{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 6:AC Motor Drives" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.1,Page no:153" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Variable declaration\n", "V=400.0 #[Voltage] volt\n", "P=4.0 #[poles]\n", "f=50.0 #[Frequency] Hz\n", "Pout=10.0 #[Power out] hp\n", "\n", "#Calculation\n", "Pout=Pout*735.5 #[Power out] in W\n", "Snl=1.0/100.0 #No load Slip\n", "Sfl=4.0/100.0 #Full load slip\n", "Ns=120.0*f/P #[Synchronous speed] rpm\n", "N1=Ns*(1.0-Snl) #[Speed at no load] rpm\n", "N2=Ns*(1.0-Sfl) #[Speed at full load] rpm\n", "\n", "f2=Sfl*f #[Frequency at full load] Hz\n", "omega_n=N2*2*math.pi/60.0 #[Angular velocity] rad/s\n", "T=Pout/omega_n #[Full load torque] N-m\n", "\n", "#Result\n", "print\"(a) Synchronous speed \",Ns,\"rpm\"\n", "print\"(b) Speed at no load : \",N1,\"rpm\"\n", "print\"(c) Speed at full load in rpm : \",N2,\"rpm\"\n", "print\"(d) Frequency of rotor current at full load : \",f2,\"Hz\"\n", "print\"(e) Full load Torque : \",round(T,2),\"N-m\\n\\n\"\n", "print\"NOTE:Answer of Part (C) full load speed in the book is wrong.\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Synchronous speed 1500.0 rpm\n", "(b) Speed at no load : 1485.0 rpm\n", "(c) Speed at full load in rpm : 1440.0 rpm\n", "(d) Frequency of rotor current at full load : 2.0 Hz\n", "(e) Full load Torque : 48.77 N-m\n", "\n", "\n", "NOTE:Answer of Part (C) full load speed in the book is wrong.\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.2,Page no:153" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "P=6.0 #poles\n", "f1=50.0 #[Input frequency] Hz\n", "Pg=80.0 #[Power of induction motor] KW\n", "f2=100.0 #[alternation/min]\n", "\n", "#Calculation\n", "f2=f2/60.0 #[Frequency] Hz\n", "Ns=120*f1/P #[Synchronous speed] rpm\n", "Ns=Ns/60.0 #rps\n", "S=f2/f1 #[Slip]\n", "print\"Slip is : \",S\n", "N=Ns*(1.0-S) #[Motor speed] rps\n", "print\"Motor speed : \",round(N*60.0,2),\"rpm\"\n", "Pm=Pg*(1-S) #[Mechanical power developed] KW\n", "print\"Developed mechanical power : \",round(Pm,3),\"kW\"\n", "CuLoss=S*Pg #[Rotor copper loss] KW\n", "CuLoss_per_phase=CuLoss/3.0 #KW\n", "print\"Rotor Copper Loss per phase : \",round(CuLoss_per_phase*1000,1),\"W\"\n", "I2=65 #A\n", "r2=CuLoss_per_phase*1000.0/I2**2 #ohm/phase\n", "print\"Rotor resistance per phase : \",round(r2,2),\"ohm/phase\"\n", "T=Pg*1000.0/2.0/math.pi/Ns #N-m\n", "\n", "#Result\n", "print\"Torque developed : \",round(T,2),\"N-m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Slip is : 0.0333333333333\n", "Motor speed : 966.67 rpm\n", "Developed mechanical power : 77.333 kW\n", "Rotor Copper Loss per phase : 888.9 W\n", "Rotor resistance per phase : 0.21 ohm/phase\n", "Torque developed : 763.94 N-m\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.3,Page no:154" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "N=288.0 #[Full load speed] rpm\n", "f=50.0 #[Supply frequency] Hz\n", "CuLoss=275.0 #[Copper loss] W\n", "Ns=300.0 #[Synchronous speed] rpm(For S=0.03:0.05)\n", "\n", "#Calculation\n", "P=120.0*f/Ns #poles\n", "print\"No. of poles : \",P\n", "S=(Ns-N)/Ns #Slip\n", "print\"Slip : \",S\n", "S=2.0*S #(as rotor reistance doubled, slip is doubled)\n", "print\"Slip for full load if rotor resiatance doubled : \",S\n", "#CuLoss=I2**2*r2\n", "CuLoss=2*CuLoss #KW(rotor resiatance doubled & current constant)\n", "\n", "#Result\n", "print\"New value of rotor copper loss : \",CuLoss,\"W\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "No. of poles : 20.0\n", "Slip : 0.04\n", "Slip for full load if rotor resiatance doubled : 0.08\n", "New value of rotor copper loss : 550.0 W\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.4,Page no:158" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "T_directStartBYTfl=1.5 #[ratio]\n", "\n", "#Calculation\n", "K=math.sqrt(T_directStartBYTfl) #Ratio of full load torque to starting torque direct starting\n", "#Vapplied=1/K*Vline\n", "VappliedBYVline=1/K \n", "LineCurrentBYIfl=1/K**2*4 #V\n", "\n", "#Result\n", "print\"Applied voltage is \",round(VappliedBYVline,3),\"* Line voltage.\"\n", "print\"Line current at starting is \",round(LineCurrentBYIfl,2),\" * full load current.\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Applied voltage is 0.816 * Line voltage.\n", "Line current at starting is 2.67 * full load current.\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.5,Page no:158" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Variable declaration\n", "Ist=300.0 #[Starting current] A\n", "X=50/100.0 #[Percentage tapping] tapping\n", "Imotor=X*Ist #[Motor current] A\n", "\n", "#Calculation\n", "\n", "Iline=X**2*Ist #A\n", "ratio=X**2 #Ratio of starting Torque 50% tapping to full voltage torque\n", "\n", "#Result\n", "print\"(a) Motor current : \",Imotor,\"A\"\n", "print\"(b) Line current : \",Iline,\"A\"\n", "print\"(c) Ratio of starting Torque 50% tapping to full voltage torque : \",ratio\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Motor current : 150.0 A\n", "(b) Line current : 75.0 A\n", "(c) Ratio of starting Torque 50% tapping to full voltage torque : 0.25\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.6,Page no:163" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=400.0 #[Volatge] volt\n", "P=8.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "r1=1.2 #[Resistance] ohm\n", "r2dash=1.2 #[R2] ohm\n", "x1=2.5 #[Resistance parameter 3] ohm\n", "x2dash=2.5 #[Resistance] ohm\n", "N=720.0 #rpm\n", "\n", "#Calculation\n", "Ns=120.0*f/P #rpm\n", "S=(Ns-N)/Ns #full load slip\n", "S2=2.0-S #Slip during plugging\n", "V1=V/math.sqrt(3.0) #V\n", "I2dash1=V1/math.sqrt((r1+r2dash/S2)**2.0+(x1+x2dash)**2.0) #A(Initial braking current)\n", "Ifl=V1/math.sqrt((r1+r2dash/S)**2.0+(x1+x2dash)**2.0) #A(Full load current)\n", "\n", "RatioCurrent=I2dash1/Ifl #ratio of initial braking current to full load current\n", "Tfl=3.0*Ifl**2*r1/(2.0*math.pi*S*Ns/60.0) #N-m\n", "T2dash=3.0*I2dash1**2.0*r2dash/(2.0*math.pi*S2*Ns/60.0) #N-m(initail braking T)\n", "RatioT=T2dash/Tfl #ratio of initial braking Torque to full load Torque\n", "#Let R be the additional resistance\n", "I2dash=2*Ifl #A\n", "#I2dash=V1/math.sqrt((r1+r2dash/S2+R/S2)**2+(x1+x2dash)**2) #A(Initial braking current)\n", "R=(math.sqrt(V1**2.0/I2dash**2.0-(x1+x2dash)**2.0)-r1-r2dash/S2)*S2 #in ohm\n", "Ractual=R/2.0**2.0 #ohm\n", "T_braking=3*I2dash**2*(r2dash+R)/(2.0*math.pi*S2*Ns/60.0) #N-m(initail braking T)\n", "TbBYTfl=T_braking/T2dash #ratio\n", "\n", "#Calculation\n", "print\"(a) Initial Braking current : \",round(I2dash1,2),\"A\"\n", "print\" Full load current is:\",round(Ifl,2),\"A\"\n", "print\" Ratio is \",round(RatioCurrent,3)\n", "print\" Full load troque=\",round(Tfl,2),\"N-m\"\n", "print\" Initial Braking torque: \",round(T2dash,2),\"N-m\"\n", "print\" Ratio of braking \",RatioT,\" times of full load Torque.\\n\"\n", "print\"(b) Actual additional rotor resistance per phase :\",round(Ractual,3),\"ohm\\n\"\n", "print\"(c) Braking torque in N-m : \",round(T_braking,2),\"N-m\"\n", "print\" Ratio of braking torque to full load torque : \",round(TbBYTfl,2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Initial Braking current : 43.42 A\n", " Full load current is: 7.31 A\n", " Ratio is 5.941\n", " Full load troque= 61.21 N-m\n", " Initial Braking torque: 44.1 N-m\n", " Ratio of braking 0.720412943871 times of full load Torque.\n", "\n", "(b) Actual additional rotor resistance per phase : 6.456 ohm\n", "\n", "(c) Braking torque in N-m : 112.52 N-m\n", " Ratio of braking torque to full load torque : 2.55\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.7,Page no:169" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Variable declaration\n", "V=400.0 #[Volatge] volt\n", "P=8.0 #[pole]\n", "f=50.0 #Frequency Hz\n", "r1=0.1 #Resistance ohm\n", "r2dash=0.1 #Resistance ohm\n", "x1=0.4 #Resistance ohm\n", "x2dash=0.4 #Resistance ohm\n", "J=10.0 #Inertia of motor Kg-m**2\n", "\n", "#Calculation\n", "Sm=r2dash/math.sqrt(r1**2+(x1+x2dash)**2)\n", "Ns=2*f/P #rps\n", "omega_ms=2*math.pi*Ns #rad/s\n", "V1=V/math.sqrt(3) #V\n", "Tmax=1.5*V1**2/(2.0*math.pi*Ns)*(1.0/(r1+math.sqrt(r2dash**2+(2*x2dash)**2))) #N-m\n", "tau_m=J*omega_ms/Tmax #sec\n", "ts=tau_m*(1.5*Sm+0.25/Sm) #sec\n", "E=0.5*J*omega_ms**2 #Watt-s\n", "Etot=2*E #Watts-s\n", "tb=tau_m*(0.7/Sm+0.334*Sm) #sec\n", "E=1.4*J*omega_ms**2 #Watt-s\n", "E=2*E/1000 #KW-s(taking cU loss into account)\n", "\n", "#Result\n", "print\"(a) Starting time : \",round(ts,2),\"seconds\"\n", "print\"(b) Energy dissipated during starting : \",round(Etot/1000,2),\"kW-s\"\n", "print\"(c) Pluggingfg time : \",round(tb,2),\"secs\"\n", "print\"(d) Energy dissipated during plugging : \",round(E,2),\"kW-s\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Starting time : 1.54 seconds\n", "(b) Energy dissipated during starting : 61.69 kW-s\n", "(c) Pluggingfg time : 3.97 secs\n", "(d) Energy dissipated during plugging : 172.72 kW-s\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.8,Page no:177" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=400.0 #[Voltage] volt\n", "P=4.0 #[pole]\n", "f=50.0 #Frequency Hz\n", "r1=0.64 #Resistances ohm\n", "r2=0.08 #Resistance ohm\n", "x1=1.1 #Resistance ohm \n", "x2=0.12 #Resistance ohm\n", "T1=40.0 #Load torque N-m\n", "N=1440.0 #Speed rpm\n", "n=2.0*f/P #[Load torque at1300] rps\n", "n=n*60.0 #rpm\n", "N1=1300.0 #[Motor speed] rpm\n", "#Calculation\n", "Tload=T1*(N1/N)**2 #N-m\n", "S=(n-N1)/n #slip\n", "r2dash=r2*2**2 #ohm\n", "x2dash=x2*2**2 #ohm\n", "#Tload=3*I2dash**2*r2dash/(2*math.pi*S*n/60)\n", "I2dash=math.sqrt(Tload/3/r2dash*(2*math.pi*S*n/60)) #A\n", "I2=2*I2dash #A\n", "I1=I2dash #A\n", "V1=I1*(r1+r2dash+r2dash*(1-S)/S+(1j)*(x1+x2dash)) #Vplt\n", "StatorVoltage=abs(V1)*math.sqrt(3) #Volt\n", "\n", "#Result\n", "print\"(a) Load torque : \",round(Tload,1),\"N-m\"\n", "print\"Rotor current:\",round(I2,2),\"A\"\n", "print\"Stator Applied Voltage : \",round(StatorVoltage,1),\"V\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Load torque : 32.6 N-m\n", "Rotor current: 53.34 A\n", "Stator Applied Voltage : 158.3 V\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.9,Page no:177" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=400.0 #[Voltage] volt\n", "P=4.0 #[pole]\n", "f=50.0 #[Frequecy] Hz\n", "r1=0.64 #[Resistance] ohm\n", "r2=0.08 #[Resistance] ohm\n", "x1=1.1 #[Resistance] ohm\n", "x2=0.12 #[Resistance] ohm\n", "T1=40.0 #[Torqu] N-m\n", "N=1440.0 #[Speed] rpm\n", "N1=1300.0 #[Motor speed] rpm\n", "\n", "#Calculation\n", "r2dash=r2*2**2 #ohm\n", "x2dash=x2*2**2 #ohm\n", "S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip\n", "print\"(a) Slip for maximum torque at 50 Hz : \",round(S,4)\n", "V1=V/math.sqrt(3) #volt/phase\n", "ns=2*f/P #rps\n", "Tmax=1.5*V1**2/(2*math.pi*ns)*(1/(r1+math.sqrt(r1**2+(x1+x2dash)**2))) #Nm\n", "print\"Maximum torque at 50 Hz : \",round(Tmax,1),\"N-m\"\n", "n=ns*(1-S) #rps\n", "N=n*60 #rpm\n", "print\"Speed at 50 Hz : \",round(N,2),\"rpm\"\n", "f=25 #Hz\n", "x1=x1/2 #ohm\n", "x2dash=x2dash/2 #ohm\n", "S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip\n", "print\"(b) Slip for maximum torque at 25 Hz : \",round(S,4)\n", "V1=V1/2 #volt/phase\n", "ns=2*f/P #rps\n", "Tmax=1.5*V1**2/(2*math.pi*ns)*(1/(r1+math.sqrt(r1**2+(x1+x2dash)**2))) #Nm\n", "print\"Maximum torque at 25 Hz: \",round(Tmax,2),\"N-m\"\n", "n=ns*(1-S) #rps\n", "N=n*60 #rpm\n", "\n", "\n", "#Result\n", "print\"Speed at 25 Hz : \",round(N,3),\"rpm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Slip for maximum torque at 50 Hz : 0.1877\n", "Maximum torque at 50 Hz : 217.2 N-m\n", "Speed at 50 Hz : 1218.43 rpm\n", "(b) Slip for maximum torque at 25 Hz : 0.3147\n", "Maximum torque at 25 Hz: 153.71 N-m\n", "Speed at 25 Hz : 513.945 rpm\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.10,Page no:178" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Variable declaration\n", "\n", "V=400.0 #[Voltage[ volt\n", "P=4.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "r1=0.64 #[Resistance] ohm\n", "r2=0.08 #[Resistance] ohm\n", "x1=1.1 #[Resistance] ohm\n", "x2=0.12 #[Resistance] ohm\n", "T1=40.0 #[Troque] N-m\n", "N=1440.0 #[Speed] rpm\n", "N1=1300.0 #[Motor speed] rpm\n", "\n", "#Calculation\n", "r2dash=r2*2**2 #ohm\n", "x2dash=x2*2**2 #ohm\n", "S=r2dash/math.sqrt(r1**2+(x1+x2dash)**2) #slip\n", "V1=V/math.sqrt(3) #volt/phase\n", "ns=2*f/P #rps\n", "Tst1=3*V1**2*r2dash/(2*math.pi*ns*((r1+r2dash)**2+(x1+x2dash)**2)) #N-m\n", "f=25 #Hz\n", "x1=x1/2 #ohm\n", "x2dash=x2dash/2 #ohm\n", "V1=V1/2 #volt/phase\n", "ns=2*f/P #rps\n", "Tst2=3*V1**2*r2dash/(2*math.pi*ns*((r1+r2dash)**2+(x1+x2dash)**2)) #N-m\n", "\n", "#Calculation\n", "print\"Starting torque at 50 Hz : \",round(Tst1,2),\"N-m\"\n", "print\"Starting torque at 25 Hz : \",round(Tst2,2),\"N-m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Starting torque at 50 Hz : 95.36 N-m\n", "Starting torque at 25 Hz : 105.44 N-m\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.11,Page no:179" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=400.0 #[Voltage] volt\n", "P=4.0 #[pole ]\n", "f=50.0 #[Frequency] Hz\n", "r2dash=1.0 #[Rotor resistance] ohm/phase\n", "#Neglecting r1,x1,x2\n", "f1=400.0 #[Frequency] Hz\n", "S=4.0/100.0 #[Slip]\n", "t2=1.5 #[Time] ms\n", "\n", "#Calculation\n", "t2=t2*10**-3 #sec\n", "t=1.0/f1 #sec\n", "t1=t-t2 #sec\n", "R=2.0 #ohm(additional resistance)\n", "R2dash=(r2dash*t1+(r2dash+R)*t2)/t #ohm\n", "V1=V/math.sqrt(3) #volt\n", "T=3*V1**2*S/R2dash #N-m\n", "\n", "#Result\n", "print\"Torque : \",round(T,1),\" synch.watts\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque : 2909.1 synch.watts\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.12,Page no:179" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Variable declaration\n", "V1=400.0 #[Volatge] volt\n", "P=4.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "Sm=10.0/100.0 #[slip]\n", "S1=0.04 #[slip]\n", "N2=900.0 #[Speed] rpm\n", "#r2dash=0.01*x2 #ohm/phase\n", "r2dash=0.01 #[Stator resistance]\n", "r1dash=0.1 #[Stator resistance]\n", "\n", "#Calculation\n", "Ns=120.0*f/P #rpm\n", "N1=Ns*(1-S1) #rpm\n", "S2=(Ns-N2)/Ns #slip\n", "T2ByT1=(N2/N1)**2 \n", "#T=3/(2*math.pi*ns)*[V1**2/((rdash/S2)**2+xdash**2)]*(rdash/S2)\n", "#T2/T1=V2**2/V1**2*S1/S2*[(1+625*r1dash**2)/(1+6.25*r1dash**2)]\n", "V2=math.sqrt(T2ByT1*V1**2*S2/S1/((1+625*r1dash**2)/(1+6.25*r1dash**2))) #volt\n", "\n", "#Result\n", "print\"Stator applied voltage: \",round(V2,2),\"V\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Stator applied voltage: 302.65 V\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.13,Page no:180" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "P=4.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "S=4/100.0 #[slip]\n", "T=1000.0 #[Torque] synch.Watts\n", "f1=25.0 #[New I/P frequency] Hz\n", "\n", "#Calculation\n", "Tnew=T*f/f1 #synch.watts\n", "\n", "#Result\n", "print\"Torque : \",Tnew,\"synch.Watts\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque : 2000.0 synch.Watts\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.14,Page no:181" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "P=4.0 #pole\n", "f=50.0 #[Frequency] Hz\n", "r1=0.04 #[Resitance] ohm\n", "r1dash=0.04 #[Rotor Resistance] ohm\n", "r2dash=0.04 #[Rotor resistance] ohm\n", "x1=0.2 #[Reactance] ohm\n", "x2dash=0.2 #[Reactace] ohm\n", "f1=20.0 #[New Frequency] Hz\n", "\n", "#Calculation\n", "k=f1/f #ratio of frequencies\n", "Tmax20BYTmax50=(r1+math.sqrt(r1**2+(x1+x2dash)**2))/(r1/k+math.sqrt((r1/k)**2+(x1+x2dash)**2)) \n", "Tst20BYTst50=((r1+r2dash)**2+(x1+x2dash)**2)/k/((r1/k+r2dash/k)**2+(x1+x2dash)**2) \n", "#at 20 Hz :\n", "x11=x1*f1/f #ohm\n", "x22dash=x2dash*f1/f #ohm\n", "Ir20ByIr50=(f1/f)*(math.sqrt((r1+r2dash/r1dash)**2+(x1+x2dash)**2))/(math.sqrt((r1+r2dash/r1dash)**2+(x11+x22dash)**2)) \n", "\n", "#Result\n", "print\"(a) Ratio of max torque at 20 Hz to max Torque at 50 Hz : \",round(Tmax20BYTmax50,3)\n", "print\"(b) Ratio of starting torque at 20 Hz to starting Torque at 50 Hz : \",Tst20BYTst50\n", "print\"(c) Ratio of rotor current at 20 Hz to rotor current at 50 Hz : \",round(Ir20ByIr50,3)\n", "print\"\\nNOTE:Answer of rotor current ratio is wrong in the book.\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Ratio of max torque at 20 Hz to max Torque at 50 Hz : 0.863\n", "(b) Ratio of starting torque at 20 Hz to starting Torque at 50 Hz : 2.08\n", "(c) Ratio of rotor current at 20 Hz to rotor current at 50 Hz : 0.424\n", "\n", "NOTE:Answer of rotor current ratio is wrong in the book.\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.15,Page no:182" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "P=4.0 #[pole]\n", "f=50.0 #Frequency] Hz\n", "S=0.04 #[slip]\n", "r1=0.04 #[Resistance] ohm\n", "r1dash=0.04 #[Resistance] ohm\n", "r2dash=0.04 #[Resistance] ohm\n", "x1=0.2 #ohm\n", "x2dash=0.2 #ohm\n", "f1=30.0 #[Frequency new ] Hz\n", "\n", "#Calculation\n", "import numpy as np\n", "k=f1/f #ratio of frequencies\n", "S1=k*S #slip\n", "#For 50 Hz\n", "#T=3*V1**2*S*r2dash/(2*math.pi*ns)/[(S*r1+r2dash)**2+S**2*(x1+x2dash)**2] \n", "#For 30 Hz\n", "#T=3*V1**2/(2*math.pi*ns)*S/(0.6*S1)/[(S/0.6+S/0.6/S1)**2+S**2] \n", "#0.16445*S1**2-0.74*S1+0.00445=0\n", "p=[0.16445,-0.074,0.00445] #polynomial for S1\n", "S1=np.roots(p) \n", "S1=S1[1] #as another value is for unstable region\n", "Ns=2*f1/P*60 #rpm\n", "N=Ns-S1*Ns #rpm\n", "\n", "#Result\n", "print\"Motor speed at 30 Hz operation m : \",round(N),\"rpm (approx)\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Motor speed at 30 Hz operation m : 836.0 rpm (approx)\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.16,Page no:183" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "P=6.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "S=0.04 #[slip] \n", "Ton=40.0 #[Torque] N-m\n", "Toff=30.0 #[Torque at off chopper] N-m\n", "t_onBYt_off=1.0 #[ratio] \n", "\n", "#Calculation\n", "Ns=2*f/P*60 #rpm\n", "N=Ns*(1.0-S) #rpm\n", "Tavg1=(Ton+Toff)/2.0 #N-m\n", "Navg=math.sqrt((N**2)*Tavg1/Ton) #rpm\n", "N1=800.0 #rpm\n", "T=Ton*(N1/N)**2 #N-m\n", "Tavg2=32.0 #N-m\n", "#Tavg=32=(Ton*t_on+T*t_off)/(t_on+t_off) #N-m\n", "tonBYtoff=(T-Tavg2)/(Tavg2-Ton) #\n", "\n", "#Result\n", "print\"Part(a) : \"\n", "print\"Average torque : \",Tavg1,\"N-m\"\n", "print\"Average speed : \",round(Navg),\"rpm\"\n", "print\"Part(b) : \"\n", "print\"Ratio ton/toff is : \",round(tonBYtoff,4)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part(a) : \n", "Average torque : 35.0 N-m\n", "Average speed : 898.0 rpm\n", "Part(b) : \n", "Ratio ton/toff is : 0.5278\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.17,Page no:184" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from scipy import integrate\n", "#Variable declaration\n", "Vrms=415.0 #[rms voltage] volt\n", "f=50.0 #[Frequency] Hz\n", "\n", "#Calculation\n", "def f(t):\n", " return(1)\n", "X=integrate.quad(f,0,2*math.pi/3.0) \n", "Vdc=Vrms/math.sqrt(1.0/math.pi*X[0])\n", "\n", "#Result\n", "print\"Value of Vdc : \",round(Vdc,2),\"V\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Value of Vdc : 508.27 V\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.18,Page no:184" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=400.0 #[Volatge] volt\n", "f=50.0 #[Frequency] Hz\n", "P=4.0 #[poles]\n", "N1=1350.0 #[Rotor speed] rpm\n", "N2=900.0 #[Rotor speed] rpm\n", "Rs=1.5 #[Resisatance] ohm\n", "R=4.0 #[Resistance] ohm\n", "X=4.0 #[Stator resistance] ohm\n", "\n", "#Calculation\n", "ns=2*f/P*60.0 #rpm\n", "S=(ns-N1)/ns #slip\n", "T=3.0/2.0/math.pi/(ns/60)*((V/math.sqrt(3))**2*(P/S)/((Rs+P/S)**2+(R+X)**2))\n", "T2=T*(N2/N1)**2 #N-m\n", "Snew=(ns-N2)/ns #slip\n", "V=math.sqrt((T2/3.0*2.0*math.pi*(ns/60.0))*((Rs+P/Snew)**2+(R+X)**2)/(P/Snew))*math.sqrt(3)\n", "\n", "#Calculation\n", "print\"Torque at 900 rpm : \",round(T2,2),\"N-m\"\n", "print\"Voltage at speed of 900 rpm : \",round(V,1),\"V\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque at 900 rpm : 10.14 N-m\n", "Voltage at speed of 900 rpm : 176.8 V\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.19,Page no:195" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "V=415.0 #[Voltage] volt\n", "P=4.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "N=1370.0 #[Speed] rpm\n", "r1=2.0 #[Resistance] ohm\n", "r2dash=3.0 #[Resitance] ohm\n", "x1=3.5 #[Resitance] ohm\n", "x2dash=3.5 #ohm\n", "X0=55.0 #ohm\n", "\n", "#Calculation\n", "Ns=120.0*f/P #rpm\n", "S=(Ns-N)/Ns #slip\n", "Nfl=Ns-N #rpm\n", "Z=(r1+1j*x1)+1j*X0*(r2dash/S+1j*x2dash)/(r2dash/S+1j*(X0+x2dash)) #ohm\n", "Istator=V/math.sqrt(3)/abs(Z) #A\n", "I2dash=Istator*(1j*X0/(r2dash/S+1j*(X0+x2dash))) #A\n", "Tfl=3*abs(I2dash)**2*r2dash/2/math.pi/S/(Ns/60) #N-m\n", "#Torque is equal so stator current will be same.\n", "N=1200 #rpm\n", "Ns=N+Nfl #rpm\n", "f_inv=4*Ns/120 #Hz\n", "\n", "#Result\n", "print\"Part(a) : \"\n", "print\"Slip speed : \",Nfl,\"rpm\"\n", "print\"Stator current: \",round(Istator,2),\"A\"\n", "print\"Motor torque : \",round(Tfl,2),\"N-m\"\n", "print\"Part(b) : \" \n", "print\"Stator current: \",round(Istator,2),\"A\"\n", "print\"Inverter frequency : \",round(f_inv,2),\"Hz\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Part(a) : \n", "Slip speed : 130.0 rpm\n", "Stator current: 7.52 A\n", "Motor torque : 24.45 N-m\n", "Part(b) : \n", "Stator current: 7.52 A\n", "Inverter frequency : 44.33 Hz\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.20,Page no:196" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "Is=6.0 #[Stator current] A\n", "f=40.0 #[Frequency] Hz\n", "SlipSpeed=100.0 #[Slip speed] rpm\n", "V=415.0 #[Volage] volt\n", "P=4.0 #[pole]\n", "r1=2.0 #[Resistance] ohm\n", "r2dash=3.0#[Resistance] ohm\n", "x1=3.5 #[Resistance] ohm\n", "x2dash=3.5 #[Resistance] ohm\n", "X0=55.0 #[Resistance] ohm\n", "N=1370.0 #[Motor speed] rpm\n", "\n", "#Calculation\n", "Ns=120.0*50.0/P #rpm\n", "S=(Ns-N)/Ns #slip\n", "I2dash=Is*X0/abs(r2dash/S+1j*(X0+x2dash)) #A\n", "T=3.0*I2dash**2.0*r2dash/(2.0*math.pi*S*(Ns/60.0)) #N-m\n", "Ns2=120*f/P #rpm\n", "MotorSpeed=Ns2-SlipSpeed #rpm\n", "\n", "#Result\n", "print\"Rotor current :\",round(I2dash,3),\"A\"\n", "print\"Full load torque : \",round(T,2),\"N-m\"\n", "print\"Motor speed : \",MotorSpeed,\"rpm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Rotor current : 4.855 A\n", "Full load torque : 15.58 N-m\n", "Motor speed : 1100.0 rpm\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.20,Page no:205" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "Pout=2500.0 #[Power out] hp\n", "V=2300.0 #[Voltage] volt\n", "P=20.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "Xs=1.77 #[ohm/phase]\n", "\n", "#Calculation\n", "Pout=Pout*735.5/1000.0 #KW\n", "V=V/math.sqrt(3) #Volt/phase\n", "cos_theta=1.0 \n", "I=Pout*10**3.0/3.0/V/cos_theta #A\n", "Ixs=I*Xs #V\n", "E=math.sqrt(V**2+Ixs**2) #V\n", "Pout_max=3*V*E/Xs/1000.0 #KW\n", "Tmax=Pout_max*1000.0 #synch. Watts\n", "ns=2*f/P #rps\n", "Tmax=Pout_max*1000.0/2.0/math.pi/ns #N-m\n", "\n", "#Result\n", "print\"Maximum torque : %.3e\"%Tmax,\"N-m\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum torque : 1.117e+05 N-m\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6.21,Page no:206" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Variable declaration\n", "Pout=2500.0 #[Power out] hp\n", "V1=2300.0 #[Volatge] volt\n", "P=20.0 #[pole]\n", "f=50.0 #[Frequency] Hz\n", "Xs=1.77 #[ohm/phase]\n", "\n", "#Calculation\n", "Pout=Pout*735.5/1000.0 #KW\n", "print Pout\n", "V=V1/math.sqrt(3) #Volt/phase\n", "cos_theta=1 \n", "I=Pout*10**3.0/3.0/V/cos_theta #A\n", "Ixs=I*Xs #V\n", "E=math.sqrt(V**2.0+Ixs**2) #V\n", "dell=math.acos(V/E) #degree\n", "Pout=3*V*E/Xs*math.cos(dell) #W\n", "\n", "#Result\n", "print\"Part(a) Power output : %.3e\"%Pout,\"W\"\n", "T=Pout #synch. Watts\n", "N=300 #rpm\n", "ns=N/60.0 #rps\n", "T=T/2.0/math.pi/ns #N-m\n", "print\" Torque in N-m :%.2e\"%T,\"N-m\"\n", "f1=25 #Hz\n", "N1=2*f1/P*60 #rpm\n", "print\"Part(b) Speed : \",N1,\"rpm\"\n", "T=T*(N1/N)**2 #N-m\n", "print\" Torque : %.3e\"%T,\"N-m\"\n", "Vapplied=V1*f1/f #Volts\n", "print\"Part(b) Applied voltage : \",Vapplied,\"VoltS\"\n", "Pout=T*2*math.pi*N1/60 #W\n", "print\"Part(b) Power output:\",round(Pout/1000,2),\"kW\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1838.75\n", "Part(a) Power output : 2.989e+06 W\n", " Torque in N-m :9.51e+04 N-m\n", "Part(b) Speed : 150.0 rpm\n", " Torque : 2.378e+04 N-m\n", "Part(b) Applied voltage : 1150.0 VoltS\n", "Part(b) Power output: 373.59 kW\n" ] } ], "prompt_number": 24 } ], "metadata": {} } ] }