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diff --git a/Electrical_Machines_II_by_Tarlok_Singh/chapter_1.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/chapter_1.ipynb new file mode 100755 index 00000000..d7710dba --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/chapter_1.ipynb @@ -0,0 +1,1296 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:71f7bb8af90f7646594735a45487d4bfd13546103b9649bd9552504ec18c8029" + }, + "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 pi, sqrt, sin, cos\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": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.4, Page 38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.5, Page 39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.6, Page 39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.7, Page 40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.8, Page 41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.9, Page 58" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.10, Page 60" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.11, Page 61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, cos, sin\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": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.12, Page 62" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 21 + }, + { + "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 pi, sqrt, sin, cos\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 pi, sqrt, sin, cos\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 pi, sqrt, sin, cos\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 pi, sqrt, sin, cos, atan, tan\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": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.18, Page 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.19, Page 82" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos, acos, tan, atan\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": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.20, Page 84" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos, atan, tan, acos\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": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.21, Page 97" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.22, Page 97" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\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": 31 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Electrical_Machines_II_by_Tarlok_Singh/chapter_2.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/chapter_2.ipynb new file mode 100755 index 00000000..59f03184 --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/chapter_2.ipynb @@ -0,0 +1,2810 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0e3f32e542105b85338ffef953c9f9ed43138aa30c5d9cb997a0731312a71a64" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Induction Motors" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1, Page 130" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=2;#no. of poles\n", + "f=60;#in Hz\n", + "N=3460.;#in rpm\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm\n", + "Slip=Ns-N;#in rpm\n", + "PercentageSlip=((Ns-N)/Ns)*100;#in %\n", + "\n", + "#Results\n", + "print \"Synchronous speed in rpm : \",Ns;\n", + "print \"Percentage Slip : \",round(PercentageSlip,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed in rpm : 3600\n", + "Percentage Slip : 3.89\n" + ] + } + ], + "prompt_number": 124 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2, Page 131" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=8.;#no. of poles\n", + "f=50.;#in Hz\n", + "N=700.;#in rpm\n", + "\n", + "#Calculations&Results\n", + "#Part (a) :\n", + "Ns=120*f/P;#in rpm\n", + "print \"Synchronous speed in rpm : \",Ns;\n", + "#Part (b) :\n", + "S=(Ns-N)*100/Ns;#in %\n", + "print \"Slip(in %) : \",round(S,2);\n", + "#Part (c) :\n", + "#At the time of stsrt S=1;\n", + "fdash=f;#in Hz\n", + "print \"Rotor frequeny at the time of starting(in Hz) : \",fdash;\n", + "#Part (d) :\n", + "fdash=(S/100)*f;#in Hz\n", + "print \"Rotor frequeny at the given speed(in Hz) : \",round(fdash,1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed in rpm : 750.0\n", + "Slip(in %) : 6.67\n", + "Rotor frequeny at the time of starting(in Hz) : 50.0\n", + "Rotor frequeny at the given speed(in Hz) : 3.3\n" + ] + } + ], + "prompt_number": 125 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3, Page 131" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=10;#no. of poles\n", + "f=50;#in Hz\n", + "N=600;#in rpm\n", + "Nr=1440;#in rpm\n", + "\n", + "#Calculations&Results\n", + "f=P*N/120;#in Hz\n", + "#When P=2\n", + "P=2;#no. of poles\n", + "Ns=120*f/P;#in rpm\n", + "#When P=4\n", + "P=4;#no. of poles\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-Nr)*100/Ns;#Slip in %\n", + "print \"Percentage Slip(in %) : \",(S);\n", + "print \"No. of poles : \",(S);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage Slip(in %) : 4\n", + "No. of poles : 4\n" + ] + } + ], + "prompt_number": 126 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4, Page 132" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=8;#no. of poles\n", + "f=50;#in Hz\n", + "fr=1.5;#in Hz\n", + "\n", + "#Calculations\n", + "#Formula : fr=S*f\n", + "S=fr/f;#slip(unitless)\n", + "Ns=120*f/P;#in rpm\n", + "#Formula : S=(Ns-Nr)/Ns\n", + "Nr=Ns-S*Ns;#in rpm\n", + "\n", + "#Results\n", + "print \"Motor running speed in rpm : \",round(Nr);\n", + "print \"Slip(in %):\",(S*100);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Motor running speed in rpm : 728.0\n", + "Slip(in %): 3.0\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5, Page 133" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=2;#no. of poles\n", + "f=50;#in Hz\n", + "S=4.;#in %\n", + "\n", + "#Calculations&Results\n", + "#Part (i) : \n", + "Ns=f/P;#in rps\n", + "Ns=Ns*60;#in rpm\n", + "print \"Synchronous speed in rpm : \",Ns;\n", + "#Part (ii) :\n", + "print \"Slip = \",(S),\"% or \",(S/100);\n", + "#Part (iii) :\n", + "N=Ns*(1-S/100);#in rpm\n", + "print \"Actual speed in rpm :\",N;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed in rpm : 1500\n", + "Slip = 4.0 % or 0.04\n", + "Actual speed in rpm : 1440.0\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6, Page 133" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "P=4;#no. of poles\n", + "f1=50;#in Hz\n", + "fdash=1.5;#in Hz\n", + "\n", + "#Calculations\n", + "S=fdash/f1;#unitless\n", + "print \"Slip : \",S;\n", + "Ns=120*f1/P;#in rpm\n", + "N=Ns*(1-S);#in rpm\n", + "\n", + "#Result\n", + "print \"Speed of motor in rpm :\",N;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.03\n", + "Speed of motor in rpm : 1455.0\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7, Page 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "N=1440;#in rpm\n", + "\n", + "#Calculations&Results\n", + "f=50;#in Hz\n", + "print \"For this speed of 1440 rpm the synchronous speed may be either 1500 rpm or 3000 rpm.\";\n", + "Ns=1500;#in rpm\n", + "P=4;#no. of poles\n", + "print \"No. of poles : \",P;\n", + "Slip=(Ns-N)*100/Ns;#in %\n", + "print Slip,\"Slip(in %) : \",Slip;\n", + "speed1=Ns-N;#Speed of rotor flux with respect to rotor\n", + "print \"Speed of rotor flux with respect to rotor in rpm : \",speed1;\n", + "speed2=(speed1)+N;#Speed of rotor flux with respect to stator\n", + "print \"Speed of rotor flux with respect to stator in rpm :\",speed2;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For this speed of 1440 rpm the synchronous speed may be either 1500 rpm or 3000 rpm.\n", + "No. of poles : 4\n", + "4 Slip(in %) : 4\n", + "Speed of rotor flux with respect to rotor in rpm : 60\n", + "Speed of rotor flux with respect to stator in rpm : 1500\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8, Page 140" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos, acos, tan, atan, degrees\n", + "\n", + "#Given data : \n", + "E2=100;#in volt\n", + "R2=0.05;#in ohm\n", + "X2=0.1;#im ohm\n", + "\n", + "#Calculations&Results\n", + "E2perphase=E2/sqrt(3);#in volt\n", + "#part (a) : \n", + "S=0.04;#slip\n", + "I2=S*E2perphase/sqrt(R2**2+(S*X2)**2);#in Ampere\n", + "print \"At 4% slip, Rotor current in Ampere : \",round(I2,2);\n", + "fi2=degrees(acos(R2/sqrt(R2**2+(S*X2)**2)));#in degree\n", + "print \"At 4% slip, Phase angle between rotor voltage and rotor current in degree :\",round(fi2,2);\n", + "#part (b) : \n", + "S=1;#slip\n", + "I2=S*E2perphase/sqrt(R2**2+(S*X2)**2);#in Ampere\n", + "print \"At 100% slip, Rotor current in Ampere : \",round(I2,2);\n", + "fi2=degrees(acos(R2/sqrt(R2**2+(S*X2)**2)));#in degree\n", + "print \"At 100% slip, Phase angle between rotor voltage and rotor current in degree :\",round(fi2,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "At 4% slip, Rotor current in Ampere : 46.04\n", + "At 4% slip, Phase angle between rotor voltage and rotor current in degree : 4.57\n", + "At 100% slip, Rotor current in Ampere : 516.4\n", + "At 100% slip, Phase angle between rotor voltage and rotor current in degree : 63.43\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9, Page 141" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "#Given data : \n", + "E2=100.;#in volt\n", + "R2=0.4;#in ohm\n", + "X2=2.25;#im ohm\n", + "\n", + "#Calculations\n", + "E2perphase=E2/sqrt(3);#in volt\n", + "S=4.;#in %\n", + "E=(S/100)*E2perphase;#rotor induced emf at a slip=4% in volt\n", + "Z2=sqrt(R2**2+((S/100)*X2)**2);\n", + "I2=E/Z2;#in Ampere\n", + "\n", + "#Result\n", + "print \"Rotor current in Ampere : \",round(I2,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor current in Ampere : 5.63\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10, Page 141" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data : \n", + "f=50;#in Hz\n", + "R2=0.2;#in ohm\n", + "X2=2;#im ohm\n", + "E2=60;#in volt\n", + "\n", + "#Calculations&Results\n", + "E2perphase=E2/sqrt(3);#in volt\n", + "#case (i) : S=1 \n", + "S=1;#unitless\n", + "Z2=sqrt(R2**2+(S*X2)**2);\n", + "I2=E2perphase*S/Z2;#in Ampere\n", + "print \"At standstill : Rotor current in Ampere : \",round(I2,2);\n", + "#case (ii) : S=0.1 \n", + "S=0.1;#unitless\n", + "Z2=sqrt(R2**2+(S*X2)**2);\n", + "I2=E2perphase*S/Z2;#in Ampere\n", + "print \"for 10% slip : Rotor current in Ampere : \",round(I2,2);\n", + "#case (iii) : S=0.05 \n", + "S=0.05;#unitless\n", + "Z2=sqrt(R2**2+(S*X2)**2);\n", + "I2=E2perphase*S/Z2;#in Ampere\n", + "print \"for 5% slip : Rotor current in Ampere : \",round(I2,2);\n", + "#case (iv) : S=0.01 \n", + "S=0.01;#unitless\n", + "Z2=sqrt(R2**2+(S*X2)**2);\n", + "I2=E2perphase*S/Z2;#in Ampere\n", + "print \"for 1% slip : Rotor current in Ampere : \",round(I2,2);\n", + "#Note : Answer in the book is wrong for S=0.05 and S=0.01" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "At standstill : Rotor current in Ampere : 17.23\n", + "for 10% slip : Rotor current in Ampere : 12.25\n", + "for 5% slip : Rotor current in Ampere : 7.75\n", + "for 1% slip : Rotor current in Ampere : 1.72\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11, Page 142" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data : \n", + "R2=0.5;#in ohm\n", + "X=4.5;#im ohm\n", + "E=50;#line voltage in volt\n", + "\n", + "#Calculations&Results\n", + "Eperphase=E/sqrt(3);#in volt\n", + "#part (a) : Sliprings are short circuited\n", + "Z2=sqrt(R2**2+X**2);#in ohm\n", + "I2=Eperphase/Z2;#in Ampere\n", + "print \"Sliprings are short circuited, Rotor current in Ampere : \",round(I2,2);\n", + "cosfi2=R2/Z2;#unitless\n", + "print \"Power factor : \",round(cosfi2,2);\n", + "#part (b) : Sliprings are connected \n", + "R2=0.4;#in ohm\n", + "Z2=sqrt(R2**2+X**2);#in ohm\n", + "I2=Eperphase/Z2;#in Ampere\n", + "print \"Sliprings are short circuited, Rotor current in Ampere : \",round(I2,2);\n", + "cosfi2=R2/Z2;#unitless\n", + "print \"Power factor : \",round(cosfi2,2);\n", + "#Note : answer of part (a) I2 is not curate in the book." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Sliprings are short circuited, Rotor current in Ampere : 6.38\n", + "Power factor : 0.11\n", + "Sliprings are short circuited, Rotor current in Ampere : 6.39\n", + "Power factor : 0.09\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12, Page 146" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data : \n", + "R2=0.02;#in ohm\n", + "X2=0.1;#im ohm\n", + "\n", + "#Calculations&Results\n", + "#let external resistance per phase = r then R2=R2+r ohm\n", + "S=1;#slip at starting\n", + "print \"Since at start speed is zero and slip is, therefore, unity or R2=X2\";\n", + "r=X2-R2;#in ohm\n", + "print \"External resistance per phase added to the rotor circuit in ohms : \",r;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Since at start speed is zero and slip is, therefore, unity or R2=X2\n", + "External resistance per phase added to the rotor circuit in ohms : 0.08\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13, Page 147" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data : \n", + "P=4;#no. of poles\n", + "f=50;#in Hz\n", + "R2=0.03;#in ohm\n", + "X2=0.12;#im ohm\n", + "\n", + "#Calculations&Results\n", + "Smax=R2/X2;#unitless\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns*(1-Smax);#in rpm\n", + "print \"Speed corresponding to maximum torque(in rpm) :\",N;\n", + "#alfa=(R2+r)/X2\n", + "#Ratio of starting torque to max torque=75/100=2*alfa/(alfa^2+1)\n", + "#It gives : 3*alfa^2-8*alfa+3=0\n", + "#coefficients :\n", + "a=3;b=-8;c=3;\n", + "alfa1=(-b+sqrt(b**2-4*a*c))/(2*a);alfa2=(-b-sqrt(b**2-4*a*c))/(2*a);\n", + "print \"rejecting higher values, alfa = \",round(alfa2,4);\n", + "fdash=1.5;#in Hz\n", + "r=alfa2*X2-R2;#in ohm;\n", + "print \"External rotor resistance per phase(in ohm) : \",round(r,4);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed corresponding to maximum torque(in rpm) : 1125.0\n", + "rejecting higher values, alfa = 0.4514\n", + "External rotor resistance per phase(in ohm) : 0.0242\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14, Page 147" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=4;#no. of poles\n", + "f=50;#in Hz\n", + "R2=0.024;#in ohm\n", + "X2=0.6;#in ohm \n", + "\n", + "#Calculations&Results\n", + "Sm=R2/X2;#slip corresponding to max torque\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns*(1-Sm);#in rpm\n", + "print \"Speed corresponding to maximum torque in rpm : \",N;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed corresponding to maximum torque in rpm : 1440.0\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15, Page 148" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=6;#no. of poles\n", + "f=50;#in Hz\n", + "Sf=4.;#in %\n", + "R2=0.01;#in ohm\n", + "X2=0.05;#im \n", + "\n", + "#Calculations&Results\n", + "Ratio=((R2/X2)**2+(Sf/100)**2)/(2*R2*(Sf/100)/X2);#ratio of max torque to full load torque\n", + "print \"Maximum torque, Tmax=\",(Ratio),\"Tf\";\n", + "Sm=R2/X2;#slip corresponding to max torque\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns*(1-Sm);#in rpm\n", + "print \"Speed corresponding to maximum torque in rpm : \",N;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum torque, Tmax= 2.6 Tf\n", + "Speed corresponding to maximum torque in rpm : 800.0\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.16, Page 149" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=12;#no. of poles\n", + "f=50.;#in Hz\n", + "R2=0.03;#in ohm\n", + "X2=0.5;#im \n", + "\n", + "#Calculations&Results\n", + "S=R2/X2;#unitless\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns*(1-S);#in rpm\n", + "print \"Speed at maximum torque in rpm : \",N;\n", + "S=(Ns-495)/Ns;#slip at 495 rpm speed\n", + "Ratio=(2*R2*S/X2)/((R2/X2)**2+S**2);#ratio of max torque to full load torque\n", + "print \"Ratio of full load torque to max torque(in %) :\",round((Ratio*100),1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed at maximum torque in rpm : 470.0\n", + "Ratio of full load torque to max torque(in %) : 32.4\n" + ] + } + ], + "prompt_number": 142 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.17, Page 149" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data :\n", + "P=12;#no. of poles\n", + "f=50;#in Hz\n", + "R2=0.5;#in ohm\n", + "N=475.;#in rpm\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-N)/Ns;#unitless\n", + "X2=R2/S;#in ohm\n", + "#\"At maximum torque, Tmax is proportional to 1/2*X2 or 1/20\";\n", + "# \"Ts is proportional to (R2+R)/((R2+R)^2+X2^2)\";\n", + "# \"Also, Ts is proportional to 1(20*3)\";\n", + "# \"Equating the two eqn we have : (0.5*R)/(R2+R)^2+X2^2\";\n", + "#R^2-59R+70.25=0 : \n", + "#coefficients :\n", + "a=1;b=-59;c=70.25;\n", + "R=(-b-sqrt(b**2-4*a*c))/(2*a);\n", + "print \"Resistance R to be inserted in series (in ohm) :\",round(R,1);\n", + "#Note : answer in the book is wrong." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistance R to be inserted in series (in ohm) : 1.2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.18, Page 150" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=4;#no. of poles\n", + "f=50;#in Hz\n", + "R2=0.04;#in ohm\n", + "N=1200.;#in rpm(speed at max torque)\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm(synchronous speed)\n", + "S=(Ns-N)/Ns;#unitless\n", + "X2=R2/S;#in ohm\n", + "#Starting torque is the torque devloped when S=1: Tst=K*R2/(R2^2+X2^2)\n", + "#Let say, m=R2/(R2^2+X2^2) then Tst=K*m\n", + "m=R2/(R2**2+X2**2);#assumed\n", + "\n", + "#Results\n", + "print \"Starting torque, Tst=\",round(m,2),\"k\";\n", + "print \"Maximum torque, Tm=K/\",(2*X2);\n", + "print \"Thus, Tst in terms of Tm can be expressed as : \";\n", + "print \"Tst/Tm=\",(0.96*0.4),\" or Tst=\",(0.96*0.4),\"Tm\";\n", + "print \"Therefore, staring torque is \",(0.96*0.4*100),\"% of maximum torque.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Starting torque, Tst= 0.96 k\n", + "Maximum torque, Tm=K/ 0.4\n", + "Thus, Tst in terms of Tm can be expressed as : \n", + "Tst/Tm= 0.384 or Tst= 0.384 Tm\n", + "Therefore, staring torque is 38.4 % of maximum torque.\n" + ] + } + ], + "prompt_number": 144 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.19, Page 155" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=6;#no. of poles\n", + "f=50;#in Hz\n", + "fr=3.;#in Hz\n", + "R2=0.5;#in ohm\n", + "N=475;#in rpm\n", + "RotorInput=111.9;#in KW\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=fr*100/f;#unitless\n", + "print \"% Slip : \",S;\n", + "N=Ns*(1-S/100);#in rpm\n", + "print \"Speed of motor in rpm : \",N;\n", + "RotorCopperLoss=RotorInput*S/100;#in KW\n", + "RotorCopperLoss=RotorCopperLoss/3;#in KW/Phase\n", + "print \"Rotor Copper Loss per phase(in KW) : \",RotorCopperLoss;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "% Slip : 6.0\n", + "Speed of motor in rpm : 940.0\n", + "Rotor Copper Loss per phase(in KW) : 2.238\n" + ] + } + ], + "prompt_number": 146 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.20, Page 156" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "phase=3.;#no. of phase\n", + "Pin_stator=60.;#Power input of stator in KW\n", + "TotalStatorLosses=1.;#in KW\n", + "\n", + "#Calculations&Results\n", + "Pin_rotor=Pin_stator-TotalStatorLosses;#Power input of rotor in KW\n", + "S=3.;#slip in %\n", + "RotorCopperLosses=(S/100)*Pin_rotor;#in KW\n", + "RotorCopperLosses=RotorCopperLosses/phase;#in KW per phase\n", + "print \"Rotor Copper Losses per phase(in watts) : \",(RotorCopperLosses*10**3);\n", + "TotalMechPowerDev=Pin_rotor*(1-S/100);#in KW\n", + "print \"Total mechanial power developed(in KW) : \",TotalMechPowerDev;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor Copper Losses per phase(in watts) : 590.0\n", + "Total mechanial power developed(in KW) : 57.23\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21, Page 156" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=6;#no. of poles\n", + "S=4.;#slip in %\n", + "Output=20;#in KW\n", + "\n", + "#Calculations&Results\n", + "FrictionalLoss=250;#in watts\n", + "f=50;#in Hz\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns-Ns*(S/100);#in rpm\n", + "print \"Speed of motor(in rpm) : \",N;\n", + "MechPowerDeveloped=Output*10**3+FrictionalLoss;#in Watts\n", + "S=S/100;#unitless\n", + "RotorCopperLoss=(S/(1-S))*MechPowerDeveloped;#in watts\n", + "print \"Rotor Copper Loss(in watts) : \",RotorCopperLoss;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Speed of motor(in rpm) : 960.0\n", + "Rotor Copper Loss(in watts) : 843.75\n" + ] + } + ], + "prompt_number": 147 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22, Page 157" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "phase=3;#no. of phase\n", + "P=6;#no. of poles\n", + "Pin_rotor=80;#Power input of rotor in KW\n", + "f=50;#in Hz\n", + "fdash=100;#alternations per minute\n", + "\n", + "#Calculations&Results\n", + "fdash=100./60;#in Hz\n", + "S=fdash/f;#unitless\n", + "print \"Slip : \",round(S,4);\n", + "Ns=120*f/P;#synchronous speed in rpm\n", + "N=Ns-Ns*S;#in rpm\n", + "print \"Rotor Speed(in rpm) : \",round(N);\n", + "MechPowerDev=Pin_rotor*(1-S)*10**3/735.5;#in H.P.\n", + "print \"Total mechanial power developed(in KW) : \",round(MechPowerDev,2);\n", + "RotorCopperLoss=S*Pin_rotor*10**3;#in watts\n", + "print \"Rotor Copper Loss(in watts) : \",RotorCopperLoss;\n", + "CopperLoss=RotorCopperLoss/phase;#in watts/phase\n", + "print \"Copper Loss per phase(in watts) : \",round(CopperLoss);\n", + "I2=60;#in Ampere\n", + "R2=CopperLoss/I2**2;#in ohm\n", + "print \"Rotor resistance per phase(in ohm) : \",round(R2,3);\n", + "#Note : Some answers are not accurate in the book." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.0333\n", + "Rotor Speed(in rpm) : 967.0\n", + "Total mechanial power developed(in KW) : 105.14\n", + "Rotor Copper Loss(in watts) : 2666.66666667\n", + "Copper Loss per phase(in watts) : 889.0\n", + "Rotor resistance per phase(in ohm) : 0.247\n" + ] + } + ], + "prompt_number": 148 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23, Page 158" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "UsefulOutput=55;#in H.P.\n", + "MechLosses=2;#in H.P.\n", + "Stator_Losses=13.5;#in KW\n", + "\n", + "#Calculations&Results\n", + "MechPowerDev=UsefulOutput+MechLosses;#in H.P.\n", + "MechPowerDev=MechPowerDev*735.5/1000;#in KW\n", + "S=50.;#in %\n", + "Pin_Rotor=MechPowerDev/(1-S/100);#in KW\n", + "RotorCopperLoss=(S/100)*Pin_Rotor;#in KW\n", + "print \"Rotor Copper Loss(in KW) : \",round(RotorCopperLoss,2);\n", + "Pin_Motor=Pin_Rotor+Stator_Losses;#in KW\n", + "Efficiency=UsefulOutput*0.7355/Pin_Motor;#/unitless\n", + "print \"Effiiency(in %) :\",round((Efficiency*100),1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor Copper Loss(in KW) : 41.92\n", + "Effiiency(in %) : 41.6\n" + ] + } + ], + "prompt_number": 149 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24, Page 159" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "phase=3;#no. of phase\n", + "P=6;#no. of poles\n", + "Pin_rotor=80;#Power input of rotor in KW\n", + "f=50;#in Hz\n", + "fdash=100;#alternations per minute\n", + "\n", + "#Calculations&Results\n", + "fdash=100./60;#in Hz\n", + "S=fdash/f;#unitless\n", + "print \"Slip : \",round(S,3);\n", + "Ns=120*f/P;#synchronous speed in rpm\n", + "N=Ns-Ns*S;#in rpm\n", + "print \"Rotor Speed(in rpm) : \",round(N);\n", + "RotorCopperLoss=S*Pin_rotor*10**3;#in watts\n", + "#print \"Rotor Copper Loss(in watts) : \",RotorCopperLoss;\n", + "CopperLoss=RotorCopperLoss/phase;#in watts/phase\n", + "print \"Copper Loss per phase(in watts) : \",round(CopperLoss);\n", + "I2=60;#in Ampere\n", + "R2=CopperLoss/I2**2;#in ohm\n", + "print \"Rotorresistance per phase(in ohm) : \",round(R2,3);\n", + "MechPowerDev=Pin_rotor*(1-S)*10**3/735.5;#in H.P.\n", + "print \"Total mechanial power developed(in H.P.) : \",round(MechPowerDev,1);\n", + "#Note : Some answers are not accurate in the book." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.033\n", + "Rotor Speed(in rpm) : 967.0\n", + "Copper Loss per phase(in watts) : 889.0\n", + "Rotorresistance per phase(in ohm) : 0.247\n", + "Total mechanial power developed(in H.P.) : 105.1\n" + ] + } + ], + "prompt_number": 150 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.25, Page 160" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "Efficiency=0.9;#unitless\n", + "Output=50;#in H.P.\n", + "\n", + "#Calculations\n", + "#formula : Efficiency=Output/(Output+Losses) \n", + "Losses=((1-Efficiency)/Efficiency)*Output*735.5;#in watts\n", + "Losses=round(Losses);#round\n", + "#Let, Ststor Cu loss = Rotor Cu los = Iron loss=K\n", + "#Mechanical Loss = Iron Loss/3 = K/3\n", + "#TotalLosses=k+K+K+K/3\n", + "K=Losses*3/10;#in watts\n", + "Pin_rotor=Output*735.5+Losses;#in watts\n", + "Slip=K/Pin_rotor;#unitless\n", + "\n", + "#Results\n", + "print \"Slip :\",round(Slip,3);\n", + "print \"or \",round((Slip*100)),\"%\"; #answer differes due to rouding" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.03\n", + "or 3.0 %\n" + ] + } + ], + "prompt_number": 154 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.26, Page 160" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "Pin_rotor=20;#Power input of rotor in KW\n", + "phase=3;#no. of phase\n", + "P=6;#no. of poles\n", + "f=50.;#in Hz\n", + "N=960;#in rpm(Actual speed of motor)\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#synchronous speed in rpm\n", + "S=(Ns-N)/Ns;#unitless\n", + "RotorCuLoss=S*Pin_rotor*10**3;#in watts\n", + "RotorCuLoss=RotorCuLoss/phase;#in watts/phase\n", + "R2=1./3;#in ohm(Rotor resistance per phase)\n", + "I2=sqrt(RotorCuLoss/R2);#in Ampere\n", + "\n", + "#Result\n", + "print \"Motor current per phase(in Ampere) :\",round(I2,1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Motor current per phase(in Ampere) : 28.3\n" + ] + } + ], + "prompt_number": 155 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.27, Page 161" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "V=500;#in volt\n", + "Pout_rotor=20;#Power output of rotor in H.P.\n", + "phase=3;#no. of phase\n", + "P=6;#no. of poles\n", + "f=50;#in Hz\n", + "N=995.;#in rpm(Actual speed of motor)\n", + "cosfi=0.87;#powerfactor(unitless)\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#synchronous speed in rpm\n", + "S=(Ns-N)/Ns;#unitless\n", + "print \"Slip : \",S;\n", + "RotorCuLoss=(S/(1-S))*Pout_rotor*735.5;#in watts\n", + "print \"Rotor Cu Loss(in watts) : \",round(RotorCuLoss,2);\n", + "Pin_rotor=RotorCuLoss/S;#in watts\n", + "print \"Power input to rotor(in KW) :\",round((Pin_rotor/10**3),2);\n", + "LineCurrent=Pin_rotor/(sqrt(3)*V*cosfi);#in Ampere\n", + "print \"Line Current(in A) :\",round(LineCurrent,2);\n", + "RotorFreq=S*f;#in Hz\n", + "print \"Rotor Frequency(in Hz) :\",RotorFreq;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.005\n", + "Rotor Cu Loss(in watts) : 73.92\n", + "Power input to rotor(in KW) : 14.78\n", + "Line Current(in A) : 19.62\n", + "Rotor Frequency(in Hz) : 0.25\n" + ] + } + ], + "prompt_number": 156 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.28, Page 162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "phase=3;#no. of phase\n", + "Efficiency=90;#in %\n", + "Speed=480;#in rpm\n", + "VL=400;#in volt\n", + "IL=75;#in Ampere\n", + "cosfi=0.77;#powerfactor(unitless)\n", + "d=0.75;#diameter of pulley in meter\n", + "\n", + "#Calculations\n", + "Pin_motor=sqrt(3)*VL*IL*cosfi;#Power input of motor in watts\n", + "OutputPower=Pin_motor*Efficiency/100;#in watts\n", + "Omega=Speed*2*pi/60;#angular speed in radians/sec\n", + "Torque=OutputPower/Omega;#in N-meter\n", + "Torque=Torque/9.81;#in Kg-meter\n", + "PullOnBelt=Torque/(d/2);#in Kg\n", + "\n", + "#Result\n", + "print \"Pull On Belt(in Kg.) : \",round(PullOnBelt,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Pull On Belt(in Kg.) : 194.74\n" + ] + } + ], + "prompt_number": 157 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.29, Page 162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "#At 3% slip\n", + "OutputPower=24;#in KW(At 3% slip)\n", + "S=3.;#in %\n", + "\n", + "#Calculations\n", + "Efficiency=(1-S/100);#unitless\n", + "InputPower=OutputPower/Efficiency;#in KW\n", + "#At 5% slip\n", + "S=5;#in %\n", + "Efficiency=(1-S/100);#unitless\n", + "OutputPower=InputPower*Efficiency;#in KW\n", + "\n", + "#Result\n", + "print \"Mechanical power output at a slip of 5%(in KW) : \",round(OutputPower,1);\n", + "#answer differs due to rounding" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mechanical power output at a slip of 5%(in KW) : 24.7\n" + ] + } + ], + "prompt_number": 158 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.30, Page 162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "#At 50% speed of synchronous speed\n", + "S=50.;#in %\n", + "UsefulOutput=55;#in H.P.\n", + "MechLoss=2;#in H.P.\n", + "StatorLoss=13.5;#in KW\n", + "\n", + "#Calculations&Results\n", + "Pout_rotor=UsefulOutput+MechLoss;#in H.P.\n", + "Pout_rotor=Pout_rotor*0.7355;#in KW\n", + "Efficiency=(1-S/100);#unitless\n", + "RotorInputPower=Pout_rotor/Efficiency;#in KW\n", + "RotorCuLoss=RotorInputPower-Pout_rotor;#in KW\n", + "print \"Cu Loss in the rotor circuit(in KW) :\",round(RotorCuLoss,2);\n", + "TotalLosses=StatorLoss+RotorCuLoss+MechLoss*0.7355;#in KW\n", + "MotorEfficiency=UsefulOutput*0.7355/(UsefulOutput*0.7355+TotalLosses);\n", + "print \"Motor Efficiency(in %) : \",round((MotorEfficiency*100),1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Cu Loss in the rotor circuit(in KW) : 41.92\n", + "Motor Efficiency(in %) : 41.6\n" + ] + } + ], + "prompt_number": 159 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.31, Page 163" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data :\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "N=1440.;#in rpm(Actual speed of motor)\n", + "Power_dev=10;#Power developed in H.P.\n", + "VL=400;#in volt\n", + "cosfi=0.8;#powerfactor(unitless)\n", + "f=50;#in Hz\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-N)/Ns;#fractional slip(unitless)\n", + "print \"Slip :\",S;\n", + "Omega=N*2*pi/60;#angular speed in radians/sec\n", + "Torque=Power_dev*735.5/Omega;#in N-meter\n", + "Torque=Torque/9.81;#in Kg-meter\n", + "print \"Torque(in Kg-meter) :\",round(Torque,2);\n", + "RotorCuLoss=(S/(1-S))*Power_dev*735.5;#in watts\n", + "print \"Rotor Cu Loss per phase(in watts) : \",round((RotorCuLoss/3),1);\n", + "Pin_rotor=RotorCuLoss/S;#in watts\n", + "print \"Power input to rotor(in KW) :\",round((Pin_rotor/10**3),2);\n", + "LineCurrent=Pin_rotor/(sqrt(3)*VL*cosfi);#in Ampere\n", + "print \"Line Current(in A) :\",round(LineCurrent,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.04\n", + "Torque(in Kg-meter) : 4.97\n", + "Rotor Cu Loss per phase(in watts) : 102.2\n", + "Power input to rotor(in KW) : 7.66\n", + "Line Current(in A) : 13.82\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.32, Page 164" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "VL=440;#in volt\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "Pin_rotor=80;#in KW\n", + "fr=100;#revolutions/min\n", + "\n", + "#Calculations&Results\n", + "fr=100./60;#in Hz\n", + "S=fr/f;#slip(unitless)\n", + "print \"Slip : \",round(S,3);\n", + "Ns=120*f/P;#in rpm\n", + "N=Ns*(1-S);#in rpm(Speed of Rotor)\n", + "print \"Rotor speed(in rpm) : \",round(N);\n", + "RotorCuLoss=S*Pin_rotor*10**3;#in watts\n", + "print \"Rotor Cu Loss per phase(in watts) : \",round(RotorCuLoss/phase);\n", + "I2=65;#in Ampere\n", + "R2=(RotorCuLoss/phase)/I2**2;#in ohm\n", + "print \"Rotor resistance per phase(in ohm) : \",round(R2,2);\n", + "Pout_rotor=Pin_rotor-RotorCuLoss/10**3;#in KW\n", + "print \"Output power of rotor(in H.P.) : \",round((Pout_rotor/0.735),1);\n", + "#Note : answers of few part are not accurate in the book." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.033\n", + "Rotor speed(in rpm) : 967.0\n", + "Rotor Cu Loss per phase(in watts) : 889.0\n", + "Rotor resistance per phase(in ohm) : 0.21\n", + "Output power of rotor(in H.P.) : 105.2\n" + ] + } + ], + "prompt_number": 161 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.33, Page 165" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "VL=440;#in volt\n", + "f=50.;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "Pin_rotor=20;#in KW\n", + "N=960.;#in rpm(Speed of Motor)\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-N)/Ns;#slip(unitless)\n", + "RotorCuLoss=S*Pin_rotor*10**3;#in watts\n", + "RotorCuLoss=RotorCuLoss/phase;#in watts/phase\n", + "R2=1./3;#Rotor Resistance in ohm per phase\n", + "I2=sqrt(RotorCuLoss/R2)\n", + "\n", + "#Result\n", + "print \"Motor current per phase(in Ampere) :\",round(I2,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Motor current per phase(in Ampere) : 28.28\n" + ] + } + ], + "prompt_number": 162 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.34, Page 166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data :\n", + "VL=500;#in volt\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "Pout_rotor=20;#in H.P.\n", + "cosfi=0.87;#power factor\n", + "N=995.;#in rpm(Speed of Motor)\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-N)/Ns;#slip(unitless)\n", + "print \"Slip : \",S;\n", + "RotorCuLoss=(S/(1-S))*Pout_rotor*735.5;#in watts\n", + "print \"Rotor Cu Loss(in watts) :\",round(RotorCuLoss,2);\n", + "Pin_rotor=RotorCuLoss/S;#in watts\n", + "print \"Power input to rotor(in KW) :\",round((Pin_rotor/10**3),3);\n", + "IL=Pin_rotor/(sqrt(3)*VL*cosfi);#in Ampere\n", + "print \"Line current (in Ampere) :\",round(IL,2);\n", + "Rotorfreq=S*f;#in Hz\n", + "print \"Rotor frequency(in Hz) :\",round(Rotorfreq,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.005\n", + "Rotor Cu Loss(in watts) : 73.92\n", + "Power input to rotor(in KW) : 14.784\n", + "Line current (in Ampere) : 19.62\n", + "Rotor frequency(in Hz) : 0.25\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.35, Page 166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "Efficiency=85.;#in %\n", + "OutputPower=17.;#in KW\n", + "OutputPower=17*10**3;#in watts\n", + "StatorLosses=900.;#in watt\n", + "MechLosses=1100;#in watt\n", + "\n", + "#Calculations&Results\n", + "Pin=OutputPower/(Efficiency/100);#in watts\n", + "#Stator input or rotor input :\n", + "Pin_rotor=Pin-StatorLosses;#in watts\n", + "P_MechDev=OutputPower+MechLosses;#in watts\n", + "RotorCuLosses=Pin_rotor-P_MechDev;#in watts\n", + "S=RotorCuLosses/Pin_rotor;#slip(unitless)\n", + "print \"Slip :\",round(S,3);\n", + "Ns=120*f/P\n", + "N=Ns*(1-S);#in rpm(Speed of Motor)\n", + "Omega=2*pi*N/60;#angular speed in rad/sec\n", + "Torque=P_MechDev/Omega;#in Nm\n", + "print \"Torque developed(in Nm) :\",round(Torque,1);\n", + "Tm=OutputPower/Omega;#in Nm\n", + "Tm=Tm/9.81;#in Kg-meter\n", + "print \"Torque at the shaft(in Kg-meter) :\",round(Tm,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.052\n", + "Torque developed(in Nm) : 121.6\n", + "Torque at the shaft(in Kg-meter) : 11.64\n" + ] + } + ], + "prompt_number": 164 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.36, Page 168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "VL=500;#in volt\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "Pin_stator=50;#in KW\n", + "Statorlosses=2;#in KW\n", + "MechLosses=1;#in KW\n", + "\n", + "#Calculations&Results\n", + "Pin_rotor=Pin_stator-Statorlosses;#in KW\n", + "S=3.;#in %\n", + "RotorI2RLoss=(S/100)*Pin_rotor;#in KW\n", + "print \"Rotor I2R Loss(in KW) :\",RotorI2RLoss;\n", + "print \"Rotor core loss at 3% slip is very less and can be neglected.\";\n", + "Power_dev=Pin_rotor-RotorI2RLoss;#in KW\n", + "print \"Power developed by the rotor(in H.P.) : \",round((Power_dev/0.7355),1);\n", + "Outputpower=Power_dev-MechLosses;#in KW\n", + "Efficiency=Outputpower/Pin_stator;#unitless\n", + "print \"Efficiency of the motor(in %) :\",(Efficiency*100);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor I2R Loss(in KW) : 1.44\n", + "Rotor core loss at 3% slip is very less and can be neglected.\n", + "Power developed by the rotor(in H.P.) : 63.3\n", + "Efficiency of the motor(in %) : 91.12\n" + ] + } + ], + "prompt_number": 165 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.37, Page 168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "MotorOutput=20;#in H.P.\n", + "MotorOutput=20*735.5;#in watts\n", + "S=4.;#full load slip in %\n", + "MechLosses=500;#in watts\n", + "\n", + "#Calculations&Results\n", + "Pdev_rotor=MotorOutput+MechLosses;#in watts\n", + "S=S/100;#fractional slip\n", + "RotorI2RLoss=(S/(1-S))*Pdev_rotor;#in watts\n", + "print \"Rotor I2R Loss(in watts) :\",RotorI2RLoss;\n", + "Ns=120*f/P;#in rpm\n", + "Nr=Ns-Ns*S;#in rpm\n", + "print \"Rotor speed(in rpm) :\",Nr;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor I2R Loss(in watts) : 633.75\n", + "Rotor speed(in rpm) : 1440.0\n" + ] + } + ], + "prompt_number": 80 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.38, Page 169" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, sin, cos\n", + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "R2=0.02;#in ohm\n", + "X2=0.1;#in ohm\n", + "\n", + "#Calculations\n", + "S=R2/X2;#slip(unitless)\n", + "Ns=120*f/P;#in rpm\n", + "Nr=Ns-Ns*S;#in rpm\n", + "#At starting S=1\n", + "S=1;#slip\n", + "#Formula : T=K*S*R2/(R2^2+X2^2)\n", + "#Starting torque, Tst=K*R2/(R2^2+S^2*X2^2)\n", + "#Maximum torque, Tm=K/(2*X2)\n", + "#Tst=(2/3)*Tm : gives a equation\n", + "#100*R2^2-30*R2+1=0\n", + "a=100;b=-30;c=1;\n", + "R21=(-b+sqrt(b**2-4*a*c))/(2*a);#in ohm\n", + "R22=(-b-sqrt(b**2-4*a*c))/(2*a);#in ohm\n", + "#This R2 is the value of rotor circuit resistance.\n", + "RotWinResistance=0.02;#in ohm per phase\n", + "Extra_R1=R21-RotWinResistance;#in ohm\n", + "Extra_R2=R22-RotWinResistance;#in ohm\n", + "\n", + "#Result\n", + "print \"Extra Resistance(in ohm) : \",round(Extra_R1,3),\" ohm or \",round((Extra_R2),3),\" ohm.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Extra Resistance(in ohm) : 0.242 ohm or 0.018 ohm.\n" + ] + } + ], + "prompt_number": 166 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.39, Page 170" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "MotorShaftOutput=20;#in H.P.\n", + "\n", + "#Calculations&Results\n", + "MotorShaftOutput=20*735.5;#in watts\n", + "MechLosses=MotorShaftOutput*2/100;#in watts(2% of the output)\n", + "Pdev_rotor=MotorShaftOutput+MechLosses;#in watts\n", + "S=3.;#slip in %\n", + "S=S/100;#fractional slip\n", + "RotorI2RLoss=(S/(1-S))*Pdev_rotor;#in watts\n", + "print \"Rotor I2R Loss(in watts) :\",round(RotorI2RLoss);\n", + "print \"Rotor iron loss at 3% slip is very small and can be neglected.\";\n", + "RotorInput=Pdev_rotor+RotorI2RLoss;#in watts\n", + "print \"Rotor Input(in Watts) :\",round(RotorInput,1);\n", + "Ns=120*f/P;#in rpm\n", + "Nr=Ns-Ns*S;#in rpm\n", + "Nr=Nr/60;#in rps\n", + "T=MotorShaftOutput/(2*pi*Nr);#in Nm\n", + "print \"Output torque(in Nm) : \",round(T,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor I2R Loss(in watts) : 464.0\n", + "Rotor iron loss at 3% slip is very small and can be neglected.\n", + "Rotor Input(in Watts) : 15468.2\n", + "Output torque(in Nm) : 96.54\n" + ] + } + ], + "prompt_number": 167 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.40, Page 171" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "VL=500;#in volt\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "Nr=975.;#in rpm\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-Nr)/Ns;#slip\n", + "print \"Slip :\",S;\n", + "Pin_stator=40;#in KW\n", + "StatorLosses=1;#in KW\n", + "Pin_rotor=Pin_stator-StatorLosses;#in KW\n", + "RotorCuLosses=S*Pin_rotor;#in KW\n", + "print \"Rotor Cu Losses(in KW) :\",RotorCuLosses;\n", + "RotorOutput=Pin_rotor-RotorCuLosses;#in KW\n", + "OutputHP=RotorOutput/0.735;#in H.P.\n", + "print \"Output Horse Power : \",round(OutputHP,2);\n", + "Efficiency=RotorOutput/Pin_stator;#unitless\n", + "print \"Efficiency(in %) :\",round(Efficiency*100);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.025\n", + "Rotor Cu Losses(in KW) : 0.975\n", + "Output Horse Power : 51.73\n", + "Efficiency(in %) : 95.0\n" + ] + } + ], + "prompt_number": 168 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.41, Page 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "VL=440;#in volt\n", + "f=50.;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3.;#no. of phase\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "fr=120;#alternations per minute\n", + "fr=fr/60;#in Hz\n", + "S=fr/f;#slip\n", + "print \"Slip : \",S;\n", + "Nr=Ns-S*Ns;#in rpm\n", + "print \"Rotor speed(in rpm) :\",Nr;\n", + "Rotor_input=80;#in KW\n", + "RotorCuLoss=S*Rotor_input;#in KW\n", + "print \"Rotor Cu Loss per phase(in watts) :\",round((RotorCuLoss*10**3)/phase);\n", + "P_Mechdev=Rotor_input*10**3-RotorCuLoss*10**3;#in watts\n", + "P_Mechdev=P_Mechdev/735.5;#in H.P.\n", + "print \"Mechanical power devloped(in H.P.) :\",round(P_Mechdev,1);\n", + "Ir=60;#in Ampere\n", + "R2=(RotorCuLoss*10**3/phase)/Ir**2;#in ohm\n", + "print \"Rotor resistance per phase(in ohm) :\",round(R2,3);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip : 0.04\n", + "Rotor speed(in rpm) : 960.0\n", + "Rotor Cu Loss per phase(in watts) : 1067.0\n", + "Mechanical power devloped(in H.P.) : 104.4\n", + "Rotor resistance per phase(in ohm) : 0.296\n" + ] + } + ], + "prompt_number": 169 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.43, Page 175 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50.;#in Hz\n", + "P=6;#no. of poles\n", + "R2=0.2;#rotor resistance per phase in ohm\n", + "Nr=960;#in rpm\n", + "Nr_dash=600;#in rpm\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-Nr)/Ns;#slip(unitless)\n", + "Sdash=(Ns-Nr_dash)/Ns;#slip(unitless)\n", + "#Let the new value of resistance is R2dash=(R+0.2)\n", + "R=R2*(Sdash/S)-R2;#Resistance to be added in ohm\n", + "\n", + "#Result\n", + "print \"Resistance to be added(in ohm) : \",R;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistance to be added(in ohm) : 1.8\n" + ] + } + ], + "prompt_number": 91 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.44, Page 176" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=6;#no. of poles\n", + "phase=3;#no. of phase\n", + "RotorIntResistance=0.1;#in ohm per phase\n", + "X2=1;#in ohm/phase\n", + "\n", + "#Calculation\n", + "Rext=X2-RotorIntResistance;#in ohm\n", + "\n", + "#Result\n", + "print \"External resistance to be included(in ohm/phase) : \",Rext;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "External resistance to be included(in ohm/phase) : 0.9\n" + ] + } + ], + "prompt_number": 92 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.45, Page 176" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50.;#in Hz\n", + "P=6.;#no. of poles\n", + "phase=3.;#no. of phase\n", + "R2=0.2;#rotor resistance per phase in ohm\n", + "N1=960.;#Full load speed in rpm\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm\n", + "S1=(Ns-N1)/Ns;#Full load slip(unitless)\n", + "N2=N1*(1-10./100);#New speed in rpm(reduced 10%)\n", + "S2=(Ns-N2)/Ns;#New slip(unitless)\n", + "#Formula : S=RotorCuLoss/Pin_rotor=3*I2^2*R2/Pin_rotor\n", + "#Let the additional resistance is R\n", + "R=R2*S2/S1-R2;#Resistance to be added in ohm\n", + "\n", + "#Result\n", + "print \"Additional Rotor Resistance(in ohm) : \",R;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Additional Rotor Resistance(in ohm) : 0.48\n" + ] + } + ], + "prompt_number": 97 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.46, Page 180" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "R2inner=0.4;#in ohm\n", + "X2inner=2;#in ohm \n", + "R2outer=2;#in ohm\n", + "X2outer=0.4;#in ohm \n", + "#At standstill :\n", + "S=1;#unitless\n", + "\n", + "#Calculations&Results\n", + "Ratio=(R2outer*S/(R2outer**2+S**2*X2outer**2))/(R2inner*S/(R2inner**2+S**2*X2inner**2));#unitless\n", + "print \"Ratio of torque produced by two cages at standstill : \",Ratio;\n", + "#At Full load :\n", + "S=5;#in %\n", + "S=5./100;#fractional\n", + "Ratio=(R2outer*S/(R2outer**2+S**2*X2outer**2))/(R2inner*S/(R2inner**2+S**2*X2inner**2));#unitless\n", + "print \"Ratio of torque produced by two cages at full load(slip=5%) : \",round(Ratio,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of torque produced by two cages at standstill : 5.0\n", + "Ratio of torque produced by two cages at full load(slip=5%) : 0.21\n" + ] + } + ], + "prompt_number": 171 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.47, Page 187" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "#Given data :\n", + "Output=10;#in H.P.\n", + "Output=Output*735.5;#in watts\n", + "cosfi=0.8;#unitless\n", + "ETA=0.83;#unitless\n", + "ISCbyIFL=3.5;#ratio of SC current to full load current\n", + "VL=500;#in volt\n", + "\n", + "#Calculations\n", + "Input=Output/ETA;#in watts\n", + "IFL=Input/(sqrt(3)*VL*cosfi);#in Ampere\n", + "ISC=IFL*ISCbyIFL;#in Ampere\n", + "Is=ISC/3;#in Ampere\n", + "\n", + "#Result\n", + "print \"Strting current(in Ampere) :\",round(Is,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Strting current(in Ampere) : 14.92\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.48, Page 187" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "ISCbyIFL=5;#ratio of SC current to full load current\n", + "S=0.04;#Full load slip\n", + "\n", + "#Calculations&Results\n", + "#(i) for star delta starter : \n", + "print \"for star delta starter : \";\n", + "Ratio=(1./3)*(ISCbyIFL)**2*S;#Ratio of starting torque to full load torque\n", + "print \"Starting torque is \",round((Ratio*100),2),\"% of full load torque.\";\n", + "#(i) for auto transformer starter :\n", + "print \"for auto transformer starter : \";\n", + "K=50./100;#tappings\n", + "Ratio=K**2*(ISCbyIFL)**2*S;#Ratio of starting torque to full load torque\n", + "print \"Starting torque is \",(Ratio*100),\"% of full load torque.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "for star delta starter : \n", + "Starting torque is 33.33 % of full load torque.\n", + "for auto transformer starter : \n", + "Starting torque is 25.0 % of full load torque.\n" + ] + } + ], + "prompt_number": 173 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.49, Page 188" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "ISCbyIFL=4;#ratio of SC current to full load current\n", + "TsBYTf=1./4;#ratio of atarting torque to full load torque\n", + "Slip=3;#in %\n", + "Slip=3./100;#in fraction\n", + "\n", + "#Calculations\n", + "#Formula : TsBYTf=Percent_Tapping^2*ISCbyIFL^2*Slip\n", + "tapping=sqrt(TsBYTf/(Slip*ISCbyIFL**2));#in %\n", + "\n", + "#Result\n", + "print \"Tapping(in %) :\",round((tapping*100),1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Tapping(in %) : 72.2\n" + ] + } + ], + "prompt_number": 174 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.50, Page 189" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "ISCbyIFL=5.;#ratio of SC current to full load current\n", + "Slip=5;#in %\n", + "Slip=5./100;#in fraction\n", + "\n", + "#Calculations\n", + "#Formula : 3*IFL=K^2*ISC\n", + "K=sqrt(1./(ISCbyIFL/3));#unitless\n", + "TsBYTfl=K**2*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque\n", + "\n", + "#Result\n", + "print \"Starting torque is \",(TsBYTfl*100),\"% of full load torque.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Starting torque is 75.0 % of full load torque.\n" + ] + } + ], + "prompt_number": 175 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.51, Page 189" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "print \"Star delta starter :\";\n", + "ISCbyIFL=6;#ratio of SC current to full load current\n", + "Slip=4;#in %\n", + "Slip=4./100;#in fraction\n", + "\n", + "#Calculations&Results\n", + "TsBYTfl=(1./3)*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque\n", + "print \"Starting torque is \",(TsBYTfl*100),\"% of full load value.\";\n", + "print \"For an auto transformer :\";\n", + "K=70.70;#in %\n", + "K=70.70/100;#in fraction\n", + "TsBYTfl=K**2*(ISCbyIFL)**2*Slip;#ratio of starting torque to full load torque\n", + "print \"Starting torque is \",round(TsBYTfl*100),\"% of full load torque.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Star delta starter :\n", + "Starting torque is 48.0 % of full load value.\n", + "For an auto transformer :\n", + "Starting torque is 72.0 % of full load torque.\n" + ] + } + ], + "prompt_number": 176 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.52, Page 190" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "V=400.;#in volt\n", + "S=3.5;#in %\n", + "S=3.5/100;#in fraction\n", + "VL=92;#in volts\n", + "\n", + "#Calculations&Results\n", + "#ISC=(V/VL)*IFL;#in Ampere\n", + "ISCbyIFL=V/VL;#ratio of SC current to full load current\n", + "#2*IFL=K^2*ISC imples that 2*IFL=K^2*(V/VL)*IFL\n", + "K=sqrt(2./(V/VL));#in fraction\n", + "print \"Necessary tapping(in %) :\",round((K*100),1);\n", + "TsBYTfl=K**2*(ISCbyIFL)**2*S;#ratio of starting torque to full load torque\n", + "print \"Starting torque is \",round((TsBYTfl*100),1),\"% of full load value.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Necessary tapping(in %) : 67.8\n", + "Starting torque is 30.4 % of full load value.\n" + ] + } + ], + "prompt_number": 179 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.53, Page 190" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "ISCbyIFL=4;#ratio of SC current to full load current\n", + "ISbyIFL=2;#ratio of Supply current to full load current\n", + "S=2.5;#in %\n", + "S=2.5/100;#in fraction\n", + "\n", + "#Calculations\n", + "#Formula : ISbyIFL=(1/K^2)*ISCbyIFL\n", + "K=sqrt(ISCbyIFL/ISbyIFL);#in fraction\n", + "print \"Auto Transormation ratio :\",round(K,2);\n", + "TsBYTfl=(1./K**2)*(ISCbyIFL)**2*S;#ratio of starting torque to full load torque\n", + "\n", + "#Results\n", + "print \"Ratio of starting torque to full load torque :\",TsBYTfl;\n", + "print \"or Starting torque is \",(TsBYTfl*100),\"% of full load value.\";" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Auto Transormation ratio : 1.41\n", + "Ratio of starting torque to full load torque : 0.2\n", + "or Starting torque is 20.0 % of full load value.\n" + ] + } + ], + "prompt_number": 180 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.54, Page 191" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "ISCbyIFL=4;#ratio of SC current to full load current\n", + "S=3;#in %\n", + "S=3./100;#in fraction\n", + "TsBYTfl=1./4;#ratio of starting torque to full load torque\n", + "\n", + "#Calculations\n", + "#Formula : TsBYTfl=ISCbyIFL^2*K^2*S\n", + "K=sqrt(TsBYTfl/(ISCbyIFL**2*S));#in fraction\n", + "\n", + "#Result\n", + "print \"Auto Transormation ratio(in %) :\",round((K*100),2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Auto Transormation ratio(in %) : 72.17\n" + ] + } + ], + "prompt_number": 181 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.55, Page 191" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "#Given data :\n", + "Output=3;#in H.P.\n", + "Output=3*735.5;#in watts\n", + "Efficiency=0.83;#unitless\n", + "cosfi=0.8;#power factor\n", + "\n", + "#Calculations\n", + "Vl=500;#in volt\n", + "Input=Output/Efficiency;#in watts\n", + "#Formula : Input=sqrt(3)*Vl*Il*cosfi\n", + "Il=Input/(sqrt(3)*Vl*cosfi);#in Ampere\n", + "ISCbyIFL=3.5;#ratio of SC current to full load current\n", + "ISC=ISCbyIFL*Il;#in Ampere\n", + "LineCurrent=ISC/3;#in Ampere(for star delta starter)\n", + "\n", + "#Result\n", + "print \"Line Current(in Ampere) :\",round(LineCurrent,2);\n", + "#Note : Ans in the book is not accurate." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Line Current(in Ampere) : 4.48\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.56, Page 192" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "#Given data :\n", + "Output=15;#in H.P.\n", + "Output=15*735.5;#in watts\n", + "Vl=400;#in volt\n", + "ISCat200=40;#in Ampere(at 200 volt)\n", + "Efficiency=0.88;#unitless\n", + "cosfi=0.85;#power factor\n", + "\n", + "#Calculations\n", + "ISCat400=ISCat200*(400./200);#in Ampere(at 400 volt)\n", + "Input=Output/Efficiency;#in watts\n", + "Ifl=Input/(sqrt(3)*Vl*cosfi);#in Ampere\n", + "#starting line current with star delta starter\n", + "Is=ISCat400/3;#in Ampere\n", + "Ratio=Is/Ifl;#ratio of starting current to full load current\n", + "\n", + "#Result\n", + "print \"Ratio of line current at starting to full load current :\",round(Ratio,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of line current at starting to full load current : 1.25\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.57, Page 192" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "#Given data :\n", + "#With star delta starter : \n", + "TstBYTfl=0.35;#ratio of starting torque to full load torque\n", + "IstBYIfl=1.75;#ratio of starting current to full load current\n", + "\n", + "#Calculations&Results\n", + "ISCBYIs=sqrt(3);#ratio of SC current to starting current\n", + "ISCBYIfl=sqrt(3)*IstBYIfl;#ratio of SC current to full load current\n", + "#Formula : TstBYTfl=(ISCBYIfl)^2*S\n", + "S=TstBYTfl/(ISCBYIfl)**2;#in fraction\n", + "print \"Full load Slip : \",round(S,3);\n", + "#With auto transformer with winding in delta : \n", + "Ip=sqrt(3)*1.750*0.8;#full voltage phase current in Ampere\n", + "IlBYIf=4.2;#ratio of Line current to full load current\n", + "Ratio=IlBYIf**2*S;#ratio of starting current to full load current\n", + "print \"Ratio of line current at starting to full load current :\",round(Ratio,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Full load Slip : 0.038\n", + "Ratio of line current at starting to full load current : 0.67\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.58, Page 196" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "R2=0.25;#in ohm per phase\n", + "S=2;#in %\n", + "S=2./100;#in fraction\n", + "\n", + "#Calculations\n", + "Ns=120*f/P;#in rpm\n", + "Nr=Ns-Ns*S;#in rpm\n", + "#When speed reduced to 10%\n", + "NewSpeed=Nr*90/100;#in rpm\n", + "Sdash=(Ns-NewSpeed)/Ns;#in fraction\n", + "R2dash=(Sdash/S)*R2;#in ohm per phase\n", + "R=R2dash-R2;#in ohm\n", + "\n", + "#Result\n", + "print \"Value of resistance to be added(in ohm) :\",R;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Value of resistance to be added(in ohm) : 1.225\n" + ] + } + ], + "prompt_number": 114 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.59, Page 197" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "R2=0.25;#in ohm per phase\n", + "N=1440.;#in rpm at full load\n", + "NewSpeed=1200;#in rpm\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "S=(Ns-N)/Ns;#in %\n", + "NewS=(Ns-NewSpeed)/Ns;#in fraction\n", + "S1=S;S2=NewS;#slip new and old\n", + "#Torque remaining same : S1/R2=S2/(R2+R)\n", + "R=S2*R2/S1-R2;#in ohm\n", + "print \"External resistance per phase(in ohm) :\",R; #incorrect answer in textbook\n", + "Nr=Ns-Ns*S;#in rpm\n", + "#If S1 is taken as 0.03 and S2 as 0.127\n", + "S1=0.03;#slip in fraction\n", + "S2=0.127;#slip in fraction\n", + "R=S2*R2/S1-R2;#in ohm\n", + "print \"External resistance per phase(in ohm) :\",round(R,3);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "External resistance per phase(in ohm) : -0.25\n", + "External resistance per phase(in ohm) : 0.808\n" + ] + } + ], + "prompt_number": 194 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.60, Page 198" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "S=4;#in %\n", + "S=4./100;#in fraction\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "N1=Ns-Ns*S;#in rpm\n", + "#When speed reduced to 10%\n", + "N2=N1*85/100;#in rpm(NewSpeed)\n", + "print \"New speed(in rpm) :\",N2;\n", + "#New speed is reduced by 15 %\n", + "Sdash=(Ns-N2)/Ns;#in fraction\n", + "print \"New Slip : \",Sdash;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "New speed(in rpm) : 1224.0\n", + "New Slip : 0.184\n" + ] + } + ], + "prompt_number": 118 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.61, Page 202" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "f=50;#in Hz\n", + "P=4;#no. of poles\n", + "phase=3;#no. of phase\n", + "Pin=60;#in KW\n", + "StatorLoss=1.2;#in KW\n", + "WindingLoss=1.8;#in KW\n", + "S=4;#in %\n", + "S=4./100;#in fraction\n", + "\n", + "#Calculations&Results\n", + "Ns=120*f/P;#in rpm\n", + "Nr=Ns-Ns*S;#in rpm\n", + "print \"Rotor speed(in rpm) :\",Nr;\n", + "Pin_rotor=Pin-StatorLoss;#in KW\n", + "RotorCuLoss=S*Pin_rotor;#in KW\n", + "print \"Rotor Cu Loss(in KW) : \",RotorCuLoss;\n", + "Pout_rotor=Pin_rotor-WindingLoss-RotorCuLoss;#in KW\n", + "Efficiency=(Pout_rotor/Pin)*100;#in %\n", + "print \"Efficiency(in %) :\",round(Efficiency);\n", + "HP=Pout_rotor*10**3/735.5;#in H.P.\n", + "print \"Horse Power(inH.P.) :\",round(HP,2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor speed(in rpm) : 1440.0\n", + "Rotor Cu Loss(in KW) : 2.352\n", + "Efficiency(in %) : 91.0\n", + "Horse Power(inH.P.) : 74.3\n" + ] + } + ], + "prompt_number": 195 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Electrical_Machines_II_by_Tarlok_Singh/chapter_3.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/chapter_3.ipynb new file mode 100755 index 00000000..957e357c --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/chapter_3.ipynb @@ -0,0 +1,68 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:ee219f57423897626f36b1403a7ddfed52f292b3adbd144afa54ccec5692e036" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3: Fractional K.W. \n", + "(FKW) Motors" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.1, Page 242" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, tan\n", + "\n", + "\n", + "#Given data :\n", + "Za=complex(3,3);#in ohm\n", + "Zm=complex(6,3);#in ohm\n", + "\n", + "#Calculations\n", + "#Phase difference 90 degree : so angle between Im and V is 90-45 degree\n", + "theta=90-45;#in degree\n", + "f=50;#in Hz\n", + "#Formula : tand(theta)=(Xc-Xl)/R\n", + "Xl=3;#in ohm and Xc=1/(2*%pi*C)\n", + "R=6;#in ohm\n", + "C=1./(2*pi*f*(tan(theta*pi/180)*R+Xl));\n", + "\n", + "#Result\n", + "print \"Capacitance(in micro Farad) :\",(C*10**6);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Capacitance(in micro Farad) : 353.677651315\n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Electrical_Machines_II_by_Tarlok_Singh/chapter_4.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/chapter_4.ipynb new file mode 100755 index 00000000..632c52df --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/chapter_4.ipynb @@ -0,0 +1,183 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9e27d5dc9ee72aa8af2a87478e959a0f346f3cc04c2f1acb86835886294034d4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4: Special Purpose Machines" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1, Page 281" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "P=8;#no. of poles\n", + "T=5;#no. of teeteh in each pole\n", + "Nr=50.;#no. of teeth in rotor\n", + "\n", + "#Calculations\n", + "Ns=P*T;#no. of teeth\n", + "Beta=(Nr-Ns)*360/(Nr*Ns);#in degree\n", + "\n", + "#Result\n", + "print \"Stepping Angle(in degree) : = \",Beta;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Stepping Angle(in degree) : = 1.8\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.2, Page 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "Beta=2.5;#in degree\n", + "f=3600;#in PPs\n", + "Resolution=360;#in degree\n", + "\n", + "#Calculations&Results\n", + "print \"Resolution : \",Resolution;\n", + "Beta1=Resolution/Beta;#steps/revolution\n", + "print \"Steps per revolution : \",Beta1;\n", + "n=Beta*f/360;#in rps\n", + "print \"Steps required for making 25 revolution(in rps) : \",n;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resolution : 360\n", + "Steps per revolution : 144.0\n", + "Steps required for making 25 revolution(in rps) : 25.0\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3, Page 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "Beta=15;#in degree\n", + "Phase=3;#no. of phase\n", + "\n", + "#Calculations&Results\n", + "#Formula : Beta*Nr=(360/phase)\n", + "Nr=(360./Phase)/Beta;#unitless\n", + "print \"No. of rotor :\",Nr;\n", + "#Case (i) : when Ns>Nr : Formula : Beta=(Ns-Nr)*360/(Ns*Nr)\n", + "Ns=Nr/(1-Beta*Nr/360);\n", + "print \"No. of stator poles if Ns>Nr :\",Ns;\n", + "#Case (ii) : when Nr>Ns : Formula : Beta=(Nr-Ns)*360/(Ns*Nr)\n", + "Ns=Nr/(1+Beta*Nr/360);\n", + "print \"No. of stator poles if Nr>Ns :\",Ns;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of rotor : 8.0\n", + "No. of stator poles if Ns>Nr : 12.0\n", + "No. of stator poles if Nr>Ns : 6.0\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4, Page 282" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Given data :\n", + "Beta=1.8;#in degree\n", + "m=4;#no. of phases\n", + "\n", + "#Calculations\n", + "#Formula : Beta*Nr=(360/m)\n", + "Nr=(360/m)/Beta;#unitless\n", + "\n", + "#Results\n", + "print \"No. of rotor teeth : = \",Nr;\n", + "print \"In multi stack motor rotor teeth equals to stator teeth equals to : \",Nr;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "No. of rotor teeth : = 50.0\n", + "In multi stack motor rotor teeth equals to stator teeth equals to : 50.0\n" + ] + } + ], + "prompt_number": 5 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Electrical_Machines_II_by_Tarlok_Singh/extra-chapter1.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/extra-chapter1.ipynb new file mode 100755 index 00000000..aa84025a --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/extra-chapter1.ipynb @@ -0,0 +1,961 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:73456f874b64111f39ff6e1df283939e5a576ba362e30194dc5083b7ddd99204" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Synchronous Machines(Additional problems)" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 1, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "phase = 3 #three phase winding\n", + "ns = 36. #number of slots\n", + "np = 4 #number of poles\n", + "\n", + "#Calculations\n", + "nsp = ns/phase #number of slots per phase\n", + "npp = nsp/np #number of slots pole/phase\n", + "alpha = 180*np/ns #slot angle\n", + "Kd = math.sin(npp*alpha/2*math.pi/180)/(3*math.sin(alpha/2*math.pi/180))\n", + "\n", + "#Results\n", + "print \"The distribution factor is %.2f\"%Kd" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The distribution factor is 0.96\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 2, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "np = 3 #number of phases\n", + "npl = 4 #number of poles\n", + "ns = 24 #number of slots\n", + "\n", + "#calculaions\n", + "nsp = ns/npl #number of slot/pole\n", + "alpha = 180/nsp #slot pitch(degrees)\n", + "m = ns/(npl*np) \n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "Kc = math.cos(alpha/2*math.pi/180)\n", + "\n", + "#Results\n", + "print \"Distribution factor = %.2f\"%Kd\n", + "print \"Pitch factor = %.3f degrees\"%Kc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distribution factor = 0.97\n", + "Pitch factor = 0.966 degrees\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 3, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Vl= 11000 #V\n", + "N = 1500 #rpm\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "P = (120*f)/N\n", + "Vp = Vl/math.sqrt(3)\n", + "\n", + "#Results\n", + "print \"Number of poles = %d\"%P\n", + "print \"Voltage per phase of alternator = %d V\"%Vp" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of poles = 4\n", + "Voltage per phase of alternator = 6350 V\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 4, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 4 #number of poles\n", + "ph = 3 #number of phases\n", + "s = 36 #number of slots\n", + "cs = 8 #coil span\n", + "\n", + "#calculations\n", + "nsp = s/P #number of slots/pole\n", + "alpha = 180/nsp #slot pitch\n", + "m = s/(P*ph)\n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "ns = nsp-cs #no. of slots by which coil is short pitched\n", + "B = 1*alpha\n", + "Kc= math.cos(B/2*math.pi/180)\n", + "\n", + "#Results\n", + "print \"Distribution factor = %.3f\"%Kd\n", + "print \"Pitch factor = %.3f degrees\"%Kc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distribution factor = 0.960\n", + "Pitch factor = 0.985 degrees\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 5, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P= 16. #number of poles\n", + "N = 375 #rpm\n", + "s = 144. #number of slots\n", + "c = 10 #number of conductors\n", + "phase = 3\n", + "phi = 0.035 #flux per pole\n", + "\n", + "#Calculations\n", + "f = (P*N)/120 #Hz\n", + "ns = s/P #slot/pole\n", + "m = ns/phase\n", + "alpha = 180/ns #slot angle\n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "Tc = s*c #total number of conductor\n", + "Tcp = Tc/phase #total number of conductors/phase\n", + "Ncp = Tcp/2 #number of turns/phase\n", + "emf = 4.44*Kd*phi*f*Ncp\n", + "Vl = math.sqrt(3)*emf\n", + "\n", + "#Results\n", + "print \"Frequency = %d Hz\"%f\n", + "print \"E.M.F = %d V\"%emf\n", + "print \"Line voltage = %d V\"%Vl" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency = 50 Hz\n", + "E.M.F = 1789 V\n", + "Line voltage = 3100 V\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 6, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 4 #no. of poles\n", + "s = 36 #no. of slots\n", + "ph = 3 #no. of phases\n", + "cs = 8 #coil span\n", + "\n", + "#Calculations\n", + "ns = s/P #no. of slots/pole\n", + "alpha = 180/ns #slot pitch\n", + "m = s/(P*ph)\n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "Ns = ns-cs\n", + "Kc = math.cos(alpha/2*math.pi/180)\n", + "\n", + "#Results\n", + "print \"Distribution factor = %.2f\"%Kd\n", + "print \"Pitch factor = %.4f degrees\"%Kc" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distribution factor = 0.96\n", + "Pitch factor = 0.9848 degrees\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 7, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "El = 6600 #V\n", + "P = 4 #number of poles\n", + "s = 60 #number of slots\n", + "ph = 3 #number of phases\n", + "c = 2 #number of conductors\n", + "sn = 13 #slot number\n", + "f = 50 #Hz\n", + "T = 20 #V\n", + "\n", + "#Calculations\n", + "n = s/P\n", + "m = n/ph\n", + "Zp = (s*c)/ph\n", + "B = 180/n #degrees\n", + "Kd = math.sin(m*B/2*math.pi/180)/(m*math.sin(B/2*math.pi/180))\n", + "Cs = (sn-1)*180/n #degrees\n", + "Kp = math.cos((180-Cs)/2*math.pi/180)\n", + "phi = El/(math.sqrt(3)*4.44*Kd*Kp*f*T)\n", + "\n", + "#Results\n", + "print \"The required flux pole is %.3f V\"%phi" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required flux pole is 0.943 V\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 8, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Varible declaration\n", + "Vl = 230 #V\n", + "Rt = 10*10**3 #VA\n", + "ph = 3 #no. of phases\n", + "Ra = 0.5 #ohms/phase\n", + "Xs = 1.2 #ohms/phase\n", + "cos_phi = 0.8 #lagging\n", + "sin_phi = 0.6 #leading\n", + "V = 132.8 #V\n", + "\n", + "#Calculations\n", + "I = Rt/(ph*V) #A\n", + "print I\n", + "#Part(a)\n", + "Eo = math.sqrt(((V*cos_phi)+(I*Ra))**2+((V*sin_phi)+(I*Xs))**2)\n", + "Reg1 = (Eo-V)/V*100\n", + "\n", + "#Part(b)\n", + "Eo = math.sqrt((V*cos_phi+I*Ra)**2+(V*sin_phi-I*Xs)**2)\n", + "Reg2 = (Eo-V)/V*100\n", + "\n", + "#Results\n", + "print \"Part(a): Regulation = %.2f %%\"%Reg1\n", + "print \"Part(b): Regulation = %.2f %%\"%Reg2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "25.1004016064\n", + "Part(a): Regulation = 21.81 %\n", + "Part(b): Regulation = -3.08 %\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 9, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "El = 10000 #V\n", + "Kd = 0.96\n", + "Kp = 1.0\n", + "phi = 15*10**-2 #wb\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "T = El/(math.sqrt(3)*4.44*Kd*Kp*phi*f)\n", + "Zp = 2*T\n", + "\n", + "#Result\n", + "print \"Number of armature conductors in series/phase = %d\"%Zp\n", + "#Answer differs due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of armature conductors in series/phase = 361\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 10, Page 120" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "s = 90 #no. of slots\n", + "P = 10 #no. of poles\n", + "ph = 3 #no. of phases\n", + "E = 11000. #E.M.F(V)\n", + "phi = 0.16 #flux(Wb)\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "nsp = s/(P*ph) #slot/pole/phase\n", + "alpha = 180/(s/P) #slot angle\n", + "m = s/(P*ph)\n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "N = E/(math.sqrt(3)*4.44*Kd*phi*f)\n", + "Nc = 2*N\n", + "\n", + "#Result\n", + "print \"Number of conductors/phase are %d\"%Nc\n", + "#Incorrect answer for N in the textbook. Hence the result differs" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of conductors/phase are 372\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 11, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Vl = 400 #V\n", + "cos_phi = 1 #pf\n", + "n = 85./100 #efficiency\n", + "Zs = 10 #reactance(ohms)\n", + "\n", + "#Calculations\n", + "out = Zs*735.5 #output\n", + "mi = out/n #motor input(W)\n", + "Il = mi/(math.sqrt(3)*Vl*cos_phi)\n", + "I = Il #since current is minimum when power factor is unity\n", + "Er = I*Zs\n", + "V = Vl/math.sqrt(3)\n", + "E = math.sqrt(V**2+Er**2)\n", + "emf = math.sqrt(3)*E\n", + "\n", + "#Results\n", + "print \"Minimum current = %.1f A\"%I\n", + "print \"Line induces e.m.f. = %d V\"%emf\n", + "#Answers differ due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum current = 12.5 A\n", + "Line induces e.m.f. = 454 V\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 12, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 6\n", + "phi = 25*10**-3 #wb\n", + "f = 50 #Hz\n", + "ph = 3 #no. of phases\n", + "s = 12 #no. of slots/pole\n", + "nc = 4 #no. of conductors/slot\n", + "\n", + "#Calculations\n", + "Zph = nc*s*P/ph\n", + "T = Zph/2\n", + "alpha = 180*(1-5./P)\n", + "Kc = math.cos(alpha/2*math.pi/180)\n", + "m = s/ph\n", + "B = 180/s\n", + "Kd = math.sin(m*alpha/2*math.pi/180)/(m*math.sin(alpha/2*math.pi/180))\n", + "Eph = 4.44*Kc*Kd*f*phi*T\n", + "El = math.sqrt(3)*Eph\n", + "\n", + "#Results\n", + "print \"Line e.m.f. = %.1f V\"%El\n", + "#incorrect answer for Kd in the textbook. Hence the result differs" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Line e.m.f. = 372.8 V\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 13, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 1200 #kW\n", + "V = 2300 #V\n", + "Ia = 200 #A\n", + "cos_phi_a = 0.9 #lagging\n", + "\n", + "#Calculations\n", + "Pa = V*Ia*cos_phi_a/10**3 #kW\n", + "phi = math.atan(cos_phi_a)\n", + "Pra = Pa*math.tan(phi)\n", + "Pr = 0 #since power factor is unity\n", + "Prb = Pr-Pra\n", + "Pb = P-Pa\n", + "tan_phi = Prb/Pb\n", + "cos_phi_b = math.cos(math.atan(tan_phi))\n", + "Ia = Pb*10**3/(V*cos_phi_b)\n", + "\n", + "#Results\n", + "print \"Power = %d kW\"%Pb\n", + "print \"Power factor = %.3f\"%cos_phi_b\n", + "print \"Current = %.1f A\"%Ia\n", + "#incorrect answers in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power = 786 kW\n", + "Power factor = 0.904\n", + "Current = 378.2 A\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 14, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "\n", + "#Part (a) - for lighting load\n", + "P1 = 600 #kW\n", + "cos_phi =1 #power factor\n", + "tan_phi = 0\n", + "Prl = P1*tan_phi\n", + "\n", + "#Part(b) - for inductive load\n", + "P2 = 800 #W\n", + "cos_phi = 0.9\n", + "tan_phi = 0.4843\n", + "Pri = P2*tan_phi\n", + "\n", + "#Part(c) - for capacitive power\n", + "P3 = 800\n", + "cos_phi = 0.8\n", + "tan_phi = 0.75\n", + "Prc = -P3*tan_phi\n", + "\n", + "P = P1+P2+P3\n", + "Pr = Prl+Pri+Prc\n", + "Pa = 1000 #kW\n", + "cos_phi_a = 0.85\n", + "tan_phi_a = math.tan(math.acos(cos_phi_a))\n", + "Pra = Pa*tan_phi_a\n", + "Pb = P-Pa\n", + "Prb = Pr-Pra\n", + "tan_phi_2 = Prb/Pb\n", + "cos_phi_b = math.cos(math.atan(tan_phi_2))\n", + "\n", + "#Results\n", + "print \"Active power supplied by alternator B = %d kW\"%Pb\n", + "print \"Power factor of alternator B = %.4f leading\"%cos_phi_b\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Active power supplied by alternator B = 1200 kW\n", + "Power factor of alternator B = 0.8217 leading\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 15, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "E = 1000 #KVa\n", + "Vl = 11000 #V\n", + "ph = 3 #no. of phases\n", + "Ra = 3.5 #armature resistance(ohms)\n", + "Xs = 40 #armature reactance(ohms)\n", + "cos_phi = 0.8\n", + "\n", + "#Calculations\n", + "Ia = round(E*1000/(math.sqrt(3)*Vl),1)\n", + "V = Vl/math.sqrt(3)\n", + "phi = math.degrees(math.acos(cos_phi))\n", + "Rad = round(Ia*Ra) #armature resistance drop/phase\n", + "Xad = round(Ia*Xs) #armature reactance drop per phase\n", + "Er = math.sqrt(Rad**2+Xad**2) #incorrect answer in the textbook\n", + "theta = math.degrees(math.atan(Xs/Ra))\n", + "\n", + "#Part a - Unity p.f.\n", + "Eba = math.sqrt(V**2+Er**2-(2*V*Er*math.cos(theta*math.pi/180)))\n", + "Vla = Eba*math.sqrt(3)\n", + "#From triangle OAB\n", + "alpha_a = math.degrees(math.asin((Er*math.sin(theta*math.pi/180))/Eba))\n", + "\n", + "#Part b - At p.f. 0.8 lagging\n", + "BOA_b = theta-phi\n", + "Ebb = math.sqrt(V**2+Er**2-(2*V*Er*math.cos(BOA_b*math.pi/180)))\n", + "Vlb = Ebb*math.sqrt(3)\n", + "alpha_b = math.degrees(math.asin(Er*math.sin(BOA_b*math.pi/180)/Ebb))\n", + "\n", + "#Part c - At p.f. 0.8 leading\n", + "BOA_c = theta+phi\n", + "Ebc = math.sqrt(V**2+Er**2-(2*V*Er*math.cos(BOA_c*math.pi/180)))\n", + "Vlc = Ebc*math.sqrt(3)\n", + "alpha_c = math.degrees(math.asin(Er*math.sin(BOA_c*math.pi/180)/Ebc))\n", + "\n", + "#Results\n", + "print \"Induced e.m.f. and angular retardation are as below:\"\n", + "print \"Part a : %d V,%.2f degrees\"%(Vla,alpha_a)\n", + "print \"Part b : %d V,%.2f degrees\"%(Vlb,alpha_b)\n", + "print \"Part c : %d V,%.2f degrees\"%(Vlc,alpha_c)\n", + "\n", + "#Incorrect answers in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induced e.m.f. and angular retardation are as below:\n", + "Part a : 11284 V,18.80 degrees\n", + "Part b : 8984 V,17.62 degrees\n", + "Part c : 13294 V,13.49 degrees\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 16, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Em = 6000 #V\n", + "Xs = 1.5 #ohms/phase\n", + "Il = 1000 #amps\n", + "sin_phi = 1 #power factor\n", + "\n", + "#Calculations\n", + "#Since load is inductive\n", + "Vt = Em-Il*Xs\n", + "Vl = round(math.sqrt(3)*Vt) #since winding is connected in star\n", + "Pr = math.sqrt(3)*Vl*Il*sin_phi/10**6\n", + "\n", + "#Results\n", + "print \"Reactive power supplied to the load is %.2f MVAR\"%Pr\n", + "#Incorrect answer in textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Reactive power supplied to the load is 13.50 MVAR\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 17, Page 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "V = 7000 #V\n", + "I = 1400 #amps\n", + "Xs = 1.2 #ohms\n", + "f = 50 #Hz\n", + "Po = 4 #number of poles\n", + "cos_phi = 1 #power factor, since load is resistive\n", + "\n", + "#Calculations\n", + "E = math.sqrt(V**2+(I*Xs)**2) #V\n", + "P = 3*V*I*cos_phi #W\n", + "N = 120*f/Po #rpm\n", + "w = (2*math.pi*N)/60 #rad/sec\n", + "T = P/(w*9.81)\n", + "\n", + "#Result\n", + "print \"The required torque is %.2e kg-meter\"%T" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required torque is 1.91e+04 kg-meter\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 18, Page 122" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "Ep = 5700 #V\n", + "Xs = 1.5 #ohms\n", + "\n", + "#Calculations\n", + "#Since windings are connected in star\n", + "Ip = Ep/Xs #phase current(A)\n", + "Il = Ip\n", + "\n", + "#Result\n", + "print \"The current per phase is %d Amps\"%Il" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The current per phase is 3800 Amps\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 19, Page 122" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Vt = 15 #KV\n", + "Ps = 100*10**6 #power supplied by generator VA\n", + "cos_phi = 0.8 #power factor(lagging)\n", + "Xs = 0.7 #ohm per phase\n", + "Vl = 15 #KV\n", + "f = 50 #Hz\n", + "Po = 2 #no. of poles\n", + "\n", + "#Calculations\n", + "Vp = Vl/math.sqrt(3) #KV\n", + "AC = Vp*cos_phi\n", + "sin_phi = 0.6\n", + "BC = Vp*sin_phi #KV\n", + "Il = Ps/(math.sqrt(3)*Vl*10**3) #amps\n", + "Vd = Il*Xs #voltage drop in synchronous reactance KV\n", + "BL = 2.697\n", + "LC = BL+BC #V\n", + "AL = math.sqrt(AC**2+LC**2) #V\n", + "Em = AL*math.sqrt(3) #V\n", + "Ns = (120*f)/Po #rpm\n", + "P = Ps*cos_phi #W\n", + "wT = 80*10**6\n", + "T = (wT*60)/(2*math.pi*Ns)\n", + "print \n", + "#Result\n", + "print \"Induced e.m.f. = %.2f V\"%Em\n", + "print \"Torque = %.2e Nw-m\"%T\n", + "print \"Speed = %d rpm\"%Ns\n", + "#Answers differ due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Induced e.m.f. = 18.19 V\n", + "Torque = 2.55e+05 Nw-m\n", + "Speed = 3000 rpm\n" + ] + } + ], + "prompt_number": 21 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Electrical_Machines_II_by_Tarlok_Singh/extra.ipynb b/Electrical_Machines_II_by_Tarlok_Singh/extra.ipynb new file mode 100755 index 00000000..6fd7afb3 --- /dev/null +++ b/Electrical_Machines_II_by_Tarlok_Singh/extra.ipynb @@ -0,0 +1,869 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:f8b31f19cbf3c6b3dce4ba746cfebc233c9801395be699bc2538e86d3ab6c5f4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Induction Motors(Additional problems)" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 1, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "P = 8 #number of poles\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "Ns = (120*f)/P\n", + "\n", + "#Result\n", + "print \"Synchronous speed = %d r.p.m.\"%Ns" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed = 750 r.p.m.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 2, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "P = 2 #assumption - number of poles\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "Ns = (120*f)/P\n", + "\n", + "#Result\n", + "print \"Maximum speed = %d r.p.m.\"%Ns" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum speed = 3000 r.p.m.\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 3, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "Pa = 6 #number of poles in alternator\n", + "N = 1000 #rpm\n", + "Pi = 16 #number of poles in induction motor\n", + "S = 2.5 #slip\n", + "\n", + "#Calculations\n", + "f = (N*Pa)/120 #Hz\n", + "Ns = (120*f)/Pi #rpm\n", + "Nr = Ns - ((S*Ns)/100)\n", + "\n", + "#Results\n", + "print \"The actual motor speed is %.2f r.p.m.\"%Nr" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The actual motor speed is 365.62 r.p.m.\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 4, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "P = 14. #no. of poles\n", + "f = 50. #Hz\n", + "N = 414. #r.p.m.\n", + "\n", + "#calculations\n", + "Ns = (120*f)/P #rpm\n", + "S = ((Ns-N)/Ns)*100\n", + "fr = (S*f)/100\n", + "\n", + "#Results\n", + "print \"Rotor frequency = %.2f Hz\"%fr\n", + "print \"Slip = %.2f %%\"%S\n", + "#Incorrect answers in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor frequency = 1.70 Hz\n", + "Slip = 3.40 %\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 5, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "Pi = 50 #motor input - KW\n", + "S = 3./100 #slip - %\n", + "\n", + "#Calculations\n", + "Lc = Pi*S #rotor copper loss\n", + "Pm = Pi-Lc\n", + "\n", + "#Result\n", + "print \"Total mechanical power = %.1f kW\"%Pm" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total mechanical power = 48.5 kW\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 6, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 4 #no. of poles\n", + "m = 3\n", + "f = 50 #Hz\n", + "n = 85 #efficiency %\n", + "Po = 17. #useful output power kW\n", + "Ls = 900 #stator losses W\n", + "Lwf = 1100 #windage&friction losses W\n", + "Lrc = 1. #rotor copper loss kW\n", + "\n", + "#Calculations\n", + "Pi = Po/n*100 #input power\n", + "Tl = Pi-Po #total losses kW\n", + "Lc = Tl - Ls - Lwf #copper loss W\n", + "Pir = Pi-Ls #input to rotor kW\n", + "S = Lrc/Pi\n", + "Ns = 120*f/P #rpm\n", + "N = Ns-(S*Ns) #rpm\n", + "wT = 19.1*1000 #W\n", + "Td = (wT*60)/(math.pi*2*N)\n", + "Ta = (Po*1000*60)/(2*math.pi*N)\n", + "\n", + "#Results\n", + "print \"Slip = %.3f\"%S\n", + "print \"Torque developed = %.2f N-m\"%Td\n", + "print \"Torque available = %.1f N\"%Ta\n", + "#Answers vary due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip = 0.050\n", + "Torque developed = 127.99 N-m\n", + "Torque available = 113.9 N\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 7, Page 225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "P = 6 #no. of poles\n", + "f = 60 #Hz\n", + "T = 70 #N-m\n", + "N = 1152. #rpm\n", + "\n", + "#Calculations\n", + "#Part a\n", + "Pi = (2*math.pi*1200*T)/60/1000 #input to rotor W\n", + "Ns = (120.*f)/P #rpm\n", + "S = (Ns-N)/Ns\n", + "\n", + "#Part b\n", + "Lrc = S*Pi*1000 #W\n", + "Td = (2*math.pi*N*T)/60\n", + "\n", + "#Part c\n", + "Pm = Td #W\n", + "\n", + "#Results\n", + "print \"Total input to the rotor = %.1f kW\"%Pi\n", + "print \"Rotor copper loss = %d W\"%Lrc\n", + "print \"Mechanical power developed = %.2f W\"%Pm\n", + "#answers vary due to rounding-off errors" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total input to the rotor = 8.8 kW\n", + "Rotor copper loss = 351 W\n", + "Mechanical power developed = 8444.60 W\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 8, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Vs = 100 #voltage between two slip rings V\n", + "R2 = 0.2 #ohms/phase\n", + "Xo = 1 #ohm/phase\n", + "S = 0.04 #slip\n", + "\n", + "#Calculations\n", + "Eo = Vs/math.sqrt(3)\n", + "I2 = (S*Eo)/math.sqrt(R2**2+(S*Xo)**2)\n", + "#During maximum torque,\n", + "Sm = R2/Xo \n", + "Ir = (Sm*Eo)/math.sqrt(S**2+(S*Xo)**2)\n", + "\n", + "#Results\n", + "print \"Rotor current when slip is 4%% is %.1f A\"%I2\n", + "print \"Slip during maximum torque is %.1f\"%Sm\n", + "print \"Rotor current during maximum torque is %.1f A\"%Ir #incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor current when slip is 4% is 11.3 A\n", + "Slip during maximum torque is 0.2\n", + "Rotor current during maximum torque is 204.1 A\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 9, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "S = 1 #slip at the time of starting\n", + "X2 = 1 #ohms/pase\n", + "X1 = 0.1 #internal rotor resistance ohms/phase\n", + "\n", + "#Calculations\n", + "#Total resistance required for maximum torque is 1 Ohm\n", + "Re = X2-X1\n", + "\n", + "#Result\n", + "print \"External resistance needed to be added is %.1f ohms/phase\"%Re" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "External resistance needed to be added is 0.9 ohms/phase\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 10, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import sympy\n", + "from sympy.solvers import solve\n", + "from sympy import Symbol\n", + "\n", + "#Variable declaration\n", + "T = 162.8 #maximum torque Nw-m\n", + "N = 1365 #speed rpm\n", + "f = 50 #Hz\n", + "P = 4 #no. of poles\n", + "R2 = 0.2 #ohms/phase\n", + "\n", + "#Calculations\n", + "Ns = 120*f/P\n", + "S = Ns-N/Ns #slip at maximum torque\n", + "X2 = R2/S #ohms\n", + "Th = T/2 #half of maximum torque\n", + "R2 = Symbol('R2')\n", + "x = solve((Th*R2**2-18.1*40*R2+400),R2) #solving the equation\n", + "\n", + "#Results\n", + "print \"Required resistance = \",round(x[0],2),\"ohms\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Required resistance = 0.59 ohms\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 11, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "N = 290. #speed of motor at full load rpm\n", + "f = 50 #Hz\n", + "\n", + "#Calculations\n", + "P = 20 #since motors running at full load\n", + "Ns= 120*f/P\n", + "S1 = (Ns-N)/Ns*100\n", + "#since S is directly proportinal to R2,\n", + "#when R2 is doubled, S is also doubled\n", + "S = 2*S1\n", + "\n", + "#Results\n", + "print \"The number of poles are %d\"%P\n", + "print \"Slip = %.1f %%\"%S1\n", + "print \"Slip if the rotor resistance is doubled = %.1f %%\"%S" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of poles are 20\n", + "Slip = 3.3 %\n", + "Slip if the rotor resistance is doubled = 6.7 %\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 12, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declarartion\n", + "S = 2.5/100 #slip\n", + "#Isc=4*If\n", + "\n", + "#Calculations\n", + "'''\n", + "Ts Isc ^2\n", + "-- = --- * slip\n", + "Tf If\n", + "'''\n", + "Ts_by_Tf = 4**2*S*100\n", + "\n", + "#Result\n", + "print \"Starting torque is %d %% of full load torque\"%Ts_by_Tf" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Starting torque is 40 % of full load torque\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 13, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "f = 50 #Hz\n", + "P = 6 #no. of poles\n", + "S = 1 #slip\n", + "Eo = 62.8 #phase voltage V\n", + "m = 3.\n", + "Xo = 6 #rotor reactance ohms\n", + "R2 = 1 #resistance ohms\n", + "\n", + "#Calculations\n", + "Ns = 120*f/P #rpm\n", + "ws = 2*math.pi*Ns/60 #rad/sec\n", + "K = m/ws\n", + "Ts = (K*S*Eo**2*R2)/((R2**2)+(S*Xo)**2) #at starting\n", + "#For maximum torque\n", + "R2 = 1 #ohm\n", + "X2 = 6 #ohms\n", + "S = R2/X2\n", + "Tmax = (K*Eo**2)/(2*X2)\n", + "\n", + "#Result\n", + "print \"The starting torque is %.3f N-m\"%Ts\n", + "print \"The maximum torque develped is %.1f N-m\"%Tmax\n", + "#Incorrect soltion in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The starting torque is 3.054 N-m\n", + "The maximum torque develped is 9.4 N-m\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 14, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Vl = 200. #line voltage of stator V\n", + "t = 0.67 #turn ratio\n", + "Ns = 1500. #rpm\n", + "R2 = 0.1 #resistance ohms\n", + "S = 0.04 #slip\n", + "X = 0.9 #reactance ohms\n", + "m = 3. #number of phases\n", + "\n", + "#Calculations\n", + "Vp = Vl/math.sqrt(3) #phase voltage of stator V\n", + "E = Vp*t\n", + "ws = (2*math.pi*Ns)/60\n", + "K = m/ws\n", + "T = (K*S*E**2*R2)/(R2**2+(S*X)**2)\n", + "\n", + "#Result\n", + "print \"Total torque = %d N-m\"%T\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total torque = 40 N-m\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 15, Page 226" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "P = 8 #number of pos\n", + "f = 50. #Hz\n", + "S = 0.04 #slip\n", + "Po = 15*1000 #oput power W\n", + "R2 = 0.2 #rotor resistance Ohms\n", + "X = 1.5 #rotor reactance Ohms\n", + "N = 400 #ohms\n", + "\n", + "#Calculations\n", + "Ns = (120*f)/P #rpm\n", + "S_dash = (Ns-N)/Ns\n", + "R2_dash = (R2*S_dash)/S #ohms\n", + "R = R2_dash-R2 #resistance to be added\n", + "Pi = Po/(1-S) #W\n", + "Lc = S_dash*Pi #rotor copper loss W\n", + "P = Pi - Lc #ouput power W\n", + "\n", + "#Results\n", + "print \"The external resistance to be connected per phase is %.2f ohms\"%R\n", + "print \"Total rotor copper loss = %d W\"%Lc\n", + "print \"Ouput power of motor = %d W\"%P\n", + "\n", + "#Incorrect answers in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The external resistance to be connected per phase is 2.13 ohms\n", + "Total rotor copper loss = 7291 W\n", + "Ouput power of motor = 8333 W\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 16, Page 227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "n = 0.8 #efficiency \n", + "O = 20*735.5 #load/output\n", + "\n", + "#Calculations\n", + "i = O/n #input W\n", + "Tl = i - O #total losses W\n", + "#since total losses is a sum of rotor copper loss+stator copper loss+iron loss+mechanical loss\n", + "K = (Tl*3)/10 #rotor copper loss W\n", + "Ri = O+(K/3)+K #input to the rotor W \n", + "S = K/Ri #slip\n", + "\n", + "#Result \n", + "print \"Slip = %.3f\"%S" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip = 0.068\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 17, Page 227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable declaration\n", + "Pi = 20 #input power KW\n", + "N = 960. #speed rpm\n", + "f = 50 #Hz\n", + "P = 6 #number of poles\n", + "R2 = 1./3 #resistance ohms\n", + "\n", + "#Calculations\n", + "Ns = 1000.\n", + "S = (Ns-N)/Ns #slip\n", + "Lrc = S*Pi*1000 #rotor copper loss W\n", + "Lrc_ph = Lrc/3 #rotor copper loss per phase\n", + "I2 = math.sqrt(Lrc_ph/R2)\n", + "\n", + "#Result\n", + "print \"Rotor current per phase = %.1f A\"%I2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor current per phase = 28.3 A\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 18, Page 227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "P = 4 #number of poles \n", + "f = 50. #Hz\n", + "N = 645. #speed rpm\n", + "R2 = 0.04 #rotor resistance ohms\n", + "\n", + "#Calculations\n", + "Ns = (120*f)/P #rpm\n", + "S = (Ns-N)/Ns #slip\n", + "X2 = R2/S #rotor reactance ohms\n", + "a = R2/X2\n", + "St_by_mt = (2*a)/(a*2+1) #starting torque/maximum torque\n", + "S = 0.03\n", + "Flt_by_mt = (2*a*S)/(a**2+S**2) #full load torque/maximum torque\n", + "\n", + "#Results\n", + "print \"Maximum torque at starting is %d %%\"%(St_by_mt*100)\n", + "print \"Maximum torque when slip is 3%% is %d %%\"%(Flt_by_mt*100)\n", + "\n", + "#Value of Ns ic wrongly calculated in the textbook. Hence the answers vary" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum torque at starting is 53 %\n", + "Maximum torque when slip is 3% is 10 %\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Problem 20, Page 227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Variable declaration\n", + "R2 = 0.5 #rotor resistance ohms\n", + "X2 = 5 #rotor reactance ohms\n", + "Tm_by_tfl = 2.5 #max torque/full load torque\n", + "\n", + "#Calculations\n", + "#Tfl = Tm/2.5 = KE^2/2.5*2*X2\n", + "#Part a\n", + "Tst_by_Tfl_a = (25*R2)/(R2**2+X2**2)\n", + "\n", + "#Part b\n", + "Tst_by_Tfl_b = (25*R2)/(3*(R2**2+X2**2))\n", + "\n", + "#Part c\n", + "#Rotor voltage at starting = 0.75E2\n", + "Tst_by_Tfl_c = (0.75**2*25*R2)/(R2**2+X2**2)\n", + "\n", + "#Results\n", + "print \"The ratio of starting torque to full load torque for the given cases are as below:\"\n", + "print \"Part a: %.2f\"%Tst_by_Tfl_a\n", + "print \"Part a: %.2f\"%Tst_by_Tfl_b\n", + "print \"Part a: %.2f\"%Tst_by_Tfl_c" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of starting torque to full load torque for the given cases are as below:\n", + "Part a: 0.50\n", + "Part a: 0.17\n", + "Part a: 0.28\n" + ] + } + ], + "prompt_number": 21 + } + ], + "metadata": {} + } + ] +}
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