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diff --git a/Electrical_Machines_by_S._K._Bhattacharya/ch4.ipynb b/Electrical_Machines_by_S._K._Bhattacharya/ch4.ipynb new file mode 100644 index 00000000..930b14d4 --- /dev/null +++ b/Electrical_Machines_by_S._K._Bhattacharya/ch4.ipynb @@ -0,0 +1,1509 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b6827bab8bcac6e2fc731c1e29fb824cdddabc14d1fbfce91735b0bd239d066e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4 : Three Phase Induction Machines" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1 Page No : 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data;\n", + "f = 50.; #frequency\n", + "p = 6.; # number of poles\n", + "V = 400.; #voltage supply\n", + "S = 4.; #percentage slip\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/p; #synchronous speed\n", + "print \"Syhchronous speed, Ns = %d \"%(Ns);\n", + "Nr = (1-(S/100))*Ns;\n", + "print \"speed of rotor with slip 4 percent, Nr is %d rpm \"%(Nr);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Syhchronous speed, Ns = 1000 \n", + "speed of rotor with slip 4 percent, Nr is 960 rpm \n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.2 Page No : 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data;\n", + "f = 50.; #frequency\n", + "V = 400.; #voltage supply\n", + "\n", + "# Calculations and Results\n", + "p = 2.;\n", + "print \"when P = 2, Syhchronous speed, Ns = %d \"%((120*f)/p);\n", + "p = 4;\n", + "print \"when P = 2, Syhchronous speed,Ns = %d \"%(120*f/p);\n", + "p = 6;\n", + "print \"when P = 2, Syhchronous speed, Ns = %d \"%(120*f/p);\n", + "p = 8;\n", + "print \"when P = 2 Syhchronous speed, Ns = %d \"%(120*f/p);\n", + "print (\"for Nr to be 1440 , Ns will be 1500, thus p = 4\")\n", + "Ns = 1500;Nr1 = 1440;\n", + "S1 = ((Ns-Nr1)/Ns)*100;\n", + "print \"slip = %d\"%(S1);\n", + "print (\"for Nr to be 940 , Ns will be 1000, thus p = 6\")\n", + "Ns = 1000;Nr2 = 940;\n", + "S2 = ((Ns-Nr2)/Ns)*100;\n", + "print \"slip = %d\"%(S2);\n", + "if S1>S2:\n", + " print (\"motor running at 1440 rpm is running at higher slip\")\n", + "elif S2>S1:\n", + " print (\"motor running at 940 rpm is running at higher slip\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "when P = 2, Syhchronous speed, Ns = 3000 \n", + "when P = 2, Syhchronous speed,Ns = 1500 \n", + "when P = 2, Syhchronous speed, Ns = 1000 \n", + "when P = 2 Syhchronous speed, Ns = 750 \n", + "for Nr to be 1440 , Ns will be 1500, thus p = 4\n", + "slip = 0\n", + "for Nr to be 940 , Ns will be 1000, thus p = 6\n", + "slip = 0\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3 Page No : 289" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data;\n", + "P = 10.; #poles of alternator\n", + "N = 600.; #speed of alternator\n", + "\n", + "# Calculations and Results\n", + "f = (P*N)/120 #frequency\n", + "print \"frequency = %d\"%(f);\n", + "print (\"when P = 2\");p = 2\n", + "Ns = (120*f)/p; #synchronous speed\n", + "print \"Syhchronous speed, Ns = %d \"%(Ns);\n", + "print (\"when P = 4\");p = 4;\n", + "Ns = (120*f)/p; #synchronous speed\n", + "print \"Syhchronous speed, Ns = %d \"%(Ns);\n", + "#speed of rotor(1440) is less than synchronous speed 1500, therefore P = 4\n", + "print (\"speed of rotor(1440) is less than synchronous speed 1500, therefore P = 4\")\n", + "Ns = 1500.;\n", + "Nr = 1440.;\n", + "S = ((Ns-Nr)/Ns)*100\n", + "print \"slip is %d percent and number of poles is 4\"%(S)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frequency = 50\n", + "when P = 2\n", + "Syhchronous speed, Ns = 3000 \n", + "when P = 4\n", + "Syhchronous speed, Ns = 1500 \n", + "speed of rotor(1440) is less than synchronous speed 1500, therefore P = 4\n", + "slip is 4 percent and number of poles is 4\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4 Page No : 293" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "Nr = 1440.; #rotor speed in rpm\n", + "f = 50.; #frequency in hertz\n", + "\n", + "# Calculations\n", + "#calculating Ns for values of P = 2,4,6,8 etc\n", + "#by checking P = 4\n", + "P = 4;\n", + "Ns = (120*f)/P; #Synchronous speed\n", + "S = (Ns-Nr)/Ns; #slip\n", + "Fr = S*f; #rotor frequency\n", + "\n", + "# Results\n", + "print \"Rotor frequency = %dHz\"%(Fr)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor frequency = 2Hz\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.5 Page No : 294" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #induction motor frequency in hertz\n", + "fr = 1.5; #rotor frequency in hertz\n", + "\n", + "# Calculations and Results\n", + "S = fr/f; #slip\n", + "P = 8; #pole\n", + "Ns = (120*f)/P;\n", + "print \"synchronous speed = %frpm\"%(Ns)\n", + "Nr = Ns-(S*Ns);\n", + "print \"motor running speed = %frpm\"%(Nr)\n", + "S1 = S*100;\n", + "print \"slip percent = %fpercent\"%(S1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "synchronous speed = 750.000000rpm\n", + "motor running speed = 727.500000rpm\n", + "slip percent = 3.000000percent\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.7 Page No : 297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "# Given Data\n", + "E20 = 100.; #induced emf in volts\n", + "R2 = 0.05; #rotor resistance in ohms\n", + "X20 = 0.1; #rotor reactance in ohms\n", + "\n", + "# Calculations and Results\n", + "E20p = E20/math.sqrt(3);\n", + "print (\"When S = 0.04\")\n", + "S = 0.04;\n", + "I2 = (S*E20p)/math.sqrt(R2**2+(S*X20)**2)\n", + "print \"I2 = %dA\"%(I2);\n", + "phi2 = math.degrees(math.acos(R2/(math.sqrt(R2**2+(S*X20)**2))));\n", + "print \"Phase angle between rotor voltage and rotor current = %f degrees\"%(phi2);\n", + "print (\"When S = 1\")\n", + "S = 1;\n", + "I2 = (S*E20p)/math.sqrt(R2**2+(S*X20)**2)\n", + "print \"I2 = %dA\"%(I2);\n", + "phi2 = math.degrees(math.acos(R2/(math.sqrt(R2**2+(S*X20)**2))));\n", + "print \"Phase angle between rotor voltage and rotor current = %f degrees\"%(phi2);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "When S = 0.04\n", + "I2 = 46A\n", + "Phase angle between rotor voltage and rotor current = 4.573921 degrees\n", + "When S = 1\n", + "I2 = 516A\n", + "Phase angle between rotor voltage and rotor current = 63.434949 degrees\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.8 Page No : 298" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #frequency of induction motor\n", + "P = 4.; #pole\n", + "Ns = (120*f)/P;\n", + "S = 3.; #slip percent\n", + "\n", + "# Calculations\n", + "Nr = Ns-((Ns*S)/100)\n", + "fr = (S*f)/100;\n", + "\n", + "# Results\n", + "print \"synchronous speed = %frpm\"%(Ns)\n", + "print \"speed of running motor = %frpm\"%(Nr)\n", + "print \"rotor frequency = %fHz\"%(fr)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "synchronous speed = 1500.000000rpm\n", + "speed of running motor = 1455.000000rpm\n", + "rotor frequency = 1.500000Hz\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.9 Page No : 299" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "fr = 2.; #frequency of motor induced emf in hertz\n", + "f = 50.; #frequency of induction motor in hertz\n", + "S = (fr/f)*100; #slip percent\n", + "P = 6.; #pole\n", + "# Calculations\n", + "Ns = (120*f)/P;\n", + "Nr = Ns-((Ns*S)/100);\n", + "\n", + "# Results\n", + "print \"percentage slip = %fpercent\"%(S)\n", + "print \"rotor speed = %frpm\"%(Nr)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "percentage slip = 4.000000percent\n", + "rotor speed = 960.000000rpm\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.10 Page No : 299" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "P = 12.; #pole\n", + "f = 50.; #frequency of induction motor in hertz\n", + "Nr = 485.; #induction motor speed in rpm\n", + "\n", + "# Calculations\n", + "Ns = (120*f)/P;\n", + "S = (Ns-Nr)/Nr;\n", + "fr = S*f;\n", + "\n", + "# Results\n", + "print \"frequency of rotor current = %fHz\"%(fr)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frequency of rotor current = 1.546392Hz\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11 Page No : 299" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given Data\n", + "E20 = 100.; #induced emf of induction motor at stanstill in volts\n", + "E20p = E20/math.sqrt(3); #induced emf per phase in volts\n", + "S = 0.40; #slip\n", + "\n", + "# Calculations and Results\n", + "E2 = S*E20p; #rotor induced emf at slip S in volts\n", + "print \"Rotor induced emf at a slip E2 = %fV\"%(E2);\n", + "R2 = 0.4; #resistance per phase in ohms\n", + "X20 = 2.25; #stanstill resistance per phase i ohms\n", + "Z2 = math.sqrt((R2)**2+(S*X20)**2); #rotor impedence at slip S in ohms\n", + "print \"Rotor impedence at a slip S, Z2 = %fohms\"%(Z2)\n", + "I = E2/Z2;\n", + "print \"rotor current = %fA\"%(I)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Rotor induced emf at a slip E2 = 23.094011V\n", + "Rotor impedence at a slip S, Z2 = 0.984886ohms\n", + "rotor current = 23.448415A\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12 Page No : 308" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "S = 0.03; #slip\n", + "SI = 50.; #stator input in kilowatts\n", + "SL = 2.; #stator loss in kilowatts\n", + "\n", + "# Calculations and Results\n", + "RI = SI-SL; #rotor input in kilowatts\n", + "RIL = S*RI; #rotor I**2R loss\n", + "#rotor core loss can be neglected at 3percent slip\n", + "PDR = RI-RIL; #power developed by the rotor\n", + "print \"Power developed by the rotor = %fkW\"%(PDR);\n", + "FWL = 1; #friction and windage loss in kilowatt\n", + "OP = PDR-FWL; #output power\n", + "print \"Output power = %fkW\"%(OP);\n", + "effi = (OP*100)/SI;\n", + "print \"Efficiency of the motor = %f percent\"%(effi)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power developed by the rotor = 46.560000kW\n", + "Output power = 45.560000kW\n", + "Efficiency of the motor = 91.120000 percent\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.13 Page No : 309" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given Data\n", + "f = 50.; #frequency of induction motor in hertz\n", + "hp = 20.; #horse power\n", + "ph = 3.; #Three phase supply\n", + "P = 4.; #number of poles\n", + "\n", + "# Calculations and Results\n", + "losses = 500; #friction and vintage losses\n", + "print \"Output of the motor = %fW\"%(hp*735.5)\n", + "Pd = (hp*735.5)+losses; #power developed in watt\n", + "print \"Power developed by the rotor = %dW\"%(Pd);\n", + "s = 0.04; #slip\n", + "rotorloss = (s*Pd)/(1-s);\n", + "print \"Rotor I**2R-loss = %fW\"%(rotorloss);\n", + "Ns = (120*f)/P;\n", + "print \"Ns = %drpm\"%(Ns);\n", + "Nr = Ns*(1-s);\n", + "print \"Nr = %drpm\"%(Nr);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Output of the motor = 14710.000000W\n", + "Power developed by the rotor = 15210W\n", + "Rotor I**2R-loss = 633.750000W\n", + "Ns = 1500rpm\n", + "Nr = 1440rpm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.14 Page No : 310" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given Data\n", + "f = 50.; #frequency of induction motor in hertz\n", + "P = 6.; #number of poles\n", + "ph = 3.; #Three phase supply\n", + "\n", + "# Calculations and Results\n", + "R2 = 0.1; #rotor resistance in ohms\n", + "Ns = (120*f)/P;\n", + "print \"Syncronous speed, Ns = %drpm\"%(Ns);\n", + "Nr = 940; #rotor speed in rpm\n", + "S = (Ns-Nr)/Ns;\n", + "print \"Slip, S = %f\"%(S);\n", + "print \"stanstill rotor reactance, X20 = %fohms\"%(R2/S);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Syncronous speed, Ns = 1000rpm\n", + "Slip, S = 0.060000\n", + "stanstill rotor reactance, X20 = 1.666667ohms\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15 Page No : 310" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #frequency of induction motor in hertz\n", + "P = 4.; #number of poles\n", + "Nr = 1440.; #rotor speed in rpm\n", + "R2 = 0.1; #rotor resistance in ohms\n", + "X20 = 0.6; #rotor stanstill resistance in ohms\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/P;\n", + "print \"Synchronous speed = %drpm\"%(Ns);\n", + "S1 = (Ns-Nr)*(100/Ns);\n", + "print \"Full-load slip with rotor resistance, R2 i.e. S1 = %f\"%(S1);\n", + "print (\"on adding extra resistance o.1ohm\")\n", + "#on solving we get S2 = 0.08\n", + "S2 = 0.08;\n", + "Nr2 = Ns*(1-S2);\n", + "print \"New rotor speed = %drpm\"%(Nr2);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed = 1500rpm\n", + "Full-load slip with rotor resistance, R2 i.e. S1 = 4.000000\n", + "on adding extra resistance o.1ohm\n", + "New rotor speed = 1380rpm\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.16 Page No : 311" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #frequency in hertz\n", + "P = 4.; #number of poles\n", + "R2 = 0.04; #rotor resistance in ohms\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/P;\n", + "print \"Syncronous speed = %drpm\"%(Ns);\n", + "Nr = 1200; #rotor speed at maximium torque in rpm\n", + "S = (Ns-Nr)/Ns;\n", + "print \"Slip at maximium torque = %f\"%(S);\n", + "X20 = R2/S;\n", + "#starting torque is developed when S = 1\n", + "#r = (Tst/Tm)\n", + "r = (R2/(R2**2+X20**2))*(2*X20);\n", + "print \"Therefore, starting torque is %fpercent of the maximium torque\"%(r*100)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Syncronous speed = 1500rpm\n", + "Slip at maximium torque = 0.200000\n", + "Therefore, starting torque is 38.461538percent of the maximium torque\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.18 Page No : 313" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "P = 4.; #number of poles\n", + "f = 50.; #frequency in hertz\n", + "ph = 3.; #three phase supply\n", + "R2 = 0.25; #rotor resistance in ohms\n", + "Nr = 1440.; #rotor speed in rpm\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/P;\n", + "S1 = (Ns-Nr)/Ns;\n", + "print \"S1 = %f\"%(S1);\n", + "Nr2 = 1200; #rotor speed when external is added\n", + "S2 = (Ns-Nr2)/Ns;\n", + "#torque remains consmath.tant,we get the relation R2' = R2*(S2/S1)\n", + "R2dash = R2*(S2/S1)\n", + "print \"Extra resistance to be connected in the motor circuit = %fohms\"%(R2dash-R2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "S1 = 0.040000\n", + "Extra resistance to be connected in the motor circuit = 1.000000ohms\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.20 Page No : 311" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "hp = 20.; \n", + "P = 4.; #number of poles\n", + "f = 50.;\n", + "S = 0.03; #slip\n", + "\n", + "# Calculations and Results\n", + "MSO = hp*735.5; #motor shaft output\n", + "losses = 0.02*MSO #friction and windage loss in watts\n", + "Pd = MSO+losses; #power developed by the rotor in watts\n", + "RCL = (S*Pd)/(1-S); #rotor I**2*R loss\n", + "print \"rotor copper loss = %fW\"%(RCL);\n", + "Ri = Pd+RCL #rotor iron loss is neglected\n", + "print \"Rotor input = %fW\"%(Ri);\n", + "Ns = (120*f)/P;\n", + "Nr = Ns*(1-S)*(1./60); #rotor speed in rps\n", + "OT = MSO/(2*3.14*Nr); #outp[ut torque in Nm\n", + "print \"output torque = %fNm\"%(OT)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "rotor copper loss = 464.047423W\n", + "Rotor input = 15468.247423W\n", + "output torque = 96.592028Nm\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.21 Page No : 316" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #frequency of induction motor in hertz\n", + "P = 6.; #pole\n", + "Ns = (120.*f)/P;\n", + "Nr = 975.; #induction motor running speed in rpm\n", + "\n", + "# Calculations and Results\n", + "S = (Ns-Nr)/Ns;\n", + "print \"the slip = %f\"%(S)\n", + "Pin = 40.; #power input to stator in kW\n", + "Sl = 1.; #stator losses in kW\n", + "Rin = Pin-Sl; #output from stator in kW\n", + "Rc = S*Rin;\n", + "print \"rotor copper losses = %fkW\"%(Rc)\n", + "l = 2.; #total losses in kW\n", + "p = Rin-Rc-l; #output power in kw\n", + "HP = (p*1000)/735.5;\n", + "print \"output horse output = %fHP\"%(HP)\n", + "in1 = 40.; #input in kW\n", + "effi = (p/in1)*100;\n", + "print \"efficiency = %fpercent\"%(effi)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the slip = 0.025000\n", + "rotor copper losses = 0.975000kW\n", + "output horse output = 48.980286HP\n", + "efficiency = 90.062500percent\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.22 Page No : 316" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "f = 50.; #frequency of induction motor in hertz\n", + "P = 6.; #pole\n", + "\n", + "# Calculations and Results\n", + "Ns = (120.*f)/P;\n", + "print \"synchronous speed = %frpm\"%(Ns)\n", + "fr = 120./60; #rotor frequency\n", + "S = fr/f;\n", + "print \"the slip = %f\"%(S)\n", + "Nr = Ns-(Ns*S);\n", + "print \"rotor speed = %frpm\"%(Nr)\n", + "Rin = 80.; #rotor input in kW\n", + "Rc = S*Rin; #Rotor copper loss in kW\n", + "Ph = 3.; #number of phases\n", + "Rcp = (Rc/Ph)*1000; #loss per phase in watt\n", + "p = ((Rin-Rc)*1000)/735.5;\n", + "print \"mechanical power developed = %fhp\"%(p)\n", + "Ir = 60; #rotor current in amperes\n", + "R2 = Rcp/(Ir)**2;\n", + "print \"rotor resistance per phase at rotor current 60A = %fohms\"%(R2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "synchronous speed = 1000.000000rpm\n", + "the slip = 0.040000\n", + "rotor speed = 960.000000rpm\n", + "mechanical power developed = 104.418763hp\n", + "rotor resistance per phase at rotor current 60A = 0.296296ohms\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.23 Page No : 320" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "# we know (Ts/Tm) = ((2*a)/(1+a**2))\n", + "#where a = (R2/X20)\n", + "#at starting contion math.since Tm = Ts\n", + "print (\"At starting contion math.since Tm = Ts\")\n", + "\n", + "# Calculations and Results\n", + "a = 1 #we obtain from the relations\n", + "R2 = 0.05; #circuit resistance in ohms\n", + "X2 = 0.4; #stanstill reactance in ohms\n", + "r = (a*X2)-R2; #r is the extra that is added to the rotor circuit\n", + "print \"extra resistance added ,r = %fohms\"%(r)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "At starting contion math.since Tm = Ts\n", + "extra resistance added ,r = 0.350000ohms\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.24 Page No : 321" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "V = 400.; #supply voltage in volts\n", + "f = 50.; #frequency in hertz\n", + "P = 6.; #number of poles\n", + "ph = 3.; #three phase supply\n", + "R2 = 0.03; #rotor resistance in ohms\n", + "X20 = 0.4; #rptor reactance in ohms\n", + "Nr = 960.; #full load speed in rpm\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/P;\n", + "print \"synchronous speed = %drpm\"%(Ns)\n", + "S = (Ns-Nr)/Ns; #corresponding slip\n", + "#maximium torque Tm occurs at S = (R2/X20)\n", + "#we get Tm = k/(2*X20)\n", + "a = R2/X20;\n", + "#r = Tm/T\n", + "r = (a**2+S**2)/(2*a*S);\n", + "Sm = (R2/X20);\n", + "print \"Slip at maximium torque, Sm = %f\"%(Sm);\n", + "#corresponding speed\n", + "Nr2 = Ns*(1-Sm);\n", + "print \"Rotor speed at maximium torque = %drpm\"%(Nr2)\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "synchronous speed = 1000rpm\n", + "Slip at maximium torque, Sm = 0.075000\n", + "Rotor speed at maximium torque = 925rpm\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.25 Page No : 321" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Given Data\n", + "V = 400.; #supply voltage in volts\n", + "f = 50.; #frequency in hertz\n", + "P = 4.; #number of poles\n", + "ph = 3.; #three phase supply\n", + "S = 0.04;\n", + "If = 30.; #Full load current in amperes\n", + "\n", + "# Calculations and Results\n", + "Isc = 6*If;\n", + "#let r be the ratio of starting torque nd full load torque, r = Ts/Tf\n", + "r = (Isc/If)**2*S;\n", + "#Tf = Tm is produced when voltage is Vm\n", + "Vm = math.sqrt(V**2/r);\n", + "print \"voltage at maximium torque = %fvolts\"%(Vm);\n", + "Is = 6*If*(Vm/V);\n", + "print \"Full-load current at 333.3 volts is = %fA\"%(Is)\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "voltage at maximium torque = 333.333333volts\n", + "Full-load current at 333.3 volts is = 150.000000A\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.26 Page No : 330" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "V = 400.; #supply voltage in volts\n", + "f = 50.; #frequency in hertz\n", + "Id = 75.; #current taken when delta-connected in amperes\n", + "\n", + "# Calculations and Results\n", + "print \"current taken when delta-connected = %dA\"%(Id);\n", + "Is = Id/3; #current taken when star-connected in amperes\n", + "print \"current taken when star-connected = %dA\"%(Is);\n", + "#Tfl be the full load torque\n", + "#r = Ts/Tfl\n", + "r = 1.5;\n", + "#math.since voltage becomes (1/math.sqrt(3)) when star connected \n", + "#torque is directly proportional to square of voltage\n", + "print \"Starting torque with winding star connected = %f times of Tfl\"%(r/3);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "current taken when delta-connected = 75A\n", + "current taken when star-connected = 25A\n", + "Starting torque with winding star connected = 0.500000 times of Tfl\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.28 Page No : 333" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Given Data\n", + "ph = 3;\n", + "#rotor copper loss = slip*rotor input\n", + "#Tst = starting torque\n", + "#Tfl = torque at full load\n", + "#Ist/Ifl = r\n", + "r = 6;\n", + "\n", + "# Calculations and Results\n", + "S = 0.04\n", + "print \" At slip = 0.04\"\n", + "print \"For direct-on-line starting ( Tst/Tfl) = %f\"%(r**2*S);\n", + "#phase current in start is (1/math.sqrt(3)) times the phase current in delta\n", + "\n", + "print \"For direct-on-line starting( Tst/Tfl) = %f\"%((r/math.sqrt(3))**2*S);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " At slip = 0.04\n", + "For direct-on-line starting ( Tst/Tfl) = 1.440000\n", + "For direct-on-line starting( Tst/Tfl) = 0.480000\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.29 Page No : 334" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "V = 400.; #voltage in volts\n", + "f = 50.; #frequency in hertz\n", + "P = 4.; #number of poles\n", + "#r1 = (Ts/Tfl)\n", + "r1 = 1.6;\n", + "#r2 = (Tm/Tfl)\n", + "r2 = 2.;\n", + "#r3 = (Ts/Tm) = (2*a)/(1+a**2)\n", + "r3 = 0.8;\n", + "#on solving , we get a = 0.04 ,\n", + "a = 0.04;\n", + "\n", + "# Calculations and Results\n", + "Sm = 0.04; #slip at maximium torque\n", + "print \"Slip at maximium torque, Sm = %f\"%(Sm)\n", + "Ns = (120*f)/P; #synchronous speed in rpm\n", + "Nr = Ns*(1-Sm) #rotor speed in rpm\n", + "#r2 = (a**2+Sfl**2)/(2*a*Sfl)\n", + "Sfl = 0.01;\n", + "Nr2 = Ns*(1-Sfl);\n", + "print \"full load speed, Nr = %drpm\"%(Nr2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slip at maximium torque, Sm = 0.040000\n", + "full load speed, Nr = 1485rpm\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.30 Page No : 345" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given Data\n", + "hp = 20.; #power in horsepower\n", + "f = 50.; #frequency in hertz\n", + "P = 4.; #number of poles\n", + "\n", + "# Calculations and Results\n", + "Ns = (120*f)/P; #synchronous speed\n", + "print \"Synchronous speed, Ns = %drpm\"%(Ns);\n", + "S = 0.04; #slip\n", + "Nr = Ns*(1-S);\n", + "OP = hp*735.5;\n", + "print \"Output power = %fW\"%(OP);\n", + "OT = OP/(2*3.14*(Nr/60));\n", + "print \"Output torque = %fNm\"%(OT);\n", + "FL = 0.02*OP; #Friction and windage loss\n", + "PD = OP+FL;\n", + "print \"Power developed by the rotor = %fW\"%(PD);\n", + "#from relation, (rotor I**2R-loss = S*Rotor input) we get following relation \n", + "RL = (S*PD)/(1-S); \n", + "print \"Rotor I**2R-loss = %fW\"%(RL);\n", + "RI = RL/S;\n", + "print \"Rotor input = %dW\"%(RI)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed, Ns = 1500rpm\n", + "Output power = 14710.000000W\n", + "Output torque = 97.598195Nm\n", + "Power developed by the rotor = 15004.200000W\n", + "Rotor I**2R-loss = 625.175000W\n", + "Rotor input = 15629W\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.31 Page No : 347" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "P = 4.; #number of poles\n", + "f = 50.; #frequency in hertz\n", + "V = 230.; #voltage in volts\n", + "hp = 5.; #power in horsepower\n", + "Ib = 15.; #current in block rotor test in amperes\n", + "\n", + "# Calculations and Results\n", + "output = hp*735.5; #output in watts\n", + "#in block rotor test: power input = Full = load I**2R losses = 735W\n", + "FLl = 735; #Full-load I**2R losses\n", + "print \"Full-load I**2R losses = %fW\"%(FLl);\n", + "Re = FLl/(3*Ib**2);\n", + "Io = 6.3; #current in no load condition in amperes\n", + "lossNL = (3*(Io)**2*Re); #I**2R loss at no-load condition\n", + "print \"I**2R loss at no-load = %fW\"%(lossNL);\n", + "PiNL = 275; #power input at no-load\n", + "print \"Core loss plus friction and windage loss = %dW\"%(PiNL-lossNL);\n", + "TL = FLl+(PiNL-lossNL);\n", + "effi = (output*100)/(output+TL);\n", + "print \"Efficiency = %fpercent\"%(effi)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Full-load I**2R losses = 735.000000W\n", + "I**2R loss at no-load = 129.654000W\n", + "Core loss plus friction and windage loss = 145W\n", + "Efficiency = 80.685043percent\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.32 Page No : 347" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Given Data\n", + "Vl = 415.; #voltage in volts\n", + "Il = 50.; #line current in amperes\n", + "R1 = 0.5; #resistrance of stator winding per phase in ohms\n", + "pf = 0.85; #power factor\n", + "S = 0.04;\n", + "\n", + "# Calculations and Results\n", + "IFL = (math.sqrt(3)*Vl*Il*pf) #input to the motor on full load\n", + "print \"Input to the motor on full load = %dW\"%(IFL);\n", + "I1 = Il/math.sqrt(3);\n", + "SLFL = (3*I1**2*R1) #Stator I**2R loss on full load\n", + "print \"Stator I**2R loss on full load = %dW\"%(SLFL);\n", + "#given ratio of stator core loss friction and windahe loss be r = (r1:r2)\n", + "r1 = 3.;\n", + "r2 = 2.;\n", + "TL = 1500.; #total loss\n", + "SCL = (r1*TL)/(r1+r2); #stator core loss\n", + "FWL = (r2*TL)/(r1+r2); #Friction and windage loss\n", + "SL = SLFL+SCL; #total stator loss\n", + "SI = IFL; #Stator input\n", + "Pa = SI-SL; #power transferred through the air-gap = input to the rotor\n", + "RI = Pa\n", + "RL = S*RI; #rotor losses\n", + "TRL = FWL+RL; #total rotor losses \n", + "OP = RI-TRL; #Output power at the shaft\n", + "effi = (OP*100)/SI;\n", + "print \"Efficiency = %f percent\"%(effi)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Input to the motor on full load = 30549W\n", + "Stator I**2R loss on full load = 1250W\n", + "Efficiency = 87.279597 percent\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.33 Page No : 351" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "E20 = 100.; #induced emf between slip terminals in volts\n", + "\n", + "# Calculations and Results\n", + "E20p = E20/math.sqrt(3); #induced emf per phase in volts\n", + "print \"induced emf per phase = %fV\"%(E20p)\n", + "S = 3/100; #slip\n", + "R2 = 0.2; #resistance in ohms\n", + "X20 = 1; #stanstill resistance in ohms\n", + "I2 = (S*E20p)/math.sqrt((R2)**2+(S*X20)**2)\n", + "print \"rotor current at slip 0.03 = %fA per phase\"%(I2)\n", + "Sm = R2/X20;\n", + "I2m = (Sm*E20p)/math.sqrt((R2)**2+(Sm*X20)**2)\n", + "print \"rotor current when the rotor develops maximum torque = %fA per phase\"%(I2m)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "induced emf per phase = 57.735027V\n", + "rotor current at slip 0.03 = 0.000000A per phase\n", + "rotor current when the rotor develops maximum torque = 40.824829A per phase\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.34 Page No : 352" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Given Data\n", + "E20 = 120.; #induced emf of motor at stanstill in volts\n", + "E20p = 120./math.sqrt(3); #induced emf per phase\n", + "f = 50.; #frequency of the motor in hertz\n", + "R2 = 0.2; #Rotor resistance per phase\n", + "X20 = 1.; #stanstill resistance in ohms\n", + "P = 4.; #pole\n", + "I = 16.; #\n", + "\n", + "# Calculations and Results\n", + "S = (I*R2)/math.sqrt((E20)**2-(I*X20)**2);\n", + "Ns = (120*f)/P;\n", + "print \"Synchronous speed = %frpm\"%(Ns)\n", + "Nr = Ns-(Ns*S)\n", + "Sm = R2/X20;\n", + "Nr = Ns-(Ns*Sm)\n", + "I2 = (Sm*E20p)/math.sqrt((R2)**2+(Sm*X20)**2)\n", + "print \"rotor current at maximum torque = %fAper Phase\"%(I2)\n", + "Pi = (3*((I2)**2)*R2)/Sm;\n", + "print \"Rotor input for the three phase = %fW\"%(Pi)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Synchronous speed = 1500.000000rpm\n", + "rotor current at maximum torque = 48.989795Aper Phase\n", + "Rotor input for the three phase = 7200.000000W\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.35 Page No : 356" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Given Data\n", + "R1dc = 0.01; #DC resistance in ohms\n", + "V = 400.; #voltage in volts\n", + "r = 1.5; #ratio of ac to dc resistance\n", + "R1 = r*R1dc; #AC resistance in ohms\n", + "#at no-load\n", + "Io = 20.; #no-load current in amperes\n", + "SL = (3*Io**2*R1); #I**2R loss in the stator phases in watts\n", + "FWL = 300.; #Friction and windage loss in watts\n", + "TL = 1200.; #total losses = no-load power input in watts\n", + "\n", + "# Calculations\n", + "CL = TL-(SL+FWL); #core loss in watt\n", + "CLp = CL/math.sqrt(3); #core loss per phase\n", + "Vp = V/math.sqrt(3); #voltage per phase\n", + "Rm = (Vp**3)/CL; #motor resistance\n", + "pf = CL/(Vp*Io);\n", + "phi0 = math.degrees(math.acos(pf));\n", + "Xm = Vp/(Io*math.sin(math.radians(phi0))); #motor reactance\n", + "#Under blocked rotor test\n", + "Vb = 100; #voltage in volts\n", + "Isc = 45; #current in amperes\n", + "Vbp = 100/math.sqrt(3); #voltage per phase in volts\n", + "P = 2750; #power supplied in watts\n", + "Ze = Vbp/Isc; #Motor impedance reffered to stator side in ohms\n", + "Re = P/(3*Isc**2);\n", + "R2 = Re-R1; #rotor resistance referred to stator side\n", + "Xe = math.sqrt(Ze**2-Re**2);\n", + "#assuming X1 = X2\n", + "X2 = Xe/2\n", + "X1 = X2;\n", + "\n", + "# Results\n", + "print \"Thus the elements of the equivalent circuit are:\";\n", + "print \"Rm = %fohms\"%(Rm);\n", + "print \"Xm = %fohms\"%(Xm);\n", + "print \"R1 = %fohms\"%(R1);\n", + "print \"rotor resistance referred to stator side, R2 = %fohms\"%(R2);\n", + "print \"equivalent resistance referred to stator side, Re = %fohms\"%(Re);\n", + "\n", + "print \"X1 = %fohms\"%(X1);\n", + "print \"rotor reactance referred to stator side, X2 = %fohms\"%(X2);\n", + "print \"equivalent reactance referred to stator side, Xe = %fohms\"%(Xe);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thus the elements of the equivalent circuit are:\n", + "Rm = 13964.632361ohms\n", + "Xm = 11.763476ohms\n", + "R1 = 0.015000ohms\n", + "rotor resistance referred to stator side, R2 = -0.015000ohms\n", + "equivalent resistance referred to stator side, Re = 0.000000ohms\n", + "X1 = 0.641500ohms\n", + "rotor reactance referred to stator side, X2 = 0.641500ohms\n", + "equivalent reactance referred to stator side, Xe = 1.283001ohms\n" + ] + } + ], + "prompt_number": 38 + } + ], + "metadata": {} + } + ] +}
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