{ "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": {} } ] }