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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 11: Speed and Torque Control"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.1, Page number: 561"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "#Variable declaration:\n",
      "Vdc=240                             #DC supply (V)\n",
      "D=0.75                              #Duty cycle\n",
      "Rf=187                              #field resistance(ohm)\n",
      "Lf=4.2                              #field winding inductance(H)\n",
      "T=1                                 #switching period(msec)\n",
      "\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "If=D*(Vdc/Rf)\n",
      "tau=Lf/Rf                           #time constant(msec)\n",
      "del_if=(2*Vdc/Rf)*(T/tau)*D*(1-D)\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Avg field current:\",round(If,2),\"A\"\n",
      "print \"Magnitude of currnet ripple:\",round(del_if,1),\"mA\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Avg field current: 0.96 A\n",
        "Magnitude of currnet ripple: 21.4 mA\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.2, Page number: 563"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import *\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "n1=1800                                 #r/min\n",
      "n2=3600                                 #r/min\n",
      "Va=240                                  #terminal voltage(V)\n",
      "Ifo=0.34                                #No-load field current(A)\n",
      "Ra=0.05                                 #Armature resistance(ohm)\n",
      "Rsh=187                                 #Shunt field resistance(ohm)\n",
      "\n",
      "#Calculations:\n",
      "wm=symbols('wm')\n",
      "wm1=float(2*pi*n1/60)\n",
      "wm2=float(2*pi*n2/60)\n",
      "def Pload(wm):\n",
      "    return (22.4*(120*pi)**-3)*(wm)**3\n",
      "\n",
      "T1=Pload(wm1)*1000/wm1\n",
      "T2=Pload(wm2)*1000/wm2\n",
      "\n",
      "Kf=Va/(Ifo*wm2)\n",
      "def If(T,wm):\n",
      "    return (Va/(2*Kf*wm))*(1+sqrt(1-(4*wm*T*Ra)/Va**2))\n",
      "\n",
      "Rf1tot=round(Va/float(If(T1,wm1)))\n",
      "Rf2tot=round(Va/float(If(T2,wm2)))\n",
      "Rrh1=Rf1tot-Rsh\n",
      "Rrh2=Rf2tot-Rsh\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"----------------------------------------------------------------\"\n",
      "print \"r/min    Tload[N.m]      If[A]      R(f)tot[ohm]   Rrheostat[ohm]\"\n",
      "print \"----------------------------------------------------------------\"\n",
      "print n1,\"\\t \",round(float(T1),1),\"\\t\\t \",round(float(If(T1,wm1)),3),\"\\t\",Rf1tot,\"\\t      \",Rrh1\n",
      "print n2,\"\\t \",round(float(T2),1),\"\\t\\t \",round(float(If(T2,wm2)),3),\"\\t\",Rf2tot,\"\\t      \",Rrh2\n",
      "print \"----------------------------------------------------------------\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "----------------------------------------------------------------\n",
        "r/min    Tload[N.m]      If[A]      R(f)tot[ohm]   Rrheostat[ohm]\n",
        "----------------------------------------------------------------\n",
        "1800 \t  14.9 \t\t  0.678 \t354.0 \t       167.0\n",
        "3600 \t  59.4 \t\t  0.333 \t720.0 \t       533.0\n",
        "----------------------------------------------------------------\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.3, Page number: 567"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from math import *\n",
      "from pylab import *\n",
      "\n",
      "#Variable declaration:\n",
      "Rf=109                                  #Field resistance(ohm)\n",
      "Vf=300                                  #Rated field voltage(V)\n",
      "Ra=0.084                                #Armature resistance(ohm)\n",
      "Kf=0.694                                #Geometric constant(A.rad/sec)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "If=Vf/Rf                                #Resulting field current(A)\n",
      "w_rated=2500*(pi/30)                    #Rated speed(rad/sec)\n",
      "P_rated=100*746                         #Watts\n",
      "T_rated=P_rated/w_rated                 #Nm\n",
      "Va=[0]*102\n",
      "NoLoadRPM=[0]*102\n",
      "FullLoadRPM=[0]*102                      \n",
      "for n in range(1,102,1):\n",
      "    Va[n-1]=250*(1+(n-1)/100)\n",
      "    T=0                                     #Zero torque\n",
      "    w=(Va[n-1]-T*Ra/(Kf*If))/(Kf*If)\n",
      "    NoLoadRPM[n-1]=w*30/pi\n",
      "    T=T_rated\n",
      "    w=(Va[n-1]-T*Ra/(Kf*If))/(Kf*If)\n",
      "    FullLoadRPM[n-1]=w*30/pi\n",
      "\n",
      "print\"The plot is as shown:\"\n",
      "plot(Va,NoLoadRPM)\n",
      "plot(Va[20] ,NoLoadRPM[20] ,'r+')\n",
      "plot (Va[50] , NoLoadRPM[50] , 'r+')\n",
      "plot (Va[80] ,NoLoadRPM[80] , 'r+')\n",
      "plot (Va, FullLoadRPM,'.')\n",
      "plot (Va[20] ,FullLoadRPM[20] ,'o')\n",
      "plot (Va[50] , FullLoadRPM[50] , ' o' )\n",
      "plot (Va[80] , FullLoadRPM[80] ,'o' )\n",
      "title('Speed vs Armature voltage')\n",
      "xlabel('Armature voltage [V] ')\n",
      "ylabel('Speed [r/min] ')\n",
      "annotate('+ = Zero torque',xy=(270,2300))\n",
      "annotate('o =   Full load torque',xy=(270,2100))\n",
      "ylim(1000,2500)\n",
      "xlim(250,500)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The plot is as shown:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DvCo0sVPjozsQFWzatAlCoRBCoRCbNzf82I46Ojrlrw8dOoTp06eXv1d8lFfV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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2718810>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.4, Page number: 571"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import *\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "Rf=109                                  #Field resistance(ohm)\n",
      "Vf=300                                  #Rated field voltage(V)\n",
      "n1=2000                                  #rpm\n",
      "T_rated=285                            #Rated torque(Nm)\n",
      "n2=1975                                 #Dropped rpm\n",
      "Kf=0.694                                #Geometric constant(A.rad/sec\n",
      "Ra=0.084                                #Armature resistance(ohm)\n",
      "\n",
      "#Calculations:\n",
      "If=Vf/Rf                                #Resulting field current(A)\n",
      "wm1=2*pi*n1/60\n",
      "w_ref=wm1\n",
      "Vao=Kf*If*wm1\n",
      "Ia=T_rated/(Kf*If)\n",
      "wm2=2*pi*n2/60\n",
      "Ea=Kf*If*wm2\n",
      "Va=Ea+Ia*Ra\n",
      "G=symbols('G')\n",
      "x=solve(Vao-round(Va)+G*(w_ref-wm2),G)\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Armature voltage,Vao:\",round(Va,0),\"V\"\n",
      "print \"Multiplicative constant,G:\",float(round(x[0],2)),\"A.sec/rad\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Armature voltage,Vao: 408.0 V\n",
        "Multiplicative constant,G: 3.04 A.sec/rad\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.5, Page number: 573"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "from sympy import *\n",
      "\n",
      "#Variable Declaration:\n",
      "Km=0.22                             #torque constant(V/(rad/sec))\n",
      "Ra=1.03                             #ohm\n",
      "Pl=100                            #Power load(W)\n",
      "Va1=40                              #Armature voltage(V)\n",
      "Va2=50                              #  \"        \"     \"\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "wm1=(Va1/(2*Km))*(1+sqrt(1-(4*Pl*Ra/Va1**2)))\n",
      "wm2=(Va2/(2*Km))*(1+sqrt(1-(4*Pl*Ra/Va2**2)))\n",
      "\n",
      "#Results:\n",
      "print \"for Va=40 V, wm=\",round(wm1,1),\"rad/sec\"\n",
      "print \"for Va=50 V, wm=\",round(wm2,1),\"rad/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "for Va=40 V, wm= 169.2 rad/sec\n",
        "for Va=50 V, wm= 217.5 rad/sec\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.6, Page number: 575"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "\n",
      "Rf=109                                  #Field resistance(ohm)\n",
      "Vf=300                                  #Rated field voltage(V)\n",
      "Ra=0.084                                #Armature resistance(ohm)\n",
      "Kf=0.694                                #Geometric constant(A.rad/sec)\n",
      "Tfl=285                                 #Full load torque(Nm)\n",
      "nf=2500                                 #Speed at full load(r/min)\n",
      "#wm=2500                                 #rated r/min\n",
      "\n",
      "#for part (1):\n",
      "n1=2000                                 #r/min\n",
      "n2=2500                                 #r/min\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#part (a):\n",
      "If=Vf/Rf\n",
      "w1=n1*2*pi/60\n",
      "w2=n2*2*pi/60\n",
      "Ea1=Kf*If*w1                    #Avg Amature voltage(V)\n",
      "Ea2=Kf*If*w2\n",
      "Ia1=n1*Tfl/(nf*Kf*If)\n",
      "Ia2=n2*Tfl/(nf*Kf*If)\n",
      "Va1 = Ea1 + Ia1*Ra\n",
      "Va2 = Ea2 + Ia2*Ra\n",
      "Tl1=(n1/nf)*Tfl\n",
      "Tl2=(n2/nf)*Tfl\n",
      "\n",
      "#part (b):\n",
      "\n",
      "# The dynamic equation governing the speed of the motor is\n",
      "\n",
      "#   J*(dwm/dt)=Tmech-Tload\n",
      "#   wm=(pi/30)*n & wr=(pi/30)*nf\n",
      "#      Tload= (Tfl/wf)*wm\n",
      "#   Tmech = Kf*If*Ia=Kf*If*(Va-Ea)/Ra          #Under armature-voltage control\n",
      "\n",
      "#   Thus the governing differential equation is\n",
      "#   d(wm)/dt + 48.4*wm - 24.7*Va = 0\n",
      " \n",
      "#   wm = wf + (wi-wf)*exp(-t/tau)          #tau=1/48.4=20.7 msec\n",
      "#   n = 2500- 50*exp( -t/tau )\n",
      "\n",
      "#   The armature current will decrease exponentially with the \n",
      "#   same 20.7 msec time constant from an initial value of \n",
      "#   (Vf - Vi)/Ra = 1190 A to its final value of 149 A.\n",
      "\n",
      "#   Ia = 149 + 1041*exp(-t/tau)\n",
      "\n",
      "#part (c):\n",
      "#        J*d(wm)/dt = Tmech-Tload = Tf-(Tf/wm)*wm\n",
      "# or      d(wm)/dt + 1.18*wm - 310 = 0\n",
      "\n",
      "#In this case, the speed will rise exponentially to wm=wf=262 rad/sec as\n",
      "#         wm = 262-53*exp(-t/tau)           #tau=1/1.18=845 msec\n",
      "\n",
      "#Results:\n",
      "print \"part(a):\\n\"\n",
      "print \"-------------------------------------------------\"\n",
      "print \"r/min\\tw[rad/s]\\tVa(V)\\tIa(A)\\tTload[Nm]\"\n",
      "print \"-------------------------------------------------\"\n",
      "print n1,\"\\t\",round(w1),\"\\t\\t\",round(Va1),\"\\t\",round(Ia1),\"\\t\",Tl1,\"Nm\"\n",
      "print n2,\"\\t\",round(w2),\"\\t\\t\",round(Va2),\"\\t\",round(Ia2),\"\\t\",Tl2,\"Nm\"\n",
      "print \"-------------------------------------------------\"\n",
      "print \"\\npart (b):\"\n",
      "print \" The resultant motor speed, n = 2500 - 50*exp(-t/tau) where tau=20.7 msec\"\n",
      "\n",
      "print \"\\npart (c):\"\n",
      "print \" The resultant motor speed, wm = 262 - 53*exp(-t/tau) where tau=845 msec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part(a):\n",
        "\n",
        "-------------------------------------------------\n",
        "r/min\tw[rad/s]\tVa(V)\tIa(A)\tTload[Nm]\n",
        "-------------------------------------------------\n",
        "2000 \t209.0 \t\t410.0 \t119.0 \t228.0 Nm\n",
        "2500 \t262.0 \t\t513.0 \t149.0 \t285.0 Nm\n",
        "-------------------------------------------------\n",
        "\n",
        "part (b):\n",
        " The resultant motor speed, n = 2500 - 50*exp(-t/tau) where tau=20.7 msec\n",
        "\n",
        "part (c):\n",
        " The resultant motor speed, wm = 262 - 53*exp(-t/tau) where tau=845 msec\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.7, Page number: 581"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "\n",
      "\n",
      "#Variable Calculations:\n",
      "f1=60                                #Initial frequency(Hz)\n",
      "f2=50                               #Changed frequency(Hz)\n",
      "Xs=0.836                            #Saturated synch reactance(ohm)\n",
      "Va=1+0j                             #Armature voltage(V p.u)\n",
      "Ia=1+0j                             #Armature current(A p.u)\n",
      "If_rated=2.84                       #Rated field current(A)\n",
      "p=6                                 #No. of poles\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#for part (a):\n",
      "ns1=120*f1/p\n",
      "ns2=120*f2/p\n",
      "Eaf=Va-1j*Xs*Ia*exp(1j*0)          #field voltage(V)\n",
      "Ifo=abs(Eaf)*If_rated                   #motor field current(A)\n",
      "\n",
      "#for part(b):\n",
      "#Eaf= (wm/wmo)*(If/Ifo)*Eafo\n",
      "If=Ifo\n",
      "\n",
      "#Results:\n",
      "print \"part(a):\"\n",
      "print \"(i)  The motor speed:\",ns1,\"r/min\"\n",
      "print \"(ii) The motor field current:\",round(Ifo,2),\"A\"\n",
      "print \"part(b):\"\n",
      "print \"(i)  The changed speed:\",ns2,\"A\"\n",
      "print \"(ii) The mototr field current:\",round(If,2),\"A\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part(a):\n",
        "(i)  The motor speed: 1200.0 r/min\n",
        "(ii) The motor field current: 3.7 A\n",
        "part(b):\n",
        "(i)  The changed speed: 1000.0 A\n",
        "(ii) The mototr field current: 3.7 A\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.8, Page number: 588"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "from sympy import *\n",
      "\n",
      "#Variable declaration:\n",
      "iF=2.84                                 #rated field current(A)\n",
      "Vbase=220                               #base voltage(V)\n",
      "Eaf=220/sqrt(3)                         #Rms voltage line-to-neutral(V)\n",
      "f=60                                    #Hz\n",
      "p=6                                     #poles\n",
      "P_rated=45*10**3                        #rated power(W)\n",
      "Xs_pu=0.836                             #per unit synchronous reactance(ohm)\n",
      "\n",
      "#Calculations:\n",
      "we=2*pi*f\n",
      "Laf=sqrt(2)*Eaf/(we*iF)                 #Armature field reactance(H)\n",
      "T_rated=P_rated/(we*2/p)\n",
      "#setting rated values to reference values.\n",
      "Tref=T_rated\n",
      "iFref=iF\n",
      "iQ=round((2/3)*(2/p)*Tref/(Laf*iFref),2)\n",
      "iD=0\n",
      "\n",
      "#since theta_me=wc*t, iD=0,we have,\n",
      "t=symbols('t')\n",
      "wc=120*pi\n",
      "def ia(t):\n",
      "    return iD*cos(wc*t)-iQ*sin(wc*t)\n",
      "def ib(t):\n",
      "    return iD*cos(wc*t-2*pi/3)-iQ*sin(wc*t-2*pi/3)\n",
      "def ic(t):\n",
      "    return iD*cos(wc*t+2*pi/3)-iQ*sin(wc*t+2*pi/3)\n",
      "Ibase=P_rated/(sqrt(3)*Eaf)\n",
      "Imax=round(ia((pi/(2*wc))))\n",
      "Ia=1j*abs(round(Imax/sqrt(2)))\n",
      "Eaf=1j*we*Laf*iF/sqrt(2)\n",
      "Zbase=Vbase**2/P_rated\n",
      "Xs=Xs_pu*Zbase\n",
      "Va=1j*Xs*Ia+Eaf                             #line-to-neutral voltage\n",
      "Vt=abs(sqrt(3)*Va)/Vbase                #p.u terminal voltage(line-to-line)(V)\n",
      "\n",
      "#Results:\n",
      "print \"part(a):\"\n",
      "print \"\\tia(t)=\",ia(t),\"A\"\n",
      "print \"\\tib(t)=\",ib(t),\"A\"\n",
      "print \"\\tic(t)=\",ic(t),\"A\"\n",
      "print \"part(b):\"\n",
      "print \"\\tTerminal voltage:\",round(float(Vt),2),\"per unit\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part(a):\n",
        "\tia(t)= -167.01*sin(120*pi*t) A\n",
        "\tib(t)= 167.01*sin(120*pi*t + pi/3) A\n",
        "\tic(t)= -167.01*cos(120*pi*t + pi/6) A\n",
        "part(b):\n",
        "\tTerminal voltage: 1.3 per unit\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.9, Page number: 591"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "iF=2.84                                 #rated field current(A)\n",
      "Vrated=220                              #rated terminal voltage,l-l(V)\n",
      "Ibase=118                               #base current(A)\n",
      "Eaf=220/sqrt(3)                         #Rms voltage, line-to-neutral(V)\n",
      "f=60                                    #Hz\n",
      "p=6                                     #poles\n",
      "P_rated=45*10**3                        #rated power(W)\n",
      "Xs=0.899                                #Synchronous reactance(ohm)\n",
      "Xs_pu=0.836                             #per unit synchronous reactance(ohm)\n",
      "Tref=358                                #Reference torque(Nm) (from Ex11.8)\n",
      "\n",
      "#Calculations:\n",
      "Va=Vrated/sqrt(3)                        #base voltage, line to neutral(V)\n",
      "we=2*pi*f\n",
      "wm=(2/p)*we\n",
      "Laf=sqrt(2)*Eaf/(we*iF)                 #Armature field reactance(H)\n",
      "Ia=Tref*wm/(3*Va)\n",
      "Ls=Xs/we                                #Synchronous inductance(mH)\n",
      "delta=-atan(we*Ls*Ia/Va)\n",
      "iQ_ref=sqrt(2)*Ia*cos(delta)\n",
      "iD_ref=sqrt(2)*Ia*sin(delta)\n",
      "iF_ref=(2./3)*(2/p)*Tref/(Laf*iQ_ref)\n",
      "\n",
      "#since motor is running at rated voltage, base voltage and rated voltage \n",
      "# are assumed to be same.\n",
      "Va_pu=Va/Va                      \n",
      "Ia_pu=Ia/Ibase\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"The reqd motor field current:\",round(iF_ref,2),\"A\"\n",
      "print \"Per unit voltage:\",Va_pu,\"p.u\"\n",
      "print \"Per unit current:\",round(Ia_pu),\"p.u\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " The reqd motor field current: 3.7 A\n",
        "Per unit voltage: 1.0 p.u\n",
        "Per unit current: 1.0 p.u\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.10, Page number: 593"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "ns=4000                             #rated speed(rpm)\n",
      "Va=220                              #rated voltage(V)\n",
      "Ls=1.75*10**-3                      #synchronous inductance(H)\n",
      "Prated=25000                        #Watts\n",
      "n=3200                              #rated OC speed(rpm)\n",
      "p=2                                 #No. of poles\n",
      "\n",
      "#Calculations:\n",
      "#for part(a):\n",
      "Eaf=Va/sqrt(3)\n",
      "wm=ns*pi/30                         #rad/sec\n",
      "Trated=Prated/wm\n",
      "we=(p/2)*n*pi/30\n",
      "lambdaPM=sqrt(2)*Eaf/we             #flux linked wth permanent magnet(Wb)  \n",
      "Tref=Trated*0.65                #since motor is operated at 65% of Trated\n",
      "iQref=(2./3)*(2/p)*(Tref/lambdaPM)\n",
      "\n",
      "#for part(b:)\n",
      "lambdaD=lambdaPM                         #since iD=0\n",
      "lambdaQ=Ls*iQref\n",
      "lambdaa=sqrt((lambdaD**2+lambdaQ**2)/2)  #rms line-to-neutral armature flux(Wb)\n",
      "lambdaa_base=Eaf/wm\n",
      "lambda_pu=lambdaa/lambdaa_base\n",
      "\n",
      "#for part(c)\n",
      "lambdaD=sqrt(2*(lambdaa_base)**2-lambdaQ**2)\n",
      "iDref=(lambdaD-lambdaPM)/Ls\n",
      "Ia=sqrt((iDref**2+iQref**2)/2)          #rms armature current(A)\n",
      "Ibase=Prated/(sqrt(3)*Va)\n",
      "I_pu=Ia/Ibase\n",
      "\n",
      "#Results:\n",
      "print \"(a)  Required quadrature-axis current:\",round(iQref,1),\"A\"\n",
      "print \"(b)  Resultant armature flux linkage\",round(lambda_pu,2),\"p.u\"\n",
      "print \"(c)  iD:\",round(iDref,1),\"A\"\n",
      "print \"     Rms value of armature current:\",round(Ia),\"A\"\n",
      "print \"     Per unit value of armature current:\",round(I_pu,2),\"A\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)  Required quadrature-axis current: 48.2 A\n",
        "(b)  Resultant armature flux linkage 1.27 p.u\n",
        "(c)  iD: -66.1 A\n",
        "     Rms value of armature current: 58.0 A\n",
        "     Per unit value of armature current: 0.88 A\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.11, Page number: 600"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "V10=230/sqrt(3)\n",
      "Nph=3\n",
      "p=4\n",
      "fe0=60\n",
      "R1=0.095                                #Armature resistance(ohm)\n",
      "R2=0.2                                  #Rotor resistance(ohm)\n",
      "X10=0.680                               #Armature leakage reactance(ohm)\n",
      "X20=0.672                               #Rotor leakage reactance(ohm)\n",
      "Xm0=18.7                                #Inductice reactance(ohm)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#taking two frequency values:\n",
      "fe1=40\n",
      "fe2=60\n",
      "\n",
      "for m in range(1,3,1):\n",
      "    if m==1:\n",
      "        fe=fe1\n",
      "    else:\n",
      "        fe=fe2\n",
      "    X1=X10*(fe/fe0)\n",
      "    X2=X20*(fe/fe0)\n",
      "    Xm=Xm0*(fe/fe0)\n",
      "    V1=V10*(fe/fe0)\n",
      "    \n",
      "    ws=4*pi*fe/p\n",
      "    ns=120*fe/p\n",
      "    V1eq=abs(V1*1j*Xm/(R1+1j*(X1+Xm)))\n",
      "    Z1eq=1j*Xm*(R1+1j*X1)/(R1+1j*(X1+Xm))\n",
      "    R1eq=Z1eq.real\n",
      "    X1eq=Z1eq.imag\n",
      "    \n",
      "#Search over the slip until the Pload = Pmech   \n",
      "    s=0                             #slip initialised to 0\n",
      "    error=1\n",
      "    \n",
      "    while error >=0:\n",
      "        s=s+0.00001\n",
      "        rpm=ns*(1-s)\n",
      "        wm=ws*(1-s)\n",
      "        Tmech=(1/ws)*Nph*V1eq**2*(R2/s)\n",
      "        Tmech = Tmech/((R1+R2/s)**2 + (X1+X2)**2)\n",
      "        Pmech=Tmech*wm\n",
      "        Pload=10.5*10**3*(rpm/1800)**3\n",
      "        error=Pload-Pmech\n",
      "    \n",
      "    print \"\\nFor fe =\",fe,\"Hz :\"\n",
      "    print \"\\tTerminal voltage=\",round(V1*sqrt(3)),\"V l-l\"\n",
      "    print \"\\trpm =\",round(rpm)\n",
      "    print \"\\tslip =\",round(100*s,1),\"%\"\n",
      "    print \"\\tPload =\",round(Pload/1000,2),\"kW\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "For fe = 40 Hz :\n",
        "\tTerminal voltage= 153.0 V l-l\n",
        "\trpm = 1166.0\n",
        "\tslip = 2.8 %\n",
        "\tPload = 2.86 kW\n",
        "\n",
        "For fe = 60 Hz :\n",
        "\tTerminal voltage= 230.0 V l-l\n",
        "\trpm = 1721.0\n",
        "\tslip = 4.4 %\n",
        "\tPload = 9.17 kW\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.12, Page number: 608"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "V10=230/sqrt(3)\n",
      "Nph=3\n",
      "p=4\n",
      "fe0=60\n",
      "R1=0.095                                #Armature resistance(ohm)\n",
      "R2=0.2                                  #Rotor resistance(ohm)\n",
      "X10=0.680                               #Armature leakage reactance(ohm)\n",
      "X20=0.672                               #Rotor leakage reactance(ohm)\n",
      "Xm0=18.7                                #Inductice reactance(ohm)\n",
      "n=1680                                  #rpm\n",
      "Pmech=9.7*10**3                         #Electromagnetic power(W)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "we0=2*pi*fe0\n",
      "Lm=Xm0/we0\n",
      "LS=Lm+X10/we0\n",
      "LR=Lm+X20/we0\n",
      "Ra=R1\n",
      "RaR=R2\n",
      "lambda_rated=sqrt(2)*V10/we0\n",
      "lambdaDR=lambda_rated\n",
      "#for specified operating condition\n",
      "wm=n*(pi/30)\n",
      "Tmech=Pmech/wm\n",
      "iQ=(2/3)*(2/p)*(LR/Lm)*(Tmech/lambdaDR)\n",
      "iD=lambdaDR/Lm\n",
      "Ia=sqrt((iD**2+iQ**2)/2)\n",
      "wme=(p/2)*wm\n",
      "we=wme+(RaR/LR)*(iQ/iD)\n",
      "fe=we/(2*pi)\n",
      "Va=sqrt(((Ra*iD-we*(LS-Lm**2/LR)*iQ)**2 + (Ra*iQ+we*LS*iD)**2)/2)\n",
      "\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Rms amplitude of the armature current:\",round(Ia,1),\"A\"\n",
      "print \"The electrical frequency:\",round(fe,1),\"Hz\"\n",
      "print \"Rms terminal voltage:\",round(sqrt(3)*Va,1),\"V  line-line\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Rms amplitude of the armature current: 27.9 A\n",
        "The electrical frequency: 58.4 Hz\n",
        "Rms terminal voltage: 243.6 V  line-line\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 11.13, Page number: 610"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "from math import *\n",
      "from pylab import *\n",
      "\n",
      "#Variable declaration:\n",
      "P_rated = 12*10**3                       #Watts\n",
      "V_rated = 230                            #Rated line-line voltage(v)\n",
      "Va_rated = 230/sqrt(3)                   #Rated line to neutral(V)\n",
      "fe_rated = 60                            #Hz\n",
      "we_rated = 2*pi*fe_rated                 #rad/sec\n",
      "lambda_rated = sqrt(2)*Va_rated/we_rated #Wb\n",
      "I_rated = P_rated/(sqrt(3)*V_rated)      #A\n",
      "Ipeak_base = sqrt(2)*I_rated            #A\n",
      "p = 4                                   #poles\n",
      "\n",
      "V10=V_rated/sqrt(3)\n",
      "R1=0.095                                #Armature resistance(ohm)\n",
      "R2=0.2                                  #Rotor resistance(ohm)\n",
      "X10=0.680                               #Armature leakage reactance(ohm)\n",
      "X20=0.672                               #Rotor leakage reactance(ohm)\n",
      "Xm0=18.7                                #Inductice reactance(ohm)\n",
      "\n",
      "#Calculations:\n",
      "Lm = Xm0/we_rated;\n",
      "LS = Lm + X10/we_rated;\n",
      "LR = Lm + X20/we_rated;\n",
      "Ra = R1\n",
      "RaR = R2\n",
      "#operating point:\n",
      "n = 1680                                #rpm\n",
      "lambdaDR=lambda_rated\n",
      "wm = n*pi/30\n",
      "wme = (p/2)*wm\n",
      "Pmech = 9.7*10**3\n",
      "Tmech = Pmech/wm\n",
      "lambda_DRpu=[0]*42\n",
      "iDpu=[0]*42\n",
      "Iapu=[0]*42\n",
      "fe=[0]*42\n",
      "Vapu=[0]*42\n",
      "\n",
      "for n in range(1,43,1):\n",
      "    lambdaDR = (0.8+(n-1)*0.4/40)*lambda_rated\n",
      "    lambda_DRpu[n-1]=lambdaDR/lambda_rated\n",
      "    iQ=(2/3)*(2/p)*(LR/Lm)*(Tmech/lambdaDR)\n",
      "    iD=(lambdaDR/Lm)\n",
      "    iDpu[n-1]=iD/Ipeak_base\n",
      "    iQR=-(Lm/LR)**iQ\n",
      "    Ia=sqrt((iD**2+iQ**2)/2)\n",
      "    Iapu[n-1]=Ia/I_rated\n",
      "    we=wme-(RaR/LR)*(iQ/iD)\n",
      "    fe[n-1]=we/(2*pi)\n",
      "    Va_rms=sqrt(((Ra*iD-we*(LS-Lm**2/LR)*iQ)**2 +(Ra*iQ+ we*LS*iD)**2)/2)\n",
      "    Vapu[n-1]=Va_rms/Va_rated\n",
      "\n",
      "#Results:\n",
      "print \"The required plot is as shown:\"\n",
      "plot(iDpu,Iapu)\n",
      "plot(iDpu,Vapu,':')\n",
      "xlabel('i_D [per unit] ')\n",
      "ylabel('per unit')\n",
      "annotate('Ia',xy=(0.21,1.05))\n",
      "annotate('Va',xy=(0.21,0.85))\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The required plot is as shown:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MmYPJkyfDx8cHAQEB8PT01FPExFDUymtxt+Yu12EQPZFIJJBIJDp/Lqd10+ZqF2fPnh3R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\nEOPH4wETJgAnTrCd6zk5gKs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       "text": [
        "<matplotlib.figure.Figure at 0x27d0450>"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}