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author | Trupti Kini | 2016-07-19 23:30:36 +0600 |
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committer | Trupti Kini | 2016-07-19 23:30:36 +0600 |
commit | 10c80b1dd1eb129240f34e72a7404b771a9bbdc2 (patch) | |
tree | 0562a252e056d175c2b706fe313c15b6ab93545e /basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7.ipynb | |
parent | 6c4ae200cf807d3837540f33bfbce25acce517e4 (diff) | |
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A basic_electrical_engineering_by_nagsarkar_and_sukhija/Chapter2.ipynb
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A basic_electrical_engineering_by_nagsarkar_and_sukhija/Chapter5.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter1.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter11.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter3_(2).ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter6.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter8.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter9.ipynb
A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chap1.png
A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chapter2.png
A basic_electrical_engineering_by_nagsarkar_and_sukhija/screenshots/chapter6.png
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diff --git a/basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7.ipynb b/basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7.ipynb new file mode 100644 index 00000000..3a143961 --- /dev/null +++ b/basic_electrical_engineering_by_nagsarkar_and_sukhija/chapter7.ipynb @@ -0,0 +1,660 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7:Synchronous Machines" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1:Page number-412" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n= 3000.0 rpm\n", + "D= 0.764 m\n", + "output of the alternator= 3505.213 KVA\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#case a\n", + "\n", + "f=150\n", + "p=2\n", + "\n", + "#assume the diameter of the stator bore is d meter\n", + "n=120*50/2 #where n is rotor speed\n", + "\n", + "print \"n=\",round(n,0),\"rpm\"\n", + "\n", + "pi=3.14\n", + "d=(120*60)/(pi*3000) \n", + "\n", + "print \"D=\",round(d,3),\"m\"\n", + "\n", + "#case b\n", + "\n", + "k=2\n", + "l=1\n", + "o=k*d**2*n*l\n", + "\n", + "print \"output of the alternator=\",round(o,3),\"KVA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2:Page number-423 " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total number of cycles the clock should perform in 24 hours for correct time is= 4320000.0\n", + "The number of cycles clock performs from 8am to 7pm is= 1977120.0\n", + "The desired average frequency for correct time for remaining 13 hours is= 50.06154\n", + "s= 0.8\n", + "time= 57.6\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#The total number of cycles the clock should perform in 24 hours for correct time is\n", + "\n", + "t=24*60*60*50\n", + "\n", + "print \"The total number of cycles the clock should perform in 24 hours for correct time is=\",round(t,0)\n", + "\n", + "#The number of cycles the clock performs from 8am to 7pm is\n", + "\n", + "n=(6*49.95+5*49.90)*60*60\n", + "\n", + "print \"The number of cycles clock performs from 8am to 7pm is=\",round(n,0)\n", + "\n", + "#the number of cycles required in remaining 13 hours is t-n that is 2342.88*10**3\n", + "\n", + "a=(2342.88*10**3)/(13*60*60)\n", + "\n", + "print \"The desired average frequency for correct time for remaining 13 hours is=\",round(a,5)\n", + "\n", + "#The shortfall in number of cycles from 8am to 7pm\n", + "\n", + "s=0.05*6+0.10*5\n", + "\n", + "print \"s=\",round(s,3)\n", + "\n", + "#The time by which the clock is incorrect at 7pm\n", + "\n", + "time=(0.8*60*60)/50\n", + " \n", + "print \"time=\",round(time,5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3:Page number-423" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "frequency= 50.0 Hz\n", + "Phase emf= 2301.696 v\n", + "The line voltage is= 3986.654 v\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#given\n", + "\n", + "n=500 #speed to rotation\n", + "p=12 #poles\n", + "\n", + "#case a\n", + "\n", + "f=n*p/120 #frequency\n", + "print \"frequency=\",round(f,0),\"Hz\"\n", + " \n", + "#case b\n", + "\n", + "kp=1 #kp is the winding at full pitch\n", + "\n", + "#kd is the distribution factor where kd=sin[mk/2]/msin(k/2) where k is a gama function\n", + "\n", + "#m=108/12*3\n", + "m=3\n", + "\n", + "#gama or k=180/slots per pole=9 k=20\n", + "\n", + "#after substituting above values in kd we get kd=0.96\n", + "\n", + "#z=108*12/3 = 432\n", + "\n", + "ep=2.22*1*0.96*432*50*50*10**-3\n", + "\n", + "print \"Phase emf=\",round(ep,3),\"v\"\n", + "\n", + "#case c\n", + "\n", + "vl=3**0.5*ep\n", + "\n", + "print \"The line voltage is=\",round(vl,3),\"v\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4:Page number-424" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n= 600.0 rpm\n", + "phase emf= 1864.44569 v\n", + "the line voltage= 3229.315 v\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#given\n", + "\n", + "f=50 #frequency\n", + "p=10 #number of poles\n", + "\n", + "#case a\n", + "n=120*f/p\n", + "\n", + "print \"n=\",round(n,0),\"rpm\"\n", + "\n", + "#case b\n", + "\n", + "#the pitch factor kp=0.966\n", + "\n", + "#m=2 and gama=180/slots per pole and it is obtained as 30\n", + "\n", + "#kd=sin[(mgama)/2]/msin(gama/2)=0.966\n", + "\n", + "z=6*2*10\n", + "\n", + "ep=z*2.22*0.966*0.966*50*0.15\n", + "\n", + "print \"phase emf=\",round(ep,5),\"v\"\n", + "\n", + "#case c\n", + "\n", + "el=3**0.5*ep\n", + "\n", + "print \"the line voltage=\",round(el,3),\"v\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5:Page number-436" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5.44650074006\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#given\n", + "\n", + "vt=1905.26 #at angle 0\n", + "angle=36.87\n", + "ia=43.74 #at angle -36.87\n", + "zs=3.51 #at angle 85.91\n", + "\n", + "#e=vt+ia*zs\n", + "#(1905.26+43.74*3.51angle(85.91-36.87))\n", + "#1905.26+153.35angle(49.04)\n", + "#1905.26+153.35*(0.6558+j0.7551)\n", + "#=2009.03 angle(3.31)\n", + "\n", + "p=((2009.03-1905.26)/1905.26)*100\n", + "\n", + "print p\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6:Page number-439" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.46227272727\n", + "-9.335\n", + "17.7059090909\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#given\n", + "\n", + "zs=4 # at angle 84.26\n", + "xs=3.98\n", + "impangle=84.26\n", + "\n", + "#case a\n", + "\n", + "#vt=2200+j0\n", + "#ia=120\n", + "#e=vt+ia*zs\n", + "#on substituting and calculating we get the value of e as 2298.17 at 12 degrees\n", + "\n", + "p=((2298.17-2200)/2200)*100\n", + "\n", + "print p\n", + "\n", + "#case b\n", + "\n", + "#performing same functions as above for pf leading 0.8 we get e=1994.63 at 12 degrees\n", + "\n", + "p=((1994.63-2200)/2200)*100\n", + "\n", + "print p\n", + "\n", + "#case c\n", + "\n", + "#same as above but pf lags by 0.707 and on calculating generates e as 2589.53\n", + "\n", + "p=((2589.53-2200)/2200)*100\n", + "\n", + "print p\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7:Page number-444" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "load voltage= 209.4847 v\n", + "the load current is 20.95 at angle -38.65\n", + "The output of generator1= 2094.4 VA\n", + "The output of generator2= 2514.6 VA\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#From the circuit diagram of the figure we can obtain tha following equations based on which the problems are solved\n", + "#eqn 1..........vl=(i1+i2)*zl....the load voltage\n", + "#eqn 2..........vl=e1-i1*z1=e2-i2*z2\n", + "#eqn 3..........i1=(e1-vl)*y1 and i2=(e2-vl)*y2\n", + "#eqn 4..........vl=(e1*y1+e2+y2)/(y1+y2+yl)\n", + "\n", + "#load voltage case a\n", + "\n", + "#vl=209.26-j*9.7 in x+iy form and angle is calculated \n", + "\n", + "vl=(209.26**2+9.7**2)**0.5\n", + "\n", + "print \"load voltage=\",round(vl,5),\"v\"\n", + "\n", + "#using eqn 3 the following generator currents are generated\n", + "\n", + "#i1=7.45-j5.92 for which i1=9.52 at angle -38.45 is generated\n", + "#i2=8.91-j7.17 for which i2=11.43 at angle -38.83 is generated\n", + "\n", + "#case b\n", + "\n", + "#the load current il=i1+i2 is obtained as 20.95 at angle -38.65\n", + "\n", + "print \"the load current is 20.95 at angle -38.65\"\n", + "\n", + "#case c\n", + "\n", + "g1=220*9.52\n", + "g2=220*11.43\n", + "\n", + "print \"The output of generator1=\",round(g1,3),\"VA\"\n", + "print \"The output of generator2=\",round(g2,4),\"VA\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8:Page number-446" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "E= 6600.12121 V\n", + "The power angle=13.63\n", + "Armature current= 295.18199 A\n", + "power factor=0.68\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#case a\n", + "\n", + "#case 1\n", + "\n", + "v=6600 #voltage\n", + "ir=200 #armature current\n", + "xs=8 #reactance\n", + "\n", + "e=(v**2+(ir*xs))**0.5\n", + "\n", + "print \"E=\",round(e,5),\"V\"\n", + "\n", + "#case 2\n", + "\n", + "#from triangle in the firgure the power angle is obtained as 13.63\n", + "\n", + "print \"The power angle=13.63\"\n", + "\n", + "#case b\n", + "\n", + "#due to excitation we obtain ix=217.10A\n", + "\n", + "#case 3\n", + "ix=217.10\n", + "i=((ir**2+ix**2))**0.5\n", + "\n", + "print \"Armature current=\",round(i,5),\"A\"\n", + "\n", + "#case 4\n", + "\n", + "#power factor cos(angle)=ir/i=0.68\n", + "\n", + "print \"power factor=0.68\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9:Page number-447" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "armature current= 356.6275 A\n", + "power factor= 0.84121\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#this problem has few notations and values taken from problem above\n", + "#case a\n", + "\n", + "#the generator output becomes 1.5*6600*200\n", + "\n", + "o=1980 #generator output\n", + "#the power angle is obtaimed as 16.42\n", + "\n", + "#applying cosine to the triangle in the problem gives ixs=2853.02\n", + "#hence armature current is\n", + "i=2853.02/8\n", + "\n", + "print \"armature current=\",round(i,5),\"A\"\n", + "\n", + "#case b\n", + "\n", + "pf=1980000/(6600*356.63) #power factor=o/(V*I)\n", + "\n", + "print \"power factor=\",round(pf,5)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10:Page number-454" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Power supplied to the motor is= 467500.0 kW\n", + "emf induced=5744.08 at angle -10.39\n", + "emf induced=7051.44 at angle -8.88\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#case a\n", + "\n", + "vl=11000\n", + "il=50\n", + "pf=0.85 #powerfactor\n", + "\n", + "p=vl*il*pf\n", + "\n", + "print \"Power supplied to the motor is=\",round(p,5),\"kW\"\n", + "\n", + "#case b\n", + "\n", + "vt=6350.85 #at angle 0 \n", + "zs=25.02 #at angle 0\n", + "\n", + "#subcase 1 powerfactor at 0.85 lag\n", + "\n", + "#e=vt-ia*zs\n", + "#e=6350.85-50(at angle -31.79)*25.02(at angle 87.71)\n", + "\n", + "#substituting and solving as in x+iy form we get 5744.08 at angle -10.39 as the value of e\n", + "\n", + "print \"emf induced=5744.08 at angle -10.39\"\n", + "\n", + "#subcase 2\n", + "\n", + "#for a 0.85 lead same process as above is followed except angles are considered positive due to lead\n", + "\n", + "print \"emf induced=7051.44 at angle -8.88\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11:Page number-455" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "input KVA to the motor is= 15.069\n", + "the power factor=0.70\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "#given and calculted using regular formulas\n", + "\n", + "p=14.38\n", + "q=10.78 #reactive power component \n", + "\n", + "pm=8.95 #mechanical load driven by motor \n", + "#In order to make pf of the circuit load to improve to unity the motor must supply power to the circuit equalling q\n", + "#hence total input power s to the motor maybe written as s=(pm/n)+jQ\n", + "#on sustituting values we get s=10.53+j10.78 KVA\n", + "\n", + "i=((10.53**2+10.78**2)**0.5)\n", + "\n", + "print \"input KVA to the motor is=\",round(i,3)\n", + "\n", + "#from the triangle the angle is obtained as 45.67\n", + "#hence the power factor is cos(45.67)=0.70\n", + "\n", + "print \"the power factor=0.70\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |