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diff --git a/DC_Machines_and_Synchronous_Machines/ch5.ipynb b/DC_Machines_and_Synchronous_Machines/ch5.ipynb deleted file mode 100755 index 4aca598c..00000000 --- a/DC_Machines_and_Synchronous_Machines/ch5.ipynb +++ /dev/null @@ -1,1612 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:ae2b9384b1b13f79321d75082b020b6a54688771e761bc6446ad00de14bf068e" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Chapter 5 : Methods for Calculating Regulation of Alternator" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.1 page no : 12" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "P = 1000.*10**3 \t\t\t#load power\n", - "phi = math.acos(math.radians(0.8)) \t\t\t#power factor lagging angle\n", - "V_L = 11.*10**3 \t\t\t#rated terminal voltae\n", - "R_a = 0.4 \t\t\t#armature resistance per phase\n", - "X_s = 3.\t\t\t#synchronous reactance per phase\n", - "\n", - "# Calculations\n", - "I_L = P/(math.sqrt(3)*V_L*math.cos(math.radians(phi)))\n", - "I_aph = I_L \t\t\t#for star connected load\n", - "I_a = I_L\t\t\t#current through armature\n", - "V_ph = V_L/math.sqrt(3) \t\t\t#rated terminal volatge phase value\n", - "\n", - "E_ph = math.sqrt( (V_ph*math.cos(math.radians(phi))+I_a*R_a)**2+(V_ph*math.sin(math.radians(phi))+I_a*X_s)**2 ) \t\t\t#emf generated phase value\n", - "E_line = E_ph*math.sqrt(3) \t\t\t#line value of emf generated\n", - "regulation = 100*(E_ph-V_ph)/V_ph \t\t\t#pecentage regulation\n", - "\n", - "# Results\n", - "print 'Line value of e.m.f generated is %.2f kV \\nRegulation is %.3f percent'%(E_line*10**-3,regulation)\n", - "\n", - "# note : book answer is wrong.\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Line value of e.m.f generated is 11.05 kV \n", - "Regulation is 0.428 percent\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.2 Page no : 14" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "VA = 1200.*10**3\n", - "V_L = 6600.\n", - "R_a = 0.25 \t\t\t#armature resistance per phase\n", - "X_s = 5.\t\t\t#synchronous reactance per phase\n", - "\n", - "# Calculations and Results\n", - "I_L = VA/(math.sqrt(3)*V_L)\n", - "I_aph = I_L \t\t\t#for star connected load\n", - "I_a = I_L\n", - "V_ph = V_L/math.sqrt(3)\n", - "\n", - "#Part(i)\n", - "phi1 = math.acos(0.8)\t\t\t#and lagging\n", - "E_ph1 = math.sqrt( (V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2 )\n", - "regulation = 100*(E_ph1-V_ph)/V_ph \t\t\t#percentage regulation\n", - "print 'i)Regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n", - "#Part(ii)\n", - "phi2 = math.acos(0.8)\t\t\t#and leading\n", - "E_ph2 = math.sqrt( (V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2 )\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph \t\t\t#percentage regulation\n", - "print 'ii)Regulation at 0.8 leading pf is %.f percent'%(regulation2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)Regulation at 0.8 lagging pf is 9.33 percent\n", - "ii)Regulation at 0.8 leading pf is -7 percent\n" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.3 Page no : 17" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "#full load\n", - "V_L_FL = 1100.\n", - "V_ph_FL = V_L_FL/math.sqrt(3)\n", - "\n", - "# Calculations\n", - "#no load\n", - "V_L_NL = 1266\n", - "E_line = V_L_NL\n", - "E_ph = E_line/math.sqrt(3)\n", - "regulation = 100*(E_ph-V_ph_FL)/V_ph_FL\n", - "\n", - "# Results\n", - "print 'Regulation at full load is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at full load is 15.09 percent\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.4 Page no : 23" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 866.\n", - "VA = 100.*10**3\n", - "I_L = VA/(math.sqrt(3)*V_L) \t\t\t#because VA = math.sqrt(3)*V_L*I_L\n", - "I_aph = I_L\t\t\t#full load and star connected alternator\n", - "V_ph = V_L/math.sqrt(3)\n", - "\n", - "# Calculations\n", - "#Graph is plotted and V_oc_ph and I_asc_Ph is obtained for \n", - "#SCC for I_asc = 66.67 A\n", - "I_f = 2.4 # A\n", - "#OCC for I_f = 2.4 A\n", - "V_oc_ph = 240 # V\n", - "\n", - "#for measruemnt of impedance\n", - "V_oc_ph = 240 \t\t\t#for I_f = 2.4..From o.c.c graph\n", - "I_asc_ph = 66.67 \t\t\t#for I_f = 2.4...From s.c.c graph\n", - "Z_s = V_oc_ph/I_asc_ph\n", - "R_a = 0.15\n", - "X_s = math.sqrt( Z_s**2-R_a**2 )\n", - "\n", - "V_ph_FL = 500.\n", - "phi = math.acos(0.8) \t\t\t#lagging pf\n", - "E_ph = math.sqrt((V_ph_FL*math.cos(phi)+I_aph*R_a)**2+(V_ph_FL*math.sin(phi)+I_aph*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Full-load regulation at 0.8 lagging pf is %.2f percent '%(regulation )\n", - "\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Full-load regulation at 0.8 lagging pf is 35.57 percent \n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.5 Page no : 25" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_OC_line = 230.\n", - "I_asc = 12.5 \t\t\t# when I_f = 0.38\n", - "V_OC_ph = V_OC_line/math.sqrt(3)\n", - "Z_s = V_OC_ph/I_asc \n", - "\n", - "R_a = 1.8/2 \t\t\t#1.8 is between terminals..0.9 is per phase\n", - "X_s = math.sqrt(Z_s**2-R_a**2)\n", - "\n", - "I_a = 10.\t\t\t# when regulation is needed\n", - "V_L = 230.\n", - "V_ph = V_L/math.sqrt(3)\n", - "\n", - "# Calculations and Results\n", - "#Part(i)\n", - "phi1 = math.acos(0.8) \t\t\t#and lagging\n", - "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n", - "regulation1 = 100*(E_ph1-V_ph)/V_ph\n", - "print 'Regulation for 10 A at 0.8 lagging pf is %.2f percent'%(regulation1)\n", - "#Part(ii)\n", - "phi2 = math.acos(0.8) \t\t\t#and leading\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Regulation for 10 A at 0.8 leading pf is %.2f percent'%(regulation2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation for 10 A at 0.8 lagging pf is 64.47 percent\n", - "Regulation for 10 A at 0.8 leading pf is -11.01 percent\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.6 Page no : 31" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "phi = math.acos(0.8)\n", - "VA = 1000.*10**3\n", - "V_L = 1905.\n", - "V_ph = V_L/math.sqrt(3)\n", - "R_a = 0.2\t\t\t#Armature reactance per phase\n", - "\n", - "# Calculations and Results\n", - "#Part(i)\n", - "#Ampere-turn method\n", - "I_L = VA/(math.sqrt(3)*V_L)\n", - "I_aph = I_L\n", - "V_dash = V_ph+I_aph*R_a*math.cos(phi)\t\t\t#V_dash is a dummy quantity and has no significance..it's used only for mapping correcponding current\n", - "F_o = 32 \t\t\t#F_o corresponds to voltage V_dash = 1148.5 from O.C.C graph\n", - "F_AR = 27.5 \t\t\t#Field current required to circulate full-load short circuit current of 303.07A.From SCC F_AR = 27.5\n", - "F_R = math.sqrt( F_o**2 + F_AR**2-2*F_o*F_AR*math.cos(phi+math.pi/2) )\t\t\t#using Comath.sine rule\n", - "\n", - "# for F_R = 53.25 E_ph = 1490 V from O.C.C\n", - "E_ph = 1490.\n", - "regulation1 = 100*(E_ph-V_ph)/V_ph\n", - "print 'Regulation on full-load by ampere-turn method is %.2f percent'%(regulation1)\n", - "\n", - "#Part (ii)\n", - "#Synchronous Impedance method\n", - "\n", - "I_sc = I_L\n", - "I_aph2 = I_sc\n", - "I_f = 27.5\n", - "\n", - "V_OC_ph = 1060. \t\t\t#corresponding to I-f = 27.5 in the graph\n", - "Z_s = V_OC_ph/I_aph2\n", - "X_s = math.sqrt(Z_s**2-R_a**2)\n", - "\n", - "E_ph2 = math.sqrt( (V_ph*math.cos(phi)+I_aph2*R_a)**2+(V_ph*math.sin(phi)+I_aph2*X_s)**2 ) \t\t\t#from phasor diagram\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Regulation on full-load by synchronous impedance method is %.2f percent'%(regulation2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation on full-load by ampere-turn method is 35.47 percent\n", - "Regulation on full-load by synchronous impedance method is 78.09 percent\n" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.7 Page no : 39" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "#case(i)\n", - "V_L = 440.\n", - "V_ph = V_L/math.sqrt(3)\n", - "phi = math.acos(0.8)\n", - "\n", - "#armature resistance drop from the graph\n", - "#RS = 1.1 cm and scale = 50 V/cm\n", - "arm_leak_resis = 1.1*50 \t\t\t#armature leakage resistance\n", - "\n", - "OB = V_ph*math.cos(phi)\n", - "AB = V_ph*math.sin(phi) + arm_leak_resis\n", - "E_1ph = math.sqrt( OB**2+AB**2 )\n", - "\n", - "F_f1 = 6.1 \t\t\t#corresponding value from OCC\n", - "F_AR = 3.1*1\n", - "\n", - "# Calculations and Results\n", - "F_R = math.sqrt( F_f1**2 + F_AR**2 -2*F_f1*F_AR*math.cos(math.radians(90+math.acos(math.radians(0.8)))))\n", - "E_ph = 328. \t\t\t#voltage corresponding to F_R = 8.33 A from OCC graph\n", - "regulation1 = 100*(E_ph - V_ph)/V_ph\n", - "print 'i)Regulation for 0.8 pf lagging is %.2f percent '%(regulation1)\n", - "\n", - "#case(ii)\n", - "\n", - "OC = V_ph*math.cos(phi)\n", - "BC = V_ph*math.sin(phi) - arm_leak_resis\n", - "E_1ph = math.sqrt( OC**2+BC**2 )\n", - "\n", - "F_f1 = 6.1 \t\t\t#corresponding value from OCC\n", - "F_R = math.sqrt( F_f1**2 + F_AR**2 -2*F_f1*F_AR*math.cos(math.radians(90-math.acos(math.radians(0.8)))))\n", - "E_ph = 90 \t\t\t#volatge corresponding to F_R = 3.34 A from OCC graph\n", - "regulation2 = 100*(E_ph - V_ph)/V_ph\n", - "print 'ii)Regulation for 0.8 pf leading is %.2f percent '%(regulation2)\n", - "print 'The answer in part ii doesnt match with textbook because of calculation mistake done in last step in the textbook'\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)Regulation for 0.8 pf lagging is 29.12 percent \n", - "ii)Regulation for 0.8 pf leading is -64.57 percent \n", - "The answer in part ii doesnt match with textbook because of calculation mistake done in last step in the textbook\n" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.8 Page no : 44" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "P = 1200.*10**3\n", - "V_line = 12000.\n", - "R_a = 2.\n", - "X_s = 35.\t\t\t#armature resistance and synchronous reactance\n", - "phi = math.acos(0.8)\n", - "\n", - "# Calculations\n", - "I_L = P/(math.sqrt(3)*V_line*math.cos(phi))\n", - "I_a = I_L\n", - "V_ph = V_line/math.sqrt(3)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Regulation at 0.8 lag power factor is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at 0.8 lag power factor is 26.66 percent\n" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.9 Page no : 45" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 11000. \n", - "V_ph = V_L/math.sqrt(3)\n", - "VA = 1000.*1000\n", - "I_L = VA/(V_L*math.sqrt(3))\n", - "\n", - "V_OC_ph = 433/math.sqrt(3)\n", - "I_asc_ph = I_L\n", - "\n", - "Z_s = V_OC_ph /I_asc_ph \t\t\t#ohms per phase\n", - "R_a = 0.45 \t\t\t#ohms per phase\n", - "X_s = math.sqrt(Z_s**2-R_a**2)\n", - "\n", - "# Calculations and Results\n", - "#part(i)\n", - "phi = math.acos(0.8) \t\t\t#lagging\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_L*R_a)**2 +(V_ph*math.sin(phi)+ I_L*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'Voltage regulation at 0.8 pf lagging is %f percent'%(regulation)\n", - "\n", - "#part(ii)\n", - "phi = math.acos(0.8) \t\t\t#leading\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi)+I_L*R_a)**2 +(V_ph*math.sin(phi)- I_L*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Voltage regulation at 0.8 pf lagging is %f percent'%(regulation2)\n", - "print 'Answer mismatches due to improper approximation'\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Voltage regulation at 0.8 pf lagging is 2.690067 percent\n", - "Voltage regulation at 0.8 pf lagging is -1.996182 percent\n", - "Answer mismatches due to improper approximation\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.10 Page no : 46" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "VA = 125.*10**3\n", - "V_L = 400.\n", - "V_ph = V_L/math.sqrt(3)\n", - "I_L = VA/(math.sqrt(3)*V_L)\n", - "I_aph = I_L\n", - "\n", - "# Calculations\n", - "I_f = 4.\n", - "I_asc = I_aph/2 \t\t\t#for half load.. refer to graph\n", - "V_OC_line = 140.\n", - "V_OC_ph = V_OC_line/math.sqrt(3)\n", - "I_asc_ph = I_asc\n", - "Z_s = V_OC_ph/I_asc_ph\n", - "R_a = 0.1\n", - "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#armature resistance and synchronous reactance\n", - "\n", - "phi = math.acos(0.8)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_asc*R_a)**2 +(V_ph*math.sin(phi)- I_asc*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Voltage regulation at 0.8 pf leading for half load is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Voltage regulation at 0.8 pf leading for half load is -12.39 percent\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.11 Page no : 48" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "from numpy import roots\n", - "\n", - "# Variables\n", - "V_OC_line = 575.\n", - "V_OC_ph = V_OC_line/math.sqrt(3)\n", - "I_asc_line = 75.\n", - "I_asc_ph = I_asc_line \n", - "I_aph = I_asc_ph\n", - "I_L = I_aph\n", - "\n", - "Z_s = V_OC_ph/I_asc_ph\n", - "R_a = 2.16/2\n", - "X_s = math.sqrt(Z_s**2 - R_a**2)\n", - "\n", - "# Calculations and Results\n", - "#on full load\n", - "E_ph = 6100.\n", - "phi = math.acos(0.8) \t\t\t#leading\n", - "\n", - "#using E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)- I_a*X_s)**2)\n", - "p = [1, -256.68, -3.71*10**7]\n", - "ans = roots(p)\n", - "V_ph = ans[0] \t\t\t#second root is ignored as its -ve\n", - "V_L = V_ph*math.sqrt(3)\n", - "print 'Rated terminal voltage between the lines is %.3f V '%(V_L)\n", - "VA_rating = math.sqrt(3)*V_L*I_L\n", - "print 'kVA rating of the alternator is %.f kVA'%(VA_rating*10**-3)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Rated terminal voltage between the lines is 10774.515 V \n", - "kVA rating of the alternator is 1400 kVA\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.12 Page no : 49" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "from numpy import roots\n", - "\n", - "# Variables\n", - "V_L = 6600.\n", - "V_ph = V_L/math.sqrt(3)\n", - "VA = 1500.*10**3\n", - "I_L = VA/(math.sqrt(3)*V_L)\n", - "I_aph = I_L\n", - "\n", - "# Calculations and Results\n", - "R_a = 0.5\n", - "X_s = 5\t\t\t#armature resistance and synchronous reactance\n", - "phi = math.acos(0.8)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n", - "print 'Induced EMF per phase is %f V'%(E_ph)\n", - "\n", - "#full load \n", - "phi = math.acos(1)\n", - "#using E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)- I_a*X_s)**2)\n", - "p = [1, 131.215, -1.791*10**7]\n", - "ans = roots(p)\n", - "V_ph = ans[1] \t\t\t#first root is ignored as it is -ve\n", - "print 'Terminal voltage per phase is %f V'%(V_ph)\n", - "\n", - "# note : rounding off error." - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Induced EMF per phase is 4284.243828 V\n", - "Terminal voltage per phase is 4166.921808 V\n" - ] - } - ], - "prompt_number": 16 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.13 Page no : 50" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_ph = 2000.\n", - "R_a = 0.8\n", - "I_sc = 100.\n", - "V_OC = 500.\n", - "I_f = 2.5\n", - "Z_s = V_OC/I_sc\n", - "X_s = math.sqrt(Z_s**2 - R_a**2 )\n", - "I_aFL = 100.\n", - "I_a = I_aFL\n", - "\n", - "# Calculations and Results\n", - "#part(i)\n", - "phi = math.acos(1)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'i)Voltage regulation is %.2f percent'%(regulation)\n", - "\n", - "#part(ii)\n", - "phi2 = math.acos(0.8)\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2 +(V_ph*math.sin(phi2)- I_a*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'ii)Voltage regulation is %.2f percent'%(regulation2)\n", - "\n", - "#part(iii)\n", - "phi3 = math.acos(0.71)\n", - "E_ph3 = math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2 +(V_ph*math.sin(phi3)+ I_a*X_s)**2)\n", - "regulation3 = 100*(E_ph3-V_ph)/V_ph\n", - "print 'iii)Voltage regulation is %.2f percent'%(regulation3)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)Voltage regulation is 6.89 percent\n", - "ii)Voltage regulation is -8.88 percent\n", - "iii)Voltage regulation is 21.11 percent\n" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.14 Page no : 51" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "VA = 1000.*1000\n", - "V_L = 4600. \n", - "V_ph = V_L/math.sqrt(3)\n", - "I_L = VA/(math.sqrt(3)*V_L)\n", - "I_aph_FL = I_L\n", - "I_aph = I_aph_FL\n", - "I_sc = (150./100)* I_aph_FL\n", - "V_OC_line = 1744\n", - "V_OC_ph = V_OC_line/math.sqrt(3)\n", - "\n", - "# Calculations\n", - "Z_s = V_OC_ph / I_sc\n", - "R_a = 1\n", - "X_s = math.sqrt(Z_s**2-R_a**2)\n", - "\n", - "phi = math.acos(0.8 ) \t\t\t#lagging\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Voltage regulation at full load 0.8 pf is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Voltage regulation at full load 0.8 pf is 19.89 percent\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.15 Page no : 52" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "\n", - "#part(i) Ampere turn method\n", - "# Variables\n", - "F_O = 37.5\n", - "F_AR = 20.\n", - "V_L = 6600.\n", - "V_ph = V_L/math.sqrt(3)\n", - "\n", - "# Calculations and Results\n", - "#lagging\n", - "phi = math.acos(0.8) \n", - "F_R = math.sqrt((F_O+F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n", - "#E_ph corresponding to F_R can be obtained by plotting open circuit characteristics\n", - "E_ph = 4350\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'i)By Ampere-turn method or MMF methodFull-load regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n", - "#leading\n", - "phi = math.acos(0.8) \n", - "F_R = math.sqrt((F_O-F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n", - "#E_ph corresponding to F_R can be obtained by plotting open circuit characteristics\n", - "E_ph = 3000\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'Full-load regulation at 0.8 leading pf is %.2f percent'%(regulation)\n", - "\n", - "#EMF method\n", - "V_OC_ph = 100\n", - "V_ph = 100\n", - "I_sc = 100*(F_O/F_AR) \t\t\t#times the rated value\n", - "Z_s = V_OC_ph/I_sc\n", - "F_O = 100\n", - "F_AR = Z_s*100\n", - "\n", - "#lagging\n", - "phi = math.acos(0.8)\n", - "F_R = math.sqrt((F_O+F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n", - "regulation = 100*(F_R-V_ph)/V_ph\n", - "print 'iiSynchronous impedance method or EMF method'\n", - "print 'Full-load regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n", - "#leading\n", - "phi = math.acos(0.8)\n", - "F_R = math.sqrt((F_O-F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n", - "regulation = 100*(F_R-V_ph)/V_ph\n", - "print 'Full-load regulation at 0.8 leading pf is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)By Ampere-turn method or MMF methodFull-load regulation at 0.8 lagging pf is 14.16 percent\n", - "Full-load regulation at 0.8 leading pf is -21.27 percent\n", - "iiSynchronous impedance method or EMF method\n", - "Full-load regulation at 0.8 lagging pf is 38.72 percent\n", - "Full-load regulation at 0.8 leading pf is -19.72 percent\n" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.16 Page no : 56" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 6000.\n", - "V_ph = V_L/math.sqrt(3)\n", - "I_ph_X_Lph = 0.9*500 \t\t\t#leakage reactance drop in volts = 0.9 cm * 500 V/cm\n", - "phi = math.acos(0.8) \t\t\t#lagging\n", - "\n", - "# Calculations\n", - "E_1ph = math.sqrt( (V_ph*math.cos(phi))**2 + (V_ph*math.sin(phi)+I_ph_X_Lph)**2 ) \t\t\t#From triangle OAB\n", - "F_f1 = 26 \t\t\t#from OCC\n", - "F_AR = 2.9*5 \t\t\t#2.9cm * 5 A/cm\n", - "\n", - "F_R = math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) )\n", - "\n", - "# Results\n", - "print 'Required field current is %.2f A'%(F_R)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Required field current is 36.59 A\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.17 Page no : 58" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 400.\n", - "V_ph = V_L/math.sqrt(3)\n", - "VA = 40.*10**3\n", - "I_L = VA/(math.sqrt(3)*V_L) \n", - "I_aph = I_L\n", - "\n", - "# Calculations and Results\n", - "I_aph_X_Lph = 0.65*50 \t\t\t#leakage reactance drop in volts = 2.4 cm * 500 V/cm\n", - "X_Lph = I_aph_X_Lph/ I_aph\n", - "print 'Armature leakage reactance is %.3f ohms'%(X_Lph)\n", - "phi = math.acos(0.8) \t\t\t#lagging\n", - "E_ph = math.sqrt((V_ph*math.cos(phi))**2 +(V_ph*math.sin(phi)+ I_aph_X_Lph)**2)\n", - "F_f1 = 15.6 \t\t\t#as obtained from OCC corresponding to this E_ph\n", - "\n", - "F_AR = 2.3*3 \t\t\t#2.3cm * 3 A/cm\n", - "print 'Armature reaction is %.1f '%(F_AR)\n", - "F_R = math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) ) \t\t\t#math.comath.sine rule to Triangle OAB\n", - "E_ph = 267.5 \t\t\t#corresponding to F_R from open circiut characteristics\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'Voltage regulation at 0.8 pf lagging is %.1f percent'%(regulation)\n", - "\n", - "\n", - "#Note:This answer doesnt match with textbook as it has been reciprocated in textbook\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Armature leakage reactance is 0.563 ohms\n", - "Armature reaction is 6.9 \n", - "Voltage regulation at 0.8 pf lagging is 15.8 percent\n" - ] - } - ], - "prompt_number": 21 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.18 Page no : 60" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "VA = 10.*10**3\n", - "V_L = 11.*10**3\n", - "V_ph = V_L/math.sqrt(3)\n", - "I_ph_X_Lph = 2.4*500 \t\t\t#leakage reactance drop in volts = 2.4 cm * 500 V/cm\n", - "\n", - "# Calculations\n", - "I_ph_R_aph = VA/(math.sqrt(3)*V_L)\n", - "phi = math.acos(0.8)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_ph_R_aph)**2 +(V_ph*math.sin(phi)+ I_ph_X_Lph)**2)\n", - "F_f1 = 109 \t\t\t#obtained from open circuit characteristics corresponding to calculated E_ph\n", - "F_AR = 2.8*10 \t\t\t#2.8cm * 10 A/cm\n", - "F_R = math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) ) \t\t\t#math.comath.sine rule to Triangle OAB\n", - "E_ph = 7700. \t\t\t#corresponding to F_R from open circiut characteristics\n", - "\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Voltage regulation at full-load 0.8 pf lagging is %.2f percent'%(regulation)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Voltage regulation at full-load 0.8 pf lagging is 21.24 percent\n" - ] - } - ], - "prompt_number": 22 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.19 Page no : 63" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "from numpy import roots\n", - "\n", - "# Variables\n", - "VA = 2000.*1000\n", - "V_L = 11000.\n", - "V_ph = V_L/math.sqrt(3)\n", - "R_a = 0.3\n", - "X_s = 5. \t\t\t#armature resistance and synchronous reactance\n", - "\n", - "# Calculations\n", - "#case (i)\n", - "phi = math.acos(0.8) \t\t\t#lagging\n", - "I_L = VA/(math.sqrt(3)*V_L) \n", - "I_a = I_L\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2)\n", - "\n", - "#using E_ph = math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n", - "#we get V_ph**2 -579.4455 V_ph -44653301.91 = 0\n", - "p = [1, -579.4455, -44653301.91]\n", - "ans = roots(p)\n", - "V_ph = ans[0] \t\t#second root is ignored as its -ve\n", - "print 'Terminal voltage is %.4f V'%(V_ph)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Terminal voltage is 6978.3131 V\n" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.20 Page no : 64" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "from numpy import roots\n", - "\n", - "# Variables\n", - "R_a = 0.6\n", - "X_s = 6. \t\t\t#armature resistance and synchronous reactance per phase\n", - "E_L = 6599.\n", - "E_ph = E_L/math.sqrt(3)\n", - "I_L = 180.\n", - "I_a = I_L\n", - "\n", - "# Calculations and Results\n", - "#part(i)\n", - "# using E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2) and solving for V_ph\n", - "p = [1 ,1135.83, -13338836.49]\n", - "ans = roots(p)\n", - "V_ph = ans[1]\n", - "V_L = V_ph*math.sqrt(3)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "phi = math.acos(0.9)\n", - "theta = math.atan((I_a*X_s+V_ph*math.sin(phi) )/(E_ph))\n", - "delta = theta-phi\n", - "print 'i)0.9 laggingTerminal voltage is %.2f VVoltage regulation is %.2f percentLoad angle is %.2f degrees'%(V_ph*math.sqrt(3),regulation,delta*180/math.pi)\n", - "\n", - "#part(ii)\n", - "phi_2 = math.acos(0.8)\n", - "p = [1, -941.53, -11399574.87]\n", - "ans = roots(p) \n", - "V_ph = ans[0] \t\t\t#second root is ignored as its -ve\n", - "V_L = V_ph*math.sqrt(3)\n", - "regulation2 = 100*(E_ph-V_ph)/V_ph\n", - "delta_2 = math.asin( (math.tan(phi)*(V_ph*math.cos(phi_2)+I_a*R_a) -I_a*X_s )/E_ph )\n", - "print 'ii)0.8 leadingTerminal voltage is %.2f VVoltage regulation is %.2f percentLoad angle is %.2f degrees'%(V_L,regulation2,delta_2*180/math.pi)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)0.9 laggingTerminal voltage is 5418.22 VVoltage regulation is 21.79 percentLoad angle is 6.83 degrees\n", - "ii)0.8 leadingTerminal voltage is 6719.93 VVoltage regulation is -1.80 percentLoad angle is 7.17 degrees\n" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.21 Page no : 66" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_ph = 2000.\n", - "R_a = 0.8\n", - "I_sc = 100.\n", - "I_a = I_sc\n", - "V_OC = 500.\n", - "I_f = 2.5\n", - "Z_s = V_OC/I_sc\n", - "\n", - "X_s = math.sqrt(Z_s**2- R_a**2)\n", - "I_a_FL = 100.\n", - "\n", - "# Calculations and Results\n", - "#Part(i)\n", - "phi1 = math.acos(1) \t\t\t#and lagging\n", - "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n", - "regulation1 = 100*(E_ph1-V_ph)/V_ph\n", - "print 'Regulation at upf is %.2f percent'%(regulation1)\n", - "\n", - "#Part(ii)\n", - "phi2 = math.acos(0.8) \n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Regulation at 0.8 leading pf is %.2f percent'%(regulation2)\n", - "\n", - "#Part(iii)\n", - "phi3 = math.acos(0.71) \n", - "E_ph3 = math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2+(V_ph*math.sin(phi3)+I_a*X_s)**2)\n", - "regulation3 = 100*(E_ph3-V_ph)/V_ph\n", - "print 'Regulation at 0.71 lagging pf is %.2f percent'%(regulation3)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at upf is 6.89 percent\n", - "Regulation at 0.8 leading pf is -8.88 percent\n", - "Regulation at 0.71 lagging pf is 21.11 percent\n" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.22 Page no : 68" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V = 600.\n", - "VA = 60.*10**3\n", - "I_sc = 210.\n", - "V_oc = 480.\n", - "I_f = 10.\n", - "R_a = 0.2\n", - "\n", - "I = VA/V \t\t\t#VA = V*I and alternator is math.single phase\n", - "I_a = I\n", - "\n", - "# Calculations and Results\n", - "Z_s = V_oc/I_sc \t\t\t#Synchronous Impedance\n", - "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#SYnchronous reactance\n", - "print 'Synchronous impedances is %f ohms and synchronous reactance is %f ohms'%(Z_s,X_s)\n", - "\n", - "#PART (i)\n", - "phi1 = math.acos(0.8) \t\t\t#and lagging\n", - "E1 = math.sqrt((V*math.cos(phi1)+I_a*R_a)**2+(V*math.sin(phi1)+I_a*X_s)**2) \t\t\t#plus sign for lagging power factor\n", - "regulation1 = 100*(E1-V)/V\n", - "print 'Regulation at 0.8 lagging pf is %.2f percent '%(regulation1 )\n", - "\n", - "#PART (ii)\n", - "phi2 = math.acos(1) \n", - "E2 = math.sqrt((V*math.cos(phi2)+I_a*R_a)**2+(V*math.sin(phi2)+I_a*X_s)**2) \n", - "regulation2 = 100*(E2-V)/V\n", - "print 'Regulation at UNITY pf is %.2f percent '%(regulation2 )\n", - "\n", - "#PART (iii)\n", - "phi3 = math.acos(0.6) \t\t\t#and leading \n", - "E3 = math.sqrt((V*math.cos(phi3)+I_a*R_a)**2+(V*math.sin(phi3)-I_a*X_s)**2) \t\t\t#minus sign for leading power factor\n", - "regulation3 = 100*(E3-V)/V\n", - "print 'Regulation at 0.6 leading pf is %.2f percent '%(regulation3 )\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Synchronous impedances is 2.285714 ohms and synchronous reactance is 2.276947 ohms\n", - "Regulation at 0.8 lagging pf is 28.60 percent \n", - "Regulation at UNITY pf is 10.08 percent \n", - "Regulation at 0.6 leading pf is -23.98 percent \n" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.23 Page no : 69" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 3300.\n", - "V_ph = V_L/math.sqrt(3)\n", - "I_a = 100.\n", - "I_f = 5.\n", - "V_OC_line = 900. \n", - "V_OC_ph = V_OC_line/math.sqrt(3) \n", - "R_a = 0.8 \t\t\t#armature resistance\n", - "I_aph = I_a\n", - "Z_s = V_OC_ph/I_aph\n", - "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#synchronous reactance\n", - "\n", - "# Calculations and Results\n", - "#Part(i)\n", - "phi1 = math.acos(0.8) \t\t\t#and lagging\n", - "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n", - "regulation1 = 100*(E_ph1-V_ph)/V_ph\n", - "print 'Regulation at 0.8 lagging is %.2f percent'%(regulation1)\n", - "\n", - "#Part(ii)\n", - "phi2 = math.acos(0.8) \t\t\t#and leading\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Regulation at 0.8 leading pf is %.2f percent'%(regulation2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at 0.8 lagging is 21.03 percent\n", - "Regulation at 0.8 leading pf is -9.55 percent\n" - ] - } - ], - "prompt_number": 27 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.24 Page no : 70" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 13500.\n", - "R_a = 1.5 \n", - "X_s = 30. \t\t\t#armature resistance and synchronous reactance\n", - "V_ph = V_L/math.sqrt(3)\n", - "\n", - "# Calculations and Results\n", - "#CASE 1\n", - "phi1 = math.acos(0.8)\n", - "P_out = 1280*10**3\n", - "I_L = P_out/ (math.sqrt(3)*V_L*math.cos(phi1) ) \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n", - "\n", - "I_a = I_L\n", - "E_ph = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'Regulation at 0.8 lagging power factor is %.2f percent'%(regulation)\n", - "\n", - "#Case 2\n", - "phi2 = math.acos(1)\n", - "I_L = P_out/ (math.sqrt(3)*V_L*math.cos(phi2) ) \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n", - "\n", - "I_a = I_L\n", - "E_ph = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)+I_a*X_s)**2)\n", - "regulation2 = 100*(E_ph-V_ph)/V_ph\n", - "print 'Regulation at unity power factor is %.2f percent'%(regulation2)\n", - "\n", - "#case 3\n", - "phi3 = math.acos(0.8)\n", - "I_L = P_out/ (math.sqrt(3)*V_L*math.cos(phi3) ) \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n", - "I_a = I_L\n", - "E_ph = math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2+(V_ph*math.sin(phi3)-I_a*X_s)**2)\t\t\t# minus sign in the second bracket beacuse of leading pf\n", - "regulation3 = 100*(E_ph-V_ph)/V_ph\n", - "print 'Regulation at 0.8 leading power factor is %.2f percent'%(regulation3)\n", - "\n", - "# note : rounding off error" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at 0.8 lagging power factor is 18.60 percent\n", - "Regulation at unity power factor is 3.23 percent\n", - "Regulation at 0.8 leading power factor is -11.99 percent\n" - ] - } - ], - "prompt_number": 29 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.26 Page no : 72" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 11.*10**3\n", - "VA_rating = 10.**6\n", - "R_a = 2.2 \t\t\t#alternator resistance\n", - "phi = math.acos(0.8)\n", - "\n", - "# Calculations\n", - "I_L = VA_rating/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)V_L*I_L\n", - "I_a = I_L\n", - "V_ph = V_L/math.sqrt(3)\n", - "regulation = 24.\n", - "\n", - "E_ph = ((regulation/100)+1)*V_ph \t\t\t# because regulation = 100*(E_ph-V_ph)/V_ph\n", - "#using E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n", - "X_s = (math.sqrt(E_ph**2-((V_ph*math.cos(phi)+I_a*R_a)**2))-V_ph*math.sin(phi))*(1/I_a)\n", - "\n", - "phi1 = math.acos(0.8)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)-I_a*X_s)**2)\n", - "regulation1 = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Regulation at 0.8 leading power factor is %.2f percent'%(regulation1)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at 0.8 leading power factor is -13.90 percent\n" - ] - } - ], - "prompt_number": 31 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.27 Page no : 73" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 220.\n", - "VA = 100.*10**3\n", - "R_a = 0.1 \t\t\t#effective resistacne of alternator\n", - "X_a = 0.5 \t\t\t#leakage reactance\n", - "X_ar = 2*X_a\n", - "\n", - "Z_s = complex(R_a,X_a+X_ar)\n", - "\n", - "# Calculations and Results\n", - "#Part(1)\n", - "phi = math.acos(0.4)\n", - "V_ph = V_L/math.sqrt(3)\n", - "I_L = VA/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)*V_L*I_L\n", - "I_a = I_L\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*(X_a+X_ar))**2)\n", - "print 'i)Required noload voltage is %.3f V'%(E_ph)\n", - "\n", - "#Part(2)\n", - "V_ph2 = 0\n", - "E_ph2 = math.sqrt((V_ph2*math.cos(phi)+I_a*R_a)**2+(V_ph2*math.sin(phi)+I_a*(X_a+X_ar))**2)\n", - "print 'ii)Required noload voltage is %.3f V'%(E_ph2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)Required noload voltage is 515.848 V\n", - "ii)Required noload voltage is 394.522 V\n" - ] - } - ], - "prompt_number": 32 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.28 Page no : 74" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 2000.\n", - "V_ph = V_L/math.sqrt(3)\n", - "VA = 1000.*10**3\n", - "I_L = VA/(math.sqrt(3)*V_L) \t\t\t#because VA = math.sqrt(3)*V_L*I_L\n", - "I_aph = I_L\n", - "\n", - "I_f = 28.5\t\t\t#for this I_aph = 288.67513 as obtained from SCC graph\n", - "V_oc_ph = 1060.\t\t\t#for I_f = 28.5 as obtained fromOCC graph\n", - "Z_s = V_oc_ph/I_aph\n", - "R_a = 0.2 \t\t\t#armature effective resistance\n", - "X_s = math.sqrt( Z_s**2-R_a**2 )\n", - "\n", - "# Calculations and Results\n", - "#Part(i)\n", - "phi1 = math.acos(0.8)\t\t\t#lagging\n", - "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_aph*R_a)**2+(V_ph*math.sin(phi1)+I_aph*X_s)**2)\n", - "regulation1 = 100*(E_ph1-V_ph)/V_ph\n", - "print \"i)Full-load percentage regulation at 0.8 pf lagging is %.2f percent\"%(regulation1)\n", - "\n", - "#Part(ii)\n", - "phi2 = math.acos(0.8)\t\t\t#leading\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_aph*R_a)**2+(V_ph*math.sin(phi2)-I_aph*X_s)**2)\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print \"ii)Full-load percentage regulation at 0.8 pf leading is %.2f percent\"%(regulation2)\n", - "print 'Note that the answer mismatches because of calculation mistake done in the last step of part 1'\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "i)Full-load percentage regulation at 0.8 pf lagging is 73.86 percent\n", - "ii)Full-load percentage regulation at 0.8 pf leading is -9.29 percent\n", - "Note that the answer mismatches because of calculation mistake done in the last step of part 1\n" - ] - } - ], - "prompt_number": 33 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.29 Page no : 76" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 3300.\n", - "VA = 200.*10**3\n", - "R_a = 0.6\n", - "X_s = 6.\t\t\t#armature resistance and synchronous reactance\n", - "\n", - "# Calculations\n", - "I_L = VA/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)V_L*I_L\n", - "I_a = I_L\n", - "V_ph = V_L/math.sqrt(3)\n", - "phi = math.acos(0.8)\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n", - "\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "\n", - "# Results\n", - "print 'Regulation at 0.8 lagging power factor is %.3f percent'%(regulation)\n", - "print ' Note : Regulation is positive for lagging power factor loads'\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Regulation at 0.8 lagging power factor is 7.802 percent\n", - " Note : Regulation is positive for lagging power factor loads\n" - ] - } - ], - "prompt_number": 34 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 5.30 Page no : 77" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math \n", - "\n", - "# Variables\n", - "V_L = 2300. \n", - "V_ph = V_L/math.sqrt(3)\n", - "f = 50.\n", - "R_a = 0.2 \t\t\t#armature resistance\n", - "I_sc = 150.\n", - "V_OC_line = 780. \n", - "V_OC_ph = V_OC_line/math.sqrt(3)\n", - "\n", - "Z_s = V_OC_ph/I_sc\n", - "X_s = math.sqrt(Z_s**2 - R_a**2)\n", - "I_aph = 25 \n", - "I_aFL = I_aph\n", - "\n", - "# Calculations and Results\n", - "#part(i)\n", - "phi = math.acos(0.8) \t\t\t#lag\n", - "E_ph = math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n", - "regulation = 100*(E_ph-V_ph)/V_ph\n", - "print 'Voltage regulation at 0.8 pf lagging is %.3f percent'%(regulation)\n", - "\n", - "#part(ii)\n", - "phi2 = math.acos(0.8) \t\t\t#lead\n", - "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_aph*R_a)**2 +(V_ph*math.sin(phi2)- I_aph*X_s)**2 )\n", - "regulation2 = 100*(E_ph2-V_ph)/V_ph\n", - "print 'Voltage regulation at 0.8 pf leading is %.3f percent'%(regulation2)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Voltage regulation at 0.8 pf lagging is 3.774 percent\n", - "Voltage regulation at 0.8 pf leading is -2.967 percent\n" - ] - } - ], - "prompt_number": 35 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -}
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