{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 9: DC and AC Motor Drives" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.1, Page No. 377" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Field current, firing angle and power factor\n", "\n", "import math\n", "# Variable delcaration\n", "V= 230.0 # input supply voltage\n", "f = 50.0 # supply frequency\n", "alfa_f = 0 # firing angle for semi-converter for field\n", "Rf = 200.0 # field resistance\n", "Ra = 0.3 # Armature resistance\n", "T = 50.0 # torque\n", "r = 900.0 # rpm\n", "vc = 0.8 # voltage constant\n", "tc = 0.8 # torque constant\n", "\n", "#Calculations\n", "#(a)\n", "sqrt_2 = math.floor(math.sqrt(2)*1000)/1000\n", "Vm = V*sqrt_2\n", "Vf = (2*Vm/math.pi)*math.cos(alfa_f)\n", "If = Vf/Rf\n", "If = math.floor(If*10**4)/10**4\n", "#(b)\n", "Ia = T/(tc*If)\n", "Ia = math.ceil(Ia*1000)/1000\n", "w = r*2*math.pi/60\n", "w = math.ceil(w*1000)/1000\n", "back_emf =vc*w*If\n", "back_emf = math.floor(back_emf*100)/100\n", "Va = back_emf+Ia*Ra\n", "Va = math.floor(Va*1000)/1000\n", "alfa = math.acos((Va*math.pi/(Vm))-1)\n", "alfa_a = alfa*180/math.pi\n", "alfa_a = math.floor(alfa_a*1000)/1000\n", "#(c)\n", "P = Va*Ia\n", "Ii = Ia*math.sqrt((180-alfa_a)/180)\n", "Ii = math.floor(Ii*100)/100\n", "VA = V*Ii\n", "pf = P/VA\n", "\n", "\n", "#Result\n", "print(\"(a) Field current = %.4f A\\n(b) Alfa_a = %.3f\u00b0\\n(c) Input power factor = %.3f lagging\"%(If,alfa_a,pf))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Field current = 1.0352 A\n", "(b) Alfa_a = 94.076\u00b0\n", "(c) Input power factor = 0.605 lagging\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.2, Page No.378" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Torque developed and motor speed\n", "\n", "import math\n", "# Variable delcaration\n", "V= 230.0 # input supply voltage\n", "f = 50.0 # supply frequency\n", "alfa_f = 0 # firing angle of converter in the field\n", "Rf = 200.0 # field resistance\n", "Ra = 0.25 # Armature resistance\n", "Ia = 50 # Armature current\n", "vc = 1.1 # voltage constant\n", "tc = 1.1 # torque constant\n", "alfa_a = 45 # firing angle of armature ciruit\n", "\n", "#Calculations\n", "alfa_a = alfa_a*math.pi/180\n", "sqrt_2 = math.floor(math.sqrt(2)*1000)/1000\n", "Vm = V*sqrt_2\n", "Vf = 2*Vm*math.cos(alfa_f)/math.pi\n", "Va = 2*Vm*math.cos(alfa_a)/math.pi\n", "If = Vf/Rf\n", "If = math.floor(If*10**4)/10**4\n", "T = tc*Ia*If\n", "bemf = Va- Ia*Ra - 2\n", "w = bemf/(vc*If)\n", "N = w*60/(2*math.pi)\n", "\n", "#Result\n", "print(\"Torque = %.3f N-m\\n\\nMotor Speed = %.1f rpm\"%(T,N))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque = 56.936 N-m\n", "\n", "Motor Speed = 1106.1 rpm\n" ] } ], "prompt_number": 52 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.3, Page No. 378" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# firing angle of the converter in the armature circuit\n", "\n", "import math\n", "V = 400 # input 3-phase supply\n", "alfa_f = 0 # firing angle of field converter\n", "Ra = 0.3 # Armature resistance\n", "Rf = 250 # field resistance\n", "Ia = 50 # Armature current\n", "vc = 1.3 # motor voltage constant\n", "N = 1200 # speed in rpm\n", "\n", "#Calculations\n", "Vf = 3*math.sqrt(3)*V*math.sqrt(2)*math.cos(alfa_f)/(math.sqrt(3)*math.pi)\n", "If = Vf/Rf\n", "w = N*2*math.pi/60\n", "Eb = vc*If*w\n", "Va = Eb+Ia*Ra\n", "alfa_a = math.acos(Va*math.sqrt(3)*math.pi/(3*V*math.sqrt(2)*math.sqrt(3)))\n", "alfa_a = alfa_a*180/math.pi\n", "alfa_a = math.ceil(alfa_a*100)/100\n", "#Result\n", "print(\"Alfa_a = %.2f\u00b0\"%alfa_a)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Alfa_a = 47.07\u00b0\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.4, Page No. 378" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# input power, speed and torque\n", "\n", "import math\n", "# Variable declaration\n", "V = 500 # input supply voltage\n", "Ra = 0.1 # Armature resistance\n", "Ia = 200.0 # Armature current\n", "vc = 1.4 # Volatage constant\n", "tc = 1.4 # Torque constant\n", "If = 2 # Field current\n", "d = 0.5 # chopper duty cycle\n", "\n", "# Calculations\n", "#(a)\n", "Pi = d*V*Ia\n", "#(b)\n", "Va = V*d\n", "Eb = Va - Ia*Ra\n", "w = Eb/(vc*If)\n", "w = math.floor(w*100)/100\n", "N = w*60/(2*math.pi)\n", "#(c)\n", "T = tc*Ia*If\n", "\n", "#Result\n", "print(\"(a) Power input = %.0f kW \\n(b) Speed = %.2f rpm\\n(c) Torque = %.0f N-m\"%(Pi/1000,N,T))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Power input = 50 kW \n", "(b) Speed = 784.38 rpm\n", "(c) Torque = 560 N-m\n" ] } ], "prompt_number": 71 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.5, Page No. 379" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Braking DC motor using one quadrant chopper\n", "\n", "import math\n", "#Variable declaration\n", "Ra = 0.1 # Armature resistance\n", "Rb = 7.5 # Breaking resistance\n", "vc = 1.4 # voltage constant\n", "Ia = 120 # armature current\n", "If = 1.6 # field current\n", "d = 0.35 # chopper duty cycle\n", "\n", "#calculations\n", "#(a)\n", "Vavg = Rb*Ia*(1-d)\n", "#(b)\n", "Pb = (Ia**2)*Rb*((1-d)**2)\n", "#(c)\n", "Eb = Vavg+Ra*Ia\n", "w = Eb/(vc*If)\n", "w = math.ceil(w*100)/100\n", "N = w*60/(2*math.pi)\n", "\n", "#Result\n", "print(\"(a) Average voltage across chopper = %.0f V\\n(b) Pb = %.0f W\\n(c) Speed = %.4f rpm \"%(Vavg,Pb,N))\n", "#Answer for Pb and Speed is wrong in the book" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Average voltage across chopper = 585 V\n", "(b) Pb = 45630 W\n", "(c) Speed = 2545.0785 rpm \n" ] } ], "prompt_number": 87 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.6, Page No. 379" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Speed -Torque characteristics\n", "\n", "import math\n", "from pylab import *\n", "#variable declaration\n", "V = 220.0 # per phase input voltage\n", "f = 50 # frequency\n", "L = 0.012 # motor inductance\n", "R = 0.72 # Resistance\n", "a = 2 # Armature constant\n", "alfa = 90 # firing angle\n", "\n", "#Calculations\n", "sqrt_2=math.floor(math.sqrt(2)*1000)/1000\n", "sqrt_3=math.floor(math.sqrt(3)*1000)/1000\n", "Va = 3*sqrt_3*V*sqrt_2*(1+math.cos(alfa*math.pi/180))/(2*math.pi)\n", "Va = math.floor(Va*100)/100\n", "Ia1 = 5 # Armature current for case 1\n", "T1 = Ia1*a\n", "Eb1 =Va-Ia1*R\n", "Speed1 = Eb1*60/(a*2*math.pi) \n", "Speed1 = math.floor(Speed1*100)/100\n", "\n", "Ia2 = 10 # Armature current for case 2\n", "T2 = Ia2*a\n", "Eb2 =Va-Ia2*R\n", "Speed2 = Eb2*60/(a*2*math.pi) \n", "Speed2 = math.floor(Speed2*100)/100\n", "\n", "Ia3 = 20 # Armature current for case 3\n", "T3 = Ia3*a\n", "Eb3 =Va-Ia3*R\n", "Speed3 = Eb3*60/(a*2*math.pi) \n", "Speed3 = math.floor(Speed3*100)/100\n", "\n", "Ia4 = 30 # Armature current for case 4\n", "T4 = Ia4*a\n", "Eb4 =Va-Ia4*R\n", "Speed4 = Eb4*60/(a*2*math.pi) \n", "Speed4 = math.floor(Speed4*100)/100\n", "\n", "#Result\n", "print(\"Armature Voltage =%f V\"%Va)\n", "print(\"For Ia =0%d A, Torque = %d N-m and Speed = %.2f rpm\"%(Ia1,T1,Speed1))\n", "print(\"For Ia =%d A, Torque = %d N-m and Speed = %.2f rpm\"%(Ia2,T2,Speed2))\n", "print(\"For Ia =%d A, Torque = %d N-m and Speed = %.2f rpm\"%(Ia3,T3,Speed3))\n", "print(\"For Ia =%d A, Torque = %d N-m and Speed = %.2f rpm\"%(Ia4,T4,Speed4))\n", "#################-----PLOT-----#####################\n", "%pylab inline\n", "import matplotlib.pyplot as plt\n", "t = [T1, T2, T3, T4]\n", "S = [Speed1, Speed2, Speed3, Speed4 ]\n", "plt.plot(t,S)\n", "plt.plot(t,S,'ro')\n", "plt.axis([0,70,0,1500])\n", "plt.xlabel('Torque(N-m)')\n", "plt.ylabel('Speed(RPM)')\n", "plt.title('Speed torque characteristics')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Armature Voltage =257.250000 V\n", "For Ia =05 A, Torque = 10 N-m and Speed = 1211.08 rpm\n", "For Ia =10 A, Torque = 20 N-m and Speed = 1193.90 rpm\n", "For Ia =20 A, Torque = 40 N-m and Speed = 1159.52 rpm\n", "For Ia =30 A, Torque = 60 N-m and Speed = 1125.14 rpm\n", "Populating the interactive namespace from numpy and matplotlib" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "WARNING: pylab import has clobbered these variables: ['f', 'info', 'linalg', 'draw_if_interactive', 'random', 'fft', 'power']\n", "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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mzZoWrW+0y1Oenp4oKChAZmYmMjMzodFokJycDJVKhaCgIGzduhWVlZXIzMxEeno6/Pz8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\nJBtDg4iIZGNoEBGRbP8P+4nVQNPl4qUAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 121 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.7, Page No. 380" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Firing angle and no load speed\n", "\n", "import math\n", "#Variable declaration\n", "V = 400 # input 3-phase voltage\n", "f = 50 # frequency\n", "Ia = 50 # motor armature current\n", "Ra = 0.1 # armature resistance\n", "bec = 0.3 # back emf constant\n", "alfa = 30.0 # firing angle\n", "Inl = 5 # no load current\n", "n = 1600 # speed in rpm \n", "\n", "#Calculations\n", "#(a)\n", "sqrt_2=math.floor(math.sqrt(2)*1000)/1000\n", "sqrt_3=math.floor(math.sqrt(3)*100)/100\n", "Va = 3*sqrt_3*V*sqrt_2*(1+math.cos(alfa*math.pi/180))/(sqrt_3*2*math.pi)\n", "Bemf = Va-Inl*Ra\n", "Speed = Bemf/bec\n", "#(b)\n", "Bemf2 = n*bec\n", "Vi = Bemf2+(Ra*Ia)\n", "alfa2= math.acos((Vi/(3*sqrt_3*V*sqrt_2/(sqrt_3*2*math.pi)))-1)\n", "alfa2 = alfa2*180/math.pi\n", "\n", "#Result\n", "print(\"(a)\\nAverage output voltage of rectifier = %.1f V\\nBack emf = %.1f V\\nSpeed = %d rpm\"%(math.floor(Va*10)/10,Bemf,Speed))\n", "print(\"\\n(b)\\nBack emf = %.0f V\\nInput voltage to motor = %.0f V\\nfiring angle = %.2f\u00b0\"%(Bemf2,Vi,alfa2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)\n", "Average output voltage of rectifier = 503.9 V\n", "Back emf = 503.4 V\n", "Speed = 1678 rpm\n", "\n", "(b)\n", "Back emf = 480 V\n", "Input voltage to motor = 485 V\n", "firing angle = 37.26\u00b0\n" ] } ], "prompt_number": 147 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.8, Page No. 381" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#firing angle of converter and power fed back to source(refering ex.9.2)\n", "\n", "import math\n", "#Variable declaration\n", "V= 230.0 # input supply voltage\n", "f = 50.0 # supply frequency\n", "alfa_f = 0 # firing angle of converter in the field\n", "Rf = 200.0 # field resistance\n", "Ra = 0.25 # Armature resistance\n", "Ia = 50 # Armature current\n", "vc = 1.1 # voltage constant\n", "tc = 1.1 # torque constant\n", "alfa_a = 45 # firing angle of armature ciruit\n", "\n", "#Calculations\n", "alfa_a = alfa_a*math.pi/180\n", "sqrt_2 = math.floor(math.sqrt(2)*1000)/1000\n", "Vm = V*sqrt_2\n", "Vf = 2*Vm*math.cos(alfa_f)/math.pi\n", "Va1 = 2*Vm*math.cos(alfa_a)/math.pi\n", "bemf = Va1- Ia*Ra - 2\n", "Eg = -bemf\n", "Va = Eg + Ia*Ra +2\n", "alfa = math.acos(Va*math.pi/(2*sqrt_2*V))\n", "alfa = alfa*180/math.pi\n", "P = -Va*Ia\n", "\n", "#Result\n", "print(\"When field current is reversed, the direction of back emf is reversed. The motor now acts as generator.\\n\\nEg = %f\"%Eg)\n", "print(\"\\nAlfa = %.2f\u00b0\\n\\nPower fed back to source = %d W\"%(alfa,P))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "When field current is reversed, the direction of back emf is reversed. The motor now acts as generator.\n", "\n", "Eg = -131.900436\n", "\n", "Alfa = 124.54\u00b0\n", "\n", "Power fed back to source = 5870 W\n" ] } ], "prompt_number": 152 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.9, Page No.381" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Half controlled single phase bridge converter\n", "\n", "import math\n", "#variable declaration\n", "V = 240 # input DC voltage\n", "alfa = 100 # firing angle \n", "Ra = 6 # armature Resistance\n", "Ia = 1.8 # armature current\n", "\n", "#Calculations\n", "alfa = alfa*math.pi/180\n", "sqrt_2=math.floor(math.sqrt(2)*1000)/1000\n", "Vdc = sqrt_2*V*(1+math.cos(alfa))/math.pi\n", "Vdc = math.floor(Vdc*100)/100\n", "Bemf = Vdc-Ra*Ia\n", "\n", "#Result\n", "print(\"Back emf = %.2f V\"%Bemf)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Back emf = 78.46 V\n" ] } ], "prompt_number": 96 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.10, Page No.381" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Speed and Torue\n", "\n", "import math\n", "#Variable declaration\n", "V = 230.0 # input voltage\n", "N = 1500.0 # rpm \n", "Ra = 1.0 # armature resistance\n", "Ia = 10 # Armature current\n", "T1 = 5 # Torque for case-1\n", "alfa1 = 30 # Firing angle for case-1\n", "N2 = 950.0 # rpm in case-2\n", "alfa2 = 45 # Firing angle for case-2\n", "\n", "#Calculations\n", "w = N*2*math.pi/60\n", "k = (V-Ia*Ra)/w\n", "k = math.floor(k*10)/10\n", "#(a)\n", "Ia1 = T1/k\n", "V1 = 2*V*math.sqrt(2)*math.cos(alfa1*math.pi/180)/math.pi\n", "V1 = math.floor(V1*10)/10\n", "w1 = (V1-Ia1*Ra)/k\n", "w1 = w1*60/(2*math.pi)\n", "#(b)\n", "V2 = 2*V*math.sqrt(2)*math.cos(alfa2*math.pi/180)/math.pi\n", "V2 = math.ceil(V2*100)/100\n", "Ia2 = V2-(k*N2*2*math.pi/60)\n", "#Ia2 = math.floor(Ia2*100)/100\n", "T2 = k*Ia2\n", "\n", "#Result\n", "print(\"k - Torque constant = %.1f N-m/A\"%k)\n", "print(\"\\n(a) Speed = %.1f rpm\\n\\n(b) Torque = %f N-m\"%(w1,T2))\n", "#Answer for torque is wrong in the book" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "k - Torque constant = 1.4 N-m/A\n", "\n", "(a) Speed = 1198.6 rpm\n", "\n", "(b) Torque = 10.013816 N-m\n" ] } ], "prompt_number": 177 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.11, Page No.382" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# rms source, rms and average thyristor current and power factor\n", "\n", "import math\n", "#Variable declaration\n", "V = 500.0 # Morot max. voltage rating\n", "N = 1500.0 # motor max. speed in rpm\n", "Ia = 100.0 # Motor max. current\n", "Vi = 350.0 # 3-phase input supply voltage\n", "Ra = 1.1 # armature resistance\n", "alfa = 45 # firing angle\n", "N1 = 1200.0 # actual speed \n", "\n", "#Calculations\n", "w = N*2*math.pi/60\n", "w1 = N1*2*math.pi/60\n", "k = (V-Ia*Ra)/w\n", "k = math.floor(k*10**4)/10**4\n", "sqrt_2=math.floor(math.sqrt(2)*1000)/1000\n", "sqrt_3=math.floor(math.sqrt(3)*100)/100\n", "Va = 3*sqrt_3*Vi*sqrt_2*(1+math.cos(alfa*math.pi/180))/(sqrt_3*2*3.142)#--math.pi = 3.142 to match the ans\n", "Va = math.ceil(Va*100)/100\n", "Ia = (Va -k*w1)/Ra\n", "Ia = math.ceil(Ia*100)/100\n", "Irms_i = Ia*math.sqrt(120.0/180.0)\n", "Iavg = Ia/3\n", "Irms = Ia/math.sqrt(3)\n", "pf = (Ia*Va)/(sqrt_3*Vi*Irms_i)\n", "\n", "#Result\n", "print(\"Torque constant, k = %.2f V-s/rad\\n\\n(a)\\nConverter output voltage = %.2f V\\nIa = %.2f A \"%(k,Va,Ia))\n", "print(\"\\n(b)\\nRMS input current = %.2f A\\nAverage thyristor current = %.2f A\\nRMS thyristor current = %.2f A\"%(Irms_i,Iavg,Irms))\n", "print(\"Input power factor = %.3f lagging\"%(math.floor(pf*1000)/1000))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Torque constant, k = 2.48 V-s/rad\n", "\n", "(a)\n", "Converter output voltage = 403.34 V\n", "Ia = 83.04 A \n", "\n", "(b)\n", "RMS input current = 67.80 A\n", "Average thyristor current = 27.68 A\n", "RMS thyristor current = 47.94 A\n", "Input power factor = 0.815 lagging\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.12, Page No.383" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# time taken by motor to reach 1000rpm speed\n", "\n", "import math\n", "#Variable declaration\n", "T = 40 # Load torque\n", "N = 500.0 # motor speed \n", "i = 0.01 # inertia of the drive\n", "T1 = 100.0 # increased value of torque\n", "N1 = 1000.0 # speed value\n", "\n", "#Calculations\n", "w = N*2*math.pi/60\n", "w1 = N1*2*math.pi/60\n", "A = -w/((T1-T)/i)\n", "t = (w1/((T1-T)/i))+A\n", "t = math.floor(t*10**6)/10**6\n", "\n", "#Result\n", "print(\"Time taken by motor to reach 1000 rpm speed = %f seconds\"%t)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Time taken by motor to reach 1000 rpm speed = 0.008726 seconds\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.13, Page No.384" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# motor parameters:motor driven by DC chopper\n", "\n", "import math\n", "#Variavble declaration\n", "f = 400.0 # chopper operating frequency\n", "V = 200.0 # input voltage\n", "T = 30.0 # load torque\n", "N = 1000.0 # speed in rpm\n", "Ra = 0.2 # motor resistance\n", "L = 2*10**-3 # motor inductance\n", "emf = 1.5 # emf\n", "k = 1.5 # torque constant\n", "\n", "#calculations\n", "\n", "w = N*math.pi*2/60\n", "Ia = T/k\n", "Be = emf*w\n", "Be = math.ceil(Be*100)/100\n", "alfa = (Be+Ia*Ra)/V\n", "\n", "t = 1/f\n", "Ton = alfa*t\n", "Toff = t-Ton\n", "x = t*Ra/L\n", "b1 = (1-(math.e**(-alfa*x)))\n", "b1 = math.ceil(b1*10**4)/10**4\n", "b2 = (1-(math.e**(-x)))\n", "b2 = math.ceil(b2*10**4)/10**4\n", "Imax = ((V/Ra)*(b1/b2))-(Be/Ra)\n", "Imin= ((V/Ra)*(((math.e**(alfa*x))-1)/(((math.e**(x))-1))))-(Be/Ra)\n", "x1 = (V-Be)/Ra\n", "x2 = Ra/L\n", "\n", "#Result\n", "print(\"(a)\\nImax = %.3f A\\nImin = %d A\\n\\n(b) Excursion of armature current = %.3f A\"%(Imax,Imin,Imax))\n", "print(\"\\n(c)\\nVariation of cuurent during on period of chopper is \\ni = %.1f*(1-e^(-%d*t'))\"%(x1,x2))\n", "print(\"\\nVariation of cuurent during off period of chopper is \\ni = %.3f*e^(-%d*t')-%.1f*(1-e^(-%d*t'))\"%(Imax,x2,Be/Ra,x2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)\n", "Imax = 39.193 A\n", "Imin = 0 A\n", "\n", "(b) Excursion of armature current = 39.193 A\n", "\n", "(c)\n", "Variation of cuurent during on period of chopper is \n", "i = 214.6*(1-e^(-100*t'))\n", "\n", "Variation of cuurent during off period of chopper is \n", "i = 39.193*e^(-100*t')-785.4*(1-e^(-100*t'))\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.14, Page No.391" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Average motor current and speed\n", "\n", "import math\n", "# Variable declaration\n", "f = 50.0 # input frequency\n", "V = 230 # input voltage\n", "Ra = 1.5 # armature resistance\n", "Rf = 1.5 # field resistance\n", "K = 0.25 # torque constant\n", "TL = 25 # load torque\n", "emf = 0.25 # emf constant\n", "\n", "#Calculations\n", "Vo = 2*math.sqrt(2)*V/math.pi\n", "Vo = math.floor(Vo)\n", "Ia = math.sqrt(T/K)\n", "Ia = math.floor(Ia)\n", "w = (Vo-Ia*Ra)/(emf*Ia)\n", "N =w*60/(2*math.pi)\n", "N = math.floor(N*100)/100\n", "\n", "#Result\n", "print(\"Ia = %d A\\nN = %.2f RPM\"%(Ia,N))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ia = 10 A\n", "N = 733.38 RPM\n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.15, Page No.391" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Armature current and firing angle of semi-converter\n", "\n", "import math\n", "#Variable declaration\n", "Vo = 675.0 # transformer secondary voltage\n", "alfa1 = 90.5 # case 1 firing angle\n", "N1 = 350.0 # case 1 motor speed in rpm\n", "Ia1 = 30.0 # case 1 armature current\n", "N2 = 500.0 # expected speed\n", "Ra = 0.22 # armature resistance\n", "Rf = 0.22 # field resistance\n", "\n", "#Calculations\n", "Ia2 = Ia1*N2/N1\n", "Ia2 = math.ceil(Ia2*100)/100\n", "Va1 = Vo*math.sqrt(2)*(1+math.cos(alfa1*math.pi/180))/math.pi\n", "Eb1 = Va1-(Ia1*(Ra+Rf))\n", "Va2 = (Eb1/((Ia1*N1)/(Ia2*N2)))+Ia2*(Ra+Rf)\n", "alfa2 = math.acos(((Va2*math.pi)/(math.sqrt(2)*Vo))-1)\n", "alfa2 = alfa2*180/math.pi\n", "\n", "#Result\n", "print(\"Armature current = %.2f A\\n\\nFiring Angle = %.2f\u00b0\"%(Ia2,alfa2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Armature current = 42.86 A\n", "\n", "Firing Angle = 4.77\u00b0\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.16, Page No. 392" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Torque and armature current\n", "\n", "import math\n", "# Variable declaration\n", "P = 15.0 # motor power rating\n", "V = 220.0 # motor voltage rating\n", "N = 1500.0 # motor max. speed\n", "Vi = 230.0 # input voltage\n", "emf = 0.03 # emf constant\n", "K = 0.03 # Torque constant\n", "alfa =45 # firing angle\n", "\n", "#Calculations\n", "#(a)\n", "sqrt_2 = math.floor(math.sqrt(2)*1000)/1000\n", "alfa = alfa*math.pi/180\n", "Vm = Vi*sqrt_2\n", "N = N*2*math.pi/60\n", "T = (4*emf*(Vm**2)*(math.cos(alfa)**2))/(((math.pi)**2)*(K*N)**2)\n", "Ia = math.sqrt(T/K)\n", "Ia = math.floor(Ia*100)/100\n", "#(b)\n", "Ia2 = Vm*(1+math.cos(alfa))/(math.pi*K*N)\n", "Ia2 = math.floor(Ia2*10)/10\n", "T2 = K*Ia2**2\n", "\n", "#Result\n", "print(\"(a)\\n Torque = %.2f N-m\\n Armature current = %.2f A\"%(T,Ia))\n", "print(\"\\n(b)\\n Armature current = %.1f A\\n Torque = %.4f N-m\"%(Ia2,T2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)\n", " Torque = 28.96 N-m\n", " Armature current = 31.06 A\n", "\n", "(b)\n", " Armature current = 37.5 A\n", " Torque = 42.1875 N-m\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.17, Page No.392" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# motor current and Torque \n", "\n", "import math\n", "# variable declaration\n", "Pr = 15.0 # motor power rating\n", "Vr = 220.0 # motor voltage rating\n", "N = 1000.0 # motor max. speed\n", "R = 0.2 # total armature and series resistance\n", "Vi = 230.0 # input voltage\n", "Ks = 0.03 # speed constant\n", "K = 0.03 # Torque constant\n", "alfa = 30 # Firing angle\n", "\n", "#Calculation\n", "sqrt_2 = math.floor(math.sqrt(2)*1000)/1000\n", "alfa = alfa*math.pi/180\n", "Vm = Vi*sqrt_2\n", "N = N*2*math.pi/60\n", "N = math.ceil(N*100)/100\n", "V = Vm*(1+math.cos(alfa))/math.pi\n", "V = math.floor(V*100)/100\n", "Ia = V/((Ks*N)+R)\n", "Ia = math.floor(Ia*1000)/1000\n", "T = K*(Ia*Ia)\n", "\n", "# Result\n", "print(\"Armature current = %.3f A\\n\\nTorque = %.2f N-m\"%(Ia,T))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Armature current = 57.807 A\n", "\n", "Torque = 100.25 N-m\n" ] } ], "prompt_number": 69 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.18, Page No. 400" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# load torque, rotor current and stator voltage\n", "\n", "import math\n", "# Variable declaration\n", "V = 400.0 # motor voltage rating\n", "p = 4.0 # no of poles\n", "f = 50.0 # frequency\n", "r1 = 0.64 # Stator resistance \n", "x1 = 1.1 # leakage resistance\n", "r2 = 0.08 # rotor resistance\n", "x2 = 0.12 # leakage resistance\n", "T = 40.0 # Torque at given speed\n", "N1 = 1440.0 # Speed value for given torque\n", "N2 = 1300.0 # Speed value for which torque is asked to calculate\n", "\n", "#Calculations\n", "#(a)\n", "ns = 60*2*f/p\n", "Tl = T*(N2/N1)**2\n", "Tl = math.floor(Tl*10)/10\n", "#(b)\n", "s = (ns -N2)/ns\n", "r2_dash = r2*(2)**2\n", "x2_dash = x2*(2)**2\n", "pi = math.floor(math.pi*100)/100\n", "I2_dash = math.sqrt((Tl*2*pi*s*(ns/60))/(3*r2_dash)) \n", "I2 = 2*I2_dash\n", "#(c)\n", "I1 = I2_dash\n", "V1 = I1*math.sqrt(((r1+r2_dash+r2_dash*((1-s)/s))**2)+(x1+x2_dash)**2)\n", "StV = V1*math.sqrt(3)\n", "\n", "#Result\n", "print(\"(a) At %d rpm , Load torque = %.1f N-m\\n(b) Rotor current = %.2f A\\n(c) Stator voltage = %.1f V\"%(N2,Tl,I2,StV))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) At 1300 rpm , Load torque = 32.6 N-m\n", "(b) Rotor current = 53.32 A\n", "(c) Stator voltage = 158.2 V\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 2.19, Page No. 400" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# slip for max torque, speed and corresponding max torque\n", "\n", "import math\n", "#Variable declaration\n", "V = 400.0 # motor voltage rating\n", "p = 4.0 # no of poles\n", "f = 50.0 # frequency\n", "r1 = 0.64 # Stator resistance \n", "x1 = 1.1 # leakage resistance\n", "r2 = 0.08 # rotor resistance\n", "x2 = 0.12 # leakage resistance\n", "T = 40.0 # Torque at given speed\n", "N1 = 1440.0 # Speed value for given torque\n", "N2 = 1300.0 # Speed value for which torque is asked to calculate\n", "f1 = 50 # case 1 frequency\n", "f2 = 25 # case 2 frequency\n", "\n", "#Calculation\n", "#(a)\n", "ns = 2*f1/p\n", "r2_dash = r2*(2)**2\n", "x2_dash = x2*(2)**2\n", "s = r2_dash/math.sqrt(r1**2+(x1+x2_dash)**2)\n", "s = math.floor(s*10000)/10000\n", "V1 = V/math.sqrt(3)\n", "V1 = math.ceil(V1*100)/100\n", "Tmax = (1.5*V1**2/(2*math.pi*ns))*(1/(r1+math.sqrt(r1**2+(x1+x2_dash)**2)))\n", "Tmax = math.floor(Tmax*10)/10\n", "n = ns*(1-s)\n", "N = n*60\n", "#(b)\n", "x1_b = x1/2\n", "x2_dash_b = x2_dash/2\n", "s2 = r2_dash/math.sqrt(r1**2+(x1_b+x2_dash_b)**2)\n", "s2 = math.floor(s2*10000)/10000\n", "ns2 = 2*f2/p\n", "V1_b = V1*0.5\n", "Tmax2 = (1.5*V1_b**2/(2*math.pi*ns2))*(1/(r1+math.sqrt(r1**2+(x1_b+x2_dash_b)**2)))\n", "n2 = ns2*(1-s2)\n", "N2 = n2*60\n", "\n", "#Result\n", "print(\"(a) for f = %d Hz\\n\\nslip = %.4f\\n\\nTmax = %.1f N-m\\n\\nSpeed corresponds to max torque = %.2f rpm\"%(f1,s,Tmax,N))\n", "print(\"\\n\\n(b) for f = %d Hz\\n\\nslip = %.4f\\n\\nTmax = %.2f N-m\\n\\nSpeed corresponds to max torque = %.3f rpm\"%(f2,s2,Tmax2,N2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) for f = 50 Hz\n", "\n", "slip = 0.1877\n", "\n", "Tmax = 217.2 N-m\n", "\n", "Speed corresponds to max torque = 1218.45 rpm\n", "\n", "\n", "(b) for f = 25 Hz\n", "\n", "slip = 0.3147\n", "\n", "Tmax = 153.72 N-m\n", "\n", "Speed corresponds to max torque = 513.975 rpm\n" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "example 9.20, Page No. 401" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Starting torque\n", "\n", "import math\n", "# Variable declaration\n", "V = 400.0 # motor voltage rating\n", "p = 4.0 # no of poles\n", "f = 50.0 # frequency\n", "r1 = 0.64 # Stator resistance \n", "x1 = 1.1 # leakage resistance\n", "r2 = 0.08 # rotor resistance\n", "x2 = 0.12 # leakage resistance\n", "T = 40.0 # Torque at given speed\n", "N1 = 1440.0 # Speed value for given torque\n", "N2 = 1300.0 # Speed value for which torque is asked to calculate\n", "f1 = 50 # case 1 frequency\n", "f2 = 25 # case 2 frequency\n", "\n", "#Calculation\n", "#(a)\n", "ns = 2*f1/p\n", "r2_dash = r2*(2)**2\n", "x2_dash = x2*(2)**2\n", "#s = r2_dash/math.sqrt(r1**2+(x1+x2_dash)**2)\n", "#s = math.floor(s*10000)/10000\n", "V1 = V/math.sqrt(3)\n", "V1 = math.ceil(V1*100)/100\n", "Tstarting = (3*(V1**2)*(r2_dash))/(2*math.pi*ns*((r1+r2_dash)**2+(x1+x2_dash)**2))\n", "#(b)\n", "x1_b = x1/2\n", "x2_dash_b = x2_dash/2\n", "#s2 = math.floor(s2*10000)/10000\n", "ns2 = 2*f2/p\n", "V1_b = V1*0.5\n", "Tstarting_b = (3*(V1_b**2)*(r2_dash))/(2*math.pi*ns2*((r1+r2_dash)**2+(x1_b+x2_dash_b)**2))\n", "\n", "#Result\n", "print(\"(a) for %d Hz,\\nT_starting = %.2f N-m\"%(f1,Tstarting))\n", "print(\"\\n(b) for %d Hz,\\nT_starting = %.2f N-m\"%(f2,Tstarting_b))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) for 50 Hz,\n", "T_starting = 95.37 N-m\n", "\n", "(b) for 25 Hz,\n", "T_starting = 105.45 N-m\n" ] } ], "prompt_number": 57 } ], "metadata": {} } ] }