{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 5: Three Phase Systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.1: Page number-317" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ia= 51.962 A\n", "ib= 43.30129 A\n", "ic= 34.64103 A\n", "IN= 15.0 A\n" ] } ], "source": [ "import math\n", "#given\n", "vl=400 #line voltage\n", "va=vl/math.sqrt(3)\n", "vb=230.94 #angle(-120)\n", "vc=230.94 #angle(-240)\n", "#case a\n", "#the line currents are given by\n", "ia=12000/230.94 #with angle 0\n", "ib=10000/230.94 #with angle 120\n", "ic=8000/230.94 #with angle 240\n", "print\"ia=\",round(ia,3),\"A\"\n", "print \"ib=\",round(ib,5),\"A\"\n", "print \"ic=\",round(ic,5),\"A\"\n", "#case b\n", "#IN=ia+ib+ic\n", "#ia,ib and ic are phase currents hence contain with angles they are in the form sin(angle)+icos(angle)\n", "#IN=51.96*(sin(0)+i*cos(0))+43.3*(sin(120)+i*cos(120))+34.64*(sin(240)+i*cos(240))\n", "#IN=51.96+(-21.65+i*37.5)+34.64*(-0.5-i*0.866)\n", "#12.99+i*7.5 on which the sin+icos=sin**2+cos**2 operation is performed\n", "#therefore \n", "IN=15 #at angle 30\n", "print \"IN=\",round(IN,10),\"A\"\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.2:Page number-320 " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iab= 2.0 A\n", "ibc=5.4414-j3.1416 A\n", "ica=3.1463+j4.2056 A\n", "ia=4.2328 with an angle of -96.51 A\n", "ib=4.1915 with angle of -48.55 A\n", "ic=7.6973 with an angle of 107.35 A\n" ] } ], "source": [ "import math\n", "#case a\n", "vab=400 #phase angle of 0\n", "vbc=400 #phase angle of 120\n", "vca=400 #phase angle of 240\n", "#the phase currents are given by iab,ibc,ica\n", "iab=400/150 #from the diagram \n", "print \"iab=\",round(iab,5),\"A\"\n", "#ibc=(400*314*50)/10**6 numerator with an angle of -120 and denominator angle of -90 which amounts to -30 in numerator\n", "#this leads to simplifying with the formula as the value obtained for ibc after simplification from above mutiplied by values of cos(-30)+jsin(-30)\n", "#therefore print as below\n", "print\"ibc=5.4414-j3.1416\",\"A\"\n", "#same method for ica\n", "print \"ica=3.1463+j4.2056\",\"A\"\n", "#case b\n", "#ia=iab-ica\n", "#ia=2.667-(3.1463+j4.2056)\n", "#leads to 4.2328 with an angle of -96.51\n", "#angle calculated using tan formula\n", "print \"ia=4.2328 with an angle of -96.51\",\"A\"\n", "#same for ib and ic\n", "print \"ib=4.1915 with angle of -48.55\",\"A\"\n", "print \"ic=7.6973 with an angle of 107.35\",\"A\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.3:Page number:321" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power factor =0.8\n", "p= 25601.1 KW\n", "q= 19200.82 Kvar\n", "t= 32001.0 KVA\n" ] } ], "source": [ "import math\n", "#case a\n", "#given\n", "zl=5 #load impedanc with an angle of 36.87 degrees\n", "vl=400 #line voltage\n", "il=46.19\n", "va=400/3**0.5 #phase voltage\n", "ia=va/zl #line current with an angle of -36.87 degrees\n", "#ib and ic are also the same values with changes in in their angles\n", "#case b\n", "#cos(-36.87)=0.8 lagging\n", "print \"power factor =0.8\"\n", "#case c\n", "p=3**0.5*vl*il*0.8 #power where 0.8 is power factor\n", "print\"p=\",round(p,2),\"KW\"\n", "#case d\n", "q=3**0.5*vl*il*0.6 #where 0.6 is sin(36.87) and q is reactive volt ampere\n", "print\"q=\",round(q,2),\"Kvar\"\n", "#case e\n", "t=3**0.5*vl*il #total volt ampere\n", "print \"t=\",round(t,0),\"KVA\"\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.4: Page number-321" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ia=29.33A\n", "ib=73.83A\n", "ic=73.82A\n", "vr=1466.5V\n", "vl=73.83V\n", "vc=73.83V\n", "vn=1212.45V\n" ] } ], "source": [ "import math\n", "#given\n", "za=50\n", "zb=15 #j15\n", "zc=-15 #-j15\n", "vl=440\n", "vab=440 #with an angle of 0\n", "vbc=440 #with an angle of -120\n", "vca=440 #with an angle of -240\n", "#applying kvl to meshes as in the diagram we get the following equations\n", "#50i1+j15(i1-i2)-440(angle 0)=0,j15(i2-i1)+(-j15)i2-440(angle 120)=0\n", "#solving the above 2 eqns we get the values of ia,ib and ic as follows\n", "print \"ia=29.33A\" #at angle -30\n", "print \"ib=73.83A\" #at angle -131.45\n", "print \"ic=73.82A\" #at angle 71.5\n", "#the voltage drops across vr,vl and vc which are voltages across resistance ,inducctance and capacitance are given as follows\n", "print \"vr=1466.5V\" #at angle -30\n", "print \"vl=73.83V\" #at angle -41.45\n", "print \"vc=73.83V\" #at angle -18.5\n", "#the potential of neutral point\n", "print \"vn=1212.45V\" #at angle 150\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.5:Page number-323" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "il= 42.88104 A\n", "ip= 24.75738 A\n" ] } ], "source": [ "import math\n", "#given\n", "v=440 #voltage\n", "o=25000 #output power\n", "e=0.9 #efficiency\n", "p=0.85 #poer factor\n", "#case a\n", "il=o/(3**0.5*v*p*e) #line current\n", "print \"il=\",round(il,5),\"A\"\n", "#case b\n", "ip=o/(3*v*e*p) #phase current for delta current winding\n", "print \"ip=\",round(ip,5),\"A\"\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Example 5.7:Page number-329" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iab= 34.78 A\n", "ibc= 55.648 A\n", "ica= 41.736 A\n", "ia=76.38A\n", "ib=87.85A\n", "ic=32.21A\n", "w1=31.63KW\n", "w2=12.827KW\n" ] } ], "source": [ "import math\n", "#given\n", "#25kW at power factor 1 for branch AB\n", "#40KVA at power factor 0.85 for branch BC\n", "#30KVA at power factor 0.6 for branch CA\n", "#line voltages with vab as reference phasor\n", "vab=415 #at angle 0\n", "vbc=415 #at angle -120\n", "vca=415 #at angle -240\n", "#phase currents are given with x+jy form of an imaginary number and vary according to angles.The values below are only the values of the currents without conversion into imaginary form\n", "iab=(25*10**3)/(3**0.5*415*1)\n", "print \"iab=\",round(iab,3),\"A\"\n", "ibc=(40*10**3)/(3**0.5*415)\n", "print \"ibc=\",round(ibc,3),\"A\"\n", "ica=(30*10**3)/(3**0.5*415)\n", "print \"ica=\",round(ica,3),\"A\"\n", "#the line currents are as below.The following values can also be converted to x+iy form where x is real and y is imaginary\n", "#ia=iab-ibc and subtraction is done of x+iy forms where the value of the term varies as obtained by sqrt(x**2+y**2)\n", "print \"ia=76.38A\" #at angle -3.75\n", "#ib=ibc-iab\n", "print \"ib=87.85A\"\n", "#ic=ica-ibc\n", "print \"ic=32.21A\"\n", "#wattmeter readings on phase A\n", "#w1=vab*ia*cos(-3.35) where the cos angle is given by phase angle between ia and vab\n", "print \"w1=31.63KW\"\n", "#same formula for wattmeter readings in phase c where the angle is 16.35\n", "print \"w2=12.827KW\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 5.8:Page number-331" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the total input power= 700.0 KW\n", "power factor=0.803\n", "il= 0.22877 A\n", "output= 0.845 hp\n" ] } ], "source": [ "import math\n", "#given\n", "w1=500\n", "w2=200\n", "w=w1+w2\n", "#case a\n", "print \"the total input power=\",round(w,0),\"KW\"\n", "#case b\n", "#tan(angle)=3**0.5*(w1-w2)/(w1+w2) where the angle=36.58 and cos(36.58)=0.803 which is the power factor\n", "print \"power factor=0.803\"\n", "#case c\n", "#given\n", "vl=2200\n", "il=w/(3**0.5*vl*0.803) #0.803 is the value of the cos angle and il is the line current\n", "print \"il=\",round(il,5),\"A\"\n", "#case d\n", "#efficiency=o/i #i is input and o is output\n", "hp=746 #horse power\n", "o=0.9*w/hp #0.9 is efficiency\n", "print \"output=\",round(o,3),\"hp\"\n", "\n", "\n" ] }, { "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": "2.7.5" } }, "nbformat": 4, 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