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-{
- "metadata": {
- "name": "",
- "signature": "sha256:e4feee2966703522c4e009f16556422b345ba2813bb92ad5cc7b8ab8058895bb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 1: Synchronous Machines\n"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.1, Page 24"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#given data\n",
- "slots=24;#no. of slotes\n",
- "NoOfPhase=3;#no of phase\n",
- "MotorSpeed=1450;#in rpm\n",
- "N=1500;#Synchonous Speed in rpm\n",
- "f=50;#in Hz\n",
- "\n",
- "#Calculations&Results\n",
- "print \"As the winding is in single layer, each slot contains one coil slide only.\";\n",
- "CoilSlidePerSlot=1;#coil slide per slot\n",
- "CoilSlidePerCoil=2;#coil slide per Coil\n",
- "TotalCoils=slots*CoilSlidePerSlot/CoilSlidePerCoil;#no. of coils\n",
- "print \"Total no. of Coils : \",TotalCoils;\n",
- "P=120*f/N;#no. of poles\n",
- "print \"No. of poles : \",P;\n",
- "PolesPitch=slots/P;#unitless\n",
- "print \"Poles Pitch = \",PolesPitch;\n",
- "print \"In case of single layer winding, the pole ppitch is generally taken in odd numbers only\"\n",
- "print \"let pole pitch = 5(for short pitch winding)\";\n",
- "PolesPitch=5;#for short pitch winding\n",
- "print \"Coil Span or coil through = 1-6\";\n",
- "CoilsPerPolePerPhase=TotalCoils/(P*NoOfPhase);#No. of Coils/Pole/Phase\n",
- "print \"No. of Coils/Pole/Phase = \",CoilsPerPolePerPhase;\n",
- "pair_of_poles=2;#no. of pair of poles\n",
- "TotalElectricalDegree=360*pair_of_poles;#in degree \n",
- "ElectricalDegreesPerSlot=TotalElectricalDegree/slots;#in degree electrical\n",
- "print \"Electrical Degrees/Slot = \",ElectricalDegreesPerSlot;\n",
- "Slots_required=120/ElectricalDegreesPerSlot;#No. of slotes required for proper phase displacement\n",
- "print \"No. of slotes required for proper phase displacement = \",Slots_required;\n",
- "print \"Winding Table is as follows :\";\n",
- "print \"Coil No. Connection Lead from Coil Span Phase and Group No.\";\n",
- "print \" 1 A1 1-6 A1\";\n",
- "print \" 2 3-8 C4\";\n",
- "print \" 3 B1 5-10 B1\";\n",
- "print \" 4 7-12 A2\";\n",
- "print \" 5 C1 9-14 C1\";\n",
- "print \" 6 11-16 B2\";\n",
- "print \" 7 13-18 A3\";\n",
- "print \" 8 15-20 C2\";\n",
- "print \" 9 17-22 B3\";\n",
- "print \" 10 19-24 A4\";\n",
- "print \" 11 21-2 C3\";\n",
- "print \" 12 23-4 B4\";"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "As the winding is in single layer, each slot contains one coil slide only.\n",
- "Total no. of Coils : 12\n",
- "No. of poles : 4\n",
- "Poles Pitch = 6\n",
- "In case of single layer winding, the pole ppitch is generally taken in odd numbers only\n",
- "let pole pitch = 5(for short pitch winding)\n",
- "Coil Span or coil through = 1-6\n",
- "No. of Coils/Pole/Phase = 1\n",
- "Electrical Degrees/Slot = 30\n",
- "No. of slotes required for proper phase displacement = 4\n",
- "Winding Table is as follows :\n",
- "Coil No. Connection Lead from Coil Span Phase and Group No.\n",
- " 1 A1 1-6 A1\n",
- " 2 3-8 C4\n",
- " 3 B1 5-10 B1\n",
- " 4 7-12 A2\n",
- " 5 C1 9-14 C1\n",
- " 6 11-16 B2\n",
- " 7 13-18 A3\n",
- " 8 15-20 C2\n",
- " 9 17-22 B3\n",
- " 10 19-24 A4\n",
- " 11 21-2 C3\n",
- " 12 23-4 B4\n"
- ]
- }
- ],
- "prompt_number": 52
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.2, Page 28"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#given data\n",
- "slots=24;#no. of slotes\n",
- "P=4;#no. of poles\n",
- "CoilPitch=5;#unitless\n",
- "NoOfPhase=3;#no of phase\n",
- "\n",
- "#Calculations&Results\n",
- "print \"As the winding is in double layer, each slot contains 2 coils per slide.\";\n",
- "CoilSlidePerSlot=2;#coil slide per slot\n",
- "CoilSlidePerCoil=2;#coil slide per Coil\n",
- "TotalCoils=slots*CoilSlidePerSlot/CoilSlidePerCoil;#no. of coils\n",
- "print \"Total no. of Coils : \",TotalCoils;\n",
- "PolesPitch=slots/P;#unitless\n",
- "print \"Pole Pitch = \",PolesPitch;\n",
- "CoilsPerPolePerPhase=TotalCoils/(P*NoOfPhase);#No. of Coils/Pole/Phase\n",
- "print \"No. of Coils/Pole/Phase = \",CoilsPerPolePerPhase;\n",
- "pair_of_poles=2;#no. of pair of poles\n",
- "TotalElectricalDegree=360*pair_of_poles;#in degree \n",
- "ElectricalDegreesPerSlot=TotalElectricalDegree/slots;#in degree electrical\n",
- "print \"Electrical Degrees/Slot = \",ElectricalDegreesPerSlot;\n",
- "Slots_required=120/ElectricalDegreesPerSlot;#No. of slotes required for proper phase displacement\n",
- "print \"No. of slots required for proper phase displacement = \",Slots_required;\n",
- "print \"ie. Phase A1 is brought out from slot no. = 1\";\n",
- "print \"Phase B1 at slot no. = 1+4 = 5\";\n",
- "print \"Phase C1 at slot no. = 5+4 = 9\";\n",
- "print \"Col Connection - end to start to start\";\n",
- "print \"Winding Table is as follows :\";\n",
- "print \"Coil No. Connection Lead from Coil Span Phase and Group No.\";\n",
- "print \" 1 A1 1-6 A1\";\n",
- "print \" 2 2-7 \";\n",
- "print \" 3 3-8 C4\";\n",
- "print \" 4 4-9 \";\n",
- "print \" 5 B1 5-10 B1\";\n",
- "print \" 6 6-11 \";\n",
- "print \" 7 7-12 A2\";\n",
- "print \" 8 8-13 \";\n",
- "print \" 9 C1 9-14 C1\";\n",
- "print \" 10 10-15 \";\n",
- "print \" 11 11-16 B2\";\n",
- "print \" 12 12-17 \";\n",
- "print \" 13 13-18 A3\";\n",
- "print \" 14 14-19 \";\n",
- "print \" 15 15-20 C2\";\n",
- "print \" 16 16-21 \";\n",
- "print \" 17 17-22 B3\";\n",
- "print \" 18 18-23 \";\n",
- "print \" 19 19-24 A4\";\n",
- "print \" 20 20-1 \";\n",
- "print \" 21 21-2 C3\";\n",
- "print \" 22 22-3 \";\n",
- "print \" 23 23-4 \";\n",
- "print \" 24 24-5 B4\";"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "As the winding is in double layer, each slot contains 2 coils per slide.\n",
- "Total no. of Coils : 24\n",
- "Pole Pitch = 6\n",
- "No. of Coils/Pole/Phase = 2\n",
- "Electrical Degrees/Slot = 30\n",
- "No. of slots required for proper phase displacement = 4\n",
- "ie. Phase A1 is brought out from slot no. = 1\n",
- "Phase B1 at slot no. = 1+4 = 5\n",
- "Phase C1 at slot no. = 5+4 = 9\n",
- "Col Connection - end to start to start\n",
- "Winding Table is as follows :\n",
- "Coil No. Connection Lead from Coil Span Phase and Group No.\n",
- " 1 A1 1-6 A1\n",
- " 2 2-7 \n",
- " 3 3-8 C4\n",
- " 4 4-9 \n",
- " 5 B1 5-10 B1\n",
- " 6 6-11 \n",
- " 7 7-12 A2\n",
- " 8 8-13 \n",
- " 9 C1 9-14 C1\n",
- " 10 10-15 \n",
- " 11 11-16 B2\n",
- " 12 12-17 \n",
- " 13 13-18 A3\n",
- " 14 14-19 \n",
- " 15 15-20 C2\n",
- " 16 16-21 \n",
- " 17 17-22 B3\n",
- " 18 18-23 \n",
- " 19 19-24 A4\n",
- " 20 20-1 \n",
- " 21 21-2 C3\n",
- " 22 22-3 \n",
- " 23 23-4 \n",
- " 24 24-5 B4\n"
- ]
- }
- ],
- "prompt_number": 53
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.3, Page 35"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import *\n",
- "\n",
- "#given data\n",
- "StatorSlots=36;#No. of stator slots\n",
- "Poles=4;#No. of poles\n",
- "#coilSpan=1:8;#unitless\n",
- "\n",
- "#Calculations&Results\n",
- "SlotsPerPole=StatorSlots/Poles;# no. of slots per pole\n",
- "print \"Slots/Pole = \",SlotsPerPole;\n",
- "print \"Here the coil span falls short by, \",((2./9)*180),\" Degree\";\n",
- "alfa=40*pi/180;#short pitch angle in degree\n",
- "Kp=cos(alfa/2);#Coil span Factor\n",
- "print \"Pitch Factor or coil span factor : \",round(Kp,1);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Slots/Pole = 9\n",
- "Here the coil span falls short by, 40.0 Degree\n",
- "Pitch Factor or coil span factor : 0.9\n"
- ]
- }
- ],
- "prompt_number": 62
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.4, Page 38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import *\n",
- "\n",
- "#given data\n",
- "NoOfPhase=3;#no of phase\n",
- "P=16;#No. of pole alternator\n",
- "Slots=144;#No. of slots\n",
- "Conductors=10;#per slot\n",
- "fi=0.03;#in Weber\n",
- "N=375;#machine speed in rpm\n",
- "\n",
- "#Calculations\n",
- "f=P*N/120;#in Hz\n",
- "SlotsPerPole=Slots/P;#unitless\n",
- "m=Slots/(P*NoOfPhase);#unitless\n",
- "Beta=180/(SlotsPerPole);#in Degree\n",
- "Kd=sin(m*Beta/2*pi/180)/(m*sin(Beta/2*pi/180));#unitless\n",
- "TotalConductors=Conductors*Slots;#no. of conductors\n",
- "TotalConductorsPerPhase=Conductors*Slots/NoOfPhase;#no. of conductors/phase\n",
- "TurnsPerPhase=TotalConductorsPerPhase/2;#No. of turns per phase\n",
- "EMFPerPhase=4.44*Kd*fi*f*TurnsPerPhase;#in Volt\n",
- "LineVoltage=sqrt(3)*EMFPerPhase;#in Volt\n",
- "\n",
- "#Results\n",
- "print \"Frequency in Hz : \",f;\n",
- "print \"Phase Electromotive force in Volt : \",round(EMFPerPhase,1);\n",
- "print \"Line Electromotive force in Volt : \",round(LineVoltage,3);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Frequency in Hz : 50\n",
- "Phase Electromotive force in Volt : 1534.1\n",
- "Line Electromotive force in Volt : 2657.202\n"
- ]
- }
- ],
- "prompt_number": 76
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.5, Page 39"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "NoOfPhase=3;#no of phase\n",
- "SlotsPerPhase=3;#o. of slots\n",
- "\n",
- "#Calculations&Results\n",
- "m=SlotsPerPhase;#no. of slots\n",
- "SlotsPerPolePerPhase=SlotsPerPhase*NoOfPhase;#unitless\n",
- "Beta=180./SlotsPerPolePerPhase;#in degree\n",
- "print \"The phase difference between the induced emf in two coils lying in adjacent slots = \",(Beta),\" degree\";\n",
- "Kb=sin((m*Beta*pi)/(2*180))/(m*sin((Beta*pi)/(2*180)));#unitless\n",
- "print \"The breadth factor : \",round(Kb,3);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The phase difference between the induced emf in two coils lying in adjacent slots = 20.0 degree\n",
- "The breadth factor : 0.96\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.6, Page 39"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "StatorSlots=24#No. of stator slots\n",
- "Poles=4;#No. of poles\n",
- "SlotsPerPole=StatorSlots/Poles;# no. of slots per pole\n",
- "#coilSpan=1:6;#unitless\n",
- "\n",
- "#Calculations&Results\n",
- "print \"If the sides of the coil are placed in slots 1 and 7, then it is full pitched, \\nIf the coil slides are placed\" \\\n",
- " + \" in 1 and 6 then it is short pitched and the distance equal to 5/6th of pole-pitch.\";\n",
- "print \"Since it falls short by 1/6th of the pole-pitch, hence it is short by :\"\n",
- "theta=180/SlotsPerPole;#in Degree\n",
- "print (theta),\" Degree.\"\n",
- "Kp=cos(theta/2*pi/180);#unitless\n",
- "print \"Pitch-factor Kp : \",round(Kp,4);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "If the sides of the coil are placed in slots 1 and 7, then it is full pitched, \n",
- "If the coil slides are placed in 1 and 6 then it is short pitched and the distance equal to 5/6th of pole-pitch.\n",
- "Since it falls short by 1/6th of the pole-pitch, hence it is short by :\n",
- "30 Degree.\n",
- "Pitch-factor Kp : 0.9659\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.7, Page 40"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#given data\n",
- "NoOfPhase=3;#no of phase\n",
- "Eph=3300/sqrt(3);#in Volts\n",
- "f=50;#in Hz\n",
- "Poles=12;#No. of poles\n",
- "StatorSlots=144#No. of stator slots\n",
- "\n",
- "#Calculations\n",
- "SlotsPerPhase=StatorSlots/NoOfPhase;#no. of slots/phase\n",
- "Conductors=5;#per slot\n",
- "ConductorsPerphase=SlotsPerPhase*Conductors;#Conductors/Phase\n",
- "S=ConductorsPerphase;#Conductors/phase\n",
- "SlotsPerPolePerPhase=SlotsPerPhase/Poles;#no. of slots/phase\n",
- "Kf=1.11;#Form Factor\n",
- "Kb=0.96;#Breadth Factor\n",
- "Kp=1;#For concentric winding\n",
- "fi=Eph/(2*Kf*Kb*Kp*S*f);#in weber\n",
- "\n",
- "#Result\n",
- "print \"The Flux per pole in weber : \",round(fi,4);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Flux per pole in weber : 0.0745\n"
- ]
- }
- ],
- "prompt_number": 93
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.8, Page 41"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "Phase=3;#no. of phase\n",
- "f=50;#in Hz\n",
- "P=16;#No. of pole alternator\n",
- "Slots=144.;#No. of slots\n",
- "conductors=10;#conductors per slot\n",
- "\n",
- "#Calculations&Results\n",
- "fi=2.48*10**-2;#in weber\n",
- "n=Slots/P;#No. of slots/pole\n",
- "Zr=Slots*conductors/Phase;#No. of conductors/Phase\n",
- "T=Zr/2;#N. of turns/phase\n",
- "Beta=180/n;#Angular displacement between slots in degree\n",
- "m=n/Phase;#No. of slots/pole/Phase\n",
- "Kd=sin(m*Beta/2*pi/180)/(m*sin(Beta/2*pi/180));#Distribution factor :unitless \n",
- "print \"The coil span falls short of 2 slots i.e. \",(2*180/9),\" degree.\";\n",
- "alfa=40;#short pitch angle in degree\n",
- "Kp=(cos(alfa/2*pi/180));#Unitless\n",
- "#Formula : f=P*N/120;#in Hz\n",
- "N=120*f/P;#in rpm\n",
- "Ep=4.44*Kd*Kp*fi*f*T;#in Volts\n",
- "LineVoltage=sqrt(3)*Ep;#in Volts\n",
- "print \"The speed is \",(N),\" in rpm\";\n",
- "print \"The line emf is \",round(LineVoltage,2),\" Volts\";\n",
- "#Note : Answer in the book is not accurate for last part due to rounding off errors"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The coil span falls short of 2 slots i.e. 40 degree.\n",
- "The speed is 375 in rpm\n",
- "The line emf is 2064.15 Volts\n"
- ]
- }
- ],
- "prompt_number": 109
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.9, Page 58"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "RatedPower=100;#in KVA\n",
- "RatedPower=100*1000;#in VA\n",
- "VL=1040;#in Volt\n",
- "Phase=3;#Machine phase\n",
- "If=40;#in Ampere\n",
- "Isc=200;#in Ampere\n",
- "EL=1040;#in Volt\n",
- "\n",
- "#Calculations&Results\n",
- "Eph=EL/sqrt(3);#in Volt\n",
- "Zs=Eph/Isc;#in Ohm\n",
- "Rs=0.2;#in Ohm\n",
- "Xs=sqrt(Zs**2-Rs**2);#in Ohm\n",
- "IL=19.25;#in Ampere\n",
- "V=3000/sqrt(3);#in Volt\n",
- "#At 0.8 power factor lagging\n",
- "IRa=IL*0.2;#in Volt\n",
- "IXs=IL*Xs;#in Volt\n",
- "Vsin_fi=V*0.6;#in Volt\n",
- "Vcos_fi=V*0.8;#in Volt\n",
- "Eo=sqrt((Vcos_fi+IRa)**2+(Vsin_fi+IXs)**2);#in Volts\n",
- "Regulation=((Eo-V)/V)*100;#in %\n",
- "print \"Full load percentage regulation at a power factor of 0.8 lagging : \",round(Regulation,1);\n",
- "\n",
- "#At 0.8 power factor leading\n",
- "Eo=sqrt((Vcos_fi+IRa)**2+(Vsin_fi-IXs)**2);#in Volts\n",
- "Regulation=((Eo-V)/V)*100;#in %\n",
- "print \"Full load percentage regulation at a power factor of 0.8 leading : \",round(Regulation,2);\n",
- "print \"Negative regulation due to leading power factor.\";"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Full load percentage regulation at a power factor of 0.8 lagging : 2.2\n",
- "Full load percentage regulation at a power factor of 0.8 leading : -1.78\n",
- "Negative regulation due to leading power factor.\n"
- ]
- }
- ],
- "prompt_number": 110
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.10, Page 60"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "RatedPower=50;#in KVA\n",
- "RatedPower=50*1000;#in VA\n",
- "VL=173;#in Volts\n",
- "Ra=0.1;#in Ohm\n",
- "\n",
- "#Calculations&Results\n",
- "VP=VL/sqrt(3);#in Volts\n",
- "print \"Some exciting curent on short circuit produces a current of 100 A.\";\n",
- "OC_PhaseVoltage=100;#in Volt\n",
- "SC_Current=100;#in Ampere\n",
- "Zs=OC_PhaseVoltage/SC_Current;#n ohm\n",
- "Xs=sqrt(Zs**2-Ra**2);#in Ohm\n",
- "print \"Impedence of the alternator in Ohm : \",round(Xs,2);\n",
- "V=400;#in Volts\n",
- "I_FL=RatedPower/(sqrt(3)*V);#in Ampere\n",
- "V=400/sqrt(3);#in Volts\n",
- "Eo=sqrt((V+I_FL*Ra)**2+(I_FL*Xs)**2);#in Volts\n",
- "Regulation=(Eo-V)*100/V;#in %\n",
- "print \"Regulation at U.P.F. in % :\",round(Regulation,2);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Some exciting curent on short circuit produces a current of 100 A.\n",
- "Impedence of the alternator in Ohm : 0.99\n",
- "Regulation at U.P.F. in % : 7.71\n"
- ]
- }
- ],
- "prompt_number": 112
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.11, Page 61"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "OutputPower=500;#in KVA\n",
- "OutputPower=500*1000;#in VA\n",
- "VL=3300;#in Volts\n",
- "Ra=0.3;#in Ohm\n",
- "Xs=4;#in Ohm\n",
- "PF=0.8;#Lagging Power factor\n",
- "\n",
- "#Calculations&Results\n",
- "#Formula : outputPower=sqrt(3)*VL*IL\n",
- "IL=OutputPower/(sqrt(3)*VL);#in Ampere\n",
- "print \"For a star connected alternator, line current is equal to phase current. Therefore Ia=IL\";\n",
- "Ia=IL;#in Ampere\n",
- "#PF=cosd(fi)=0.8 and sind(fi)=0.6\n",
- "cos_fi=0.8;#Power factor\n",
- "sin_fi=0.6;#Unitless\n",
- "VPerPhase=VL/sqrt(3);#in Volts\n",
- "E=sqrt((VPerPhase*cos_fi+Ia*Ra)**2+(VPerPhase*sin_fi+Ia*Xs)**2);#in Volts/Phase\n",
- "Regulation=(E-VPerPhase)*100/VPerPhase;#in %\n",
- "print \"Voltage Regulation at Full Load in % :\",round(Regulation,2);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "For a star connected alternator, line current is equal to phase current. Therefore Ia=IL\n",
- "Voltage Regulation at Full Load in % : 12.98\n"
- ]
- }
- ],
- "prompt_number": 113
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.12, Page 62"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "V=2000;#in Volt\n",
- "Ia=100;#in Ampere\n",
- "OC_Voltage=500;#in Volt\n",
- "SC_Current=100;#in Ampere\n",
- "\n",
- "#Calculations&Results\n",
- "Zs=OC_Voltage/SC_Current;#in ohm\n",
- "Ra=0.8;#in Ohm\n",
- "Xs=sqrt(Zs**2-Ra**2);#in Ohm\n",
- "#formula : Induced EMF, E=sqrt((V*cos_fi+Ia*Ra)^2+(V*sin_fi+Ia*Xs)^2)\n",
- "#Part (a) : at unity pf\n",
- "cos_fi=1;#Unitless\n",
- "sin_fi=0;#Unitless\n",
- "E=sqrt((V*cos_fi+Ia*Ra)**2+(V*sin_fi+Ia*Xs)**2)\n",
- "Regulation=(E-V)*100/V;#in %\n",
- "print \"Regulation at U.P.F. in % :\",round(Regulation,2);\n",
- "\n",
- "#Part (b) : at 0.71 pf lagging\n",
- "cos_fi=0.71;#Unitless\n",
- "sin_fi=0.704;#Unitless\n",
- "E=sqrt((V*cos_fi+Ia*Ra)**2+(V*sin_fi+Ia*Xs)**2)\n",
- "Regulation=(E-V)*100/V;#in %\n",
- "print \"Regulation at 0.71 pf lagging in % :\",round(Regulation,2);\n",
- "\n",
- "#Part (c) : at 0.8 pf leading\n",
- "cos_fi=0.8;#Unitless\n",
- "sin_fi=0.6;#Unitless\n",
- "E=sqrt((V*cos_fi+Ia*Ra)**2+(V*sin_fi-Ia*Xs)**2)\n",
- "Regulation=(E-V)*100/V;#in %\n",
- "print \"Regulation at 0.8 pf leading in % :\",round(Regulation,2);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Regulation at U.P.F. in % : 6.89\n",
- "Regulation at 0.71 pf lagging in % : 21.1\n",
- "Regulation at 0.8 pf leading in % : -8.88\n"
- ]
- }
- ],
- "prompt_number": 114
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.13, Page 63"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "#given data\n",
- "Ia=60;#in Ampere\n",
- "\n",
- "#Calculations&Results\n",
- "print \"The value of synchronous impedence at this excitation :\" ;\n",
- "OC_Voltage=900;#in Volt\n",
- "SC_Current=150;#in Ampere\n",
- "Zs=OC_Voltage/SC_Current;#in ohm\n",
- "print \"Zs equals to \",(Zs),\" Ohm\";\n",
- "print \"Internal Voltage drop when tthe load current is 60A=Ia*Zs=\",(Ia*Zs),\" Volts\";"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of synchronous impedence at this excitation :\n",
- "Zs equals to 6 Ohm\n",
- "Internal Voltage drop when tthe load current is 60A=Ia*Zs= 360 Volts\n"
- ]
- }
- ],
- "prompt_number": 118
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.14, Page 63"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "V=6600;#in Volts\n",
- "OutputPower=2000;#in KVA\n",
- "\n",
- "#Calculations\n",
- "OutputPower=2000*1000;#in VA\n",
- "#Formula : outputPower=sqrt(3)*VL*IL\n",
- "IL=OutputPower/(sqrt(3)*V);#in Ampere\n",
- "Ia=IL;#in Ampere\n",
- "Ra=0.4;#in Ohm\n",
- "Xs=4.5;#in Ohm\n",
- "#PF=cosd(fi)=0.8 and sind(fi)=0.6\n",
- "cos_fi=0.8;#Power factor\n",
- "sin_fi=0.6;#Unitless\n",
- "VPerPhase=V/sqrt(3);#in Volts\n",
- "E=sqrt((VPerPhase*cos_fi+Ia*Ra)**2+(VPerPhase*sin_fi+Ia*Xs)**2);#in Volts/Phase\n",
- "Regulation=(E-VPerPhase)*100/VPerPhase;#in %\n",
- "\n",
- "#Result\n",
- "print \"Percentage Change in Terminal Voltage :\",round(Regulation,1);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Percentage Change in Terminal Voltage : 14.9\n"
- ]
- }
- ],
- "prompt_number": 119
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.15, Page 63"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "OutputPower=1200;#in KVA\n",
- "OutputPower=1200*1000;#in VA\n",
- "V=3300;#in Volt\n",
- "Ra=0.25;#in Ohm\n",
- "\n",
- "#Calculations&Results\n",
- "#Formula : outputPower=sqrt(3)*VL*IL\n",
- "IL=OutputPower/(sqrt(3)*V);#in Ampere\n",
- "Ia=IL;#in Ampere\n",
- "VPerPhase=V/sqrt(3);#in Volts\n",
- "OC_Voltage=1100;#in Volt\n",
- "SC_Current=200;#in Ampere\n",
- "Zs=OC_Voltage/(sqrt(3)*SC_Current);#in ohmRa\n",
- "Xs=sqrt(Zs**2-Ra**2);#in Ohm\n",
- "#formula : Induced EMF, E=sqrt((V*cos_fi+Ia*Ra)^2+(V*sin_fi+Ia*Xs)^2)\n",
- "\n",
- "#Part (a) : For lagging pf load\n",
- "cos_fi=0.8;#Unitless\n",
- "sin_fi=0.6;#Unitless\n",
- "E=sqrt((VPerPhase*cos_fi+Ia*Ra)**2+(VPerPhase*sin_fi+Ia*Xs)**2);\n",
- "Regulation=(E-VPerPhase)*100/VPerPhase;#in %\n",
- "print \"Regulation at U.P.F. in % :\",round(Regulation,2);\n",
- "\n",
- "#Part (b) : For leading pf load\n",
- "cos_fi=0.8;#Unitless\n",
- "sin_fi=0.6;#Unitless\n",
- "E=sqrt((VPerPhase*cos_fi+Ia*Ra)**2+(VPerPhase*sin_fi-Ia*Xs)**2)\n",
- "Regulation=(E-VPerPhase)*100/VPerPhase;#in %\n",
- "print \"Regulation at 0.71 pf lagging in % :\",round(Regulation,2);\n",
- "#Note: For leading power factor load, the regulation s negative. "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Regulation at U.P.F. in % : 25.9\n",
- "Regulation at 0.71 pf lagging in % : -13.52\n"
- ]
- }
- ],
- "prompt_number": 120
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.16, Page 64"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "OutputPower=1500;#in KVA\n",
- "OutputPower=1500*1000;#in VA\n",
- "V=6600;#in Volt\n",
- "Ra=0.4;#in Ohm\n",
- "Xs=6;#in Ohm per phase\n",
- "pf=0.8;#lagging power factor\n",
- "\n",
- "#Calculations&Results\n",
- "#Formula : outputPower=sqrt(3)*VL*IL\n",
- "Ia=OutputPower/(sqrt(3)*V);#in Ampere\n",
- "VPerPhase=V/sqrt(3);#in Volts\n",
- "#formula : Induced EMF, E=sqrt((V*cos_fi+Ia*Ra)^2+(V*sin_fi+Ia*Xs)^2)\n",
- "cos_fi=0.8;#Unitless\n",
- "sin_fi=0.6;#Unitless\n",
- "E=sqrt((VPerPhase*cos_fi+Ia*Ra)**2+(VPerPhase*sin_fi+Ia*Xs)**2);#in volt\n",
- "print \"Induced emf in volt : \",round(E,2);\n",
- "print \"As excitation remains constant, E at 4364 volt remains constant.\";\n",
- "E=4364;#in Volt\n",
- "V=4743;#in Volts\n",
- "TerminalVoltage=sqrt(3)*V;#in Volts\n",
- "print \"Terminal voltage line to line in Volts : \",round(TerminalVoltage);\n",
- "#Note ans of 1st part is wrong in the books"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Induced emf in volt : 4366.07\n",
- "As excitation remains constant, E at 4364 volt remains constant.\n",
- "Terminal voltage line to line in Volts : 8215.0\n"
- ]
- }
- ],
- "prompt_number": 123
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.17, Page 81"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "OutputPower=2500;#in KVA\n",
- "OutputPower=2500*1000;#in VA\n",
- "V=6600;#in Volt\n",
- " \n",
- "#Calculations\n",
- "#For first load i.e. Lighting load : \n",
- "KW1=2500;#in KWatts\n",
- "KVAR1=0;#Kwatts\n",
- "#For second load i.e. Motor load : \n",
- "KW2=5000;#in KWatts\n",
- "cos_fi=0.707;#unitless\n",
- "sin_fi=0.707;#unitless\n",
- "KVAR2=KW2*sin_fi/cos_fi;#Kwatts\n",
- "#For total load\n",
- "TotalKW=KW1+KW2;#in KWatts\n",
- "TotalKVAR=KVAR1+KVAR2;#Kwatts \n",
- "#For first Machine\n",
- "KWm=4000;#in KWatts\n",
- "cos_fi=0.8;#unitless\n",
- "sin_fi=0.6;#unitless\n",
- "KVARm=KWm*sin_fi/cos_fi;#Kwatts\n",
- "#so, second machine will be supplying\n",
- "KW=TotalKW-KWm;#in Kwatts\n",
- "print \"KW output of second machine : \",KW;\n",
- "KVAR=TotalKVAR-KVARm;#in KWatts\n",
- "tan_fi=KVAR/KW;#unitless\n",
- "fi=atan(tan_fi);#ib degree\n",
- "#Power factor of other machine\n",
- "pf=cos(fi);#unitless\n",
- "\n",
- "#Result\n",
- "print \"Power factor of other machine : \",round(pf,4),\" lagging\";"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "KW output of second machine : 3500\n",
- "Power factor of other machine : 0.8682 lagging\n"
- ]
- }
- ],
- "prompt_number": 126
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.18, Page 82"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "\n",
- "#Load1 : \n",
- "KW1=500;#in KWatts\n",
- "KVAR1=0;#Kwatts\n",
- "\n",
- "#Load2 : \n",
- "KW2=1000;#in KWatts\n",
- "pf=0.9;#lagging\n",
- "cos_fi=0.9;#unitless\n",
- "fi=acos(pf);\n",
- "sin_fi=sin(fi);#unitless\n",
- "KVAR2=KW2*sin_fi/cos_fi;#Kwatts\n",
- "\n",
- "#Load3 : \n",
- "KW3=800;#in KWatts\n",
- "pf=0.8;#lagging\n",
- "cos_fi=0.8;#unitless\n",
- "fi=acos(pf);\n",
- "sin_fi=sin(fi);#unitless\n",
- "KVAR3=KW3*sin_fi/cos_fi;#Kwatts\n",
- "\n",
- "#Load4 : \n",
- "KW4=500;#in KWatts\n",
- "pf=0.9;#lagging\n",
- "cos_fi=0.9;#unitless\n",
- "fi=acos(pf);\n",
- "sin_fi=sin(fi);#unitless\n",
- "KVAR4=-KW4*sin_fi/cos_fi;#Kwatts\n",
- "#TOtalKW and TotalKVAR\n",
- "TotalKW=KW1+KW2+KW3+KW4;#in KWatts\n",
- "TotalKVAR=KVAR1+KVAR2+KVAR3+KVAR4;#in KWAtts\n",
- "#For the first Machine :\n",
- "KW=1500;#n Kwatts\n",
- "cos_fi=0.95;#unitless\n",
- "sin_fi=0.3123;#unitless\n",
- "KVAR=KW*sin_fi/cos_fi;#Kwatts\n",
- "\n",
- "KW1=TotalKW-KW;#in KWatts\n",
- "KVAR1=TotalKVAR-KVAR;#in Volts\n",
- "print \"KW supplied by other machine : \",(TotalKW-KW);\n",
- "print \"KVAR supplied by other machine : \",round(TotalKVAR-KVAR); #answer differs due to rounding off the digits\n",
- "tan_fi=KVAR1/KW1;#unitless\n",
- "#fi=atand(tan_fi);#in degree\n",
- "cos_fi=cos(atan(tan_fi));#unitless\n",
- "\n",
- "#Result\n",
- "print \"Power factor of the other machine : \",round(cos_fi,3);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "KW supplied by other machine : 1300\n",
- "KVAR supplied by other machine : 349.0\n",
- "Power factor of the other machine : 0.966\n"
- ]
- }
- ],
- "prompt_number": 129
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.19, Page 82"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "\n",
- "#Lighting Load : \n",
- "MW1=20;#load in Mwatts\n",
- "KW1=MW1*1000;#in KWatts\n",
- "KVAR1=0;#Kwatts\n",
- "\n",
- "#Motor Load : \n",
- "MW2=40;#load in Mwatts\n",
- "KW2=MW2*1000;#in KWatts\n",
- "pf=0.8;#unitless\n",
- "cos_fi=0.8\n",
- "fi=acos(pf);\n",
- "sin_fi=sin(fi);#unitless\n",
- "KVAR2=KW2*sin_fi/cos_fi;#Kwatts\n",
- "\n",
- "#For Total Load : \n",
- "TotalKW=KW1+KW2;#load in Mwatts\n",
- "TotalKVAR=KVAR1+KVAR2;#in KWatts\n",
- "#For first machine : \n",
- "MWm=32;#load in Mwatts\n",
- "KWm=MWm*1000;#in KWatts\n",
- "cos_fi=0.866;#unitless\n",
- "fi=acos(cos_fi);\n",
- "tan_fi=tan(fi);#unitless\n",
- "KVARm=KWm*tan_fi;#in KWatts\n",
- "#so, load supplied by the second machine\n",
- "KW2=TotalKW-KWm;#in Kwatts\n",
- "print \"Load of other machine,KW : \",(KW2);\n",
- "KVAR2=TotalKVAR-KVARm;#in Kwatts\n",
- "tan_fi=KVAR2/KW2;#unitless\n",
- "fi=atan(tan_fi);#in degree\n",
- "cos_fi=cos(atan(tan_fi));#unitless\n",
- "\n",
- "#Result\n",
- "print \"Power factor of the other machine : \",round(cos_fi,3);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Load of other machine,KW : 28000\n",
- "Power factor of the other machine : 0.925\n"
- ]
- }
- ],
- "prompt_number": 131
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.20, Page 84"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "cos_fi=0.8;#unitless\n",
- "fi=acos(cos_fi);\n",
- "tan_fi=tan(fi);#unitless\n",
- "\n",
- "#For Alternator A : \n",
- "cos_fi_A=0.9;#unitless\n",
- "fi_A=acos(cos_fi_A);\n",
- "tan_fi_A=tan(fi_A);#unitless\n",
- "#Formula : Active load, KW=V*I*cos_fi\n",
- "#Formula : Reactive load, KVAR=V*I*sin_fi\n",
- "ActiveLoad=8000;#in KW\n",
- "ReactiveLoad=ActiveLoad*tan_fi;#in KVAR\n",
- "\n",
- "#For A:\n",
- "ActiveLoadA=5000;#in KW\n",
- "ReactiveLoadA=ActiveLoadA*tan_fi_A;#in KVAR\n",
- "\n",
- "#For B :\n",
- "ActiveLoadB=ActiveLoad-ActiveLoadA;#in KW\n",
- "ReactiveLoadB=ReactiveLoad-ReactiveLoadA;#in KVAR\n",
- "tan_fi_B=ReactiveLoadB/ActiveLoadB;#unitless\n",
- "fi_B=atan(tan_fi_B);#in degree\n",
- "cos_fi=cos(atan(tan_fi_B));#unitless\n",
- "\n",
- "#Result\n",
- "print \"Power factor of the other machine : \",round(cos_fi,3);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Power factor of the other machine : 0.642\n"
- ]
- }
- ],
- "prompt_number": 133
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.21, Page 97"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "V=6600;#in Volts\n",
- "KW=6000.;#in KWatts\n",
- "pf=0.8;#unitless\n",
- "cos_fi=pf;#unitless\n",
- "Eff=90.;#in %\n",
- "\n",
- "#Calculations&Results\n",
- "#Part (a) : \n",
- "KVA=KW/cos_fi;#in KVAR\n",
- "print \"KVA rating of the alternator : \",(KVA),\" KVA\";\n",
- "#Part (b) : \n",
- "TotalRating=KVA;#in KVA\n",
- "VA=TotalRating*1000;#in VA\n",
- "I=VA/(sqrt(3)*KW);#in Ampere\n",
- "print \"Current Rating in Ampere : \",round(I,2);\n",
- "#Part (c) :\n",
- "Input=KW/(Eff/100);#in KW\n",
- "print \"Power Input(in KW) :\",round(Input,2);\n",
- "Input=Input*1000/735.5;#in hp\n",
- "print \"Power Input(in hp) :\",round(Input,2);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "KVA rating of the alternator : 7500.0 KVA\n",
- "Current Rating in Ampere : 721.69\n",
- "Power Input(in KW) : 6666.67\n",
- "Power Input(in hp) : 9064.13\n"
- ]
- }
- ],
- "prompt_number": 139
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.22, Page 97"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from math import * \n",
- "\n",
- "#given data\n",
- "Ecoil=8000;#in Volts\n",
- "Icoil=418;#in Ampere\n",
- "pf=80.;#in % lgging\n",
- "\n",
- "#Calculations&Results\n",
- "pf=pf/100;#in fraction\n",
- "cos_fi=pf;#unitless\n",
- "#Part (i) : \n",
- "EL=sqrt(3)*Ecoil;#in volt\n",
- "print \"Line volts(in V): \",round(EL);\n",
- "#Part (ii) : \n",
- "IL=Icoil;#in Ampere\n",
- "print \"Line Current in Ampere : \",IL;\n",
- "#Part (iii) :\n",
- "Rating=sqrt(3)*EL*IL/1000;#in KVA\n",
- "print \"Rating (in KVA) :\",Rating;\n",
- "#Part (iv) :\n",
- "FullLoadPower=sqrt(3)*EL*IL*cos_fi/1000;#in KW\n",
- "print \"Full Load Power in KW :\",FullLoadPower;"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Line volts(in V): 13856.0\n",
- "Line Current in Ampere : 418\n",
- "Rating (in KVA) : 10032.0\n",
- "Full Load Power in KW : 8025.6\n"
- ]
- }
- ],
- "prompt_number": 140
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 16:21:48 +0000