.sqrt(2/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Power delivered to battery=%.1f W\" %P_b)\n",
+ "print(\"Power delivered to load=%.2f W\" %P_d)\n",
+ "print(\"Displacement factor=%.2f\" %DF)\n",
+ "print(\"Current distortion factor=%.3f\" %CDF)\n",
+ "print(\"i/p pf=%.3f\"%pf)\n",
+ "print(\"Harmonic factor=%.2f\" %HF)\n",
+ "print(\"Tranformer rating=%.2f VA\" %tr)\n",
+ "#answers have small variations from the book due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to battery=2118.3 W\n",
+ "Power delivered to load=2741.48 W\n",
+ "Displacement factor=1.00\n",
+ "Current distortion factor=0.955\n",
+ "i/p pf=0.955\n",
+ "Harmonic factor=0.31\n",
+ "Tranformer rating=0.00 VA\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.21, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50 #Hz\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "R=400.0\n",
+ "RF=0.05\n",
+ "C=(1/(4*f*R))*(1+(1/(math.sqrt(2)*RF)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"capacitor value=%.2f uF\" %(C/10**-6))\n",
+ "V_o=V_m*(1-1/(4*f*R*C))\n",
+ "print(\"o/p voltage with filter=%.2f V\" %V_o)\n",
+ "V_o=2*V_m/math.pi \n",
+ "print(\"o/p voltage without filter=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "capacitor value=189.28 uF\n",
+ "o/p voltage with filter=303.79 V\n",
+ "o/p voltage without filter=207.07 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.22, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50\n",
+ "CRF=0.05\n",
+ "R=300\n",
+ "\n",
+ "#Calculations\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "print(\"L=%.2f H\" %L)\n",
+ "R=30\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nL=%.2f H\" %L)\n",
+ "L=0\n",
+ "CRF=.4715*R/math.sqrt(R**2+(2*2*math.pi*f*L)**2) \n",
+ "print(\"\\nCRF=%.2f\" %CRF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "L=4.48 H\n",
+ "\n",
+ "L=0.45 H\n",
+ "\n",
+ "CRF=0.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.23, Page No 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=50\n",
+ "L_L=10*10**-3\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "\n",
+ "#Calculations\n",
+ "C=10/(2*w*math.sqrt(R**2+(2*w*L_L)**2))\n",
+ "\n",
+ "#Results\n",
+ "print(\"C=%.2f uF\" %(C*10**6))\n",
+ "VRF=0.1\n",
+ "L=(1/(4*w**2*C))*((math.sqrt(2)/(3*VRF))+1)\n",
+ "print(\"\\nL=%.2f mH\" %(L*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C=315.83 uF\n",
+ "\n",
+ "L=45.83 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter3_2.ipynb b/_Power_Electronics/Chapter3_2.ipynb new file mode 100755 index 00000000..2e53ef9d --- /dev/null +++ b/_Power_Electronics/Chapter3_2.ipynb @@ -0,0 +1,1001 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 03 : Diode Circuits and Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page No 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0 #V\n",
+ "V_o=100.0 #V\n",
+ "L=100.0 #uH\n",
+ "C=30.0 #uF\n",
+ "\n",
+ "#Calculations\n",
+ "t_o=math.pi*math.sqrt(L*C)\n",
+ "print(\"conduction time of diode = %.2f us\" %t_o)\n",
+ "#in book solution is t_o=54.77 us. The ans is incorrect as %pi is not muliplied in ans. Formulae mentioned in correct.\n",
+ "I_p=(V_s-V_o)*math.sqrt(C/L)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak current through diode=%.2f A\" %I_p)\n",
+ "v_D=-V_s+V_o \n",
+ "print(\"Voltage across diode = %.2f V\" %v_D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of diode = 172.07 us\n",
+ "Peak current through diode=164.32 A\n",
+ "Voltage across diode = -300.00 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page No 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=10 #ohm\n",
+ "L=0.001 #H\n",
+ "C=5*10**-6 #F\n",
+ "V_s=230 #V\n",
+ "xi=R/(2*L)\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t=math.pi/w_r \n",
+ "\n",
+ "#Results\n",
+ "print('Conduction time of diode=%.3f us'%(t*10**6))\n",
+ "t=0\n",
+ "di=V_s/L\n",
+ "print('Rate of change of current at t=0 is %.2f A/s' %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Conduction time of diode=237.482 us\n",
+ "Rate of change of current at t=0 is 230000.00 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7 Page No 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_or=100 #A\n",
+ "R=1.0 #assumption\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=I_or*2*R\n",
+ "I_o=V_m/(math.pi*R)\n",
+ "q=200 #Ah\n",
+ "t=q/I_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"time required to deliver charge=%.02f hrs\" %t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to deliver charge=3.14 hrs\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page No 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "P=1000 #W\n",
+ "R=V_s**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(2)*V_s/2\n",
+ "P_h=V_or**2/R \n",
+ "print(\"Power delivered to the heater = %.2f W\" %P_h)\n",
+ "V_m=math.sqrt(2)*230\n",
+ "I_m=V_m/R\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak value of diode current = %.2f A\" %I_m)\n",
+ "pf=V_or/V_s\n",
+ "print(\"Input power factor=%.2f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to the heater = 500.00 W\n",
+ "Peak value of diode current = 6.15 A\n",
+ "Input power factor=0.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9 Page No 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "V_m=V_s*math.sqrt(2)\n",
+ "E=150 #V\n",
+ "\n",
+ "#Calculations\n",
+ "theta1=math.degrees(E/(math.sqrt(2)*V_s))\n",
+ "R=8 #ohm\n",
+ "f=50 #Hz\n",
+ "I_o=(1/(2*math.pi*R))*((2*math.sqrt(2)*V_s*math.cos(math.radians(theta1)))-E*(math.pi-2*theta1*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg value of charging current=%.2f A\" %I_o)\n",
+ "P_d=E*I_o\n",
+ "print(\"\\npower delivered to battery=%.2f W\" %P_d)\n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V_s**2+E**2)*(math.pi-2*theta1*math.pi/180)+V_s**2*math.sin(math.radians(2*theta1))-4*V_m*E*math.cos(math.radians(theta1))))\n",
+ "print(\"\\nrms value of the load current=%.2f A\" %I_or)\n",
+ "pf=(E*I_o+I_or**2*R)/(V_s*I_or)\n",
+ "print(\"\\nsupply pf=%.3f\" %pf)\n",
+ "P_dd=I_or**2*R\n",
+ "print(\"\\npower dissipated in the resistor=%.2f W\" %P_dd)\n",
+ "q=1000.00 #Wh\n",
+ "t=q/P_d \n",
+ "print(\"\\ncharging time=%.2f hr\" %t)\n",
+ "n=P_d*100/(P_d+P_dd)\n",
+ "print(\"rectifier efficiency =%.2f \" %n)\n",
+ "PIV=math.sqrt(2)*V_s+E\n",
+ "print(\"PIV of diode=%.2f V\" %PIV)\n",
+ "#solutions have small variations due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg value of charging current=4.97 A\n",
+ "\n",
+ "power delivered to battery=745.11 W\n",
+ "\n",
+ "rms value of the load current=9.29 A\n",
+ "\n",
+ "supply pf=0.672\n",
+ "\n",
+ "power dissipated in the resistor=690.74 W\n",
+ "\n",
+ "charging time=1.34 hr\n",
+ "rectifier efficiency =51.89 \n",
+ "PIV of diode=475.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10 Page No 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "t_rr=40*10**-6 #s reverde recovery time\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*math.sqrt(2)*V_s/math.pi\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "f=50\n",
+ "V_r1=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg1=V_r1*100/V_o*10**3\n",
+ "f=2500\n",
+ "V_r2=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg2=V_r2*100/V_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"when f=50Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage=%.2f x 10^-3\" %v_avg1)\n",
+ "print(\"when f=2500Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage = %.3f\" %v_avg2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when f=50Hz\n",
+ "Percentage reduction in avg o/p voltage=3.95 x 10^-3\n",
+ "when f=2500Hz\n",
+ "Percentage reduction in avg o/p voltage = 9.549\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page No 79 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "R=10.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "print(\"Avg value of o/p voltage = %.2f V\" %V_o)\n",
+ "I_o=V_o/R\n",
+ "print(\"Avg value of o/p current = %.2f A\" %I_o)\n",
+ "I_DA=I_o/2\n",
+ "print(\"Avg value of diode current=%.2f A\" %I_DA)\n",
+ "I_Dr=I_o/math.sqrt(2) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"rms value of o/p current = %.2f A\" %I_o)\n",
+ "print(\"rms value of i/p current = %.2f A\" %I_o)\n",
+ "pf=(V_o/V_s)\n",
+ "print(\"supply pf = %.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg value of o/p voltage = 207.07 V\n",
+ "Avg value of o/p current = 20.71 A\n",
+ "Avg value of diode current=10.35 A\n",
+ "rms value of diode current=14.64 A\n",
+ "rms value of o/p current = 20.71 A\n",
+ "rms value of i/p current = 20.71 A\n",
+ "supply pf = 0.90\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12 Page No 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "R=1000.0 #ohm\n",
+ "R_D=20.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_om=V_m/(R+R_D) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak load current = %.2f A\" %I_om)\n",
+ "I_o=I_om/math.pi\n",
+ "print(\"dc load current = %.2f A\" %I_o)\n",
+ "V_D=I_o*R_D-V_m/math.pi\n",
+ "print(\"dc diode voltage = %.2f V\" %V_D)\n",
+ "V_on=V_m/math.pi\n",
+ "print(\"at no load, load voltage = %.2f V\" %V_on)\n",
+ "V_o1=I_o*R \n",
+ "print(\"at given load, load voltage = %.2f V\" %V_o1)\n",
+ "vr=(V_on-V_o1)*100/V_on \n",
+ "print(\"Voltage regulation(in percent)=%.2f\" %vr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Peak load current = 0.32 A\n",
+ "dc load current = 0.10 A\n",
+ "dc diode voltage = -101.51 V\n",
+ "at no load, load voltage = 103.54 V\n",
+ "at given load, load voltage = 101.51 V\n",
+ "Voltage regulation(in percent)=1.96\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13 Page No 82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_L=6.8 #V\n",
+ "V_smax=20*1.2 #V\n",
+ "V_smin=20*.8 #V\n",
+ "I_Lmax=30*1.5 #mA\n",
+ "I_Lmin=30*0.5 #mA\n",
+ "I_z=1 #mA\n",
+ "\n",
+ "#Calculations\n",
+ "R_smax=(V_smax-V_L)/((I_Lmin+I_z)*10**-3)\n",
+ "print(\"max source resistance = %.2f ohm\" %R_smax)\n",
+ "R_smin=(V_smin-V_L)/((I_Lmax+I_z)*10**-3) \n",
+ "print(\"Min source resistance = %.2f ohm\" %R_smin) #in book solution, error is committed in putting the values in formulea(printing error) but solution is correct\n",
+ "R_Lmax=V_L*1000/I_Lmin\n",
+ "print(\"Max load resistance = %.2f ohm\" %R_Lmax)\n",
+ "R_Lmin=V_L*1000/I_Lmax \n",
+ "V_d=0.6 #V\n",
+ "V_r=V_L-V_d\n",
+ "\n",
+ "#Results\n",
+ "print(\"Min load resistance=%.2f ohm\" %R_Lmin)\n",
+ "print(\"Voltage rating of zener diode=%.2f V\" %V_r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max source resistance = 1075.00 ohm\n",
+ "Min source resistance = 200.00 ohm\n",
+ "Max load resistance = 453.33 ohm\n",
+ "Min load resistance=151.11 ohm\n",
+ "Voltage rating of zener diode=6.20 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14 Page No 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I2=200*10**-6 #A\n",
+ "V_z=20 #V\n",
+ "R_G=500.0 #hm\n",
+ "\n",
+ "#Calculations\n",
+ "R2=(V_z/I2)-R_G\n",
+ "print(\"R2=%.2f kilo-ohm\" %(R2/1000))\n",
+ "\n",
+ "V_v=25 #V\n",
+ "I1=I2\n",
+ "R1=(V_v-V_z)/I1\n",
+ "\n",
+ "#Results\n",
+ "print(\"R1=%.0f kilo-ohm\"%(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2=99.50 kilo-ohm\n",
+ "R1=25 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=2*230 #V\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(math.sqrt(2)*V_s)/math.pi\n",
+ "R=60 #ohm\n",
+ "P_dc=(V_o)**2/R\n",
+ "TUF=0.2865\n",
+ "VA=P_dc/TUF\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"kVA rating of the transformer = %.2f kVA\" %(VA/1000));\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA rating of the transformer = 2.49 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=0.5 #turns ratio\n",
+ "I_o=10.0\n",
+ "V=230.0\n",
+ "V_s=V/tr\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "phi1=0\n",
+ "#displacemnt angle=0 as fundamnetal component of i/p source current in phase with source voltage\n",
+ "DF=math.cos(math.radians(phi1))\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*math.pi/math.pi)\n",
+ "CDF=I_s1/I_o\n",
+ "pf=CDF*DF\n",
+ "HF=math.sqrt((I_s/I_s1)**2-1)\n",
+ "CF=I_o/I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p voltage = %.2f V\" %V_o)\n",
+ "print(\"distortion factor = %.2f\" %DF)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"Current displacent factor=%.2f\" %CDF)\n",
+ "print(\"Harmonic factor = %.2f\" %HF)\n",
+ "print(\"Creast factor = %.2f\" %CF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p voltage = 414.15 V\n",
+ "distortion factor = 1.00\n",
+ "i/p pf=0.90\n",
+ "Current displacent factor=0.90\n",
+ "Harmonic factor = 0.48\n",
+ "Creast factor = 1.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=230.0\n",
+ "R=10.0\n",
+ "V_s=V_o*math.pi/(2*math.sqrt(2))\n",
+ "I_o=V_o/R\n",
+ "I_m=math.sqrt(2)*V_s/R\n",
+ "I_DAV=I_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "#avg value of diode current\n",
+ "I_Dr=I_m/2\n",
+ "PIV=math.sqrt(2)*V_s\n",
+ "I_s=I_m/math.sqrt(2)\n",
+ "TF=V_s*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak diode current=%.2f A\" %I_m)\n",
+ "print(\"I_DAV=%.2f A\" %I_DAV)\n",
+ "print(\"I_Dr=%.2f A\" %I_Dr) #rms value of diode current\n",
+ "print(\"PIV=%.1f V\" %PIV)\n",
+ "print(\"Transformer rating = %.2f kVA\" %(TF/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak diode current=36.13 A\n",
+ "I_DAV=11.50 A\n",
+ "I_Dr=18.06 A\n",
+ "PIV=361.3 V\n",
+ "Transformer rating = 6.53 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.18, Page No 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=5\n",
+ "V=1100.0\n",
+ "R=10.0\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"In case of 3ph-3pulse type\")\n",
+ "V_ph=V/tr\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*math.sqrt(3)*V_mp/(2*math.pi)\n",
+ "print(\"avg o/p voltage=%.1f V\" %V_o)\n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/3) \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3))) \n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "V_or=V_mp*math.sqrt((3/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3)))\n",
+ "P=(V_or**2)/R \n",
+ "print(\"\\npower delivered=%.1f W\" %P)\n",
+ "print(\"in case of 3ph-M6 type\")\n",
+ "V_ph=V_ph/2\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*V_mp/(math.pi) \n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/6) \n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6))) \n",
+ "V_or=V_mp*math.sqrt((6/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6)))\n",
+ "P=(V_or**2)/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"\\navg value of diode current=%.2f A\" %I_D)\n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"\\npower delivered=%.0f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "In case of 3ph-3pulse type\n",
+ "avg o/p voltage=257.3 V\n",
+ "\n",
+ "avg value of diode current=8.577 A\n",
+ "\n",
+ "rms value of diode current=15.10 A\n",
+ "\n",
+ "power delivered=6841.3 W\n",
+ "in case of 3ph-M6 type\n",
+ "avg o/p voltage=148.55 V\n",
+ "\n",
+ "avg value of diode current=2.48 A\n",
+ "\n",
+ "rms value of diode current=6.07 A\n",
+ "\n",
+ "power delivered=2211 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.19, Page No 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=400\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=V_o*math.pi/3\n",
+ "V_s=V_ml/(math.sqrt(2)*math.sqrt(3))\n",
+ "I_m=V_ml/R\n",
+ "I_s=.7804*I_m\n",
+ "tr=3*V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer rating=%.1f VA\" %tr)\n",
+ "I_Dr=.5518*I_m \n",
+ "print(\"\\nrms value of diode current=%.3f A\" %I_Dr)\n",
+ "I_D=I_m/math.pi \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "print(\"\\npeak diode current=%.2f A\" %I_m)\n",
+ "PIV=V_ml \n",
+ "print(\"\\nPIV=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer rating=16770.3 VA\n",
+ "\n",
+ "rms value of diode current=23.114 A\n",
+ "\n",
+ "avg value of diode current=13.333 A\n",
+ "\n",
+ "peak diode current=41.89 A\n",
+ "\n",
+ "PIV=418.88 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.20, Page No 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=230\n",
+ "E=240\n",
+ "R=8\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "V_o=3*V_ml/math.pi\n",
+ "I_o=(V_o-E)/R\n",
+ "P_b=E*I_o \n",
+ "P_d=E*I_o+I_o**2*R \n",
+ "phi1=0\n",
+ "math.cos(math.radians(phi1))\n",
+ "I_s1=2*math.sqrt(3)*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*2*math.pi/(3*math.pi))\n",
+ "CDF=I_s1/I_s \n",
+ "pf=DF*CDF \n",
+ "HF=math.sqrt(CDF**-2-1) \n",
+ "tr=math.sqrt(3)*V_l*I_o*math.sqrt(2/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Power delivered to battery=%.1f W\" %P_b)\n",
+ "print(\"Power delivered to load=%.2f W\" %P_d)\n",
+ "print(\"Displacement factor=%.2f\" %DF)\n",
+ "print(\"Current distortion factor=%.3f\" %CDF)\n",
+ "print(\"i/p pf=%.3f\"%pf)\n",
+ "print(\"Harmonic factor=%.2f\" %HF)\n",
+ "print(\"Tranformer rating=%.2f VA\" %tr)\n",
+ "#answers have small variations from the book due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to battery=2118.3 W\n",
+ "Power delivered to load=2741.48 W\n",
+ "Displacement factor=1.00\n",
+ "Current distortion factor=0.955\n",
+ "i/p pf=0.955\n",
+ "Harmonic factor=0.31\n",
+ "Tranformer rating=0.00 VA\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.21, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50 #Hz\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "R=400.0\n",
+ "RF=0.05\n",
+ "C=(1/(4*f*R))*(1+(1/(math.sqrt(2)*RF)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"capacitor value=%.2f uF\" %(C/10**-6))\n",
+ "V_o=V_m*(1-1/(4*f*R*C))\n",
+ "print(\"o/p voltage with filter=%.2f V\" %V_o)\n",
+ "V_o=2*V_m/math.pi \n",
+ "print(\"o/p voltage without filter=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "capacitor value=189.28 uF\n",
+ "o/p voltage with filter=303.79 V\n",
+ "o/p voltage without filter=207.07 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.22, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50\n",
+ "CRF=0.05\n",
+ "R=300\n",
+ "\n",
+ "#Calculations\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "print(\"L=%.2f H\" %L)\n",
+ "R=30\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nL=%.2f H\" %L)\n",
+ "L=0\n",
+ "CRF=.4715*R/math.sqrt(R**2+(2*2*math.pi*f*L)**2) \n",
+ "print(\"\\nCRF=%.2f\" %CRF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "L=4.48 H\n",
+ "\n",
+ "L=0.45 H\n",
+ "\n",
+ "CRF=0.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.23, Page No 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=50\n",
+ "L_L=10*10**-3\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "\n",
+ "#Calculations\n",
+ "C=10/(2*w*math.sqrt(R**2+(2*w*L_L)**2))\n",
+ "\n",
+ "#Results\n",
+ "print(\"C=%.2f uF\" %(C*10**6))\n",
+ "VRF=0.1\n",
+ "L=(1/(4*w**2*C))*((math.sqrt(2)/(3*VRF))+1)\n",
+ "print(\"\\nL=%.2f mH\" %(L*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C=315.83 uF\n",
+ "\n",
+ "L=45.83 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter3_3.ipynb b/_Power_Electronics/Chapter3_3.ipynb new file mode 100755 index 00000000..2e53ef9d --- /dev/null +++ b/_Power_Electronics/Chapter3_3.ipynb @@ -0,0 +1,1001 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 03 : Diode Circuits and Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page No 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0 #V\n",
+ "V_o=100.0 #V\n",
+ "L=100.0 #uH\n",
+ "C=30.0 #uF\n",
+ "\n",
+ "#Calculations\n",
+ "t_o=math.pi*math.sqrt(L*C)\n",
+ "print(\"conduction time of diode = %.2f us\" %t_o)\n",
+ "#in book solution is t_o=54.77 us. The ans is incorrect as %pi is not muliplied in ans. Formulae mentioned in correct.\n",
+ "I_p=(V_s-V_o)*math.sqrt(C/L)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak current through diode=%.2f A\" %I_p)\n",
+ "v_D=-V_s+V_o \n",
+ "print(\"Voltage across diode = %.2f V\" %v_D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of diode = 172.07 us\n",
+ "Peak current through diode=164.32 A\n",
+ "Voltage across diode = -300.00 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page No 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=10 #ohm\n",
+ "L=0.001 #H\n",
+ "C=5*10**-6 #F\n",
+ "V_s=230 #V\n",
+ "xi=R/(2*L)\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t=math.pi/w_r \n",
+ "\n",
+ "#Results\n",
+ "print('Conduction time of diode=%.3f us'%(t*10**6))\n",
+ "t=0\n",
+ "di=V_s/L\n",
+ "print('Rate of change of current at t=0 is %.2f A/s' %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Conduction time of diode=237.482 us\n",
+ "Rate of change of current at t=0 is 230000.00 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7 Page No 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_or=100 #A\n",
+ "R=1.0 #assumption\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=I_or*2*R\n",
+ "I_o=V_m/(math.pi*R)\n",
+ "q=200 #Ah\n",
+ "t=q/I_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"time required to deliver charge=%.02f hrs\" %t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to deliver charge=3.14 hrs\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page No 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "P=1000 #W\n",
+ "R=V_s**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(2)*V_s/2\n",
+ "P_h=V_or**2/R \n",
+ "print(\"Power delivered to the heater = %.2f W\" %P_h)\n",
+ "V_m=math.sqrt(2)*230\n",
+ "I_m=V_m/R\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak value of diode current = %.2f A\" %I_m)\n",
+ "pf=V_or/V_s\n",
+ "print(\"Input power factor=%.2f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to the heater = 500.00 W\n",
+ "Peak value of diode current = 6.15 A\n",
+ "Input power factor=0.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9 Page No 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "V_m=V_s*math.sqrt(2)\n",
+ "E=150 #V\n",
+ "\n",
+ "#Calculations\n",
+ "theta1=math.degrees(E/(math.sqrt(2)*V_s))\n",
+ "R=8 #ohm\n",
+ "f=50 #Hz\n",
+ "I_o=(1/(2*math.pi*R))*((2*math.sqrt(2)*V_s*math.cos(math.radians(theta1)))-E*(math.pi-2*theta1*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg value of charging current=%.2f A\" %I_o)\n",
+ "P_d=E*I_o\n",
+ "print(\"\\npower delivered to battery=%.2f W\" %P_d)\n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V_s**2+E**2)*(math.pi-2*theta1*math.pi/180)+V_s**2*math.sin(math.radians(2*theta1))-4*V_m*E*math.cos(math.radians(theta1))))\n",
+ "print(\"\\nrms value of the load current=%.2f A\" %I_or)\n",
+ "pf=(E*I_o+I_or**2*R)/(V_s*I_or)\n",
+ "print(\"\\nsupply pf=%.3f\" %pf)\n",
+ "P_dd=I_or**2*R\n",
+ "print(\"\\npower dissipated in the resistor=%.2f W\" %P_dd)\n",
+ "q=1000.00 #Wh\n",
+ "t=q/P_d \n",
+ "print(\"\\ncharging time=%.2f hr\" %t)\n",
+ "n=P_d*100/(P_d+P_dd)\n",
+ "print(\"rectifier efficiency =%.2f \" %n)\n",
+ "PIV=math.sqrt(2)*V_s+E\n",
+ "print(\"PIV of diode=%.2f V\" %PIV)\n",
+ "#solutions have small variations due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg value of charging current=4.97 A\n",
+ "\n",
+ "power delivered to battery=745.11 W\n",
+ "\n",
+ "rms value of the load current=9.29 A\n",
+ "\n",
+ "supply pf=0.672\n",
+ "\n",
+ "power dissipated in the resistor=690.74 W\n",
+ "\n",
+ "charging time=1.34 hr\n",
+ "rectifier efficiency =51.89 \n",
+ "PIV of diode=475.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10 Page No 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "t_rr=40*10**-6 #s reverde recovery time\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*math.sqrt(2)*V_s/math.pi\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "f=50\n",
+ "V_r1=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg1=V_r1*100/V_o*10**3\n",
+ "f=2500\n",
+ "V_r2=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg2=V_r2*100/V_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"when f=50Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage=%.2f x 10^-3\" %v_avg1)\n",
+ "print(\"when f=2500Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage = %.3f\" %v_avg2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when f=50Hz\n",
+ "Percentage reduction in avg o/p voltage=3.95 x 10^-3\n",
+ "when f=2500Hz\n",
+ "Percentage reduction in avg o/p voltage = 9.549\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page No 79 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "R=10.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "print(\"Avg value of o/p voltage = %.2f V\" %V_o)\n",
+ "I_o=V_o/R\n",
+ "print(\"Avg value of o/p current = %.2f A\" %I_o)\n",
+ "I_DA=I_o/2\n",
+ "print(\"Avg value of diode current=%.2f A\" %I_DA)\n",
+ "I_Dr=I_o/math.sqrt(2) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"rms value of o/p current = %.2f A\" %I_o)\n",
+ "print(\"rms value of i/p current = %.2f A\" %I_o)\n",
+ "pf=(V_o/V_s)\n",
+ "print(\"supply pf = %.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg value of o/p voltage = 207.07 V\n",
+ "Avg value of o/p current = 20.71 A\n",
+ "Avg value of diode current=10.35 A\n",
+ "rms value of diode current=14.64 A\n",
+ "rms value of o/p current = 20.71 A\n",
+ "rms value of i/p current = 20.71 A\n",
+ "supply pf = 0.90\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12 Page No 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "R=1000.0 #ohm\n",
+ "R_D=20.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_om=V_m/(R+R_D) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak load current = %.2f A\" %I_om)\n",
+ "I_o=I_om/math.pi\n",
+ "print(\"dc load current = %.2f A\" %I_o)\n",
+ "V_D=I_o*R_D-V_m/math.pi\n",
+ "print(\"dc diode voltage = %.2f V\" %V_D)\n",
+ "V_on=V_m/math.pi\n",
+ "print(\"at no load, load voltage = %.2f V\" %V_on)\n",
+ "V_o1=I_o*R \n",
+ "print(\"at given load, load voltage = %.2f V\" %V_o1)\n",
+ "vr=(V_on-V_o1)*100/V_on \n",
+ "print(\"Voltage regulation(in percent)=%.2f\" %vr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Peak load current = 0.32 A\n",
+ "dc load current = 0.10 A\n",
+ "dc diode voltage = -101.51 V\n",
+ "at no load, load voltage = 103.54 V\n",
+ "at given load, load voltage = 101.51 V\n",
+ "Voltage regulation(in percent)=1.96\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13 Page No 82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_L=6.8 #V\n",
+ "V_smax=20*1.2 #V\n",
+ "V_smin=20*.8 #V\n",
+ "I_Lmax=30*1.5 #mA\n",
+ "I_Lmin=30*0.5 #mA\n",
+ "I_z=1 #mA\n",
+ "\n",
+ "#Calculations\n",
+ "R_smax=(V_smax-V_L)/((I_Lmin+I_z)*10**-3)\n",
+ "print(\"max source resistance = %.2f ohm\" %R_smax)\n",
+ "R_smin=(V_smin-V_L)/((I_Lmax+I_z)*10**-3) \n",
+ "print(\"Min source resistance = %.2f ohm\" %R_smin) #in book solution, error is committed in putting the values in formulea(printing error) but solution is correct\n",
+ "R_Lmax=V_L*1000/I_Lmin\n",
+ "print(\"Max load resistance = %.2f ohm\" %R_Lmax)\n",
+ "R_Lmin=V_L*1000/I_Lmax \n",
+ "V_d=0.6 #V\n",
+ "V_r=V_L-V_d\n",
+ "\n",
+ "#Results\n",
+ "print(\"Min load resistance=%.2f ohm\" %R_Lmin)\n",
+ "print(\"Voltage rating of zener diode=%.2f V\" %V_r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max source resistance = 1075.00 ohm\n",
+ "Min source resistance = 200.00 ohm\n",
+ "Max load resistance = 453.33 ohm\n",
+ "Min load resistance=151.11 ohm\n",
+ "Voltage rating of zener diode=6.20 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14 Page No 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I2=200*10**-6 #A\n",
+ "V_z=20 #V\n",
+ "R_G=500.0 #hm\n",
+ "\n",
+ "#Calculations\n",
+ "R2=(V_z/I2)-R_G\n",
+ "print(\"R2=%.2f kilo-ohm\" %(R2/1000))\n",
+ "\n",
+ "V_v=25 #V\n",
+ "I1=I2\n",
+ "R1=(V_v-V_z)/I1\n",
+ "\n",
+ "#Results\n",
+ "print(\"R1=%.0f kilo-ohm\"%(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2=99.50 kilo-ohm\n",
+ "R1=25 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=2*230 #V\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(math.sqrt(2)*V_s)/math.pi\n",
+ "R=60 #ohm\n",
+ "P_dc=(V_o)**2/R\n",
+ "TUF=0.2865\n",
+ "VA=P_dc/TUF\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"kVA rating of the transformer = %.2f kVA\" %(VA/1000));\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA rating of the transformer = 2.49 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=0.5 #turns ratio\n",
+ "I_o=10.0\n",
+ "V=230.0\n",
+ "V_s=V/tr\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "phi1=0\n",
+ "#displacemnt angle=0 as fundamnetal component of i/p source current in phase with source voltage\n",
+ "DF=math.cos(math.radians(phi1))\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*math.pi/math.pi)\n",
+ "CDF=I_s1/I_o\n",
+ "pf=CDF*DF\n",
+ "HF=math.sqrt((I_s/I_s1)**2-1)\n",
+ "CF=I_o/I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p voltage = %.2f V\" %V_o)\n",
+ "print(\"distortion factor = %.2f\" %DF)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"Current displacent factor=%.2f\" %CDF)\n",
+ "print(\"Harmonic factor = %.2f\" %HF)\n",
+ "print(\"Creast factor = %.2f\" %CF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p voltage = 414.15 V\n",
+ "distortion factor = 1.00\n",
+ "i/p pf=0.90\n",
+ "Current displacent factor=0.90\n",
+ "Harmonic factor = 0.48\n",
+ "Creast factor = 1.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=230.0\n",
+ "R=10.0\n",
+ "V_s=V_o*math.pi/(2*math.sqrt(2))\n",
+ "I_o=V_o/R\n",
+ "I_m=math.sqrt(2)*V_s/R\n",
+ "I_DAV=I_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "#avg value of diode current\n",
+ "I_Dr=I_m/2\n",
+ "PIV=math.sqrt(2)*V_s\n",
+ "I_s=I_m/math.sqrt(2)\n",
+ "TF=V_s*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak diode current=%.2f A\" %I_m)\n",
+ "print(\"I_DAV=%.2f A\" %I_DAV)\n",
+ "print(\"I_Dr=%.2f A\" %I_Dr) #rms value of diode current\n",
+ "print(\"PIV=%.1f V\" %PIV)\n",
+ "print(\"Transformer rating = %.2f kVA\" %(TF/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak diode current=36.13 A\n",
+ "I_DAV=11.50 A\n",
+ "I_Dr=18.06 A\n",
+ "PIV=361.3 V\n",
+ "Transformer rating = 6.53 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.18, Page No 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=5\n",
+ "V=1100.0\n",
+ "R=10.0\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"In case of 3ph-3pulse type\")\n",
+ "V_ph=V/tr\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*math.sqrt(3)*V_mp/(2*math.pi)\n",
+ "print(\"avg o/p voltage=%.1f V\" %V_o)\n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/3) \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3))) \n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "V_or=V_mp*math.sqrt((3/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3)))\n",
+ "P=(V_or**2)/R \n",
+ "print(\"\\npower delivered=%.1f W\" %P)\n",
+ "print(\"in case of 3ph-M6 type\")\n",
+ "V_ph=V_ph/2\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*V_mp/(math.pi) \n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/6) \n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6))) \n",
+ "V_or=V_mp*math.sqrt((6/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6)))\n",
+ "P=(V_or**2)/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"\\navg value of diode current=%.2f A\" %I_D)\n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"\\npower delivered=%.0f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "In case of 3ph-3pulse type\n",
+ "avg o/p voltage=257.3 V\n",
+ "\n",
+ "avg value of diode current=8.577 A\n",
+ "\n",
+ "rms value of diode current=15.10 A\n",
+ "\n",
+ "power delivered=6841.3 W\n",
+ "in case of 3ph-M6 type\n",
+ "avg o/p voltage=148.55 V\n",
+ "\n",
+ "avg value of diode current=2.48 A\n",
+ "\n",
+ "rms value of diode current=6.07 A\n",
+ "\n",
+ "power delivered=2211 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.19, Page No 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=400\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=V_o*math.pi/3\n",
+ "V_s=V_ml/(math.sqrt(2)*math.sqrt(3))\n",
+ "I_m=V_ml/R\n",
+ "I_s=.7804*I_m\n",
+ "tr=3*V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer rating=%.1f VA\" %tr)\n",
+ "I_Dr=.5518*I_m \n",
+ "print(\"\\nrms value of diode current=%.3f A\" %I_Dr)\n",
+ "I_D=I_m/math.pi \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "print(\"\\npeak diode current=%.2f A\" %I_m)\n",
+ "PIV=V_ml \n",
+ "print(\"\\nPIV=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer rating=16770.3 VA\n",
+ "\n",
+ "rms value of diode current=23.114 A\n",
+ "\n",
+ "avg value of diode current=13.333 A\n",
+ "\n",
+ "peak diode current=41.89 A\n",
+ "\n",
+ "PIV=418.88 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.20, Page No 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=230\n",
+ "E=240\n",
+ "R=8\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "V_o=3*V_ml/math.pi\n",
+ "I_o=(V_o-E)/R\n",
+ "P_b=E*I_o \n",
+ "P_d=E*I_o+I_o**2*R \n",
+ "phi1=0\n",
+ "math.cos(math.radians(phi1))\n",
+ "I_s1=2*math.sqrt(3)*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*2*math.pi/(3*math.pi))\n",
+ "CDF=I_s1/I_s \n",
+ "pf=DF*CDF \n",
+ "HF=math.sqrt(CDF**-2-1) \n",
+ "tr=math.sqrt(3)*V_l*I_o*math.sqrt(2/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Power delivered to battery=%.1f W\" %P_b)\n",
+ "print(\"Power delivered to load=%.2f W\" %P_d)\n",
+ "print(\"Displacement factor=%.2f\" %DF)\n",
+ "print(\"Current distortion factor=%.3f\" %CDF)\n",
+ "print(\"i/p pf=%.3f\"%pf)\n",
+ "print(\"Harmonic factor=%.2f\" %HF)\n",
+ "print(\"Tranformer rating=%.2f VA\" %tr)\n",
+ "#answers have small variations from the book due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to battery=2118.3 W\n",
+ "Power delivered to load=2741.48 W\n",
+ "Displacement factor=1.00\n",
+ "Current distortion factor=0.955\n",
+ "i/p pf=0.955\n",
+ "Harmonic factor=0.31\n",
+ "Tranformer rating=0.00 VA\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.21, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50 #Hz\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "R=400.0\n",
+ "RF=0.05\n",
+ "C=(1/(4*f*R))*(1+(1/(math.sqrt(2)*RF)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"capacitor value=%.2f uF\" %(C/10**-6))\n",
+ "V_o=V_m*(1-1/(4*f*R*C))\n",
+ "print(\"o/p voltage with filter=%.2f V\" %V_o)\n",
+ "V_o=2*V_m/math.pi \n",
+ "print(\"o/p voltage without filter=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "capacitor value=189.28 uF\n",
+ "o/p voltage with filter=303.79 V\n",
+ "o/p voltage without filter=207.07 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.22, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50\n",
+ "CRF=0.05\n",
+ "R=300\n",
+ "\n",
+ "#Calculations\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "print(\"L=%.2f H\" %L)\n",
+ "R=30\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nL=%.2f H\" %L)\n",
+ "L=0\n",
+ "CRF=.4715*R/math.sqrt(R**2+(2*2*math.pi*f*L)**2) \n",
+ "print(\"\\nCRF=%.2f\" %CRF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "L=4.48 H\n",
+ "\n",
+ "L=0.45 H\n",
+ "\n",
+ "CRF=0.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.23, Page No 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=50\n",
+ "L_L=10*10**-3\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "\n",
+ "#Calculations\n",
+ "C=10/(2*w*math.sqrt(R**2+(2*w*L_L)**2))\n",
+ "\n",
+ "#Results\n",
+ "print(\"C=%.2f uF\" %(C*10**6))\n",
+ "VRF=0.1\n",
+ "L=(1/(4*w**2*C))*((math.sqrt(2)/(3*VRF))+1)\n",
+ "print(\"\\nL=%.2f mH\" %(L*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C=315.83 uF\n",
+ "\n",
+ "L=45.83 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter3_4.ipynb b/_Power_Electronics/Chapter3_4.ipynb new file mode 100755 index 00000000..2e53ef9d --- /dev/null +++ b/_Power_Electronics/Chapter3_4.ipynb @@ -0,0 +1,1001 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 03 : Diode Circuits and Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page No 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0 #V\n",
+ "V_o=100.0 #V\n",
+ "L=100.0 #uH\n",
+ "C=30.0 #uF\n",
+ "\n",
+ "#Calculations\n",
+ "t_o=math.pi*math.sqrt(L*C)\n",
+ "print(\"conduction time of diode = %.2f us\" %t_o)\n",
+ "#in book solution is t_o=54.77 us. The ans is incorrect as %pi is not muliplied in ans. Formulae mentioned in correct.\n",
+ "I_p=(V_s-V_o)*math.sqrt(C/L)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak current through diode=%.2f A\" %I_p)\n",
+ "v_D=-V_s+V_o \n",
+ "print(\"Voltage across diode = %.2f V\" %v_D)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of diode = 172.07 us\n",
+ "Peak current through diode=164.32 A\n",
+ "Voltage across diode = -300.00 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page No 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=10 #ohm\n",
+ "L=0.001 #H\n",
+ "C=5*10**-6 #F\n",
+ "V_s=230 #V\n",
+ "xi=R/(2*L)\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t=math.pi/w_r \n",
+ "\n",
+ "#Results\n",
+ "print('Conduction time of diode=%.3f us'%(t*10**6))\n",
+ "t=0\n",
+ "di=V_s/L\n",
+ "print('Rate of change of current at t=0 is %.2f A/s' %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Conduction time of diode=237.482 us\n",
+ "Rate of change of current at t=0 is 230000.00 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7 Page No 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I_or=100 #A\n",
+ "R=1.0 #assumption\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=I_or*2*R\n",
+ "I_o=V_m/(math.pi*R)\n",
+ "q=200 #Ah\n",
+ "t=q/I_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"time required to deliver charge=%.02f hrs\" %t)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time required to deliver charge=3.14 hrs\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page No 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "P=1000 #W\n",
+ "R=V_s**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(2)*V_s/2\n",
+ "P_h=V_or**2/R \n",
+ "print(\"Power delivered to the heater = %.2f W\" %P_h)\n",
+ "V_m=math.sqrt(2)*230\n",
+ "I_m=V_m/R\n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak value of diode current = %.2f A\" %I_m)\n",
+ "pf=V_or/V_s\n",
+ "print(\"Input power factor=%.2f\" %pf)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to the heater = 500.00 W\n",
+ "Peak value of diode current = 6.15 A\n",
+ "Input power factor=0.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9 Page No 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "V_m=V_s*math.sqrt(2)\n",
+ "E=150 #V\n",
+ "\n",
+ "#Calculations\n",
+ "theta1=math.degrees(E/(math.sqrt(2)*V_s))\n",
+ "R=8 #ohm\n",
+ "f=50 #Hz\n",
+ "I_o=(1/(2*math.pi*R))*((2*math.sqrt(2)*V_s*math.cos(math.radians(theta1)))-E*(math.pi-2*theta1*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg value of charging current=%.2f A\" %I_o)\n",
+ "P_d=E*I_o\n",
+ "print(\"\\npower delivered to battery=%.2f W\" %P_d)\n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V_s**2+E**2)*(math.pi-2*theta1*math.pi/180)+V_s**2*math.sin(math.radians(2*theta1))-4*V_m*E*math.cos(math.radians(theta1))))\n",
+ "print(\"\\nrms value of the load current=%.2f A\" %I_or)\n",
+ "pf=(E*I_o+I_or**2*R)/(V_s*I_or)\n",
+ "print(\"\\nsupply pf=%.3f\" %pf)\n",
+ "P_dd=I_or**2*R\n",
+ "print(\"\\npower dissipated in the resistor=%.2f W\" %P_dd)\n",
+ "q=1000.00 #Wh\n",
+ "t=q/P_d \n",
+ "print(\"\\ncharging time=%.2f hr\" %t)\n",
+ "n=P_d*100/(P_d+P_dd)\n",
+ "print(\"rectifier efficiency =%.2f \" %n)\n",
+ "PIV=math.sqrt(2)*V_s+E\n",
+ "print(\"PIV of diode=%.2f V\" %PIV)\n",
+ "#solutions have small variations due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg value of charging current=4.97 A\n",
+ "\n",
+ "power delivered to battery=745.11 W\n",
+ "\n",
+ "rms value of the load current=9.29 A\n",
+ "\n",
+ "supply pf=0.672\n",
+ "\n",
+ "power dissipated in the resistor=690.74 W\n",
+ "\n",
+ "charging time=1.34 hr\n",
+ "rectifier efficiency =51.89 \n",
+ "PIV of diode=475.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10 Page No 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "t_rr=40*10**-6 #s reverde recovery time\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*math.sqrt(2)*V_s/math.pi\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "f=50\n",
+ "V_r1=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg1=V_r1*100/V_o*10**3\n",
+ "f=2500\n",
+ "V_r2=(V_m/math.pi)*(1-math.cos(math.radians(2*math.pi*f*t_rr*180/math.pi)))\n",
+ "v_avg2=V_r2*100/V_o\n",
+ "\n",
+ "#Results\n",
+ "print(\"when f=50Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage=%.2f x 10^-3\" %v_avg1)\n",
+ "print(\"when f=2500Hz\")\n",
+ "print(\"Percentage reduction in avg o/p voltage = %.3f\" %v_avg2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when f=50Hz\n",
+ "Percentage reduction in avg o/p voltage=3.95 x 10^-3\n",
+ "when f=2500Hz\n",
+ "Percentage reduction in avg o/p voltage = 9.549\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page No 79 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230 #V\n",
+ "R=10.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "print(\"Avg value of o/p voltage = %.2f V\" %V_o)\n",
+ "I_o=V_o/R\n",
+ "print(\"Avg value of o/p current = %.2f A\" %I_o)\n",
+ "I_DA=I_o/2\n",
+ "print(\"Avg value of diode current=%.2f A\" %I_DA)\n",
+ "I_Dr=I_o/math.sqrt(2) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"rms value of o/p current = %.2f A\" %I_o)\n",
+ "print(\"rms value of i/p current = %.2f A\" %I_o)\n",
+ "pf=(V_o/V_s)\n",
+ "print(\"supply pf = %.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Avg value of o/p voltage = 207.07 V\n",
+ "Avg value of o/p current = 20.71 A\n",
+ "Avg value of diode current=10.35 A\n",
+ "rms value of diode current=14.64 A\n",
+ "rms value of o/p current = 20.71 A\n",
+ "rms value of i/p current = 20.71 A\n",
+ "supply pf = 0.90\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12 Page No 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "R=1000.0 #ohm\n",
+ "R_D=20.0 #ohm\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "I_om=V_m/(R+R_D) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Peak load current = %.2f A\" %I_om)\n",
+ "I_o=I_om/math.pi\n",
+ "print(\"dc load current = %.2f A\" %I_o)\n",
+ "V_D=I_o*R_D-V_m/math.pi\n",
+ "print(\"dc diode voltage = %.2f V\" %V_D)\n",
+ "V_on=V_m/math.pi\n",
+ "print(\"at no load, load voltage = %.2f V\" %V_on)\n",
+ "V_o1=I_o*R \n",
+ "print(\"at given load, load voltage = %.2f V\" %V_o1)\n",
+ "vr=(V_on-V_o1)*100/V_on \n",
+ "print(\"Voltage regulation(in percent)=%.2f\" %vr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Peak load current = 0.32 A\n",
+ "dc load current = 0.10 A\n",
+ "dc diode voltage = -101.51 V\n",
+ "at no load, load voltage = 103.54 V\n",
+ "at given load, load voltage = 101.51 V\n",
+ "Voltage regulation(in percent)=1.96\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13 Page No 82"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_L=6.8 #V\n",
+ "V_smax=20*1.2 #V\n",
+ "V_smin=20*.8 #V\n",
+ "I_Lmax=30*1.5 #mA\n",
+ "I_Lmin=30*0.5 #mA\n",
+ "I_z=1 #mA\n",
+ "\n",
+ "#Calculations\n",
+ "R_smax=(V_smax-V_L)/((I_Lmin+I_z)*10**-3)\n",
+ "print(\"max source resistance = %.2f ohm\" %R_smax)\n",
+ "R_smin=(V_smin-V_L)/((I_Lmax+I_z)*10**-3) \n",
+ "print(\"Min source resistance = %.2f ohm\" %R_smin) #in book solution, error is committed in putting the values in formulea(printing error) but solution is correct\n",
+ "R_Lmax=V_L*1000/I_Lmin\n",
+ "print(\"Max load resistance = %.2f ohm\" %R_Lmax)\n",
+ "R_Lmin=V_L*1000/I_Lmax \n",
+ "V_d=0.6 #V\n",
+ "V_r=V_L-V_d\n",
+ "\n",
+ "#Results\n",
+ "print(\"Min load resistance=%.2f ohm\" %R_Lmin)\n",
+ "print(\"Voltage rating of zener diode=%.2f V\" %V_r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max source resistance = 1075.00 ohm\n",
+ "Min source resistance = 200.00 ohm\n",
+ "Max load resistance = 453.33 ohm\n",
+ "Min load resistance=151.11 ohm\n",
+ "Voltage rating of zener diode=6.20 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14 Page No 83"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "I2=200*10**-6 #A\n",
+ "V_z=20 #V\n",
+ "R_G=500.0 #hm\n",
+ "\n",
+ "#Calculations\n",
+ "R2=(V_z/I2)-R_G\n",
+ "print(\"R2=%.2f kilo-ohm\" %(R2/1000))\n",
+ "\n",
+ "V_v=25 #V\n",
+ "I1=I2\n",
+ "R1=(V_v-V_z)/I1\n",
+ "\n",
+ "#Results\n",
+ "print(\"R1=%.0f kilo-ohm\"%(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R2=99.50 kilo-ohm\n",
+ "R1=25 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=2*230 #V\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(math.sqrt(2)*V_s)/math.pi\n",
+ "R=60 #ohm\n",
+ "P_dc=(V_o)**2/R\n",
+ "TUF=0.2865\n",
+ "VA=P_dc/TUF\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"kVA rating of the transformer = %.2f kVA\" %(VA/1000));\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA rating of the transformer = 2.49 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page No 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=0.5 #turns ratio\n",
+ "I_o=10.0\n",
+ "V=230.0\n",
+ "V_s=V/tr\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "V_o=2*V_m/math.pi\n",
+ "phi1=0\n",
+ "#displacemnt angle=0 as fundamnetal component of i/p source current in phase with source voltage\n",
+ "DF=math.cos(math.radians(phi1))\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*math.pi/math.pi)\n",
+ "CDF=I_s1/I_o\n",
+ "pf=CDF*DF\n",
+ "HF=math.sqrt((I_s/I_s1)**2-1)\n",
+ "CF=I_o/I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p voltage = %.2f V\" %V_o)\n",
+ "print(\"distortion factor = %.2f\" %DF)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"Current displacent factor=%.2f\" %CDF)\n",
+ "print(\"Harmonic factor = %.2f\" %HF)\n",
+ "print(\"Creast factor = %.2f\" %CF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p voltage = 414.15 V\n",
+ "distortion factor = 1.00\n",
+ "i/p pf=0.90\n",
+ "Current displacent factor=0.90\n",
+ "Harmonic factor = 0.48\n",
+ "Creast factor = 1.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=230.0\n",
+ "R=10.0\n",
+ "V_s=V_o*math.pi/(2*math.sqrt(2))\n",
+ "I_o=V_o/R\n",
+ "I_m=math.sqrt(2)*V_s/R\n",
+ "I_DAV=I_m/math.pi\n",
+ "\n",
+ "#Calculations\n",
+ "#avg value of diode current\n",
+ "I_Dr=I_m/2\n",
+ "PIV=math.sqrt(2)*V_s\n",
+ "I_s=I_m/math.sqrt(2)\n",
+ "TF=V_s*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak diode current=%.2f A\" %I_m)\n",
+ "print(\"I_DAV=%.2f A\" %I_DAV)\n",
+ "print(\"I_Dr=%.2f A\" %I_Dr) #rms value of diode current\n",
+ "print(\"PIV=%.1f V\" %PIV)\n",
+ "print(\"Transformer rating = %.2f kVA\" %(TF/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak diode current=36.13 A\n",
+ "I_DAV=11.50 A\n",
+ "I_Dr=18.06 A\n",
+ "PIV=361.3 V\n",
+ "Transformer rating = 6.53 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.18, Page No 103"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tr=5\n",
+ "V=1100.0\n",
+ "R=10.0\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"In case of 3ph-3pulse type\")\n",
+ "V_ph=V/tr\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*math.sqrt(3)*V_mp/(2*math.pi)\n",
+ "print(\"avg o/p voltage=%.1f V\" %V_o)\n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/3) \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3))) \n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "V_or=V_mp*math.sqrt((3/(2*math.pi))*(math.pi/3+.5*math.sin(2*math.pi/3)))\n",
+ "P=(V_or**2)/R \n",
+ "print(\"\\npower delivered=%.1f W\" %P)\n",
+ "print(\"in case of 3ph-M6 type\")\n",
+ "V_ph=V_ph/2\n",
+ "V_mp=math.sqrt(2)*V_ph\n",
+ "V_o=3*V_mp/(math.pi) \n",
+ "I_mp=V_mp/R\n",
+ "I_D=(I_mp/math.pi)*math.sin(math.pi/6) \n",
+ "I_Dr=I_mp*math.sqrt((1/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6))) \n",
+ "V_or=V_mp*math.sqrt((6/(2*math.pi))*(math.pi/6+.5*math.sin(2*math.pi/6)))\n",
+ "P=(V_or**2)/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"\\navg value of diode current=%.2f A\" %I_D)\n",
+ "print(\"\\nrms value of diode current=%.2f A\" %I_Dr)\n",
+ "print(\"\\npower delivered=%.0f W\" %P)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "In case of 3ph-3pulse type\n",
+ "avg o/p voltage=257.3 V\n",
+ "\n",
+ "avg value of diode current=8.577 A\n",
+ "\n",
+ "rms value of diode current=15.10 A\n",
+ "\n",
+ "power delivered=6841.3 W\n",
+ "in case of 3ph-M6 type\n",
+ "avg o/p voltage=148.55 V\n",
+ "\n",
+ "avg value of diode current=2.48 A\n",
+ "\n",
+ "rms value of diode current=6.07 A\n",
+ "\n",
+ "power delivered=2211 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.19, Page No 115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=400\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=V_o*math.pi/3\n",
+ "V_s=V_ml/(math.sqrt(2)*math.sqrt(3))\n",
+ "I_m=V_ml/R\n",
+ "I_s=.7804*I_m\n",
+ "tr=3*V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"transformer rating=%.1f VA\" %tr)\n",
+ "I_Dr=.5518*I_m \n",
+ "print(\"\\nrms value of diode current=%.3f A\" %I_Dr)\n",
+ "I_D=I_m/math.pi \n",
+ "print(\"\\navg value of diode current=%.3f A\" %I_D)\n",
+ "print(\"\\npeak diode current=%.2f A\" %I_m)\n",
+ "PIV=V_ml \n",
+ "print(\"\\nPIV=%.2f V\" %PIV)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "transformer rating=16770.3 VA\n",
+ "\n",
+ "rms value of diode current=23.114 A\n",
+ "\n",
+ "avg value of diode current=13.333 A\n",
+ "\n",
+ "peak diode current=41.89 A\n",
+ "\n",
+ "PIV=418.88 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.20, Page No 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_l=230\n",
+ "E=240\n",
+ "R=8\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_l\n",
+ "V_o=3*V_ml/math.pi\n",
+ "I_o=(V_o-E)/R\n",
+ "P_b=E*I_o \n",
+ "P_d=E*I_o+I_o**2*R \n",
+ "phi1=0\n",
+ "math.cos(math.radians(phi1))\n",
+ "I_s1=2*math.sqrt(3)*I_o/(math.sqrt(2)*math.pi)\n",
+ "I_s=math.sqrt(I_o**2*2*math.pi/(3*math.pi))\n",
+ "CDF=I_s1/I_s \n",
+ "pf=DF*CDF \n",
+ "HF=math.sqrt(CDF**-2-1) \n",
+ "tr=math.sqrt(3)*V_l*I_o*math.sqrt(2/3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Power delivered to battery=%.1f W\" %P_b)\n",
+ "print(\"Power delivered to load=%.2f W\" %P_d)\n",
+ "print(\"Displacement factor=%.2f\" %DF)\n",
+ "print(\"Current distortion factor=%.3f\" %CDF)\n",
+ "print(\"i/p pf=%.3f\"%pf)\n",
+ "print(\"Harmonic factor=%.2f\" %HF)\n",
+ "print(\"Tranformer rating=%.2f VA\" %tr)\n",
+ "#answers have small variations from the book due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power delivered to battery=2118.3 W\n",
+ "Power delivered to load=2741.48 W\n",
+ "Displacement factor=1.00\n",
+ "Current distortion factor=0.955\n",
+ "i/p pf=0.955\n",
+ "Harmonic factor=0.31\n",
+ "Tranformer rating=0.00 VA\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.21, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50 #Hz\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "R=400.0\n",
+ "RF=0.05\n",
+ "C=(1/(4*f*R))*(1+(1/(math.sqrt(2)*RF)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"capacitor value=%.2f uF\" %(C/10**-6))\n",
+ "V_o=V_m*(1-1/(4*f*R*C))\n",
+ "print(\"o/p voltage with filter=%.2f V\" %V_o)\n",
+ "V_o=2*V_m/math.pi \n",
+ "print(\"o/p voltage without filter=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "capacitor value=189.28 uF\n",
+ "o/p voltage with filter=303.79 V\n",
+ "o/p voltage without filter=207.07 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.22, Page No 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50\n",
+ "CRF=0.05\n",
+ "R=300\n",
+ "\n",
+ "#Calculations\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "print(\"L=%.2f H\" %L)\n",
+ "R=30\n",
+ "L=math.sqrt((CRF/(.4715*R))**-2-R**2)/(2*2*math.pi*f) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nL=%.2f H\" %L)\n",
+ "L=0\n",
+ "CRF=.4715*R/math.sqrt(R**2+(2*2*math.pi*f*L)**2) \n",
+ "print(\"\\nCRF=%.2f\" %CRF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "L=4.48 H\n",
+ "\n",
+ "L=0.45 H\n",
+ "\n",
+ "CRF=0.47\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.23, Page No 127"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=50\n",
+ "L_L=10*10**-3\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "\n",
+ "#Calculations\n",
+ "C=10/(2*w*math.sqrt(R**2+(2*w*L_L)**2))\n",
+ "\n",
+ "#Results\n",
+ "print(\"C=%.2f uF\" %(C*10**6))\n",
+ "VRF=0.1\n",
+ "L=(1/(4*w**2*C))*((math.sqrt(2)/(3*VRF))+1)\n",
+ "print(\"\\nL=%.2f mH\" %(L*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "C=315.83 uF\n",
+ "\n",
+ "L=45.83 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter4.ipynb b/_Power_Electronics/Chapter4.ipynb new file mode 100755 index 00000000..22311574 --- /dev/null +++ b/_Power_Electronics/Chapter4.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 04 : Thyristors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=.5 #P=V_g*I_g\n",
+ "s=130 #s=V_g/I_g\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=math.sqrt(P/s)\n",
+ "V_g=s*I_g\n",
+ "E=15\n",
+ "R_s=(E-V_g)/I_g \n",
+ "\n",
+ "#Results\n",
+ "print(\"Gate source resistance=%.2f ohm\" %R_s)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gate source resistance=111.87 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R_s=120 #slope of load line is -120V/A. This gives gate source resistance\n",
+ "print(\"gate source resistance=%.0f ohm\" %R_s)\n",
+ "\n",
+ "P=.4 #P=V_g*I_g\n",
+ "E_s=15\n",
+ "\n",
+ "#Calculations\n",
+ " #E_s=I_g*R_s+V_g % after solving this\n",
+ " #120*I_g**2-15*I_g+0.4=0 so\n",
+ "a=120 \n",
+ "b=-15\n",
+ "c=0.4\n",
+ "D=math.sqrt((b**2)-4*a*c)\n",
+ "I_g=(-b+D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.3f V\" %V_g)\n",
+ "I_g=(-b-D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.2f V\" %V_g)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "gate source resistance=120 ohm\n",
+ "\n",
+ "trigger current=86.44 mA\n",
+ "\n",
+ "then trigger voltage=4.628 V\n",
+ "\n",
+ "trigger current=38.56 mA\n",
+ "\n",
+ "then trigger voltage=10.37 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#V_g=1+10*I_g\n",
+ "P_gm=5 #P_gm=V_g*I_g\n",
+ "#after solving % eqn becomes 10*I_g**2+I_g-5=0\n",
+ "a=10.0 \n",
+ "b=1.0 \n",
+ "c=-5\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
+ "E_s=15\n",
+ "#using E_s=R_s*I_g+V_g\n",
+ "R_s=(E_s-1)/I_g-10 \n",
+ "P_gav=.3 #W\n",
+ "T=20*10**-6\n",
+ "f=P_gav/(P_gm*T)\n",
+ "dl=f*T\n",
+ "\n",
+ "#Results\n",
+ "print(\"Reistance=%.3f ohm\" %R_s)\n",
+ "print(\"Triggering freq=%.0f kHz\" %(f/1000))\n",
+ "print(\"Tduty cycle=%.2f\" %dl)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reistance=11.248 ohm\n",
+ "Triggering freq=3 kHz\n",
+ "Tduty cycle=0.06\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=.1\n",
+ "E=200.0\n",
+ "L=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "t=I*L/E \n",
+ "R=20.0\n",
+ "t1=(-L/R)*math.log(1-(R*I/E)) \n",
+ "L=2.0\n",
+ "t2=(-L/R)*math.log(1-(R*I/E)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"in case load consists of (a)L=.2H\")\n",
+ "print(\"min gate pulse width=%.0f us\" %(t*10**6))\n",
+ "print(\"(b)R=20ohm in series with L=.2H\")\n",
+ "print(\"min gate pulse width=%.3f us\" %(t1*10**6))\n",
+ "print(\"(c)R=20ohm in series with L=2H\")\n",
+ "print(\"min gate pulse width=%.2f us\" %(t2*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "in case load consists of (a)L=.2H\n",
+ "min gate pulse width=100 us\n",
+ "(b)R=20ohm in series with L=.2H\n",
+ "min gate pulse width=100.503 us\n",
+ "(c)R=20ohm in series with L=2H\n",
+ "min gate pulse width=1005.03 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " I_m=1 #supposition\n",
+ " I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))\n",
+ " I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when conduction angle=180\")\n",
+ "th=0\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "th=90\n",
+ "I_TAV=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=30\")\n",
+ "th=150\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=22.282 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=15.756 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=8.790 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " n=360.0/th\n",
+ " I=1.0 #supposition\n",
+ " I_av=I/n\n",
+ " I_rms=I/math.sqrt(n)\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "th=180.0\n",
+ "I_TAV1=theta(th)\n",
+ "th=90.0\n",
+ "I_TAV2=theta(th)\n",
+ "th=30.0\n",
+ "I_TAV3=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"when conduction angle=180\")\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"avg on current rating=%.1f A\" %I_TAV2)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"avg on current rating=%.4f A\" %I_TAV3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=8.790 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=17.5 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=10.1036 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "f=50.0 #Hz\n",
+ "\n",
+ "#Calculations\n",
+ "I_sb=3000.0\n",
+ "t=1/(4*f)\n",
+ "T=1/(2*f)\n",
+ "I=math.sqrt(I_sb**2*t/T) \n",
+ "r=(I_sb/math.sqrt(2))**2*T \n",
+ "\n",
+ "#Results\n",
+ "print(\"surge current rating=%.2f A\" %I)\n",
+ "print(\"\\nI**2*t rating=%.0f A^2.s\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "surge current rating=2121.32 A\n",
+ "\n",
+ "I**2*t rating=45000 A^2.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=300.0 #V\n",
+ "R=60.0 #ohm\n",
+ "L=2.0 #H\n",
+ "\n",
+ "#Calculations\n",
+ "t=40*10**-6 #s\n",
+ "i_T=(V_s/R)*(1-math.exp(-R*t/L))\n",
+ "i=.036 #A\n",
+ "R1=V_s/(i-i_T)\n",
+ "\n",
+ "#Results\n",
+ "print(\"maximum value of remedial parameter=%.3f kilo-ohm\" %(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum value of remedial parameter=9.999 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_p=230.0*math.sqrt(2)\n",
+ "\n",
+ "#Calculations\n",
+ "R=1+((1)**-1+(10)**-1)**-1\n",
+ "A=V_p/R\n",
+ "s=1 #s\n",
+ "t_c=20*A**-2*s\n",
+ "\n",
+ "#Results\n",
+ "print(\"fault clearance time=%.4f ms\" %(t_c*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fault clearance time=0.6890 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=math.sqrt(2)*230 #V\n",
+ "L=15*10**-6 #H\n",
+ "I=V_s/L #I=(di/dt)_max\n",
+ "R_s=10 #ohm\n",
+ "v=I*R_s #v=(dv/dt)_max\n",
+ "\n",
+ "#Calculations\n",
+ "f=50 #Hz\n",
+ "X_L=L*2*math.pi*f\n",
+ "R=2\n",
+ "I_max=V_s/(R+X_L) \n",
+ "FF=math.pi/math.sqrt(2)\n",
+ "I_TAV1=I_max/FF \n",
+ "FF=3.98184\n",
+ "I_TAV2=I_max/FF \n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"(di/dt)_max=%.3f A/usec\" %(I/10**6))\n",
+ "print(\"\\n(dv/dt)_max=%.2f V/usec\" %(v/10**6))\n",
+ "print(\"\\nI_rms=%.3f A\" %I_max)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV1)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV2)\n",
+ "print(\"\\nvoltage rating=%.3f V\" %(2.75*V_s)) #rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(di/dt)_max=21.685 A/usec\n",
+ "\n",
+ "(dv/dt)_max=216.85 V/usec\n",
+ "\n",
+ "I_rms=162.252 A\n",
+ "when conduction angle=90\n",
+ "I_TAV=73.039 A\n",
+ "when conduction angle=30\n",
+ "I_TAV=40.748 A\n",
+ "\n",
+ "voltage rating=894.490 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_j=125.0 #degC\n",
+ "T_s=70.0 #degC\n",
+ "th_jc=.16 #degC/W\n",
+ "th_cs=.08 #degC/W\n",
+ "\n",
+ "#Calculations\n",
+ "P_av1=(T_j-T_s)/(th_jc+th_cs) \n",
+ "\n",
+ "T_s=60 #degC\n",
+ "P_av2=(T_j-T_s)/(th_jc+th_cs) \n",
+ "inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss in thristor sink combination=%.2f W\" %P_av1)\n",
+ "print(\"Percentage inc in rating=%.2f\" %inc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss in thristor sink combination=229.17 W\n",
+ "Percentage inc in rating=8.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=25000.0\n",
+ "I_l1=.021 #I_l=leakage current\n",
+ "I_l2=.025\n",
+ "I_l3=.018\n",
+ "I_l4=.016\n",
+ " #V1=(I-I_l1)*R\n",
+ " #V2=(I-I_l2)*R\n",
+ " #V3=(I-I_l3)*R\n",
+ " #V4=(I-I_l4)*R\n",
+ " #V=V1+V2+V3+V4\n",
+ " \n",
+ "#Calculations\n",
+ "V=10000.0\n",
+ "I_l=I_l1+I_l2+I_l3+I_l4\n",
+ " #after solving\n",
+ "I=((V/R)+I_l)/4\n",
+ "R_c=40.0\n",
+ "V1=(I-I_l1)*R \n",
+ "\n",
+ "#Resluts\n",
+ "print(\"voltage across SCR1=%.0f V\" %V1)\n",
+ "V2=(I-I_l2)*R \n",
+ "print(\"\\nvoltage across SCR2=%.0f V\" %V2)\n",
+ "V3=(I-I_l3)*R \n",
+ "print(\"\\nvoltage across SCR3=%.0f V\" %V3)\n",
+ "V4=(I-I_l4)*R \n",
+ "print(\"\\nvoltage across SCR4=%.0f V\" %V4)\n",
+ "\n",
+ "I1=V1/R_c \n",
+ "print(\"\\ndischarge current through SCR1=%.3f A\" %I1)\n",
+ "I2=V2/R_c \n",
+ "print(\"\\ndischarge current through SCR2=%.3f A\" %I2)\n",
+ "I3=V3/R_c \n",
+ "print(\"\\ndischarge current through SCR3=%.3f A\" %I3)\n",
+ "I4=V4/R_c \n",
+ "print(\"\\ndischarge current through SCR4=%.3f A\" %I4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage across SCR1=2475 V\n",
+ "\n",
+ "voltage across SCR2=2375 V\n",
+ "\n",
+ "voltage across SCR3=2550 V\n",
+ "\n",
+ "voltage across SCR4=2600 V\n",
+ "\n",
+ "discharge current through SCR1=61.875 A\n",
+ "\n",
+ "discharge current through SCR2=59.375 A\n",
+ "\n",
+ "discharge current through SCR3=63.750 A\n",
+ "\n",
+ "discharge current through SCR4=65.000 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.22, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_r=1000 #rating of SCR\n",
+ "I_r=200 #rating of SCR\n",
+ "V_s=6000 #rating of String\n",
+ "I_s=1000 #rating of String\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when DRF=.1\")\n",
+ "DRF=.1\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))\n",
+ "print(\"when DRF=.2\")\n",
+ "DRF=.2\n",
+ "\n",
+ "#Results\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when DRF=.1\n",
+ "number of series units=7\n",
+ "\n",
+ "number of parrallel units=6\n",
+ "when DRF=.2\n",
+ "number of series units=8\n",
+ "\n",
+ "number of parrallel units=7\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.23, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.6 #on state voltage drop of SCR1\n",
+ "V2=1.2 #on state voltage drop of SCR2\n",
+ "I1=250.0 #current rating of SCR1\n",
+ "I2=350.0 #current rating of SCR2\n",
+ "\n",
+ "#Calculations\n",
+ "R1=V1/I1\n",
+ "R2=V2/I2\n",
+ "I=600.0 #current to be shared\n",
+ " #for SCR1 % I*(R1+R)/(total resistance)=k*I1 (1)\n",
+ " #for SCR2 % I*(R2+R)/(total resistance)=k*I2 (2)\n",
+ " #(1)/(2)\n",
+ "R=(R2*I2-R1*I1)/(I1-I2)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"RSequired value of resistance=%.3f ohm\" %R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RSequired value of resistance=0.004 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.25, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=2000.0 #Hz\n",
+ "C=0.04*10**-6\n",
+ "n=.72\n",
+ "\n",
+ "#Calculations\n",
+ "R=1/(f*C*math.log(1/(1-n))) \n",
+ "V_p=18\n",
+ "V_BB=V_p/n\n",
+ "R2=10**4/(n*V_BB) \n",
+ "I=4.2*10**-3 #leakage current\n",
+ "R_BB=5000\n",
+ "R1=(V_BB/I)-R2-R_BB\n",
+ "\n",
+ "#Results\n",
+ "print(\"R=%.2f kilo-ohm\" %(R/1000))\n",
+ "print(\"\\nR2=%.2f ohm\" %R2)\n",
+ "print(\"\\nR1=%.0f ohm\" %R1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R=9.82 kilo-ohm\n",
+ "\n",
+ "R2=555.56 ohm\n",
+ "\n",
+ "R1=397 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.26, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_p=18.0\n",
+ "n=.72\n",
+ "V_BB=V_p/n\n",
+ "I_p=.6*10**-3\n",
+ "I_v=2.5*10**-3\n",
+ "V_v=1\n",
+ "\n",
+ "#Calculations\n",
+ "R_max=V_BB*(1-n)/I_p \n",
+ "print(\"R_max=%.2f kilo-ohm\" %(R_max/1000))\n",
+ "R_min=(V_BB-V_v)/I_v \n",
+ "print(\"\\nR_min=%.2f kilo-ohm\" %(R_min/1000))\n",
+ "\n",
+ "C=.04*10**-6\n",
+ "f_min=1/(R_max*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_min=%.3f kHz\" %(f_min/1000))\n",
+ "f_max=1/(R_min*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_max=%.2f kHz\" %(f_max/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_max=11.67 kilo-ohm\n",
+ "\n",
+ "R_min=9.60 kilo-ohm\n",
+ "\n",
+ "f_min=1.683 kHz\n",
+ "\n",
+ "f_max=2.05 kHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter4_1.ipynb b/_Power_Electronics/Chapter4_1.ipynb new file mode 100755 index 00000000..22311574 --- /dev/null +++ b/_Power_Electronics/Chapter4_1.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 04 : Thyristors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=.5 #P=V_g*I_g\n",
+ "s=130 #s=V_g/I_g\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=math.sqrt(P/s)\n",
+ "V_g=s*I_g\n",
+ "E=15\n",
+ "R_s=(E-V_g)/I_g \n",
+ "\n",
+ "#Results\n",
+ "print(\"Gate source resistance=%.2f ohm\" %R_s)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gate source resistance=111.87 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R_s=120 #slope of load line is -120V/A. This gives gate source resistance\n",
+ "print(\"gate source resistance=%.0f ohm\" %R_s)\n",
+ "\n",
+ "P=.4 #P=V_g*I_g\n",
+ "E_s=15\n",
+ "\n",
+ "#Calculations\n",
+ " #E_s=I_g*R_s+V_g % after solving this\n",
+ " #120*I_g**2-15*I_g+0.4=0 so\n",
+ "a=120 \n",
+ "b=-15\n",
+ "c=0.4\n",
+ "D=math.sqrt((b**2)-4*a*c)\n",
+ "I_g=(-b+D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.3f V\" %V_g)\n",
+ "I_g=(-b-D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.2f V\" %V_g)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "gate source resistance=120 ohm\n",
+ "\n",
+ "trigger current=86.44 mA\n",
+ "\n",
+ "then trigger voltage=4.628 V\n",
+ "\n",
+ "trigger current=38.56 mA\n",
+ "\n",
+ "then trigger voltage=10.37 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#V_g=1+10*I_g\n",
+ "P_gm=5 #P_gm=V_g*I_g\n",
+ "#after solving % eqn becomes 10*I_g**2+I_g-5=0\n",
+ "a=10.0 \n",
+ "b=1.0 \n",
+ "c=-5\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
+ "E_s=15\n",
+ "#using E_s=R_s*I_g+V_g\n",
+ "R_s=(E_s-1)/I_g-10 \n",
+ "P_gav=.3 #W\n",
+ "T=20*10**-6\n",
+ "f=P_gav/(P_gm*T)\n",
+ "dl=f*T\n",
+ "\n",
+ "#Results\n",
+ "print(\"Reistance=%.3f ohm\" %R_s)\n",
+ "print(\"Triggering freq=%.0f kHz\" %(f/1000))\n",
+ "print(\"Tduty cycle=%.2f\" %dl)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reistance=11.248 ohm\n",
+ "Triggering freq=3 kHz\n",
+ "Tduty cycle=0.06\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=.1\n",
+ "E=200.0\n",
+ "L=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "t=I*L/E \n",
+ "R=20.0\n",
+ "t1=(-L/R)*math.log(1-(R*I/E)) \n",
+ "L=2.0\n",
+ "t2=(-L/R)*math.log(1-(R*I/E)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"in case load consists of (a)L=.2H\")\n",
+ "print(\"min gate pulse width=%.0f us\" %(t*10**6))\n",
+ "print(\"(b)R=20ohm in series with L=.2H\")\n",
+ "print(\"min gate pulse width=%.3f us\" %(t1*10**6))\n",
+ "print(\"(c)R=20ohm in series with L=2H\")\n",
+ "print(\"min gate pulse width=%.2f us\" %(t2*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "in case load consists of (a)L=.2H\n",
+ "min gate pulse width=100 us\n",
+ "(b)R=20ohm in series with L=.2H\n",
+ "min gate pulse width=100.503 us\n",
+ "(c)R=20ohm in series with L=2H\n",
+ "min gate pulse width=1005.03 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " I_m=1 #supposition\n",
+ " I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))\n",
+ " I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when conduction angle=180\")\n",
+ "th=0\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "th=90\n",
+ "I_TAV=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=30\")\n",
+ "th=150\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=22.282 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=15.756 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=8.790 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " n=360.0/th\n",
+ " I=1.0 #supposition\n",
+ " I_av=I/n\n",
+ " I_rms=I/math.sqrt(n)\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "th=180.0\n",
+ "I_TAV1=theta(th)\n",
+ "th=90.0\n",
+ "I_TAV2=theta(th)\n",
+ "th=30.0\n",
+ "I_TAV3=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"when conduction angle=180\")\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"avg on current rating=%.1f A\" %I_TAV2)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"avg on current rating=%.4f A\" %I_TAV3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=8.790 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=17.5 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=10.1036 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "f=50.0 #Hz\n",
+ "\n",
+ "#Calculations\n",
+ "I_sb=3000.0\n",
+ "t=1/(4*f)\n",
+ "T=1/(2*f)\n",
+ "I=math.sqrt(I_sb**2*t/T) \n",
+ "r=(I_sb/math.sqrt(2))**2*T \n",
+ "\n",
+ "#Results\n",
+ "print(\"surge current rating=%.2f A\" %I)\n",
+ "print(\"\\nI**2*t rating=%.0f A^2.s\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "surge current rating=2121.32 A\n",
+ "\n",
+ "I**2*t rating=45000 A^2.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=300.0 #V\n",
+ "R=60.0 #ohm\n",
+ "L=2.0 #H\n",
+ "\n",
+ "#Calculations\n",
+ "t=40*10**-6 #s\n",
+ "i_T=(V_s/R)*(1-math.exp(-R*t/L))\n",
+ "i=.036 #A\n",
+ "R1=V_s/(i-i_T)\n",
+ "\n",
+ "#Results\n",
+ "print(\"maximum value of remedial parameter=%.3f kilo-ohm\" %(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum value of remedial parameter=9.999 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_p=230.0*math.sqrt(2)\n",
+ "\n",
+ "#Calculations\n",
+ "R=1+((1)**-1+(10)**-1)**-1\n",
+ "A=V_p/R\n",
+ "s=1 #s\n",
+ "t_c=20*A**-2*s\n",
+ "\n",
+ "#Results\n",
+ "print(\"fault clearance time=%.4f ms\" %(t_c*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fault clearance time=0.6890 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=math.sqrt(2)*230 #V\n",
+ "L=15*10**-6 #H\n",
+ "I=V_s/L #I=(di/dt)_max\n",
+ "R_s=10 #ohm\n",
+ "v=I*R_s #v=(dv/dt)_max\n",
+ "\n",
+ "#Calculations\n",
+ "f=50 #Hz\n",
+ "X_L=L*2*math.pi*f\n",
+ "R=2\n",
+ "I_max=V_s/(R+X_L) \n",
+ "FF=math.pi/math.sqrt(2)\n",
+ "I_TAV1=I_max/FF \n",
+ "FF=3.98184\n",
+ "I_TAV2=I_max/FF \n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"(di/dt)_max=%.3f A/usec\" %(I/10**6))\n",
+ "print(\"\\n(dv/dt)_max=%.2f V/usec\" %(v/10**6))\n",
+ "print(\"\\nI_rms=%.3f A\" %I_max)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV1)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV2)\n",
+ "print(\"\\nvoltage rating=%.3f V\" %(2.75*V_s)) #rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(di/dt)_max=21.685 A/usec\n",
+ "\n",
+ "(dv/dt)_max=216.85 V/usec\n",
+ "\n",
+ "I_rms=162.252 A\n",
+ "when conduction angle=90\n",
+ "I_TAV=73.039 A\n",
+ "when conduction angle=30\n",
+ "I_TAV=40.748 A\n",
+ "\n",
+ "voltage rating=894.490 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_j=125.0 #degC\n",
+ "T_s=70.0 #degC\n",
+ "th_jc=.16 #degC/W\n",
+ "th_cs=.08 #degC/W\n",
+ "\n",
+ "#Calculations\n",
+ "P_av1=(T_j-T_s)/(th_jc+th_cs) \n",
+ "\n",
+ "T_s=60 #degC\n",
+ "P_av2=(T_j-T_s)/(th_jc+th_cs) \n",
+ "inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss in thristor sink combination=%.2f W\" %P_av1)\n",
+ "print(\"Percentage inc in rating=%.2f\" %inc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss in thristor sink combination=229.17 W\n",
+ "Percentage inc in rating=8.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=25000.0\n",
+ "I_l1=.021 #I_l=leakage current\n",
+ "I_l2=.025\n",
+ "I_l3=.018\n",
+ "I_l4=.016\n",
+ " #V1=(I-I_l1)*R\n",
+ " #V2=(I-I_l2)*R\n",
+ " #V3=(I-I_l3)*R\n",
+ " #V4=(I-I_l4)*R\n",
+ " #V=V1+V2+V3+V4\n",
+ " \n",
+ "#Calculations\n",
+ "V=10000.0\n",
+ "I_l=I_l1+I_l2+I_l3+I_l4\n",
+ " #after solving\n",
+ "I=((V/R)+I_l)/4\n",
+ "R_c=40.0\n",
+ "V1=(I-I_l1)*R \n",
+ "\n",
+ "#Resluts\n",
+ "print(\"voltage across SCR1=%.0f V\" %V1)\n",
+ "V2=(I-I_l2)*R \n",
+ "print(\"\\nvoltage across SCR2=%.0f V\" %V2)\n",
+ "V3=(I-I_l3)*R \n",
+ "print(\"\\nvoltage across SCR3=%.0f V\" %V3)\n",
+ "V4=(I-I_l4)*R \n",
+ "print(\"\\nvoltage across SCR4=%.0f V\" %V4)\n",
+ "\n",
+ "I1=V1/R_c \n",
+ "print(\"\\ndischarge current through SCR1=%.3f A\" %I1)\n",
+ "I2=V2/R_c \n",
+ "print(\"\\ndischarge current through SCR2=%.3f A\" %I2)\n",
+ "I3=V3/R_c \n",
+ "print(\"\\ndischarge current through SCR3=%.3f A\" %I3)\n",
+ "I4=V4/R_c \n",
+ "print(\"\\ndischarge current through SCR4=%.3f A\" %I4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage across SCR1=2475 V\n",
+ "\n",
+ "voltage across SCR2=2375 V\n",
+ "\n",
+ "voltage across SCR3=2550 V\n",
+ "\n",
+ "voltage across SCR4=2600 V\n",
+ "\n",
+ "discharge current through SCR1=61.875 A\n",
+ "\n",
+ "discharge current through SCR2=59.375 A\n",
+ "\n",
+ "discharge current through SCR3=63.750 A\n",
+ "\n",
+ "discharge current through SCR4=65.000 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.22, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_r=1000 #rating of SCR\n",
+ "I_r=200 #rating of SCR\n",
+ "V_s=6000 #rating of String\n",
+ "I_s=1000 #rating of String\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when DRF=.1\")\n",
+ "DRF=.1\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))\n",
+ "print(\"when DRF=.2\")\n",
+ "DRF=.2\n",
+ "\n",
+ "#Results\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when DRF=.1\n",
+ "number of series units=7\n",
+ "\n",
+ "number of parrallel units=6\n",
+ "when DRF=.2\n",
+ "number of series units=8\n",
+ "\n",
+ "number of parrallel units=7\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.23, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.6 #on state voltage drop of SCR1\n",
+ "V2=1.2 #on state voltage drop of SCR2\n",
+ "I1=250.0 #current rating of SCR1\n",
+ "I2=350.0 #current rating of SCR2\n",
+ "\n",
+ "#Calculations\n",
+ "R1=V1/I1\n",
+ "R2=V2/I2\n",
+ "I=600.0 #current to be shared\n",
+ " #for SCR1 % I*(R1+R)/(total resistance)=k*I1 (1)\n",
+ " #for SCR2 % I*(R2+R)/(total resistance)=k*I2 (2)\n",
+ " #(1)/(2)\n",
+ "R=(R2*I2-R1*I1)/(I1-I2)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"RSequired value of resistance=%.3f ohm\" %R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RSequired value of resistance=0.004 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.25, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=2000.0 #Hz\n",
+ "C=0.04*10**-6\n",
+ "n=.72\n",
+ "\n",
+ "#Calculations\n",
+ "R=1/(f*C*math.log(1/(1-n))) \n",
+ "V_p=18\n",
+ "V_BB=V_p/n\n",
+ "R2=10**4/(n*V_BB) \n",
+ "I=4.2*10**-3 #leakage current\n",
+ "R_BB=5000\n",
+ "R1=(V_BB/I)-R2-R_BB\n",
+ "\n",
+ "#Results\n",
+ "print(\"R=%.2f kilo-ohm\" %(R/1000))\n",
+ "print(\"\\nR2=%.2f ohm\" %R2)\n",
+ "print(\"\\nR1=%.0f ohm\" %R1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R=9.82 kilo-ohm\n",
+ "\n",
+ "R2=555.56 ohm\n",
+ "\n",
+ "R1=397 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.26, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_p=18.0\n",
+ "n=.72\n",
+ "V_BB=V_p/n\n",
+ "I_p=.6*10**-3\n",
+ "I_v=2.5*10**-3\n",
+ "V_v=1\n",
+ "\n",
+ "#Calculations\n",
+ "R_max=V_BB*(1-n)/I_p \n",
+ "print(\"R_max=%.2f kilo-ohm\" %(R_max/1000))\n",
+ "R_min=(V_BB-V_v)/I_v \n",
+ "print(\"\\nR_min=%.2f kilo-ohm\" %(R_min/1000))\n",
+ "\n",
+ "C=.04*10**-6\n",
+ "f_min=1/(R_max*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_min=%.3f kHz\" %(f_min/1000))\n",
+ "f_max=1/(R_min*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_max=%.2f kHz\" %(f_max/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_max=11.67 kilo-ohm\n",
+ "\n",
+ "R_min=9.60 kilo-ohm\n",
+ "\n",
+ "f_min=1.683 kHz\n",
+ "\n",
+ "f_max=2.05 kHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter4_2.ipynb b/_Power_Electronics/Chapter4_2.ipynb new file mode 100755 index 00000000..22311574 --- /dev/null +++ b/_Power_Electronics/Chapter4_2.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 04 : Thyristors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=.5 #P=V_g*I_g\n",
+ "s=130 #s=V_g/I_g\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=math.sqrt(P/s)\n",
+ "V_g=s*I_g\n",
+ "E=15\n",
+ "R_s=(E-V_g)/I_g \n",
+ "\n",
+ "#Results\n",
+ "print(\"Gate source resistance=%.2f ohm\" %R_s)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gate source resistance=111.87 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R_s=120 #slope of load line is -120V/A. This gives gate source resistance\n",
+ "print(\"gate source resistance=%.0f ohm\" %R_s)\n",
+ "\n",
+ "P=.4 #P=V_g*I_g\n",
+ "E_s=15\n",
+ "\n",
+ "#Calculations\n",
+ " #E_s=I_g*R_s+V_g % after solving this\n",
+ " #120*I_g**2-15*I_g+0.4=0 so\n",
+ "a=120 \n",
+ "b=-15\n",
+ "c=0.4\n",
+ "D=math.sqrt((b**2)-4*a*c)\n",
+ "I_g=(-b+D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.3f V\" %V_g)\n",
+ "I_g=(-b-D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.2f V\" %V_g)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "gate source resistance=120 ohm\n",
+ "\n",
+ "trigger current=86.44 mA\n",
+ "\n",
+ "then trigger voltage=4.628 V\n",
+ "\n",
+ "trigger current=38.56 mA\n",
+ "\n",
+ "then trigger voltage=10.37 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#V_g=1+10*I_g\n",
+ "P_gm=5 #P_gm=V_g*I_g\n",
+ "#after solving % eqn becomes 10*I_g**2+I_g-5=0\n",
+ "a=10.0 \n",
+ "b=1.0 \n",
+ "c=-5\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
+ "E_s=15\n",
+ "#using E_s=R_s*I_g+V_g\n",
+ "R_s=(E_s-1)/I_g-10 \n",
+ "P_gav=.3 #W\n",
+ "T=20*10**-6\n",
+ "f=P_gav/(P_gm*T)\n",
+ "dl=f*T\n",
+ "\n",
+ "#Results\n",
+ "print(\"Reistance=%.3f ohm\" %R_s)\n",
+ "print(\"Triggering freq=%.0f kHz\" %(f/1000))\n",
+ "print(\"Tduty cycle=%.2f\" %dl)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reistance=11.248 ohm\n",
+ "Triggering freq=3 kHz\n",
+ "Tduty cycle=0.06\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=.1\n",
+ "E=200.0\n",
+ "L=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "t=I*L/E \n",
+ "R=20.0\n",
+ "t1=(-L/R)*math.log(1-(R*I/E)) \n",
+ "L=2.0\n",
+ "t2=(-L/R)*math.log(1-(R*I/E)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"in case load consists of (a)L=.2H\")\n",
+ "print(\"min gate pulse width=%.0f us\" %(t*10**6))\n",
+ "print(\"(b)R=20ohm in series with L=.2H\")\n",
+ "print(\"min gate pulse width=%.3f us\" %(t1*10**6))\n",
+ "print(\"(c)R=20ohm in series with L=2H\")\n",
+ "print(\"min gate pulse width=%.2f us\" %(t2*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "in case load consists of (a)L=.2H\n",
+ "min gate pulse width=100 us\n",
+ "(b)R=20ohm in series with L=.2H\n",
+ "min gate pulse width=100.503 us\n",
+ "(c)R=20ohm in series with L=2H\n",
+ "min gate pulse width=1005.03 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " I_m=1 #supposition\n",
+ " I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))\n",
+ " I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when conduction angle=180\")\n",
+ "th=0\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "th=90\n",
+ "I_TAV=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=30\")\n",
+ "th=150\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=22.282 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=15.756 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=8.790 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " n=360.0/th\n",
+ " I=1.0 #supposition\n",
+ " I_av=I/n\n",
+ " I_rms=I/math.sqrt(n)\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "th=180.0\n",
+ "I_TAV1=theta(th)\n",
+ "th=90.0\n",
+ "I_TAV2=theta(th)\n",
+ "th=30.0\n",
+ "I_TAV3=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"when conduction angle=180\")\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"avg on current rating=%.1f A\" %I_TAV2)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"avg on current rating=%.4f A\" %I_TAV3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=8.790 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=17.5 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=10.1036 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "f=50.0 #Hz\n",
+ "\n",
+ "#Calculations\n",
+ "I_sb=3000.0\n",
+ "t=1/(4*f)\n",
+ "T=1/(2*f)\n",
+ "I=math.sqrt(I_sb**2*t/T) \n",
+ "r=(I_sb/math.sqrt(2))**2*T \n",
+ "\n",
+ "#Results\n",
+ "print(\"surge current rating=%.2f A\" %I)\n",
+ "print(\"\\nI**2*t rating=%.0f A^2.s\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "surge current rating=2121.32 A\n",
+ "\n",
+ "I**2*t rating=45000 A^2.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=300.0 #V\n",
+ "R=60.0 #ohm\n",
+ "L=2.0 #H\n",
+ "\n",
+ "#Calculations\n",
+ "t=40*10**-6 #s\n",
+ "i_T=(V_s/R)*(1-math.exp(-R*t/L))\n",
+ "i=.036 #A\n",
+ "R1=V_s/(i-i_T)\n",
+ "\n",
+ "#Results\n",
+ "print(\"maximum value of remedial parameter=%.3f kilo-ohm\" %(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum value of remedial parameter=9.999 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_p=230.0*math.sqrt(2)\n",
+ "\n",
+ "#Calculations\n",
+ "R=1+((1)**-1+(10)**-1)**-1\n",
+ "A=V_p/R\n",
+ "s=1 #s\n",
+ "t_c=20*A**-2*s\n",
+ "\n",
+ "#Results\n",
+ "print(\"fault clearance time=%.4f ms\" %(t_c*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fault clearance time=0.6890 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=math.sqrt(2)*230 #V\n",
+ "L=15*10**-6 #H\n",
+ "I=V_s/L #I=(di/dt)_max\n",
+ "R_s=10 #ohm\n",
+ "v=I*R_s #v=(dv/dt)_max\n",
+ "\n",
+ "#Calculations\n",
+ "f=50 #Hz\n",
+ "X_L=L*2*math.pi*f\n",
+ "R=2\n",
+ "I_max=V_s/(R+X_L) \n",
+ "FF=math.pi/math.sqrt(2)\n",
+ "I_TAV1=I_max/FF \n",
+ "FF=3.98184\n",
+ "I_TAV2=I_max/FF \n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"(di/dt)_max=%.3f A/usec\" %(I/10**6))\n",
+ "print(\"\\n(dv/dt)_max=%.2f V/usec\" %(v/10**6))\n",
+ "print(\"\\nI_rms=%.3f A\" %I_max)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV1)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV2)\n",
+ "print(\"\\nvoltage rating=%.3f V\" %(2.75*V_s)) #rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(di/dt)_max=21.685 A/usec\n",
+ "\n",
+ "(dv/dt)_max=216.85 V/usec\n",
+ "\n",
+ "I_rms=162.252 A\n",
+ "when conduction angle=90\n",
+ "I_TAV=73.039 A\n",
+ "when conduction angle=30\n",
+ "I_TAV=40.748 A\n",
+ "\n",
+ "voltage rating=894.490 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_j=125.0 #degC\n",
+ "T_s=70.0 #degC\n",
+ "th_jc=.16 #degC/W\n",
+ "th_cs=.08 #degC/W\n",
+ "\n",
+ "#Calculations\n",
+ "P_av1=(T_j-T_s)/(th_jc+th_cs) \n",
+ "\n",
+ "T_s=60 #degC\n",
+ "P_av2=(T_j-T_s)/(th_jc+th_cs) \n",
+ "inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss in thristor sink combination=%.2f W\" %P_av1)\n",
+ "print(\"Percentage inc in rating=%.2f\" %inc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss in thristor sink combination=229.17 W\n",
+ "Percentage inc in rating=8.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=25000.0\n",
+ "I_l1=.021 #I_l=leakage current\n",
+ "I_l2=.025\n",
+ "I_l3=.018\n",
+ "I_l4=.016\n",
+ " #V1=(I-I_l1)*R\n",
+ " #V2=(I-I_l2)*R\n",
+ " #V3=(I-I_l3)*R\n",
+ " #V4=(I-I_l4)*R\n",
+ " #V=V1+V2+V3+V4\n",
+ " \n",
+ "#Calculations\n",
+ "V=10000.0\n",
+ "I_l=I_l1+I_l2+I_l3+I_l4\n",
+ " #after solving\n",
+ "I=((V/R)+I_l)/4\n",
+ "R_c=40.0\n",
+ "V1=(I-I_l1)*R \n",
+ "\n",
+ "#Resluts\n",
+ "print(\"voltage across SCR1=%.0f V\" %V1)\n",
+ "V2=(I-I_l2)*R \n",
+ "print(\"\\nvoltage across SCR2=%.0f V\" %V2)\n",
+ "V3=(I-I_l3)*R \n",
+ "print(\"\\nvoltage across SCR3=%.0f V\" %V3)\n",
+ "V4=(I-I_l4)*R \n",
+ "print(\"\\nvoltage across SCR4=%.0f V\" %V4)\n",
+ "\n",
+ "I1=V1/R_c \n",
+ "print(\"\\ndischarge current through SCR1=%.3f A\" %I1)\n",
+ "I2=V2/R_c \n",
+ "print(\"\\ndischarge current through SCR2=%.3f A\" %I2)\n",
+ "I3=V3/R_c \n",
+ "print(\"\\ndischarge current through SCR3=%.3f A\" %I3)\n",
+ "I4=V4/R_c \n",
+ "print(\"\\ndischarge current through SCR4=%.3f A\" %I4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage across SCR1=2475 V\n",
+ "\n",
+ "voltage across SCR2=2375 V\n",
+ "\n",
+ "voltage across SCR3=2550 V\n",
+ "\n",
+ "voltage across SCR4=2600 V\n",
+ "\n",
+ "discharge current through SCR1=61.875 A\n",
+ "\n",
+ "discharge current through SCR2=59.375 A\n",
+ "\n",
+ "discharge current through SCR3=63.750 A\n",
+ "\n",
+ "discharge current through SCR4=65.000 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.22, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_r=1000 #rating of SCR\n",
+ "I_r=200 #rating of SCR\n",
+ "V_s=6000 #rating of String\n",
+ "I_s=1000 #rating of String\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when DRF=.1\")\n",
+ "DRF=.1\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))\n",
+ "print(\"when DRF=.2\")\n",
+ "DRF=.2\n",
+ "\n",
+ "#Results\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when DRF=.1\n",
+ "number of series units=7\n",
+ "\n",
+ "number of parrallel units=6\n",
+ "when DRF=.2\n",
+ "number of series units=8\n",
+ "\n",
+ "number of parrallel units=7\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.23, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.6 #on state voltage drop of SCR1\n",
+ "V2=1.2 #on state voltage drop of SCR2\n",
+ "I1=250.0 #current rating of SCR1\n",
+ "I2=350.0 #current rating of SCR2\n",
+ "\n",
+ "#Calculations\n",
+ "R1=V1/I1\n",
+ "R2=V2/I2\n",
+ "I=600.0 #current to be shared\n",
+ " #for SCR1 % I*(R1+R)/(total resistance)=k*I1 (1)\n",
+ " #for SCR2 % I*(R2+R)/(total resistance)=k*I2 (2)\n",
+ " #(1)/(2)\n",
+ "R=(R2*I2-R1*I1)/(I1-I2)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"RSequired value of resistance=%.3f ohm\" %R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RSequired value of resistance=0.004 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.25, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=2000.0 #Hz\n",
+ "C=0.04*10**-6\n",
+ "n=.72\n",
+ "\n",
+ "#Calculations\n",
+ "R=1/(f*C*math.log(1/(1-n))) \n",
+ "V_p=18\n",
+ "V_BB=V_p/n\n",
+ "R2=10**4/(n*V_BB) \n",
+ "I=4.2*10**-3 #leakage current\n",
+ "R_BB=5000\n",
+ "R1=(V_BB/I)-R2-R_BB\n",
+ "\n",
+ "#Results\n",
+ "print(\"R=%.2f kilo-ohm\" %(R/1000))\n",
+ "print(\"\\nR2=%.2f ohm\" %R2)\n",
+ "print(\"\\nR1=%.0f ohm\" %R1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R=9.82 kilo-ohm\n",
+ "\n",
+ "R2=555.56 ohm\n",
+ "\n",
+ "R1=397 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.26, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_p=18.0\n",
+ "n=.72\n",
+ "V_BB=V_p/n\n",
+ "I_p=.6*10**-3\n",
+ "I_v=2.5*10**-3\n",
+ "V_v=1\n",
+ "\n",
+ "#Calculations\n",
+ "R_max=V_BB*(1-n)/I_p \n",
+ "print(\"R_max=%.2f kilo-ohm\" %(R_max/1000))\n",
+ "R_min=(V_BB-V_v)/I_v \n",
+ "print(\"\\nR_min=%.2f kilo-ohm\" %(R_min/1000))\n",
+ "\n",
+ "C=.04*10**-6\n",
+ "f_min=1/(R_max*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_min=%.3f kHz\" %(f_min/1000))\n",
+ "f_max=1/(R_min*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_max=%.2f kHz\" %(f_max/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_max=11.67 kilo-ohm\n",
+ "\n",
+ "R_min=9.60 kilo-ohm\n",
+ "\n",
+ "f_min=1.683 kHz\n",
+ "\n",
+ "f_max=2.05 kHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter4_3.ipynb b/_Power_Electronics/Chapter4_3.ipynb new file mode 100755 index 00000000..22311574 --- /dev/null +++ b/_Power_Electronics/Chapter4_3.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 04 : Thyristors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=.5 #P=V_g*I_g\n",
+ "s=130 #s=V_g/I_g\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=math.sqrt(P/s)\n",
+ "V_g=s*I_g\n",
+ "E=15\n",
+ "R_s=(E-V_g)/I_g \n",
+ "\n",
+ "#Results\n",
+ "print(\"Gate source resistance=%.2f ohm\" %R_s)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gate source resistance=111.87 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R_s=120 #slope of load line is -120V/A. This gives gate source resistance\n",
+ "print(\"gate source resistance=%.0f ohm\" %R_s)\n",
+ "\n",
+ "P=.4 #P=V_g*I_g\n",
+ "E_s=15\n",
+ "\n",
+ "#Calculations\n",
+ " #E_s=I_g*R_s+V_g % after solving this\n",
+ " #120*I_g**2-15*I_g+0.4=0 so\n",
+ "a=120 \n",
+ "b=-15\n",
+ "c=0.4\n",
+ "D=math.sqrt((b**2)-4*a*c)\n",
+ "I_g=(-b+D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.3f V\" %V_g)\n",
+ "I_g=(-b-D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.2f V\" %V_g)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "gate source resistance=120 ohm\n",
+ "\n",
+ "trigger current=86.44 mA\n",
+ "\n",
+ "then trigger voltage=4.628 V\n",
+ "\n",
+ "trigger current=38.56 mA\n",
+ "\n",
+ "then trigger voltage=10.37 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#V_g=1+10*I_g\n",
+ "P_gm=5 #P_gm=V_g*I_g\n",
+ "#after solving % eqn becomes 10*I_g**2+I_g-5=0\n",
+ "a=10.0 \n",
+ "b=1.0 \n",
+ "c=-5\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
+ "E_s=15\n",
+ "#using E_s=R_s*I_g+V_g\n",
+ "R_s=(E_s-1)/I_g-10 \n",
+ "P_gav=.3 #W\n",
+ "T=20*10**-6\n",
+ "f=P_gav/(P_gm*T)\n",
+ "dl=f*T\n",
+ "\n",
+ "#Results\n",
+ "print(\"Reistance=%.3f ohm\" %R_s)\n",
+ "print(\"Triggering freq=%.0f kHz\" %(f/1000))\n",
+ "print(\"Tduty cycle=%.2f\" %dl)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reistance=11.248 ohm\n",
+ "Triggering freq=3 kHz\n",
+ "Tduty cycle=0.06\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=.1\n",
+ "E=200.0\n",
+ "L=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "t=I*L/E \n",
+ "R=20.0\n",
+ "t1=(-L/R)*math.log(1-(R*I/E)) \n",
+ "L=2.0\n",
+ "t2=(-L/R)*math.log(1-(R*I/E)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"in case load consists of (a)L=.2H\")\n",
+ "print(\"min gate pulse width=%.0f us\" %(t*10**6))\n",
+ "print(\"(b)R=20ohm in series with L=.2H\")\n",
+ "print(\"min gate pulse width=%.3f us\" %(t1*10**6))\n",
+ "print(\"(c)R=20ohm in series with L=2H\")\n",
+ "print(\"min gate pulse width=%.2f us\" %(t2*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "in case load consists of (a)L=.2H\n",
+ "min gate pulse width=100 us\n",
+ "(b)R=20ohm in series with L=.2H\n",
+ "min gate pulse width=100.503 us\n",
+ "(c)R=20ohm in series with L=2H\n",
+ "min gate pulse width=1005.03 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " I_m=1 #supposition\n",
+ " I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))\n",
+ " I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when conduction angle=180\")\n",
+ "th=0\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "th=90\n",
+ "I_TAV=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=30\")\n",
+ "th=150\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=22.282 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=15.756 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=8.790 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " n=360.0/th\n",
+ " I=1.0 #supposition\n",
+ " I_av=I/n\n",
+ " I_rms=I/math.sqrt(n)\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "th=180.0\n",
+ "I_TAV1=theta(th)\n",
+ "th=90.0\n",
+ "I_TAV2=theta(th)\n",
+ "th=30.0\n",
+ "I_TAV3=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"when conduction angle=180\")\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"avg on current rating=%.1f A\" %I_TAV2)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"avg on current rating=%.4f A\" %I_TAV3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=8.790 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=17.5 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=10.1036 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "f=50.0 #Hz\n",
+ "\n",
+ "#Calculations\n",
+ "I_sb=3000.0\n",
+ "t=1/(4*f)\n",
+ "T=1/(2*f)\n",
+ "I=math.sqrt(I_sb**2*t/T) \n",
+ "r=(I_sb/math.sqrt(2))**2*T \n",
+ "\n",
+ "#Results\n",
+ "print(\"surge current rating=%.2f A\" %I)\n",
+ "print(\"\\nI**2*t rating=%.0f A^2.s\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "surge current rating=2121.32 A\n",
+ "\n",
+ "I**2*t rating=45000 A^2.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=300.0 #V\n",
+ "R=60.0 #ohm\n",
+ "L=2.0 #H\n",
+ "\n",
+ "#Calculations\n",
+ "t=40*10**-6 #s\n",
+ "i_T=(V_s/R)*(1-math.exp(-R*t/L))\n",
+ "i=.036 #A\n",
+ "R1=V_s/(i-i_T)\n",
+ "\n",
+ "#Results\n",
+ "print(\"maximum value of remedial parameter=%.3f kilo-ohm\" %(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum value of remedial parameter=9.999 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_p=230.0*math.sqrt(2)\n",
+ "\n",
+ "#Calculations\n",
+ "R=1+((1)**-1+(10)**-1)**-1\n",
+ "A=V_p/R\n",
+ "s=1 #s\n",
+ "t_c=20*A**-2*s\n",
+ "\n",
+ "#Results\n",
+ "print(\"fault clearance time=%.4f ms\" %(t_c*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fault clearance time=0.6890 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=math.sqrt(2)*230 #V\n",
+ "L=15*10**-6 #H\n",
+ "I=V_s/L #I=(di/dt)_max\n",
+ "R_s=10 #ohm\n",
+ "v=I*R_s #v=(dv/dt)_max\n",
+ "\n",
+ "#Calculations\n",
+ "f=50 #Hz\n",
+ "X_L=L*2*math.pi*f\n",
+ "R=2\n",
+ "I_max=V_s/(R+X_L) \n",
+ "FF=math.pi/math.sqrt(2)\n",
+ "I_TAV1=I_max/FF \n",
+ "FF=3.98184\n",
+ "I_TAV2=I_max/FF \n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"(di/dt)_max=%.3f A/usec\" %(I/10**6))\n",
+ "print(\"\\n(dv/dt)_max=%.2f V/usec\" %(v/10**6))\n",
+ "print(\"\\nI_rms=%.3f A\" %I_max)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV1)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV2)\n",
+ "print(\"\\nvoltage rating=%.3f V\" %(2.75*V_s)) #rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(di/dt)_max=21.685 A/usec\n",
+ "\n",
+ "(dv/dt)_max=216.85 V/usec\n",
+ "\n",
+ "I_rms=162.252 A\n",
+ "when conduction angle=90\n",
+ "I_TAV=73.039 A\n",
+ "when conduction angle=30\n",
+ "I_TAV=40.748 A\n",
+ "\n",
+ "voltage rating=894.490 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_j=125.0 #degC\n",
+ "T_s=70.0 #degC\n",
+ "th_jc=.16 #degC/W\n",
+ "th_cs=.08 #degC/W\n",
+ "\n",
+ "#Calculations\n",
+ "P_av1=(T_j-T_s)/(th_jc+th_cs) \n",
+ "\n",
+ "T_s=60 #degC\n",
+ "P_av2=(T_j-T_s)/(th_jc+th_cs) \n",
+ "inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss in thristor sink combination=%.2f W\" %P_av1)\n",
+ "print(\"Percentage inc in rating=%.2f\" %inc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss in thristor sink combination=229.17 W\n",
+ "Percentage inc in rating=8.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=25000.0\n",
+ "I_l1=.021 #I_l=leakage current\n",
+ "I_l2=.025\n",
+ "I_l3=.018\n",
+ "I_l4=.016\n",
+ " #V1=(I-I_l1)*R\n",
+ " #V2=(I-I_l2)*R\n",
+ " #V3=(I-I_l3)*R\n",
+ " #V4=(I-I_l4)*R\n",
+ " #V=V1+V2+V3+V4\n",
+ " \n",
+ "#Calculations\n",
+ "V=10000.0\n",
+ "I_l=I_l1+I_l2+I_l3+I_l4\n",
+ " #after solving\n",
+ "I=((V/R)+I_l)/4\n",
+ "R_c=40.0\n",
+ "V1=(I-I_l1)*R \n",
+ "\n",
+ "#Resluts\n",
+ "print(\"voltage across SCR1=%.0f V\" %V1)\n",
+ "V2=(I-I_l2)*R \n",
+ "print(\"\\nvoltage across SCR2=%.0f V\" %V2)\n",
+ "V3=(I-I_l3)*R \n",
+ "print(\"\\nvoltage across SCR3=%.0f V\" %V3)\n",
+ "V4=(I-I_l4)*R \n",
+ "print(\"\\nvoltage across SCR4=%.0f V\" %V4)\n",
+ "\n",
+ "I1=V1/R_c \n",
+ "print(\"\\ndischarge current through SCR1=%.3f A\" %I1)\n",
+ "I2=V2/R_c \n",
+ "print(\"\\ndischarge current through SCR2=%.3f A\" %I2)\n",
+ "I3=V3/R_c \n",
+ "print(\"\\ndischarge current through SCR3=%.3f A\" %I3)\n",
+ "I4=V4/R_c \n",
+ "print(\"\\ndischarge current through SCR4=%.3f A\" %I4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage across SCR1=2475 V\n",
+ "\n",
+ "voltage across SCR2=2375 V\n",
+ "\n",
+ "voltage across SCR3=2550 V\n",
+ "\n",
+ "voltage across SCR4=2600 V\n",
+ "\n",
+ "discharge current through SCR1=61.875 A\n",
+ "\n",
+ "discharge current through SCR2=59.375 A\n",
+ "\n",
+ "discharge current through SCR3=63.750 A\n",
+ "\n",
+ "discharge current through SCR4=65.000 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.22, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_r=1000 #rating of SCR\n",
+ "I_r=200 #rating of SCR\n",
+ "V_s=6000 #rating of String\n",
+ "I_s=1000 #rating of String\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when DRF=.1\")\n",
+ "DRF=.1\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))\n",
+ "print(\"when DRF=.2\")\n",
+ "DRF=.2\n",
+ "\n",
+ "#Results\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when DRF=.1\n",
+ "number of series units=7\n",
+ "\n",
+ "number of parrallel units=6\n",
+ "when DRF=.2\n",
+ "number of series units=8\n",
+ "\n",
+ "number of parrallel units=7\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.23, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.6 #on state voltage drop of SCR1\n",
+ "V2=1.2 #on state voltage drop of SCR2\n",
+ "I1=250.0 #current rating of SCR1\n",
+ "I2=350.0 #current rating of SCR2\n",
+ "\n",
+ "#Calculations\n",
+ "R1=V1/I1\n",
+ "R2=V2/I2\n",
+ "I=600.0 #current to be shared\n",
+ " #for SCR1 % I*(R1+R)/(total resistance)=k*I1 (1)\n",
+ " #for SCR2 % I*(R2+R)/(total resistance)=k*I2 (2)\n",
+ " #(1)/(2)\n",
+ "R=(R2*I2-R1*I1)/(I1-I2)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"RSequired value of resistance=%.3f ohm\" %R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RSequired value of resistance=0.004 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.25, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=2000.0 #Hz\n",
+ "C=0.04*10**-6\n",
+ "n=.72\n",
+ "\n",
+ "#Calculations\n",
+ "R=1/(f*C*math.log(1/(1-n))) \n",
+ "V_p=18\n",
+ "V_BB=V_p/n\n",
+ "R2=10**4/(n*V_BB) \n",
+ "I=4.2*10**-3 #leakage current\n",
+ "R_BB=5000\n",
+ "R1=(V_BB/I)-R2-R_BB\n",
+ "\n",
+ "#Results\n",
+ "print(\"R=%.2f kilo-ohm\" %(R/1000))\n",
+ "print(\"\\nR2=%.2f ohm\" %R2)\n",
+ "print(\"\\nR1=%.0f ohm\" %R1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R=9.82 kilo-ohm\n",
+ "\n",
+ "R2=555.56 ohm\n",
+ "\n",
+ "R1=397 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.26, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_p=18.0\n",
+ "n=.72\n",
+ "V_BB=V_p/n\n",
+ "I_p=.6*10**-3\n",
+ "I_v=2.5*10**-3\n",
+ "V_v=1\n",
+ "\n",
+ "#Calculations\n",
+ "R_max=V_BB*(1-n)/I_p \n",
+ "print(\"R_max=%.2f kilo-ohm\" %(R_max/1000))\n",
+ "R_min=(V_BB-V_v)/I_v \n",
+ "print(\"\\nR_min=%.2f kilo-ohm\" %(R_min/1000))\n",
+ "\n",
+ "C=.04*10**-6\n",
+ "f_min=1/(R_max*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_min=%.3f kHz\" %(f_min/1000))\n",
+ "f_max=1/(R_min*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_max=%.2f kHz\" %(f_max/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_max=11.67 kilo-ohm\n",
+ "\n",
+ "R_min=9.60 kilo-ohm\n",
+ "\n",
+ "f_min=1.683 kHz\n",
+ "\n",
+ "f_max=2.05 kHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter4_4.ipynb b/_Power_Electronics/Chapter4_4.ipynb new file mode 100755 index 00000000..22311574 --- /dev/null +++ b/_Power_Electronics/Chapter4_4.ipynb @@ -0,0 +1,946 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 04 : Thyristors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "P=.5 #P=V_g*I_g\n",
+ "s=130 #s=V_g/I_g\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=math.sqrt(P/s)\n",
+ "V_g=s*I_g\n",
+ "E=15\n",
+ "R_s=(E-V_g)/I_g \n",
+ "\n",
+ "#Results\n",
+ "print(\"Gate source resistance=%.2f ohm\" %R_s)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Gate source resistance=111.87 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4, Page No 149"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R_s=120 #slope of load line is -120V/A. This gives gate source resistance\n",
+ "print(\"gate source resistance=%.0f ohm\" %R_s)\n",
+ "\n",
+ "P=.4 #P=V_g*I_g\n",
+ "E_s=15\n",
+ "\n",
+ "#Calculations\n",
+ " #E_s=I_g*R_s+V_g % after solving this\n",
+ " #120*I_g**2-15*I_g+0.4=0 so\n",
+ "a=120 \n",
+ "b=-15\n",
+ "c=0.4\n",
+ "D=math.sqrt((b**2)-4*a*c)\n",
+ "I_g=(-b+D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.3f V\" %V_g)\n",
+ "I_g=(-b-D)/(2*a) \n",
+ "V_g=P/I_g\n",
+ "print(\"\\ntrigger current=%.2f mA\" %(I_g*10**3)) \n",
+ "print(\"\\nthen trigger voltage=%.2f V\" %V_g)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "gate source resistance=120 ohm\n",
+ "\n",
+ "trigger current=86.44 mA\n",
+ "\n",
+ "then trigger voltage=4.628 V\n",
+ "\n",
+ "trigger current=38.56 mA\n",
+ "\n",
+ "then trigger voltage=10.37 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#V_g=1+10*I_g\n",
+ "P_gm=5 #P_gm=V_g*I_g\n",
+ "#after solving % eqn becomes 10*I_g**2+I_g-5=0\n",
+ "a=10.0 \n",
+ "b=1.0 \n",
+ "c=-5\n",
+ "\n",
+ "#Calculations\n",
+ "I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
+ "E_s=15\n",
+ "#using E_s=R_s*I_g+V_g\n",
+ "R_s=(E_s-1)/I_g-10 \n",
+ "P_gav=.3 #W\n",
+ "T=20*10**-6\n",
+ "f=P_gav/(P_gm*T)\n",
+ "dl=f*T\n",
+ "\n",
+ "#Results\n",
+ "print(\"Reistance=%.3f ohm\" %R_s)\n",
+ "print(\"Triggering freq=%.0f kHz\" %(f/1000))\n",
+ "print(\"Tduty cycle=%.2f\" %dl)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Reistance=11.248 ohm\n",
+ "Triggering freq=3 kHz\n",
+ "Tduty cycle=0.06\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.6, Page No 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=.1\n",
+ "E=200.0\n",
+ "L=0.2\n",
+ "\n",
+ "#Calculations\n",
+ "t=I*L/E \n",
+ "R=20.0\n",
+ "t1=(-L/R)*math.log(1-(R*I/E)) \n",
+ "L=2.0\n",
+ "t2=(-L/R)*math.log(1-(R*I/E)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"in case load consists of (a)L=.2H\")\n",
+ "print(\"min gate pulse width=%.0f us\" %(t*10**6))\n",
+ "print(\"(b)R=20ohm in series with L=.2H\")\n",
+ "print(\"min gate pulse width=%.3f us\" %(t1*10**6))\n",
+ "print(\"(c)R=20ohm in series with L=2H\")\n",
+ "print(\"min gate pulse width=%.2f us\" %(t2*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "in case load consists of (a)L=.2H\n",
+ "min gate pulse width=100 us\n",
+ "(b)R=20ohm in series with L=.2H\n",
+ "min gate pulse width=100.503 us\n",
+ "(c)R=20ohm in series with L=2H\n",
+ "min gate pulse width=1005.03 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " I_m=1 #supposition\n",
+ " I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))\n",
+ " I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when conduction angle=180\")\n",
+ "th=0\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "th=90\n",
+ "I_TAV=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=30\")\n",
+ "th=150\n",
+ "I_TAV=theta(th)\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=22.282 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=15.756 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=8.790 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.10, Page No 164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "def theta(th):\n",
+ " n=360.0/th\n",
+ " I=1.0 #supposition\n",
+ " I_av=I/n\n",
+ " I_rms=I/math.sqrt(n)\n",
+ " FF=I_rms/I_av\n",
+ " I_rms=35\n",
+ " I_TAV=I_rms/FF\n",
+ " return I_TAV\n",
+ "\n",
+ "#Calculations\n",
+ "th=180.0\n",
+ "I_TAV1=theta(th)\n",
+ "th=90.0\n",
+ "I_TAV2=theta(th)\n",
+ "th=30.0\n",
+ "I_TAV3=theta(th)\n",
+ "\n",
+ "#Results\n",
+ "print(\"when conduction angle=180\")\n",
+ "print(\"avg on current rating=%.3f A\" %I_TAV)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"avg on current rating=%.1f A\" %I_TAV2)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"avg on current rating=%.4f A\" %I_TAV3)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when conduction angle=180\n",
+ "avg on current rating=8.790 A\n",
+ "when conduction angle=90\n",
+ "avg on current rating=17.5 A\n",
+ "when conduction angle=30\n",
+ "avg on current rating=10.1036 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.11 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "f=50.0 #Hz\n",
+ "\n",
+ "#Calculations\n",
+ "I_sb=3000.0\n",
+ "t=1/(4*f)\n",
+ "T=1/(2*f)\n",
+ "I=math.sqrt(I_sb**2*t/T) \n",
+ "r=(I_sb/math.sqrt(2))**2*T \n",
+ "\n",
+ "#Results\n",
+ "print(\"surge current rating=%.2f A\" %I)\n",
+ "print(\"\\nI**2*t rating=%.0f A^2.s\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "surge current rating=2121.32 A\n",
+ "\n",
+ "I**2*t rating=45000 A^2.s\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Page No 165"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=300.0 #V\n",
+ "R=60.0 #ohm\n",
+ "L=2.0 #H\n",
+ "\n",
+ "#Calculations\n",
+ "t=40*10**-6 #s\n",
+ "i_T=(V_s/R)*(1-math.exp(-R*t/L))\n",
+ "i=.036 #A\n",
+ "R1=V_s/(i-i_T)\n",
+ "\n",
+ "#Results\n",
+ "print(\"maximum value of remedial parameter=%.3f kilo-ohm\" %(R1/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum value of remedial parameter=9.999 kilo-ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 Page No 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_p=230.0*math.sqrt(2)\n",
+ "\n",
+ "#Calculations\n",
+ "R=1+((1)**-1+(10)**-1)**-1\n",
+ "A=V_p/R\n",
+ "s=1 #s\n",
+ "t_c=20*A**-2*s\n",
+ "\n",
+ "#Results\n",
+ "print(\"fault clearance time=%.4f ms\" %(t_c*10**3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fault clearance time=0.6890 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.17, Page No 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_s=math.sqrt(2)*230 #V\n",
+ "L=15*10**-6 #H\n",
+ "I=V_s/L #I=(di/dt)_max\n",
+ "R_s=10 #ohm\n",
+ "v=I*R_s #v=(dv/dt)_max\n",
+ "\n",
+ "#Calculations\n",
+ "f=50 #Hz\n",
+ "X_L=L*2*math.pi*f\n",
+ "R=2\n",
+ "I_max=V_s/(R+X_L) \n",
+ "FF=math.pi/math.sqrt(2)\n",
+ "I_TAV1=I_max/FF \n",
+ "FF=3.98184\n",
+ "I_TAV2=I_max/FF \n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"(di/dt)_max=%.3f A/usec\" %(I/10**6))\n",
+ "print(\"\\n(dv/dt)_max=%.2f V/usec\" %(v/10**6))\n",
+ "print(\"\\nI_rms=%.3f A\" %I_max)\n",
+ "print(\"when conduction angle=90\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV1)\n",
+ "print(\"when conduction angle=30\")\n",
+ "print(\"I_TAV=%.3f A\" %I_TAV2)\n",
+ "print(\"\\nvoltage rating=%.3f V\" %(2.75*V_s)) #rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(di/dt)_max=21.685 A/usec\n",
+ "\n",
+ "(dv/dt)_max=216.85 V/usec\n",
+ "\n",
+ "I_rms=162.252 A\n",
+ "when conduction angle=90\n",
+ "I_TAV=73.039 A\n",
+ "when conduction angle=30\n",
+ "I_TAV=40.748 A\n",
+ "\n",
+ "voltage rating=894.490 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.19, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "T_jm=125\n",
+ "th_jc=.15 #degC/W\n",
+ "th_cs=0.075 #degC/W\n",
+ "\n",
+ "\n",
+ "#Calculations\n",
+ "dT=54 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "dT=58 #dT=T_s-T_a\n",
+ "P_av=120\n",
+ "th_sa=dT/P_av\n",
+ "T_a=40 #ambient temp\n",
+ "P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)\n",
+ "if (P_av-120)<1 :\n",
+ " print(\"selection of heat sink is satisfactory\")\n",
+ "\n",
+ "V_m=math.sqrt(2)*230\n",
+ "R=2\n",
+ "I_TAV=V_m/(R*math.pi)\n",
+ "P_av=90\n",
+ "th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)\n",
+ "dT=P_av*th_sa\n",
+ "print(\"for heat sink\") \n",
+ "print(\"T_s-T_a=%.2f degC\" %dT) \n",
+ "print(\"\\nP_av=%.0f W\" %P_av)\n",
+ "P=(V_m/2)**2/R\n",
+ "eff=P/(P+P_av) \n",
+ "print(\"\\nckt efficiency=%.3f pu\" %eff)\n",
+ "a=60 #delay angle\n",
+ "I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))\n",
+ "print(\"\\nI_TAV=%.2f A\" %I_TAV)\n",
+ "dT=46\n",
+ "T_s=dT+T_a\n",
+ "T_c=T_s+P_av*th_cs \n",
+ "T_j=T_c+P_av*th_jc \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\ncase temp=%.2f degC\" %T_c)\n",
+ "print(\"\\njunction temp=%.2f degC\" %T_j)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for heat sink\n",
+ "T_s-T_a=-20.25 degC\n",
+ "\n",
+ "P_av=90 W\n",
+ "\n",
+ "ckt efficiency=0.993 pu\n",
+ "\n",
+ "I_TAV=38.83 A\n",
+ "\n",
+ "case temp=92.75 degC\n",
+ "\n",
+ "junction temp=106.25 degC\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.20, Page No 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_j=125.0 #degC\n",
+ "T_s=70.0 #degC\n",
+ "th_jc=.16 #degC/W\n",
+ "th_cs=.08 #degC/W\n",
+ "\n",
+ "#Calculations\n",
+ "P_av1=(T_j-T_s)/(th_jc+th_cs) \n",
+ "\n",
+ "T_s=60 #degC\n",
+ "P_av2=(T_j-T_s)/(th_jc+th_cs) \n",
+ "inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1) \n",
+ "\n",
+ "#Results\n",
+ "print(\"Total avg power loss in thristor sink combination=%.2f W\" %P_av1)\n",
+ "print(\"Percentage inc in rating=%.2f\" %inc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Total avg power loss in thristor sink combination=229.17 W\n",
+ "Percentage inc in rating=8.71\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.21, Page No 197"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "R=25000.0\n",
+ "I_l1=.021 #I_l=leakage current\n",
+ "I_l2=.025\n",
+ "I_l3=.018\n",
+ "I_l4=.016\n",
+ " #V1=(I-I_l1)*R\n",
+ " #V2=(I-I_l2)*R\n",
+ " #V3=(I-I_l3)*R\n",
+ " #V4=(I-I_l4)*R\n",
+ " #V=V1+V2+V3+V4\n",
+ " \n",
+ "#Calculations\n",
+ "V=10000.0\n",
+ "I_l=I_l1+I_l2+I_l3+I_l4\n",
+ " #after solving\n",
+ "I=((V/R)+I_l)/4\n",
+ "R_c=40.0\n",
+ "V1=(I-I_l1)*R \n",
+ "\n",
+ "#Resluts\n",
+ "print(\"voltage across SCR1=%.0f V\" %V1)\n",
+ "V2=(I-I_l2)*R \n",
+ "print(\"\\nvoltage across SCR2=%.0f V\" %V2)\n",
+ "V3=(I-I_l3)*R \n",
+ "print(\"\\nvoltage across SCR3=%.0f V\" %V3)\n",
+ "V4=(I-I_l4)*R \n",
+ "print(\"\\nvoltage across SCR4=%.0f V\" %V4)\n",
+ "\n",
+ "I1=V1/R_c \n",
+ "print(\"\\ndischarge current through SCR1=%.3f A\" %I1)\n",
+ "I2=V2/R_c \n",
+ "print(\"\\ndischarge current through SCR2=%.3f A\" %I2)\n",
+ "I3=V3/R_c \n",
+ "print(\"\\ndischarge current through SCR3=%.3f A\" %I3)\n",
+ "I4=V4/R_c \n",
+ "print(\"\\ndischarge current through SCR4=%.3f A\" %I4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "voltage across SCR1=2475 V\n",
+ "\n",
+ "voltage across SCR2=2375 V\n",
+ "\n",
+ "voltage across SCR3=2550 V\n",
+ "\n",
+ "voltage across SCR4=2600 V\n",
+ "\n",
+ "discharge current through SCR1=61.875 A\n",
+ "\n",
+ "discharge current through SCR2=59.375 A\n",
+ "\n",
+ "discharge current through SCR3=63.750 A\n",
+ "\n",
+ "discharge current through SCR4=65.000 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.22, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_r=1000 #rating of SCR\n",
+ "I_r=200 #rating of SCR\n",
+ "V_s=6000 #rating of String\n",
+ "I_s=1000 #rating of String\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"when DRF=.1\")\n",
+ "DRF=.1\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))\n",
+ "print(\"when DRF=.2\")\n",
+ "DRF=.2\n",
+ "\n",
+ "#Results\n",
+ "n_s=V_s/(V_r*(1-DRF)) \n",
+ "print(\"number of series units=%.0f\" %math.ceil(n_s))\n",
+ "n_p=I_s/(I_r*(1-DRF)) \n",
+ "print(\"\\nnumber of parrallel units=%.0f\" %math.ceil(n_p))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when DRF=.1\n",
+ "number of series units=7\n",
+ "\n",
+ "number of parrallel units=6\n",
+ "when DRF=.2\n",
+ "number of series units=8\n",
+ "\n",
+ "number of parrallel units=7\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.23, Page No 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.6 #on state voltage drop of SCR1\n",
+ "V2=1.2 #on state voltage drop of SCR2\n",
+ "I1=250.0 #current rating of SCR1\n",
+ "I2=350.0 #current rating of SCR2\n",
+ "\n",
+ "#Calculations\n",
+ "R1=V1/I1\n",
+ "R2=V2/I2\n",
+ "I=600.0 #current to be shared\n",
+ " #for SCR1 % I*(R1+R)/(total resistance)=k*I1 (1)\n",
+ " #for SCR2 % I*(R2+R)/(total resistance)=k*I2 (2)\n",
+ " #(1)/(2)\n",
+ "R=(R2*I2-R1*I1)/(I1-I2)\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"RSequired value of resistance=%.3f ohm\" %R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RSequired value of resistance=0.004 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.25, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=2000.0 #Hz\n",
+ "C=0.04*10**-6\n",
+ "n=.72\n",
+ "\n",
+ "#Calculations\n",
+ "R=1/(f*C*math.log(1/(1-n))) \n",
+ "V_p=18\n",
+ "V_BB=V_p/n\n",
+ "R2=10**4/(n*V_BB) \n",
+ "I=4.2*10**-3 #leakage current\n",
+ "R_BB=5000\n",
+ "R1=(V_BB/I)-R2-R_BB\n",
+ "\n",
+ "#Results\n",
+ "print(\"R=%.2f kilo-ohm\" %(R/1000))\n",
+ "print(\"\\nR2=%.2f ohm\" %R2)\n",
+ "print(\"\\nR1=%.0f ohm\" %R1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R=9.82 kilo-ohm\n",
+ "\n",
+ "R2=555.56 ohm\n",
+ "\n",
+ "R1=397 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.26, Page No 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "\n",
+ "V_p=18.0\n",
+ "n=.72\n",
+ "V_BB=V_p/n\n",
+ "I_p=.6*10**-3\n",
+ "I_v=2.5*10**-3\n",
+ "V_v=1\n",
+ "\n",
+ "#Calculations\n",
+ "R_max=V_BB*(1-n)/I_p \n",
+ "print(\"R_max=%.2f kilo-ohm\" %(R_max/1000))\n",
+ "R_min=(V_BB-V_v)/I_v \n",
+ "print(\"\\nR_min=%.2f kilo-ohm\" %(R_min/1000))\n",
+ "\n",
+ "C=.04*10**-6\n",
+ "f_min=1/(R_max*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_min=%.3f kHz\" %(f_min/1000))\n",
+ "f_max=1/(R_min*C*math.log(1/(1-n))) \n",
+ "print(\"\\nf_max=%.2f kHz\" %(f_max/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_max=11.67 kilo-ohm\n",
+ "\n",
+ "R_min=9.60 kilo-ohm\n",
+ "\n",
+ "f_min=1.683 kHz\n",
+ "\n",
+ "f_max=2.05 kHz\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter5.ipynb b/_Power_Electronics/Chapter5.ipynb new file mode 100755 index 00000000..1d261f20 --- /dev/null +++ b/_Power_Electronics/Chapter5.ipynb @@ -0,0 +1,511 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 05 : Thyristor Commutation Techniques"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1, Page No 252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=5.0*10**-3 #mH\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "V_s=200 #V\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/s\n",
+ "t_o=math.pi/w_o #ms\n",
+ "\n",
+ "#Results\n",
+ "print('conduction time of thyristor = %.2f ms' %(t_o*1000))\n",
+ "print('voltage across thyristor=%.0f V' %V_s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor = 0.99 ms\n",
+ "voltage across thyristor=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2, Page No 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "L=5.0*10**-6 #\u00b5H\n",
+ "V_s=230.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/sec\n",
+ "t_o=math.pi/w_o #\u00b5S\n",
+ "I_o=300 \n",
+ "a = math.degrees(math.asin(I_o/(2*V_s))) \n",
+ "V_ab = V_s*math.cos(math.radians(a)) #V \n",
+ "t_c=C*V_ab/I_o #\u00b5s\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"conduction time of auxillery thyristor=%.2f us\" %(t_o*10**6))\n",
+ "print(\"voltage across main thyristor=%.2f V\" %V_ab)\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of auxillery thyristor=31.42 us\n",
+ "voltage across main thyristor=174.36 V\n",
+ "ckt turn off time=11.62 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3 Page No 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R1=10.0 #\u2126\n",
+ "R2=100.0 #\u2126\n",
+ "C=0 # value of capacitor\n",
+ "\n",
+ "#Calculations\n",
+ "I1=V_s*(1/R1+2/R2) #A\n",
+ "I2=V_s*(2/R1+1/R2) #A\n",
+ "t_c1=40*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C1=t_c1*fos/(R1*math.log(2))\n",
+ "C2=t_c1*fos/(R2*math.log(2))\n",
+ "if C1 > C2 :\n",
+ " C = C1*10**6\n",
+ "else :\n",
+ " C = C2*10**6\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of current through SCR1=%.2f A\" %I1); \n",
+ "print(\"Peak value of current through SCR2=%.2f A\" %I2);\n",
+ "print(\"Value of capacitor=%.2f uF\" %C);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of current through SCR1=24.00 A\n",
+ "Peak value of current through SCR2=42.00 A\n",
+ "Value of capacitor=11.54 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4, Page No 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "I_o=120.0 #A\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "t_c=C*V_s/I_o #\u00b5s\n",
+ "w_o=math.sqrt(1/(L*C)) \n",
+ "t_c1=math.pi/(2*w_o) #\u00b5s\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through main thyristor=%.2f A\" %(I_o+I_p))\n",
+ "print(\"Current through auxillery thyristor=%.2f A\" %I_o)\n",
+ "print(\"Circuit turn off time for main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"Circuit turn off time for auxillery thyristor=%.2f us\" %(t_c1*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through main thyristor=445.27 A\n",
+ "Current through auxillery thyristor=120.00 A\n",
+ "Circuit turn off time for main thyristor=76.67 us\n",
+ "Circuit turn off time for auxillery thyristor=44.43 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "C_j=25*10**-12 #pF\n",
+ "I_c=5*10**-3 #charging current\n",
+ "V_s=200.0 #V\n",
+ "R=50.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=(C_j*V_s)/(I_c*R)\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Value of C=%.2f \u00b5F\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of C=0.02 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R=5.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=10.0*10**-6\n",
+ "#for turn off V_s*(1-2*exp(-t/(R*C)))=0, so after solving\n",
+ "t_c=R*C*math.log(2.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"circuit turn off time=%.2f us\" %(t_c*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circuit turn off time=34.66 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7, Page No 264 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0 #\u2126\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "\n",
+ "#Calculations\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t_1=math.pi/w_r\n",
+ "\n",
+ "#Results\n",
+ "print(\"conduction time of thyristor=%.3f us\" %(t_1*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor=125.664 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "dv=400*10.0**-6 #dv=dv_T/dt(V/s)\n",
+ "V_s=200.0 #v\n",
+ "R=20.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=V_s/(R*dv) \n",
+ "C_j=.025*10**-12\n",
+ "C_s=C-C_j\n",
+ "I_T=40;\n",
+ "R_s=1/((I_T/V_s)-(1/R)) \n",
+ "#value of R_s in book is wrongly calculated\n",
+ "\n",
+ "#Results\n",
+ "print(\"R_s=%.2f ohm\" %R_s)\n",
+ "print(\"C_s=%.3f uF\" %(C_s/10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_s=6.67 ohm\n",
+ "C_s=0.025 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "C=20.0*10**-6 #\u00b5H \n",
+ "L=0.2*10**-3 #\u00b5F\n",
+ "i_c=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=V_s*math.sqrt(C/L)\n",
+ "w_o=1.0/math.sqrt(L*C)\n",
+ "t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))\n",
+ "t_o=math.pi/w_o\n",
+ "t_c=t_o-2*t_1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"reqd time=%.2f us\" %(t_1*10**6))\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"ckt turn off time=%.5f us\" %t_1)\n",
+ "#solution in book wrong, as wrong values are selected while filling the formuleas"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "reqd time=575.37 us\n",
+ "ckt turn off time=-952.05 us\n",
+ "ckt turn off time=0.00058 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11 Page No 268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #\u00b5H\n",
+ "R=50.0 #\u2126\n",
+ "V_s=200.0 #V\n",
+ "t=0.01 #sec\n",
+ "Vd=0.7\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "t=8*10**-3\n",
+ "i1=i-t*Vd \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through L = %.2f A\" %i1)\n",
+ "i_R=0 #current in R at t=.008s\n",
+ "print(\"Current through R = %.2f A\" %i_R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through L = 1.57 A\n",
+ "Current through R = 0.00 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12, Page No 269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #H\n",
+ "R=50.0 #ohm\n",
+ "V_s=200.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "t=0.01 #s\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "C=1*10**-6 #F\n",
+ "V_c=math.sqrt(L/C)*i\n",
+ "\n",
+ "#Results\n",
+ "print(\"current in R,L=%.2f A\" %i)\n",
+ "print(\"voltage across C=%.2f kV\" %(V_c/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current in R,L=1.57 A\n",
+ "voltage across C=1.57 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter5_1.ipynb b/_Power_Electronics/Chapter5_1.ipynb new file mode 100755 index 00000000..1d261f20 --- /dev/null +++ b/_Power_Electronics/Chapter5_1.ipynb @@ -0,0 +1,511 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 05 : Thyristor Commutation Techniques"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1, Page No 252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=5.0*10**-3 #mH\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "V_s=200 #V\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/s\n",
+ "t_o=math.pi/w_o #ms\n",
+ "\n",
+ "#Results\n",
+ "print('conduction time of thyristor = %.2f ms' %(t_o*1000))\n",
+ "print('voltage across thyristor=%.0f V' %V_s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor = 0.99 ms\n",
+ "voltage across thyristor=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2, Page No 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "L=5.0*10**-6 #\u00b5H\n",
+ "V_s=230.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/sec\n",
+ "t_o=math.pi/w_o #\u00b5S\n",
+ "I_o=300 \n",
+ "a = math.degrees(math.asin(I_o/(2*V_s))) \n",
+ "V_ab = V_s*math.cos(math.radians(a)) #V \n",
+ "t_c=C*V_ab/I_o #\u00b5s\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"conduction time of auxillery thyristor=%.2f us\" %(t_o*10**6))\n",
+ "print(\"voltage across main thyristor=%.2f V\" %V_ab)\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of auxillery thyristor=31.42 us\n",
+ "voltage across main thyristor=174.36 V\n",
+ "ckt turn off time=11.62 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3 Page No 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R1=10.0 #\u2126\n",
+ "R2=100.0 #\u2126\n",
+ "C=0 # value of capacitor\n",
+ "\n",
+ "#Calculations\n",
+ "I1=V_s*(1/R1+2/R2) #A\n",
+ "I2=V_s*(2/R1+1/R2) #A\n",
+ "t_c1=40*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C1=t_c1*fos/(R1*math.log(2))\n",
+ "C2=t_c1*fos/(R2*math.log(2))\n",
+ "if C1 > C2 :\n",
+ " C = C1*10**6\n",
+ "else :\n",
+ " C = C2*10**6\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of current through SCR1=%.2f A\" %I1); \n",
+ "print(\"Peak value of current through SCR2=%.2f A\" %I2);\n",
+ "print(\"Value of capacitor=%.2f uF\" %C);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of current through SCR1=24.00 A\n",
+ "Peak value of current through SCR2=42.00 A\n",
+ "Value of capacitor=11.54 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4, Page No 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "I_o=120.0 #A\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "t_c=C*V_s/I_o #\u00b5s\n",
+ "w_o=math.sqrt(1/(L*C)) \n",
+ "t_c1=math.pi/(2*w_o) #\u00b5s\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through main thyristor=%.2f A\" %(I_o+I_p))\n",
+ "print(\"Current through auxillery thyristor=%.2f A\" %I_o)\n",
+ "print(\"Circuit turn off time for main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"Circuit turn off time for auxillery thyristor=%.2f us\" %(t_c1*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through main thyristor=445.27 A\n",
+ "Current through auxillery thyristor=120.00 A\n",
+ "Circuit turn off time for main thyristor=76.67 us\n",
+ "Circuit turn off time for auxillery thyristor=44.43 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "C_j=25*10**-12 #pF\n",
+ "I_c=5*10**-3 #charging current\n",
+ "V_s=200.0 #V\n",
+ "R=50.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=(C_j*V_s)/(I_c*R)\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Value of C=%.2f \u00b5F\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of C=0.02 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R=5.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=10.0*10**-6\n",
+ "#for turn off V_s*(1-2*exp(-t/(R*C)))=0, so after solving\n",
+ "t_c=R*C*math.log(2.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"circuit turn off time=%.2f us\" %(t_c*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circuit turn off time=34.66 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7, Page No 264 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0 #\u2126\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "\n",
+ "#Calculations\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t_1=math.pi/w_r\n",
+ "\n",
+ "#Results\n",
+ "print(\"conduction time of thyristor=%.3f us\" %(t_1*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor=125.664 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "dv=400*10.0**-6 #dv=dv_T/dt(V/s)\n",
+ "V_s=200.0 #v\n",
+ "R=20.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=V_s/(R*dv) \n",
+ "C_j=.025*10**-12\n",
+ "C_s=C-C_j\n",
+ "I_T=40;\n",
+ "R_s=1/((I_T/V_s)-(1/R)) \n",
+ "#value of R_s in book is wrongly calculated\n",
+ "\n",
+ "#Results\n",
+ "print(\"R_s=%.2f ohm\" %R_s)\n",
+ "print(\"C_s=%.3f uF\" %(C_s/10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_s=6.67 ohm\n",
+ "C_s=0.025 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "C=20.0*10**-6 #\u00b5H \n",
+ "L=0.2*10**-3 #\u00b5F\n",
+ "i_c=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=V_s*math.sqrt(C/L)\n",
+ "w_o=1.0/math.sqrt(L*C)\n",
+ "t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))\n",
+ "t_o=math.pi/w_o\n",
+ "t_c=t_o-2*t_1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"reqd time=%.2f us\" %(t_1*10**6))\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"ckt turn off time=%.5f us\" %t_1)\n",
+ "#solution in book wrong, as wrong values are selected while filling the formuleas"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "reqd time=575.37 us\n",
+ "ckt turn off time=-952.05 us\n",
+ "ckt turn off time=0.00058 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11 Page No 268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #\u00b5H\n",
+ "R=50.0 #\u2126\n",
+ "V_s=200.0 #V\n",
+ "t=0.01 #sec\n",
+ "Vd=0.7\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "t=8*10**-3\n",
+ "i1=i-t*Vd \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through L = %.2f A\" %i1)\n",
+ "i_R=0 #current in R at t=.008s\n",
+ "print(\"Current through R = %.2f A\" %i_R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through L = 1.57 A\n",
+ "Current through R = 0.00 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12, Page No 269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #H\n",
+ "R=50.0 #ohm\n",
+ "V_s=200.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "t=0.01 #s\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "C=1*10**-6 #F\n",
+ "V_c=math.sqrt(L/C)*i\n",
+ "\n",
+ "#Results\n",
+ "print(\"current in R,L=%.2f A\" %i)\n",
+ "print(\"voltage across C=%.2f kV\" %(V_c/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current in R,L=1.57 A\n",
+ "voltage across C=1.57 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter5_2.ipynb b/_Power_Electronics/Chapter5_2.ipynb new file mode 100755 index 00000000..1d261f20 --- /dev/null +++ b/_Power_Electronics/Chapter5_2.ipynb @@ -0,0 +1,511 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 05 : Thyristor Commutation Techniques"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1, Page No 252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=5.0*10**-3 #mH\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "V_s=200 #V\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/s\n",
+ "t_o=math.pi/w_o #ms\n",
+ "\n",
+ "#Results\n",
+ "print('conduction time of thyristor = %.2f ms' %(t_o*1000))\n",
+ "print('voltage across thyristor=%.0f V' %V_s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor = 0.99 ms\n",
+ "voltage across thyristor=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2, Page No 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "L=5.0*10**-6 #\u00b5H\n",
+ "V_s=230.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/sec\n",
+ "t_o=math.pi/w_o #\u00b5S\n",
+ "I_o=300 \n",
+ "a = math.degrees(math.asin(I_o/(2*V_s))) \n",
+ "V_ab = V_s*math.cos(math.radians(a)) #V \n",
+ "t_c=C*V_ab/I_o #\u00b5s\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"conduction time of auxillery thyristor=%.2f us\" %(t_o*10**6))\n",
+ "print(\"voltage across main thyristor=%.2f V\" %V_ab)\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of auxillery thyristor=31.42 us\n",
+ "voltage across main thyristor=174.36 V\n",
+ "ckt turn off time=11.62 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3 Page No 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R1=10.0 #\u2126\n",
+ "R2=100.0 #\u2126\n",
+ "C=0 # value of capacitor\n",
+ "\n",
+ "#Calculations\n",
+ "I1=V_s*(1/R1+2/R2) #A\n",
+ "I2=V_s*(2/R1+1/R2) #A\n",
+ "t_c1=40*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C1=t_c1*fos/(R1*math.log(2))\n",
+ "C2=t_c1*fos/(R2*math.log(2))\n",
+ "if C1 > C2 :\n",
+ " C = C1*10**6\n",
+ "else :\n",
+ " C = C2*10**6\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of current through SCR1=%.2f A\" %I1); \n",
+ "print(\"Peak value of current through SCR2=%.2f A\" %I2);\n",
+ "print(\"Value of capacitor=%.2f uF\" %C);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of current through SCR1=24.00 A\n",
+ "Peak value of current through SCR2=42.00 A\n",
+ "Value of capacitor=11.54 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4, Page No 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "I_o=120.0 #A\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "t_c=C*V_s/I_o #\u00b5s\n",
+ "w_o=math.sqrt(1/(L*C)) \n",
+ "t_c1=math.pi/(2*w_o) #\u00b5s\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through main thyristor=%.2f A\" %(I_o+I_p))\n",
+ "print(\"Current through auxillery thyristor=%.2f A\" %I_o)\n",
+ "print(\"Circuit turn off time for main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"Circuit turn off time for auxillery thyristor=%.2f us\" %(t_c1*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through main thyristor=445.27 A\n",
+ "Current through auxillery thyristor=120.00 A\n",
+ "Circuit turn off time for main thyristor=76.67 us\n",
+ "Circuit turn off time for auxillery thyristor=44.43 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "C_j=25*10**-12 #pF\n",
+ "I_c=5*10**-3 #charging current\n",
+ "V_s=200.0 #V\n",
+ "R=50.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=(C_j*V_s)/(I_c*R)\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Value of C=%.2f \u00b5F\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of C=0.02 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R=5.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=10.0*10**-6\n",
+ "#for turn off V_s*(1-2*exp(-t/(R*C)))=0, so after solving\n",
+ "t_c=R*C*math.log(2.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"circuit turn off time=%.2f us\" %(t_c*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circuit turn off time=34.66 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7, Page No 264 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0 #\u2126\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "\n",
+ "#Calculations\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t_1=math.pi/w_r\n",
+ "\n",
+ "#Results\n",
+ "print(\"conduction time of thyristor=%.3f us\" %(t_1*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor=125.664 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "dv=400*10.0**-6 #dv=dv_T/dt(V/s)\n",
+ "V_s=200.0 #v\n",
+ "R=20.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=V_s/(R*dv) \n",
+ "C_j=.025*10**-12\n",
+ "C_s=C-C_j\n",
+ "I_T=40;\n",
+ "R_s=1/((I_T/V_s)-(1/R)) \n",
+ "#value of R_s in book is wrongly calculated\n",
+ "\n",
+ "#Results\n",
+ "print(\"R_s=%.2f ohm\" %R_s)\n",
+ "print(\"C_s=%.3f uF\" %(C_s/10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_s=6.67 ohm\n",
+ "C_s=0.025 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "C=20.0*10**-6 #\u00b5H \n",
+ "L=0.2*10**-3 #\u00b5F\n",
+ "i_c=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=V_s*math.sqrt(C/L)\n",
+ "w_o=1.0/math.sqrt(L*C)\n",
+ "t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))\n",
+ "t_o=math.pi/w_o\n",
+ "t_c=t_o-2*t_1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"reqd time=%.2f us\" %(t_1*10**6))\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"ckt turn off time=%.5f us\" %t_1)\n",
+ "#solution in book wrong, as wrong values are selected while filling the formuleas"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "reqd time=575.37 us\n",
+ "ckt turn off time=-952.05 us\n",
+ "ckt turn off time=0.00058 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11 Page No 268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #\u00b5H\n",
+ "R=50.0 #\u2126\n",
+ "V_s=200.0 #V\n",
+ "t=0.01 #sec\n",
+ "Vd=0.7\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "t=8*10**-3\n",
+ "i1=i-t*Vd \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through L = %.2f A\" %i1)\n",
+ "i_R=0 #current in R at t=.008s\n",
+ "print(\"Current through R = %.2f A\" %i_R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through L = 1.57 A\n",
+ "Current through R = 0.00 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12, Page No 269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #H\n",
+ "R=50.0 #ohm\n",
+ "V_s=200.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "t=0.01 #s\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "C=1*10**-6 #F\n",
+ "V_c=math.sqrt(L/C)*i\n",
+ "\n",
+ "#Results\n",
+ "print(\"current in R,L=%.2f A\" %i)\n",
+ "print(\"voltage across C=%.2f kV\" %(V_c/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current in R,L=1.57 A\n",
+ "voltage across C=1.57 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter5_3.ipynb b/_Power_Electronics/Chapter5_3.ipynb new file mode 100755 index 00000000..1d261f20 --- /dev/null +++ b/_Power_Electronics/Chapter5_3.ipynb @@ -0,0 +1,511 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 05 : Thyristor Commutation Techniques"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1, Page No 252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=5.0*10**-3 #mH\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "V_s=200 #V\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/s\n",
+ "t_o=math.pi/w_o #ms\n",
+ "\n",
+ "#Results\n",
+ "print('conduction time of thyristor = %.2f ms' %(t_o*1000))\n",
+ "print('voltage across thyristor=%.0f V' %V_s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor = 0.99 ms\n",
+ "voltage across thyristor=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2, Page No 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "L=5.0*10**-6 #\u00b5H\n",
+ "V_s=230.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/sec\n",
+ "t_o=math.pi/w_o #\u00b5S\n",
+ "I_o=300 \n",
+ "a = math.degrees(math.asin(I_o/(2*V_s))) \n",
+ "V_ab = V_s*math.cos(math.radians(a)) #V \n",
+ "t_c=C*V_ab/I_o #\u00b5s\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"conduction time of auxillery thyristor=%.2f us\" %(t_o*10**6))\n",
+ "print(\"voltage across main thyristor=%.2f V\" %V_ab)\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of auxillery thyristor=31.42 us\n",
+ "voltage across main thyristor=174.36 V\n",
+ "ckt turn off time=11.62 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3 Page No 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R1=10.0 #\u2126\n",
+ "R2=100.0 #\u2126\n",
+ "C=0 # value of capacitor\n",
+ "\n",
+ "#Calculations\n",
+ "I1=V_s*(1/R1+2/R2) #A\n",
+ "I2=V_s*(2/R1+1/R2) #A\n",
+ "t_c1=40*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C1=t_c1*fos/(R1*math.log(2))\n",
+ "C2=t_c1*fos/(R2*math.log(2))\n",
+ "if C1 > C2 :\n",
+ " C = C1*10**6\n",
+ "else :\n",
+ " C = C2*10**6\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of current through SCR1=%.2f A\" %I1); \n",
+ "print(\"Peak value of current through SCR2=%.2f A\" %I2);\n",
+ "print(\"Value of capacitor=%.2f uF\" %C);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of current through SCR1=24.00 A\n",
+ "Peak value of current through SCR2=42.00 A\n",
+ "Value of capacitor=11.54 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4, Page No 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "I_o=120.0 #A\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "t_c=C*V_s/I_o #\u00b5s\n",
+ "w_o=math.sqrt(1/(L*C)) \n",
+ "t_c1=math.pi/(2*w_o) #\u00b5s\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through main thyristor=%.2f A\" %(I_o+I_p))\n",
+ "print(\"Current through auxillery thyristor=%.2f A\" %I_o)\n",
+ "print(\"Circuit turn off time for main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"Circuit turn off time for auxillery thyristor=%.2f us\" %(t_c1*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through main thyristor=445.27 A\n",
+ "Current through auxillery thyristor=120.00 A\n",
+ "Circuit turn off time for main thyristor=76.67 us\n",
+ "Circuit turn off time for auxillery thyristor=44.43 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "C_j=25*10**-12 #pF\n",
+ "I_c=5*10**-3 #charging current\n",
+ "V_s=200.0 #V\n",
+ "R=50.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=(C_j*V_s)/(I_c*R)\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Value of C=%.2f \u00b5F\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of C=0.02 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R=5.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=10.0*10**-6\n",
+ "#for turn off V_s*(1-2*exp(-t/(R*C)))=0, so after solving\n",
+ "t_c=R*C*math.log(2.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"circuit turn off time=%.2f us\" %(t_c*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circuit turn off time=34.66 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7, Page No 264 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0 #\u2126\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "\n",
+ "#Calculations\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t_1=math.pi/w_r\n",
+ "\n",
+ "#Results\n",
+ "print(\"conduction time of thyristor=%.3f us\" %(t_1*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor=125.664 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "dv=400*10.0**-6 #dv=dv_T/dt(V/s)\n",
+ "V_s=200.0 #v\n",
+ "R=20.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=V_s/(R*dv) \n",
+ "C_j=.025*10**-12\n",
+ "C_s=C-C_j\n",
+ "I_T=40;\n",
+ "R_s=1/((I_T/V_s)-(1/R)) \n",
+ "#value of R_s in book is wrongly calculated\n",
+ "\n",
+ "#Results\n",
+ "print(\"R_s=%.2f ohm\" %R_s)\n",
+ "print(\"C_s=%.3f uF\" %(C_s/10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_s=6.67 ohm\n",
+ "C_s=0.025 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "C=20.0*10**-6 #\u00b5H \n",
+ "L=0.2*10**-3 #\u00b5F\n",
+ "i_c=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=V_s*math.sqrt(C/L)\n",
+ "w_o=1.0/math.sqrt(L*C)\n",
+ "t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))\n",
+ "t_o=math.pi/w_o\n",
+ "t_c=t_o-2*t_1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"reqd time=%.2f us\" %(t_1*10**6))\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"ckt turn off time=%.5f us\" %t_1)\n",
+ "#solution in book wrong, as wrong values are selected while filling the formuleas"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "reqd time=575.37 us\n",
+ "ckt turn off time=-952.05 us\n",
+ "ckt turn off time=0.00058 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11 Page No 268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #\u00b5H\n",
+ "R=50.0 #\u2126\n",
+ "V_s=200.0 #V\n",
+ "t=0.01 #sec\n",
+ "Vd=0.7\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "t=8*10**-3\n",
+ "i1=i-t*Vd \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through L = %.2f A\" %i1)\n",
+ "i_R=0 #current in R at t=.008s\n",
+ "print(\"Current through R = %.2f A\" %i_R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through L = 1.57 A\n",
+ "Current through R = 0.00 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12, Page No 269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #H\n",
+ "R=50.0 #ohm\n",
+ "V_s=200.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "t=0.01 #s\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "C=1*10**-6 #F\n",
+ "V_c=math.sqrt(L/C)*i\n",
+ "\n",
+ "#Results\n",
+ "print(\"current in R,L=%.2f A\" %i)\n",
+ "print(\"voltage across C=%.2f kV\" %(V_c/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current in R,L=1.57 A\n",
+ "voltage across C=1.57 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter5_4.ipynb b/_Power_Electronics/Chapter5_4.ipynb new file mode 100755 index 00000000..1d261f20 --- /dev/null +++ b/_Power_Electronics/Chapter5_4.ipynb @@ -0,0 +1,511 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 05 : Thyristor Commutation Techniques"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.1, Page No 252"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=5.0*10**-3 #mH\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "V_s=200 #V\n",
+ "\n",
+ "#Calculations\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/s\n",
+ "t_o=math.pi/w_o #ms\n",
+ "\n",
+ "#Results\n",
+ "print('conduction time of thyristor = %.2f ms' %(t_o*1000))\n",
+ "print('voltage across thyristor=%.0f V' %V_s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor = 0.99 ms\n",
+ "voltage across thyristor=200 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.2, Page No 255"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "C=20.0*10**-6 #\u00b5F\n",
+ "L=5.0*10**-6 #\u00b5H\n",
+ "V_s=230.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "w_o=math.sqrt(1/(L*C)) #rad/sec\n",
+ "t_o=math.pi/w_o #\u00b5S\n",
+ "I_o=300 \n",
+ "a = math.degrees(math.asin(I_o/(2*V_s))) \n",
+ "V_ab = V_s*math.cos(math.radians(a)) #V \n",
+ "t_c=C*V_ab/I_o #\u00b5s\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"conduction time of auxillery thyristor=%.2f us\" %(t_o*10**6))\n",
+ "print(\"voltage across main thyristor=%.2f V\" %V_ab)\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of auxillery thyristor=31.42 us\n",
+ "voltage across main thyristor=174.36 V\n",
+ "ckt turn off time=11.62 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.3 Page No 258"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R1=10.0 #\u2126\n",
+ "R2=100.0 #\u2126\n",
+ "C=0 # value of capacitor\n",
+ "\n",
+ "#Calculations\n",
+ "I1=V_s*(1/R1+2/R2) #A\n",
+ "I2=V_s*(2/R1+1/R2) #A\n",
+ "t_c1=40*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "C1=t_c1*fos/(R1*math.log(2))\n",
+ "C2=t_c1*fos/(R2*math.log(2))\n",
+ "if C1 > C2 :\n",
+ " C = C1*10**6\n",
+ "else :\n",
+ " C = C2*10**6\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of current through SCR1=%.2f A\" %I1); \n",
+ "print(\"Peak value of current through SCR2=%.2f A\" %I2);\n",
+ "print(\"Value of capacitor=%.2f uF\" %C);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of current through SCR1=24.00 A\n",
+ "Peak value of current through SCR2=42.00 A\n",
+ "Value of capacitor=11.54 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.4, Page No 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0 #V\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "I_o=120.0 #A\n",
+ "\n",
+ "#Calculations\n",
+ "I_p=V_s*math.sqrt(C/L) #A\n",
+ "t_c=C*V_s/I_o #\u00b5s\n",
+ "w_o=math.sqrt(1/(L*C)) \n",
+ "t_c1=math.pi/(2*w_o) #\u00b5s\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through main thyristor=%.2f A\" %(I_o+I_p))\n",
+ "print(\"Current through auxillery thyristor=%.2f A\" %I_o)\n",
+ "print(\"Circuit turn off time for main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"Circuit turn off time for auxillery thyristor=%.2f us\" %(t_c1*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through main thyristor=445.27 A\n",
+ "Current through auxillery thyristor=120.00 A\n",
+ "Circuit turn off time for main thyristor=76.67 us\n",
+ "Circuit turn off time for auxillery thyristor=44.43 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.5 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "C_j=25*10**-12 #pF\n",
+ "I_c=5*10**-3 #charging current\n",
+ "V_s=200.0 #V\n",
+ "R=50.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=(C_j*V_s)/(I_c*R)\n",
+ "\n",
+ "\n",
+ "#RESULTS\n",
+ "print(\"Value of C=%.2f \u00b5F\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of C=0.02 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.6 Page No 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "R=5.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=10.0*10**-6\n",
+ "#for turn off V_s*(1-2*exp(-t/(R*C)))=0, so after solving\n",
+ "t_c=R*C*math.log(2.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"circuit turn off time=%.2f us\" %(t_c*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circuit turn off time=34.66 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.7, Page No 264 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0 #\u2126\n",
+ "L=20*10**-6 #\u00b5H\n",
+ "C=40*10**-6 #\u00b5F\n",
+ "\n",
+ "#Calculations\n",
+ "w_r=math.sqrt((1/(L*C))-(R/(2*L))**2)\n",
+ "t_1=math.pi/w_r\n",
+ "\n",
+ "#Results\n",
+ "print(\"conduction time of thyristor=%.3f us\" %(t_1*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conduction time of thyristor=125.664 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.8 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math \n",
+ "\n",
+ "#initialisation of variables\n",
+ "dv=400*10.0**-6 #dv=dv_T/dt(V/s)\n",
+ "V_s=200.0 #v\n",
+ "R=20.0 #\u2126\n",
+ "\n",
+ "#Calculations\n",
+ "C=V_s/(R*dv) \n",
+ "C_j=.025*10**-12\n",
+ "C_s=C-C_j\n",
+ "I_T=40;\n",
+ "R_s=1/((I_T/V_s)-(1/R)) \n",
+ "#value of R_s in book is wrongly calculated\n",
+ "\n",
+ "#Results\n",
+ "print(\"R_s=%.2f ohm\" %R_s)\n",
+ "print(\"C_s=%.3f uF\" %(C_s/10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "R_s=6.67 ohm\n",
+ "C_s=0.025 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.9 Page No 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=200.0 #V\n",
+ "C=20.0*10**-6 #\u00b5H \n",
+ "L=0.2*10**-3 #\u00b5F\n",
+ "i_c=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=V_s*math.sqrt(C/L)\n",
+ "w_o=1.0/math.sqrt(L*C)\n",
+ "t_1 = (1/w_o)*math.degrees(math.asin(i_c/i))\n",
+ "t_o=math.pi/w_o\n",
+ "t_c=t_o-2*t_1 \n",
+ "\n",
+ "#Results\n",
+ "print(\"reqd time=%.2f us\" %(t_1*10**6))\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"ckt turn off time=%.5f us\" %t_1)\n",
+ "#solution in book wrong, as wrong values are selected while filling the formuleas"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "reqd time=575.37 us\n",
+ "ckt turn off time=-952.05 us\n",
+ "ckt turn off time=0.00058 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.11 Page No 268 "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #\u00b5H\n",
+ "R=50.0 #\u2126\n",
+ "V_s=200.0 #V\n",
+ "t=0.01 #sec\n",
+ "Vd=0.7\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "t=8*10**-3\n",
+ "i1=i-t*Vd \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"current through L = %.2f A\" %i1)\n",
+ "i_R=0 #current in R at t=.008s\n",
+ "print(\"Current through R = %.2f A\" %i_R)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current through L = 1.57 A\n",
+ "Current through R = 0.00 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5.12, Page No 269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialisation of variables\n",
+ "\n",
+ "#initialisation of variables\n",
+ "L=1.0 #H\n",
+ "R=50.0 #ohm\n",
+ "V_s=200.0 #V\n",
+ "\n",
+ "#Calculations\n",
+ "tau=L/R\n",
+ "t=0.01 #s\n",
+ "i=(V_s/R)*(1-math.exp(-t/tau))\n",
+ "C=1*10**-6 #F\n",
+ "V_c=math.sqrt(L/C)*i\n",
+ "\n",
+ "#Results\n",
+ "print(\"current in R,L=%.2f A\" %i)\n",
+ "print(\"voltage across C=%.2f kV\" %(V_c/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "current in R,L=1.57 A\n",
+ "voltage across C=1.57 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter6.ipynb b/_Power_Electronics/Chapter6.ipynb new file mode 100755 index 00000000..dff6564b --- /dev/null +++ b/_Power_Electronics/Chapter6.ipynb @@ -0,0 +1,1761 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 06 : Phase Controlled Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "P=1000.0\n",
+ "R=V**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "a=math.pi/4\n",
+ "V_or1=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P1=V_or1**2/R \n",
+ "a=math.pi/2\n",
+ "V_or2=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P2=V_or2**2/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle delay is of 45deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P1)\n",
+ "print(\"when firing angle delay is of 90deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle delay is of 45deg\n",
+ "power absorbed=454.58 W\n",
+ "when firing angle delay is of 90deg\n",
+ "power absorbed=250.00 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "a=35.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "th2=180-th1\n",
+ "I_o=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(th2)))-E*((th2-a)*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*((th2-a)*math.pi/180)-(V**2/2)*(math.sin(math.radians(2*th2))-math.sin(math.radians(2*a)))-2*math.sqrt(2)*V*E*(math.cos(math.radians(a))-math.cos(math.radians(th2)))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.2f W\" %P_r)\n",
+ "print(\"supply pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=4.9208 A\n",
+ "power supplied to the battery=738.12 W\n",
+ "power dissipated by the resistor=689.54 W\n",
+ "supply pf=0.6686\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, Page No 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=210\n",
+ "f=50.0 #Hz\n",
+ "w=2*math.pi*f\n",
+ "a=40.0 #firing angle\n",
+ "V=230.0\n",
+ "R=5.0\n",
+ "L=2*10**-3\n",
+ "\n",
+ "#Calculations\n",
+ "t_c1=(360-B)*math.pi/(180*w) \n",
+ "V_o1=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o1=V_o1/R \n",
+ "E=110\n",
+ "R=5\n",
+ "L=2*10**-3\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "t_c2=(360-B+th1)*math.pi/(180*w) \n",
+ "V_o2=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o2=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(B)))-E*((B-a)*math.pi/180)) \n",
+ "V_o2=R*I_o2+E \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for R=5ohm and L=2mH\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c1*1000))\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"avg output current=%.4f A\" %I_o1)\n",
+ "print(\"for R=5ohm % L=2mH and E=110V\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c2*1000))\n",
+ "print(\"avg output current=%.4f A\" %I_o2)\n",
+ "print(\"avg output voltage=%.3f V\" %V_o2) "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for R=5ohm and L=2mH\n",
+ "ckt turn off time=8.333 msec\n",
+ "avg output voltage=84.489 V\n",
+ "avg output current=16.8979 A\n",
+ "for R=5ohm % L=2mH and E=110V\n",
+ "ckt turn off time=9.431 msec\n",
+ "avg output current=6.5090 A\n",
+ "avg output voltage=142.545 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "R=10.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=(math.sqrt(2)*V_s)\n",
+ "V_o=V_m/(2*math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=(V_m/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a*math.pi/180)+.5*math.sin(math.radians(2*a)))\n",
+ "I_or=V_or/R\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "TUF=P_dc/(V_s*I_or) \n",
+ "PIV=V_m \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"t/f utilisation factor=%.4f\" %TUF)\n",
+ "print(\"PIV of thyristor=%.2f V\" %PIV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.2834\n",
+ "form factor=1.879\n",
+ "voltage ripple factor=1.5903\n",
+ "t/f utilisation factor=0.1797\n",
+ "PIV of thyristor=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=1000.0\n",
+ "fos=2.5 #factor of safety\n",
+ "I_TAV=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m1=V/(2*fos)\n",
+ "P1=(2*V_m1/math.pi)*I_TAV \n",
+ "V_m2=V/(fos)\n",
+ "P2=(2*V_m2/math.pi)*I_TAV \n",
+ "\n",
+ "#Results\n",
+ "print(\"for mid pt convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P1/1000))\n",
+ "print(\"for bridge convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for mid pt convertor\n",
+ "power handled=5.093 kW\n",
+ "for bridge convertor\n",
+ "power handled=10.186 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, Page No 297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=.4\n",
+ "I_o=10\n",
+ "I_or=I_o\n",
+ "E=120.0\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m)))\n",
+ "pf1=(E*I_o+I_or**2*R)/(V_s*I_or) \n",
+ "E=-120.0\n",
+ "a2=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m))) \n",
+ "pf2=(-E*I_o-I_or**2*R)/(V_s*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"pf=%.4f\" %pf1)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n",
+ "print(\"pf=%.4f\" %pf2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=53.21 deg\n",
+ "pf=0.5391\n",
+ "firing angle delay=124.07 deg\n",
+ "pf=0.5043\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "a=45.0\n",
+ "R=5.0\n",
+ "E=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=((math.sqrt(2)*V_s)/(2*math.pi))*(3+math.cos(math.radians(a)))\n",
+ "I_o=(V_o-E)/R \n",
+ "P=E*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.3f A\" %I_o)\n",
+ "print(\"power delivered to battery=%.4f kW\" %(P/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=18.382 A\n",
+ "power delivered to battery=1.8382 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No 300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "f=50.0\n",
+ "a=50.0\n",
+ "R=6.0\n",
+ "E=60.0\n",
+ "V_o1=((math.sqrt(2)*2*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o1=(V_o1-E)/R \n",
+ "\n",
+ "#ATQ after applying the conditions\n",
+ "V_o2=((math.sqrt(2)*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o2=(V_o2-E)/R \n",
+ "\n",
+ "print(\"avg o/p current=%.3f A\" %I_o1)\n",
+ "print(\"avg o/p current after change=%.2f A\" %I_o2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=12.184 A\n",
+ "avg o/p current after change=1.09 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(2*V_m/math.pi)*math.cos(math.radians(a))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_m/math.sqrt(2)\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o/math.pi\n",
+ "DF=math.cos(math.radians(a))\n",
+ "CDF=.90032\n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=2*V_m*I_o*math.sin(math.radians(a))/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.4f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"pf=%.5f\" %pf)\n",
+ "print(\"HF=%.5f\" %HF)\n",
+ "print(\"active power=%.2f W\" %P_dc) \n",
+ "print(\"reactive power=%.3f Var\" %Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.6366\n",
+ "form factor=1.5708\n",
+ "voltage ripple factor=1.2114\n",
+ "pf=0.63662\n",
+ "HF=0.48342\n",
+ "active power=2143.96 W\n",
+ "reactive power=2143.956 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12, Page No 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(V_m/math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o*math.cos(math.radians(a/2))/math.pi\n",
+ "DF=math.cos(math.radians(a/2)) \n",
+ "CDF=2*math.sqrt(2)*math.cos(math.radians(a/2))/math.sqrt(math.pi*(math.pi-a*math.pi/180)) \n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=V_m*I_o*math.sin(math.radians(a))/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"voltage ripple factor=%.3f\" %VRF) \n",
+ "print(\"DF=%.4f\" %DF)\n",
+ "print(\"CDF=%.4f\" %CDF)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"HF=%.4f\" %HF)\n",
+ "print(\"active power=%.3f W\" %P_dc)\n",
+ "print(\"reactive power=%.2f Var\" %Q)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "form factor=1.241\n",
+ "rectification efficiency=0.8059\n",
+ "voltage ripple factor=0.735\n",
+ "DF=0.9239\n",
+ "CDF=0.9605\n",
+ "pf=0.8874\n",
+ "HF=0.2899\n",
+ "active power=3123.973 W\n",
+ "reactive power=1293.99 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13, Page No 319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_om=3*V_ml/(2*math.pi)\n",
+ "V_o=V_om/2\n",
+ "th=30\n",
+ "a=math.degrees(math.acos((2*math.pi*math.sqrt(3)*V_o/(3*V_ml)-1)))-th \n",
+ "I_o=V_o/R \n",
+ "V_or=V_ml/(2*math.sqrt(math.pi))*math.sqrt((5*math.pi/6-a*math.pi/180)+.5*math.sin(math.radians(2*a+2*th)))\n",
+ "I_or=V_or/R \n",
+ "RE=V_o*I_o/(V_or*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"delay angle=%.1f deg\" %a)\n",
+ "print(\"avg load current=%.3f A\" %I_o)\n",
+ "print(\"rms load current=%.3f A\" %I_or)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle=67.7 deg\n",
+ "avg load current=7.765 A\n",
+ "rms load current=10.477 A\n",
+ "rectification efficiency=0.5494\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15, Page No 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "v_T=1.4\n",
+ "a1=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=3*V_ml/(2*math.pi)*math.cos(math.radians(a1))-v_T \n",
+ "a2=60.0\n",
+ "V_o2=3*V_ml/(2*math.pi)*math.cos(math.radians(a2))-v_T \n",
+ "I_o=36\n",
+ "I_TA=I_o/3 \n",
+ "I_Tr=I_o/math.sqrt(3) \n",
+ "P=I_TA*v_T \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle = 30deg\")\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"for firing angle = 60deg\")\n",
+ "print(\"avg output voltage=%.2f V\" %V_o2)\n",
+ "print(\"avg current rating=%.0f A\" %I_TA)\n",
+ "print(\"rms current rating=%.3f A\" %I_Tr)\n",
+ "print(\"PIV of SCR=%.1f V\" %V_ml)\n",
+ "print(\"power dissipated=%.1f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17, Page No 331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200\n",
+ "I_o=20\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a1=math.degrees(math.acos(V_o1*math.pi/(3*V_ml)))\n",
+ "th=120\n",
+ "I_s=math.sqrt((1/math.pi)*I_o**2*th*math.pi/180)\n",
+ "P=E*I_o+I_o**2*R\n",
+ "pf=P/(math.sqrt(3)*V_s*I_s) \n",
+ "V_o2=E-I_o*R\n",
+ "a2=math.degrees(math.acos(-V_o2*math.pi/(3*V_ml))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.3f deg\" %a1)\n",
+ "print(\"pf=%.3f\" %pf)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18, Page No 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a1=0\n",
+ "t_c1=(4*math.pi/3-a1*math.pi/180)/w \n",
+ "a2=30\n",
+ "t_c2=(4*math.pi/3-a2*math.pi/180)/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle delay=0deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c1*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n",
+ "print(\"for firing angle delay=30deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c2*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle delay=0deg\n",
+ "commutation time=13.33 ms\n",
+ "peak reverse voltage=325.27 V\n",
+ "for firing angle delay=30deg\n",
+ "commutation time=11.67 ms\n",
+ "peak reverse voltage=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.19, Page No 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.20, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/(2*math.pi/3+math.sqrt(3)*(1+math.cos(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=102.459 V\n",
+ "for constant load current\n",
+ "V_ph=102.46 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.21, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=90.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/((math.pi-math.pi/2)+(math.sin(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.2f V\" %V_ph)\n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.1f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=191.19 V\n",
+ "for constant load current\n",
+ "V_ph=191.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.22 Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200.0\n",
+ "I_o=20.0\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml)-1)) \n",
+ "a1=180-a\n",
+ "I_sr=math.sqrt((1/math.pi)*I_o**2*(a1*math.pi/180))\n",
+ "P=V_o*I_o\n",
+ "pf=P/(math.sqrt(3)*V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "print(\"pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=69.38 deg\n",
+ "pf=0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.23, Page No 335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "f=50.0\n",
+ "I_o=15.0\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TA=I_o*120.0/360.0\n",
+ "I_Tr=math.sqrt(I_o**2*120/360)\n",
+ "I_sr=math.sqrt(I_o**2*120/180)\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "V_or=V_ml*math.sqrt((3/(2*math.pi))*(math.pi/3+math.sqrt(3/2)*math.cos(math.radians(2*a))))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "VA=3*V_s/math.sqrt(3)*I_sr\n",
+ "TUF=P_dc/VA \n",
+ "pf=P_ac/VA \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.5f\" %RE)\n",
+ "print(\"TUF=%.4f\" %TUF)\n",
+ "print(\"Input pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.95493\n",
+ "TUF=0.6752\n",
+ "Input pf=0.707\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.24, Page No 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=10.0\n",
+ "a=45.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "DF=math.cos(math.radians(a))\n",
+ "I_o=10\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)*math.sin(math.pi/3)\n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "I_o=1 #suppose\n",
+ "CDF=I_s1/I_sr \n",
+ "THD=math.sqrt(1/CDF**2-1) \n",
+ "pf=CDF*DF \n",
+ "P=(3*math.sqrt(2)*V*math.cos(math.radians(a))/math.pi)*I\n",
+ "Q=(3*math.sqrt(2)*V*math.sin(math.radians(a))/math.pi)*I \n",
+ " \n",
+ "#Results\n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"CDF=%.3f\" %CDF)\n",
+ "print(\"THD=%.5f\" %THD)\n",
+ "print(\"PF=%.4f\" %pf)\n",
+ "print(\"active power=%.2f W\" %P) \n",
+ "print(\"reactive power=%.2f Var\" %Q)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "DF=0.707\n",
+ "CDF=0.955\n",
+ "THD=0.31084\n",
+ "PF=0.6752\n",
+ "active power=3819.72 W\n",
+ "reactive power=3819.72 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.25, Page No 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "print(\"for firing angle=30deg\")\n",
+ "a=30.0\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=350\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P1=V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P1/VA \n",
+ "a=180-60\n",
+ "V=400\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=-350\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P2=-V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P2/VA \n",
+ "\n",
+ "print(\"power delivered to load=%.2f W\" %P1)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"for firing advance angle=60deg\")\n",
+ "print(\"power delivered to load=%.2f W\" %P2)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "power delivered to load=5511.74 W\n",
+ "pf=0.4775\n",
+ "for firing advance angle=60deg\n",
+ "power delivered to load=2158.20 W\n",
+ "pf=0.4775\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.26, Page No 347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0\n",
+ "u=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=math.cos(math.radians(a))-math.cos(math.radians(a+u))\n",
+ "a=30\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=45\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=60\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=30deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=45deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=60deg\") \n",
+ "print(\"overlap angle=%.2f deg\" %u)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=45deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=60deg\n",
+ "overlap angle=2.23 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.28, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=400.0\n",
+ "I_o=20.0\n",
+ "R=1\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.004\n",
+ "V=230 #per phase voltage\n",
+ "V_ml=math.sqrt(6)*V\n",
+ "a=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o+3*w*L*I_o/math.pi))) \n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "u=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o-3*w*L*I_o/math.pi)))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"overlap angle=%.2f deg\" %u)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=34.382 deg\n",
+ "overlap angle=8.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.29, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=1\n",
+ "E=230\n",
+ "I=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=-E+I*R\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml))) \n",
+ "L=0.004\n",
+ "a=math.degrees(math.acos((2*math.pi)/(3*V_ml)*(V_o+3*w*L*I/(2*math.pi)))) \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-3*f*L*I/V_ml))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "print(\"overlap angle=%.3f deg\" %u)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=139.702 deg\n",
+ "firing angle delay=139.702 deg\n",
+ "overlap angle=1.431 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.31, Page No 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0 #per phase\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(3.0)*math.sqrt(2)*V\n",
+ "w=2*math.pi*f\n",
+ "a1=60.0\n",
+ "L=0.015\n",
+ "i_cp=(math.sqrt(3)*V_ml/(w*L))*(1-math.sin(math.radians(a1))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"circulating current=%.4f A\" %i_cp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circulating current=27.7425 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.32, Page No 362"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*math.pi/(math.pi)) \n",
+ "I_o=I_s\n",
+ "pf=(V_o*I_o/(V*I_s)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=179.330 V\n",
+ "avg o/p current=17.93 A\n",
+ "avg value of thyristor current=8.967 A\n",
+ "rms value of thyristor current=12.68 A\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.33, Page No 363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "L=.0015\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "V_ox=2*V_m*math.cos(math.radians(a))/math.pi-w*L*I_o/math.pi \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-I_o*w*L/V_m))-a \n",
+ "I=I_o\n",
+ "pf=V_o*I_o/(V*I) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_ox)\n",
+ "print(\"angle of overlap=%.3f deg\" %u)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=176.640 V\n",
+ "angle of overlap=2.855 deg\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.34, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a1=35.0 #firing angle advance\n",
+ "\n",
+ "#Calculations\n",
+ "a=180-a1\n",
+ "I_o=80.0\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "X_l=.25 #reactance=w*L\n",
+ "E=-3*V_ml*math.cos(math.radians(a))/math.pi+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean generator voltage=487.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.35, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "R=0.2\n",
+ "I_o=80\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "\n",
+ "#Calculations\n",
+ "X_l=.25 #reactance=w*L\n",
+ "a=35\n",
+ "E=-(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "a1=35\n",
+ "a=180-a1\n",
+ "E=(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle=35deg\") \n",
+ "print(\"mean generator voltage=%.3f V\" %E)\n",
+ "print(\"when firing angle advance=35deg\")\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle=35deg\n",
+ "mean generator voltage=503.590 V\n",
+ "when firing angle advance=35deg\n",
+ "mean generator voltage=503.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.36, Page No 365"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=5.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_mp=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "E=150.0\n",
+ "B=180-math.degrees(math.asin(E/V_mp))\n",
+ "I_o=(3/(2*math.pi*R))*(V_mp*(math.cos(math.radians(a+30))-math.cos(math.radians(B)))-E*((B-a-30)*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg current flowing=%.2f A\" %I_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg current flowing=19.96 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.37, Page No 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "V_o=V_m*(1+math.cos(math.radians(a)))/math.pi \n",
+ "E=100\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*(1-a/180)*math.pi/(math.pi))\n",
+ "I_or=I_o\n",
+ "P=E*I_o+I_or**2*R\n",
+ "pf=(P/(V*I_s)) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=(1-a/180)*math.pi/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\navg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "print(\"avg value of diode current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"circuit turn off time=%.2f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "avg o/p current=9.32 A\n",
+ "avg o/p voltage=193.202 V\n",
+ "avg value of thyristor current=4.66 A\n",
+ "rms value of thyristor current=6.590 A\n",
+ "avg value of diode current=4.66 A\n",
+ "rms value of diode current=6.590 A\n",
+ "pf=0.9202\n",
+ "circuit turn off time=8.33 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.38, Page No 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "L=0.05\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a=30\n",
+ "i_cp=2*V_m*(1-math.cos(math.radians(a)))/(w*L) \n",
+ "R=30.0\n",
+ "i_l=V_m/R\n",
+ "i1=i_cp+i_l \n",
+ "i2=i_cp \n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of circulating current=%.3f A\" %i_cp)\n",
+ "print(\"peak value of current in convertor 1=%.3f A\" %i1)\n",
+ "print(\"peak value of current in convertor 2=%.3f A\" %i2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of circulating current=5.548 A\n",
+ "peak value of current in convertor 1=16.391 A\n",
+ "peak value of current in convertor 2=5.548 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.39, Page No 370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=5.0\n",
+ "L=0.05\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(w*L/R)) \n",
+ "phi=90+math.degrees(math.atan(w*L/R)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"for no current transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)\n",
+ "print(\"for worst transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for no current transients\n",
+ "triggering angle=162.34 deg\n",
+ "for worst transients\n",
+ "triggering angle=162.34 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter6_1.ipynb b/_Power_Electronics/Chapter6_1.ipynb new file mode 100755 index 00000000..dff6564b --- /dev/null +++ b/_Power_Electronics/Chapter6_1.ipynb @@ -0,0 +1,1761 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 06 : Phase Controlled Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "P=1000.0\n",
+ "R=V**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "a=math.pi/4\n",
+ "V_or1=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P1=V_or1**2/R \n",
+ "a=math.pi/2\n",
+ "V_or2=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P2=V_or2**2/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle delay is of 45deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P1)\n",
+ "print(\"when firing angle delay is of 90deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle delay is of 45deg\n",
+ "power absorbed=454.58 W\n",
+ "when firing angle delay is of 90deg\n",
+ "power absorbed=250.00 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "a=35.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "th2=180-th1\n",
+ "I_o=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(th2)))-E*((th2-a)*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*((th2-a)*math.pi/180)-(V**2/2)*(math.sin(math.radians(2*th2))-math.sin(math.radians(2*a)))-2*math.sqrt(2)*V*E*(math.cos(math.radians(a))-math.cos(math.radians(th2)))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.2f W\" %P_r)\n",
+ "print(\"supply pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=4.9208 A\n",
+ "power supplied to the battery=738.12 W\n",
+ "power dissipated by the resistor=689.54 W\n",
+ "supply pf=0.6686\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, Page No 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=210\n",
+ "f=50.0 #Hz\n",
+ "w=2*math.pi*f\n",
+ "a=40.0 #firing angle\n",
+ "V=230.0\n",
+ "R=5.0\n",
+ "L=2*10**-3\n",
+ "\n",
+ "#Calculations\n",
+ "t_c1=(360-B)*math.pi/(180*w) \n",
+ "V_o1=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o1=V_o1/R \n",
+ "E=110\n",
+ "R=5\n",
+ "L=2*10**-3\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "t_c2=(360-B+th1)*math.pi/(180*w) \n",
+ "V_o2=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o2=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(B)))-E*((B-a)*math.pi/180)) \n",
+ "V_o2=R*I_o2+E \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for R=5ohm and L=2mH\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c1*1000))\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"avg output current=%.4f A\" %I_o1)\n",
+ "print(\"for R=5ohm % L=2mH and E=110V\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c2*1000))\n",
+ "print(\"avg output current=%.4f A\" %I_o2)\n",
+ "print(\"avg output voltage=%.3f V\" %V_o2) "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for R=5ohm and L=2mH\n",
+ "ckt turn off time=8.333 msec\n",
+ "avg output voltage=84.489 V\n",
+ "avg output current=16.8979 A\n",
+ "for R=5ohm % L=2mH and E=110V\n",
+ "ckt turn off time=9.431 msec\n",
+ "avg output current=6.5090 A\n",
+ "avg output voltage=142.545 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "R=10.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=(math.sqrt(2)*V_s)\n",
+ "V_o=V_m/(2*math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=(V_m/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a*math.pi/180)+.5*math.sin(math.radians(2*a)))\n",
+ "I_or=V_or/R\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "TUF=P_dc/(V_s*I_or) \n",
+ "PIV=V_m \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"t/f utilisation factor=%.4f\" %TUF)\n",
+ "print(\"PIV of thyristor=%.2f V\" %PIV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.2834\n",
+ "form factor=1.879\n",
+ "voltage ripple factor=1.5903\n",
+ "t/f utilisation factor=0.1797\n",
+ "PIV of thyristor=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=1000.0\n",
+ "fos=2.5 #factor of safety\n",
+ "I_TAV=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m1=V/(2*fos)\n",
+ "P1=(2*V_m1/math.pi)*I_TAV \n",
+ "V_m2=V/(fos)\n",
+ "P2=(2*V_m2/math.pi)*I_TAV \n",
+ "\n",
+ "#Results\n",
+ "print(\"for mid pt convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P1/1000))\n",
+ "print(\"for bridge convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for mid pt convertor\n",
+ "power handled=5.093 kW\n",
+ "for bridge convertor\n",
+ "power handled=10.186 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, Page No 297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=.4\n",
+ "I_o=10\n",
+ "I_or=I_o\n",
+ "E=120.0\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m)))\n",
+ "pf1=(E*I_o+I_or**2*R)/(V_s*I_or) \n",
+ "E=-120.0\n",
+ "a2=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m))) \n",
+ "pf2=(-E*I_o-I_or**2*R)/(V_s*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"pf=%.4f\" %pf1)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n",
+ "print(\"pf=%.4f\" %pf2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=53.21 deg\n",
+ "pf=0.5391\n",
+ "firing angle delay=124.07 deg\n",
+ "pf=0.5043\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "a=45.0\n",
+ "R=5.0\n",
+ "E=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=((math.sqrt(2)*V_s)/(2*math.pi))*(3+math.cos(math.radians(a)))\n",
+ "I_o=(V_o-E)/R \n",
+ "P=E*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.3f A\" %I_o)\n",
+ "print(\"power delivered to battery=%.4f kW\" %(P/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=18.382 A\n",
+ "power delivered to battery=1.8382 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No 300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "f=50.0\n",
+ "a=50.0\n",
+ "R=6.0\n",
+ "E=60.0\n",
+ "V_o1=((math.sqrt(2)*2*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o1=(V_o1-E)/R \n",
+ "\n",
+ "#ATQ after applying the conditions\n",
+ "V_o2=((math.sqrt(2)*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o2=(V_o2-E)/R \n",
+ "\n",
+ "print(\"avg o/p current=%.3f A\" %I_o1)\n",
+ "print(\"avg o/p current after change=%.2f A\" %I_o2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=12.184 A\n",
+ "avg o/p current after change=1.09 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(2*V_m/math.pi)*math.cos(math.radians(a))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_m/math.sqrt(2)\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o/math.pi\n",
+ "DF=math.cos(math.radians(a))\n",
+ "CDF=.90032\n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=2*V_m*I_o*math.sin(math.radians(a))/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.4f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"pf=%.5f\" %pf)\n",
+ "print(\"HF=%.5f\" %HF)\n",
+ "print(\"active power=%.2f W\" %P_dc) \n",
+ "print(\"reactive power=%.3f Var\" %Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.6366\n",
+ "form factor=1.5708\n",
+ "voltage ripple factor=1.2114\n",
+ "pf=0.63662\n",
+ "HF=0.48342\n",
+ "active power=2143.96 W\n",
+ "reactive power=2143.956 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12, Page No 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(V_m/math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o*math.cos(math.radians(a/2))/math.pi\n",
+ "DF=math.cos(math.radians(a/2)) \n",
+ "CDF=2*math.sqrt(2)*math.cos(math.radians(a/2))/math.sqrt(math.pi*(math.pi-a*math.pi/180)) \n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=V_m*I_o*math.sin(math.radians(a))/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"voltage ripple factor=%.3f\" %VRF) \n",
+ "print(\"DF=%.4f\" %DF)\n",
+ "print(\"CDF=%.4f\" %CDF)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"HF=%.4f\" %HF)\n",
+ "print(\"active power=%.3f W\" %P_dc)\n",
+ "print(\"reactive power=%.2f Var\" %Q)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "form factor=1.241\n",
+ "rectification efficiency=0.8059\n",
+ "voltage ripple factor=0.735\n",
+ "DF=0.9239\n",
+ "CDF=0.9605\n",
+ "pf=0.8874\n",
+ "HF=0.2899\n",
+ "active power=3123.973 W\n",
+ "reactive power=1293.99 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13, Page No 319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_om=3*V_ml/(2*math.pi)\n",
+ "V_o=V_om/2\n",
+ "th=30\n",
+ "a=math.degrees(math.acos((2*math.pi*math.sqrt(3)*V_o/(3*V_ml)-1)))-th \n",
+ "I_o=V_o/R \n",
+ "V_or=V_ml/(2*math.sqrt(math.pi))*math.sqrt((5*math.pi/6-a*math.pi/180)+.5*math.sin(math.radians(2*a+2*th)))\n",
+ "I_or=V_or/R \n",
+ "RE=V_o*I_o/(V_or*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"delay angle=%.1f deg\" %a)\n",
+ "print(\"avg load current=%.3f A\" %I_o)\n",
+ "print(\"rms load current=%.3f A\" %I_or)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle=67.7 deg\n",
+ "avg load current=7.765 A\n",
+ "rms load current=10.477 A\n",
+ "rectification efficiency=0.5494\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15, Page No 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "v_T=1.4\n",
+ "a1=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=3*V_ml/(2*math.pi)*math.cos(math.radians(a1))-v_T \n",
+ "a2=60.0\n",
+ "V_o2=3*V_ml/(2*math.pi)*math.cos(math.radians(a2))-v_T \n",
+ "I_o=36\n",
+ "I_TA=I_o/3 \n",
+ "I_Tr=I_o/math.sqrt(3) \n",
+ "P=I_TA*v_T \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle = 30deg\")\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"for firing angle = 60deg\")\n",
+ "print(\"avg output voltage=%.2f V\" %V_o2)\n",
+ "print(\"avg current rating=%.0f A\" %I_TA)\n",
+ "print(\"rms current rating=%.3f A\" %I_Tr)\n",
+ "print(\"PIV of SCR=%.1f V\" %V_ml)\n",
+ "print(\"power dissipated=%.1f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17, Page No 331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200\n",
+ "I_o=20\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a1=math.degrees(math.acos(V_o1*math.pi/(3*V_ml)))\n",
+ "th=120\n",
+ "I_s=math.sqrt((1/math.pi)*I_o**2*th*math.pi/180)\n",
+ "P=E*I_o+I_o**2*R\n",
+ "pf=P/(math.sqrt(3)*V_s*I_s) \n",
+ "V_o2=E-I_o*R\n",
+ "a2=math.degrees(math.acos(-V_o2*math.pi/(3*V_ml))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.3f deg\" %a1)\n",
+ "print(\"pf=%.3f\" %pf)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18, Page No 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a1=0\n",
+ "t_c1=(4*math.pi/3-a1*math.pi/180)/w \n",
+ "a2=30\n",
+ "t_c2=(4*math.pi/3-a2*math.pi/180)/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle delay=0deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c1*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n",
+ "print(\"for firing angle delay=30deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c2*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle delay=0deg\n",
+ "commutation time=13.33 ms\n",
+ "peak reverse voltage=325.27 V\n",
+ "for firing angle delay=30deg\n",
+ "commutation time=11.67 ms\n",
+ "peak reverse voltage=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.19, Page No 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.20, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/(2*math.pi/3+math.sqrt(3)*(1+math.cos(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=102.459 V\n",
+ "for constant load current\n",
+ "V_ph=102.46 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.21, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=90.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/((math.pi-math.pi/2)+(math.sin(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.2f V\" %V_ph)\n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.1f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=191.19 V\n",
+ "for constant load current\n",
+ "V_ph=191.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.22 Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200.0\n",
+ "I_o=20.0\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml)-1)) \n",
+ "a1=180-a\n",
+ "I_sr=math.sqrt((1/math.pi)*I_o**2*(a1*math.pi/180))\n",
+ "P=V_o*I_o\n",
+ "pf=P/(math.sqrt(3)*V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "print(\"pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=69.38 deg\n",
+ "pf=0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.23, Page No 335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "f=50.0\n",
+ "I_o=15.0\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TA=I_o*120.0/360.0\n",
+ "I_Tr=math.sqrt(I_o**2*120/360)\n",
+ "I_sr=math.sqrt(I_o**2*120/180)\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "V_or=V_ml*math.sqrt((3/(2*math.pi))*(math.pi/3+math.sqrt(3/2)*math.cos(math.radians(2*a))))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "VA=3*V_s/math.sqrt(3)*I_sr\n",
+ "TUF=P_dc/VA \n",
+ "pf=P_ac/VA \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.5f\" %RE)\n",
+ "print(\"TUF=%.4f\" %TUF)\n",
+ "print(\"Input pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.95493\n",
+ "TUF=0.6752\n",
+ "Input pf=0.707\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.24, Page No 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=10.0\n",
+ "a=45.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "DF=math.cos(math.radians(a))\n",
+ "I_o=10\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)*math.sin(math.pi/3)\n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "I_o=1 #suppose\n",
+ "CDF=I_s1/I_sr \n",
+ "THD=math.sqrt(1/CDF**2-1) \n",
+ "pf=CDF*DF \n",
+ "P=(3*math.sqrt(2)*V*math.cos(math.radians(a))/math.pi)*I\n",
+ "Q=(3*math.sqrt(2)*V*math.sin(math.radians(a))/math.pi)*I \n",
+ " \n",
+ "#Results\n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"CDF=%.3f\" %CDF)\n",
+ "print(\"THD=%.5f\" %THD)\n",
+ "print(\"PF=%.4f\" %pf)\n",
+ "print(\"active power=%.2f W\" %P) \n",
+ "print(\"reactive power=%.2f Var\" %Q)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "DF=0.707\n",
+ "CDF=0.955\n",
+ "THD=0.31084\n",
+ "PF=0.6752\n",
+ "active power=3819.72 W\n",
+ "reactive power=3819.72 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.25, Page No 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "print(\"for firing angle=30deg\")\n",
+ "a=30.0\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=350\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P1=V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P1/VA \n",
+ "a=180-60\n",
+ "V=400\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=-350\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P2=-V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P2/VA \n",
+ "\n",
+ "print(\"power delivered to load=%.2f W\" %P1)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"for firing advance angle=60deg\")\n",
+ "print(\"power delivered to load=%.2f W\" %P2)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "power delivered to load=5511.74 W\n",
+ "pf=0.4775\n",
+ "for firing advance angle=60deg\n",
+ "power delivered to load=2158.20 W\n",
+ "pf=0.4775\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.26, Page No 347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0\n",
+ "u=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=math.cos(math.radians(a))-math.cos(math.radians(a+u))\n",
+ "a=30\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=45\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=60\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=30deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=45deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=60deg\") \n",
+ "print(\"overlap angle=%.2f deg\" %u)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=45deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=60deg\n",
+ "overlap angle=2.23 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.28, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=400.0\n",
+ "I_o=20.0\n",
+ "R=1\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.004\n",
+ "V=230 #per phase voltage\n",
+ "V_ml=math.sqrt(6)*V\n",
+ "a=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o+3*w*L*I_o/math.pi))) \n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "u=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o-3*w*L*I_o/math.pi)))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"overlap angle=%.2f deg\" %u)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=34.382 deg\n",
+ "overlap angle=8.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.29, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=1\n",
+ "E=230\n",
+ "I=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=-E+I*R\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml))) \n",
+ "L=0.004\n",
+ "a=math.degrees(math.acos((2*math.pi)/(3*V_ml)*(V_o+3*w*L*I/(2*math.pi)))) \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-3*f*L*I/V_ml))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "print(\"overlap angle=%.3f deg\" %u)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=139.702 deg\n",
+ "firing angle delay=139.702 deg\n",
+ "overlap angle=1.431 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.31, Page No 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0 #per phase\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(3.0)*math.sqrt(2)*V\n",
+ "w=2*math.pi*f\n",
+ "a1=60.0\n",
+ "L=0.015\n",
+ "i_cp=(math.sqrt(3)*V_ml/(w*L))*(1-math.sin(math.radians(a1))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"circulating current=%.4f A\" %i_cp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circulating current=27.7425 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.32, Page No 362"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*math.pi/(math.pi)) \n",
+ "I_o=I_s\n",
+ "pf=(V_o*I_o/(V*I_s)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=179.330 V\n",
+ "avg o/p current=17.93 A\n",
+ "avg value of thyristor current=8.967 A\n",
+ "rms value of thyristor current=12.68 A\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.33, Page No 363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "L=.0015\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "V_ox=2*V_m*math.cos(math.radians(a))/math.pi-w*L*I_o/math.pi \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-I_o*w*L/V_m))-a \n",
+ "I=I_o\n",
+ "pf=V_o*I_o/(V*I) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_ox)\n",
+ "print(\"angle of overlap=%.3f deg\" %u)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=176.640 V\n",
+ "angle of overlap=2.855 deg\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.34, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a1=35.0 #firing angle advance\n",
+ "\n",
+ "#Calculations\n",
+ "a=180-a1\n",
+ "I_o=80.0\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "X_l=.25 #reactance=w*L\n",
+ "E=-3*V_ml*math.cos(math.radians(a))/math.pi+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean generator voltage=487.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.35, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "R=0.2\n",
+ "I_o=80\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "\n",
+ "#Calculations\n",
+ "X_l=.25 #reactance=w*L\n",
+ "a=35\n",
+ "E=-(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "a1=35\n",
+ "a=180-a1\n",
+ "E=(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle=35deg\") \n",
+ "print(\"mean generator voltage=%.3f V\" %E)\n",
+ "print(\"when firing angle advance=35deg\")\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle=35deg\n",
+ "mean generator voltage=503.590 V\n",
+ "when firing angle advance=35deg\n",
+ "mean generator voltage=503.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.36, Page No 365"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=5.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_mp=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "E=150.0\n",
+ "B=180-math.degrees(math.asin(E/V_mp))\n",
+ "I_o=(3/(2*math.pi*R))*(V_mp*(math.cos(math.radians(a+30))-math.cos(math.radians(B)))-E*((B-a-30)*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg current flowing=%.2f A\" %I_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg current flowing=19.96 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.37, Page No 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "V_o=V_m*(1+math.cos(math.radians(a)))/math.pi \n",
+ "E=100\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*(1-a/180)*math.pi/(math.pi))\n",
+ "I_or=I_o\n",
+ "P=E*I_o+I_or**2*R\n",
+ "pf=(P/(V*I_s)) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=(1-a/180)*math.pi/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\navg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "print(\"avg value of diode current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"circuit turn off time=%.2f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "avg o/p current=9.32 A\n",
+ "avg o/p voltage=193.202 V\n",
+ "avg value of thyristor current=4.66 A\n",
+ "rms value of thyristor current=6.590 A\n",
+ "avg value of diode current=4.66 A\n",
+ "rms value of diode current=6.590 A\n",
+ "pf=0.9202\n",
+ "circuit turn off time=8.33 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.38, Page No 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "L=0.05\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a=30\n",
+ "i_cp=2*V_m*(1-math.cos(math.radians(a)))/(w*L) \n",
+ "R=30.0\n",
+ "i_l=V_m/R\n",
+ "i1=i_cp+i_l \n",
+ "i2=i_cp \n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of circulating current=%.3f A\" %i_cp)\n",
+ "print(\"peak value of current in convertor 1=%.3f A\" %i1)\n",
+ "print(\"peak value of current in convertor 2=%.3f A\" %i2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of circulating current=5.548 A\n",
+ "peak value of current in convertor 1=16.391 A\n",
+ "peak value of current in convertor 2=5.548 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.39, Page No 370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=5.0\n",
+ "L=0.05\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(w*L/R)) \n",
+ "phi=90+math.degrees(math.atan(w*L/R)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"for no current transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)\n",
+ "print(\"for worst transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for no current transients\n",
+ "triggering angle=162.34 deg\n",
+ "for worst transients\n",
+ "triggering angle=162.34 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter6_2.ipynb b/_Power_Electronics/Chapter6_2.ipynb new file mode 100755 index 00000000..dff6564b --- /dev/null +++ b/_Power_Electronics/Chapter6_2.ipynb @@ -0,0 +1,1761 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 06 : Phase Controlled Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "P=1000.0\n",
+ "R=V**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "a=math.pi/4\n",
+ "V_or1=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P1=V_or1**2/R \n",
+ "a=math.pi/2\n",
+ "V_or2=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P2=V_or2**2/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle delay is of 45deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P1)\n",
+ "print(\"when firing angle delay is of 90deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle delay is of 45deg\n",
+ "power absorbed=454.58 W\n",
+ "when firing angle delay is of 90deg\n",
+ "power absorbed=250.00 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "a=35.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "th2=180-th1\n",
+ "I_o=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(th2)))-E*((th2-a)*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*((th2-a)*math.pi/180)-(V**2/2)*(math.sin(math.radians(2*th2))-math.sin(math.radians(2*a)))-2*math.sqrt(2)*V*E*(math.cos(math.radians(a))-math.cos(math.radians(th2)))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.2f W\" %P_r)\n",
+ "print(\"supply pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=4.9208 A\n",
+ "power supplied to the battery=738.12 W\n",
+ "power dissipated by the resistor=689.54 W\n",
+ "supply pf=0.6686\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, Page No 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=210\n",
+ "f=50.0 #Hz\n",
+ "w=2*math.pi*f\n",
+ "a=40.0 #firing angle\n",
+ "V=230.0\n",
+ "R=5.0\n",
+ "L=2*10**-3\n",
+ "\n",
+ "#Calculations\n",
+ "t_c1=(360-B)*math.pi/(180*w) \n",
+ "V_o1=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o1=V_o1/R \n",
+ "E=110\n",
+ "R=5\n",
+ "L=2*10**-3\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "t_c2=(360-B+th1)*math.pi/(180*w) \n",
+ "V_o2=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o2=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(B)))-E*((B-a)*math.pi/180)) \n",
+ "V_o2=R*I_o2+E \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for R=5ohm and L=2mH\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c1*1000))\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"avg output current=%.4f A\" %I_o1)\n",
+ "print(\"for R=5ohm % L=2mH and E=110V\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c2*1000))\n",
+ "print(\"avg output current=%.4f A\" %I_o2)\n",
+ "print(\"avg output voltage=%.3f V\" %V_o2) "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for R=5ohm and L=2mH\n",
+ "ckt turn off time=8.333 msec\n",
+ "avg output voltage=84.489 V\n",
+ "avg output current=16.8979 A\n",
+ "for R=5ohm % L=2mH and E=110V\n",
+ "ckt turn off time=9.431 msec\n",
+ "avg output current=6.5090 A\n",
+ "avg output voltage=142.545 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "R=10.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=(math.sqrt(2)*V_s)\n",
+ "V_o=V_m/(2*math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=(V_m/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a*math.pi/180)+.5*math.sin(math.radians(2*a)))\n",
+ "I_or=V_or/R\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "TUF=P_dc/(V_s*I_or) \n",
+ "PIV=V_m \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"t/f utilisation factor=%.4f\" %TUF)\n",
+ "print(\"PIV of thyristor=%.2f V\" %PIV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.2834\n",
+ "form factor=1.879\n",
+ "voltage ripple factor=1.5903\n",
+ "t/f utilisation factor=0.1797\n",
+ "PIV of thyristor=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=1000.0\n",
+ "fos=2.5 #factor of safety\n",
+ "I_TAV=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m1=V/(2*fos)\n",
+ "P1=(2*V_m1/math.pi)*I_TAV \n",
+ "V_m2=V/(fos)\n",
+ "P2=(2*V_m2/math.pi)*I_TAV \n",
+ "\n",
+ "#Results\n",
+ "print(\"for mid pt convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P1/1000))\n",
+ "print(\"for bridge convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for mid pt convertor\n",
+ "power handled=5.093 kW\n",
+ "for bridge convertor\n",
+ "power handled=10.186 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, Page No 297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=.4\n",
+ "I_o=10\n",
+ "I_or=I_o\n",
+ "E=120.0\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m)))\n",
+ "pf1=(E*I_o+I_or**2*R)/(V_s*I_or) \n",
+ "E=-120.0\n",
+ "a2=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m))) \n",
+ "pf2=(-E*I_o-I_or**2*R)/(V_s*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"pf=%.4f\" %pf1)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n",
+ "print(\"pf=%.4f\" %pf2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=53.21 deg\n",
+ "pf=0.5391\n",
+ "firing angle delay=124.07 deg\n",
+ "pf=0.5043\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "a=45.0\n",
+ "R=5.0\n",
+ "E=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=((math.sqrt(2)*V_s)/(2*math.pi))*(3+math.cos(math.radians(a)))\n",
+ "I_o=(V_o-E)/R \n",
+ "P=E*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.3f A\" %I_o)\n",
+ "print(\"power delivered to battery=%.4f kW\" %(P/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=18.382 A\n",
+ "power delivered to battery=1.8382 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No 300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "f=50.0\n",
+ "a=50.0\n",
+ "R=6.0\n",
+ "E=60.0\n",
+ "V_o1=((math.sqrt(2)*2*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o1=(V_o1-E)/R \n",
+ "\n",
+ "#ATQ after applying the conditions\n",
+ "V_o2=((math.sqrt(2)*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o2=(V_o2-E)/R \n",
+ "\n",
+ "print(\"avg o/p current=%.3f A\" %I_o1)\n",
+ "print(\"avg o/p current after change=%.2f A\" %I_o2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=12.184 A\n",
+ "avg o/p current after change=1.09 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(2*V_m/math.pi)*math.cos(math.radians(a))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_m/math.sqrt(2)\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o/math.pi\n",
+ "DF=math.cos(math.radians(a))\n",
+ "CDF=.90032\n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=2*V_m*I_o*math.sin(math.radians(a))/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.4f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"pf=%.5f\" %pf)\n",
+ "print(\"HF=%.5f\" %HF)\n",
+ "print(\"active power=%.2f W\" %P_dc) \n",
+ "print(\"reactive power=%.3f Var\" %Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.6366\n",
+ "form factor=1.5708\n",
+ "voltage ripple factor=1.2114\n",
+ "pf=0.63662\n",
+ "HF=0.48342\n",
+ "active power=2143.96 W\n",
+ "reactive power=2143.956 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12, Page No 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(V_m/math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o*math.cos(math.radians(a/2))/math.pi\n",
+ "DF=math.cos(math.radians(a/2)) \n",
+ "CDF=2*math.sqrt(2)*math.cos(math.radians(a/2))/math.sqrt(math.pi*(math.pi-a*math.pi/180)) \n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=V_m*I_o*math.sin(math.radians(a))/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"voltage ripple factor=%.3f\" %VRF) \n",
+ "print(\"DF=%.4f\" %DF)\n",
+ "print(\"CDF=%.4f\" %CDF)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"HF=%.4f\" %HF)\n",
+ "print(\"active power=%.3f W\" %P_dc)\n",
+ "print(\"reactive power=%.2f Var\" %Q)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "form factor=1.241\n",
+ "rectification efficiency=0.8059\n",
+ "voltage ripple factor=0.735\n",
+ "DF=0.9239\n",
+ "CDF=0.9605\n",
+ "pf=0.8874\n",
+ "HF=0.2899\n",
+ "active power=3123.973 W\n",
+ "reactive power=1293.99 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13, Page No 319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_om=3*V_ml/(2*math.pi)\n",
+ "V_o=V_om/2\n",
+ "th=30\n",
+ "a=math.degrees(math.acos((2*math.pi*math.sqrt(3)*V_o/(3*V_ml)-1)))-th \n",
+ "I_o=V_o/R \n",
+ "V_or=V_ml/(2*math.sqrt(math.pi))*math.sqrt((5*math.pi/6-a*math.pi/180)+.5*math.sin(math.radians(2*a+2*th)))\n",
+ "I_or=V_or/R \n",
+ "RE=V_o*I_o/(V_or*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"delay angle=%.1f deg\" %a)\n",
+ "print(\"avg load current=%.3f A\" %I_o)\n",
+ "print(\"rms load current=%.3f A\" %I_or)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle=67.7 deg\n",
+ "avg load current=7.765 A\n",
+ "rms load current=10.477 A\n",
+ "rectification efficiency=0.5494\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15, Page No 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "v_T=1.4\n",
+ "a1=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=3*V_ml/(2*math.pi)*math.cos(math.radians(a1))-v_T \n",
+ "a2=60.0\n",
+ "V_o2=3*V_ml/(2*math.pi)*math.cos(math.radians(a2))-v_T \n",
+ "I_o=36\n",
+ "I_TA=I_o/3 \n",
+ "I_Tr=I_o/math.sqrt(3) \n",
+ "P=I_TA*v_T \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle = 30deg\")\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"for firing angle = 60deg\")\n",
+ "print(\"avg output voltage=%.2f V\" %V_o2)\n",
+ "print(\"avg current rating=%.0f A\" %I_TA)\n",
+ "print(\"rms current rating=%.3f A\" %I_Tr)\n",
+ "print(\"PIV of SCR=%.1f V\" %V_ml)\n",
+ "print(\"power dissipated=%.1f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17, Page No 331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200\n",
+ "I_o=20\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a1=math.degrees(math.acos(V_o1*math.pi/(3*V_ml)))\n",
+ "th=120\n",
+ "I_s=math.sqrt((1/math.pi)*I_o**2*th*math.pi/180)\n",
+ "P=E*I_o+I_o**2*R\n",
+ "pf=P/(math.sqrt(3)*V_s*I_s) \n",
+ "V_o2=E-I_o*R\n",
+ "a2=math.degrees(math.acos(-V_o2*math.pi/(3*V_ml))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.3f deg\" %a1)\n",
+ "print(\"pf=%.3f\" %pf)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18, Page No 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a1=0\n",
+ "t_c1=(4*math.pi/3-a1*math.pi/180)/w \n",
+ "a2=30\n",
+ "t_c2=(4*math.pi/3-a2*math.pi/180)/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle delay=0deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c1*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n",
+ "print(\"for firing angle delay=30deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c2*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle delay=0deg\n",
+ "commutation time=13.33 ms\n",
+ "peak reverse voltage=325.27 V\n",
+ "for firing angle delay=30deg\n",
+ "commutation time=11.67 ms\n",
+ "peak reverse voltage=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.19, Page No 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.20, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/(2*math.pi/3+math.sqrt(3)*(1+math.cos(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=102.459 V\n",
+ "for constant load current\n",
+ "V_ph=102.46 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.21, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=90.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/((math.pi-math.pi/2)+(math.sin(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.2f V\" %V_ph)\n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.1f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=191.19 V\n",
+ "for constant load current\n",
+ "V_ph=191.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.22 Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200.0\n",
+ "I_o=20.0\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml)-1)) \n",
+ "a1=180-a\n",
+ "I_sr=math.sqrt((1/math.pi)*I_o**2*(a1*math.pi/180))\n",
+ "P=V_o*I_o\n",
+ "pf=P/(math.sqrt(3)*V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "print(\"pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=69.38 deg\n",
+ "pf=0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.23, Page No 335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "f=50.0\n",
+ "I_o=15.0\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TA=I_o*120.0/360.0\n",
+ "I_Tr=math.sqrt(I_o**2*120/360)\n",
+ "I_sr=math.sqrt(I_o**2*120/180)\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "V_or=V_ml*math.sqrt((3/(2*math.pi))*(math.pi/3+math.sqrt(3/2)*math.cos(math.radians(2*a))))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "VA=3*V_s/math.sqrt(3)*I_sr\n",
+ "TUF=P_dc/VA \n",
+ "pf=P_ac/VA \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.5f\" %RE)\n",
+ "print(\"TUF=%.4f\" %TUF)\n",
+ "print(\"Input pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.95493\n",
+ "TUF=0.6752\n",
+ "Input pf=0.707\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.24, Page No 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=10.0\n",
+ "a=45.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "DF=math.cos(math.radians(a))\n",
+ "I_o=10\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)*math.sin(math.pi/3)\n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "I_o=1 #suppose\n",
+ "CDF=I_s1/I_sr \n",
+ "THD=math.sqrt(1/CDF**2-1) \n",
+ "pf=CDF*DF \n",
+ "P=(3*math.sqrt(2)*V*math.cos(math.radians(a))/math.pi)*I\n",
+ "Q=(3*math.sqrt(2)*V*math.sin(math.radians(a))/math.pi)*I \n",
+ " \n",
+ "#Results\n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"CDF=%.3f\" %CDF)\n",
+ "print(\"THD=%.5f\" %THD)\n",
+ "print(\"PF=%.4f\" %pf)\n",
+ "print(\"active power=%.2f W\" %P) \n",
+ "print(\"reactive power=%.2f Var\" %Q)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "DF=0.707\n",
+ "CDF=0.955\n",
+ "THD=0.31084\n",
+ "PF=0.6752\n",
+ "active power=3819.72 W\n",
+ "reactive power=3819.72 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.25, Page No 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "print(\"for firing angle=30deg\")\n",
+ "a=30.0\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=350\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P1=V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P1/VA \n",
+ "a=180-60\n",
+ "V=400\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=-350\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P2=-V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P2/VA \n",
+ "\n",
+ "print(\"power delivered to load=%.2f W\" %P1)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"for firing advance angle=60deg\")\n",
+ "print(\"power delivered to load=%.2f W\" %P2)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "power delivered to load=5511.74 W\n",
+ "pf=0.4775\n",
+ "for firing advance angle=60deg\n",
+ "power delivered to load=2158.20 W\n",
+ "pf=0.4775\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.26, Page No 347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0\n",
+ "u=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=math.cos(math.radians(a))-math.cos(math.radians(a+u))\n",
+ "a=30\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=45\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=60\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=30deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=45deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=60deg\") \n",
+ "print(\"overlap angle=%.2f deg\" %u)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=45deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=60deg\n",
+ "overlap angle=2.23 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.28, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=400.0\n",
+ "I_o=20.0\n",
+ "R=1\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.004\n",
+ "V=230 #per phase voltage\n",
+ "V_ml=math.sqrt(6)*V\n",
+ "a=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o+3*w*L*I_o/math.pi))) \n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "u=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o-3*w*L*I_o/math.pi)))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"overlap angle=%.2f deg\" %u)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=34.382 deg\n",
+ "overlap angle=8.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.29, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=1\n",
+ "E=230\n",
+ "I=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=-E+I*R\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml))) \n",
+ "L=0.004\n",
+ "a=math.degrees(math.acos((2*math.pi)/(3*V_ml)*(V_o+3*w*L*I/(2*math.pi)))) \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-3*f*L*I/V_ml))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "print(\"overlap angle=%.3f deg\" %u)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=139.702 deg\n",
+ "firing angle delay=139.702 deg\n",
+ "overlap angle=1.431 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.31, Page No 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0 #per phase\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(3.0)*math.sqrt(2)*V\n",
+ "w=2*math.pi*f\n",
+ "a1=60.0\n",
+ "L=0.015\n",
+ "i_cp=(math.sqrt(3)*V_ml/(w*L))*(1-math.sin(math.radians(a1))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"circulating current=%.4f A\" %i_cp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circulating current=27.7425 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.32, Page No 362"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*math.pi/(math.pi)) \n",
+ "I_o=I_s\n",
+ "pf=(V_o*I_o/(V*I_s)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=179.330 V\n",
+ "avg o/p current=17.93 A\n",
+ "avg value of thyristor current=8.967 A\n",
+ "rms value of thyristor current=12.68 A\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.33, Page No 363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "L=.0015\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "V_ox=2*V_m*math.cos(math.radians(a))/math.pi-w*L*I_o/math.pi \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-I_o*w*L/V_m))-a \n",
+ "I=I_o\n",
+ "pf=V_o*I_o/(V*I) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_ox)\n",
+ "print(\"angle of overlap=%.3f deg\" %u)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=176.640 V\n",
+ "angle of overlap=2.855 deg\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.34, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a1=35.0 #firing angle advance\n",
+ "\n",
+ "#Calculations\n",
+ "a=180-a1\n",
+ "I_o=80.0\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "X_l=.25 #reactance=w*L\n",
+ "E=-3*V_ml*math.cos(math.radians(a))/math.pi+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean generator voltage=487.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.35, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "R=0.2\n",
+ "I_o=80\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "\n",
+ "#Calculations\n",
+ "X_l=.25 #reactance=w*L\n",
+ "a=35\n",
+ "E=-(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "a1=35\n",
+ "a=180-a1\n",
+ "E=(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle=35deg\") \n",
+ "print(\"mean generator voltage=%.3f V\" %E)\n",
+ "print(\"when firing angle advance=35deg\")\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle=35deg\n",
+ "mean generator voltage=503.590 V\n",
+ "when firing angle advance=35deg\n",
+ "mean generator voltage=503.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.36, Page No 365"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=5.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_mp=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "E=150.0\n",
+ "B=180-math.degrees(math.asin(E/V_mp))\n",
+ "I_o=(3/(2*math.pi*R))*(V_mp*(math.cos(math.radians(a+30))-math.cos(math.radians(B)))-E*((B-a-30)*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg current flowing=%.2f A\" %I_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg current flowing=19.96 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.37, Page No 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "V_o=V_m*(1+math.cos(math.radians(a)))/math.pi \n",
+ "E=100\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*(1-a/180)*math.pi/(math.pi))\n",
+ "I_or=I_o\n",
+ "P=E*I_o+I_or**2*R\n",
+ "pf=(P/(V*I_s)) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=(1-a/180)*math.pi/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\navg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "print(\"avg value of diode current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"circuit turn off time=%.2f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "avg o/p current=9.32 A\n",
+ "avg o/p voltage=193.202 V\n",
+ "avg value of thyristor current=4.66 A\n",
+ "rms value of thyristor current=6.590 A\n",
+ "avg value of diode current=4.66 A\n",
+ "rms value of diode current=6.590 A\n",
+ "pf=0.9202\n",
+ "circuit turn off time=8.33 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.38, Page No 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "L=0.05\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a=30\n",
+ "i_cp=2*V_m*(1-math.cos(math.radians(a)))/(w*L) \n",
+ "R=30.0\n",
+ "i_l=V_m/R\n",
+ "i1=i_cp+i_l \n",
+ "i2=i_cp \n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of circulating current=%.3f A\" %i_cp)\n",
+ "print(\"peak value of current in convertor 1=%.3f A\" %i1)\n",
+ "print(\"peak value of current in convertor 2=%.3f A\" %i2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of circulating current=5.548 A\n",
+ "peak value of current in convertor 1=16.391 A\n",
+ "peak value of current in convertor 2=5.548 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.39, Page No 370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=5.0\n",
+ "L=0.05\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(w*L/R)) \n",
+ "phi=90+math.degrees(math.atan(w*L/R)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"for no current transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)\n",
+ "print(\"for worst transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for no current transients\n",
+ "triggering angle=162.34 deg\n",
+ "for worst transients\n",
+ "triggering angle=162.34 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter6_3.ipynb b/_Power_Electronics/Chapter6_3.ipynb new file mode 100755 index 00000000..dff6564b --- /dev/null +++ b/_Power_Electronics/Chapter6_3.ipynb @@ -0,0 +1,1761 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 06 : Phase Controlled Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "P=1000.0\n",
+ "R=V**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "a=math.pi/4\n",
+ "V_or1=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P1=V_or1**2/R \n",
+ "a=math.pi/2\n",
+ "V_or2=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P2=V_or2**2/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle delay is of 45deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P1)\n",
+ "print(\"when firing angle delay is of 90deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle delay is of 45deg\n",
+ "power absorbed=454.58 W\n",
+ "when firing angle delay is of 90deg\n",
+ "power absorbed=250.00 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "a=35.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "th2=180-th1\n",
+ "I_o=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(th2)))-E*((th2-a)*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*((th2-a)*math.pi/180)-(V**2/2)*(math.sin(math.radians(2*th2))-math.sin(math.radians(2*a)))-2*math.sqrt(2)*V*E*(math.cos(math.radians(a))-math.cos(math.radians(th2)))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.2f W\" %P_r)\n",
+ "print(\"supply pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=4.9208 A\n",
+ "power supplied to the battery=738.12 W\n",
+ "power dissipated by the resistor=689.54 W\n",
+ "supply pf=0.6686\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, Page No 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=210\n",
+ "f=50.0 #Hz\n",
+ "w=2*math.pi*f\n",
+ "a=40.0 #firing angle\n",
+ "V=230.0\n",
+ "R=5.0\n",
+ "L=2*10**-3\n",
+ "\n",
+ "#Calculations\n",
+ "t_c1=(360-B)*math.pi/(180*w) \n",
+ "V_o1=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o1=V_o1/R \n",
+ "E=110\n",
+ "R=5\n",
+ "L=2*10**-3\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "t_c2=(360-B+th1)*math.pi/(180*w) \n",
+ "V_o2=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o2=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(B)))-E*((B-a)*math.pi/180)) \n",
+ "V_o2=R*I_o2+E \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for R=5ohm and L=2mH\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c1*1000))\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"avg output current=%.4f A\" %I_o1)\n",
+ "print(\"for R=5ohm % L=2mH and E=110V\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c2*1000))\n",
+ "print(\"avg output current=%.4f A\" %I_o2)\n",
+ "print(\"avg output voltage=%.3f V\" %V_o2) "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for R=5ohm and L=2mH\n",
+ "ckt turn off time=8.333 msec\n",
+ "avg output voltage=84.489 V\n",
+ "avg output current=16.8979 A\n",
+ "for R=5ohm % L=2mH and E=110V\n",
+ "ckt turn off time=9.431 msec\n",
+ "avg output current=6.5090 A\n",
+ "avg output voltage=142.545 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "R=10.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=(math.sqrt(2)*V_s)\n",
+ "V_o=V_m/(2*math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=(V_m/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a*math.pi/180)+.5*math.sin(math.radians(2*a)))\n",
+ "I_or=V_or/R\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "TUF=P_dc/(V_s*I_or) \n",
+ "PIV=V_m \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"t/f utilisation factor=%.4f\" %TUF)\n",
+ "print(\"PIV of thyristor=%.2f V\" %PIV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.2834\n",
+ "form factor=1.879\n",
+ "voltage ripple factor=1.5903\n",
+ "t/f utilisation factor=0.1797\n",
+ "PIV of thyristor=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=1000.0\n",
+ "fos=2.5 #factor of safety\n",
+ "I_TAV=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m1=V/(2*fos)\n",
+ "P1=(2*V_m1/math.pi)*I_TAV \n",
+ "V_m2=V/(fos)\n",
+ "P2=(2*V_m2/math.pi)*I_TAV \n",
+ "\n",
+ "#Results\n",
+ "print(\"for mid pt convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P1/1000))\n",
+ "print(\"for bridge convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for mid pt convertor\n",
+ "power handled=5.093 kW\n",
+ "for bridge convertor\n",
+ "power handled=10.186 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, Page No 297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=.4\n",
+ "I_o=10\n",
+ "I_or=I_o\n",
+ "E=120.0\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m)))\n",
+ "pf1=(E*I_o+I_or**2*R)/(V_s*I_or) \n",
+ "E=-120.0\n",
+ "a2=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m))) \n",
+ "pf2=(-E*I_o-I_or**2*R)/(V_s*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"pf=%.4f\" %pf1)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n",
+ "print(\"pf=%.4f\" %pf2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=53.21 deg\n",
+ "pf=0.5391\n",
+ "firing angle delay=124.07 deg\n",
+ "pf=0.5043\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "a=45.0\n",
+ "R=5.0\n",
+ "E=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=((math.sqrt(2)*V_s)/(2*math.pi))*(3+math.cos(math.radians(a)))\n",
+ "I_o=(V_o-E)/R \n",
+ "P=E*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.3f A\" %I_o)\n",
+ "print(\"power delivered to battery=%.4f kW\" %(P/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=18.382 A\n",
+ "power delivered to battery=1.8382 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No 300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "f=50.0\n",
+ "a=50.0\n",
+ "R=6.0\n",
+ "E=60.0\n",
+ "V_o1=((math.sqrt(2)*2*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o1=(V_o1-E)/R \n",
+ "\n",
+ "#ATQ after applying the conditions\n",
+ "V_o2=((math.sqrt(2)*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o2=(V_o2-E)/R \n",
+ "\n",
+ "print(\"avg o/p current=%.3f A\" %I_o1)\n",
+ "print(\"avg o/p current after change=%.2f A\" %I_o2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=12.184 A\n",
+ "avg o/p current after change=1.09 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(2*V_m/math.pi)*math.cos(math.radians(a))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_m/math.sqrt(2)\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o/math.pi\n",
+ "DF=math.cos(math.radians(a))\n",
+ "CDF=.90032\n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=2*V_m*I_o*math.sin(math.radians(a))/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.4f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"pf=%.5f\" %pf)\n",
+ "print(\"HF=%.5f\" %HF)\n",
+ "print(\"active power=%.2f W\" %P_dc) \n",
+ "print(\"reactive power=%.3f Var\" %Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.6366\n",
+ "form factor=1.5708\n",
+ "voltage ripple factor=1.2114\n",
+ "pf=0.63662\n",
+ "HF=0.48342\n",
+ "active power=2143.96 W\n",
+ "reactive power=2143.956 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12, Page No 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(V_m/math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o*math.cos(math.radians(a/2))/math.pi\n",
+ "DF=math.cos(math.radians(a/2)) \n",
+ "CDF=2*math.sqrt(2)*math.cos(math.radians(a/2))/math.sqrt(math.pi*(math.pi-a*math.pi/180)) \n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=V_m*I_o*math.sin(math.radians(a))/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"voltage ripple factor=%.3f\" %VRF) \n",
+ "print(\"DF=%.4f\" %DF)\n",
+ "print(\"CDF=%.4f\" %CDF)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"HF=%.4f\" %HF)\n",
+ "print(\"active power=%.3f W\" %P_dc)\n",
+ "print(\"reactive power=%.2f Var\" %Q)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "form factor=1.241\n",
+ "rectification efficiency=0.8059\n",
+ "voltage ripple factor=0.735\n",
+ "DF=0.9239\n",
+ "CDF=0.9605\n",
+ "pf=0.8874\n",
+ "HF=0.2899\n",
+ "active power=3123.973 W\n",
+ "reactive power=1293.99 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13, Page No 319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_om=3*V_ml/(2*math.pi)\n",
+ "V_o=V_om/2\n",
+ "th=30\n",
+ "a=math.degrees(math.acos((2*math.pi*math.sqrt(3)*V_o/(3*V_ml)-1)))-th \n",
+ "I_o=V_o/R \n",
+ "V_or=V_ml/(2*math.sqrt(math.pi))*math.sqrt((5*math.pi/6-a*math.pi/180)+.5*math.sin(math.radians(2*a+2*th)))\n",
+ "I_or=V_or/R \n",
+ "RE=V_o*I_o/(V_or*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"delay angle=%.1f deg\" %a)\n",
+ "print(\"avg load current=%.3f A\" %I_o)\n",
+ "print(\"rms load current=%.3f A\" %I_or)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle=67.7 deg\n",
+ "avg load current=7.765 A\n",
+ "rms load current=10.477 A\n",
+ "rectification efficiency=0.5494\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15, Page No 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "v_T=1.4\n",
+ "a1=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=3*V_ml/(2*math.pi)*math.cos(math.radians(a1))-v_T \n",
+ "a2=60.0\n",
+ "V_o2=3*V_ml/(2*math.pi)*math.cos(math.radians(a2))-v_T \n",
+ "I_o=36\n",
+ "I_TA=I_o/3 \n",
+ "I_Tr=I_o/math.sqrt(3) \n",
+ "P=I_TA*v_T \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle = 30deg\")\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"for firing angle = 60deg\")\n",
+ "print(\"avg output voltage=%.2f V\" %V_o2)\n",
+ "print(\"avg current rating=%.0f A\" %I_TA)\n",
+ "print(\"rms current rating=%.3f A\" %I_Tr)\n",
+ "print(\"PIV of SCR=%.1f V\" %V_ml)\n",
+ "print(\"power dissipated=%.1f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17, Page No 331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200\n",
+ "I_o=20\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a1=math.degrees(math.acos(V_o1*math.pi/(3*V_ml)))\n",
+ "th=120\n",
+ "I_s=math.sqrt((1/math.pi)*I_o**2*th*math.pi/180)\n",
+ "P=E*I_o+I_o**2*R\n",
+ "pf=P/(math.sqrt(3)*V_s*I_s) \n",
+ "V_o2=E-I_o*R\n",
+ "a2=math.degrees(math.acos(-V_o2*math.pi/(3*V_ml))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.3f deg\" %a1)\n",
+ "print(\"pf=%.3f\" %pf)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18, Page No 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a1=0\n",
+ "t_c1=(4*math.pi/3-a1*math.pi/180)/w \n",
+ "a2=30\n",
+ "t_c2=(4*math.pi/3-a2*math.pi/180)/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle delay=0deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c1*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n",
+ "print(\"for firing angle delay=30deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c2*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle delay=0deg\n",
+ "commutation time=13.33 ms\n",
+ "peak reverse voltage=325.27 V\n",
+ "for firing angle delay=30deg\n",
+ "commutation time=11.67 ms\n",
+ "peak reverse voltage=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.19, Page No 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.20, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/(2*math.pi/3+math.sqrt(3)*(1+math.cos(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=102.459 V\n",
+ "for constant load current\n",
+ "V_ph=102.46 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.21, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=90.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/((math.pi-math.pi/2)+(math.sin(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.2f V\" %V_ph)\n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.1f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=191.19 V\n",
+ "for constant load current\n",
+ "V_ph=191.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.22 Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200.0\n",
+ "I_o=20.0\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml)-1)) \n",
+ "a1=180-a\n",
+ "I_sr=math.sqrt((1/math.pi)*I_o**2*(a1*math.pi/180))\n",
+ "P=V_o*I_o\n",
+ "pf=P/(math.sqrt(3)*V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "print(\"pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=69.38 deg\n",
+ "pf=0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.23, Page No 335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "f=50.0\n",
+ "I_o=15.0\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TA=I_o*120.0/360.0\n",
+ "I_Tr=math.sqrt(I_o**2*120/360)\n",
+ "I_sr=math.sqrt(I_o**2*120/180)\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "V_or=V_ml*math.sqrt((3/(2*math.pi))*(math.pi/3+math.sqrt(3/2)*math.cos(math.radians(2*a))))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "VA=3*V_s/math.sqrt(3)*I_sr\n",
+ "TUF=P_dc/VA \n",
+ "pf=P_ac/VA \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.5f\" %RE)\n",
+ "print(\"TUF=%.4f\" %TUF)\n",
+ "print(\"Input pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.95493\n",
+ "TUF=0.6752\n",
+ "Input pf=0.707\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.24, Page No 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=10.0\n",
+ "a=45.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "DF=math.cos(math.radians(a))\n",
+ "I_o=10\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)*math.sin(math.pi/3)\n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "I_o=1 #suppose\n",
+ "CDF=I_s1/I_sr \n",
+ "THD=math.sqrt(1/CDF**2-1) \n",
+ "pf=CDF*DF \n",
+ "P=(3*math.sqrt(2)*V*math.cos(math.radians(a))/math.pi)*I\n",
+ "Q=(3*math.sqrt(2)*V*math.sin(math.radians(a))/math.pi)*I \n",
+ " \n",
+ "#Results\n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"CDF=%.3f\" %CDF)\n",
+ "print(\"THD=%.5f\" %THD)\n",
+ "print(\"PF=%.4f\" %pf)\n",
+ "print(\"active power=%.2f W\" %P) \n",
+ "print(\"reactive power=%.2f Var\" %Q)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "DF=0.707\n",
+ "CDF=0.955\n",
+ "THD=0.31084\n",
+ "PF=0.6752\n",
+ "active power=3819.72 W\n",
+ "reactive power=3819.72 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.25, Page No 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "print(\"for firing angle=30deg\")\n",
+ "a=30.0\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=350\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P1=V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P1/VA \n",
+ "a=180-60\n",
+ "V=400\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=-350\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P2=-V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P2/VA \n",
+ "\n",
+ "print(\"power delivered to load=%.2f W\" %P1)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"for firing advance angle=60deg\")\n",
+ "print(\"power delivered to load=%.2f W\" %P2)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "power delivered to load=5511.74 W\n",
+ "pf=0.4775\n",
+ "for firing advance angle=60deg\n",
+ "power delivered to load=2158.20 W\n",
+ "pf=0.4775\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.26, Page No 347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0\n",
+ "u=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=math.cos(math.radians(a))-math.cos(math.radians(a+u))\n",
+ "a=30\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=45\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=60\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=30deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=45deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=60deg\") \n",
+ "print(\"overlap angle=%.2f deg\" %u)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=45deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=60deg\n",
+ "overlap angle=2.23 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.28, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=400.0\n",
+ "I_o=20.0\n",
+ "R=1\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.004\n",
+ "V=230 #per phase voltage\n",
+ "V_ml=math.sqrt(6)*V\n",
+ "a=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o+3*w*L*I_o/math.pi))) \n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "u=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o-3*w*L*I_o/math.pi)))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"overlap angle=%.2f deg\" %u)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=34.382 deg\n",
+ "overlap angle=8.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.29, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=1\n",
+ "E=230\n",
+ "I=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=-E+I*R\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml))) \n",
+ "L=0.004\n",
+ "a=math.degrees(math.acos((2*math.pi)/(3*V_ml)*(V_o+3*w*L*I/(2*math.pi)))) \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-3*f*L*I/V_ml))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "print(\"overlap angle=%.3f deg\" %u)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=139.702 deg\n",
+ "firing angle delay=139.702 deg\n",
+ "overlap angle=1.431 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.31, Page No 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0 #per phase\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(3.0)*math.sqrt(2)*V\n",
+ "w=2*math.pi*f\n",
+ "a1=60.0\n",
+ "L=0.015\n",
+ "i_cp=(math.sqrt(3)*V_ml/(w*L))*(1-math.sin(math.radians(a1))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"circulating current=%.4f A\" %i_cp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circulating current=27.7425 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.32, Page No 362"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*math.pi/(math.pi)) \n",
+ "I_o=I_s\n",
+ "pf=(V_o*I_o/(V*I_s)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=179.330 V\n",
+ "avg o/p current=17.93 A\n",
+ "avg value of thyristor current=8.967 A\n",
+ "rms value of thyristor current=12.68 A\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.33, Page No 363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "L=.0015\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "V_ox=2*V_m*math.cos(math.radians(a))/math.pi-w*L*I_o/math.pi \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-I_o*w*L/V_m))-a \n",
+ "I=I_o\n",
+ "pf=V_o*I_o/(V*I) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_ox)\n",
+ "print(\"angle of overlap=%.3f deg\" %u)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=176.640 V\n",
+ "angle of overlap=2.855 deg\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.34, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a1=35.0 #firing angle advance\n",
+ "\n",
+ "#Calculations\n",
+ "a=180-a1\n",
+ "I_o=80.0\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "X_l=.25 #reactance=w*L\n",
+ "E=-3*V_ml*math.cos(math.radians(a))/math.pi+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean generator voltage=487.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.35, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "R=0.2\n",
+ "I_o=80\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "\n",
+ "#Calculations\n",
+ "X_l=.25 #reactance=w*L\n",
+ "a=35\n",
+ "E=-(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "a1=35\n",
+ "a=180-a1\n",
+ "E=(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle=35deg\") \n",
+ "print(\"mean generator voltage=%.3f V\" %E)\n",
+ "print(\"when firing angle advance=35deg\")\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle=35deg\n",
+ "mean generator voltage=503.590 V\n",
+ "when firing angle advance=35deg\n",
+ "mean generator voltage=503.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.36, Page No 365"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=5.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_mp=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "E=150.0\n",
+ "B=180-math.degrees(math.asin(E/V_mp))\n",
+ "I_o=(3/(2*math.pi*R))*(V_mp*(math.cos(math.radians(a+30))-math.cos(math.radians(B)))-E*((B-a-30)*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg current flowing=%.2f A\" %I_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg current flowing=19.96 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.37, Page No 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "V_o=V_m*(1+math.cos(math.radians(a)))/math.pi \n",
+ "E=100\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*(1-a/180)*math.pi/(math.pi))\n",
+ "I_or=I_o\n",
+ "P=E*I_o+I_or**2*R\n",
+ "pf=(P/(V*I_s)) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=(1-a/180)*math.pi/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\navg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "print(\"avg value of diode current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"circuit turn off time=%.2f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "avg o/p current=9.32 A\n",
+ "avg o/p voltage=193.202 V\n",
+ "avg value of thyristor current=4.66 A\n",
+ "rms value of thyristor current=6.590 A\n",
+ "avg value of diode current=4.66 A\n",
+ "rms value of diode current=6.590 A\n",
+ "pf=0.9202\n",
+ "circuit turn off time=8.33 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.38, Page No 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "L=0.05\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a=30\n",
+ "i_cp=2*V_m*(1-math.cos(math.radians(a)))/(w*L) \n",
+ "R=30.0\n",
+ "i_l=V_m/R\n",
+ "i1=i_cp+i_l \n",
+ "i2=i_cp \n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of circulating current=%.3f A\" %i_cp)\n",
+ "print(\"peak value of current in convertor 1=%.3f A\" %i1)\n",
+ "print(\"peak value of current in convertor 2=%.3f A\" %i2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of circulating current=5.548 A\n",
+ "peak value of current in convertor 1=16.391 A\n",
+ "peak value of current in convertor 2=5.548 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.39, Page No 370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=5.0\n",
+ "L=0.05\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(w*L/R)) \n",
+ "phi=90+math.degrees(math.atan(w*L/R)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"for no current transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)\n",
+ "print(\"for worst transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for no current transients\n",
+ "triggering angle=162.34 deg\n",
+ "for worst transients\n",
+ "triggering angle=162.34 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter6_4.ipynb b/_Power_Electronics/Chapter6_4.ipynb new file mode 100755 index 00000000..dff6564b --- /dev/null +++ b/_Power_Electronics/Chapter6_4.ipynb @@ -0,0 +1,1761 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 06 : Phase Controlled Rectifiers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.1, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "P=1000.0\n",
+ "R=V**2/P\n",
+ "\n",
+ "#Calculations\n",
+ "a=math.pi/4\n",
+ "V_or1=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P1=V_or1**2/R \n",
+ "a=math.pi/2\n",
+ "V_or2=(math.sqrt(2)*V/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a)+.5*math.sin(2*a))\n",
+ "P2=V_or2**2/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle delay is of 45deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P1)\n",
+ "print(\"when firing angle delay is of 90deg\")\n",
+ "print(\"power absorbed=%.2f W\" %P2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle delay is of 45deg\n",
+ "power absorbed=454.58 W\n",
+ "when firing angle delay is of 90deg\n",
+ "power absorbed=250.00 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.2, Page No 283"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.sin(math.radians(E/(math.sqrt(2)*V)))\n",
+ "I_o=(1/(2*math.pi*R))*(2*math.sqrt(2)*230*math.cos(math.radians(th1))-E*(math.pi-2*th1*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*(math.pi-2*th1*math.pi/180)+V**2*math.sin(math.radians(2*th1))-4*math.sqrt(2)*V*E*math.cos(math.radians(th1))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.3f W\" %P_r) \n",
+ "print(\"supply pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=3.5679 A\n",
+ "power supplied to the battery=535.18 W\n",
+ "power dissipated by the resistor=829.760 W\n",
+ "supply pf=0.583\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.3 Page No 284"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "E=150.0\n",
+ "R=8.0\n",
+ "a=35.0\n",
+ "\n",
+ "#Calculations\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "th2=180-th1\n",
+ "I_o=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(th2)))-E*((th2-a)*math.pi/180)) \n",
+ "P=E*I_o \n",
+ "I_or=math.sqrt((1/(2*math.pi*R**2))*((V**2+E**2)*((th2-a)*math.pi/180)-(V**2/2)*(math.sin(math.radians(2*th2))-math.sin(math.radians(2*a)))-2*math.sqrt(2)*V*E*(math.cos(math.radians(a))-math.cos(math.radians(th2)))))\n",
+ "P_r=I_or**2*R \n",
+ "pf=(P+P_r)/(V*I_or) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg charging curent=%.4f A\" %I_o)\n",
+ "print(\"power supplied to the battery=%.2f W\" %P)\n",
+ "print(\"power dissipated by the resistor=%.2f W\" %P_r)\n",
+ "print(\"supply pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg charging curent=4.9208 A\n",
+ "power supplied to the battery=738.12 W\n",
+ "power dissipated by the resistor=689.54 W\n",
+ "supply pf=0.6686\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.4, Page No 285"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "B=210\n",
+ "f=50.0 #Hz\n",
+ "w=2*math.pi*f\n",
+ "a=40.0 #firing angle\n",
+ "V=230.0\n",
+ "R=5.0\n",
+ "L=2*10**-3\n",
+ "\n",
+ "#Calculations\n",
+ "t_c1=(360-B)*math.pi/(180*w) \n",
+ "V_o1=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o1=V_o1/R \n",
+ "E=110\n",
+ "R=5\n",
+ "L=2*10**-3\n",
+ "th1=math.degrees(math.asin(E/(math.sqrt(2)*V)))\n",
+ "t_c2=(360-B+th1)*math.pi/(180*w) \n",
+ "V_o2=(math.sqrt(2)*230/(2*math.pi))*(math.cos(math.radians(a))-math.cos(math.radians(B))) \n",
+ "I_o2=(1/(2*math.pi*R))*(math.sqrt(2)*230*(math.cos(math.radians(a))-math.cos(math.radians(B)))-E*((B-a)*math.pi/180)) \n",
+ "V_o2=R*I_o2+E \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"for R=5ohm and L=2mH\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c1*1000))\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"avg output current=%.4f A\" %I_o1)\n",
+ "print(\"for R=5ohm % L=2mH and E=110V\")\n",
+ "print(\"ckt turn off time=%.3f msec\" %(t_c2*1000))\n",
+ "print(\"avg output current=%.4f A\" %I_o2)\n",
+ "print(\"avg output voltage=%.3f V\" %V_o2) "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for R=5ohm and L=2mH\n",
+ "ckt turn off time=8.333 msec\n",
+ "avg output voltage=84.489 V\n",
+ "avg output current=16.8979 A\n",
+ "for R=5ohm % L=2mH and E=110V\n",
+ "ckt turn off time=9.431 msec\n",
+ "avg output current=6.5090 A\n",
+ "avg output voltage=142.545 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.5 Page No 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "R=10.0\n",
+ "a=60.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=(math.sqrt(2)*V_s)\n",
+ "V_o=V_m/(2*math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=(V_m/(2*math.sqrt(math.pi)))*math.sqrt((math.pi-a*math.pi/180)+.5*math.sin(math.radians(2*a)))\n",
+ "I_or=V_or/R\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "TUF=P_dc/(V_s*I_or) \n",
+ "PIV=V_m \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"t/f utilisation factor=%.4f\" %TUF)\n",
+ "print(\"PIV of thyristor=%.2f V\" %PIV)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.2834\n",
+ "form factor=1.879\n",
+ "voltage ripple factor=1.5903\n",
+ "t/f utilisation factor=0.1797\n",
+ "PIV of thyristor=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.6 Page No 294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=1000.0\n",
+ "fos=2.5 #factor of safety\n",
+ "I_TAV=40.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m1=V/(2*fos)\n",
+ "P1=(2*V_m1/math.pi)*I_TAV \n",
+ "V_m2=V/(fos)\n",
+ "P2=(2*V_m2/math.pi)*I_TAV \n",
+ "\n",
+ "#Results\n",
+ "print(\"for mid pt convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P1/1000))\n",
+ "print(\"for bridge convertor\")\n",
+ "print(\"power handled=%.3f kW\" %(P2/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for mid pt convertor\n",
+ "power handled=5.093 kW\n",
+ "for bridge convertor\n",
+ "power handled=10.186 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.7, Page No 297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=.4\n",
+ "I_o=10\n",
+ "I_or=I_o\n",
+ "E=120.0\n",
+ "\n",
+ "#Calculations\n",
+ "a1=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m)))\n",
+ "pf1=(E*I_o+I_or**2*R)/(V_s*I_or) \n",
+ "E=-120.0\n",
+ "a2=math.degrees(math.acos((E+I_o*R)*math.pi/(2*V_m))) \n",
+ "pf2=(-E*I_o-I_or**2*R)/(V_s*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a1)\n",
+ "print(\"pf=%.4f\" %pf1)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n",
+ "print(\"pf=%.4f\" %pf2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=53.21 deg\n",
+ "pf=0.5391\n",
+ "firing angle delay=124.07 deg\n",
+ "pf=0.5043\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.9 Page No 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "f=50.0\n",
+ "a=45.0\n",
+ "R=5.0\n",
+ "E=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=((math.sqrt(2)*V_s)/(2*math.pi))*(3+math.cos(math.radians(a)))\n",
+ "I_o=(V_o-E)/R \n",
+ "P=E*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.3f A\" %I_o)\n",
+ "print(\"power delivered to battery=%.4f kW\" %(P/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=18.382 A\n",
+ "power delivered to battery=1.8382 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.10 Page No 300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "f=50.0\n",
+ "a=50.0\n",
+ "R=6.0\n",
+ "E=60.0\n",
+ "V_o1=((math.sqrt(2)*2*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o1=(V_o1-E)/R \n",
+ "\n",
+ "#ATQ after applying the conditions\n",
+ "V_o2=((math.sqrt(2)*V_s)/(math.pi))*math.cos(math.radians(a))\n",
+ "I_o2=(V_o2-E)/R \n",
+ "\n",
+ "print(\"avg o/p current=%.3f A\" %I_o1)\n",
+ "print(\"avg o/p current after change=%.2f A\" %I_o2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p current=12.184 A\n",
+ "avg o/p current after change=1.09 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.11 Page No 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(2*V_m/math.pi)*math.cos(math.radians(a))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_m/math.sqrt(2)\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o/math.pi\n",
+ "DF=math.cos(math.radians(a))\n",
+ "CDF=.90032\n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=2*V_m*I_o*math.sin(math.radians(a))/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"form factor=%.4f\" %FF)\n",
+ "print(\"voltage ripple factor=%.4f\" %VRF)\n",
+ "print(\"pf=%.5f\" %pf)\n",
+ "print(\"HF=%.5f\" %HF)\n",
+ "print(\"active power=%.2f W\" %P_dc) \n",
+ "print(\"reactive power=%.3f Var\" %Q)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.6366\n",
+ "form factor=1.5708\n",
+ "voltage ripple factor=1.2114\n",
+ "pf=0.63662\n",
+ "HF=0.48342\n",
+ "active power=2143.96 W\n",
+ "reactive power=2143.956 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.12, Page No 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=(V_m/math.pi)*(1+math.cos(math.radians(a)))\n",
+ "I_o=V_o/R\n",
+ "V_or=V_s*math.sqrt((1/math.pi)*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "FF=V_or/V_o \n",
+ "VRF=math.sqrt(FF**2-1) \n",
+ "I_s1=2*math.sqrt(2)*I_o*math.cos(math.radians(a/2))/math.pi\n",
+ "DF=math.cos(math.radians(a/2)) \n",
+ "CDF=2*math.sqrt(2)*math.cos(math.radians(a/2))/math.sqrt(math.pi*(math.pi-a*math.pi/180)) \n",
+ "pf=CDF*DF \n",
+ "HF=math.sqrt((1/CDF**2)-1) \n",
+ "Q=V_m*I_o*math.sin(math.radians(a))/math.pi\n",
+ "\n",
+ "#Results\n",
+ "print(\"form factor=%.3f\" %FF)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)\n",
+ "print(\"voltage ripple factor=%.3f\" %VRF) \n",
+ "print(\"DF=%.4f\" %DF)\n",
+ "print(\"CDF=%.4f\" %CDF)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"HF=%.4f\" %HF)\n",
+ "print(\"active power=%.3f W\" %P_dc)\n",
+ "print(\"reactive power=%.2f Var\" %Q)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "form factor=1.241\n",
+ "rectification efficiency=0.8059\n",
+ "voltage ripple factor=0.735\n",
+ "DF=0.9239\n",
+ "CDF=0.9605\n",
+ "pf=0.8874\n",
+ "HF=0.2899\n",
+ "active power=3123.973 W\n",
+ "reactive power=1293.99 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.13, Page No 319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_om=3*V_ml/(2*math.pi)\n",
+ "V_o=V_om/2\n",
+ "th=30\n",
+ "a=math.degrees(math.acos((2*math.pi*math.sqrt(3)*V_o/(3*V_ml)-1)))-th \n",
+ "I_o=V_o/R \n",
+ "V_or=V_ml/(2*math.sqrt(math.pi))*math.sqrt((5*math.pi/6-a*math.pi/180)+.5*math.sin(math.radians(2*a+2*th)))\n",
+ "I_or=V_or/R \n",
+ "RE=V_o*I_o/(V_or*I_or) \n",
+ "\n",
+ "#Results\n",
+ "print(\"delay angle=%.1f deg\" %a)\n",
+ "print(\"avg load current=%.3f A\" %I_o)\n",
+ "print(\"rms load current=%.3f A\" %I_or)\n",
+ "print(\"rectification efficiency=%.4f\" %RE)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "delay angle=67.7 deg\n",
+ "avg load current=7.765 A\n",
+ "rms load current=10.477 A\n",
+ "rectification efficiency=0.5494\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.15, Page No 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "v_T=1.4\n",
+ "a1=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=3*V_ml/(2*math.pi)*math.cos(math.radians(a1))-v_T \n",
+ "a2=60.0\n",
+ "V_o2=3*V_ml/(2*math.pi)*math.cos(math.radians(a2))-v_T \n",
+ "I_o=36\n",
+ "I_TA=I_o/3 \n",
+ "I_Tr=I_o/math.sqrt(3) \n",
+ "P=I_TA*v_T \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle = 30deg\")\n",
+ "print(\"avg output voltage=%.3f V\" %V_o1)\n",
+ "print(\"for firing angle = 60deg\")\n",
+ "print(\"avg output voltage=%.2f V\" %V_o2)\n",
+ "print(\"avg current rating=%.0f A\" %I_TA)\n",
+ "print(\"rms current rating=%.3f A\" %I_Tr)\n",
+ "print(\"PIV of SCR=%.1f V\" %V_ml)\n",
+ "print(\"power dissipated=%.1f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.17, Page No 331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200\n",
+ "I_o=20\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o1=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a1=math.degrees(math.acos(V_o1*math.pi/(3*V_ml)))\n",
+ "th=120\n",
+ "I_s=math.sqrt((1/math.pi)*I_o**2*th*math.pi/180)\n",
+ "P=E*I_o+I_o**2*R\n",
+ "pf=P/(math.sqrt(3)*V_s*I_s) \n",
+ "V_o2=E-I_o*R\n",
+ "a2=math.degrees(math.acos(-V_o2*math.pi/(3*V_ml))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.3f deg\" %a1)\n",
+ "print(\"pf=%.3f\" %pf)\n",
+ "print(\"firing angle delay=%.2f deg\" %a2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.18, Page No 332"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a1=0\n",
+ "t_c1=(4*math.pi/3-a1*math.pi/180)/w \n",
+ "a2=30\n",
+ "t_c2=(4*math.pi/3-a2*math.pi/180)/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle delay=0deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c1*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n",
+ "print(\"for firing angle delay=30deg\")\n",
+ "print(\"commutation time=%.2f ms\" %(t_c2*1000))\n",
+ "print(\"peak reverse voltage=%.2f V\" %(math.sqrt(2)*V))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle delay=0deg\n",
+ "commutation time=13.33 ms\n",
+ "peak reverse voltage=325.27 V\n",
+ "for firing angle delay=30deg\n",
+ "commutation time=11.67 ms\n",
+ "peak reverse voltage=325.27 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.19, Page No 333"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.20, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/(2*math.pi/3+math.sqrt(3)*(1+math.cos(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=102.459 V\n",
+ "for constant load current\n",
+ "V_ph=102.46 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.21, Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=90.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*4*math.pi/(2*3)/((math.pi-math.pi/2)+(math.sin(math.radians(2*a)))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*2*math.pi/(math.sqrt(2)*3*(1+math.cos(math.radians(a))))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage percent V_ph=%.2f V\" %V_ph)\n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.1f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage percent V_ph=191.19 V\n",
+ "for constant load current\n",
+ "V_ph=191.2 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.22 Page No 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=200.0\n",
+ "I_o=20.0\n",
+ "R=.5\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "V_s=230\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml)-1)) \n",
+ "a1=180-a\n",
+ "I_sr=math.sqrt((1/math.pi)*I_o**2*(a1*math.pi/180))\n",
+ "P=V_o*I_o\n",
+ "pf=P/(math.sqrt(3)*V_s*I_sr) \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle delay=%.2f deg\" %a)\n",
+ "print(\"pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=69.38 deg\n",
+ "pf=0.67\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.23, Page No 335"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=400.0\n",
+ "f=50.0\n",
+ "I_o=15.0\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TA=I_o*120.0/360.0\n",
+ "I_Tr=math.sqrt(I_o**2*120/360)\n",
+ "I_sr=math.sqrt(I_o**2*120/180)\n",
+ "V_ml=math.sqrt(2)*V_s\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "V_or=V_ml*math.sqrt((3/(2*math.pi))*(math.pi/3+math.sqrt(3/2)*math.cos(math.radians(2*a))))\n",
+ "I_or=I_o\n",
+ "P_dc=V_o*I_o\n",
+ "P_ac=V_or*I_or\n",
+ "RE=P_dc/P_ac \n",
+ "VA=3*V_s/math.sqrt(3)*I_sr\n",
+ "TUF=P_dc/VA \n",
+ "pf=P_ac/VA \n",
+ "\n",
+ "#Results\n",
+ "print(\"rectification efficiency=%.5f\" %RE)\n",
+ "print(\"TUF=%.4f\" %TUF)\n",
+ "print(\"Input pf=%.3f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rectification efficiency=0.95493\n",
+ "TUF=0.6752\n",
+ "Input pf=0.707\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.24, Page No 341"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I=10.0\n",
+ "a=45.0\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "DF=math.cos(math.radians(a))\n",
+ "I_o=10\n",
+ "I_s1=4*I_o/(math.sqrt(2)*math.pi)*math.sin(math.pi/3)\n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "I_o=1 #suppose\n",
+ "CDF=I_s1/I_sr \n",
+ "THD=math.sqrt(1/CDF**2-1) \n",
+ "pf=CDF*DF \n",
+ "P=(3*math.sqrt(2)*V*math.cos(math.radians(a))/math.pi)*I\n",
+ "Q=(3*math.sqrt(2)*V*math.sin(math.radians(a))/math.pi)*I \n",
+ " \n",
+ "#Results\n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"CDF=%.3f\" %CDF)\n",
+ "print(\"THD=%.5f\" %THD)\n",
+ "print(\"PF=%.4f\" %pf)\n",
+ "print(\"active power=%.2f W\" %P) \n",
+ "print(\"reactive power=%.2f Var\" %Q)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "DF=0.707\n",
+ "CDF=0.955\n",
+ "THD=0.31084\n",
+ "PF=0.6752\n",
+ "active power=3819.72 W\n",
+ "reactive power=3819.72 Var\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.25, Page No 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "print(\"for firing angle=30deg\")\n",
+ "a=30.0\n",
+ "V=400.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=350\n",
+ "R=10\n",
+ "\n",
+ "#Calculations\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P1=V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P1/VA \n",
+ "a=180-60\n",
+ "V=400\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "V_o=3*V_ml*math.cos(math.radians(a))/math.pi\n",
+ "E=-350\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R\n",
+ "I_or=I_o\n",
+ "P2=-V_o*I_o \n",
+ "I_sr=I_o*math.sqrt(2.0/3.0)\n",
+ "VA=3*V/math.sqrt(3)*I_sr\n",
+ "pf=P2/VA \n",
+ "\n",
+ "print(\"power delivered to load=%.2f W\" %P1)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"for firing advance angle=60deg\")\n",
+ "print(\"power delivered to load=%.2f W\" %P2)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "power delivered to load=5511.74 W\n",
+ "pf=0.4775\n",
+ "for firing advance angle=60deg\n",
+ "power delivered to load=2158.20 W\n",
+ "pf=0.4775\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.26, Page No 347"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0\n",
+ "u=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "i=math.cos(math.radians(a))-math.cos(math.radians(a+u))\n",
+ "a=30\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=45\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "a=60\n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-i))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"for firing angle=30deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=45deg\") \n",
+ "print(\"overlap angle=%.1f deg\" %u)\n",
+ "print(\"for firing angle=60deg\") \n",
+ "print(\"overlap angle=%.2f deg\" %u)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle=30deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=45deg\n",
+ "overlap angle=2.2 deg\n",
+ "for firing angle=60deg\n",
+ "overlap angle=2.23 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.28, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "E=400.0\n",
+ "I_o=20.0\n",
+ "R=1\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=E+I_o*R\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=.004\n",
+ "V=230 #per phase voltage\n",
+ "V_ml=math.sqrt(6)*V\n",
+ "a=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o+3*w*L*I_o/math.pi))) \n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "u=math.degrees(math.acos(math.pi/(3*V_ml)*(V_o-3*w*L*I_o/math.pi)))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"overlap angle=%.2f deg\" %u)\n",
+ "#Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=34.382 deg\n",
+ "overlap angle=8.22 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.29, Page No 352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=400.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=1\n",
+ "E=230\n",
+ "I=15.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=-E+I*R\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a=math.degrees(math.acos(V_o*2*math.pi/(3*V_ml))) \n",
+ "L=0.004\n",
+ "a=math.degrees(math.acos((2*math.pi)/(3*V_ml)*(V_o+3*w*L*I/(2*math.pi)))) \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-3*f*L*I/V_ml))-a \n",
+ "\n",
+ "#Results\n",
+ "print(\"firing angle=%.3f deg\" %a)\n",
+ "print(\"firing angle delay=%.3f deg\" %a)\n",
+ "print(\"overlap angle=%.3f deg\" %u)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle=139.702 deg\n",
+ "firing angle delay=139.702 deg\n",
+ "overlap angle=1.431 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.31, Page No 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0 #per phase\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_ml=math.sqrt(3.0)*math.sqrt(2)*V\n",
+ "w=2*math.pi*f\n",
+ "a1=60.0\n",
+ "L=0.015\n",
+ "i_cp=(math.sqrt(3)*V_ml/(w*L))*(1-math.sin(math.radians(a1))) \n",
+ "\n",
+ "#Results\n",
+ "print(\"circulating current=%.4f A\" %i_cp)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "circulating current=27.7425 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.32, Page No 362"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*math.pi/(math.pi)) \n",
+ "I_o=I_s\n",
+ "pf=(V_o*I_o/(V*I_s)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits.\n",
+ " \n",
+ " \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=179.330 V\n",
+ "avg o/p current=17.93 A\n",
+ "avg value of thyristor current=8.967 A\n",
+ "rms value of thyristor current=12.68 A\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.33, Page No 363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "L=.0015\n",
+ "\n",
+ "#Calculations\n",
+ "V_o=2*V_m* math.cos(math.radians(a))/math.pi \n",
+ "R=10\n",
+ "I_o=V_o/R \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "V_ox=2*V_m*math.cos(math.radians(a))/math.pi-w*L*I_o/math.pi \n",
+ "u=math.degrees(math.acos(math.cos(math.radians(a))-I_o*w*L/V_m))-a \n",
+ "I=I_o\n",
+ "pf=V_o*I_o/(V*I) \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_ox)\n",
+ "print(\"angle of overlap=%.3f deg\" %u)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=176.640 V\n",
+ "angle of overlap=2.855 deg\n",
+ "pf=0.7797\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.34, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "a1=35.0 #firing angle advance\n",
+ "\n",
+ "#Calculations\n",
+ "a=180-a1\n",
+ "I_o=80.0\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "X_l=.25 #reactance=w*L\n",
+ "E=-3*V_ml*math.cos(math.radians(a))/math.pi+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi \n",
+ "\n",
+ "#Results\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "mean generator voltage=487.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.35, Page No 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=415.0\n",
+ "V_ml=math.sqrt(2)*V\n",
+ "R=0.2\n",
+ "I_o=80\n",
+ "r_s=0.04\n",
+ "v_T=1.5\n",
+ "\n",
+ "#Calculations\n",
+ "X_l=.25 #reactance=w*L\n",
+ "a=35\n",
+ "E=-(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "a1=35\n",
+ "a=180-a1\n",
+ "E=(-3*V_ml*math.cos(math.radians(a))/math.pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/math.pi) \n",
+ "\n",
+ "#Results\n",
+ "print(\"when firing angle=35deg\") \n",
+ "print(\"mean generator voltage=%.3f V\" %E)\n",
+ "print(\"when firing angle advance=35deg\")\n",
+ "print(\"mean generator voltage=%.3f V\" %E)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when firing angle=35deg\n",
+ "mean generator voltage=503.590 V\n",
+ "when firing angle advance=35deg\n",
+ "mean generator voltage=503.590 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.36, Page No 365"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=5.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_mp=math.sqrt(2)*V\n",
+ "a=30.0\n",
+ "E=150.0\n",
+ "B=180-math.degrees(math.asin(E/V_mp))\n",
+ "I_o=(3/(2*math.pi*R))*(V_mp*(math.cos(math.radians(a+30))-math.cos(math.radians(B)))-E*((B-a-30)*math.pi/180))\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg current flowing=%.2f A\" %I_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg current flowing=19.96 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.37, Page No 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "V=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_m=math.sqrt(2)*V\n",
+ "V_o=V_m*(1+math.cos(math.radians(a)))/math.pi \n",
+ "E=100\n",
+ "R=10\n",
+ "I_o=(V_o-E)/R \n",
+ "I_TA=I_o*math.pi/(2*math.pi) \n",
+ "I_Tr=math.sqrt(I_o**2*math.pi/(2*math.pi)) \n",
+ "I_s=math.sqrt(I_o**2*(1-a/180)*math.pi/(math.pi))\n",
+ "I_or=I_o\n",
+ "P=E*I_o+I_or**2*R\n",
+ "pf=(P/(V*I_s)) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=(1-a/180)*math.pi/w \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\navg o/p current=%.2f A\" %I_o)\n",
+ "print(\"avg o/p voltage=%.3f V\" %V_o)\n",
+ "print(\"avg value of thyristor current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_Tr)\n",
+ "print(\"avg value of diode current=%.2f A\" %I_TA)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_Tr)\n",
+ "print(\"pf=%.4f\" %pf)\n",
+ "print(\"circuit turn off time=%.2f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "avg o/p current=9.32 A\n",
+ "avg o/p voltage=193.202 V\n",
+ "avg value of thyristor current=4.66 A\n",
+ "rms value of thyristor current=6.590 A\n",
+ "avg value of diode current=4.66 A\n",
+ "rms value of diode current=6.590 A\n",
+ "pf=0.9202\n",
+ "circuit turn off time=8.33 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.38, Page No 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "V_m=math.sqrt(2)*V\n",
+ "L=0.05\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "w=2*math.pi*f\n",
+ "a=30\n",
+ "i_cp=2*V_m*(1-math.cos(math.radians(a)))/(w*L) \n",
+ "R=30.0\n",
+ "i_l=V_m/R\n",
+ "i1=i_cp+i_l \n",
+ "i2=i_cp \n",
+ "\n",
+ "#Results\n",
+ "print(\"peak value of circulating current=%.3f A\" %i_cp)\n",
+ "print(\"peak value of current in convertor 1=%.3f A\" %i1)\n",
+ "print(\"peak value of current in convertor 2=%.3f A\" %i2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "peak value of circulating current=5.548 A\n",
+ "peak value of current in convertor 1=16.391 A\n",
+ "peak value of current in convertor 2=5.548 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6.39, Page No 370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "R=5.0\n",
+ "L=0.05\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(w*L/R)) \n",
+ "phi=90+math.degrees(math.atan(w*L/R)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"for no current transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)\n",
+ "print(\"for worst transients\")\n",
+ "print(\"triggering angle=%.2f deg\" %phi)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for no current transients\n",
+ "triggering angle=162.34 deg\n",
+ "for worst transients\n",
+ "triggering angle=162.34 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter7.ipynb b/_Power_Electronics/Chapter7.ipynb new file mode 100755 index 00000000..726160c8 --- /dev/null +++ b/_Power_Electronics/Chapter7.ipynb @@ -0,0 +1,1036 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07 : Choppers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page No 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.4 #duty cycle %a=T_on/T\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V=a*(V_s-2) \n",
+ "V_or=math.sqrt(a*(V_s-2)**2) \n",
+ "P_o=V_or**2/R\n",
+ "P_i=V_s*V/R\n",
+ "n=P_o*100/P_i \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.1f V\" %V)\n",
+ "print(\"rms value of o/p voltage=%.1f V\" %V_or)\n",
+ "print(\"chopper efficiency in percentage=%.2f\" %n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=91.2 V\n",
+ "rms value of o/p voltage=144.2 V\n",
+ "chopper efficiency in percentage=99.13\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page No 388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_i=220.0\n",
+ "V_o=660.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=1-V_i/V_o\n",
+ "T_on=100.0 #microsecond\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=T_off/2\n",
+ "T_on=T-T_off\n",
+ "a=T_on/T\n",
+ "V_o=V_i/(1-a)\n",
+ "\n",
+ "#Results \n",
+ "print(\"pulse width of o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.0f V\" %V_o)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width of o/p voltage=25 us\n",
+ "\n",
+ "new o/p voltage=1320 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page No 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_1=12.0\n",
+ "I_2=16.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_0=(I_1+I_2)/2\n",
+ "R=10.0\n",
+ "V_0=I_0*R\n",
+ "V_s=200.0\n",
+ "a=V_0/V_s\n",
+ "r=a/(1-a)\n",
+ "\n",
+ "#Results\n",
+ "print(\"time ratio(T_on/T_off)=%.3f\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time ratio(T_on/T_off)=2.333\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page No 390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=660.0\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=(V_o/V_s)/(1+(V_o/V_s))\n",
+ "T_on=120\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=3*T_off\n",
+ "T_on=T-T_off\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_o=V_s*(a/(1-a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pulse width o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width o/p voltage=120 us\n",
+ "\n",
+ "new o/p voltage=73.33 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.11 Page No 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0\n",
+ "L=.005\n",
+ "T_a=L/R\n",
+ "T=2000*10**-6\n",
+ "E=24.0\n",
+ "V_s=220\n",
+ "T_on=600*10**-6\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+(E/V_s)*((math.exp(T/T_a))-1))\n",
+ "if a1<a :\n",
+ " print(\"load current in continuous\")\n",
+ "else:\n",
+ " print(\"load current in discont.\")\n",
+ "\n",
+ "I_o=(a*V_s-E)/R \n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a)))-E/R \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1))-E/R \n",
+ "f=1/T\n",
+ "w=2*math.pi*f\n",
+ "I1=(2*V_s/(math.sqrt(2)*math.pi)*math.sin(math.radians(180*a)))/(math.sqrt(R**2+(w*L)**2)) \n",
+ "I2=(2*V_s/(2*math.sqrt(2)*math.pi)*math.sin(math.radians(2*180*a)))/(math.sqrt(R**2+(w*L*2)**2)) \n",
+ "I3=(2*V_s/(3*math.sqrt(2)*math.pi)*math.sin(math.radians(3*180*a)))/(math.sqrt(R**2+(w*L*3)**2)) \n",
+ "I_TAV=a*(V_s-E)/R-L*(I_mx-I_mn)/(R*T) \n",
+ "P1=I_TAV*V_s\n",
+ "P2=E*I_o\n",
+ "I_or=math.sqrt(I_o**2+I1**2+I2**2+I3**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"max value of steady current=%.2f A\" %I_mx)\n",
+ "print(\"min value of steady current=%.2f A\" %I_mn)\n",
+ "print(\"first harmonic current=%.4f A\" %I1)\n",
+ "print(\"second harmonic current=%.4f A\" %I2)\n",
+ "print(\"third harmonic current=%.5f A\" %I3)\n",
+ "print(\"avg supply current=%.4f A\" %I_TAV)\n",
+ "print(\"i/p power=%.2f W\" %P1)\n",
+ "print(\"power absorbed by load emf=%.0f W\" %P2)\n",
+ "print(\"power loss in resistor=%.2f W\" %(P1-P2))\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current in continuous\n",
+ "avg o/p current=42.00 A\n",
+ "max value of steady current=51.46 A\n",
+ "min value of steady current=33.03 A\n",
+ "first harmonic current=5.0903 A\n",
+ "second harmonic current=1.4983 A\n",
+ "third harmonic current=0.21643 A\n",
+ "avg supply current=12.7289 A\n",
+ "i/p power=2800.35 W\n",
+ "power absorbed by load emf=1008 W\n",
+ "power loss in resistor=1792.35 W\n",
+ "rms value of load current=42.334 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12 Page No 411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1\n",
+ "L=.001\n",
+ "V_s=220\n",
+ "E=72.0\n",
+ "f=500.0\n",
+ "T_on=800*10**-6\n",
+ "T_a=L/R\n",
+ "T=1.0/f\n",
+ "m=E/V_s\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+m*(math.exp(-T/T_a)-1))\n",
+ "if a1>a :\n",
+ " print(\"load current is continuous\")\n",
+ "else:\n",
+ " print(\"load current is discontinuous\")\n",
+ "\n",
+ "t_x=T_on+L*math.log(1+((V_s-E)/272)*(1-math.exp(-T_on/T_a)))\n",
+ " #Value of t_x wrongly calculated in the book so ans of V_o and I_o varies\n",
+ "V_o=a*V_s+(1-t_x/T)*E \n",
+ "I_o=(V_o-E)/R \n",
+ "I_mx=(V_s-E)/R*(1-math.exp(-T_on/T_a)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o) \n",
+ "print(\"max value of load current=%.1f A\" %I_mx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current is discontinuous\n",
+ "avg o/p voltage=121.77 V\n",
+ "avg o/p current=49.77 A\n",
+ "max value of load current=81.5 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13, Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.2\n",
+ "V_s=500\n",
+ "E=a*V_s\n",
+ "L=0.06\n",
+ "I=10\n",
+ "\n",
+ "#Calculations\n",
+ "T_on=(L*I)/(V_s-E)\n",
+ "f=a/T_on \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.2f Hz\" %f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=133.33 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14 Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.5\n",
+ "pu=0.1 #pu ripple\n",
+ "\n",
+ "#Calculations\n",
+ " #x=T/T_a\n",
+ " #y=exp(-a*x)\n",
+ "y=(1-pu)/(1+pu)\n",
+ " #after solving\n",
+ "x=math.log(1/y)/a\n",
+ "f=1000\n",
+ "T=1/f\n",
+ "T_a=T/x\n",
+ "R=2\n",
+ "L=R*T_a\n",
+ "Li=0.002\n",
+ "Le=L-Li \n",
+ "\n",
+ "#Results\n",
+ "print(\"external inductance=%.3f mH\" %(Le*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "external inductance=-2.000 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15 Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=0.015\n",
+ "T_a=L/R\n",
+ "f=1250.0\n",
+ "T=1.0/f\n",
+ "a=0.5\n",
+ "T_on=a*T\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a))) \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1)) \n",
+ "dI=I_mx-I_mn \n",
+ "V_o=a*V_s\n",
+ "I_o=V_o/R \n",
+ "I_or=math.sqrt(I_mx**2+dI**2/3+I_mx*dI) \n",
+ "I_chr=math.sqrt(a)*I_or \n",
+ "\n",
+ "#Results\n",
+ "print(\"Max value of ripple current=%.2f A\" %dI)\n",
+ "print(\"Max value of load current=%.3f A\" %I_mx)\n",
+ "print(\"Min value of load current=%.2f A\" %I_mn)\n",
+ "print(\"Avg value of load current=%.2f A\" %I_o) \n",
+ "print(\"rms value of load current=%.2f A\" %I_or)\n",
+ "print(\"rms value of chopper current=%.2f A\" %I_chr)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max value of ripple current=2.92 A\n",
+ "Max value of load current=12.458 A\n",
+ "Min value of load current=9.54 A\n",
+ "Avg value of load current=11.00 A\n",
+ "rms value of load current=13.94 A\n",
+ "rms value of chopper current=9.86 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17 Page No 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.0016\n",
+ "C=4*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "w=1/math.sqrt(L*C)\n",
+ "t=math.pi/w \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"time for which current flows=%.2f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time for which current flows=251.33 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.18, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t_q=20.0*10**-6\n",
+ "dt=20.0*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t_q+dt\n",
+ "I_0=60.0\n",
+ "V_s=60.0\n",
+ "C=t_c*I_0/V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of commutating capacitor=%.0f uF\" %(C*10**6))\n",
+ "\n",
+ "L1=(V_s/I_0)**2*C\n",
+ "L2=(2*t_c/math.pi)**2/C\n",
+ "if L1>L2 :\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L1*10**6))\n",
+ "else:\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L2*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating capacitor=40 uF\n",
+ "value of commutating inductor=40 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.19, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=100.0*10**-6\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ " #V_s*(1-2*math.exp(-t/(R*C)))=0\n",
+ "C=-t/(R*math.log(1.0/2)) \n",
+ "L=(4/9.0)*C*R**2 \n",
+ "L=(1.0/4)*C*R**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of comutating component C=%.3f uF\" %(C*10**6))\n",
+ "print(\"max permissible current through SCR is 2.5 times load current\")\n",
+ "print(\"value of comutating component L=%.1f uH\" %(L*10**6))\n",
+ "print(\"max permissible current through SCR is 1.5 times peak diode current\")\n",
+ "print(\"value of comutating component L=%.2f uH\" %(L*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of comutating component C=14.427 uF\n",
+ "max permissible current through SCR is 2.5 times load current\n",
+ "value of comutating component L=360.7 uH\n",
+ "max permissible current through SCR is 1.5 times peak diode current\n",
+ "value of comutating component L=360.67 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=800.0*10**-6\n",
+ "V_s=220.0\n",
+ "I_o=80.0\n",
+ "C=50*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+2*V_s*C/I_o \n",
+ "L=20*10**-6\n",
+ "C=50*10**-6\n",
+ "i_T1=I_o+V_s*math.sqrt(C/L) \n",
+ "i_TA=I_o \n",
+ "t_c=C*V_s/I_o \n",
+ "t_c1=(math.pi/2)*math.sqrt(L*C) \n",
+ "t=150*10**-6\n",
+ "v_c=I_o*t/C-V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"effective on period=%.0f us\" %(T*10**6))\n",
+ "print(\"peak current through main thyristor=%.2f A\" %i_T1)\n",
+ "print(\"peak current through auxillery thyristor=%.0f A\" %i_TA)\n",
+ "print(\"turn off time for main thyristor=%.1f us\" %(t_c*10**6))\n",
+ "print(\"turn off time for auxillery thyristor=%.3f us\" %(t_c1*10**6))\n",
+ "print(\"total commutation interval=%.0f us\" %(2*t_c*10**6))\n",
+ "print(\"capacitor voltage=%.0f V\" %v_c)\n",
+ "print(\"time nedded to recharge the capacitor=%.0f us\" %(2*V_s*C/I_o*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_o=260.0\n",
+ "V_s=220.0\n",
+ "fos=2 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_off=18*10**-6\n",
+ "t_c=2*t_off\n",
+ "C=t_c*I_o/V_s \n",
+ "L=(V_s/(0.8*I_o))**2*C \n",
+ "f=400\n",
+ "a_mn=math.pi*f*math.sqrt(L*C)\n",
+ "V_omn=V_s*(a_mn+2*f*t_c) \n",
+ "V_omx=V_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of C=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of L=%.3f uH\" %(L*10**6))\n",
+ "print(\"min value of o/p voltage=%.3f V\" %V_omn)\n",
+ "print(\"max value of o/p voltage=%.0f V\" %V_omx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": "*"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.22, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x=2.0\n",
+ "t_q=30*10**-6\n",
+ "dt=30*10**-6\n",
+ "t_c=t_q+dt\n",
+ "V_s=230.0\n",
+ "I_o=200.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "x=3\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.0f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.2f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=307 V\n",
+ "peak commutataing current=600 A\n",
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=306.67 V\n",
+ "peak commutataing current=600 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.23, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "C=50*10**-6\n",
+ "L=20*10**-6\n",
+ "I_cp=V_s*math.sqrt(C/L)\n",
+ "I_o=200\n",
+ "x=I_cp/I_o\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=(math.pi-2*math.asin(1/x))*math.sqrt(C*L) \n",
+ "th1=math.degrees(math.asin(1.0/x))\n",
+ "t=(5*math.pi/2-th1*math.pi/180)*math.sqrt(L*C)+C*V_s*(1-math.cos(math.radians(th1)))/I_o \n",
+ "t=(math.pi-th1*math.pi/180)*math.sqrt(L*C) \n",
+ "\n",
+ "#Results\n",
+ "print(\"turn off time of main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"total commutation interval=%.3f us\" %(t*10**6))\n",
+ "print(\"turn off time of auxillery thyristor=%.3f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "turn off time of main thyristor=62.52 us\n",
+ "total commutation interval=80.931 us\n",
+ "turn off time of auxillery thyristor=80.931 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.24, Page No 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tc=0.006\n",
+ "R=10.0\n",
+ "L=R*tc\n",
+ "f=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=1/f\n",
+ "V_o=50.0\n",
+ "V_s=100.0\n",
+ "a=V_o/V_s\n",
+ "T_on=a*T\n",
+ "T_off=T-T_on\n",
+ "dI=V_o*T_off/L\n",
+ "I_o=V_o/R\n",
+ "I2=I_o+dI/2 \n",
+ "I1=I_o-dI/2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"max value of load current=%.3f A\" %I2)\n",
+ "print(\"min value of load current=%.3f A\" %I1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of load current=5.104 A\n",
+ "min value of load current=4.896 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.27, Page No 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=30.0\n",
+ "r_a=.5\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=I_a*r_a/V_s \n",
+ "a=1\n",
+ "k=.1 #V/rpm\n",
+ "N=(a*V_s-I_a*r_a)/k \n",
+ "\n",
+ "#Results\n",
+ "print(\"min value of duty cycle=%.3f\" %a)\n",
+ "print(\"min Value of speed control=%.0f rpm\" %0)\n",
+ "print(\"max value of duty cycle=%.0f\" %a)\n",
+ "print(\"max value of speed control=%.0f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min value of duty cycle=1.000\n",
+ "min Value of speed control=0 rpm\n",
+ "max value of duty cycle=1\n",
+ "max value of speed control=2050 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.28, Page No 444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=72.0\n",
+ "I_a=200.0\n",
+ "r_a=0.045\n",
+ "N=2500.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=(V_t-I_a*r_a)/N\n",
+ "E_a=k*1000\n",
+ "L=.007\n",
+ "Rm=.045\n",
+ "Rb=0.065\n",
+ "R=Rm+Rb\n",
+ "T_a=L/R\n",
+ "I_mx=230\n",
+ "I_mn=180\n",
+ "T_on=-T_a*math.log(-((V_t-E_a)/R-I_mx)/((I_mn)-(V_t-E_a)/R))\n",
+ "R=Rm\n",
+ "T_a=L/R\n",
+ "T_off=-T_a*math.log(-((-E_a)/R-I_mn)/((I_mx)-(-E_a)/R))\n",
+ "T=T_on+T_off\n",
+ "f=1/T \n",
+ "a=T_on/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.1f Hz\" %f) \n",
+ "print(\"duty cycle ratio=%.3f\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=40.5 Hz\n",
+ "\n",
+ "duty cycle ratio=0.588\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesI_mx=425\n",
+ "I_lt=180.0 #lower limit of current pulsation\n",
+ "I_mn=I_mx-I_lt\n",
+ "T_on=0.014\n",
+ "T_off=0.011\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+T_off\n",
+ "T_a=.0635\n",
+ "a=T_on/T\n",
+ "V=(I_mx-I_mn*math.exp(-T_on/T_a))/(1-math.exp(-T_on/T_a))\n",
+ "a=.5\n",
+ "I_mn=(I_mx-V*(1-math.exp(-T_on/T_a)))/(math.exp(-T_on/T_a))\n",
+ "T=I_mx-I_mn \n",
+ "T=T_on/a\n",
+ "f=1/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"higher limit of current pulsation=%.0f A\" %T)\n",
+ "print(\"chopping freq=%.3f Hz\" %f)\n",
+ "print(\"duty cycle ratio=%.2f\" %a)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "higher limit of current pulsation=0 A\n",
+ "chopping freq=35.714 Hz\n",
+ "duty cycle ratio=0.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter7_1.ipynb b/_Power_Electronics/Chapter7_1.ipynb new file mode 100755 index 00000000..726160c8 --- /dev/null +++ b/_Power_Electronics/Chapter7_1.ipynb @@ -0,0 +1,1036 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07 : Choppers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page No 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.4 #duty cycle %a=T_on/T\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V=a*(V_s-2) \n",
+ "V_or=math.sqrt(a*(V_s-2)**2) \n",
+ "P_o=V_or**2/R\n",
+ "P_i=V_s*V/R\n",
+ "n=P_o*100/P_i \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.1f V\" %V)\n",
+ "print(\"rms value of o/p voltage=%.1f V\" %V_or)\n",
+ "print(\"chopper efficiency in percentage=%.2f\" %n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=91.2 V\n",
+ "rms value of o/p voltage=144.2 V\n",
+ "chopper efficiency in percentage=99.13\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page No 388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_i=220.0\n",
+ "V_o=660.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=1-V_i/V_o\n",
+ "T_on=100.0 #microsecond\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=T_off/2\n",
+ "T_on=T-T_off\n",
+ "a=T_on/T\n",
+ "V_o=V_i/(1-a)\n",
+ "\n",
+ "#Results \n",
+ "print(\"pulse width of o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.0f V\" %V_o)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width of o/p voltage=25 us\n",
+ "\n",
+ "new o/p voltage=1320 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page No 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_1=12.0\n",
+ "I_2=16.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_0=(I_1+I_2)/2\n",
+ "R=10.0\n",
+ "V_0=I_0*R\n",
+ "V_s=200.0\n",
+ "a=V_0/V_s\n",
+ "r=a/(1-a)\n",
+ "\n",
+ "#Results\n",
+ "print(\"time ratio(T_on/T_off)=%.3f\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time ratio(T_on/T_off)=2.333\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page No 390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=660.0\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=(V_o/V_s)/(1+(V_o/V_s))\n",
+ "T_on=120\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=3*T_off\n",
+ "T_on=T-T_off\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_o=V_s*(a/(1-a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pulse width o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width o/p voltage=120 us\n",
+ "\n",
+ "new o/p voltage=73.33 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.11 Page No 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0\n",
+ "L=.005\n",
+ "T_a=L/R\n",
+ "T=2000*10**-6\n",
+ "E=24.0\n",
+ "V_s=220\n",
+ "T_on=600*10**-6\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+(E/V_s)*((math.exp(T/T_a))-1))\n",
+ "if a1<a :\n",
+ " print(\"load current in continuous\")\n",
+ "else:\n",
+ " print(\"load current in discont.\")\n",
+ "\n",
+ "I_o=(a*V_s-E)/R \n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a)))-E/R \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1))-E/R \n",
+ "f=1/T\n",
+ "w=2*math.pi*f\n",
+ "I1=(2*V_s/(math.sqrt(2)*math.pi)*math.sin(math.radians(180*a)))/(math.sqrt(R**2+(w*L)**2)) \n",
+ "I2=(2*V_s/(2*math.sqrt(2)*math.pi)*math.sin(math.radians(2*180*a)))/(math.sqrt(R**2+(w*L*2)**2)) \n",
+ "I3=(2*V_s/(3*math.sqrt(2)*math.pi)*math.sin(math.radians(3*180*a)))/(math.sqrt(R**2+(w*L*3)**2)) \n",
+ "I_TAV=a*(V_s-E)/R-L*(I_mx-I_mn)/(R*T) \n",
+ "P1=I_TAV*V_s\n",
+ "P2=E*I_o\n",
+ "I_or=math.sqrt(I_o**2+I1**2+I2**2+I3**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"max value of steady current=%.2f A\" %I_mx)\n",
+ "print(\"min value of steady current=%.2f A\" %I_mn)\n",
+ "print(\"first harmonic current=%.4f A\" %I1)\n",
+ "print(\"second harmonic current=%.4f A\" %I2)\n",
+ "print(\"third harmonic current=%.5f A\" %I3)\n",
+ "print(\"avg supply current=%.4f A\" %I_TAV)\n",
+ "print(\"i/p power=%.2f W\" %P1)\n",
+ "print(\"power absorbed by load emf=%.0f W\" %P2)\n",
+ "print(\"power loss in resistor=%.2f W\" %(P1-P2))\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current in continuous\n",
+ "avg o/p current=42.00 A\n",
+ "max value of steady current=51.46 A\n",
+ "min value of steady current=33.03 A\n",
+ "first harmonic current=5.0903 A\n",
+ "second harmonic current=1.4983 A\n",
+ "third harmonic current=0.21643 A\n",
+ "avg supply current=12.7289 A\n",
+ "i/p power=2800.35 W\n",
+ "power absorbed by load emf=1008 W\n",
+ "power loss in resistor=1792.35 W\n",
+ "rms value of load current=42.334 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12 Page No 411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1\n",
+ "L=.001\n",
+ "V_s=220\n",
+ "E=72.0\n",
+ "f=500.0\n",
+ "T_on=800*10**-6\n",
+ "T_a=L/R\n",
+ "T=1.0/f\n",
+ "m=E/V_s\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+m*(math.exp(-T/T_a)-1))\n",
+ "if a1>a :\n",
+ " print(\"load current is continuous\")\n",
+ "else:\n",
+ " print(\"load current is discontinuous\")\n",
+ "\n",
+ "t_x=T_on+L*math.log(1+((V_s-E)/272)*(1-math.exp(-T_on/T_a)))\n",
+ " #Value of t_x wrongly calculated in the book so ans of V_o and I_o varies\n",
+ "V_o=a*V_s+(1-t_x/T)*E \n",
+ "I_o=(V_o-E)/R \n",
+ "I_mx=(V_s-E)/R*(1-math.exp(-T_on/T_a)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o) \n",
+ "print(\"max value of load current=%.1f A\" %I_mx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current is discontinuous\n",
+ "avg o/p voltage=121.77 V\n",
+ "avg o/p current=49.77 A\n",
+ "max value of load current=81.5 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13, Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.2\n",
+ "V_s=500\n",
+ "E=a*V_s\n",
+ "L=0.06\n",
+ "I=10\n",
+ "\n",
+ "#Calculations\n",
+ "T_on=(L*I)/(V_s-E)\n",
+ "f=a/T_on \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.2f Hz\" %f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=133.33 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14 Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.5\n",
+ "pu=0.1 #pu ripple\n",
+ "\n",
+ "#Calculations\n",
+ " #x=T/T_a\n",
+ " #y=exp(-a*x)\n",
+ "y=(1-pu)/(1+pu)\n",
+ " #after solving\n",
+ "x=math.log(1/y)/a\n",
+ "f=1000\n",
+ "T=1/f\n",
+ "T_a=T/x\n",
+ "R=2\n",
+ "L=R*T_a\n",
+ "Li=0.002\n",
+ "Le=L-Li \n",
+ "\n",
+ "#Results\n",
+ "print(\"external inductance=%.3f mH\" %(Le*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "external inductance=-2.000 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15 Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=0.015\n",
+ "T_a=L/R\n",
+ "f=1250.0\n",
+ "T=1.0/f\n",
+ "a=0.5\n",
+ "T_on=a*T\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a))) \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1)) \n",
+ "dI=I_mx-I_mn \n",
+ "V_o=a*V_s\n",
+ "I_o=V_o/R \n",
+ "I_or=math.sqrt(I_mx**2+dI**2/3+I_mx*dI) \n",
+ "I_chr=math.sqrt(a)*I_or \n",
+ "\n",
+ "#Results\n",
+ "print(\"Max value of ripple current=%.2f A\" %dI)\n",
+ "print(\"Max value of load current=%.3f A\" %I_mx)\n",
+ "print(\"Min value of load current=%.2f A\" %I_mn)\n",
+ "print(\"Avg value of load current=%.2f A\" %I_o) \n",
+ "print(\"rms value of load current=%.2f A\" %I_or)\n",
+ "print(\"rms value of chopper current=%.2f A\" %I_chr)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max value of ripple current=2.92 A\n",
+ "Max value of load current=12.458 A\n",
+ "Min value of load current=9.54 A\n",
+ "Avg value of load current=11.00 A\n",
+ "rms value of load current=13.94 A\n",
+ "rms value of chopper current=9.86 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17 Page No 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.0016\n",
+ "C=4*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "w=1/math.sqrt(L*C)\n",
+ "t=math.pi/w \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"time for which current flows=%.2f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time for which current flows=251.33 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.18, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t_q=20.0*10**-6\n",
+ "dt=20.0*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t_q+dt\n",
+ "I_0=60.0\n",
+ "V_s=60.0\n",
+ "C=t_c*I_0/V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of commutating capacitor=%.0f uF\" %(C*10**6))\n",
+ "\n",
+ "L1=(V_s/I_0)**2*C\n",
+ "L2=(2*t_c/math.pi)**2/C\n",
+ "if L1>L2 :\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L1*10**6))\n",
+ "else:\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L2*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating capacitor=40 uF\n",
+ "value of commutating inductor=40 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.19, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=100.0*10**-6\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ " #V_s*(1-2*math.exp(-t/(R*C)))=0\n",
+ "C=-t/(R*math.log(1.0/2)) \n",
+ "L=(4/9.0)*C*R**2 \n",
+ "L=(1.0/4)*C*R**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of comutating component C=%.3f uF\" %(C*10**6))\n",
+ "print(\"max permissible current through SCR is 2.5 times load current\")\n",
+ "print(\"value of comutating component L=%.1f uH\" %(L*10**6))\n",
+ "print(\"max permissible current through SCR is 1.5 times peak diode current\")\n",
+ "print(\"value of comutating component L=%.2f uH\" %(L*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of comutating component C=14.427 uF\n",
+ "max permissible current through SCR is 2.5 times load current\n",
+ "value of comutating component L=360.7 uH\n",
+ "max permissible current through SCR is 1.5 times peak diode current\n",
+ "value of comutating component L=360.67 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=800.0*10**-6\n",
+ "V_s=220.0\n",
+ "I_o=80.0\n",
+ "C=50*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+2*V_s*C/I_o \n",
+ "L=20*10**-6\n",
+ "C=50*10**-6\n",
+ "i_T1=I_o+V_s*math.sqrt(C/L) \n",
+ "i_TA=I_o \n",
+ "t_c=C*V_s/I_o \n",
+ "t_c1=(math.pi/2)*math.sqrt(L*C) \n",
+ "t=150*10**-6\n",
+ "v_c=I_o*t/C-V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"effective on period=%.0f us\" %(T*10**6))\n",
+ "print(\"peak current through main thyristor=%.2f A\" %i_T1)\n",
+ "print(\"peak current through auxillery thyristor=%.0f A\" %i_TA)\n",
+ "print(\"turn off time for main thyristor=%.1f us\" %(t_c*10**6))\n",
+ "print(\"turn off time for auxillery thyristor=%.3f us\" %(t_c1*10**6))\n",
+ "print(\"total commutation interval=%.0f us\" %(2*t_c*10**6))\n",
+ "print(\"capacitor voltage=%.0f V\" %v_c)\n",
+ "print(\"time nedded to recharge the capacitor=%.0f us\" %(2*V_s*C/I_o*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_o=260.0\n",
+ "V_s=220.0\n",
+ "fos=2 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_off=18*10**-6\n",
+ "t_c=2*t_off\n",
+ "C=t_c*I_o/V_s \n",
+ "L=(V_s/(0.8*I_o))**2*C \n",
+ "f=400\n",
+ "a_mn=math.pi*f*math.sqrt(L*C)\n",
+ "V_omn=V_s*(a_mn+2*f*t_c) \n",
+ "V_omx=V_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of C=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of L=%.3f uH\" %(L*10**6))\n",
+ "print(\"min value of o/p voltage=%.3f V\" %V_omn)\n",
+ "print(\"max value of o/p voltage=%.0f V\" %V_omx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": "*"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.22, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x=2.0\n",
+ "t_q=30*10**-6\n",
+ "dt=30*10**-6\n",
+ "t_c=t_q+dt\n",
+ "V_s=230.0\n",
+ "I_o=200.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "x=3\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.0f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.2f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=307 V\n",
+ "peak commutataing current=600 A\n",
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=306.67 V\n",
+ "peak commutataing current=600 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.23, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "C=50*10**-6\n",
+ "L=20*10**-6\n",
+ "I_cp=V_s*math.sqrt(C/L)\n",
+ "I_o=200\n",
+ "x=I_cp/I_o\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=(math.pi-2*math.asin(1/x))*math.sqrt(C*L) \n",
+ "th1=math.degrees(math.asin(1.0/x))\n",
+ "t=(5*math.pi/2-th1*math.pi/180)*math.sqrt(L*C)+C*V_s*(1-math.cos(math.radians(th1)))/I_o \n",
+ "t=(math.pi-th1*math.pi/180)*math.sqrt(L*C) \n",
+ "\n",
+ "#Results\n",
+ "print(\"turn off time of main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"total commutation interval=%.3f us\" %(t*10**6))\n",
+ "print(\"turn off time of auxillery thyristor=%.3f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "turn off time of main thyristor=62.52 us\n",
+ "total commutation interval=80.931 us\n",
+ "turn off time of auxillery thyristor=80.931 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.24, Page No 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tc=0.006\n",
+ "R=10.0\n",
+ "L=R*tc\n",
+ "f=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=1/f\n",
+ "V_o=50.0\n",
+ "V_s=100.0\n",
+ "a=V_o/V_s\n",
+ "T_on=a*T\n",
+ "T_off=T-T_on\n",
+ "dI=V_o*T_off/L\n",
+ "I_o=V_o/R\n",
+ "I2=I_o+dI/2 \n",
+ "I1=I_o-dI/2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"max value of load current=%.3f A\" %I2)\n",
+ "print(\"min value of load current=%.3f A\" %I1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of load current=5.104 A\n",
+ "min value of load current=4.896 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.27, Page No 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=30.0\n",
+ "r_a=.5\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=I_a*r_a/V_s \n",
+ "a=1\n",
+ "k=.1 #V/rpm\n",
+ "N=(a*V_s-I_a*r_a)/k \n",
+ "\n",
+ "#Results\n",
+ "print(\"min value of duty cycle=%.3f\" %a)\n",
+ "print(\"min Value of speed control=%.0f rpm\" %0)\n",
+ "print(\"max value of duty cycle=%.0f\" %a)\n",
+ "print(\"max value of speed control=%.0f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min value of duty cycle=1.000\n",
+ "min Value of speed control=0 rpm\n",
+ "max value of duty cycle=1\n",
+ "max value of speed control=2050 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.28, Page No 444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=72.0\n",
+ "I_a=200.0\n",
+ "r_a=0.045\n",
+ "N=2500.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=(V_t-I_a*r_a)/N\n",
+ "E_a=k*1000\n",
+ "L=.007\n",
+ "Rm=.045\n",
+ "Rb=0.065\n",
+ "R=Rm+Rb\n",
+ "T_a=L/R\n",
+ "I_mx=230\n",
+ "I_mn=180\n",
+ "T_on=-T_a*math.log(-((V_t-E_a)/R-I_mx)/((I_mn)-(V_t-E_a)/R))\n",
+ "R=Rm\n",
+ "T_a=L/R\n",
+ "T_off=-T_a*math.log(-((-E_a)/R-I_mn)/((I_mx)-(-E_a)/R))\n",
+ "T=T_on+T_off\n",
+ "f=1/T \n",
+ "a=T_on/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.1f Hz\" %f) \n",
+ "print(\"duty cycle ratio=%.3f\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=40.5 Hz\n",
+ "\n",
+ "duty cycle ratio=0.588\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesI_mx=425\n",
+ "I_lt=180.0 #lower limit of current pulsation\n",
+ "I_mn=I_mx-I_lt\n",
+ "T_on=0.014\n",
+ "T_off=0.011\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+T_off\n",
+ "T_a=.0635\n",
+ "a=T_on/T\n",
+ "V=(I_mx-I_mn*math.exp(-T_on/T_a))/(1-math.exp(-T_on/T_a))\n",
+ "a=.5\n",
+ "I_mn=(I_mx-V*(1-math.exp(-T_on/T_a)))/(math.exp(-T_on/T_a))\n",
+ "T=I_mx-I_mn \n",
+ "T=T_on/a\n",
+ "f=1/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"higher limit of current pulsation=%.0f A\" %T)\n",
+ "print(\"chopping freq=%.3f Hz\" %f)\n",
+ "print(\"duty cycle ratio=%.2f\" %a)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "higher limit of current pulsation=0 A\n",
+ "chopping freq=35.714 Hz\n",
+ "duty cycle ratio=0.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter7_2.ipynb b/_Power_Electronics/Chapter7_2.ipynb new file mode 100755 index 00000000..726160c8 --- /dev/null +++ b/_Power_Electronics/Chapter7_2.ipynb @@ -0,0 +1,1036 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07 : Choppers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page No 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.4 #duty cycle %a=T_on/T\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V=a*(V_s-2) \n",
+ "V_or=math.sqrt(a*(V_s-2)**2) \n",
+ "P_o=V_or**2/R\n",
+ "P_i=V_s*V/R\n",
+ "n=P_o*100/P_i \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.1f V\" %V)\n",
+ "print(\"rms value of o/p voltage=%.1f V\" %V_or)\n",
+ "print(\"chopper efficiency in percentage=%.2f\" %n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=91.2 V\n",
+ "rms value of o/p voltage=144.2 V\n",
+ "chopper efficiency in percentage=99.13\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page No 388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_i=220.0\n",
+ "V_o=660.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=1-V_i/V_o\n",
+ "T_on=100.0 #microsecond\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=T_off/2\n",
+ "T_on=T-T_off\n",
+ "a=T_on/T\n",
+ "V_o=V_i/(1-a)\n",
+ "\n",
+ "#Results \n",
+ "print(\"pulse width of o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.0f V\" %V_o)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width of o/p voltage=25 us\n",
+ "\n",
+ "new o/p voltage=1320 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page No 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_1=12.0\n",
+ "I_2=16.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_0=(I_1+I_2)/2\n",
+ "R=10.0\n",
+ "V_0=I_0*R\n",
+ "V_s=200.0\n",
+ "a=V_0/V_s\n",
+ "r=a/(1-a)\n",
+ "\n",
+ "#Results\n",
+ "print(\"time ratio(T_on/T_off)=%.3f\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time ratio(T_on/T_off)=2.333\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page No 390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=660.0\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=(V_o/V_s)/(1+(V_o/V_s))\n",
+ "T_on=120\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=3*T_off\n",
+ "T_on=T-T_off\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_o=V_s*(a/(1-a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pulse width o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width o/p voltage=120 us\n",
+ "\n",
+ "new o/p voltage=73.33 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.11 Page No 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0\n",
+ "L=.005\n",
+ "T_a=L/R\n",
+ "T=2000*10**-6\n",
+ "E=24.0\n",
+ "V_s=220\n",
+ "T_on=600*10**-6\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+(E/V_s)*((math.exp(T/T_a))-1))\n",
+ "if a1<a :\n",
+ " print(\"load current in continuous\")\n",
+ "else:\n",
+ " print(\"load current in discont.\")\n",
+ "\n",
+ "I_o=(a*V_s-E)/R \n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a)))-E/R \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1))-E/R \n",
+ "f=1/T\n",
+ "w=2*math.pi*f\n",
+ "I1=(2*V_s/(math.sqrt(2)*math.pi)*math.sin(math.radians(180*a)))/(math.sqrt(R**2+(w*L)**2)) \n",
+ "I2=(2*V_s/(2*math.sqrt(2)*math.pi)*math.sin(math.radians(2*180*a)))/(math.sqrt(R**2+(w*L*2)**2)) \n",
+ "I3=(2*V_s/(3*math.sqrt(2)*math.pi)*math.sin(math.radians(3*180*a)))/(math.sqrt(R**2+(w*L*3)**2)) \n",
+ "I_TAV=a*(V_s-E)/R-L*(I_mx-I_mn)/(R*T) \n",
+ "P1=I_TAV*V_s\n",
+ "P2=E*I_o\n",
+ "I_or=math.sqrt(I_o**2+I1**2+I2**2+I3**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"max value of steady current=%.2f A\" %I_mx)\n",
+ "print(\"min value of steady current=%.2f A\" %I_mn)\n",
+ "print(\"first harmonic current=%.4f A\" %I1)\n",
+ "print(\"second harmonic current=%.4f A\" %I2)\n",
+ "print(\"third harmonic current=%.5f A\" %I3)\n",
+ "print(\"avg supply current=%.4f A\" %I_TAV)\n",
+ "print(\"i/p power=%.2f W\" %P1)\n",
+ "print(\"power absorbed by load emf=%.0f W\" %P2)\n",
+ "print(\"power loss in resistor=%.2f W\" %(P1-P2))\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current in continuous\n",
+ "avg o/p current=42.00 A\n",
+ "max value of steady current=51.46 A\n",
+ "min value of steady current=33.03 A\n",
+ "first harmonic current=5.0903 A\n",
+ "second harmonic current=1.4983 A\n",
+ "third harmonic current=0.21643 A\n",
+ "avg supply current=12.7289 A\n",
+ "i/p power=2800.35 W\n",
+ "power absorbed by load emf=1008 W\n",
+ "power loss in resistor=1792.35 W\n",
+ "rms value of load current=42.334 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12 Page No 411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1\n",
+ "L=.001\n",
+ "V_s=220\n",
+ "E=72.0\n",
+ "f=500.0\n",
+ "T_on=800*10**-6\n",
+ "T_a=L/R\n",
+ "T=1.0/f\n",
+ "m=E/V_s\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+m*(math.exp(-T/T_a)-1))\n",
+ "if a1>a :\n",
+ " print(\"load current is continuous\")\n",
+ "else:\n",
+ " print(\"load current is discontinuous\")\n",
+ "\n",
+ "t_x=T_on+L*math.log(1+((V_s-E)/272)*(1-math.exp(-T_on/T_a)))\n",
+ " #Value of t_x wrongly calculated in the book so ans of V_o and I_o varies\n",
+ "V_o=a*V_s+(1-t_x/T)*E \n",
+ "I_o=(V_o-E)/R \n",
+ "I_mx=(V_s-E)/R*(1-math.exp(-T_on/T_a)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o) \n",
+ "print(\"max value of load current=%.1f A\" %I_mx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current is discontinuous\n",
+ "avg o/p voltage=121.77 V\n",
+ "avg o/p current=49.77 A\n",
+ "max value of load current=81.5 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13, Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.2\n",
+ "V_s=500\n",
+ "E=a*V_s\n",
+ "L=0.06\n",
+ "I=10\n",
+ "\n",
+ "#Calculations\n",
+ "T_on=(L*I)/(V_s-E)\n",
+ "f=a/T_on \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.2f Hz\" %f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=133.33 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14 Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.5\n",
+ "pu=0.1 #pu ripple\n",
+ "\n",
+ "#Calculations\n",
+ " #x=T/T_a\n",
+ " #y=exp(-a*x)\n",
+ "y=(1-pu)/(1+pu)\n",
+ " #after solving\n",
+ "x=math.log(1/y)/a\n",
+ "f=1000\n",
+ "T=1/f\n",
+ "T_a=T/x\n",
+ "R=2\n",
+ "L=R*T_a\n",
+ "Li=0.002\n",
+ "Le=L-Li \n",
+ "\n",
+ "#Results\n",
+ "print(\"external inductance=%.3f mH\" %(Le*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "external inductance=-2.000 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15 Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=0.015\n",
+ "T_a=L/R\n",
+ "f=1250.0\n",
+ "T=1.0/f\n",
+ "a=0.5\n",
+ "T_on=a*T\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a))) \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1)) \n",
+ "dI=I_mx-I_mn \n",
+ "V_o=a*V_s\n",
+ "I_o=V_o/R \n",
+ "I_or=math.sqrt(I_mx**2+dI**2/3+I_mx*dI) \n",
+ "I_chr=math.sqrt(a)*I_or \n",
+ "\n",
+ "#Results\n",
+ "print(\"Max value of ripple current=%.2f A\" %dI)\n",
+ "print(\"Max value of load current=%.3f A\" %I_mx)\n",
+ "print(\"Min value of load current=%.2f A\" %I_mn)\n",
+ "print(\"Avg value of load current=%.2f A\" %I_o) \n",
+ "print(\"rms value of load current=%.2f A\" %I_or)\n",
+ "print(\"rms value of chopper current=%.2f A\" %I_chr)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max value of ripple current=2.92 A\n",
+ "Max value of load current=12.458 A\n",
+ "Min value of load current=9.54 A\n",
+ "Avg value of load current=11.00 A\n",
+ "rms value of load current=13.94 A\n",
+ "rms value of chopper current=9.86 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17 Page No 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.0016\n",
+ "C=4*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "w=1/math.sqrt(L*C)\n",
+ "t=math.pi/w \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"time for which current flows=%.2f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time for which current flows=251.33 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.18, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t_q=20.0*10**-6\n",
+ "dt=20.0*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t_q+dt\n",
+ "I_0=60.0\n",
+ "V_s=60.0\n",
+ "C=t_c*I_0/V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of commutating capacitor=%.0f uF\" %(C*10**6))\n",
+ "\n",
+ "L1=(V_s/I_0)**2*C\n",
+ "L2=(2*t_c/math.pi)**2/C\n",
+ "if L1>L2 :\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L1*10**6))\n",
+ "else:\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L2*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating capacitor=40 uF\n",
+ "value of commutating inductor=40 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.19, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=100.0*10**-6\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ " #V_s*(1-2*math.exp(-t/(R*C)))=0\n",
+ "C=-t/(R*math.log(1.0/2)) \n",
+ "L=(4/9.0)*C*R**2 \n",
+ "L=(1.0/4)*C*R**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of comutating component C=%.3f uF\" %(C*10**6))\n",
+ "print(\"max permissible current through SCR is 2.5 times load current\")\n",
+ "print(\"value of comutating component L=%.1f uH\" %(L*10**6))\n",
+ "print(\"max permissible current through SCR is 1.5 times peak diode current\")\n",
+ "print(\"value of comutating component L=%.2f uH\" %(L*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of comutating component C=14.427 uF\n",
+ "max permissible current through SCR is 2.5 times load current\n",
+ "value of comutating component L=360.7 uH\n",
+ "max permissible current through SCR is 1.5 times peak diode current\n",
+ "value of comutating component L=360.67 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=800.0*10**-6\n",
+ "V_s=220.0\n",
+ "I_o=80.0\n",
+ "C=50*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+2*V_s*C/I_o \n",
+ "L=20*10**-6\n",
+ "C=50*10**-6\n",
+ "i_T1=I_o+V_s*math.sqrt(C/L) \n",
+ "i_TA=I_o \n",
+ "t_c=C*V_s/I_o \n",
+ "t_c1=(math.pi/2)*math.sqrt(L*C) \n",
+ "t=150*10**-6\n",
+ "v_c=I_o*t/C-V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"effective on period=%.0f us\" %(T*10**6))\n",
+ "print(\"peak current through main thyristor=%.2f A\" %i_T1)\n",
+ "print(\"peak current through auxillery thyristor=%.0f A\" %i_TA)\n",
+ "print(\"turn off time for main thyristor=%.1f us\" %(t_c*10**6))\n",
+ "print(\"turn off time for auxillery thyristor=%.3f us\" %(t_c1*10**6))\n",
+ "print(\"total commutation interval=%.0f us\" %(2*t_c*10**6))\n",
+ "print(\"capacitor voltage=%.0f V\" %v_c)\n",
+ "print(\"time nedded to recharge the capacitor=%.0f us\" %(2*V_s*C/I_o*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_o=260.0\n",
+ "V_s=220.0\n",
+ "fos=2 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_off=18*10**-6\n",
+ "t_c=2*t_off\n",
+ "C=t_c*I_o/V_s \n",
+ "L=(V_s/(0.8*I_o))**2*C \n",
+ "f=400\n",
+ "a_mn=math.pi*f*math.sqrt(L*C)\n",
+ "V_omn=V_s*(a_mn+2*f*t_c) \n",
+ "V_omx=V_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of C=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of L=%.3f uH\" %(L*10**6))\n",
+ "print(\"min value of o/p voltage=%.3f V\" %V_omn)\n",
+ "print(\"max value of o/p voltage=%.0f V\" %V_omx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": "*"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.22, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x=2.0\n",
+ "t_q=30*10**-6\n",
+ "dt=30*10**-6\n",
+ "t_c=t_q+dt\n",
+ "V_s=230.0\n",
+ "I_o=200.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "x=3\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.0f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.2f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=307 V\n",
+ "peak commutataing current=600 A\n",
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=306.67 V\n",
+ "peak commutataing current=600 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.23, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "C=50*10**-6\n",
+ "L=20*10**-6\n",
+ "I_cp=V_s*math.sqrt(C/L)\n",
+ "I_o=200\n",
+ "x=I_cp/I_o\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=(math.pi-2*math.asin(1/x))*math.sqrt(C*L) \n",
+ "th1=math.degrees(math.asin(1.0/x))\n",
+ "t=(5*math.pi/2-th1*math.pi/180)*math.sqrt(L*C)+C*V_s*(1-math.cos(math.radians(th1)))/I_o \n",
+ "t=(math.pi-th1*math.pi/180)*math.sqrt(L*C) \n",
+ "\n",
+ "#Results\n",
+ "print(\"turn off time of main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"total commutation interval=%.3f us\" %(t*10**6))\n",
+ "print(\"turn off time of auxillery thyristor=%.3f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "turn off time of main thyristor=62.52 us\n",
+ "total commutation interval=80.931 us\n",
+ "turn off time of auxillery thyristor=80.931 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.24, Page No 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tc=0.006\n",
+ "R=10.0\n",
+ "L=R*tc\n",
+ "f=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=1/f\n",
+ "V_o=50.0\n",
+ "V_s=100.0\n",
+ "a=V_o/V_s\n",
+ "T_on=a*T\n",
+ "T_off=T-T_on\n",
+ "dI=V_o*T_off/L\n",
+ "I_o=V_o/R\n",
+ "I2=I_o+dI/2 \n",
+ "I1=I_o-dI/2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"max value of load current=%.3f A\" %I2)\n",
+ "print(\"min value of load current=%.3f A\" %I1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of load current=5.104 A\n",
+ "min value of load current=4.896 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.27, Page No 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=30.0\n",
+ "r_a=.5\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=I_a*r_a/V_s \n",
+ "a=1\n",
+ "k=.1 #V/rpm\n",
+ "N=(a*V_s-I_a*r_a)/k \n",
+ "\n",
+ "#Results\n",
+ "print(\"min value of duty cycle=%.3f\" %a)\n",
+ "print(\"min Value of speed control=%.0f rpm\" %0)\n",
+ "print(\"max value of duty cycle=%.0f\" %a)\n",
+ "print(\"max value of speed control=%.0f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min value of duty cycle=1.000\n",
+ "min Value of speed control=0 rpm\n",
+ "max value of duty cycle=1\n",
+ "max value of speed control=2050 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.28, Page No 444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=72.0\n",
+ "I_a=200.0\n",
+ "r_a=0.045\n",
+ "N=2500.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=(V_t-I_a*r_a)/N\n",
+ "E_a=k*1000\n",
+ "L=.007\n",
+ "Rm=.045\n",
+ "Rb=0.065\n",
+ "R=Rm+Rb\n",
+ "T_a=L/R\n",
+ "I_mx=230\n",
+ "I_mn=180\n",
+ "T_on=-T_a*math.log(-((V_t-E_a)/R-I_mx)/((I_mn)-(V_t-E_a)/R))\n",
+ "R=Rm\n",
+ "T_a=L/R\n",
+ "T_off=-T_a*math.log(-((-E_a)/R-I_mn)/((I_mx)-(-E_a)/R))\n",
+ "T=T_on+T_off\n",
+ "f=1/T \n",
+ "a=T_on/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.1f Hz\" %f) \n",
+ "print(\"duty cycle ratio=%.3f\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=40.5 Hz\n",
+ "\n",
+ "duty cycle ratio=0.588\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesI_mx=425\n",
+ "I_lt=180.0 #lower limit of current pulsation\n",
+ "I_mn=I_mx-I_lt\n",
+ "T_on=0.014\n",
+ "T_off=0.011\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+T_off\n",
+ "T_a=.0635\n",
+ "a=T_on/T\n",
+ "V=(I_mx-I_mn*math.exp(-T_on/T_a))/(1-math.exp(-T_on/T_a))\n",
+ "a=.5\n",
+ "I_mn=(I_mx-V*(1-math.exp(-T_on/T_a)))/(math.exp(-T_on/T_a))\n",
+ "T=I_mx-I_mn \n",
+ "T=T_on/a\n",
+ "f=1/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"higher limit of current pulsation=%.0f A\" %T)\n",
+ "print(\"chopping freq=%.3f Hz\" %f)\n",
+ "print(\"duty cycle ratio=%.2f\" %a)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "higher limit of current pulsation=0 A\n",
+ "chopping freq=35.714 Hz\n",
+ "duty cycle ratio=0.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter7_3.ipynb b/_Power_Electronics/Chapter7_3.ipynb new file mode 100755 index 00000000..726160c8 --- /dev/null +++ b/_Power_Electronics/Chapter7_3.ipynb @@ -0,0 +1,1036 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07 : Choppers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page No 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.4 #duty cycle %a=T_on/T\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V=a*(V_s-2) \n",
+ "V_or=math.sqrt(a*(V_s-2)**2) \n",
+ "P_o=V_or**2/R\n",
+ "P_i=V_s*V/R\n",
+ "n=P_o*100/P_i \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.1f V\" %V)\n",
+ "print(\"rms value of o/p voltage=%.1f V\" %V_or)\n",
+ "print(\"chopper efficiency in percentage=%.2f\" %n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=91.2 V\n",
+ "rms value of o/p voltage=144.2 V\n",
+ "chopper efficiency in percentage=99.13\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page No 388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_i=220.0\n",
+ "V_o=660.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=1-V_i/V_o\n",
+ "T_on=100.0 #microsecond\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=T_off/2\n",
+ "T_on=T-T_off\n",
+ "a=T_on/T\n",
+ "V_o=V_i/(1-a)\n",
+ "\n",
+ "#Results \n",
+ "print(\"pulse width of o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.0f V\" %V_o)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width of o/p voltage=25 us\n",
+ "\n",
+ "new o/p voltage=1320 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page No 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_1=12.0\n",
+ "I_2=16.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_0=(I_1+I_2)/2\n",
+ "R=10.0\n",
+ "V_0=I_0*R\n",
+ "V_s=200.0\n",
+ "a=V_0/V_s\n",
+ "r=a/(1-a)\n",
+ "\n",
+ "#Results\n",
+ "print(\"time ratio(T_on/T_off)=%.3f\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time ratio(T_on/T_off)=2.333\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page No 390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=660.0\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=(V_o/V_s)/(1+(V_o/V_s))\n",
+ "T_on=120\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=3*T_off\n",
+ "T_on=T-T_off\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_o=V_s*(a/(1-a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pulse width o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width o/p voltage=120 us\n",
+ "\n",
+ "new o/p voltage=73.33 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.11 Page No 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0\n",
+ "L=.005\n",
+ "T_a=L/R\n",
+ "T=2000*10**-6\n",
+ "E=24.0\n",
+ "V_s=220\n",
+ "T_on=600*10**-6\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+(E/V_s)*((math.exp(T/T_a))-1))\n",
+ "if a1<a :\n",
+ " print(\"load current in continuous\")\n",
+ "else:\n",
+ " print(\"load current in discont.\")\n",
+ "\n",
+ "I_o=(a*V_s-E)/R \n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a)))-E/R \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1))-E/R \n",
+ "f=1/T\n",
+ "w=2*math.pi*f\n",
+ "I1=(2*V_s/(math.sqrt(2)*math.pi)*math.sin(math.radians(180*a)))/(math.sqrt(R**2+(w*L)**2)) \n",
+ "I2=(2*V_s/(2*math.sqrt(2)*math.pi)*math.sin(math.radians(2*180*a)))/(math.sqrt(R**2+(w*L*2)**2)) \n",
+ "I3=(2*V_s/(3*math.sqrt(2)*math.pi)*math.sin(math.radians(3*180*a)))/(math.sqrt(R**2+(w*L*3)**2)) \n",
+ "I_TAV=a*(V_s-E)/R-L*(I_mx-I_mn)/(R*T) \n",
+ "P1=I_TAV*V_s\n",
+ "P2=E*I_o\n",
+ "I_or=math.sqrt(I_o**2+I1**2+I2**2+I3**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"max value of steady current=%.2f A\" %I_mx)\n",
+ "print(\"min value of steady current=%.2f A\" %I_mn)\n",
+ "print(\"first harmonic current=%.4f A\" %I1)\n",
+ "print(\"second harmonic current=%.4f A\" %I2)\n",
+ "print(\"third harmonic current=%.5f A\" %I3)\n",
+ "print(\"avg supply current=%.4f A\" %I_TAV)\n",
+ "print(\"i/p power=%.2f W\" %P1)\n",
+ "print(\"power absorbed by load emf=%.0f W\" %P2)\n",
+ "print(\"power loss in resistor=%.2f W\" %(P1-P2))\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current in continuous\n",
+ "avg o/p current=42.00 A\n",
+ "max value of steady current=51.46 A\n",
+ "min value of steady current=33.03 A\n",
+ "first harmonic current=5.0903 A\n",
+ "second harmonic current=1.4983 A\n",
+ "third harmonic current=0.21643 A\n",
+ "avg supply current=12.7289 A\n",
+ "i/p power=2800.35 W\n",
+ "power absorbed by load emf=1008 W\n",
+ "power loss in resistor=1792.35 W\n",
+ "rms value of load current=42.334 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12 Page No 411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1\n",
+ "L=.001\n",
+ "V_s=220\n",
+ "E=72.0\n",
+ "f=500.0\n",
+ "T_on=800*10**-6\n",
+ "T_a=L/R\n",
+ "T=1.0/f\n",
+ "m=E/V_s\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+m*(math.exp(-T/T_a)-1))\n",
+ "if a1>a :\n",
+ " print(\"load current is continuous\")\n",
+ "else:\n",
+ " print(\"load current is discontinuous\")\n",
+ "\n",
+ "t_x=T_on+L*math.log(1+((V_s-E)/272)*(1-math.exp(-T_on/T_a)))\n",
+ " #Value of t_x wrongly calculated in the book so ans of V_o and I_o varies\n",
+ "V_o=a*V_s+(1-t_x/T)*E \n",
+ "I_o=(V_o-E)/R \n",
+ "I_mx=(V_s-E)/R*(1-math.exp(-T_on/T_a)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o) \n",
+ "print(\"max value of load current=%.1f A\" %I_mx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current is discontinuous\n",
+ "avg o/p voltage=121.77 V\n",
+ "avg o/p current=49.77 A\n",
+ "max value of load current=81.5 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13, Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.2\n",
+ "V_s=500\n",
+ "E=a*V_s\n",
+ "L=0.06\n",
+ "I=10\n",
+ "\n",
+ "#Calculations\n",
+ "T_on=(L*I)/(V_s-E)\n",
+ "f=a/T_on \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.2f Hz\" %f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=133.33 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14 Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.5\n",
+ "pu=0.1 #pu ripple\n",
+ "\n",
+ "#Calculations\n",
+ " #x=T/T_a\n",
+ " #y=exp(-a*x)\n",
+ "y=(1-pu)/(1+pu)\n",
+ " #after solving\n",
+ "x=math.log(1/y)/a\n",
+ "f=1000\n",
+ "T=1/f\n",
+ "T_a=T/x\n",
+ "R=2\n",
+ "L=R*T_a\n",
+ "Li=0.002\n",
+ "Le=L-Li \n",
+ "\n",
+ "#Results\n",
+ "print(\"external inductance=%.3f mH\" %(Le*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "external inductance=-2.000 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15 Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=0.015\n",
+ "T_a=L/R\n",
+ "f=1250.0\n",
+ "T=1.0/f\n",
+ "a=0.5\n",
+ "T_on=a*T\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a))) \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1)) \n",
+ "dI=I_mx-I_mn \n",
+ "V_o=a*V_s\n",
+ "I_o=V_o/R \n",
+ "I_or=math.sqrt(I_mx**2+dI**2/3+I_mx*dI) \n",
+ "I_chr=math.sqrt(a)*I_or \n",
+ "\n",
+ "#Results\n",
+ "print(\"Max value of ripple current=%.2f A\" %dI)\n",
+ "print(\"Max value of load current=%.3f A\" %I_mx)\n",
+ "print(\"Min value of load current=%.2f A\" %I_mn)\n",
+ "print(\"Avg value of load current=%.2f A\" %I_o) \n",
+ "print(\"rms value of load current=%.2f A\" %I_or)\n",
+ "print(\"rms value of chopper current=%.2f A\" %I_chr)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max value of ripple current=2.92 A\n",
+ "Max value of load current=12.458 A\n",
+ "Min value of load current=9.54 A\n",
+ "Avg value of load current=11.00 A\n",
+ "rms value of load current=13.94 A\n",
+ "rms value of chopper current=9.86 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17 Page No 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.0016\n",
+ "C=4*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "w=1/math.sqrt(L*C)\n",
+ "t=math.pi/w \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"time for which current flows=%.2f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time for which current flows=251.33 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.18, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t_q=20.0*10**-6\n",
+ "dt=20.0*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t_q+dt\n",
+ "I_0=60.0\n",
+ "V_s=60.0\n",
+ "C=t_c*I_0/V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of commutating capacitor=%.0f uF\" %(C*10**6))\n",
+ "\n",
+ "L1=(V_s/I_0)**2*C\n",
+ "L2=(2*t_c/math.pi)**2/C\n",
+ "if L1>L2 :\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L1*10**6))\n",
+ "else:\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L2*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating capacitor=40 uF\n",
+ "value of commutating inductor=40 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.19, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=100.0*10**-6\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ " #V_s*(1-2*math.exp(-t/(R*C)))=0\n",
+ "C=-t/(R*math.log(1.0/2)) \n",
+ "L=(4/9.0)*C*R**2 \n",
+ "L=(1.0/4)*C*R**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of comutating component C=%.3f uF\" %(C*10**6))\n",
+ "print(\"max permissible current through SCR is 2.5 times load current\")\n",
+ "print(\"value of comutating component L=%.1f uH\" %(L*10**6))\n",
+ "print(\"max permissible current through SCR is 1.5 times peak diode current\")\n",
+ "print(\"value of comutating component L=%.2f uH\" %(L*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of comutating component C=14.427 uF\n",
+ "max permissible current through SCR is 2.5 times load current\n",
+ "value of comutating component L=360.7 uH\n",
+ "max permissible current through SCR is 1.5 times peak diode current\n",
+ "value of comutating component L=360.67 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=800.0*10**-6\n",
+ "V_s=220.0\n",
+ "I_o=80.0\n",
+ "C=50*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+2*V_s*C/I_o \n",
+ "L=20*10**-6\n",
+ "C=50*10**-6\n",
+ "i_T1=I_o+V_s*math.sqrt(C/L) \n",
+ "i_TA=I_o \n",
+ "t_c=C*V_s/I_o \n",
+ "t_c1=(math.pi/2)*math.sqrt(L*C) \n",
+ "t=150*10**-6\n",
+ "v_c=I_o*t/C-V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"effective on period=%.0f us\" %(T*10**6))\n",
+ "print(\"peak current through main thyristor=%.2f A\" %i_T1)\n",
+ "print(\"peak current through auxillery thyristor=%.0f A\" %i_TA)\n",
+ "print(\"turn off time for main thyristor=%.1f us\" %(t_c*10**6))\n",
+ "print(\"turn off time for auxillery thyristor=%.3f us\" %(t_c1*10**6))\n",
+ "print(\"total commutation interval=%.0f us\" %(2*t_c*10**6))\n",
+ "print(\"capacitor voltage=%.0f V\" %v_c)\n",
+ "print(\"time nedded to recharge the capacitor=%.0f us\" %(2*V_s*C/I_o*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_o=260.0\n",
+ "V_s=220.0\n",
+ "fos=2 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_off=18*10**-6\n",
+ "t_c=2*t_off\n",
+ "C=t_c*I_o/V_s \n",
+ "L=(V_s/(0.8*I_o))**2*C \n",
+ "f=400\n",
+ "a_mn=math.pi*f*math.sqrt(L*C)\n",
+ "V_omn=V_s*(a_mn+2*f*t_c) \n",
+ "V_omx=V_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of C=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of L=%.3f uH\" %(L*10**6))\n",
+ "print(\"min value of o/p voltage=%.3f V\" %V_omn)\n",
+ "print(\"max value of o/p voltage=%.0f V\" %V_omx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": "*"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.22, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x=2.0\n",
+ "t_q=30*10**-6\n",
+ "dt=30*10**-6\n",
+ "t_c=t_q+dt\n",
+ "V_s=230.0\n",
+ "I_o=200.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "x=3\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.0f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.2f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=307 V\n",
+ "peak commutataing current=600 A\n",
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=306.67 V\n",
+ "peak commutataing current=600 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.23, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "C=50*10**-6\n",
+ "L=20*10**-6\n",
+ "I_cp=V_s*math.sqrt(C/L)\n",
+ "I_o=200\n",
+ "x=I_cp/I_o\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=(math.pi-2*math.asin(1/x))*math.sqrt(C*L) \n",
+ "th1=math.degrees(math.asin(1.0/x))\n",
+ "t=(5*math.pi/2-th1*math.pi/180)*math.sqrt(L*C)+C*V_s*(1-math.cos(math.radians(th1)))/I_o \n",
+ "t=(math.pi-th1*math.pi/180)*math.sqrt(L*C) \n",
+ "\n",
+ "#Results\n",
+ "print(\"turn off time of main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"total commutation interval=%.3f us\" %(t*10**6))\n",
+ "print(\"turn off time of auxillery thyristor=%.3f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "turn off time of main thyristor=62.52 us\n",
+ "total commutation interval=80.931 us\n",
+ "turn off time of auxillery thyristor=80.931 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.24, Page No 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tc=0.006\n",
+ "R=10.0\n",
+ "L=R*tc\n",
+ "f=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=1/f\n",
+ "V_o=50.0\n",
+ "V_s=100.0\n",
+ "a=V_o/V_s\n",
+ "T_on=a*T\n",
+ "T_off=T-T_on\n",
+ "dI=V_o*T_off/L\n",
+ "I_o=V_o/R\n",
+ "I2=I_o+dI/2 \n",
+ "I1=I_o-dI/2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"max value of load current=%.3f A\" %I2)\n",
+ "print(\"min value of load current=%.3f A\" %I1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of load current=5.104 A\n",
+ "min value of load current=4.896 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.27, Page No 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=30.0\n",
+ "r_a=.5\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=I_a*r_a/V_s \n",
+ "a=1\n",
+ "k=.1 #V/rpm\n",
+ "N=(a*V_s-I_a*r_a)/k \n",
+ "\n",
+ "#Results\n",
+ "print(\"min value of duty cycle=%.3f\" %a)\n",
+ "print(\"min Value of speed control=%.0f rpm\" %0)\n",
+ "print(\"max value of duty cycle=%.0f\" %a)\n",
+ "print(\"max value of speed control=%.0f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min value of duty cycle=1.000\n",
+ "min Value of speed control=0 rpm\n",
+ "max value of duty cycle=1\n",
+ "max value of speed control=2050 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.28, Page No 444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=72.0\n",
+ "I_a=200.0\n",
+ "r_a=0.045\n",
+ "N=2500.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=(V_t-I_a*r_a)/N\n",
+ "E_a=k*1000\n",
+ "L=.007\n",
+ "Rm=.045\n",
+ "Rb=0.065\n",
+ "R=Rm+Rb\n",
+ "T_a=L/R\n",
+ "I_mx=230\n",
+ "I_mn=180\n",
+ "T_on=-T_a*math.log(-((V_t-E_a)/R-I_mx)/((I_mn)-(V_t-E_a)/R))\n",
+ "R=Rm\n",
+ "T_a=L/R\n",
+ "T_off=-T_a*math.log(-((-E_a)/R-I_mn)/((I_mx)-(-E_a)/R))\n",
+ "T=T_on+T_off\n",
+ "f=1/T \n",
+ "a=T_on/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.1f Hz\" %f) \n",
+ "print(\"duty cycle ratio=%.3f\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=40.5 Hz\n",
+ "\n",
+ "duty cycle ratio=0.588\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesI_mx=425\n",
+ "I_lt=180.0 #lower limit of current pulsation\n",
+ "I_mn=I_mx-I_lt\n",
+ "T_on=0.014\n",
+ "T_off=0.011\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+T_off\n",
+ "T_a=.0635\n",
+ "a=T_on/T\n",
+ "V=(I_mx-I_mn*math.exp(-T_on/T_a))/(1-math.exp(-T_on/T_a))\n",
+ "a=.5\n",
+ "I_mn=(I_mx-V*(1-math.exp(-T_on/T_a)))/(math.exp(-T_on/T_a))\n",
+ "T=I_mx-I_mn \n",
+ "T=T_on/a\n",
+ "f=1/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"higher limit of current pulsation=%.0f A\" %T)\n",
+ "print(\"chopping freq=%.3f Hz\" %f)\n",
+ "print(\"duty cycle ratio=%.2f\" %a)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "higher limit of current pulsation=0 A\n",
+ "chopping freq=35.714 Hz\n",
+ "duty cycle ratio=0.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter7_4.ipynb b/_Power_Electronics/Chapter7_4.ipynb new file mode 100755 index 00000000..726160c8 --- /dev/null +++ b/_Power_Electronics/Chapter7_4.ipynb @@ -0,0 +1,1036 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 07 : Choppers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page No 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.4 #duty cycle %a=T_on/T\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "V=a*(V_s-2) \n",
+ "V_or=math.sqrt(a*(V_s-2)**2) \n",
+ "P_o=V_or**2/R\n",
+ "P_i=V_s*V/R\n",
+ "n=P_o*100/P_i \n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p voltage=%.1f V\" %V)\n",
+ "print(\"rms value of o/p voltage=%.1f V\" %V_or)\n",
+ "print(\"chopper efficiency in percentage=%.2f\" %n)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "avg o/p voltage=91.2 V\n",
+ "rms value of o/p voltage=144.2 V\n",
+ "chopper efficiency in percentage=99.13\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page No 388"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_i=220.0\n",
+ "V_o=660.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=1-V_i/V_o\n",
+ "T_on=100.0 #microsecond\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=T_off/2\n",
+ "T_on=T-T_off\n",
+ "a=T_on/T\n",
+ "V_o=V_i/(1-a)\n",
+ "\n",
+ "#Results \n",
+ "print(\"pulse width of o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.0f V\" %V_o)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width of o/p voltage=25 us\n",
+ "\n",
+ "new o/p voltage=1320 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4 Page No 288"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_1=12.0\n",
+ "I_2=16.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_0=(I_1+I_2)/2\n",
+ "R=10.0\n",
+ "V_0=I_0*R\n",
+ "V_s=200.0\n",
+ "a=V_0/V_s\n",
+ "r=a/(1-a)\n",
+ "\n",
+ "#Results\n",
+ "print(\"time ratio(T_on/T_off)=%.3f\" %r)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time ratio(T_on/T_off)=2.333\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page No 390"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_o=660.0\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=(V_o/V_s)/(1+(V_o/V_s))\n",
+ "T_on=120\n",
+ "T=T_on/a\n",
+ "T_off=T-T_on \n",
+ "T_off=3*T_off\n",
+ "T_on=T-T_off\n",
+ "a=T_on/(T_on+T_off)\n",
+ "V_o=V_s*(a/(1-a)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"pulse width o/p voltage=%.0f us\" %T_off)\n",
+ "print(\"\\nnew o/p voltage=%.2f V\" %V_o)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "pulse width o/p voltage=120 us\n",
+ "\n",
+ "new o/p voltage=73.33 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.11 Page No 408"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1.0\n",
+ "L=.005\n",
+ "T_a=L/R\n",
+ "T=2000*10**-6\n",
+ "E=24.0\n",
+ "V_s=220\n",
+ "T_on=600*10**-6\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+(E/V_s)*((math.exp(T/T_a))-1))\n",
+ "if a1<a :\n",
+ " print(\"load current in continuous\")\n",
+ "else:\n",
+ " print(\"load current in discont.\")\n",
+ "\n",
+ "I_o=(a*V_s-E)/R \n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a)))-E/R \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1))-E/R \n",
+ "f=1/T\n",
+ "w=2*math.pi*f\n",
+ "I1=(2*V_s/(math.sqrt(2)*math.pi)*math.sin(math.radians(180*a)))/(math.sqrt(R**2+(w*L)**2)) \n",
+ "I2=(2*V_s/(2*math.sqrt(2)*math.pi)*math.sin(math.radians(2*180*a)))/(math.sqrt(R**2+(w*L*2)**2)) \n",
+ "I3=(2*V_s/(3*math.sqrt(2)*math.pi)*math.sin(math.radians(3*180*a)))/(math.sqrt(R**2+(w*L*3)**2)) \n",
+ "I_TAV=a*(V_s-E)/R-L*(I_mx-I_mn)/(R*T) \n",
+ "P1=I_TAV*V_s\n",
+ "P2=E*I_o\n",
+ "I_or=math.sqrt(I_o**2+I1**2+I2**2+I3**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"avg o/p current=%.2f A\" %I_o)\n",
+ "print(\"max value of steady current=%.2f A\" %I_mx)\n",
+ "print(\"min value of steady current=%.2f A\" %I_mn)\n",
+ "print(\"first harmonic current=%.4f A\" %I1)\n",
+ "print(\"second harmonic current=%.4f A\" %I2)\n",
+ "print(\"third harmonic current=%.5f A\" %I3)\n",
+ "print(\"avg supply current=%.4f A\" %I_TAV)\n",
+ "print(\"i/p power=%.2f W\" %P1)\n",
+ "print(\"power absorbed by load emf=%.0f W\" %P2)\n",
+ "print(\"power loss in resistor=%.2f W\" %(P1-P2))\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current in continuous\n",
+ "avg o/p current=42.00 A\n",
+ "max value of steady current=51.46 A\n",
+ "min value of steady current=33.03 A\n",
+ "first harmonic current=5.0903 A\n",
+ "second harmonic current=1.4983 A\n",
+ "third harmonic current=0.21643 A\n",
+ "avg supply current=12.7289 A\n",
+ "i/p power=2800.35 W\n",
+ "power absorbed by load emf=1008 W\n",
+ "power loss in resistor=1792.35 W\n",
+ "rms value of load current=42.334 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.12 Page No 411"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=1\n",
+ "L=.001\n",
+ "V_s=220\n",
+ "E=72.0\n",
+ "f=500.0\n",
+ "T_on=800*10**-6\n",
+ "T_a=L/R\n",
+ "T=1.0/f\n",
+ "m=E/V_s\n",
+ "a=T_on/T\n",
+ "\n",
+ "#Calculations\n",
+ "a1=(T_a/T)*math.log(1+m*(math.exp(-T/T_a)-1))\n",
+ "if a1>a :\n",
+ " print(\"load current is continuous\")\n",
+ "else:\n",
+ " print(\"load current is discontinuous\")\n",
+ "\n",
+ "t_x=T_on+L*math.log(1+((V_s-E)/272)*(1-math.exp(-T_on/T_a)))\n",
+ " #Value of t_x wrongly calculated in the book so ans of V_o and I_o varies\n",
+ "V_o=a*V_s+(1-t_x/T)*E \n",
+ "I_o=(V_o-E)/R \n",
+ "I_mx=(V_s-E)/R*(1-math.exp(-T_on/T_a)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"avg o/p voltage=%.2f V\" %V_o)\n",
+ "print(\"avg o/p current=%.2f A\" %I_o) \n",
+ "print(\"max value of load current=%.1f A\" %I_mx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "load current is discontinuous\n",
+ "avg o/p voltage=121.77 V\n",
+ "avg o/p current=49.77 A\n",
+ "max value of load current=81.5 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.13, Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.2\n",
+ "V_s=500\n",
+ "E=a*V_s\n",
+ "L=0.06\n",
+ "I=10\n",
+ "\n",
+ "#Calculations\n",
+ "T_on=(L*I)/(V_s-E)\n",
+ "f=a/T_on \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.2f Hz\" %f)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=133.33 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.14 Page No 412"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.5\n",
+ "pu=0.1 #pu ripple\n",
+ "\n",
+ "#Calculations\n",
+ " #x=T/T_a\n",
+ " #y=exp(-a*x)\n",
+ "y=(1-pu)/(1+pu)\n",
+ " #after solving\n",
+ "x=math.log(1/y)/a\n",
+ "f=1000\n",
+ "T=1/f\n",
+ "T_a=T/x\n",
+ "R=2\n",
+ "L=R*T_a\n",
+ "Li=0.002\n",
+ "Le=L-Li \n",
+ "\n",
+ "#Results\n",
+ "print(\"external inductance=%.3f mH\" %(Le*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "external inductance=-2.000 mH\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.15 Page No 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=0.015\n",
+ "T_a=L/R\n",
+ "f=1250.0\n",
+ "T=1.0/f\n",
+ "a=0.5\n",
+ "T_on=a*T\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_mx=(V_s/R)*((1-math.exp(-T_on/T_a))/(1-math.exp(-T/T_a))) \n",
+ "I_mn=(V_s/R)*((math.exp(T_on/T_a)-1)/(math.exp(T/T_a)-1)) \n",
+ "dI=I_mx-I_mn \n",
+ "V_o=a*V_s\n",
+ "I_o=V_o/R \n",
+ "I_or=math.sqrt(I_mx**2+dI**2/3+I_mx*dI) \n",
+ "I_chr=math.sqrt(a)*I_or \n",
+ "\n",
+ "#Results\n",
+ "print(\"Max value of ripple current=%.2f A\" %dI)\n",
+ "print(\"Max value of load current=%.3f A\" %I_mx)\n",
+ "print(\"Min value of load current=%.2f A\" %I_mn)\n",
+ "print(\"Avg value of load current=%.2f A\" %I_o) \n",
+ "print(\"rms value of load current=%.2f A\" %I_or)\n",
+ "print(\"rms value of chopper current=%.2f A\" %I_chr)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Max value of ripple current=2.92 A\n",
+ "Max value of load current=12.458 A\n",
+ "Min value of load current=9.54 A\n",
+ "Avg value of load current=11.00 A\n",
+ "rms value of load current=13.94 A\n",
+ "rms value of chopper current=9.86 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.17 Page No 417"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.0016\n",
+ "C=4*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "w=1/math.sqrt(L*C)\n",
+ "t=math.pi/w \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"time for which current flows=%.2f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time for which current flows=251.33 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.18, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t_q=20.0*10**-6\n",
+ "dt=20.0*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t_q+dt\n",
+ "I_0=60.0\n",
+ "V_s=60.0\n",
+ "C=t_c*I_0/V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of commutating capacitor=%.0f uF\" %(C*10**6))\n",
+ "\n",
+ "L1=(V_s/I_0)**2*C\n",
+ "L2=(2*t_c/math.pi)**2/C\n",
+ "if L1>L2 :\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L1*10**6))\n",
+ "else:\n",
+ " print(\"value of commutating inductor=%.0f uH\" %(L2*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating capacitor=40 uF\n",
+ "value of commutating inductor=40 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.19, Page No 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=100.0*10**-6\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ " #V_s*(1-2*math.exp(-t/(R*C)))=0\n",
+ "C=-t/(R*math.log(1.0/2)) \n",
+ "L=(4/9.0)*C*R**2 \n",
+ "L=(1.0/4)*C*R**2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of comutating component C=%.3f uF\" %(C*10**6))\n",
+ "print(\"max permissible current through SCR is 2.5 times load current\")\n",
+ "print(\"value of comutating component L=%.1f uH\" %(L*10**6))\n",
+ "print(\"max permissible current through SCR is 1.5 times peak diode current\")\n",
+ "print(\"value of comutating component L=%.2f uH\" %(L*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Value of comutating component C=14.427 uF\n",
+ "max permissible current through SCR is 2.5 times load current\n",
+ "value of comutating component L=360.7 uH\n",
+ "max permissible current through SCR is 1.5 times peak diode current\n",
+ "value of comutating component L=360.67 uH\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.20, Page No 426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T_on=800.0*10**-6\n",
+ "V_s=220.0\n",
+ "I_o=80.0\n",
+ "C=50*10**-6\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+2*V_s*C/I_o \n",
+ "L=20*10**-6\n",
+ "C=50*10**-6\n",
+ "i_T1=I_o+V_s*math.sqrt(C/L) \n",
+ "i_TA=I_o \n",
+ "t_c=C*V_s/I_o \n",
+ "t_c1=(math.pi/2)*math.sqrt(L*C) \n",
+ "t=150*10**-6\n",
+ "v_c=I_o*t/C-V_s \n",
+ "\n",
+ "#Results \n",
+ "print(\"effective on period=%.0f us\" %(T*10**6))\n",
+ "print(\"peak current through main thyristor=%.2f A\" %i_T1)\n",
+ "print(\"peak current through auxillery thyristor=%.0f A\" %i_TA)\n",
+ "print(\"turn off time for main thyristor=%.1f us\" %(t_c*10**6))\n",
+ "print(\"turn off time for auxillery thyristor=%.3f us\" %(t_c1*10**6))\n",
+ "print(\"total commutation interval=%.0f us\" %(2*t_c*10**6))\n",
+ "print(\"capacitor voltage=%.0f V\" %v_c)\n",
+ "print(\"time nedded to recharge the capacitor=%.0f us\" %(2*V_s*C/I_o*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for firing angle = 30deg\n",
+ "avg output voltage=232.509 V\n",
+ "for firing angle = 60deg\n",
+ "avg output voltage=133.65 V\n",
+ "avg current rating=12 A\n",
+ "rms current rating=20.785 A\n",
+ "PIV of SCR=565.7 V\n",
+ "power dissipated=16.8 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 122
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.21, Page No 427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_o=260.0\n",
+ "V_s=220.0\n",
+ "fos=2 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_off=18*10**-6\n",
+ "t_c=2*t_off\n",
+ "C=t_c*I_o/V_s \n",
+ "L=(V_s/(0.8*I_o))**2*C \n",
+ "f=400\n",
+ "a_mn=math.pi*f*math.sqrt(L*C)\n",
+ "V_omn=V_s*(a_mn+2*f*t_c) \n",
+ "V_omx=V_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"Value of C=%.3f uF\" %(C*10**6))\n",
+ "print(\"value of L=%.3f uH\" %(L*10**6))\n",
+ "print(\"min value of o/p voltage=%.3f V\" %V_omn)\n",
+ "print(\"max value of o/p voltage=%.0f V\" %V_omx)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "firing angle delay=47.461 deg\n",
+ "pf=0.646\n",
+ "firing angle delay=127.71 deg\n"
+ ]
+ }
+ ],
+ "prompt_number": "*"
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.22, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "x=2.0\n",
+ "t_q=30*10**-6\n",
+ "dt=30*10**-6\n",
+ "t_c=t_q+dt\n",
+ "V_s=230.0\n",
+ "I_o=200.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "x=3\n",
+ "L=V_s*t_c/(x*I_o*(math.pi-2*math.asin(1/x))) \n",
+ "C=x*I_o*t_c/(V_s*(math.pi-2*math.asin(1/x))) \n",
+ "V_cp=V_s+I_o*math.sqrt(L/C) \n",
+ "I_cp=x*I_o \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.0f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n",
+ "print(\"value of commutating inductor=%.3f uH\" %(L*10**6))\n",
+ "print(\"value of commutating capacitor=%.3f uF\" %(C*10**6))\n",
+ "print(\"peak capacitor voltage=%.2f V\" %V_cp)\n",
+ "print(\"peak commutataing current=%.0f A\" %I_cp)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=307 V\n",
+ "peak commutataing current=600 A\n",
+ "value of commutating inductor=7.321 uH\n",
+ "value of commutating capacitor=49.822 uF\n",
+ "peak capacitor voltage=306.67 V\n",
+ "peak commutataing current=600 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.23, Page No 434"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesV_s=230\n",
+ "C=50*10**-6\n",
+ "L=20*10**-6\n",
+ "I_cp=V_s*math.sqrt(C/L)\n",
+ "I_o=200\n",
+ "x=I_cp/I_o\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=(math.pi-2*math.asin(1/x))*math.sqrt(C*L) \n",
+ "th1=math.degrees(math.asin(1.0/x))\n",
+ "t=(5*math.pi/2-th1*math.pi/180)*math.sqrt(L*C)+C*V_s*(1-math.cos(math.radians(th1)))/I_o \n",
+ "t=(math.pi-th1*math.pi/180)*math.sqrt(L*C) \n",
+ "\n",
+ "#Results\n",
+ "print(\"turn off time of main thyristor=%.2f us\" %(t_c*10**6))\n",
+ "print(\"total commutation interval=%.3f us\" %(t*10**6))\n",
+ "print(\"turn off time of auxillery thyristor=%.3f us\" %(t*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "turn off time of main thyristor=62.52 us\n",
+ "total commutation interval=80.931 us\n",
+ "turn off time of auxillery thyristor=80.931 us\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.24, Page No 440"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "tc=0.006\n",
+ "R=10.0\n",
+ "L=R*tc\n",
+ "f=2000.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=1/f\n",
+ "V_o=50.0\n",
+ "V_s=100.0\n",
+ "a=V_o/V_s\n",
+ "T_on=a*T\n",
+ "T_off=T-T_on\n",
+ "dI=V_o*T_off/L\n",
+ "I_o=V_o/R\n",
+ "I2=I_o+dI/2 \n",
+ "I1=I_o-dI/2 \n",
+ "\n",
+ "#Results\n",
+ "print(\"max value of load current=%.3f A\" %I2)\n",
+ "print(\"min value of load current=%.3f A\" %I1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of load current=5.104 A\n",
+ "min value of load current=4.896 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.27, Page No 443"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "I_a=30.0\n",
+ "r_a=.5\n",
+ "V_s=220.0\n",
+ "\n",
+ "#Calculations\n",
+ "a=I_a*r_a/V_s \n",
+ "a=1\n",
+ "k=.1 #V/rpm\n",
+ "N=(a*V_s-I_a*r_a)/k \n",
+ "\n",
+ "#Results\n",
+ "print(\"min value of duty cycle=%.3f\" %a)\n",
+ "print(\"min Value of speed control=%.0f rpm\" %0)\n",
+ "print(\"max value of duty cycle=%.0f\" %a)\n",
+ "print(\"max value of speed control=%.0f rpm\" %N)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min value of duty cycle=1.000\n",
+ "min Value of speed control=0 rpm\n",
+ "max value of duty cycle=1\n",
+ "max value of speed control=2050 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.28, Page No 444"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_t=72.0\n",
+ "I_a=200.0\n",
+ "r_a=0.045\n",
+ "N=2500.0\n",
+ "\n",
+ "#Calculations\n",
+ "k=(V_t-I_a*r_a)/N\n",
+ "E_a=k*1000\n",
+ "L=.007\n",
+ "Rm=.045\n",
+ "Rb=0.065\n",
+ "R=Rm+Rb\n",
+ "T_a=L/R\n",
+ "I_mx=230\n",
+ "I_mn=180\n",
+ "T_on=-T_a*math.log(-((V_t-E_a)/R-I_mx)/((I_mn)-(V_t-E_a)/R))\n",
+ "R=Rm\n",
+ "T_a=L/R\n",
+ "T_off=-T_a*math.log(-((-E_a)/R-I_mn)/((I_mx)-(-E_a)/R))\n",
+ "T=T_on+T_off\n",
+ "f=1/T \n",
+ "a=T_on/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"chopping freq=%.1f Hz\" %f) \n",
+ "print(\"duty cycle ratio=%.3f\" %a)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "chopping freq=40.5 Hz\n",
+ "\n",
+ "duty cycle ratio=0.588\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.29, Page No 445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variablesI_mx=425\n",
+ "I_lt=180.0 #lower limit of current pulsation\n",
+ "I_mn=I_mx-I_lt\n",
+ "T_on=0.014\n",
+ "T_off=0.011\n",
+ "\n",
+ "#Calculations\n",
+ "T=T_on+T_off\n",
+ "T_a=.0635\n",
+ "a=T_on/T\n",
+ "V=(I_mx-I_mn*math.exp(-T_on/T_a))/(1-math.exp(-T_on/T_a))\n",
+ "a=.5\n",
+ "I_mn=(I_mx-V*(1-math.exp(-T_on/T_a)))/(math.exp(-T_on/T_a))\n",
+ "T=I_mx-I_mn \n",
+ "T=T_on/a\n",
+ "f=1/T \n",
+ "\n",
+ "#Results\n",
+ "print(\"higher limit of current pulsation=%.0f A\" %T)\n",
+ "print(\"chopping freq=%.3f Hz\" %f)\n",
+ "print(\"duty cycle ratio=%.2f\" %a)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "higher limit of current pulsation=0 A\n",
+ "chopping freq=35.714 Hz\n",
+ "duty cycle ratio=0.50\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter8.ipynb b/_Power_Electronics/Chapter8.ipynb new file mode 100755 index 00000000..721a9faf --- /dev/null +++ b/_Power_Electronics/Chapter8.ipynb @@ -0,0 +1,984 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Inverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T=0.1*10**-3\n",
+ "f=1.0/T\n",
+ "k=15*10**-6 #k=th/w\n",
+ "\n",
+ "#Calculations\n",
+ "th=2*math.pi*f*k\n",
+ "X_l=10.0\n",
+ "R=2.0\n",
+ "X_c=R*math.tan(th)+X_l\n",
+ "C=1/(2*math.pi*f*X_c) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of C=1.248 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 466"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi)\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "P_d=I_01**2*R \n",
+ "V=V_s/2\n",
+ "I_s=math.sqrt(2)*I_01/math.pi\n",
+ "P_s=V*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to load=%.1f W\" %P_d)\n",
+ "print(\"power delivered by both sources=%.1f W\" %(2*P_s))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to load=5359.9 W\n",
+ "power delivered by both sources=5359.9 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=4*V_s/(math.pi*math.sqrt(2))\n",
+ "R=1.0\n",
+ "X_L=6.0\n",
+ "X_c=7.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_c)**2)\n",
+ "P=I_01**2*R \n",
+ "I_s=math.sqrt(2)*I_01*(2*math.cos(math.radians(45)))/math.pi\n",
+ "P_s=V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to the source=%.3f kW\" %(P/1000))\n",
+ "print(\"\\npower from the source=%.3f kW\" %(P_s/1000))\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to the source=21.440 kW\n",
+ "\n",
+ "power from the source=21.440 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No 469"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_01=230.0\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "I_m=I_01*math.sqrt(2)\n",
+ "I_T1=I_m/2 \n",
+ "I_D1=0 \n",
+ "X_L=8.0\n",
+ "X_C=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=math.degrees(math.atan((X_L-X_C)/R))\n",
+ "I_T1=I_T1*math.sqrt(2)*0.47675 \n",
+ "I_D1=.1507025*I_m/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"when load R=2 ohm\")\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.0f A\" %I_D1)\n",
+ "print(\"when load R=2ohm % X_L=8ohm and X_C=6ohm\")\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_D1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when load R=2 ohm\n",
+ "rms value of thyristor current=54.83 A\n",
+ "rms value of diode current=17 A\n",
+ "when load R=2ohm % X_L=8ohm and X_C=6ohm\n",
+ "rms value of thyristor current=54.826 A\n",
+ "rms value of diode current=17.331 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No 470"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=4.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.035\n",
+ "\n",
+ "#Calculations\n",
+ "C=155*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_01=I_m1/math.sqrt(2) \n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2)\n",
+ "I_0=I_m/math.sqrt(2)\n",
+ "P_0=(I_0)**2*R \n",
+ "P_01=(I_01)**2*R \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=(phi1)*math.pi/(180*w) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of fundamental load current=%.2f A\" %I_01)\n",
+ "print(\"load power=%.1f W\" %P_0)\n",
+ "print(\"fundamental load power=%.1f W\" %P_01)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_m/2))\n",
+ "print(\"conduction time for thyristor=%.3f ms\" %(t1*1000))\n",
+ "print(\"Conduction time for diodes=%.3f ms\" %(t1*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of fundamental load current=20.02 A\n",
+ "load power=1632.5 W\n",
+ "fundamental load power=1602.6 W\n",
+ "rms value of thyristor current=14.285 A\n",
+ "conduction time for thyristor=3.736 ms\n",
+ "Conduction time for diodes=3.736 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8, Page No 473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi) \n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/R\n",
+ "P=I_01**2*R \n",
+ "V_or=math.sqrt((V_s/2)**2)\n",
+ "P=V_or**2/R \n",
+ "I_TP=V_s/(2*R)\n",
+ "I_or=I_TP\n",
+ "pf=I_01**2*R/(V_or*I_or) \n",
+ "DF=V_01/V_or \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01\n",
+ "\n",
+ "#Results\n",
+ "print(\"fundamental rms o/p voltage=%.3f V\" %V_01)\n",
+ "print(\"fundamental power to load=%.1f W\" %P)\n",
+ "print(\"total o/p power to load=%.1f W\" %P)\n",
+ "print(\"avg SCR current=%.2f A\" %(I_TP*180/360))\n",
+ "print(\"i/p pf=%.3f\" %pf) \n",
+ "print(\"distortion factor=%.1f\" %DF)\n",
+ "print(\"THD=%.3f\" %THD) \n",
+ "print(\"harmonic factor=%.4f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fundamental rms o/p voltage=103.536 V\n",
+ "fundamental power to load=1322.5 W\n",
+ "total o/p power to load=1322.5 W\n",
+ "avg SCR current=5.75 A\n",
+ "i/p pf=0.811\n",
+ "distortion factor=0.9\n",
+ "THD=0.483\n",
+ "harmonic factor=0.3333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.9 Page No 474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=60\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi) \n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi) \n",
+ "P_o=V_or**2/R \n",
+ "P_01=V_01**2/R \n",
+ "I_s=V_s/R \n",
+ "I_avg=I_s*math.pi/(2*math.pi) \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01 \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.0f V\" %V_or)\n",
+ "print(\"o/p power=%.0f W\" %P_o)\n",
+ "print(\"fundamental component of rms voltage=%.2f V\" %V_01)\n",
+ "print(\"fundamental freq o/p power=%.2f W\" %P_01) \n",
+ "print(\"peak current=%.0f A\" %I_s)\n",
+ "print(\"avg current of each transistor=%.0f A\" %I_avg)\n",
+ "print(\"peak reverse blocking voltage=%.0f V\" %V_s)\n",
+ "print(\"harmonic factor=%.4f\" %HF)\n",
+ "print(\"THD=%.4f\" %THD)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=60 V\n",
+ "o/p power=1200 W\n",
+ "fundamental component of rms voltage=54.02 V\n",
+ "fundamental freq o/p power=972.68 W\n",
+ "peak current=20 A\n",
+ "avg current of each transistor=10 A\n",
+ "peak reverse blocking voltage=60 V\n",
+ "harmonic factor=0.3333\n",
+ "THD=0.4834\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.10 Page No 475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "R=6.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "C=180*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "print(\"THD of voltage=%.4f\" %THD)\n",
+ "DF=V_01/V_or \n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7-X_C/7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7-X_C/7)/R))\n",
+ "I_01=19.403\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "I_or=I_m/math.sqrt(2)\n",
+ "I_oh=math.sqrt((I_m**2-I_m1**2)/2)\n",
+ "THD=I_oh/I_01 \n",
+ "DF=I_01/I_or \n",
+ "P_o=I_or**2*R \n",
+ "I_avg=P_o/V_s \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=1/(2*f)-t1 \n",
+ "I_p=I_m1 \n",
+ "I_t1=.46135*I_p \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nDF=%.1f\" %DF)\n",
+ "print(\"THD of current=%.4f\" %THD) \n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"avg value of load current=%.2f A\" %I_avg)\n",
+ "print(\"conduction time for thyristor=%.0f ms\" %(t1*1000))\n",
+ "print(\"conduction time for diodes=%.0f ms\" %(t1*1000))\n",
+ "print(\"peak transistor current=%.2f A\" %I_p)\n",
+ "print(\"rms transistor current=%.2f A\" %I_t1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "THD of voltage=0.4834\n",
+ "\n",
+ "DF=1.0\n",
+ "THD of current=0.1557\n",
+ "DF=0.988\n",
+ "load power=2313.5 W\n",
+ "avg value of load current=10.52 A\n",
+ "conduction time for thyristor=3 ms\n",
+ "conduction time for diodes=3 ms\n",
+ "peak transistor current=27.44 A\n",
+ "rms transistor current=12.66 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11 Page No 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=450.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_or=math.sqrt((V_s/(3*R))**2*2/3+(2*V_s/(3*R))**2*1/3) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(3*R))**2*2*math.pi/3+(2*V_s/(3*R))**2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "I_or=math.sqrt((1/(math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"for 180deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"power delivered to load=%.1f kW\" %(P/1000))\n",
+ "print(\"rms value of load current=%.0f A\" %I_T1)\n",
+ "print(\"for 120deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"rms value of load current=%.2f A\" %I_T1)\n",
+ "print(\"power delivered to load=%.3f kW\" %(P/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 180deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "power delivered to load=10.1 kW\n",
+ "rms value of load current=13 A\n",
+ "for 120deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "rms value of load current=12.99 A\n",
+ "power delivered to load=10.125 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12, Page No 510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "\n",
+ "#Calculations\n",
+ "X_L=w*L\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "Z1=math.sqrt(R**2+(X_L)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7)/R))\n",
+ "I_m1=4*V_s/(math.sqrt(2)*Z1*math.pi)\n",
+ "I_m3=4*V_s/(math.sqrt(2)*3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(math.sqrt(2)*5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(math.sqrt(2)*7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "P=I_m**2*R \n",
+ "I_01=I_m1*math.sin(math.radians(45))\n",
+ "I_03=I_m3*math.sin(math.radians(3*45))\n",
+ "I_05=I_m5*math.sin(math.radians(5*45))\n",
+ "I_07=I_m7*math.sin(math.radians(7*45))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "g=(180-90)/3+45/2\n",
+ "I_01=2*I_m1*math.sin(math.radians(g))*math.sin(math.radians(45/2))\n",
+ "I_03=2*I_m3*math.sin(math.radians(g*3))*math.sin(math.radians(3*45/2))\n",
+ "I_05=2*I_m5*math.sin(math.radians(g*5))*math.sin(math.radians(5*45/2))\n",
+ "I_07=2*I_m7*math.sin(math.radians(g*7))*math.sin(math.radians(7*45/2))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"using square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using quasi-square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using two symmitrical spaced pulses\")\n",
+ "print(\"power delivered=%.2f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "using square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using quasi-square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using two symmitrical spaced pulses\n",
+ "power delivered=845.87 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.14, Page No 520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "T=1/f\n",
+ "I=0.5\n",
+ "\n",
+ "#Calculations\n",
+ "di=I/T #di=di/dt\n",
+ "V_s=220.0\n",
+ "L=V_s/di \n",
+ "t=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "t_c=t*fos\n",
+ "R=10\n",
+ "C=t_c/(R*math.log(2))\n",
+ "\n",
+ "#Results \n",
+ "print(\"source inductance=%.1f H\" %L)\n",
+ "print(\"commutating capacitor=%.2f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source inductance=8.8 H\n",
+ "commutating capacitor=5.77 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15, Page No 539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=.01\n",
+ "C=10*10**-6\n",
+ "#Calculations\n",
+ "if (R**2)<(4*L/C) :\n",
+ " print(\"ckt will commutate on its own\")\n",
+ "else:\n",
+ " print(\"ckt will not commutate on its own\")\n",
+ "\n",
+ "xie=R/(2*L)\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "phi=math.degrees(math.atan(xie/w_r))\n",
+ "t=math.pi/w_r\n",
+ "V_s=1\n",
+ "v_L=V_s*(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180+phi))\n",
+ "v_c=V_s*(1-(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180-phi))) \n",
+ "di=V_s/L \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage across inductor(*V_s)=%.5f V\" %v_L) \n",
+ "print(\"voltage across capacitor(*V_s)=%.5f V\" %v_c)\n",
+ "print(\"di/dt*V_s (for t=0)=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt will commutate on its own\n",
+ "voltage across inductor(*V_s)=-0.60468 V\n",
+ "voltage across capacitor(*V_s)=1.60468 V\n",
+ "di/dt*V_s (for t=0)=100 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.006\n",
+ "C=1.2*10**-6\n",
+ "R=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=0.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=40\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=140\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p freq=%.2f Hz\" %f)\n",
+ "print(\"for R=40ohm\")\n",
+ "print(\"upper limit o/p freq=%.1f Hz\" %f)\n",
+ "print(\"for R=140ohm\")\n",
+ "print(\"lower limit o/p freq=%.1f Hz\" %f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p freq=239.81 Hz\n",
+ "for R=40ohm\n",
+ "upper limit o/p freq=239.8 Hz\n",
+ "for R=140ohm\n",
+ "lower limit o/p freq=239.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=5000.0\n",
+ "w=2*math.pi*f\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=60*10**-6\n",
+ "xie=R/(2*L)\n",
+ "C=7.5*10**-6\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "t_c=math.pi*(1/w-1/w_r) \n",
+ "fos=1.5\n",
+ "t_q=10*10**-6\n",
+ "f_max=1/(2*math.pi*(t_q*fos/math.pi+1/w_r)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"max possible operating freq=%.1f Hz\" %f_max)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt turn off time=21.39 us\n",
+ "max possible operating freq=5341.4 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18, Page No 541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=20.0\n",
+ "fos=2.0 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t*fos\n",
+ "n=1.0/3\n",
+ "R=20.0\n",
+ "C=n**2*t_c/(4*R*math.log(2)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of capacitor=%.2f uF\" %C)\n",
+ " #printing mistake in the answer in book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitor=0.08 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "V_p=math.sqrt(2)*V_s/3 \n",
+ "V_L=math.sqrt(3)*V_p \n",
+ "V_p1=math.sqrt(2)*V_s/math.pi \n",
+ "V_L1=math.sqrt(3)*V_p1 \n",
+ "V_oh=math.sqrt(V_L**2-V_L1**2)\n",
+ "\n",
+ "#Calculations\n",
+ "THD=V_oh/V_L1 \n",
+ "V_a1=2*V_s/math.pi\n",
+ "V_a5=2*V_s/(5*math.pi)\n",
+ "V_a7=2*V_s/(7*math.pi)\n",
+ "V_a11=2*V_s/(11*math.pi)\n",
+ "R=4.0\n",
+ "L=0.02\n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "Z1=math.sqrt(R**2+(w*L)**2)\n",
+ "Z5=math.sqrt(R**2+(5*w*L)**2)\n",
+ "Z7=math.sqrt(R**2+(7*w*L)**2)\n",
+ "Z11=math.sqrt(R**2+(11*w*L)**2)\n",
+ "I_a1=V_a1/Z1\n",
+ "I_a5=V_a5/Z5\n",
+ "I_a7=V_a7/Z7\n",
+ "I_a11=V_a11/Z11\n",
+ "I_or=math.sqrt((I_a1**2+I_a5**2+I_a7**2+I_a11**2)/2)\n",
+ "P=3*I_or**2*R \n",
+ "I_s=P/V_s \n",
+ "I_TA=I_s/3 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of phasor voltages=%.2f V\" %V_p)\n",
+ "print(\"rms value of line voltages=%.2f V\" %V_L)\n",
+ "print(\"fundamental component of phase voltage=%.3f V\" %V_p1)\n",
+ "print(\"fundamental component of line voltages=%.3f V\" %V_L1)\n",
+ "print(\"THD=%.7f\" %THD)\n",
+ "print(\"load power=%.1f W\" %P)\n",
+ "print(\"avg value of source current=%.3f A\" %I_s)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of phasor voltages=103.71 V\n",
+ "rms value of line voltages=179.63 V\n",
+ "fundamental component of phase voltage=99.035 V\n",
+ "fundamental component of line voltages=171.533 V\n",
+ "THD=0.3108419\n",
+ "load power=2127.6 W\n",
+ "avg value of source current=9.671 A\n",
+ "avg value of thyristor current=3.224 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter8_1.ipynb b/_Power_Electronics/Chapter8_1.ipynb new file mode 100755 index 00000000..721a9faf --- /dev/null +++ b/_Power_Electronics/Chapter8_1.ipynb @@ -0,0 +1,984 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Inverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T=0.1*10**-3\n",
+ "f=1.0/T\n",
+ "k=15*10**-6 #k=th/w\n",
+ "\n",
+ "#Calculations\n",
+ "th=2*math.pi*f*k\n",
+ "X_l=10.0\n",
+ "R=2.0\n",
+ "X_c=R*math.tan(th)+X_l\n",
+ "C=1/(2*math.pi*f*X_c) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of C=1.248 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 466"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi)\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "P_d=I_01**2*R \n",
+ "V=V_s/2\n",
+ "I_s=math.sqrt(2)*I_01/math.pi\n",
+ "P_s=V*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to load=%.1f W\" %P_d)\n",
+ "print(\"power delivered by both sources=%.1f W\" %(2*P_s))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to load=5359.9 W\n",
+ "power delivered by both sources=5359.9 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=4*V_s/(math.pi*math.sqrt(2))\n",
+ "R=1.0\n",
+ "X_L=6.0\n",
+ "X_c=7.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_c)**2)\n",
+ "P=I_01**2*R \n",
+ "I_s=math.sqrt(2)*I_01*(2*math.cos(math.radians(45)))/math.pi\n",
+ "P_s=V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to the source=%.3f kW\" %(P/1000))\n",
+ "print(\"\\npower from the source=%.3f kW\" %(P_s/1000))\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to the source=21.440 kW\n",
+ "\n",
+ "power from the source=21.440 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No 469"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_01=230.0\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "I_m=I_01*math.sqrt(2)\n",
+ "I_T1=I_m/2 \n",
+ "I_D1=0 \n",
+ "X_L=8.0\n",
+ "X_C=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=math.degrees(math.atan((X_L-X_C)/R))\n",
+ "I_T1=I_T1*math.sqrt(2)*0.47675 \n",
+ "I_D1=.1507025*I_m/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"when load R=2 ohm\")\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.0f A\" %I_D1)\n",
+ "print(\"when load R=2ohm % X_L=8ohm and X_C=6ohm\")\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_D1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when load R=2 ohm\n",
+ "rms value of thyristor current=54.83 A\n",
+ "rms value of diode current=17 A\n",
+ "when load R=2ohm % X_L=8ohm and X_C=6ohm\n",
+ "rms value of thyristor current=54.826 A\n",
+ "rms value of diode current=17.331 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No 470"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=4.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.035\n",
+ "\n",
+ "#Calculations\n",
+ "C=155*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_01=I_m1/math.sqrt(2) \n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2)\n",
+ "I_0=I_m/math.sqrt(2)\n",
+ "P_0=(I_0)**2*R \n",
+ "P_01=(I_01)**2*R \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=(phi1)*math.pi/(180*w) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of fundamental load current=%.2f A\" %I_01)\n",
+ "print(\"load power=%.1f W\" %P_0)\n",
+ "print(\"fundamental load power=%.1f W\" %P_01)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_m/2))\n",
+ "print(\"conduction time for thyristor=%.3f ms\" %(t1*1000))\n",
+ "print(\"Conduction time for diodes=%.3f ms\" %(t1*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of fundamental load current=20.02 A\n",
+ "load power=1632.5 W\n",
+ "fundamental load power=1602.6 W\n",
+ "rms value of thyristor current=14.285 A\n",
+ "conduction time for thyristor=3.736 ms\n",
+ "Conduction time for diodes=3.736 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8, Page No 473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi) \n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/R\n",
+ "P=I_01**2*R \n",
+ "V_or=math.sqrt((V_s/2)**2)\n",
+ "P=V_or**2/R \n",
+ "I_TP=V_s/(2*R)\n",
+ "I_or=I_TP\n",
+ "pf=I_01**2*R/(V_or*I_or) \n",
+ "DF=V_01/V_or \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01\n",
+ "\n",
+ "#Results\n",
+ "print(\"fundamental rms o/p voltage=%.3f V\" %V_01)\n",
+ "print(\"fundamental power to load=%.1f W\" %P)\n",
+ "print(\"total o/p power to load=%.1f W\" %P)\n",
+ "print(\"avg SCR current=%.2f A\" %(I_TP*180/360))\n",
+ "print(\"i/p pf=%.3f\" %pf) \n",
+ "print(\"distortion factor=%.1f\" %DF)\n",
+ "print(\"THD=%.3f\" %THD) \n",
+ "print(\"harmonic factor=%.4f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fundamental rms o/p voltage=103.536 V\n",
+ "fundamental power to load=1322.5 W\n",
+ "total o/p power to load=1322.5 W\n",
+ "avg SCR current=5.75 A\n",
+ "i/p pf=0.811\n",
+ "distortion factor=0.9\n",
+ "THD=0.483\n",
+ "harmonic factor=0.3333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.9 Page No 474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=60\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi) \n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi) \n",
+ "P_o=V_or**2/R \n",
+ "P_01=V_01**2/R \n",
+ "I_s=V_s/R \n",
+ "I_avg=I_s*math.pi/(2*math.pi) \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01 \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.0f V\" %V_or)\n",
+ "print(\"o/p power=%.0f W\" %P_o)\n",
+ "print(\"fundamental component of rms voltage=%.2f V\" %V_01)\n",
+ "print(\"fundamental freq o/p power=%.2f W\" %P_01) \n",
+ "print(\"peak current=%.0f A\" %I_s)\n",
+ "print(\"avg current of each transistor=%.0f A\" %I_avg)\n",
+ "print(\"peak reverse blocking voltage=%.0f V\" %V_s)\n",
+ "print(\"harmonic factor=%.4f\" %HF)\n",
+ "print(\"THD=%.4f\" %THD)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=60 V\n",
+ "o/p power=1200 W\n",
+ "fundamental component of rms voltage=54.02 V\n",
+ "fundamental freq o/p power=972.68 W\n",
+ "peak current=20 A\n",
+ "avg current of each transistor=10 A\n",
+ "peak reverse blocking voltage=60 V\n",
+ "harmonic factor=0.3333\n",
+ "THD=0.4834\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.10 Page No 475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "R=6.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "C=180*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "print(\"THD of voltage=%.4f\" %THD)\n",
+ "DF=V_01/V_or \n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7-X_C/7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7-X_C/7)/R))\n",
+ "I_01=19.403\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "I_or=I_m/math.sqrt(2)\n",
+ "I_oh=math.sqrt((I_m**2-I_m1**2)/2)\n",
+ "THD=I_oh/I_01 \n",
+ "DF=I_01/I_or \n",
+ "P_o=I_or**2*R \n",
+ "I_avg=P_o/V_s \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=1/(2*f)-t1 \n",
+ "I_p=I_m1 \n",
+ "I_t1=.46135*I_p \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nDF=%.1f\" %DF)\n",
+ "print(\"THD of current=%.4f\" %THD) \n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"avg value of load current=%.2f A\" %I_avg)\n",
+ "print(\"conduction time for thyristor=%.0f ms\" %(t1*1000))\n",
+ "print(\"conduction time for diodes=%.0f ms\" %(t1*1000))\n",
+ "print(\"peak transistor current=%.2f A\" %I_p)\n",
+ "print(\"rms transistor current=%.2f A\" %I_t1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "THD of voltage=0.4834\n",
+ "\n",
+ "DF=1.0\n",
+ "THD of current=0.1557\n",
+ "DF=0.988\n",
+ "load power=2313.5 W\n",
+ "avg value of load current=10.52 A\n",
+ "conduction time for thyristor=3 ms\n",
+ "conduction time for diodes=3 ms\n",
+ "peak transistor current=27.44 A\n",
+ "rms transistor current=12.66 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11 Page No 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=450.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_or=math.sqrt((V_s/(3*R))**2*2/3+(2*V_s/(3*R))**2*1/3) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(3*R))**2*2*math.pi/3+(2*V_s/(3*R))**2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "I_or=math.sqrt((1/(math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"for 180deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"power delivered to load=%.1f kW\" %(P/1000))\n",
+ "print(\"rms value of load current=%.0f A\" %I_T1)\n",
+ "print(\"for 120deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"rms value of load current=%.2f A\" %I_T1)\n",
+ "print(\"power delivered to load=%.3f kW\" %(P/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 180deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "power delivered to load=10.1 kW\n",
+ "rms value of load current=13 A\n",
+ "for 120deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "rms value of load current=12.99 A\n",
+ "power delivered to load=10.125 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12, Page No 510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "\n",
+ "#Calculations\n",
+ "X_L=w*L\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "Z1=math.sqrt(R**2+(X_L)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7)/R))\n",
+ "I_m1=4*V_s/(math.sqrt(2)*Z1*math.pi)\n",
+ "I_m3=4*V_s/(math.sqrt(2)*3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(math.sqrt(2)*5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(math.sqrt(2)*7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "P=I_m**2*R \n",
+ "I_01=I_m1*math.sin(math.radians(45))\n",
+ "I_03=I_m3*math.sin(math.radians(3*45))\n",
+ "I_05=I_m5*math.sin(math.radians(5*45))\n",
+ "I_07=I_m7*math.sin(math.radians(7*45))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "g=(180-90)/3+45/2\n",
+ "I_01=2*I_m1*math.sin(math.radians(g))*math.sin(math.radians(45/2))\n",
+ "I_03=2*I_m3*math.sin(math.radians(g*3))*math.sin(math.radians(3*45/2))\n",
+ "I_05=2*I_m5*math.sin(math.radians(g*5))*math.sin(math.radians(5*45/2))\n",
+ "I_07=2*I_m7*math.sin(math.radians(g*7))*math.sin(math.radians(7*45/2))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"using square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using quasi-square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using two symmitrical spaced pulses\")\n",
+ "print(\"power delivered=%.2f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "using square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using quasi-square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using two symmitrical spaced pulses\n",
+ "power delivered=845.87 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.14, Page No 520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "T=1/f\n",
+ "I=0.5\n",
+ "\n",
+ "#Calculations\n",
+ "di=I/T #di=di/dt\n",
+ "V_s=220.0\n",
+ "L=V_s/di \n",
+ "t=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "t_c=t*fos\n",
+ "R=10\n",
+ "C=t_c/(R*math.log(2))\n",
+ "\n",
+ "#Results \n",
+ "print(\"source inductance=%.1f H\" %L)\n",
+ "print(\"commutating capacitor=%.2f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source inductance=8.8 H\n",
+ "commutating capacitor=5.77 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15, Page No 539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=.01\n",
+ "C=10*10**-6\n",
+ "#Calculations\n",
+ "if (R**2)<(4*L/C) :\n",
+ " print(\"ckt will commutate on its own\")\n",
+ "else:\n",
+ " print(\"ckt will not commutate on its own\")\n",
+ "\n",
+ "xie=R/(2*L)\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "phi=math.degrees(math.atan(xie/w_r))\n",
+ "t=math.pi/w_r\n",
+ "V_s=1\n",
+ "v_L=V_s*(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180+phi))\n",
+ "v_c=V_s*(1-(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180-phi))) \n",
+ "di=V_s/L \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage across inductor(*V_s)=%.5f V\" %v_L) \n",
+ "print(\"voltage across capacitor(*V_s)=%.5f V\" %v_c)\n",
+ "print(\"di/dt*V_s (for t=0)=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt will commutate on its own\n",
+ "voltage across inductor(*V_s)=-0.60468 V\n",
+ "voltage across capacitor(*V_s)=1.60468 V\n",
+ "di/dt*V_s (for t=0)=100 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.006\n",
+ "C=1.2*10**-6\n",
+ "R=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=0.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=40\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=140\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p freq=%.2f Hz\" %f)\n",
+ "print(\"for R=40ohm\")\n",
+ "print(\"upper limit o/p freq=%.1f Hz\" %f)\n",
+ "print(\"for R=140ohm\")\n",
+ "print(\"lower limit o/p freq=%.1f Hz\" %f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p freq=239.81 Hz\n",
+ "for R=40ohm\n",
+ "upper limit o/p freq=239.8 Hz\n",
+ "for R=140ohm\n",
+ "lower limit o/p freq=239.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=5000.0\n",
+ "w=2*math.pi*f\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=60*10**-6\n",
+ "xie=R/(2*L)\n",
+ "C=7.5*10**-6\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "t_c=math.pi*(1/w-1/w_r) \n",
+ "fos=1.5\n",
+ "t_q=10*10**-6\n",
+ "f_max=1/(2*math.pi*(t_q*fos/math.pi+1/w_r)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"max possible operating freq=%.1f Hz\" %f_max)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt turn off time=21.39 us\n",
+ "max possible operating freq=5341.4 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18, Page No 541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=20.0\n",
+ "fos=2.0 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t*fos\n",
+ "n=1.0/3\n",
+ "R=20.0\n",
+ "C=n**2*t_c/(4*R*math.log(2)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of capacitor=%.2f uF\" %C)\n",
+ " #printing mistake in the answer in book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitor=0.08 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "V_p=math.sqrt(2)*V_s/3 \n",
+ "V_L=math.sqrt(3)*V_p \n",
+ "V_p1=math.sqrt(2)*V_s/math.pi \n",
+ "V_L1=math.sqrt(3)*V_p1 \n",
+ "V_oh=math.sqrt(V_L**2-V_L1**2)\n",
+ "\n",
+ "#Calculations\n",
+ "THD=V_oh/V_L1 \n",
+ "V_a1=2*V_s/math.pi\n",
+ "V_a5=2*V_s/(5*math.pi)\n",
+ "V_a7=2*V_s/(7*math.pi)\n",
+ "V_a11=2*V_s/(11*math.pi)\n",
+ "R=4.0\n",
+ "L=0.02\n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "Z1=math.sqrt(R**2+(w*L)**2)\n",
+ "Z5=math.sqrt(R**2+(5*w*L)**2)\n",
+ "Z7=math.sqrt(R**2+(7*w*L)**2)\n",
+ "Z11=math.sqrt(R**2+(11*w*L)**2)\n",
+ "I_a1=V_a1/Z1\n",
+ "I_a5=V_a5/Z5\n",
+ "I_a7=V_a7/Z7\n",
+ "I_a11=V_a11/Z11\n",
+ "I_or=math.sqrt((I_a1**2+I_a5**2+I_a7**2+I_a11**2)/2)\n",
+ "P=3*I_or**2*R \n",
+ "I_s=P/V_s \n",
+ "I_TA=I_s/3 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of phasor voltages=%.2f V\" %V_p)\n",
+ "print(\"rms value of line voltages=%.2f V\" %V_L)\n",
+ "print(\"fundamental component of phase voltage=%.3f V\" %V_p1)\n",
+ "print(\"fundamental component of line voltages=%.3f V\" %V_L1)\n",
+ "print(\"THD=%.7f\" %THD)\n",
+ "print(\"load power=%.1f W\" %P)\n",
+ "print(\"avg value of source current=%.3f A\" %I_s)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of phasor voltages=103.71 V\n",
+ "rms value of line voltages=179.63 V\n",
+ "fundamental component of phase voltage=99.035 V\n",
+ "fundamental component of line voltages=171.533 V\n",
+ "THD=0.3108419\n",
+ "load power=2127.6 W\n",
+ "avg value of source current=9.671 A\n",
+ "avg value of thyristor current=3.224 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter8_2.ipynb b/_Power_Electronics/Chapter8_2.ipynb new file mode 100755 index 00000000..721a9faf --- /dev/null +++ b/_Power_Electronics/Chapter8_2.ipynb @@ -0,0 +1,984 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Inverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T=0.1*10**-3\n",
+ "f=1.0/T\n",
+ "k=15*10**-6 #k=th/w\n",
+ "\n",
+ "#Calculations\n",
+ "th=2*math.pi*f*k\n",
+ "X_l=10.0\n",
+ "R=2.0\n",
+ "X_c=R*math.tan(th)+X_l\n",
+ "C=1/(2*math.pi*f*X_c) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of C=1.248 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 466"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi)\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "P_d=I_01**2*R \n",
+ "V=V_s/2\n",
+ "I_s=math.sqrt(2)*I_01/math.pi\n",
+ "P_s=V*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to load=%.1f W\" %P_d)\n",
+ "print(\"power delivered by both sources=%.1f W\" %(2*P_s))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to load=5359.9 W\n",
+ "power delivered by both sources=5359.9 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=4*V_s/(math.pi*math.sqrt(2))\n",
+ "R=1.0\n",
+ "X_L=6.0\n",
+ "X_c=7.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_c)**2)\n",
+ "P=I_01**2*R \n",
+ "I_s=math.sqrt(2)*I_01*(2*math.cos(math.radians(45)))/math.pi\n",
+ "P_s=V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to the source=%.3f kW\" %(P/1000))\n",
+ "print(\"\\npower from the source=%.3f kW\" %(P_s/1000))\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to the source=21.440 kW\n",
+ "\n",
+ "power from the source=21.440 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No 469"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_01=230.0\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "I_m=I_01*math.sqrt(2)\n",
+ "I_T1=I_m/2 \n",
+ "I_D1=0 \n",
+ "X_L=8.0\n",
+ "X_C=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=math.degrees(math.atan((X_L-X_C)/R))\n",
+ "I_T1=I_T1*math.sqrt(2)*0.47675 \n",
+ "I_D1=.1507025*I_m/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"when load R=2 ohm\")\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.0f A\" %I_D1)\n",
+ "print(\"when load R=2ohm % X_L=8ohm and X_C=6ohm\")\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_D1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when load R=2 ohm\n",
+ "rms value of thyristor current=54.83 A\n",
+ "rms value of diode current=17 A\n",
+ "when load R=2ohm % X_L=8ohm and X_C=6ohm\n",
+ "rms value of thyristor current=54.826 A\n",
+ "rms value of diode current=17.331 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No 470"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=4.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.035\n",
+ "\n",
+ "#Calculations\n",
+ "C=155*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_01=I_m1/math.sqrt(2) \n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2)\n",
+ "I_0=I_m/math.sqrt(2)\n",
+ "P_0=(I_0)**2*R \n",
+ "P_01=(I_01)**2*R \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=(phi1)*math.pi/(180*w) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of fundamental load current=%.2f A\" %I_01)\n",
+ "print(\"load power=%.1f W\" %P_0)\n",
+ "print(\"fundamental load power=%.1f W\" %P_01)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_m/2))\n",
+ "print(\"conduction time for thyristor=%.3f ms\" %(t1*1000))\n",
+ "print(\"Conduction time for diodes=%.3f ms\" %(t1*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of fundamental load current=20.02 A\n",
+ "load power=1632.5 W\n",
+ "fundamental load power=1602.6 W\n",
+ "rms value of thyristor current=14.285 A\n",
+ "conduction time for thyristor=3.736 ms\n",
+ "Conduction time for diodes=3.736 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8, Page No 473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi) \n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/R\n",
+ "P=I_01**2*R \n",
+ "V_or=math.sqrt((V_s/2)**2)\n",
+ "P=V_or**2/R \n",
+ "I_TP=V_s/(2*R)\n",
+ "I_or=I_TP\n",
+ "pf=I_01**2*R/(V_or*I_or) \n",
+ "DF=V_01/V_or \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01\n",
+ "\n",
+ "#Results\n",
+ "print(\"fundamental rms o/p voltage=%.3f V\" %V_01)\n",
+ "print(\"fundamental power to load=%.1f W\" %P)\n",
+ "print(\"total o/p power to load=%.1f W\" %P)\n",
+ "print(\"avg SCR current=%.2f A\" %(I_TP*180/360))\n",
+ "print(\"i/p pf=%.3f\" %pf) \n",
+ "print(\"distortion factor=%.1f\" %DF)\n",
+ "print(\"THD=%.3f\" %THD) \n",
+ "print(\"harmonic factor=%.4f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fundamental rms o/p voltage=103.536 V\n",
+ "fundamental power to load=1322.5 W\n",
+ "total o/p power to load=1322.5 W\n",
+ "avg SCR current=5.75 A\n",
+ "i/p pf=0.811\n",
+ "distortion factor=0.9\n",
+ "THD=0.483\n",
+ "harmonic factor=0.3333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.9 Page No 474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=60\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi) \n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi) \n",
+ "P_o=V_or**2/R \n",
+ "P_01=V_01**2/R \n",
+ "I_s=V_s/R \n",
+ "I_avg=I_s*math.pi/(2*math.pi) \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01 \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.0f V\" %V_or)\n",
+ "print(\"o/p power=%.0f W\" %P_o)\n",
+ "print(\"fundamental component of rms voltage=%.2f V\" %V_01)\n",
+ "print(\"fundamental freq o/p power=%.2f W\" %P_01) \n",
+ "print(\"peak current=%.0f A\" %I_s)\n",
+ "print(\"avg current of each transistor=%.0f A\" %I_avg)\n",
+ "print(\"peak reverse blocking voltage=%.0f V\" %V_s)\n",
+ "print(\"harmonic factor=%.4f\" %HF)\n",
+ "print(\"THD=%.4f\" %THD)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=60 V\n",
+ "o/p power=1200 W\n",
+ "fundamental component of rms voltage=54.02 V\n",
+ "fundamental freq o/p power=972.68 W\n",
+ "peak current=20 A\n",
+ "avg current of each transistor=10 A\n",
+ "peak reverse blocking voltage=60 V\n",
+ "harmonic factor=0.3333\n",
+ "THD=0.4834\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.10 Page No 475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "R=6.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "C=180*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "print(\"THD of voltage=%.4f\" %THD)\n",
+ "DF=V_01/V_or \n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7-X_C/7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7-X_C/7)/R))\n",
+ "I_01=19.403\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "I_or=I_m/math.sqrt(2)\n",
+ "I_oh=math.sqrt((I_m**2-I_m1**2)/2)\n",
+ "THD=I_oh/I_01 \n",
+ "DF=I_01/I_or \n",
+ "P_o=I_or**2*R \n",
+ "I_avg=P_o/V_s \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=1/(2*f)-t1 \n",
+ "I_p=I_m1 \n",
+ "I_t1=.46135*I_p \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nDF=%.1f\" %DF)\n",
+ "print(\"THD of current=%.4f\" %THD) \n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"avg value of load current=%.2f A\" %I_avg)\n",
+ "print(\"conduction time for thyristor=%.0f ms\" %(t1*1000))\n",
+ "print(\"conduction time for diodes=%.0f ms\" %(t1*1000))\n",
+ "print(\"peak transistor current=%.2f A\" %I_p)\n",
+ "print(\"rms transistor current=%.2f A\" %I_t1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "THD of voltage=0.4834\n",
+ "\n",
+ "DF=1.0\n",
+ "THD of current=0.1557\n",
+ "DF=0.988\n",
+ "load power=2313.5 W\n",
+ "avg value of load current=10.52 A\n",
+ "conduction time for thyristor=3 ms\n",
+ "conduction time for diodes=3 ms\n",
+ "peak transistor current=27.44 A\n",
+ "rms transistor current=12.66 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11 Page No 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=450.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_or=math.sqrt((V_s/(3*R))**2*2/3+(2*V_s/(3*R))**2*1/3) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(3*R))**2*2*math.pi/3+(2*V_s/(3*R))**2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "I_or=math.sqrt((1/(math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"for 180deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"power delivered to load=%.1f kW\" %(P/1000))\n",
+ "print(\"rms value of load current=%.0f A\" %I_T1)\n",
+ "print(\"for 120deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"rms value of load current=%.2f A\" %I_T1)\n",
+ "print(\"power delivered to load=%.3f kW\" %(P/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 180deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "power delivered to load=10.1 kW\n",
+ "rms value of load current=13 A\n",
+ "for 120deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "rms value of load current=12.99 A\n",
+ "power delivered to load=10.125 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12, Page No 510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "\n",
+ "#Calculations\n",
+ "X_L=w*L\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "Z1=math.sqrt(R**2+(X_L)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7)/R))\n",
+ "I_m1=4*V_s/(math.sqrt(2)*Z1*math.pi)\n",
+ "I_m3=4*V_s/(math.sqrt(2)*3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(math.sqrt(2)*5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(math.sqrt(2)*7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "P=I_m**2*R \n",
+ "I_01=I_m1*math.sin(math.radians(45))\n",
+ "I_03=I_m3*math.sin(math.radians(3*45))\n",
+ "I_05=I_m5*math.sin(math.radians(5*45))\n",
+ "I_07=I_m7*math.sin(math.radians(7*45))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "g=(180-90)/3+45/2\n",
+ "I_01=2*I_m1*math.sin(math.radians(g))*math.sin(math.radians(45/2))\n",
+ "I_03=2*I_m3*math.sin(math.radians(g*3))*math.sin(math.radians(3*45/2))\n",
+ "I_05=2*I_m5*math.sin(math.radians(g*5))*math.sin(math.radians(5*45/2))\n",
+ "I_07=2*I_m7*math.sin(math.radians(g*7))*math.sin(math.radians(7*45/2))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"using square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using quasi-square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using two symmitrical spaced pulses\")\n",
+ "print(\"power delivered=%.2f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "using square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using quasi-square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using two symmitrical spaced pulses\n",
+ "power delivered=845.87 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.14, Page No 520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "T=1/f\n",
+ "I=0.5\n",
+ "\n",
+ "#Calculations\n",
+ "di=I/T #di=di/dt\n",
+ "V_s=220.0\n",
+ "L=V_s/di \n",
+ "t=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "t_c=t*fos\n",
+ "R=10\n",
+ "C=t_c/(R*math.log(2))\n",
+ "\n",
+ "#Results \n",
+ "print(\"source inductance=%.1f H\" %L)\n",
+ "print(\"commutating capacitor=%.2f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source inductance=8.8 H\n",
+ "commutating capacitor=5.77 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15, Page No 539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=.01\n",
+ "C=10*10**-6\n",
+ "#Calculations\n",
+ "if (R**2)<(4*L/C) :\n",
+ " print(\"ckt will commutate on its own\")\n",
+ "else:\n",
+ " print(\"ckt will not commutate on its own\")\n",
+ "\n",
+ "xie=R/(2*L)\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "phi=math.degrees(math.atan(xie/w_r))\n",
+ "t=math.pi/w_r\n",
+ "V_s=1\n",
+ "v_L=V_s*(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180+phi))\n",
+ "v_c=V_s*(1-(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180-phi))) \n",
+ "di=V_s/L \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage across inductor(*V_s)=%.5f V\" %v_L) \n",
+ "print(\"voltage across capacitor(*V_s)=%.5f V\" %v_c)\n",
+ "print(\"di/dt*V_s (for t=0)=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt will commutate on its own\n",
+ "voltage across inductor(*V_s)=-0.60468 V\n",
+ "voltage across capacitor(*V_s)=1.60468 V\n",
+ "di/dt*V_s (for t=0)=100 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.006\n",
+ "C=1.2*10**-6\n",
+ "R=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=0.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=40\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=140\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p freq=%.2f Hz\" %f)\n",
+ "print(\"for R=40ohm\")\n",
+ "print(\"upper limit o/p freq=%.1f Hz\" %f)\n",
+ "print(\"for R=140ohm\")\n",
+ "print(\"lower limit o/p freq=%.1f Hz\" %f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p freq=239.81 Hz\n",
+ "for R=40ohm\n",
+ "upper limit o/p freq=239.8 Hz\n",
+ "for R=140ohm\n",
+ "lower limit o/p freq=239.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=5000.0\n",
+ "w=2*math.pi*f\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=60*10**-6\n",
+ "xie=R/(2*L)\n",
+ "C=7.5*10**-6\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "t_c=math.pi*(1/w-1/w_r) \n",
+ "fos=1.5\n",
+ "t_q=10*10**-6\n",
+ "f_max=1/(2*math.pi*(t_q*fos/math.pi+1/w_r)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"max possible operating freq=%.1f Hz\" %f_max)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt turn off time=21.39 us\n",
+ "max possible operating freq=5341.4 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18, Page No 541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=20.0\n",
+ "fos=2.0 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t*fos\n",
+ "n=1.0/3\n",
+ "R=20.0\n",
+ "C=n**2*t_c/(4*R*math.log(2)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of capacitor=%.2f uF\" %C)\n",
+ " #printing mistake in the answer in book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitor=0.08 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "V_p=math.sqrt(2)*V_s/3 \n",
+ "V_L=math.sqrt(3)*V_p \n",
+ "V_p1=math.sqrt(2)*V_s/math.pi \n",
+ "V_L1=math.sqrt(3)*V_p1 \n",
+ "V_oh=math.sqrt(V_L**2-V_L1**2)\n",
+ "\n",
+ "#Calculations\n",
+ "THD=V_oh/V_L1 \n",
+ "V_a1=2*V_s/math.pi\n",
+ "V_a5=2*V_s/(5*math.pi)\n",
+ "V_a7=2*V_s/(7*math.pi)\n",
+ "V_a11=2*V_s/(11*math.pi)\n",
+ "R=4.0\n",
+ "L=0.02\n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "Z1=math.sqrt(R**2+(w*L)**2)\n",
+ "Z5=math.sqrt(R**2+(5*w*L)**2)\n",
+ "Z7=math.sqrt(R**2+(7*w*L)**2)\n",
+ "Z11=math.sqrt(R**2+(11*w*L)**2)\n",
+ "I_a1=V_a1/Z1\n",
+ "I_a5=V_a5/Z5\n",
+ "I_a7=V_a7/Z7\n",
+ "I_a11=V_a11/Z11\n",
+ "I_or=math.sqrt((I_a1**2+I_a5**2+I_a7**2+I_a11**2)/2)\n",
+ "P=3*I_or**2*R \n",
+ "I_s=P/V_s \n",
+ "I_TA=I_s/3 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of phasor voltages=%.2f V\" %V_p)\n",
+ "print(\"rms value of line voltages=%.2f V\" %V_L)\n",
+ "print(\"fundamental component of phase voltage=%.3f V\" %V_p1)\n",
+ "print(\"fundamental component of line voltages=%.3f V\" %V_L1)\n",
+ "print(\"THD=%.7f\" %THD)\n",
+ "print(\"load power=%.1f W\" %P)\n",
+ "print(\"avg value of source current=%.3f A\" %I_s)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of phasor voltages=103.71 V\n",
+ "rms value of line voltages=179.63 V\n",
+ "fundamental component of phase voltage=99.035 V\n",
+ "fundamental component of line voltages=171.533 V\n",
+ "THD=0.3108419\n",
+ "load power=2127.6 W\n",
+ "avg value of source current=9.671 A\n",
+ "avg value of thyristor current=3.224 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter8_3.ipynb b/_Power_Electronics/Chapter8_3.ipynb new file mode 100755 index 00000000..721a9faf --- /dev/null +++ b/_Power_Electronics/Chapter8_3.ipynb @@ -0,0 +1,984 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Inverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T=0.1*10**-3\n",
+ "f=1.0/T\n",
+ "k=15*10**-6 #k=th/w\n",
+ "\n",
+ "#Calculations\n",
+ "th=2*math.pi*f*k\n",
+ "X_l=10.0\n",
+ "R=2.0\n",
+ "X_c=R*math.tan(th)+X_l\n",
+ "C=1/(2*math.pi*f*X_c) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of C=1.248 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 466"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi)\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "P_d=I_01**2*R \n",
+ "V=V_s/2\n",
+ "I_s=math.sqrt(2)*I_01/math.pi\n",
+ "P_s=V*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to load=%.1f W\" %P_d)\n",
+ "print(\"power delivered by both sources=%.1f W\" %(2*P_s))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to load=5359.9 W\n",
+ "power delivered by both sources=5359.9 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=4*V_s/(math.pi*math.sqrt(2))\n",
+ "R=1.0\n",
+ "X_L=6.0\n",
+ "X_c=7.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_c)**2)\n",
+ "P=I_01**2*R \n",
+ "I_s=math.sqrt(2)*I_01*(2*math.cos(math.radians(45)))/math.pi\n",
+ "P_s=V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to the source=%.3f kW\" %(P/1000))\n",
+ "print(\"\\npower from the source=%.3f kW\" %(P_s/1000))\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to the source=21.440 kW\n",
+ "\n",
+ "power from the source=21.440 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No 469"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_01=230.0\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "I_m=I_01*math.sqrt(2)\n",
+ "I_T1=I_m/2 \n",
+ "I_D1=0 \n",
+ "X_L=8.0\n",
+ "X_C=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=math.degrees(math.atan((X_L-X_C)/R))\n",
+ "I_T1=I_T1*math.sqrt(2)*0.47675 \n",
+ "I_D1=.1507025*I_m/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"when load R=2 ohm\")\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.0f A\" %I_D1)\n",
+ "print(\"when load R=2ohm % X_L=8ohm and X_C=6ohm\")\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_D1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when load R=2 ohm\n",
+ "rms value of thyristor current=54.83 A\n",
+ "rms value of diode current=17 A\n",
+ "when load R=2ohm % X_L=8ohm and X_C=6ohm\n",
+ "rms value of thyristor current=54.826 A\n",
+ "rms value of diode current=17.331 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No 470"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=4.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.035\n",
+ "\n",
+ "#Calculations\n",
+ "C=155*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_01=I_m1/math.sqrt(2) \n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2)\n",
+ "I_0=I_m/math.sqrt(2)\n",
+ "P_0=(I_0)**2*R \n",
+ "P_01=(I_01)**2*R \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=(phi1)*math.pi/(180*w) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of fundamental load current=%.2f A\" %I_01)\n",
+ "print(\"load power=%.1f W\" %P_0)\n",
+ "print(\"fundamental load power=%.1f W\" %P_01)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_m/2))\n",
+ "print(\"conduction time for thyristor=%.3f ms\" %(t1*1000))\n",
+ "print(\"Conduction time for diodes=%.3f ms\" %(t1*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of fundamental load current=20.02 A\n",
+ "load power=1632.5 W\n",
+ "fundamental load power=1602.6 W\n",
+ "rms value of thyristor current=14.285 A\n",
+ "conduction time for thyristor=3.736 ms\n",
+ "Conduction time for diodes=3.736 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8, Page No 473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi) \n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/R\n",
+ "P=I_01**2*R \n",
+ "V_or=math.sqrt((V_s/2)**2)\n",
+ "P=V_or**2/R \n",
+ "I_TP=V_s/(2*R)\n",
+ "I_or=I_TP\n",
+ "pf=I_01**2*R/(V_or*I_or) \n",
+ "DF=V_01/V_or \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01\n",
+ "\n",
+ "#Results\n",
+ "print(\"fundamental rms o/p voltage=%.3f V\" %V_01)\n",
+ "print(\"fundamental power to load=%.1f W\" %P)\n",
+ "print(\"total o/p power to load=%.1f W\" %P)\n",
+ "print(\"avg SCR current=%.2f A\" %(I_TP*180/360))\n",
+ "print(\"i/p pf=%.3f\" %pf) \n",
+ "print(\"distortion factor=%.1f\" %DF)\n",
+ "print(\"THD=%.3f\" %THD) \n",
+ "print(\"harmonic factor=%.4f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fundamental rms o/p voltage=103.536 V\n",
+ "fundamental power to load=1322.5 W\n",
+ "total o/p power to load=1322.5 W\n",
+ "avg SCR current=5.75 A\n",
+ "i/p pf=0.811\n",
+ "distortion factor=0.9\n",
+ "THD=0.483\n",
+ "harmonic factor=0.3333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.9 Page No 474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=60\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi) \n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi) \n",
+ "P_o=V_or**2/R \n",
+ "P_01=V_01**2/R \n",
+ "I_s=V_s/R \n",
+ "I_avg=I_s*math.pi/(2*math.pi) \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01 \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.0f V\" %V_or)\n",
+ "print(\"o/p power=%.0f W\" %P_o)\n",
+ "print(\"fundamental component of rms voltage=%.2f V\" %V_01)\n",
+ "print(\"fundamental freq o/p power=%.2f W\" %P_01) \n",
+ "print(\"peak current=%.0f A\" %I_s)\n",
+ "print(\"avg current of each transistor=%.0f A\" %I_avg)\n",
+ "print(\"peak reverse blocking voltage=%.0f V\" %V_s)\n",
+ "print(\"harmonic factor=%.4f\" %HF)\n",
+ "print(\"THD=%.4f\" %THD)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=60 V\n",
+ "o/p power=1200 W\n",
+ "fundamental component of rms voltage=54.02 V\n",
+ "fundamental freq o/p power=972.68 W\n",
+ "peak current=20 A\n",
+ "avg current of each transistor=10 A\n",
+ "peak reverse blocking voltage=60 V\n",
+ "harmonic factor=0.3333\n",
+ "THD=0.4834\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.10 Page No 475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "R=6.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "C=180*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "print(\"THD of voltage=%.4f\" %THD)\n",
+ "DF=V_01/V_or \n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7-X_C/7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7-X_C/7)/R))\n",
+ "I_01=19.403\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "I_or=I_m/math.sqrt(2)\n",
+ "I_oh=math.sqrt((I_m**2-I_m1**2)/2)\n",
+ "THD=I_oh/I_01 \n",
+ "DF=I_01/I_or \n",
+ "P_o=I_or**2*R \n",
+ "I_avg=P_o/V_s \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=1/(2*f)-t1 \n",
+ "I_p=I_m1 \n",
+ "I_t1=.46135*I_p \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nDF=%.1f\" %DF)\n",
+ "print(\"THD of current=%.4f\" %THD) \n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"avg value of load current=%.2f A\" %I_avg)\n",
+ "print(\"conduction time for thyristor=%.0f ms\" %(t1*1000))\n",
+ "print(\"conduction time for diodes=%.0f ms\" %(t1*1000))\n",
+ "print(\"peak transistor current=%.2f A\" %I_p)\n",
+ "print(\"rms transistor current=%.2f A\" %I_t1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "THD of voltage=0.4834\n",
+ "\n",
+ "DF=1.0\n",
+ "THD of current=0.1557\n",
+ "DF=0.988\n",
+ "load power=2313.5 W\n",
+ "avg value of load current=10.52 A\n",
+ "conduction time for thyristor=3 ms\n",
+ "conduction time for diodes=3 ms\n",
+ "peak transistor current=27.44 A\n",
+ "rms transistor current=12.66 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11 Page No 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=450.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_or=math.sqrt((V_s/(3*R))**2*2/3+(2*V_s/(3*R))**2*1/3) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(3*R))**2*2*math.pi/3+(2*V_s/(3*R))**2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "I_or=math.sqrt((1/(math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"for 180deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"power delivered to load=%.1f kW\" %(P/1000))\n",
+ "print(\"rms value of load current=%.0f A\" %I_T1)\n",
+ "print(\"for 120deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"rms value of load current=%.2f A\" %I_T1)\n",
+ "print(\"power delivered to load=%.3f kW\" %(P/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 180deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "power delivered to load=10.1 kW\n",
+ "rms value of load current=13 A\n",
+ "for 120deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "rms value of load current=12.99 A\n",
+ "power delivered to load=10.125 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12, Page No 510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "\n",
+ "#Calculations\n",
+ "X_L=w*L\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "Z1=math.sqrt(R**2+(X_L)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7)/R))\n",
+ "I_m1=4*V_s/(math.sqrt(2)*Z1*math.pi)\n",
+ "I_m3=4*V_s/(math.sqrt(2)*3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(math.sqrt(2)*5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(math.sqrt(2)*7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "P=I_m**2*R \n",
+ "I_01=I_m1*math.sin(math.radians(45))\n",
+ "I_03=I_m3*math.sin(math.radians(3*45))\n",
+ "I_05=I_m5*math.sin(math.radians(5*45))\n",
+ "I_07=I_m7*math.sin(math.radians(7*45))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "g=(180-90)/3+45/2\n",
+ "I_01=2*I_m1*math.sin(math.radians(g))*math.sin(math.radians(45/2))\n",
+ "I_03=2*I_m3*math.sin(math.radians(g*3))*math.sin(math.radians(3*45/2))\n",
+ "I_05=2*I_m5*math.sin(math.radians(g*5))*math.sin(math.radians(5*45/2))\n",
+ "I_07=2*I_m7*math.sin(math.radians(g*7))*math.sin(math.radians(7*45/2))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"using square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using quasi-square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using two symmitrical spaced pulses\")\n",
+ "print(\"power delivered=%.2f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "using square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using quasi-square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using two symmitrical spaced pulses\n",
+ "power delivered=845.87 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.14, Page No 520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "T=1/f\n",
+ "I=0.5\n",
+ "\n",
+ "#Calculations\n",
+ "di=I/T #di=di/dt\n",
+ "V_s=220.0\n",
+ "L=V_s/di \n",
+ "t=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "t_c=t*fos\n",
+ "R=10\n",
+ "C=t_c/(R*math.log(2))\n",
+ "\n",
+ "#Results \n",
+ "print(\"source inductance=%.1f H\" %L)\n",
+ "print(\"commutating capacitor=%.2f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source inductance=8.8 H\n",
+ "commutating capacitor=5.77 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15, Page No 539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=.01\n",
+ "C=10*10**-6\n",
+ "#Calculations\n",
+ "if (R**2)<(4*L/C) :\n",
+ " print(\"ckt will commutate on its own\")\n",
+ "else:\n",
+ " print(\"ckt will not commutate on its own\")\n",
+ "\n",
+ "xie=R/(2*L)\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "phi=math.degrees(math.atan(xie/w_r))\n",
+ "t=math.pi/w_r\n",
+ "V_s=1\n",
+ "v_L=V_s*(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180+phi))\n",
+ "v_c=V_s*(1-(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180-phi))) \n",
+ "di=V_s/L \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage across inductor(*V_s)=%.5f V\" %v_L) \n",
+ "print(\"voltage across capacitor(*V_s)=%.5f V\" %v_c)\n",
+ "print(\"di/dt*V_s (for t=0)=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt will commutate on its own\n",
+ "voltage across inductor(*V_s)=-0.60468 V\n",
+ "voltage across capacitor(*V_s)=1.60468 V\n",
+ "di/dt*V_s (for t=0)=100 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.006\n",
+ "C=1.2*10**-6\n",
+ "R=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=0.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=40\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=140\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p freq=%.2f Hz\" %f)\n",
+ "print(\"for R=40ohm\")\n",
+ "print(\"upper limit o/p freq=%.1f Hz\" %f)\n",
+ "print(\"for R=140ohm\")\n",
+ "print(\"lower limit o/p freq=%.1f Hz\" %f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p freq=239.81 Hz\n",
+ "for R=40ohm\n",
+ "upper limit o/p freq=239.8 Hz\n",
+ "for R=140ohm\n",
+ "lower limit o/p freq=239.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=5000.0\n",
+ "w=2*math.pi*f\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=60*10**-6\n",
+ "xie=R/(2*L)\n",
+ "C=7.5*10**-6\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "t_c=math.pi*(1/w-1/w_r) \n",
+ "fos=1.5\n",
+ "t_q=10*10**-6\n",
+ "f_max=1/(2*math.pi*(t_q*fos/math.pi+1/w_r)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"max possible operating freq=%.1f Hz\" %f_max)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt turn off time=21.39 us\n",
+ "max possible operating freq=5341.4 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18, Page No 541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=20.0\n",
+ "fos=2.0 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t*fos\n",
+ "n=1.0/3\n",
+ "R=20.0\n",
+ "C=n**2*t_c/(4*R*math.log(2)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of capacitor=%.2f uF\" %C)\n",
+ " #printing mistake in the answer in book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitor=0.08 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "V_p=math.sqrt(2)*V_s/3 \n",
+ "V_L=math.sqrt(3)*V_p \n",
+ "V_p1=math.sqrt(2)*V_s/math.pi \n",
+ "V_L1=math.sqrt(3)*V_p1 \n",
+ "V_oh=math.sqrt(V_L**2-V_L1**2)\n",
+ "\n",
+ "#Calculations\n",
+ "THD=V_oh/V_L1 \n",
+ "V_a1=2*V_s/math.pi\n",
+ "V_a5=2*V_s/(5*math.pi)\n",
+ "V_a7=2*V_s/(7*math.pi)\n",
+ "V_a11=2*V_s/(11*math.pi)\n",
+ "R=4.0\n",
+ "L=0.02\n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "Z1=math.sqrt(R**2+(w*L)**2)\n",
+ "Z5=math.sqrt(R**2+(5*w*L)**2)\n",
+ "Z7=math.sqrt(R**2+(7*w*L)**2)\n",
+ "Z11=math.sqrt(R**2+(11*w*L)**2)\n",
+ "I_a1=V_a1/Z1\n",
+ "I_a5=V_a5/Z5\n",
+ "I_a7=V_a7/Z7\n",
+ "I_a11=V_a11/Z11\n",
+ "I_or=math.sqrt((I_a1**2+I_a5**2+I_a7**2+I_a11**2)/2)\n",
+ "P=3*I_or**2*R \n",
+ "I_s=P/V_s \n",
+ "I_TA=I_s/3 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of phasor voltages=%.2f V\" %V_p)\n",
+ "print(\"rms value of line voltages=%.2f V\" %V_L)\n",
+ "print(\"fundamental component of phase voltage=%.3f V\" %V_p1)\n",
+ "print(\"fundamental component of line voltages=%.3f V\" %V_L1)\n",
+ "print(\"THD=%.7f\" %THD)\n",
+ "print(\"load power=%.1f W\" %P)\n",
+ "print(\"avg value of source current=%.3f A\" %I_s)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of phasor voltages=103.71 V\n",
+ "rms value of line voltages=179.63 V\n",
+ "fundamental component of phase voltage=99.035 V\n",
+ "fundamental component of line voltages=171.533 V\n",
+ "THD=0.3108419\n",
+ "load power=2127.6 W\n",
+ "avg value of source current=9.671 A\n",
+ "avg value of thyristor current=3.224 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter8_4.ipynb b/_Power_Electronics/Chapter8_4.ipynb new file mode 100755 index 00000000..721a9faf --- /dev/null +++ b/_Power_Electronics/Chapter8_4.ipynb @@ -0,0 +1,984 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Inverters"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T=0.1*10**-3\n",
+ "f=1.0/T\n",
+ "k=15*10**-6 #k=th/w\n",
+ "\n",
+ "#Calculations\n",
+ "th=2*math.pi*f*k\n",
+ "X_l=10.0\n",
+ "R=2.0\n",
+ "X_c=R*math.tan(th)+X_l\n",
+ "C=1/(2*math.pi*f*X_c) \n",
+ "\n",
+ "#Results\n",
+ "print(\"value of C=%.3f uF\" %(C*10**6))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of C=1.248 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 466"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi)\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "P_d=I_01**2*R \n",
+ "V=V_s/2\n",
+ "I_s=math.sqrt(2)*I_01/math.pi\n",
+ "P_s=V*I_s\n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to load=%.1f W\" %P_d)\n",
+ "print(\"power delivered by both sources=%.1f W\" %(2*P_s))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to load=5359.9 W\n",
+ "power delivered by both sources=5359.9 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 468"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=4*V_s/(math.pi*math.sqrt(2))\n",
+ "R=1.0\n",
+ "X_L=6.0\n",
+ "X_c=7.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_c)**2)\n",
+ "P=I_01**2*R \n",
+ "I_s=math.sqrt(2)*I_01*(2*math.cos(math.radians(45)))/math.pi\n",
+ "P_s=V_s*I_s \n",
+ "\n",
+ "#Results\n",
+ "print(\"power delivered to the source=%.3f kW\" %(P/1000))\n",
+ "print(\"\\npower from the source=%.3f kW\" %(P_s/1000))\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "power delivered to the source=21.440 kW\n",
+ "\n",
+ "power from the source=21.440 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No 469"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_01=230.0\n",
+ "R=2.0\n",
+ "I_01=V_01/R\n",
+ "I_m=I_01*math.sqrt(2)\n",
+ "I_T1=I_m/2 \n",
+ "I_D1=0 \n",
+ "X_L=8.0\n",
+ "X_C=6.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=math.degrees(math.atan((X_L-X_C)/R))\n",
+ "I_T1=I_T1*math.sqrt(2)*0.47675 \n",
+ "I_D1=.1507025*I_m/math.sqrt(2) \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"when load R=2 ohm\")\n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.0f A\" %I_D1)\n",
+ "print(\"when load R=2ohm % X_L=8ohm and X_C=6ohm\")\n",
+ "print(\"rms value of thyristor current=%.3f A\" %I_T1)\n",
+ "print(\"rms value of diode current=%.3f A\" %I_D1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "when load R=2 ohm\n",
+ "rms value of thyristor current=54.83 A\n",
+ "rms value of diode current=17 A\n",
+ "when load R=2ohm % X_L=8ohm and X_C=6ohm\n",
+ "rms value of thyristor current=54.826 A\n",
+ "rms value of diode current=17.331 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No 470"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=4.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.035\n",
+ "\n",
+ "#Calculations\n",
+ "C=155*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_01=I_m1/math.sqrt(2) \n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2)\n",
+ "I_0=I_m/math.sqrt(2)\n",
+ "P_0=(I_0)**2*R \n",
+ "P_01=(I_01)**2*R \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=(phi1)*math.pi/(180*w) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of fundamental load current=%.2f A\" %I_01)\n",
+ "print(\"load power=%.1f W\" %P_0)\n",
+ "print(\"fundamental load power=%.1f W\" %P_01)\n",
+ "print(\"rms value of thyristor current=%.3f A\" %(I_m/2))\n",
+ "print(\"conduction time for thyristor=%.3f ms\" %(t1*1000))\n",
+ "print(\"Conduction time for diodes=%.3f ms\" %(t1*1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of fundamental load current=20.02 A\n",
+ "load power=1632.5 W\n",
+ "fundamental load power=1602.6 W\n",
+ "rms value of thyristor current=14.285 A\n",
+ "conduction time for thyristor=3.736 ms\n",
+ "Conduction time for diodes=3.736 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8, Page No 473"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_01=2*V_s/(math.sqrt(2)*math.pi) \n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_01=V_01/R\n",
+ "P=I_01**2*R \n",
+ "V_or=math.sqrt((V_s/2)**2)\n",
+ "P=V_or**2/R \n",
+ "I_TP=V_s/(2*R)\n",
+ "I_or=I_TP\n",
+ "pf=I_01**2*R/(V_or*I_or) \n",
+ "DF=V_01/V_or \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01\n",
+ "\n",
+ "#Results\n",
+ "print(\"fundamental rms o/p voltage=%.3f V\" %V_01)\n",
+ "print(\"fundamental power to load=%.1f W\" %P)\n",
+ "print(\"total o/p power to load=%.1f W\" %P)\n",
+ "print(\"avg SCR current=%.2f A\" %(I_TP*180/360))\n",
+ "print(\"i/p pf=%.3f\" %pf) \n",
+ "print(\"distortion factor=%.1f\" %DF)\n",
+ "print(\"THD=%.3f\" %THD) \n",
+ "print(\"harmonic factor=%.4f\" %HF)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fundamental rms o/p voltage=103.536 V\n",
+ "fundamental power to load=1322.5 W\n",
+ "total o/p power to load=1322.5 W\n",
+ "avg SCR current=5.75 A\n",
+ "i/p pf=0.811\n",
+ "distortion factor=0.9\n",
+ "THD=0.483\n",
+ "harmonic factor=0.3333\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.9 Page No 474"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=60\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi) \n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi) \n",
+ "P_o=V_or**2/R \n",
+ "P_01=V_01**2/R \n",
+ "I_s=V_s/R \n",
+ "I_avg=I_s*math.pi/(2*math.pi) \n",
+ "V_03=V_01/3\n",
+ "HF=V_03/V_01 \n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.0f V\" %V_or)\n",
+ "print(\"o/p power=%.0f W\" %P_o)\n",
+ "print(\"fundamental component of rms voltage=%.2f V\" %V_01)\n",
+ "print(\"fundamental freq o/p power=%.2f W\" %P_01) \n",
+ "print(\"peak current=%.0f A\" %I_s)\n",
+ "print(\"avg current of each transistor=%.0f A\" %I_avg)\n",
+ "print(\"peak reverse blocking voltage=%.0f V\" %V_s)\n",
+ "print(\"harmonic factor=%.4f\" %HF)\n",
+ "print(\"THD=%.4f\" %THD)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=60 V\n",
+ "o/p power=1200 W\n",
+ "fundamental component of rms voltage=54.02 V\n",
+ "fundamental freq o/p power=972.68 W\n",
+ "peak current=20 A\n",
+ "avg current of each transistor=10 A\n",
+ "peak reverse blocking voltage=60 V\n",
+ "harmonic factor=0.3333\n",
+ "THD=0.4834\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.10 Page No 475"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "R=6.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "C=180*10**-6\n",
+ "X_L=w*L\n",
+ "X_C=1/(w*C)\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "V_oh=math.sqrt(V_or**2-V_01**2)\n",
+ "THD=V_oh/V_01 \n",
+ "print(\"THD of voltage=%.4f\" %THD)\n",
+ "DF=V_01/V_or \n",
+ "Z1=math.sqrt(R**2+(X_L-X_C)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L-X_C)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3-X_C/3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3-X_C/3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5-X_C/5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5-X_C/5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7-X_C/7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7-X_C/7)/R))\n",
+ "I_01=19.403\n",
+ "I_m1=4*V_s/(Z1*math.pi)\n",
+ "I_m3=4*V_s/(3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "I_or=I_m/math.sqrt(2)\n",
+ "I_oh=math.sqrt((I_m**2-I_m1**2)/2)\n",
+ "THD=I_oh/I_01 \n",
+ "DF=I_01/I_or \n",
+ "P_o=I_or**2*R \n",
+ "I_avg=P_o/V_s \n",
+ "t1=(180-phi1)*math.pi/(180*w) \n",
+ "t1=1/(2*f)-t1 \n",
+ "I_p=I_m1 \n",
+ "I_t1=.46135*I_p \n",
+ "\n",
+ "#Results\n",
+ "print(\"\\nDF=%.1f\" %DF)\n",
+ "print(\"THD of current=%.4f\" %THD) \n",
+ "print(\"DF=%.3f\" %DF)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"avg value of load current=%.2f A\" %I_avg)\n",
+ "print(\"conduction time for thyristor=%.0f ms\" %(t1*1000))\n",
+ "print(\"conduction time for diodes=%.0f ms\" %(t1*1000))\n",
+ "print(\"peak transistor current=%.2f A\" %I_p)\n",
+ "print(\"rms transistor current=%.2f A\" %I_t1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "THD of voltage=0.4834\n",
+ "\n",
+ "DF=1.0\n",
+ "THD of current=0.1557\n",
+ "DF=0.988\n",
+ "load power=2313.5 W\n",
+ "avg value of load current=10.52 A\n",
+ "conduction time for thyristor=3 ms\n",
+ "conduction time for diodes=3 ms\n",
+ "peak transistor current=27.44 A\n",
+ "rms transistor current=12.66 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.11 Page No 497"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=450.0\n",
+ "R=10.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_or=math.sqrt((V_s/(3*R))**2*2/3+(2*V_s/(3*R))**2*1/3) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(3*R))**2*2*math.pi/3+(2*V_s/(3*R))**2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "I_or=math.sqrt((1/(math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "I_T1=math.sqrt((1/(2*math.pi))*((V_s/(2*R))**2*2*math.pi/3)) \n",
+ "P=3*I_or**2*R \n",
+ "\n",
+ "#Results\n",
+ "print(\"for 180deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"power delivered to load=%.1f kW\" %(P/1000))\n",
+ "print(\"rms value of load current=%.0f A\" %I_T1)\n",
+ "print(\"for 120deg mode\")\n",
+ "print(\"rms value of load current=%.3f A\" %I_or)\n",
+ "print(\"rms value of load current=%.2f A\" %I_T1)\n",
+ "print(\"power delivered to load=%.3f kW\" %(P/1000))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for 180deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "power delivered to load=10.1 kW\n",
+ "rms value of load current=13 A\n",
+ "for 120deg mode\n",
+ "rms value of load current=18.371 A\n",
+ "rms value of load current=12.99 A\n",
+ "power delivered to load=10.125 kW\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.12, Page No 510"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "R=10.0\n",
+ "f=50.0\n",
+ "w=2*math.pi*f\n",
+ "L=0.03\n",
+ "\n",
+ "#Calculations\n",
+ "X_L=w*L\n",
+ "V_or=math.sqrt(V_s**2*math.pi/math.pi)\n",
+ "V_01=4*V_s/(math.sqrt(2)*math.pi)\n",
+ "Z1=math.sqrt(R**2+(X_L)**2)\n",
+ "phi1=-math.degrees(math.atan((X_L)/R))\n",
+ "Z3=math.sqrt(R**2+(X_L*3)**2)\n",
+ "phi3=math.degrees(math.atan((X_L*3)/R))\n",
+ "Z5=math.sqrt(R**2+(X_L*5)**2)\n",
+ "phi5=math.degrees(math.atan((X_L*5)/R))\n",
+ "Z7=math.sqrt(R**2+(X_L*7)**2)\n",
+ "phi7=math.degrees(math.atan((X_L*7)/R))\n",
+ "I_m1=4*V_s/(math.sqrt(2)*Z1*math.pi)\n",
+ "I_m3=4*V_s/(math.sqrt(2)*3*Z3*math.pi)\n",
+ "I_m5=4*V_s/(math.sqrt(2)*5*Z5*math.pi)\n",
+ "I_m7=4*V_s/(math.sqrt(2)*7*Z7*math.pi)\n",
+ "I_m=math.sqrt(I_m1**2+I_m3**2+I_m5**2+I_m7**2)\n",
+ "P=I_m**2*R \n",
+ "I_01=I_m1*math.sin(math.radians(45))\n",
+ "I_03=I_m3*math.sin(math.radians(3*45))\n",
+ "I_05=I_m5*math.sin(math.radians(5*45))\n",
+ "I_07=I_m7*math.sin(math.radians(7*45))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "g=(180-90)/3+45/2\n",
+ "I_01=2*I_m1*math.sin(math.radians(g))*math.sin(math.radians(45/2))\n",
+ "I_03=2*I_m3*math.sin(math.radians(g*3))*math.sin(math.radians(3*45/2))\n",
+ "I_05=2*I_m5*math.sin(math.radians(g*5))*math.sin(math.radians(5*45/2))\n",
+ "I_07=2*I_m7*math.sin(math.radians(g*7))*math.sin(math.radians(7*45/2))\n",
+ "I_0=(I_01**2+I_03**2+I_05**2+I_07**2)\n",
+ "P=I_0*R \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"using square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using quasi-square wave o/p\")\n",
+ "print(\"power delivered=%.2f W\" %P)\n",
+ "print(\"using two symmitrical spaced pulses\")\n",
+ "print(\"power delivered=%.2f W\" %P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "using square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using quasi-square wave o/p\n",
+ "power delivered=845.87 W\n",
+ "using two symmitrical spaced pulses\n",
+ "power delivered=845.87 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.14, Page No 520"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=50.0\n",
+ "T=1/f\n",
+ "I=0.5\n",
+ "\n",
+ "#Calculations\n",
+ "di=I/T #di=di/dt\n",
+ "V_s=220.0\n",
+ "L=V_s/di \n",
+ "t=20*10**-6\n",
+ "fos=2 #factor of safety\n",
+ "t_c=t*fos\n",
+ "R=10\n",
+ "C=t_c/(R*math.log(2))\n",
+ "\n",
+ "#Results \n",
+ "print(\"source inductance=%.1f H\" %L)\n",
+ "print(\"commutating capacitor=%.2f uF\" %(C*10**6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "source inductance=8.8 H\n",
+ "commutating capacitor=5.77 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.15, Page No 539"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=10.0\n",
+ "L=.01\n",
+ "C=10*10**-6\n",
+ "#Calculations\n",
+ "if (R**2)<(4*L/C) :\n",
+ " print(\"ckt will commutate on its own\")\n",
+ "else:\n",
+ " print(\"ckt will not commutate on its own\")\n",
+ "\n",
+ "xie=R/(2*L)\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "phi=math.degrees(math.atan(xie/w_r))\n",
+ "t=math.pi/w_r\n",
+ "V_s=1\n",
+ "v_L=V_s*(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180+phi))\n",
+ "v_c=V_s*(1-(w_o/w_r)*math.exp(-xie*t)*math.cos(math.radians(180-phi))) \n",
+ "di=V_s/L \n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"voltage across inductor(*V_s)=%.5f V\" %v_L) \n",
+ "print(\"voltage across capacitor(*V_s)=%.5f V\" %v_c)\n",
+ "print(\"di/dt*V_s (for t=0)=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt will commutate on its own\n",
+ "voltage across inductor(*V_s)=-0.60468 V\n",
+ "voltage across capacitor(*V_s)=1.60468 V\n",
+ "di/dt*V_s (for t=0)=100 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.16, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "L=0.006\n",
+ "C=1.2*10**-6\n",
+ "R=100.0\n",
+ "\n",
+ "#Calculations\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=0.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=40\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "R=140\n",
+ "T=math.pi/math.sqrt(1/(L*C)-(R/(2*L))**2)\n",
+ "T_off=.2*10**-3\n",
+ "f=1/(2*(T+T_off)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"o/p freq=%.2f Hz\" %f)\n",
+ "print(\"for R=40ohm\")\n",
+ "print(\"upper limit o/p freq=%.1f Hz\" %f)\n",
+ "print(\"for R=140ohm\")\n",
+ "print(\"lower limit o/p freq=%.1f Hz\" %f)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "o/p freq=239.81 Hz\n",
+ "for R=40ohm\n",
+ "upper limit o/p freq=239.8 Hz\n",
+ "for R=140ohm\n",
+ "lower limit o/p freq=239.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.17, Page No 540"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "f=5000.0\n",
+ "w=2*math.pi*f\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "L=60*10**-6\n",
+ "xie=R/(2*L)\n",
+ "C=7.5*10**-6\n",
+ "w_o=1/math.sqrt(L*C)\n",
+ "w_r=math.sqrt(w_o**2-xie**2)\n",
+ "t_c=math.pi*(1/w-1/w_r) \n",
+ "fos=1.5\n",
+ "t_q=10*10**-6\n",
+ "f_max=1/(2*math.pi*(t_q*fos/math.pi+1/w_r)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"ckt turn off time=%.2f us\" %(t_c*10**6))\n",
+ "print(\"max possible operating freq=%.1f Hz\" %f_max)\n",
+ " #Answers have small variations from that in the book due to difference in the rounding off of digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ckt turn off time=21.39 us\n",
+ "max possible operating freq=5341.4 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.18, Page No 541"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=30.0\n",
+ "R=10.0\n",
+ "P=5000.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_s=math.sqrt(P*R*2*math.pi/(2*3)/(math.pi/3+math.sqrt(3)*math.cos(math.radians(2*a))/2))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "I_or=math.sqrt(P*R)\n",
+ "V_s=I_or*math.pi/(math.sqrt(2)*3*math.cos(math.radians(a)))\n",
+ "V_ph=V_s/math.sqrt(3) \n",
+ "\n",
+ "#Results\n",
+ "print(\"per phase voltage V_ph=%.3f V\" %V_ph) \n",
+ "print(\"for constant load current\")\n",
+ "print(\"V_ph=%.2f V\" %V_ph)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "per phase voltage V_ph=110.384 V\n",
+ "for constant load current\n",
+ "V_ph=110.38 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.19, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t=20.0\n",
+ "fos=2.0 #factor of safety\n",
+ "\n",
+ "#Calculations\n",
+ "t_c=t*fos\n",
+ "n=1.0/3\n",
+ "R=20.0\n",
+ "C=n**2*t_c/(4*R*math.log(2)) \n",
+ "\n",
+ "#Results \n",
+ "print(\"value of capacitor=%.2f uF\" %C)\n",
+ " #printing mistake in the answer in book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "value of capacitor=0.08 uF\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.20, Page No 547"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=220.0\n",
+ "V_p=math.sqrt(2)*V_s/3 \n",
+ "V_L=math.sqrt(3)*V_p \n",
+ "V_p1=math.sqrt(2)*V_s/math.pi \n",
+ "V_L1=math.sqrt(3)*V_p1 \n",
+ "V_oh=math.sqrt(V_L**2-V_L1**2)\n",
+ "\n",
+ "#Calculations\n",
+ "THD=V_oh/V_L1 \n",
+ "V_a1=2*V_s/math.pi\n",
+ "V_a5=2*V_s/(5*math.pi)\n",
+ "V_a7=2*V_s/(7*math.pi)\n",
+ "V_a11=2*V_s/(11*math.pi)\n",
+ "R=4.0\n",
+ "L=0.02\n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "Z1=math.sqrt(R**2+(w*L)**2)\n",
+ "Z5=math.sqrt(R**2+(5*w*L)**2)\n",
+ "Z7=math.sqrt(R**2+(7*w*L)**2)\n",
+ "Z11=math.sqrt(R**2+(11*w*L)**2)\n",
+ "I_a1=V_a1/Z1\n",
+ "I_a5=V_a5/Z5\n",
+ "I_a7=V_a7/Z7\n",
+ "I_a11=V_a11/Z11\n",
+ "I_or=math.sqrt((I_a1**2+I_a5**2+I_a7**2+I_a11**2)/2)\n",
+ "P=3*I_or**2*R \n",
+ "I_s=P/V_s \n",
+ "I_TA=I_s/3 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of phasor voltages=%.2f V\" %V_p)\n",
+ "print(\"rms value of line voltages=%.2f V\" %V_L)\n",
+ "print(\"fundamental component of phase voltage=%.3f V\" %V_p1)\n",
+ "print(\"fundamental component of line voltages=%.3f V\" %V_L1)\n",
+ "print(\"THD=%.7f\" %THD)\n",
+ "print(\"load power=%.1f W\" %P)\n",
+ "print(\"avg value of source current=%.3f A\" %I_s)\n",
+ "print(\"avg value of thyristor current=%.3f A\" %I_TA)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of phasor voltages=103.71 V\n",
+ "rms value of line voltages=179.63 V\n",
+ "fundamental component of phase voltage=99.035 V\n",
+ "fundamental component of line voltages=171.533 V\n",
+ "THD=0.3108419\n",
+ "load power=2127.6 W\n",
+ "avg value of source current=9.671 A\n",
+ "avg value of thyristor current=3.224 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter9.ipynb b/_Power_Electronics/Chapter9.ipynb new file mode 100755 index 00000000..052c4736 --- /dev/null +++ b/_Power_Electronics/Chapter9.ipynb @@ -0,0 +1,388 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : AC Voltage Controllers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/2)*math.sqrt(1/math.pi*((2*math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "V_o=math.sqrt(2)*V_s/(2*math.pi)*(math.cos(math.radians(a))-1)\n",
+ "I_ON=V_o/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"i/p pf=%.4f\" %pf)\n",
+ "print(\"avg i/p current=%.4f A\" %I_ON)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=224.716 V\n",
+ "load power=2524.9 W\n",
+ "i/p pf=0.9770\n",
+ "avg i/p current=-0.7581 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_s)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "I_TA=math.sqrt(2)*V_s/(2*math.pi*R)*(math.cos(math.radians(a))+1) \n",
+ "I_Tr=math.sqrt(2)*V_s/(2*R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.2f W\" %P_o)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=219.304 V\n",
+ "load power=2404.71 W\n",
+ "i/p pf=0.95\n",
+ "avg thyristor current=4.42 A\n",
+ "rms value of thyristor current=7.75 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No 564"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "n=6.0 #on cycles\n",
+ "m=4.0 #off cycles\n",
+ "\n",
+ "#Calculations\n",
+ "k=n/(n+m)\n",
+ "V_or=V_s*math.sqrt(k) \n",
+ "pf=math.sqrt(k) \n",
+ "R=15\n",
+ "I_m=V_s*math.sqrt(2)/R\n",
+ "I_TA=k*I_m/math.pi\n",
+ "I_TR=I_m*math.sqrt(k)/2 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of o/ voltage=%.2f V\" %V_or)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_TR)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/ voltage=178.16 V\n",
+ "i/p pf=0.77\n",
+ "avg thyristor current=4.14 A\n",
+ "rms value of thyristor current=8.40 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TAM1=2*V_m/(2*math.pi*R) \n",
+ "I_TRM2=V_m/(2*R) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=math.pi/w \n",
+ " \n",
+ "#Results\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM1)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TRM2)\n",
+ "print(\"ckt turn off time=%.0f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of avg thyristor current=34.512 A\n",
+ "max value of avg thyristor current=54.212 A\n",
+ "ckt turn off time=10 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=3.0\n",
+ "X_L=4.0\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R)) \n",
+ "V_s=230\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_s/Z \n",
+ "P=I_or**2*R \n",
+ "I_s=I_or\n",
+ "pf=P/(V_s*I_s) \n",
+ "I_TAM=math.sqrt(2)*V_s/(math.pi*Z) \n",
+ "I_Tm=math.sqrt(2)*V_s/(2*Z) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "di=math.sqrt(2)*V_s*w/Z \n",
+ "\n",
+ "#Results\n",
+ "print(\"min firing angle=%.2f deg\" %phi)\n",
+ "print(\"\\nmax firing angle=%.0f deg\" %180)\n",
+ "print(\"i/p pf=%.1f\" %pf)\n",
+ "print(\"max value of rms load current=%.0f A\" %I_or)\n",
+ "print(\"max power=%.0f W\" %P)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM)\n",
+ "print(\"max value of rms thyristor current=%.3f A\" %I_Tm)\n",
+ "print(\"di/dt=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min firing angle=53.13 deg\n",
+ "\n",
+ "max firing angle=180 deg\n",
+ "i/p pf=0.6\n",
+ "max value of rms load current=46 A\n",
+ "max power=6348 W\n",
+ "max value of avg thyristor current=20.707 A\n",
+ "max value of rms thyristor current=32.527 A\n",
+ "di/dt=20437 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 576"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "R=3.0 #ohm\n",
+ "X_L=5.0 #ohm\n",
+ "a=120.0 #firing angle delay\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R))\n",
+ "b=0\n",
+ "i=1\n",
+ "while (i>0) :\n",
+ " LHS=math.sin(math.radians(b-a))\n",
+ " RHS=math.sin(math.radians(a-phi))*math.exp(-(R/X_L)*(b-a)*math.pi/180)\n",
+ " if math.fabs(LHS-RHS)<= 0.01 :\n",
+ " B=b\n",
+ " i=2\n",
+ " break\n",
+ " \n",
+ " b=b+.1 \n",
+ "V_or=math.sqrt(2)*V*math.sqrt((1/(2*math.pi))*((B-a)*math.pi/180+(math.sin(math.radians(2*a))-math.sin(math.radians(2*B)))/2))\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"Extinction angle=%.1f deg\" %B) #answer in the book is wrong as formulae for RHS is wrongly employed\n",
+ "print(\"rms value of output voltage=%.2f V\" %V_or) #answer do not match due to wrong B in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extinction angle=156.1 deg\n",
+ "rms value of output voltage=97.75 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page No 581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=60.0\n",
+ "R=20.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt((V_m**2/(2*math.pi))*(a*math.pi/180-math.sin(math.radians(2*a))/2)+(2*V_m**2/(math.pi))*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2)) \n",
+ "I_T1r=(V_m/R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "I_T3r=(V_m/(2*R))*math.sqrt(1/math.pi*((a*math.pi/180)-math.sin(math.radians(2*a))/2)) \n",
+ "I1=math.sqrt(2)*I_T1r\n",
+ "I3=math.sqrt((math.sqrt(2)*I_T1r)**2+(math.sqrt(2)*I_T3r)**2)\n",
+ "r=V_s*(I1+I3) \n",
+ "P_o=V_or**2/R\n",
+ "pf=P_o/r \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms value of current for upper thyristors=%.2f A\" %I_T1r)\n",
+ "print(\"rms value of current for lower thyristors=%.2f A\" %I_T3r)\n",
+ "print(\"t/f VA rating=%.2f VA\" %r)\n",
+ "print(\"i/p pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=424.94 V\n",
+ "rms value of current for upper thyristors=14.59 A\n",
+ "rms value of current for lower thyristors=3.60 A\n",
+ "t/f VA rating=9631.61 VA\n",
+ "i/p pf=0.94\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter9_1.ipynb b/_Power_Electronics/Chapter9_1.ipynb new file mode 100755 index 00000000..052c4736 --- /dev/null +++ b/_Power_Electronics/Chapter9_1.ipynb @@ -0,0 +1,388 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : AC Voltage Controllers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/2)*math.sqrt(1/math.pi*((2*math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "V_o=math.sqrt(2)*V_s/(2*math.pi)*(math.cos(math.radians(a))-1)\n",
+ "I_ON=V_o/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"i/p pf=%.4f\" %pf)\n",
+ "print(\"avg i/p current=%.4f A\" %I_ON)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=224.716 V\n",
+ "load power=2524.9 W\n",
+ "i/p pf=0.9770\n",
+ "avg i/p current=-0.7581 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_s)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "I_TA=math.sqrt(2)*V_s/(2*math.pi*R)*(math.cos(math.radians(a))+1) \n",
+ "I_Tr=math.sqrt(2)*V_s/(2*R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.2f W\" %P_o)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=219.304 V\n",
+ "load power=2404.71 W\n",
+ "i/p pf=0.95\n",
+ "avg thyristor current=4.42 A\n",
+ "rms value of thyristor current=7.75 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No 564"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "n=6.0 #on cycles\n",
+ "m=4.0 #off cycles\n",
+ "\n",
+ "#Calculations\n",
+ "k=n/(n+m)\n",
+ "V_or=V_s*math.sqrt(k) \n",
+ "pf=math.sqrt(k) \n",
+ "R=15\n",
+ "I_m=V_s*math.sqrt(2)/R\n",
+ "I_TA=k*I_m/math.pi\n",
+ "I_TR=I_m*math.sqrt(k)/2 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of o/ voltage=%.2f V\" %V_or)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_TR)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/ voltage=178.16 V\n",
+ "i/p pf=0.77\n",
+ "avg thyristor current=4.14 A\n",
+ "rms value of thyristor current=8.40 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TAM1=2*V_m/(2*math.pi*R) \n",
+ "I_TRM2=V_m/(2*R) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=math.pi/w \n",
+ " \n",
+ "#Results\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM1)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TRM2)\n",
+ "print(\"ckt turn off time=%.0f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of avg thyristor current=34.512 A\n",
+ "max value of avg thyristor current=54.212 A\n",
+ "ckt turn off time=10 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=3.0\n",
+ "X_L=4.0\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R)) \n",
+ "V_s=230\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_s/Z \n",
+ "P=I_or**2*R \n",
+ "I_s=I_or\n",
+ "pf=P/(V_s*I_s) \n",
+ "I_TAM=math.sqrt(2)*V_s/(math.pi*Z) \n",
+ "I_Tm=math.sqrt(2)*V_s/(2*Z) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "di=math.sqrt(2)*V_s*w/Z \n",
+ "\n",
+ "#Results\n",
+ "print(\"min firing angle=%.2f deg\" %phi)\n",
+ "print(\"\\nmax firing angle=%.0f deg\" %180)\n",
+ "print(\"i/p pf=%.1f\" %pf)\n",
+ "print(\"max value of rms load current=%.0f A\" %I_or)\n",
+ "print(\"max power=%.0f W\" %P)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM)\n",
+ "print(\"max value of rms thyristor current=%.3f A\" %I_Tm)\n",
+ "print(\"di/dt=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min firing angle=53.13 deg\n",
+ "\n",
+ "max firing angle=180 deg\n",
+ "i/p pf=0.6\n",
+ "max value of rms load current=46 A\n",
+ "max power=6348 W\n",
+ "max value of avg thyristor current=20.707 A\n",
+ "max value of rms thyristor current=32.527 A\n",
+ "di/dt=20437 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 576"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "R=3.0 #ohm\n",
+ "X_L=5.0 #ohm\n",
+ "a=120.0 #firing angle delay\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R))\n",
+ "b=0\n",
+ "i=1\n",
+ "while (i>0) :\n",
+ " LHS=math.sin(math.radians(b-a))\n",
+ " RHS=math.sin(math.radians(a-phi))*math.exp(-(R/X_L)*(b-a)*math.pi/180)\n",
+ " if math.fabs(LHS-RHS)<= 0.01 :\n",
+ " B=b\n",
+ " i=2\n",
+ " break\n",
+ " \n",
+ " b=b+.1 \n",
+ "V_or=math.sqrt(2)*V*math.sqrt((1/(2*math.pi))*((B-a)*math.pi/180+(math.sin(math.radians(2*a))-math.sin(math.radians(2*B)))/2))\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"Extinction angle=%.1f deg\" %B) #answer in the book is wrong as formulae for RHS is wrongly employed\n",
+ "print(\"rms value of output voltage=%.2f V\" %V_or) #answer do not match due to wrong B in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extinction angle=156.1 deg\n",
+ "rms value of output voltage=97.75 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page No 581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=60.0\n",
+ "R=20.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt((V_m**2/(2*math.pi))*(a*math.pi/180-math.sin(math.radians(2*a))/2)+(2*V_m**2/(math.pi))*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2)) \n",
+ "I_T1r=(V_m/R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "I_T3r=(V_m/(2*R))*math.sqrt(1/math.pi*((a*math.pi/180)-math.sin(math.radians(2*a))/2)) \n",
+ "I1=math.sqrt(2)*I_T1r\n",
+ "I3=math.sqrt((math.sqrt(2)*I_T1r)**2+(math.sqrt(2)*I_T3r)**2)\n",
+ "r=V_s*(I1+I3) \n",
+ "P_o=V_or**2/R\n",
+ "pf=P_o/r \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms value of current for upper thyristors=%.2f A\" %I_T1r)\n",
+ "print(\"rms value of current for lower thyristors=%.2f A\" %I_T3r)\n",
+ "print(\"t/f VA rating=%.2f VA\" %r)\n",
+ "print(\"i/p pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=424.94 V\n",
+ "rms value of current for upper thyristors=14.59 A\n",
+ "rms value of current for lower thyristors=3.60 A\n",
+ "t/f VA rating=9631.61 VA\n",
+ "i/p pf=0.94\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter9_2.ipynb b/_Power_Electronics/Chapter9_2.ipynb new file mode 100755 index 00000000..052c4736 --- /dev/null +++ b/_Power_Electronics/Chapter9_2.ipynb @@ -0,0 +1,388 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : AC Voltage Controllers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/2)*math.sqrt(1/math.pi*((2*math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "V_o=math.sqrt(2)*V_s/(2*math.pi)*(math.cos(math.radians(a))-1)\n",
+ "I_ON=V_o/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"i/p pf=%.4f\" %pf)\n",
+ "print(\"avg i/p current=%.4f A\" %I_ON)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=224.716 V\n",
+ "load power=2524.9 W\n",
+ "i/p pf=0.9770\n",
+ "avg i/p current=-0.7581 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_s)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "I_TA=math.sqrt(2)*V_s/(2*math.pi*R)*(math.cos(math.radians(a))+1) \n",
+ "I_Tr=math.sqrt(2)*V_s/(2*R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.2f W\" %P_o)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=219.304 V\n",
+ "load power=2404.71 W\n",
+ "i/p pf=0.95\n",
+ "avg thyristor current=4.42 A\n",
+ "rms value of thyristor current=7.75 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No 564"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "n=6.0 #on cycles\n",
+ "m=4.0 #off cycles\n",
+ "\n",
+ "#Calculations\n",
+ "k=n/(n+m)\n",
+ "V_or=V_s*math.sqrt(k) \n",
+ "pf=math.sqrt(k) \n",
+ "R=15\n",
+ "I_m=V_s*math.sqrt(2)/R\n",
+ "I_TA=k*I_m/math.pi\n",
+ "I_TR=I_m*math.sqrt(k)/2 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of o/ voltage=%.2f V\" %V_or)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_TR)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/ voltage=178.16 V\n",
+ "i/p pf=0.77\n",
+ "avg thyristor current=4.14 A\n",
+ "rms value of thyristor current=8.40 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TAM1=2*V_m/(2*math.pi*R) \n",
+ "I_TRM2=V_m/(2*R) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=math.pi/w \n",
+ " \n",
+ "#Results\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM1)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TRM2)\n",
+ "print(\"ckt turn off time=%.0f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of avg thyristor current=34.512 A\n",
+ "max value of avg thyristor current=54.212 A\n",
+ "ckt turn off time=10 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=3.0\n",
+ "X_L=4.0\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R)) \n",
+ "V_s=230\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_s/Z \n",
+ "P=I_or**2*R \n",
+ "I_s=I_or\n",
+ "pf=P/(V_s*I_s) \n",
+ "I_TAM=math.sqrt(2)*V_s/(math.pi*Z) \n",
+ "I_Tm=math.sqrt(2)*V_s/(2*Z) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "di=math.sqrt(2)*V_s*w/Z \n",
+ "\n",
+ "#Results\n",
+ "print(\"min firing angle=%.2f deg\" %phi)\n",
+ "print(\"\\nmax firing angle=%.0f deg\" %180)\n",
+ "print(\"i/p pf=%.1f\" %pf)\n",
+ "print(\"max value of rms load current=%.0f A\" %I_or)\n",
+ "print(\"max power=%.0f W\" %P)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM)\n",
+ "print(\"max value of rms thyristor current=%.3f A\" %I_Tm)\n",
+ "print(\"di/dt=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min firing angle=53.13 deg\n",
+ "\n",
+ "max firing angle=180 deg\n",
+ "i/p pf=0.6\n",
+ "max value of rms load current=46 A\n",
+ "max power=6348 W\n",
+ "max value of avg thyristor current=20.707 A\n",
+ "max value of rms thyristor current=32.527 A\n",
+ "di/dt=20437 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 576"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "R=3.0 #ohm\n",
+ "X_L=5.0 #ohm\n",
+ "a=120.0 #firing angle delay\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R))\n",
+ "b=0\n",
+ "i=1\n",
+ "while (i>0) :\n",
+ " LHS=math.sin(math.radians(b-a))\n",
+ " RHS=math.sin(math.radians(a-phi))*math.exp(-(R/X_L)*(b-a)*math.pi/180)\n",
+ " if math.fabs(LHS-RHS)<= 0.01 :\n",
+ " B=b\n",
+ " i=2\n",
+ " break\n",
+ " \n",
+ " b=b+.1 \n",
+ "V_or=math.sqrt(2)*V*math.sqrt((1/(2*math.pi))*((B-a)*math.pi/180+(math.sin(math.radians(2*a))-math.sin(math.radians(2*B)))/2))\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"Extinction angle=%.1f deg\" %B) #answer in the book is wrong as formulae for RHS is wrongly employed\n",
+ "print(\"rms value of output voltage=%.2f V\" %V_or) #answer do not match due to wrong B in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extinction angle=156.1 deg\n",
+ "rms value of output voltage=97.75 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page No 581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=60.0\n",
+ "R=20.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt((V_m**2/(2*math.pi))*(a*math.pi/180-math.sin(math.radians(2*a))/2)+(2*V_m**2/(math.pi))*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2)) \n",
+ "I_T1r=(V_m/R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "I_T3r=(V_m/(2*R))*math.sqrt(1/math.pi*((a*math.pi/180)-math.sin(math.radians(2*a))/2)) \n",
+ "I1=math.sqrt(2)*I_T1r\n",
+ "I3=math.sqrt((math.sqrt(2)*I_T1r)**2+(math.sqrt(2)*I_T3r)**2)\n",
+ "r=V_s*(I1+I3) \n",
+ "P_o=V_or**2/R\n",
+ "pf=P_o/r \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms value of current for upper thyristors=%.2f A\" %I_T1r)\n",
+ "print(\"rms value of current for lower thyristors=%.2f A\" %I_T3r)\n",
+ "print(\"t/f VA rating=%.2f VA\" %r)\n",
+ "print(\"i/p pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=424.94 V\n",
+ "rms value of current for upper thyristors=14.59 A\n",
+ "rms value of current for lower thyristors=3.60 A\n",
+ "t/f VA rating=9631.61 VA\n",
+ "i/p pf=0.94\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter9_3.ipynb b/_Power_Electronics/Chapter9_3.ipynb new file mode 100755 index 00000000..052c4736 --- /dev/null +++ b/_Power_Electronics/Chapter9_3.ipynb @@ -0,0 +1,388 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : AC Voltage Controllers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/2)*math.sqrt(1/math.pi*((2*math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "V_o=math.sqrt(2)*V_s/(2*math.pi)*(math.cos(math.radians(a))-1)\n",
+ "I_ON=V_o/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"i/p pf=%.4f\" %pf)\n",
+ "print(\"avg i/p current=%.4f A\" %I_ON)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=224.716 V\n",
+ "load power=2524.9 W\n",
+ "i/p pf=0.9770\n",
+ "avg i/p current=-0.7581 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_s)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "I_TA=math.sqrt(2)*V_s/(2*math.pi*R)*(math.cos(math.radians(a))+1) \n",
+ "I_Tr=math.sqrt(2)*V_s/(2*R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.2f W\" %P_o)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=219.304 V\n",
+ "load power=2404.71 W\n",
+ "i/p pf=0.95\n",
+ "avg thyristor current=4.42 A\n",
+ "rms value of thyristor current=7.75 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No 564"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "n=6.0 #on cycles\n",
+ "m=4.0 #off cycles\n",
+ "\n",
+ "#Calculations\n",
+ "k=n/(n+m)\n",
+ "V_or=V_s*math.sqrt(k) \n",
+ "pf=math.sqrt(k) \n",
+ "R=15\n",
+ "I_m=V_s*math.sqrt(2)/R\n",
+ "I_TA=k*I_m/math.pi\n",
+ "I_TR=I_m*math.sqrt(k)/2 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of o/ voltage=%.2f V\" %V_or)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_TR)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/ voltage=178.16 V\n",
+ "i/p pf=0.77\n",
+ "avg thyristor current=4.14 A\n",
+ "rms value of thyristor current=8.40 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TAM1=2*V_m/(2*math.pi*R) \n",
+ "I_TRM2=V_m/(2*R) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=math.pi/w \n",
+ " \n",
+ "#Results\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM1)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TRM2)\n",
+ "print(\"ckt turn off time=%.0f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of avg thyristor current=34.512 A\n",
+ "max value of avg thyristor current=54.212 A\n",
+ "ckt turn off time=10 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=3.0\n",
+ "X_L=4.0\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R)) \n",
+ "V_s=230\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_s/Z \n",
+ "P=I_or**2*R \n",
+ "I_s=I_or\n",
+ "pf=P/(V_s*I_s) \n",
+ "I_TAM=math.sqrt(2)*V_s/(math.pi*Z) \n",
+ "I_Tm=math.sqrt(2)*V_s/(2*Z) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "di=math.sqrt(2)*V_s*w/Z \n",
+ "\n",
+ "#Results\n",
+ "print(\"min firing angle=%.2f deg\" %phi)\n",
+ "print(\"\\nmax firing angle=%.0f deg\" %180)\n",
+ "print(\"i/p pf=%.1f\" %pf)\n",
+ "print(\"max value of rms load current=%.0f A\" %I_or)\n",
+ "print(\"max power=%.0f W\" %P)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM)\n",
+ "print(\"max value of rms thyristor current=%.3f A\" %I_Tm)\n",
+ "print(\"di/dt=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min firing angle=53.13 deg\n",
+ "\n",
+ "max firing angle=180 deg\n",
+ "i/p pf=0.6\n",
+ "max value of rms load current=46 A\n",
+ "max power=6348 W\n",
+ "max value of avg thyristor current=20.707 A\n",
+ "max value of rms thyristor current=32.527 A\n",
+ "di/dt=20437 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 576"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "R=3.0 #ohm\n",
+ "X_L=5.0 #ohm\n",
+ "a=120.0 #firing angle delay\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R))\n",
+ "b=0\n",
+ "i=1\n",
+ "while (i>0) :\n",
+ " LHS=math.sin(math.radians(b-a))\n",
+ " RHS=math.sin(math.radians(a-phi))*math.exp(-(R/X_L)*(b-a)*math.pi/180)\n",
+ " if math.fabs(LHS-RHS)<= 0.01 :\n",
+ " B=b\n",
+ " i=2\n",
+ " break\n",
+ " \n",
+ " b=b+.1 \n",
+ "V_or=math.sqrt(2)*V*math.sqrt((1/(2*math.pi))*((B-a)*math.pi/180+(math.sin(math.radians(2*a))-math.sin(math.radians(2*B)))/2))\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"Extinction angle=%.1f deg\" %B) #answer in the book is wrong as formulae for RHS is wrongly employed\n",
+ "print(\"rms value of output voltage=%.2f V\" %V_or) #answer do not match due to wrong B in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extinction angle=156.1 deg\n",
+ "rms value of output voltage=97.75 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page No 581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=60.0\n",
+ "R=20.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt((V_m**2/(2*math.pi))*(a*math.pi/180-math.sin(math.radians(2*a))/2)+(2*V_m**2/(math.pi))*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2)) \n",
+ "I_T1r=(V_m/R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "I_T3r=(V_m/(2*R))*math.sqrt(1/math.pi*((a*math.pi/180)-math.sin(math.radians(2*a))/2)) \n",
+ "I1=math.sqrt(2)*I_T1r\n",
+ "I3=math.sqrt((math.sqrt(2)*I_T1r)**2+(math.sqrt(2)*I_T3r)**2)\n",
+ "r=V_s*(I1+I3) \n",
+ "P_o=V_or**2/R\n",
+ "pf=P_o/r \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms value of current for upper thyristors=%.2f A\" %I_T1r)\n",
+ "print(\"rms value of current for lower thyristors=%.2f A\" %I_T3r)\n",
+ "print(\"t/f VA rating=%.2f VA\" %r)\n",
+ "print(\"i/p pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=424.94 V\n",
+ "rms value of current for upper thyristors=14.59 A\n",
+ "rms value of current for lower thyristors=3.60 A\n",
+ "t/f VA rating=9631.61 VA\n",
+ "i/p pf=0.94\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/_Power_Electronics/Chapter9_4.ipynb b/_Power_Electronics/Chapter9_4.ipynb new file mode 100755 index 00000000..052c4736 --- /dev/null +++ b/_Power_Electronics/Chapter9_4.ipynb @@ -0,0 +1,388 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : AC Voltage Controllers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_m/2)*math.sqrt(1/math.pi*((2*math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "V_o=math.sqrt(2)*V_s/(2*math.pi)*(math.cos(math.radians(a))-1)\n",
+ "I_ON=V_o/R \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.1f W\" %P_o)\n",
+ "print(\"i/p pf=%.4f\" %pf)\n",
+ "print(\"avg i/p current=%.4f A\" %I_ON)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=224.716 V\n",
+ "load power=2524.9 W\n",
+ "i/p pf=0.9770\n",
+ "avg i/p current=-0.7581 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=45.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=(V_s)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "R=20\n",
+ "I_or=V_or/R\n",
+ "P_o=I_or**2*R \n",
+ "I_s=I_or\n",
+ "VA=V_s*I_s\n",
+ "pf=P_o/VA \n",
+ "I_TA=math.sqrt(2)*V_s/(2*math.pi*R)*(math.cos(math.radians(a))+1) \n",
+ "I_Tr=math.sqrt(2)*V_s/(2*R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.3f V\" %V_or)\n",
+ "print(\"load power=%.2f W\" %P_o)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_Tr)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=219.304 V\n",
+ "load power=2404.71 W\n",
+ "i/p pf=0.95\n",
+ "avg thyristor current=4.42 A\n",
+ "rms value of thyristor current=7.75 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No 564"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "n=6.0 #on cycles\n",
+ "m=4.0 #off cycles\n",
+ "\n",
+ "#Calculations\n",
+ "k=n/(n+m)\n",
+ "V_or=V_s*math.sqrt(k) \n",
+ "pf=math.sqrt(k) \n",
+ "R=15\n",
+ "I_m=V_s*math.sqrt(2)/R\n",
+ "I_TA=k*I_m/math.pi\n",
+ "I_TR=I_m*math.sqrt(k)/2 \n",
+ " \n",
+ "#Results\n",
+ "print(\"rms value of o/ voltage=%.2f V\" %V_or)\n",
+ "print(\"i/p pf=%.2f\" %pf)\n",
+ "print(\"avg thyristor current=%.2f A\" %I_TA) \n",
+ "print(\"rms value of thyristor current=%.2f A\" %I_TR)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/ voltage=178.16 V\n",
+ "i/p pf=0.77\n",
+ "avg thyristor current=4.14 A\n",
+ "rms value of thyristor current=8.40 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "R=3.0\n",
+ "\n",
+ "#Calculations\n",
+ "I_TAM1=2*V_m/(2*math.pi*R) \n",
+ "I_TRM2=V_m/(2*R) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "t_c=math.pi/w \n",
+ " \n",
+ "#Results\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM1)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TRM2)\n",
+ "print(\"ckt turn off time=%.0f ms\" %(t_c*1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "max value of avg thyristor current=34.512 A\n",
+ "max value of avg thyristor current=54.212 A\n",
+ "ckt turn off time=10 ms\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No 575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "R=3.0\n",
+ "X_L=4.0\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R)) \n",
+ "V_s=230\n",
+ "Z=math.sqrt(R**2+X_L**2)\n",
+ "I_or=V_s/Z \n",
+ "P=I_or**2*R \n",
+ "I_s=I_or\n",
+ "pf=P/(V_s*I_s) \n",
+ "I_TAM=math.sqrt(2)*V_s/(math.pi*Z) \n",
+ "I_Tm=math.sqrt(2)*V_s/(2*Z) \n",
+ "f=50\n",
+ "w=2*math.pi*f\n",
+ "di=math.sqrt(2)*V_s*w/Z \n",
+ "\n",
+ "#Results\n",
+ "print(\"min firing angle=%.2f deg\" %phi)\n",
+ "print(\"\\nmax firing angle=%.0f deg\" %180)\n",
+ "print(\"i/p pf=%.1f\" %pf)\n",
+ "print(\"max value of rms load current=%.0f A\" %I_or)\n",
+ "print(\"max power=%.0f W\" %P)\n",
+ "print(\"max value of avg thyristor current=%.3f A\" %I_TAM)\n",
+ "print(\"max value of rms thyristor current=%.3f A\" %I_Tm)\n",
+ "print(\"di/dt=%.0f A/s\" %di)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "min firing angle=53.13 deg\n",
+ "\n",
+ "max firing angle=180 deg\n",
+ "i/p pf=0.6\n",
+ "max value of rms load current=46 A\n",
+ "max power=6348 W\n",
+ "max value of avg thyristor current=20.707 A\n",
+ "max value of rms thyristor current=32.527 A\n",
+ "di/dt=20437 A/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 576"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V=230.0\n",
+ "R=3.0 #ohm\n",
+ "X_L=5.0 #ohm\n",
+ "a=120.0 #firing angle delay\n",
+ "\n",
+ "#Calculations\n",
+ "phi=math.degrees(math.atan(X_L/R))\n",
+ "b=0\n",
+ "i=1\n",
+ "while (i>0) :\n",
+ " LHS=math.sin(math.radians(b-a))\n",
+ " RHS=math.sin(math.radians(a-phi))*math.exp(-(R/X_L)*(b-a)*math.pi/180)\n",
+ " if math.fabs(LHS-RHS)<= 0.01 :\n",
+ " B=b\n",
+ " i=2\n",
+ " break\n",
+ " \n",
+ " b=b+.1 \n",
+ "V_or=math.sqrt(2)*V*math.sqrt((1/(2*math.pi))*((B-a)*math.pi/180+(math.sin(math.radians(2*a))-math.sin(math.radians(2*B)))/2))\n",
+ "\n",
+ "\n",
+ "#Results\n",
+ "print(\"Extinction angle=%.1f deg\" %B) #answer in the book is wrong as formulae for RHS is wrongly employed\n",
+ "print(\"rms value of output voltage=%.2f V\" %V_or) #answer do not match due to wrong B in book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Extinction angle=156.1 deg\n",
+ "rms value of output voltage=97.75 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8, Page No 581"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V_s=230.0\n",
+ "V_m=math.sqrt(2)*V_s\n",
+ "a=60.0\n",
+ "R=20.0\n",
+ "\n",
+ "#Calculations\n",
+ "V_or=math.sqrt((V_m**2/(2*math.pi))*(a*math.pi/180-math.sin(math.radians(2*a))/2)+(2*V_m**2/(math.pi))*(math.pi-a*math.pi/180+math.sin(math.radians(2*a))/2)) \n",
+ "I_T1r=(V_m/R)*math.sqrt(1/math.pi*((math.pi-a*math.pi/180)+math.sin(math.radians(2*a))/2)) \n",
+ "I_T3r=(V_m/(2*R))*math.sqrt(1/math.pi*((a*math.pi/180)-math.sin(math.radians(2*a))/2)) \n",
+ "I1=math.sqrt(2)*I_T1r\n",
+ "I3=math.sqrt((math.sqrt(2)*I_T1r)**2+(math.sqrt(2)*I_T3r)**2)\n",
+ "r=V_s*(I1+I3) \n",
+ "P_o=V_or**2/R\n",
+ "pf=P_o/r \n",
+ "\n",
+ "#Results\n",
+ "print(\"rms value of o/p voltage=%.2f V\" %V_or)\n",
+ "print(\"rms value of current for upper thyristors=%.2f A\" %I_T1r)\n",
+ "print(\"rms value of current for lower thyristors=%.2f A\" %I_T3r)\n",
+ "print(\"t/f VA rating=%.2f VA\" %r)\n",
+ "print(\"i/p pf=%.2f\" %pf)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "rms value of o/p voltage=424.94 V\n",
+ "rms value of current for upper thyristors=14.59 A\n",
+ "rms value of current for lower thyristors=3.60 A\n",
+ "t/f VA rating=9631.61 VA\n",
+ "i/p pf=0.94\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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