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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5:Dc Motor Drives"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.1,Page No:63"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from sympy import Symbol\n",
      "\n",
      "#variable declaration\n",
      "#motor ratings\n",
      "V1=200     #rated voltage\n",
      "Ia1=10.5   #rated current\n",
      "N1=2000    #speed in rpm\n",
      "Ra=0.5     #armature resistance\n",
      "Rs=400     #field resistance\n",
      "V2=175     #drop in source voltage \n",
      "\n",
      "#calculation\n",
      "flux1 = Symbol('flux1')\n",
      "flux2=V2/V1*flux1\n",
      "Ia2=flux1/flux2*Ia1    #since load torque\n",
      "E1=V1-Ia1*Ra\n",
      "E2=V2-Ia2*Ra\n",
      "N2=(E2/E1)*(flux1/flux2)*N1\n",
      "\n",
      "#results\n",
      "#answer in the book is wrong due to accuracy\n",
      "print\"\\nmotor speed is:N2=\",round(N2,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "motor speed is:N2= 1983.5 rpm\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.2,Page No:63"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from sympy import Symbol\n",
      "\n",
      "#variable declaration\n",
      "V1=220      #rated voltage\n",
      "Ia1=100     #rated current\n",
      "N1=1000     #rated speed in rpm clockwise\n",
      "Ra=0.05     #armature resistance\n",
      "Rs=0.05     #field resistance\n",
      "\n",
      "#calculation\n",
      "#turns is reduced to 80% then flux is also reduced by the same value and hence current is also reduced\n",
      "Ke = Symbol('Ke')\n",
      "Ia2 = Symbol('Ia2')\n",
      "T1=Ke*Ia1**2      #flux is directly proportional to current Ia\n",
      "T2=Ke*0.8*Ia2**2  #flux is directly proportional to current Ia\n",
      "Ia2=-Ia1/math.sqrt(0.8)   #since T1=T2 and the direction is opposite\n",
      "\n",
      "E1=V1-Ia1*(Ra+Rs)\n",
      "\n",
      "Rs=.8*Rs       #Rs=80% of the field resistance 0.05ohm since the flux is reduced to 80%\n",
      "E2=-(V1+Ia2*(Ra+Rs))   \n",
      "\n",
      "N2=(E2/E1)*(Ia1/Ia2)*(N1/0.8)   #since E=Kn*flux*N\n",
      "\n",
      "#results\n",
      "print\"\\nmotor speed is:N2=\",round(N2,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "motor speed is:N2= 1117.7 rpm\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.3,Page No:70"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#motor ratings\n",
      "V1=220     #rated voltage\n",
      "Ia1=200    #rated current\n",
      "Ra=0.06    #armature resistance\n",
      "Rb=0.04    #internal resistance of the variable source\n",
      "N1=800     #speed in rpm\n",
      "N2=600     #speed when motor is operatingin regenerative braking\n",
      "\n",
      "#Calculation\n",
      "Ia2=0.8*Ia1        #motor is opereting in regenerative braking at 80% of Ia1\n",
      "E1=V1-Ia1*Ra       #back emf at rated operation\n",
      "E2=(N2/N1)*E1      #back emf at the given speed N2\n",
      "V2=E2-Ia2*(Ra+Rb)  #internal voltage of thevariable source\n",
      "\n",
      "#results\n",
      "print\"\\n internal voltage of thevariable source:\",round(V2),\"V\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " internal voltage of thevariable source: 140.0 V\n"
       ]
      }
     ],
     "prompt_number": 161
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.4,Page No:70"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from sympy import Symbol\n",
      "\n",
      "#variable declaration\n",
      "#The ratings of the motor is same as that of Ex-5.2\n",
      "V1=220      #rated voltage\n",
      "Ia1=100     #rated current\n",
      "N1=1000     #speed in rpm clockwise\n",
      "N2=800      #given speed during the dynamic braking\n",
      "Ra=0.05     #armature resistance\n",
      "Rs=0.05     #field resistance\n",
      "\n",
      "#calculation\n",
      "T1 = Symbol('T1')\n",
      "T2 = 2*T1   #dynamic torque is twice the rated torque\n",
      "Ia2=Ia1*math.sqrt(T2/T1)   #since T=Kf*Ia**2\n",
      "E1=V1-Ia1*(Ra+Rs)\n",
      "E2=(Ia2/Ia1)*(N2/N1)*E1    #since E=Ke*Ia*N\n",
      "Rb=E2/Ia2-(Ra+Rs)          #since E2=Ia2(Rb+Ra+Rs)  during braking\n",
      "\n",
      "#results\n",
      "print\"\\n braking current Ia2:\",round(Ia2,1),\"A\"\n",
      "print\"\\n required braking resistance Rb:\",round(Rb,2),\"ohm\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " braking current Ia2: 141.4 A\n",
        "\n",
        " required braking resistance Rb: 1.58 ohm\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.5,Page No:70"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the DC shunt motor which operated under dynamic braking\n",
      "Rb=1      #braking resisance\n",
      "Ra=0.04   #armature resistance\n",
      "Rf=10     #field resistance\n",
      "T=400     #load torque in N-m\n",
      "\n",
      "#magnetisation curve at N1\n",
      "N1=600    #speed in rpm\n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]    #field current\n",
      "E =[25,50,73.5,90,102.5,110,116,121,125,129] #back emf\n",
      "\n",
      "#calculation\n",
      "print\"Field current   If:\",If,\"A\"\n",
      "x=(Rb+Rf)/Rb\n",
      "Ia = [If * x for If in If]    #armature current\n",
      "Wm=2*math.pi*N1/60\n",
      "Ke_flux=[E / Wm for E in E]    #Ke*flux=constant\n",
      "Ke_flux=[round(Ke_flux,3) for Ke_flux in Ke_flux]  \n",
      "\n",
      "Ke_flux=numpy.array(Ke_flux)\n",
      "Ia=numpy.array(Ia)\n",
      "T=numpy.array(Ke_flux)*numpy.array(Ia)   #torque\n",
      "print\"\\nKe_flux :\",Ke_flux\n",
      "T=[round(T,1) for T in T]\n",
      "print\"\\nTorque  :\",T,\"N-m\"\n",
      "\n",
      "\n",
      "#results\n",
      "#plotting the values of Ke*flux vs If \n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]    #field current\n",
      "plt.subplot(2,1,1)\n",
      "plt.plot(If,Ke_flux,'y')\n",
      "plt.xlabel('field current $I_f$')\n",
      "plt.ylabel('$Ke*flux$')\n",
      "plt.title('$If  vs  Ke*flux$')\n",
      "plt.grid(True)\n",
      "\n",
      "#plotting the values of  T vs If \n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]    #field current\n",
      "plt.subplot(2,1,2)\n",
      "plt.plot(T,If)\n",
      "plt.xlabel('Torque $T$')\n",
      "plt.ylabel('field current $I_f$')\n",
      "plt.title('$T vs If$')\n",
      "plt.grid()\n",
      "plt.tight_layout()\n",
      "plt.show()\n",
      "\n",
      "print\"\\nFrom the plot we can see that when the torque is 400 N-m, \"\n",
      "print\"the field current is If=19.3 A, and Ke*flux=1.898 when If=19.3 A\"\n",
      "T=400          # braking torque\n",
      "If=19.13       # field current\n",
      "Ke_flux=1.898  # Ke*flux\n",
      "Ia=x*If\n",
      "E=If*Rf+Ia*Ra    #since E=V+Ia*Ra\n",
      "N2=(E/Ke_flux)*(60/(2*math.pi))  #required speed\n",
      "print\"Hence the required speed in is :\",round(N2),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Field current   If: [2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25] A\n",
        "\n",
        "Ke_flux : [ 0.398  0.796  1.17   1.432  1.631  1.751  1.846  1.926  1.989  2.053]\n",
        "\n",
        "Torque  : [10.9, 43.8, 96.5, 157.5, 224.3, 288.9, 355.4, 423.7, 492.3, 564.6] N-m\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0m1FbHYF8lir4+voSFhYGgJubG4GBgVy9elU+R9XcrZ6g/p+lJpOo6vLAsNDR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\n+vpy/fr1u854MXfuXP1IQ09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oSzPyxg3YuFHXWnJy0nXtzZoFnp4WClIIIQRgpeeozp8/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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff4f028dc10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "From the plot we can see that when the torque is 400 N-m, \n",
        "the field current is If=19.3 A, and Ke*flux=1.898 when If=19.3 A\n",
        "Hence the required speed in is : 1005.0 rpm\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.6,Page No:71"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#variable declaration\n",
      "#the motor rating is same as that of Ex-5.5\n",
      "N=600      #value of the speed given from the magnetization curve in Ex-5.5\n",
      "\n",
      "Ra=0.04    #armature resistance\n",
      "Rf=10      #field resistance\n",
      "T=400      #load torque in N-m\n",
      "N1=1200    #given speed in rpm to hold the overhauling torque\n",
      "\n",
      "#calculation\n",
      "Wm=2*math.pi*N1/60    #angular speed at the given speed N1\n",
      "\n",
      "#magnetisation curve at N=600rpm\n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]       #field current\n",
      "E =[25,50,73.5,90,102.5,110,116,121,125,129]    #value of the back emf as given in Ex-5.5 for the speed N\n",
      "\n",
      "#magnetisation curve at N=1200rpm\n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]       #field current\n",
      "E1=[N1/N*E for E in E]                          #back emf at the speed N1\n",
      "print\"Hence the magnetization curve at 1200rpm is\"\n",
      "print\"Field current   If:\",If,\"A\"\n",
      "print\"Back emf is     E1:\",E1,\"V\"\n",
      "\n",
      "Pd=round(T*Wm,2)                               #power developed\n",
      "x=round(Pd*Ra,1)\n",
      "V=[(E1-Pd*Ra/E1) for E1 in E1]       #terminal voltage\n",
      "V=[round(V,2) for V in V]\n",
      "print\"Terminal voltage V:\",V,\"V\"\n",
      "\n",
      "\n",
      "#results\n",
      "#plotting the values of V vs If\n",
      "plt.subplot(2,1,1)\n",
      "plt.plot(V,If)\n",
      "plt.xlabel('Terminal voltage $V$')\n",
      "plt.ylabel('Field current $I_f$')\n",
      "plt.title('$V vs If$')\n",
      "plt.grid()\n",
      "\n",
      "#plotting the values of E vs If\n",
      "If=[2.5,5,7.5,10,12.5,15,17.5,20,22.5,25]       #field current\n",
      "E =[25,50,73.5,90,102.5,110,116,121,125,129]    #value of the back emf as given in Ex-5.5 for the speed N\n",
      "E1=[N1/N*E for E in E]                          #back emf at the speed N1\n",
      "\n",
      "plt.subplot(2,1,2)\n",
      "plt.plot(E1,If,'y')\n",
      "plt.xlabel('$E$')\n",
      "plt.ylabel('Field current $I_f$')\n",
      "plt.title('$E vs If$')\n",
      "plt.grid()\n",
      "plt.tight_layout()\n",
      "plt.show()\n",
      "print\"\\nFrom the plot we can see that when the current If=25 A the terminal voltage is V=250 V with the back emf E=258V\"\n",
      "\n",
      "E=258           #value of the back emf in V at from the plot \n",
      "V=250           #value of terminal voltage in V from the plot at E=258 V\n",
      "If=25           #value of If in A from the plot at E=258 V\n",
      "Ia=(E-V)/Ra     #armature current\n",
      "If=V/Rf         #field current\n",
      "Ir=Ia-If \n",
      "Rb=V/Ir         #braking resistance\n",
      "\n",
      "print\"Hence the rquired braking resistance is \",round(Rb,3),\"ohm\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hence the magnetization curve at 1200rpm is\n",
        "Field current   If: [2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25] A\n",
        "Back emf is     E1: [50.0, 100.0, 147.0, 180.0, 205.0, 220.0, 232.0, 242.0, 250.0, 258.0] V\n",
        "Terminal voltage V: [9.79, 79.89, 133.32, 168.83, 195.19, 210.86, 223.33, 233.69, 241.96, 250.21] V\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KkqCEEEJYJUlQQgghrJIkKCGEEFZJEpQQQgirJAlKtHuXL182LAjn6elpWCBu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\nQgghrNL/B/LwApWB5UraAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7432763950>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "From the plot we can see that when the current If=25 A the terminal voltage is V=250 V with the back emf E=258V\n",
        "Hence the rquired braking resistance is  1.429 ohm\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.7,Page No:72"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy \n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the DC series motor which operated under dynamic braking\n",
      "Ra=0.5         #total resistance of armature and field windings\n",
      "Rf=10          #field resistance\n",
      "T=500          #overhauling load torque in N-m\n",
      "N=600          #speed at the overhauling torque T\n",
      "\n",
      "#magnetisation curve at a speed of 500 rpm\n",
      "N1=500    #speed in rpm\n",
      "Ia=[20, 30, 40, 50, 60, 70, 80]       #armature current\n",
      "E =[215,310,381,437,482,519,550]     #back emf\n",
      "\n",
      "#calculation\n",
      "Wm1=2*math.pi*N1/60\n",
      "print\"\\nArmature current :\",Ia,\"A\"\n",
      "Ke_flux=[E / Wm1 for E in E]    #Ke*flux=constant\n",
      "Ke_flux=[round(Ke_flux,3) for Ke_flux in Ke_flux]  \n",
      "print\"\\nKe_flux :\",Ke_flux\n",
      "Ke_flux=numpy.array(Ke_flux)\n",
      "Ia=numpy.array(Ia)\n",
      "T=numpy.array(Ke_flux)*numpy.array(Ia)   #torque\n",
      "T=[round(T,1) for T in T]\n",
      "print\"\\nTorque  :\",T,\"N-m\"\n",
      "\n",
      "\n",
      "#results\n",
      "#plotting the values of Ke*flux vs Ia and T vs Ia\n",
      "plt.subplot(2,1,1)\n",
      "plt.plot(Ia,Ke_flux,'y')\n",
      "plt.xlabel('Armature current $I_a$')\n",
      "plt.ylabel('$Ke*flux$')\n",
      "plt.title('$Ke*flux vs Ia$')\n",
      "plt.grid()\n",
      "\n",
      "plt.subplot(2,1,2)\n",
      "plt.plot(T,Ia)\n",
      "plt.xlabel('Torque $T$')\n",
      "plt.ylabel('Armature current $I_a$')\n",
      "plt.title('$T vs Ia$')\n",
      "plt.grid(True)\n",
      "plt.tight_layout()\n",
      "plt.show()\n",
      "\n",
      "print\"\\nFrom the plot we can see that at the given torque T=500 N-m the current Ia is 56 A, and Ke*flux is 8.9 at Ia=56 A\"\n",
      "Ke_flux=8.9    #value of Ke*flux at T=500 N-m from the plot\n",
      "Ia=56          #value of Ia at at T=500 N-m from the plot\n",
      "Wm=2*math.pi*N/60\n",
      "E=Ke_flux*Wm   #required emf\n",
      "x=E/Ia         #x=Ra+Rb\n",
      "Rb=x-Ra        #required braking resistance\n",
      "print\"Hence the rquired braking resistance is \",round(Rb,3),\"ohm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Armature current : [20, 30, 40, 50, 60, 70, 80] A\n",
        "\n",
        "Ke_flux : [4.106, 5.921, 7.277, 8.346, 9.206, 9.912, 10.504]\n",
        "\n",
        "Torque  : [82.1, 177.6, 291.1, 417.3, 552.4, 693.8, 840.3] N-m\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JSYmhQ2h3krN5MMecwXzzbimj+a0+f/58/vGPf3D+/Plrvuf06S9xd5+Nn9+X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\nwi0qUoQQQrhFRYoQQgi3qEgRQgjh1j9O3WMryW1X+AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f989876da50>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "From the plot we can see that at the given torque T=500 N-m the current Ia is 56 A, and Ke*flux is 8.9 at Ia=56 A\n",
        "Hence the rquired braking resistance is  9.486 ohm\n"
       ]
      }
     ],
     "prompt_number": 170
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.8,Page No:74"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=220     # rated voltage\n",
      "N=970     # rated speed\n",
      "Ia=100    # rated current\n",
      "Ra=0.05   # armature resistance\n",
      "N1=1000   # initial speed of the motor in rpm\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra\n",
      "E1=N1/N*E   #value of back emf at the speed N1\n",
      "#(a)the resistance to be placed\n",
      "Ia1=2*Ia         #value of the braking current is twice the rated current\n",
      "Rb=(E1+V)/Ia1-Ra  #required resistance\n",
      "\n",
      "#(b)The braking torque\n",
      "Wm=(2*math.pi*N1)/60\n",
      "T=E1*Ia1/Wm\n",
      "\n",
      "#(c)when the speed has fallen to zero the back emf is zero\n",
      "E2=0\n",
      "Ia2=V/(Ra+Rb)\n",
      "T2=Ia2/Ia1*T   #since the torque is directly proportional to the current\n",
      "\n",
      "\n",
      "#results \n",
      "print\"(a)Hence required resistance is :\",round(Rb,2),\"ohm\"\n",
      "#answer for the resistance in the book is wrong due to accuracy\n",
      "print\"\\n(b)Hence the required braking torque is :\",round(T,1),\"N-m\"\n",
      "print\"\\n(c)Hence the required torque is :\",round(T2,1),\"N-m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Hence required resistance is : 2.16 ohm\n",
        "\n",
        "(b)Hence the required braking torque is : 423.3 N-m\n",
        "\n",
        "(c)Hence the required torque is : 210.9 N-m\n"
       ]
      }
     ],
     "prompt_number": 171
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.9,Page No:84"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor which operates under rheostatic braking\n",
      "V=220     # rated voltage\n",
      "N=1000    # rated speed\n",
      "Ia=175    # rated current\n",
      "Ra=0.08   # armature resistance\n",
      "N1=1050   # initial speed of the motor in rpm\n",
      "J=8       # moment of inertia of the motor load system kg-m2\n",
      "La=0.12   # armature curcuit inductance in H\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra\n",
      "Wm=N*2*math.pi/60     #rated speed in rad/s\n",
      "\n",
      "#(a)when  the braking current is twice the rated current\n",
      "Ia1=2*Ia\n",
      "E1=N1/N*E\n",
      "x=E1/Ia1   #x=Rb+Ra\n",
      "Rb=x-Ra    #required braking resistance\n",
      "\n",
      "#(b)to obtain the expression for the transient value of speed and current including the effect of armature inductance\n",
      "Ra=x                   #total armature current\n",
      "K1=N1*2*math.pi/60     #initial speed in rad/s\n",
      "K=E/Wm\n",
      "B=0\n",
      "ta=La/Ra                    #time constant in sec\n",
      "Trated=E*Ia/Wm              #rated torque\n",
      "Tl=0.15*Trated              #load torque is 15% of the rated torque\n",
      "tm1= float('inf')           #tm1=J/B and B=0 which is equal to infinity\n",
      "tm2=J*Ra/(B*Ra+K**2)\n",
      "\n",
      "a = ta\n",
      "b = -(1+ta/tm1)\n",
      "c = 1/tm2\n",
      "# calculate the discriminant\n",
      "d = (b**2) - (4*a*c)\n",
      "# find two solutions\n",
      "alpha1 = (-b-cmath.sqrt(d))/(2*a)\n",
      "alpha2 = (-b+cmath.sqrt(d))/(2*a)\n",
      "\n",
      "K3=tm2*Tl/J\n",
      "K4=tm2*K*Tl/J/Ra\n",
      "\n",
      "#transient value for speed\n",
      "x1=((J*alpha2-B)*K1-(Tl-J*alpha2*K3))/(J*(alpha2-alpha1))\n",
      "y1=((J*alpha1-B)*K1-(Tl-J*alpha1*K3))/(J*(alpha1-alpha2))\n",
      "\n",
      "#transient value for the current\n",
      "x2=(K*K1+alpha2*La*K4)/(La*(alpha2-alpha1))\n",
      "y2=(K*K1+alpha1*La*K4)/(La*(alpha1-alpha2))\n",
      "\n",
      "\n",
      "#(c) to calculate the time taken by braking operation and the maximum value of the armature current\n",
      "#now Wm=0 for the braking operation and hence 151.5 exp(-0.963*t1)- 8.247 = 0 from the previous answer in (b)\n",
      "a=K3/x1    #a=exp(-0.963*t1)\n",
      "t1=-alpha1*math.log(a.real)        #take log base e on both sides\n",
      "#now d/dt(ia)=0 for themaximum current and hence d/dt(26.25-593.1exp(-0.963*t)+566.8exp(-4.19*t) = 0 from the previous answer in (b)\n",
      "b=abs(alpha2*y2)/abs(alpha1*x2)    #b=exp(-0.963*t)/exp(-4.19*t)\n",
      "t2=math.log(b)/(-alpha1+alpha2)    #take log base e on both sides\n",
      "t2=abs(t2)\n",
      "ia=K4-x2.real*math.exp(-alpha1.real*t2)-y2.real*math.exp(-alpha2.real*t2)\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(a)Hence the braking resistance is :\",round(Rb,3),\"ohm\"\n",
      "print\"\\nb)The value of alpha1 :\",round(alpha1.real,3),\"and alpha2 :\",round(alpha2.real,3)\n",
      "print\"\\nHence the expression for the transient value for the speed is\"\n",
      "print\"Wm=\",round(x1.real,1),\"exp(\",-round(alpha1.real,3),\"*t)\",round(y1.real,1),\"exp(\",-round(alpha2.real,2),\"*t)\",\"-\",round(K3,3)\n",
      "print\"\\nHence the expression for the transient value for the current is\"\n",
      "print\"ia=\",round(K4,2),\"-\",round(x2.real,1),\"exp(\",-round(alpha1.real,3),\"*t) +\",-round(y2.real,1),\"exp(\",-round(alpha2.real,2),\"*t)\"\n",
      "print\"\\n(c)Hence the time taken is :\",round(t2,2),\"sec\"\n",
      "print\"   Hence the maximum current is: \",round(ia,2),\"A\"\n",
      "print\"\\n Note : There is a slight difference in the answers due to more number of the decimal place \""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Hence the braking resistance is : 0.538 ohm\n",
        "\n",
        "b)The value of alpha1 : 0.963 and alpha2 : 4.187\n",
        "\n",
        "Hence the expression for the transient value for the speed is\n",
        "Wm= 151.5 exp( -0.963 *t) -33.3 exp( -4.19 *t) - 8.247\n",
        "\n",
        "Hence the expression for the transient value for the current is\n",
        "ia= 26.25 - 593.1 exp( -0.963 *t) + 566.8 exp( -4.19 *t)\n",
        "\n",
        "(c)Hence the time taken is : 0.44 sec\n",
        "   Hence the maximum current is:  -272.23 A\n",
        "\n",
        " Note : There is a slight difference in the answers due to more number of the decimal place \n"
       ]
      }
     ],
     "prompt_number": 151
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.10,Page No:86"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "import numpy as np\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor of Ex-5.9 which operates plugging\n",
      "V=220     # rated voltage\n",
      "N=1000    # rated speed\n",
      "Ia=175    # rated current\n",
      "Ra=0.08   # armature resistance\n",
      "N1=1050   # initial speed of the motor in rpm\n",
      "J=8       # moment of inertia of the motor load system kg-m2\n",
      "La=0.12   # armature curcuit inductance in H\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra\n",
      "Wm=N*2*math.pi/60     #rated speed in rad/s\n",
      "#(a)when  the braking current is twice the rated current\n",
      "Ia1=2*Ia\n",
      "E1=N1/N*E\n",
      "x=(V+E1)/Ia1   #x=Rb+Ra\n",
      "Rb=x-Ra        #required braking resistance\n",
      "\n",
      "#(b)to obtain the expression for the transient value of speed and current including the effect of armature inductance\n",
      "#the values given below are taken from Ex-5.9\n",
      "ta=0.194                    #time constant in sec\n",
      "B=0\n",
      "tm1= float('inf')           #tm1=J/B and B=0 which is equal to infinity\n",
      "tm2=1.274\n",
      "K=1.967\n",
      "Trated=E*Ia/Wm             #rated torque\n",
      "Tl=0.5*Trated              #load torque is 50% of the rated torque\n",
      "Ra=Rb\n",
      "K1=N1*2*math.pi/60         #initial speed in rad/s\n",
      "#values of the coefficient of the quadratic equation for Wm\n",
      "x1=(1+ta/tm1)/ta\n",
      "x2=1/tm2/ta\n",
      "x3=-(K*V+Ra*Tl)/J/Ra/ta   \n",
      "#values of the coefficient of the quadratic equation ia\n",
      "y1=(1+ta/tm1)/ta\n",
      "y2=1/tm2/ta\n",
      "y3=-B*V/J/Ra/ta+K*Tl/J/Ra/ta   \n",
      "\n",
      "#solving the quadratic equation\n",
      "a = 1 \n",
      "b = x1\n",
      "c = x2\n",
      "# calculate the discriminant\n",
      "d = (b**2) - (4*a*c)\n",
      "# find two solutions\n",
      "alpha1 = (-b+cmath.sqrt(d))/(2*a)\n",
      "alpha2 = (-b-cmath.sqrt(d))/(2*a)\n",
      "\n",
      "K3=x3/x2\n",
      "K4=y3/y2\n",
      "\n",
      "Wm_0=K1                       ;ia_0=0\n",
      "d_Wm_dt_0=(K*ia_0-B*Wm-Tl)/J  ;d_ia_dt_0=(-V-Ra*ia_0-K*K1)/La    #Wm=K1 at t=0 and during braking rated voltage V is equal to -V\n",
      "\n",
      "A = np.array([[1,1],[alpha1.real,alpha2.real]])\n",
      "B = np.array([Wm_0,d_Wm_dt_0])\n",
      "x = np.linalg.solve(A,B)\n",
      "C = np.array([[1,1],[alpha1.real,alpha2.real]])\n",
      "D = np.array([-K4,d_ia_dt_0])\n",
      "y = np.linalg.solve(C,D)\n",
      "\n",
      "#(c)to calculate the time taken for the speed to fall to zero value\n",
      "a=-K3/x[0]                      #a=exp(-0.966*t1)\n",
      "t1=alpha1*math.log(a)           #take log base e on both sides\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(a)Hence the braking resistance is :\",round(Rb,3),\"ohm\"\n",
      "print\"\\n(b)The solution for alpha are \",round(alpha1.real,3),\"and\",round(alpha2.real,3)\n",
      "print\"   Wm=\",round(K3,2),\"+ A*exp(\",round(alpha1.real,3),\"*t) +\",\"+ B*exp(\",round(alpha2.real,2),\"*t)\"\n",
      "print\"   ia=\",round(K4,2),\"+ C*exp(\",round(alpha1.real,3),\"*t) +\",\"+ D*exp(\",round(alpha2.real,2),\"*t)\"\n",
      "print\"   We have to find the value of A,B,C and D in the linear equation using the initial condition\"\n",
      "print\"   A=\",round(x[0],2),\"B=\",round(x[1],2), \"C=\",round(y[0],2),\"D=\",round(y[1],2)\n",
      "print\"\\nHence the expression for the transient value for the speed is\"\n",
      "print\"   Wm=\",round(K3,2),\"+\",round(x[0],2),\"*exp(\",round(alpha1.real,3),\"*t)\",round(x[1],2),\"*exp(\",round(alpha2.real,2),\"*t)\"\n",
      "print\"\\nHence the expression for the transient value for the current is\"\n",
      "print\"   ia=\",round(K4,2),round(y[0],2),\"*exp(\",round(alpha1.real,3),\"*t) +\",round(y[1],2),\"*exp(\",round(alpha2.real,2),\"*t)\"\n",
      "print\"\\n(c)Hence the time taken is :\",round(t1.real,2),\"sec\"\n",
      "print\"\\n Note :There is slight difference in the answers due to accuracy i.e more number of decimal place\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Hence the braking resistance is : 1.167 ohm\n",
        "\n",
        "(b)The solution for alpha are  -0.966 and -4.189\n",
        "   Wm= -86.48 + A*exp( -0.966 *t) + + B*exp( -4.19 *t)\n",
        "   ia= 46.22 + C*exp( -0.966 *t) + + D*exp( -4.19 *t)\n",
        "   We have to find the value of A,B,C and D in the linear equation using the initial condition\n",
        "   A= 136.24 B= -26.28 C= -1188.2 D= 1141.98\n",
        "\n",
        "Hence the expression for the transient value for the speed is\n",
        "   Wm= -86.48 + 136.24 *exp( -0.966 *t) -26.28 *exp( -4.19 *t)\n",
        "\n",
        "Hence the expression for the transient value for the current is\n",
        "   ia= 46.22 -1188.2 *exp( -0.966 *t) + 1141.98 *exp( -4.19 *t)\n",
        "\n",
        "(c)Hence the time taken is : 0.44 sec\n",
        "\n",
        " Note :There is slight difference in the answers due to accuracy i.e more number of decimal place\n"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.11,Page No:89"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=220     # rated voltage\n",
      "N=600     # rated speed\n",
      "Ia=500   # rated current\n",
      "Ra=0.02   # armature resistance\n",
      "Rf=10     # field resistance\n",
      "\n",
      "#calculation   \n",
      "E1=V-Ia*Ra            #rated back emf at rated operation\n",
      "Wm1=2*math.pi*N/60    #angular speed\n",
      "Trated=E1*Ia1/Wm1     #rated torque\n",
      "#(i) when the speed of the motor is 450rpm\n",
      "N1=450             #given speed in rpm\n",
      "Tl=2000-2*N1       #load torque is a function of the speed as given\n",
      "Ia2=Tl/Trated*Ia1  #for a torque of  Tl as a function of current\n",
      "E2=N1/N*E1         #for a given speed of 450rpm\n",
      "V2=E2+Ia2*Ra       #terminal voltage for a given speed of 450 rpm\n",
      "\n",
      "#(ii) when the speed of the motor is 750rpm\n",
      "N1=750          #given speed in rpm\n",
      "Tl=2000-2*N1    #load torque is a function of the speed as given\n",
      "Wm_=2*math.pi*N1/60\n",
      "Ke_phi1=E1/Wm1\n",
      "\n",
      "#Since we know that V=Ke*phi*Wm+Ia*Ra  by solving we get that  0.02*(Ia_)**2 -220*Ia_ + 39270 = 0\"\n",
      "a = 0.02\n",
      "b = -220\n",
      "c = 39270\n",
      "# calculate the discriminant\n",
      "d = (b**2) - (4*a*c)\n",
      "# find two solutions\n",
      "Ia_1 = (-b-cmath.sqrt(d))/(2*a)\n",
      "Ia_2 = (-b+cmath.sqrt(d))/(2*a)\n",
      "\n",
      "Ke_phi=Tl/abs(Ia_1)\n",
      "V1=V*Ke_phi/Ke_phi1   #required field voltage\n",
      "\n",
      "#results\n",
      "print\"(i)Hence motor terminal voltage is :\",round(V2),\"V\"\n",
      "print\"   And the armature current is :\",round(Ia2),\"A\"\n",
      "print\"\\n(ii)The solution for Ia_ are \",round(abs(Ia_1),1),\"A and\",round(abs(Ia_2)),\"A\"\n",
      "print\"    We ignore \",round(abs(Ia_2)),\"A since it is unfeasible,\\n    Hence armature current is :\",round(abs(Ia_1),1),\"A\"\n",
      "print\"    Hence the required field voltage is :\",round(V1,1),\"V\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence motor terminal voltage is : 164.0 V\n",
        "   And the armature current is : 329.0 A\n",
        "\n",
        "(ii)The solution for Ia_ are  181.5 A and 10819.0 A\n",
        "    We ignore  10819.0 A since it is unfeasible,\n",
        "    Hence armature current is : 181.5 A\n",
        "    Hence the required field voltage is : 181.3 V\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.12,Page No:91"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import cmath\n",
      "from __future__ import division\n",
      "import numpy\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the 2-pole separately excited DC motor with the fields coils connected in parallel\n",
      "V=220      # rated voltage\n",
      "N=750      # rated speed\n",
      "Ia1=100    # rated current\n",
      "Ra=0.1     # armature resistance\n",
      "\n",
      "#calculation\n",
      "E1=V-Ia1*Ra            #rated back emf at rated operation\n",
      "Wm1=2*math.pi*N/60     #angular speed\n",
      "Trated=E1*Ia1/Wm1      #rated torque\n",
      "Ke_phi1=E1/Wm1\n",
      "#(i) when the armature voltage is reduced to 110V\n",
      "Wm2=2*math.pi*N2/60    #angular speed\n",
      "E2=Ke_phi1*Wm2\n",
      "#Now there are two linear equations...that we have to solve\n",
      "#They are given by 0.3*N2+2.674*Ia2=500 and 0.28*N2+0.1*Ia2=110\n",
      "a = np.array([[0.3,2.674], [0.28,0.1]])\n",
      "b = np.array([500,110])\n",
      "x = np.linalg.solve(a, b)\n",
      "N2=round(x[0],1)      #let the motor speed be N2\n",
      "Ia2=round(x[1],1)     #let the motor current be Ia2\n",
      "\n",
      "#(ii)when the field coils are connected in series\n",
      "K=Ke_phi1/2\n",
      "Wm3=2*math.pi*N3/60    #angular speed\n",
      "E3=K*Wm3\n",
      "#Now there are two linear equations...that we have to solve\"\n",
      "#They are given by 0.3*N3+1.337*Ia3=500 and 0.14*N3+0.1*Ia3=220\"\n",
      "a = np.array([[0.3,1.337], [0.14,0.1]])\n",
      "b = np.array([500,220])\n",
      "x = np.linalg.solve(a, b)\n",
      "N3=round(x[0],1)            #let the motor speed be N3\n",
      "Ia3=round(x[1],2)           #let the motor current be Ia3\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the motor armature current is Ia2 :\",Ia2,\"A\"\n",
      "print\"   And the required speed is N2 :\",N2,\"rpm\"\n",
      "print\"\\n(ii)Hence the motor armature current is Ia3 :\",Ia3,\"A\"\n",
      "print\"    And the required speed is N3 :\",N3,\"rpm\"\n",
      " "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the motor armature current is Ia2 : 148.9 A\n",
        "   And the required speed is N2 : 339.7 rpm\n",
        "\n",
        "(ii)Hence the motor armature current is Ia3 : 25.45 A\n",
        "    And the required speed is N3 : 1553.3 rpm\n"
       ]
      }
     ],
     "prompt_number": 173
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.13,Page No:102"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=200    # rated voltage\n",
      "N=875    # rated speed\n",
      "Ia=150   # rated current\n",
      "Ra=0.06  # armature resistance\n",
      "Vs=220   # source voltage\n",
      "f=50     # frequency of the source voltage\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra            #back emf\n",
      "Vm=math.sqrt(2)*Vs   #peak voltage\n",
      "\n",
      "#(i)when the speed is 750 rpm and at rated torque\n",
      "N1=750         #given speed in rpm\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1+Ia*Ra    #terminal voltage\n",
      "cos_alpha=Va*math.pi/2/Vm\n",
      "alpha=math.acos(cos_alpha)   #required firing angle in radian\n",
      "alpha1=math.degrees(alpha)    #required firing angle in degrees\n",
      "\n",
      "#(ii)when the speed is -500rpm and at rated torque\n",
      "N1=-500         #given speed in rpm\n",
      "E1=N1/N*E       #back emf at the given speed N1\n",
      "Va=E1+Ia*Ra     #terminal voltage\n",
      "cos_alpha=Va*math.pi/2/Vm\n",
      "alpha=math.acos(cos_alpha)   #required firing angle in radian\n",
      "alpha2=math.degrees(alpha)    #required firing angle in degrees\n",
      "\n",
      "#(iii)when the firing angle is 160 degrees\n",
      "alpha=160    #firing angle in degrees\n",
      "Va=2*Vm/math.pi*math.cos(math.radians(alpha))\n",
      "E1=Va-Ia*Ra    #since Va=E1+Ia*Ra\n",
      "N1=E1/E*N      #the required speed at the given firing angle\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the required firing angle is :\",round(alpha1,1),\"\u00b0\"\n",
      "print\"\\n(ii)Hence the required firing angle is :\",round(alpha2),\"\u00b0\"\n",
      "print\"\\n(iii)Hence the required speed is :\",round(N1,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the required firing angle is : 29.3 \u00b0\n",
        "\n",
        "(ii)Hence the required firing angle is : 120.0 \u00b0\n",
        "\n",
        "(iii)Hence the required speed is : -893.9 rpm\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.14,Page No:103"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor is same as that of Ex-5.13\n",
      "V=200    # rated voltage\n",
      "N=875    # rated speed\n",
      "Ia=150   # rated current\n",
      "Ra=0.06  # armature resistance\n",
      "Vs=220   # source voltage\n",
      "f=50     #frequency of the source voltage\n",
      "La=0.85e-3   # armature curcuit inductance in H\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra            #back emf\n",
      "Vm=math.sqrt(2)*Vs   #peak voltage\n",
      "Wm=2*math.pi*N/60    #synchronous angular speed\n",
      "\n",
      "#(i)when the speed is 400 rpm and firing angle is 60 degrees\n",
      "N1=400         #given speed in rpm\n",
      "alpha=60       #firing angle in degrees\n",
      "W=2*math.pi*f  \n",
      "x=W*La/Ra\n",
      "phi=math.atan(x)\n",
      "cot_phi=1/math.tan(phi)\n",
      "Z=math.sqrt(Ra**2+(W*La)**2)\n",
      "K=E/Wm\n",
      "\n",
      "y=Ra*Vm/Z/K\n",
      "a=(1+math.exp(-(math.pi*cot_phi)))/(math.exp(-(math.pi*cot_phi))-1)\n",
      "Wmc=y*math.sin(math.radians(alpha)-phi)*a   #required angular speed in rps\n",
      "Nmc=Wmc*60/2/math.pi     #required angular speed in rpm\n",
      "\n",
      "E1=N1/N*E    \n",
      "\n",
      "#The equation Vm/Z*sin(beta-phi)-E/Ra+(E/Ra-Vm/Z*sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=0\n",
      "#can be solved using trial method such that beta=230 degrees\n",
      "beta=230                   #in degrees\n",
      "beta=math.radians(beta)    #in radians\n",
      "alpha=math.radians(alpha)  #in radians\n",
      "\n",
      "Va=(Vm*(math.cos(alpha)-math.cos(beta))+(math.pi+alpha-beta)*E1)/math.pi\n",
      "Ia=(Va-E1)/Ra\n",
      "T1=K*Ia\n",
      "\n",
      "#(ii)when the speed is -400 rpm and firing angle is 120 degrees\n",
      "Le=2e-3        #external inductance added to the armature\n",
      "L=La+Le\n",
      "N2=-400         #given speed in rpm\n",
      "alpha=120       #firing angle in degrees\n",
      "x=W*L/Ra\n",
      "phi=math.atan(x)\n",
      "cot_phi=1/math.tan(phi)\n",
      "Z=math.sqrt(Ra**2+(W*L)**2)\n",
      "K=E/Wm\n",
      "\n",
      "y=Ra*Vm/Z/K\n",
      "a=(1+math.exp(-(math.pi*cot_phi)))/(math.exp(-(math.pi*cot_phi))-1)\n",
      "Wmc=y*math.sin(math.radians(alpha)-phi)*a   #required angular speed in rps\n",
      "Nmc1=Wmc*60/2/math.pi     #required angular speed in rpm\n",
      "#The motor is operating under discontinous condition\"\n",
      "E2=N2/N*E    \n",
      "\n",
      "#The equation Vm/Z*sin(beta-phi)-E/Ra+(E/Ra-Vm/Z*sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=0\n",
      "#can be solved using trial method such that beta=281 degrees\n",
      "beta=281                   #in degrees\n",
      "beta=math.radians(beta)    #in radians\n",
      "alpha=math.radians(alpha)  #in radians\n",
      "\n",
      "Va=(Vm*(math.cos(alpha)-math.cos(beta))+(math.pi+alpha-beta)*E2)/math.pi\n",
      "Ia=(Va-E2)/Ra\n",
      "T2=K*Ia\n",
      "\n",
      "#(iii)when the speed is -600 rpm and firing angle is 120 degrees\n",
      "N3=-600        #speed in rpm\n",
      "alpha=120      #firing angle in degrees\n",
      "Va=2*Vm/math.pi*math.cos(math.radians(alpha))\n",
      "E3=N3/N*E    #since Va=E1+Ia*Ra\n",
      "Ia=(Va-E3)/Ra\n",
      "T3=K*Ia\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the required torque is :\",round(T1),\"N-m \"\n",
      "print\"\\n(ii)Hence the required torque is :\",round(T2,1),\"N-m\"\n",
      "print\"\\n(iii)Hence the required torque is :\",round(T3),\"N-m\"    \n",
      "print\"\\nNote : There is a slight difference in the answers because of accuracy i.e more number of decimal place\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the required torque is : 1067.0 N-m \n",
        "\n",
        "(ii)Hence the required torque is : 336.4 N-m\n",
        "\n",
        "(iii)Hence the required torque is : 1110.0 N-m\n",
        "\n",
        "Note : There is a slight difference in the answers because of accuracy i.e more number of decimal place\n"
       ]
      }
     ],
     "prompt_number": 179
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.15,Page No:105"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor is same as that of Ex-5.13\n",
      "V=200    # rated voltage\n",
      "N=875    # rated speed\n",
      "Ia=150   # rated current\n",
      "Ra=0.06  # armature resistance\n",
      "Vs=220   # source voltage\n",
      "f=50     #frequency of the source voltage\n",
      "La=2.85e-3   # armature curcuit inductance in H\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra            #back emf\n",
      "Vm=math.sqrt(2)*Vs   #peak voltage\n",
      "Wm=2*math.pi*N/60    #angular speed\n",
      "W=2*math.pi*f\n",
      "\n",
      "alpha=120       #firing angle in degrees\n",
      "x=W*La/Ra\n",
      "phi=math.atan(x)\n",
      "cot_phi=1/math.tan(phi)\n",
      "Z=math.sqrt(Ra**2+(W*La)**2)\n",
      "K=E/Wm\n",
      "\n",
      "y=Ra*Vm/Z/K\n",
      "a=(1+math.exp(-(math.pi*cot_phi)))/(math.exp(-(math.pi*cot_phi))-1)\n",
      "Wmc=round(y,3)*math.sin(math.radians(alpha)-phi)*a   #required angular speed in rps\n",
      "Nmc=Wmc*60/2/math.pi     #required angular speed in rpm\n",
      "\n",
      "Va=2*Vm/math.pi*math.cos(math.radians(alpha))\n",
      "E1=Nmc/N*E     #value of back emf at the critical speed of Nmc     \n",
      "Ia=(Va-E1)/Ra\n",
      "Tc=K*Ia\n",
      "\n",
      "#(i)when the torque is 1200 N-m and firing angle is 120 degrees\n",
      "T2=1200         #given torque in N-m\n",
      "Ia2=T2/K        #given terminal current for the given torque and the answer in the book is wrong\n",
      "E2=Va-Ia*Ra   \n",
      "N2=E2/E*N\n",
      "\n",
      "#(ii)when the torque is 300 N-m and firing angle is 120 degrees\n",
      "T=300    #required torque in N-m\n",
      "beta=233.492   #required angle in degrees\n",
      "beta=math.radians(beta)    #in radians\n",
      "alpha=math.radians(alpha)  #in radians\n",
      "x=beta-alpha\n",
      "E1=(Vm*(math.cos(alpha)-math.cos(beta)))/x-(math.pi*Ra*T)/(K*x)\n",
      "N1=E1/E*N   #required speed \n",
      "\n",
      "\n",
      "#results\n",
      "print\"The motor is operating under continuous condition\"\n",
      "print\"The torque Tc is :\",round(Tc),\"N-m\"\n",
      "print\"The answer for torque Tc in the book is wrong  due to accuracy in the decimal place  which leads to subsequent \"\n",
      "print\"incorrect answers\"\n",
      "print\"\\n(i)Hence the required speed is :\",round(N2),\"rpm\"\n",
      "print\"\\n(ii)The equation Vm/Z*sin(beta-phi)-sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=\"\n",
      "print\"    (Vm*(cos(alpha)-cos(beta))/Ra/(beta-alpha)-pi*T/K/(beta-alpha) )*(1-exp(-(beta-alpha)*cot_phi)\"\n",
      "print\"    can be solved using trial method such that beta=233.492 degrees\"\n",
      "print\"\\n  Hence the required speed is :\",round(N1,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The motor is operating under continuous condition\n",
        "The torque Tc is : 396.0 N-m\n",
        "The answer for torque Tc in the book is wrong  due to accuracy in the decimal place  which leads to subsequent \n",
        "incorrect answers\n",
        "\n",
        "(i)Hence the required speed is : -506.0 rpm\n",
        "\n",
        "(ii)The equation Vm/Z*sin(beta-phi)-sin(alpha-phi))*exp(-(beta-alpha)*cot_phi)=\n",
        "    (Vm*(cos(alpha)-cos(beta))/Ra/(beta-alpha)-pi*T/K/(beta-alpha) )*(1-exp(-(beta-alpha)*cot_phi)\n",
        "    can be solved using trial method such that beta=233.492 degrees\n",
        "\n",
        "  Hence the required speed is : 5.6 rpm\n"
       ]
      }
     ],
     "prompt_number": 181
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.16,Page No:110"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=220       # rated voltage\n",
      "N=960       # rated speed\n",
      "Ia=12.8     # rated current\n",
      "Ra=2        # armature resistance\n",
      "Vs=230      # source voltage\n",
      "f=50        #frequency of the source voltage\n",
      "La=150e-3   # armature curcuit inductance in H\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra            #back emf\n",
      "Vm=math.sqrt(2)*Vs   #peak voltage\n",
      "Wm=2*math.pi*N/60    #angular speed\n",
      "W=2*math.pi*f\n",
      "\n",
      "#(i)when speed is 600rpm and the firing angle is 60 degrees\n",
      "alpha=60       #firing angle in degrees\n",
      "N1=600         #motor speed in rpm\n",
      "x=W*La/Ra\n",
      "phi=math.atan(x)\n",
      "cot_phi=1/math.tan(phi)\n",
      "Z=math.sqrt(Ra**2+(W*La)**2)\n",
      "K=E/Wm\n",
      "\n",
      "y=Ra*Vm/Z/K\n",
      "b=math.sin(phi)*math.exp(-(math.radians(alpha)*cot_phi))\n",
      "c=math.sin(math.radians(alpha)-phi)*math.exp(-(math.pi*cot_phi))\n",
      "a=1-math.exp(-(math.pi*cot_phi))\n",
      "Wmc=round(y,3)*(b-c)/a   #required angular speed in rps\n",
      "Nmc=Wmc*60/2/math.pi     #required angular speed in rpm\n",
      "\n",
      "Va=Vm/math.pi*(1+math.cos(math.radians(alpha)))\n",
      "E1=N1/N*E     #value of back emf at the speed of N1\n",
      "Ia=(Va-E1)/Ra\n",
      "T=K*Ia\n",
      "\n",
      "#(ii)when the torque is 20 N-m and firing angle is 60 degrees\n",
      "T1=20       #required torque in N-m\n",
      "alpha=60   #required firing angle in degrees\n",
      "Ec=Nmc/N*E #motor back emf at critical speed of Nmc\n",
      "Tc=K*(Va-Ec)/Ra    #torque at the critical speed\n",
      "\n",
      "Ia=T1/K\n",
      "E1=Va-Ia*Ra\n",
      "N1=E1/E*N   #required speed \n",
      "\n",
      "\n",
      "#results\n",
      "if N1<Nmc :\n",
      "    print\"(i)The motor is operating under continuous condition\"\n",
      "print\"   Hence the required torque is :\",round(T,2),\"N-m\"\n",
      "if Tc<T1 :\n",
      "    print\"\\n(ii)The motor is operating under continuous condition\"\n",
      "print\"    Hence the required speed is :\",round(N1,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)The motor is operating under continuous condition\n",
        "   Hence the required torque is : 32.68 N-m\n",
        "\n",
        "(ii)The motor is operating under continuous condition\n",
        "    Hence the required speed is : 664.8 rpm\n"
       ]
      }
     ],
     "prompt_number": 182
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.17,Page No:113"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=220    # rated voltage\n",
      "N=1500   # rated speed\n",
      "Ia=50    # rated current\n",
      "Ra=0.5   # armature resistance\n",
      "Vl=440   # line  voltage with 3-phase ac supply\n",
      "f=50     #frequency of the source voltage\n",
      "\n",
      "#calculation\n",
      "#(i) tranformer ratio\n",
      "alpha=0    #firing angle\n",
      "Va=V       #motor terminal voltage is equal to the rated voltage when the firing angle is 0 degrees\n",
      "Vm=math.pi/3*Va/math.cos(alpha)\n",
      "Vrms=Vm/math.sqrt(2)        #rms value of the converter input voltage\n",
      "a=(Vl/math.sqrt(3))/Vrms    #required transformer ratio\n",
      "\n",
      "#(ii)value of the firing angle\n",
      "E=V-Ia*Ra      #back emf at the rated speed\n",
      "\n",
      "#(a)when the speed of the motor is 1200 rpm and rated torque\n",
      "N1=1200        #speed of the motor\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1+Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha=math.acos(math.pi/3*Va/Vm)  #required firing angle in radians\n",
      "alpha1=math.degrees(alpha)         #required firing angle in degrees\n",
      "\n",
      "#(b)when the speed of the motor is -800 rpm and twice the rated torque\n",
      "N1=-800        #speed of the motor\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Ia=2*Ia        #torque is directly proportional to the current hence twice the rated current\n",
      "Va=E1+Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha=math.acos(math.pi/3*Va/Vm)  #required firing angle in radians\n",
      "alpha2=math.degrees(alpha)         #required firing angle in degrees\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the required transformer ratio is :\",round(a,3)\n",
      "print\"\\n(ii)(a)Hence the required firing angle is :\",round(alpha1,2),\"\u00b0\"\n",
      "print\"\\n    (b)Hence the required firing angle is :\",round(alpha2,2),\"\u00b0\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the required transformer ratio is : 1.559\n",
        "\n",
        "(ii)(a)Hence the required firing angle is : 34.64 \u00b0\n",
        "\n",
        "    (b)Hence the required firing angle is : 104.21 \u00b0\n"
       ]
      }
     ],
     "prompt_number": 183
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.18,Page No:117"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor is same as that of Ex-5.17 but is fed from a circulating dual converter\n",
      "V=220    # rated voltage\n",
      "N=1500   # rated speed\n",
      "Ia=50    # rated current\n",
      "Ra=0.5   # armature resistance\n",
      "Vl=165   # line  voltage \n",
      "f=50     # frequency of the source voltage\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra            #back emf at the rated speed\n",
      "Vm=Vl*math.sqrt(2)   #peak voltage\n",
      "\n",
      "#(i)during motoring operation when the speed is 1000 rpm and at rated torque\n",
      "N1=1000        #speed of the motor\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1+Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha_A=math.acos(math.pi/3*Va/Vm)      \n",
      "alpha_B=180-math.degrees(alpha_A)         #required converter firing angle in degrees\n",
      "\n",
      "#(ii)during braking operation when the speed is 1000 rpm and at rated torque\n",
      "N1=1000        #speed of the motor in the book it is given as 100 rpm which is wrong\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1-Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha_A1=math.acos(math.pi/3*Va/Vm)      \n",
      "alpha_B1=180-math.degrees(alpha_A1)         #required converter firing angle in degrees\n",
      "\n",
      "#(iii)during motoring operation when the speed is -1000 rpm and at rated torque\n",
      "N1=-1000        #speed of the motor\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1-Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha_A2=math.acos(math.pi/3*Va/Vm)      \n",
      "alpha_B2=180-math.degrees(alpha_A2)         #required converter firing angle in degrees\n",
      "\n",
      "#(iv)during braking operation when the speed is -1000 rpm and at rated torque\n",
      "N1=-1000       #speed of the motor in the book it is given as 100 rpm which is wrong\n",
      "E1=N1/N*E      #back emf at the given speed N1\n",
      "Va=E1+Ia*Ra    #terminal voltage at the given speed N1\n",
      "alpha_A3=math.acos(math.pi/3*Va/Vm)      \n",
      "alpha_B3=180-math.degrees(alpha_A3)         #required converter firing angle in degrees\n",
      "\n",
      "\n",
      "#results\n",
      "print\"\\n(i)Hence the required firing angle is :\",round(alpha_B,1),\"\u00b0\"\n",
      "print\"\\n(ii)Hence the required firing angle is :\",round(alpha_B1,1),\"\u00b0\"\n",
      "print\"\\n(iii)Hence for negative speed during motoring operation the required firing angle are :\"\n",
      "print\"     alpha_A :\",round(math.degrees(alpha_A2),1),\"\u00b0 and alpha_B :\",round(alpha_B2,1),\"\u00b0\"\n",
      "print\"\\n(iv)Hence for negative speed during braking operation the required firing angle are :\"\n",
      "print\"    alpha_A :\",round(math.degrees(alpha_A3),1),\"\u00b0 and alpha_B :\",round(alpha_B3,1),\"\u00b0\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "(i)Hence the required firing angle is : 134.1 \u00b0\n",
        "\n",
        "(ii)Hence the required firing angle is : 118.1 \u00b0\n",
        "\n",
        "(iii)Hence for negative speed during motoring operation the required firing angle are :\n",
        "     alpha_A : 134.1 \u00b0 and alpha_B : 45.9 \u00b0\n",
        "\n",
        "(iv)Hence for negative speed during braking operation the required firing angle are :\n",
        "    alpha_A : 118.1 \u00b0 and alpha_B : 61.9 \u00b0\n"
       ]
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.19,Page No:126"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor\n",
      "V=230    # rated voltage\n",
      "N=960    # rated speed\n",
      "Ia=200   # rated current\n",
      "Ra=0.02  # armature resistance\n",
      "Vs=230   # source voltage\n",
      "\n",
      "#calculation\n",
      "E=V-Ia*Ra    #back emf\n",
      "\n",
      "#(i) When the speed of motor is 350 rpm with the rated torque during motoring operation\n",
      "N1=350      #given speed in rpm\n",
      "E1=N1/N*E   #given back emf at N1\n",
      "Va=E1+Ia*Ra  #motor terminal voltage\n",
      "delta=Va/V  #duty ratio\n",
      "\n",
      "#(ii) When the speed of motor is 350 rpm with the rated torque during braking operation\n",
      "Va=E1-Ia*Ra  #motor terminal voltage\n",
      "delta1=Va/V   #duty ratio\n",
      "\n",
      "#(iii)maximum duty ratio is 0.95\n",
      "delta2=0.95   #maximum duty ratio\n",
      "Va=delta2*V   #terminal voltage\n",
      "Ia1=2*Ia      #maximum permissable current\n",
      "E1=Va+Ia1*Ra  #back emf\n",
      "N1=E1/E*N     #maximum permissible speed\n",
      "Pa=Va*Ia1     #power fed to the source\n",
      "\n",
      "#(iv) if the speed of the motor is 1200 rpm and the field of the motor is also controlled\n",
      "N2=1200      #given speed\n",
      "#now the field current is directly proportional to the speed of the motor\n",
      "If=N/N2     #field current as a ratio of the rated current\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i) Duty ratio is :\",round(delta,3)\n",
      "print\"\\n(ii)Duty ratio is :\",round(delta1,2)\n",
      "print\"\\n(iii)Maximum permissible speed is :\",round(N1),\"rpm\"\n",
      "print\"     Power fed to the source is :\",round(Pa/1000,1),\"kW\"\n",
      "print\"\\n(iv)Field current as a ratio of the rated current is :\",If"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i) Duty ratio is : 0.376\n",
        "\n",
        "(ii)Duty ratio is : 0.34\n",
        "\n",
        "(iii)Maximum permissible speed is : 962.0 rpm\n",
        "     Power fed to the source is : 87.4 kW\n",
        "\n",
        "(iv)Field current as a ratio of the rated current is : 0.8\n"
       ]
      }
     ],
     "prompt_number": 185
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.20,Page No:127"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the separately excited motor when it is operated in dynamic breaking\n",
      "V=230    # rated voltage\n",
      "N=960    # rated speed\n",
      "Ia=200   # rated current\n",
      "Ra=0.02  # armature resistance\n",
      "Vs=230   # source voltage\n",
      "Rb=2     # braking resistance in ohm\n",
      "\n",
      "#calculation\n",
      "#when the motor speed is 600 rpm and the braking torque is twice the rated value\n",
      "Ia1=2*Ia     #torque is directly proportional to current\n",
      "N1=600       #speed of the motor in rpm\n",
      "E=V-Ia*Ra    #back emf\n",
      "E1=N1/N*E\n",
      "x=E1/Ia1-Ra  #x=(1-delta)*Rb\n",
      "y=x/Rb       #y=1-delta\n",
      "delta=1-y    #duty ratio\n",
      "\n",
      "#(ii)if the duty ratio is 0.6 and and the braking torque is twice the rated value\n",
      "delta1=0.6  #duty ratio\n",
      "Ia1=2*Ia   #torque is directly proportional to current\n",
      "E1=Ia1*((1-delta1)*Rb+Ra)   #back emf\n",
      "N1=E1/E*N\n",
      "\n",
      "\n",
      "#results \n",
      "print\"(i)Duty ratio is :\",round(delta,2)\n",
      "print\"\\n(ii)Hence the motor speed is :\",round(N1,1),\"rpm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Duty ratio is : 0.83\n",
        "\n",
        "(ii)Hence the motor speed is : 1393.3 rpm\n"
       ]
      }
     ],
     "prompt_number": 140
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.21,Page No:128"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy as np\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the series motor\n",
      "N=600     #speed in rpm\n",
      "Vs=220    #source voltage\n",
      "Ra_Rf=0.12    #combine armature resistance field resistance\n",
      "#magnetisation curve at N\n",
      "If=[10, 20,30, 40, 50,  60, 70, 80]    #field current\n",
      "E =[64,118,150,170,184,194,202,210]    #terminal voltage\n",
      "\n",
      "#calculation\n",
      "#(i)when the duty ratio is 0.6 and motor current is 60 A\n",
      "delta=0.6    #duty ratio\n",
      "Ia1=60       #motor current\n",
      "Va1=delta*Vs #terminal voltage for the given duty ratio\n",
      "E1=Va1-Ia1*Ra_Rf      #back emf for the given duty ratio\n",
      "\n",
      "#for Ia1=60 A the terminal voltage is 194 V as given in the magnetization curve\n",
      "N1=E1/E[5]*N          #motor speed for the given duty ratio\n",
      "\n",
      "#(ii)when the speed is 400rpm and the duty ratio is 0.65\n",
      "delta=0.65    #duty ratio\n",
      "N2=400        #speed in rpm\n",
      "Va1=delta*Vs #terminal voltage for the given duty ratio\n",
      "\n",
      "#from the magnetization characteristic for the speed of 400rpm the current Ia=70 A\n",
      "E1=Va1-If[6]*Ra_Rf      #back emf for the given duty ratio\n",
      "T=(E1*If[6])/N2/(2*math.pi/60)    #required torque\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the motor speed is :\",round(N1),\"rpm\"\n",
      "print\"\\n(ii)Hence the required torque is :\",round(T),\"N-m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the motor speed is : 386.0 rpm\n",
        "\n",
        "(ii)Hence the required torque is : 225.0 N-m\n"
       ]
      }
     ],
     "prompt_number": 186
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.22,Page No:129"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy as np\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the series motor which is the same as that of Ex-6.21\n",
      "#The motor is operated using regenarative braking method\n",
      "N=600     #speed in rpm\n",
      "Vs=220    #source voltage\n",
      "Ra_Rf=0.12    #combine armature resistance field resistance\n",
      "#magnetisation curve at N\n",
      "If=[10, 20,30, 40, 50,  60, 70, 80]    #field current\n",
      "E =[64,118,150,170,184,194,202,210]    #terminal voltage\n",
      "\n",
      "#calculation\n",
      "#(i)when  the duty ratio is 0.5 and the braking torque is equal to the motor torque\n",
      "delta=0.5       #duty ratio\n",
      "Va1=delta*Vs    #terminal voltage\n",
      "Ia1=If[6]       #current at rated motor torque\n",
      "E1=Va1+Ia1*Ra_Rf      #back emf for the given duty ratio\n",
      "N1=E1/E[6]*N          #for a current of 70 A E=202 V from the magnetization curve\n",
      "\n",
      "#(ii)when maximum permisssible duty ratio is 0.95 and current is 70A\n",
      "delta_max=0.95      #maximum duty ratio\n",
      "Va1=delta_max*Vs    #terminal voltage\n",
      "Ia1=70              #maximum permissible current\n",
      "E2=Va1+Ia1*Ra_Rf    #back emf for the given duty ratio\n",
      "N2=E2/E[6]*N        #for a current of 70 A E=202 V\n",
      "\n",
      "#(iii)when the motor speed is 1000rpm and maximum current is 70A with duty ratio in the range of 0.05 to 0.95\n",
      "Ia1=70              #maximum permissible current\n",
      "N3=1000             #given speed in rpm\n",
      "delta_max=0.95      #maximum duty ratio\n",
      "E3=N3/N*E[6]        #terminal voltage\n",
      "x=(E3-delta_max*Vs)/Ia1    #x=R+Ra_Rf   where R is the required external resistance\n",
      "R=x-Ra_Rf    #external resistance\n",
      "\n",
      "#(iv)when the motor is running at 1000rpm with current at 70 \n",
      "Ia1=70              #maximum permissible current\n",
      "N4=1000             #given speed in rpm\n",
      "Ra=Ra_Rf            #total value of armature resistance is assumed to be the same\n",
      "E4=Va1+Ia1*Ra       #back emf for the given speed N4\n",
      "E_=N/N4*E4\n",
      "ratio=E_/E[6]       #fraction of the requuired number of turns to be reduced\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i)Hence the motor speed is :\",round(N1,1),\"rpm\"\n",
      "print\"\\n(ii)Hence the motor speed is :\",round(N2,1),\"rpm\"\n",
      "print\"\\n(iii)Hence the required external resistance is :\",round(R,1),\"ohm\"\n",
      "print\"\\n(iv)Hence fraction of the  number of turns to be reduced is :\",round(ratio,3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence the motor speed is : 351.7 rpm\n",
        "\n",
        "(ii)Hence the motor speed is : 645.7 rpm\n",
        "\n",
        "(iii)Hence the required external resistance is : 1.7 ohm\n",
        "\n",
        "(iv)Hence fraction of the  number of turns to be reduced is : 0.646\n"
       ]
      }
     ],
     "prompt_number": 187
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example No:5.23,Page No:130"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "from array import array\n",
      "import numpy as np\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the series motor which is the same as that of Ex-6.21\n",
      "#The motor is operated using dynamic braking method\n",
      "N=600     #speed in rpm\n",
      "Vs=220    #source voltage\n",
      "Ra=0.12   # armature resistance\n",
      "delta_min=0.1   #manimum value of duty ratio\n",
      "delta_max=0.9   #maximum value of duty ratio\n",
      "#magnetisation curve at N\n",
      "If=[10, 20,30, 40, 50,  60, 70, 80]    #field current\n",
      "E =[64,118,150,170,184,194,202,210]    #terminal voltage\n",
      "\n",
      "#calculation\n",
      "#(i) maximum braking speed is 800rpm with armature current of 70 A\n",
      "N1=800   #maximum braking speed \n",
      "Ia=70    #armature current\n",
      "E1=N1/N*E[6]   #at 70A motor back emf is 202V \n",
      "Rbe=E1/Ia-Ra   #effective value of braking resistance\n",
      "Rb=Rbe/(1-delta_min)   #required braking resistance\n",
      "\n",
      "#(ii)when the speed of the motor is 87 rpm\n",
      "#now torque is maximum when the duty ratio is maximum\n",
      "N1=87   #speed in rpm\n",
      "R=Rb*(1-delta_max)+Ra\n",
      "\n",
      "Ia=If[4]   #value of armature current for the given value of E=184V \n",
      "Ke_phi=E[4]/(2*math.pi*N)*60\n",
      "T=Ke_phi*Ia   #required torque\n",
      "\n",
      "\n",
      "#results\n",
      "print\"(i)Hence braking resistance is:\",round(Rb,2),\"ohm\"\n",
      "print\"\\n(ii)Hence the required torque is :\",round(T,1),\"N-m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(i)Hence braking resistance is: 4.14 ohm\n",
        "\n",
        "(ii)Hence the required torque is : 146.4 N-m\n"
       ]
      }
     ],
     "prompt_number": 188
    }
   ],
   "metadata": {}
  }
 ]
}