{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 10: Introduction to Power Electronics"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.5, Page number: 508"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%pylab inline\n",
      "from pylab import *\n",
      "import numpy as np\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "w=2*pi*60                               #frequency of voltage(Hz)\n",
      "R=10                                    #ohm\n",
      "C=0.01                                  #F\n",
      "Vo=120*sqrt(2)                          #maximum voltage(V)\n",
      "Nmax=800\n",
      "tau=R*C                                 #time constant(s)\n",
      "\n",
      "#Calculations:\n",
      "# diode = 1 when rectifier bridge is conducting\n",
      "\n",
      "diode=1\n",
      "t=[0]*801\n",
      "vs=[0]*801\n",
      "vrect=[0]*801\n",
      "vR=[0]*801\n",
      "iB=[0]*801\n",
      "\n",
      "t=[0]*801\n",
      "for n in range(1,Nmax+2,1):\n",
      "    t[n-1] = (2.5*pi/w)*(n-1)/Nmax\n",
      "    vs[n-1]=Vo*math.cos(w*t[n-1])\n",
      "    vrect[n-1]=abs(vs[n-1])\n",
      "#if the rectifier bridge is ON:\n",
      "    if diode==1:\n",
      "        vR[n-1]=vrect[n-1]\n",
      "        if (w*t[n-1])<=(pi/2):\n",
      "            iB[n-1]=vR[n-1]-Vo*C*w*math.sin(w*t[n-1])\n",
      "        elif (w*t[n-1])<=3*pi/2:\n",
      "            iB[n-1]=vR[n-1]/R+Vo*C*w*math.sin(w*t[n-1])\n",
      "        else:\n",
      "            iB[n-1]=vR[n-1]/R-Vo*C*w*math.sin(w*t[n-1])\n",
      "        if iB[n-1]<0:\n",
      "            diode=0\n",
      "            toff=t[n-1]\n",
      "            Voff=vrect[n-1]\n",
      "    else:\n",
      "        vR[n-1]=Voff*exp(-(t[n-1]-toff/tau))\n",
      "        iB[n-1]=0\n",
      "        if (vrect[n-1]-vR[n-1])>0:\n",
      "            diode=1\n",
      "\n",
      "\n",
      "\n",
      "#Results:\n",
      "iR=(1/R)*np.array(vR)\n",
      "plot(1000*np.array(t),vR)\n",
      "xlabel('time [msec]')\n",
      "ylabel('voltage [V]')\n",
      "xlim(0,22)\n",
      "ylim(0,180)\n",
      "plot(1000*np.array(t),vrect,'--')\n",
      "grid()\n",
      "print \"The required plots are shown below:\"\n",
      "show()\n",
      "plot(1000*np.array(t),iR)\n",
      "xlabel('time [msec]')\n",
      "ylabel('source current [A]')\n",
      "xlim(0 ,22)\n",
      "ylim(-50,250)      \n",
      "plot(1000*np.array(t),1.5*np.array(iB),'--')\n",
      "grid()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "The required plots are shown below:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ibCiGqVKvAU4DsP/GfszznydsKIbxuYNUw2K96m0CQpzAsLS0REFBASwsLJCf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\nOE6H/T8o9Q6nwzgdWAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f054c060710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CsWppbSLgX0cGLlysTua8ZMS8lJExL4eaQXV1NVauXIlJkyZh0qRJWL16Ncxm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\niIjYDIiICGwGREQENgMiIgK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       "text": [
        "<matplotlib.figure.Figure at 0x2986d90>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.6, Page number: 522"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%pylab inline\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "w=2*pi*60                               #Angular freq of voltage(rad/sec)\n",
      "Vo=230*sqrt(2)                          #volt\n",
      "R=5.6                                   #Resistance(ohm)\n",
      "\n",
      "#Calculations:\n",
      "Ls=[0]*101\n",
      "tc=[0]*101\n",
      "Idc=[0]*101\n",
      "for n in range(1,101,1):\n",
      "    Ls[n-1]=n*10**-3\n",
      "    Idc[n-1]=2*Vo/(pi*R+2*w*Ls[n-1])\n",
      "    tc[n-1]=(1/w)*acos(1-(2*Idc[n-1]*w*Ls[n-1])/Vo)\n",
      "\n",
      "#Results:\n",
      "plot(1000*np.array(Ls),Idc,'g.')\n",
      "xlabel('Commutating inductance Ls [mH]')\n",
      "ylabel('Idc [A]')\n",
      "title('Load current,Idc vs Commutating inductance,Ls')\n",
      "show()\n",
      "plot(1000*np.array(Ls),1000*np.array(tc),'g.')\n",
      "xlabel('Commutating inductance L [mH]')\n",
      "ylabel('tc [msec]')\n",
      "title('Commutating Inductance,Ls vs time,tc')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['fmod', 'sinh', 'trunc', 'tan', 'gamma', 'cosh', 'radians', 'modf', 'expm1', 'ldexp', 'linalg', 'random', 'frexp', 'ceil', 'isnan', 'copysign', 'cos', 'degrees', 'tanh', 'fabs', 'sqrt', 'hypot', 'power', 'log', 'log10', 'info', 'log1p', 'floor', 'fft', 'pi', 'exp', 'isinf', 'e', 'sin']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ExEQAQGJiIsLDw7UZRoum3oVkZmLGAWci0poGtRCKiopgZmaGNm3aALh9nYSS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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2c18b90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AgAHFlTP4iYiqzayDv8rKGfxERNVm1qdzEhGR+amTs3pqit+0RURUe+rFiJ/f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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2981fd0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.7, Page number: 528"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%pylab inline\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "R=12.5*10**-3                               #ohm\n",
      "L=1.2                                       #H\n",
      "Vo=15                                       #volt\n",
      "w=120*pi                                    #angular freq(Hz)\n",
      "Idc=35                                      #DC current(A)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#for part (a):\n",
      "theta=[0]*1301\n",
      "t=[0]*1301\n",
      "vL=[0]*1301\n",
      "vs=[0]*1301\n",
      "\n",
      "Vdc_a=R*Idc                                 #Dc voltage(V)\n",
      "P=Vdc_a*Idc                                 #Power\n",
      "alpha_da = acos(pi*R*Idc/(2*Vo)) ;    #delay angle\n",
      "for n in range(1,1301,1):                 #loop for calculating load voltage\n",
      "    theta[n-1]=2*pi*(n-1)/1000\n",
      "    t[n-1]=theta[n-1]/w\n",
      "    vs[n-1]=Vo*sin(theta[n-1])\n",
      "    if theta[n-1]<alpha_da:\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    elif (theta[n-1]<pi+alpha_da):\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    elif theta[n-1]<2*pi+alpha_da:\n",
      "        vL[n-1]=vs[n-1]\n",
      "    elif theta[n-1]<3*pi+alpha_da:\n",
      "        vL[n-1]=vs[n-1]\n",
      "    elif theta[n-1]<4*pi+alpha_da:\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    else:\n",
      "        vL[n-1]=vs[n-1]\n",
      "\n",
      "figure(1)\n",
      "plot(1000*np.array(t),vL,'g.')\n",
      "xlabel('time [msec]')\n",
      "ylabel('Load voltage [V]')\n",
      "grid()\n",
      "show()\n",
      "\n",
      "\n",
      "#part(b):\n",
      "alpha_db=0.9*pi                             #delay angle\n",
      "Vdc_b=(2*Vo/pi)*cos(alpha_db)          #new dc voltage(V)\n",
      "tau=L/R                                     #time constant(s)\n",
      "imo=Idc                                     #Initial curent(A)\n",
      "tzero=-tau*log((-Vdc_b/R)/(imo-Vdc_b/R))\n",
      "for n in range(1,1301,1):\n",
      "    theta[n-1]=2*pi*(n-1)/1000\n",
      "    t[n-1]=theta[n-1]/w\n",
      "    vs[n-1]=Vo*sin(theta[n-1])\n",
      "    if theta< alpha_db:\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    elif (theta[n-1]<pi+alpha_db):\n",
      "        vL[n-1]=vs[n-1]\n",
      "    elif theta[n-1]<2*pi+alpha_db:\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    elif theta[n-1]<3*pi+alpha_db:\n",
      "        vL[n-1]=vs[n-1]\n",
      "    elif theta[n-1]<4*pi+alpha_db:\n",
      "        vL[n-1]=-vs[n-1]\n",
      "    else:\n",
      "        vL[n-1]=vs[n-1]\n",
      "\n",
      "#Results:\n",
      "figure(2)\n",
      "plot (1000*np.array(t), vL,'g.')\n",
      "xlabel('time [msec] ')\n",
      "ylabel('Load voltage [V]')\n",
      "print \"part (a):\"\n",
      "print \"\\n Vdc_a=\",round(1000*Vdc_a,2),\"mV\"\n",
      "print \"\\n Power=\",round(P),\"W\"        \n",
      "print \"\\n alpha_d=\",round((180/pi)*alpha_da,1),\"degrees\"\n",
      "print \"\\n part (b):\"\n",
      "print \"\\n alpha_d=\",round((180/pi)*alpha_db,1),\"degrees\"   \n",
      "print \"\\n Vdc_b=\",round(Vdc_b,1),\"V\"\n",
      "print \"\\n Current will reach zero at\",round(tzero,1),\"sec\"\n",
      "grid()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['fmod', 'cosh', 'sinh', 'trunc', 'tan', 'gamma', 'degrees', 'radians', 'sin', 'expm1', 'ldexp', 'isnan', 'frexp', 'ceil', 'copysign', 'cos', 'tanh', 'fabs', 'sqrt', 'hypot', 'log', 'log10', 'pi', 'log1p', 'floor', 'modf', 'exp', 'isinf', 'e']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0J06fPo0NGzaYfZ0gCHjppZcQGxsLANDr9UhNTTXOh279l0NGRgb07+hx9Z9X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\nhNj0/wELMsFZawmOEgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1e16bd0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a):\n",
        "\n",
        " Vdc_a= 437.5 mV\n",
        "\n",
        " Power= 15.0 W\n",
        "\n",
        " alpha_d= 87.4 degrees\n",
        "\n",
        " part (b):\n",
        "\n",
        " alpha_d= 162.0 degrees\n",
        "\n",
        " Vdc_b= -9.1 V\n",
        "\n",
        " Current will reach zero at 4.5 sec\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jOp0OL730EsrLy1FeXm4XIIg20Cwn/8gpzEFmQSayP8722XRVmuWkLi6DxIYN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\nCCHEqf8PfsUAKezuFf4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2983e10>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.8, Page number: 533"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import *\n",
      "import math\n",
      "\n",
      "#Variable declaration:\n",
      "f=60                                #Hz\n",
      "Vrms=35                             #rms voltage of waveform\n",
      "Ra=3.5                              #Armature resistance(ohm)\n",
      "La=0.175                            #H\n",
      "no=8000                             #No load speed(r/min)\n",
      "Va=50                               #armature voltage(V)\n",
      "\n",
      "#Calculations:\n",
      "Edc,alphad=symbols('Edc alphad')\n",
      "Vdc=Edc                                 #at no load, Vdc=Edc\n",
      "Edc=round(float(2*sqrt(2)*(Vrms/math.pi)),2)*cos(alphad)\n",
      "n=Edc*float(no/50)\n",
      "\n",
      "#Results:\n",
      "print \"Speed at no-load =\",n,\" r/min      (where 0 <= alphad <= pi/2)\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Speed at no-load = 5041.6*cos(alphad)  r/min      (where 0 <= alphad <= pi/2)\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.9, Page number: 537"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "Vll_rms=460                                 #rms voltage,line-to-line(V)\n",
      "R=68                                        #resistance of load\n",
      "Im=2.5                                      #magnet current(A)\n",
      "\n",
      "#Calculations:\n",
      "Vdc_max=3*sqrt(2)*Vll_rms/pi\n",
      "Idc_max=Vdc_max/R\n",
      "Vdc=Im*R\n",
      "alpha=acos(pi*Vdc/(3*sqrt(3)*Vll_rms))\n",
      "\n",
      "#Results:\n",
      "print \"(a) Maximum dc voltage:\",round(Vdc_max),\"V\"\n",
      "print \"\\n  Maximum dc current:\",round(Idc_max,1),\"V\"\n",
      "print \"\\n(b) Delay angle alpha:\",round(math.degrees(round(alpha,1)),1),\"degrees\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Maximum dc voltage: 621.0 V\n",
        "\n",
        "  Maximum dc current: 9.1 V\n",
        "\n",
        "(b) Delay angle alpha: 74.5 degrees\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.10, Page number: 541"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "T=20*10**-3                                 #Time period(sec) \n",
      "p=4                                         #no. of poles\n",
      "delta=0.44                                  #ON- time fraction\n",
      "Vo=125                                      #DC supply voltage(V)\n",
      "\n",
      "\n",
      "#Calculation:\n",
      "fc=1/T\n",
      "ns=(120*fc/p)\n",
      "Va_peak=(4*Vo*sin(delta*pi))/pi\n",
      "Vll_rms=sqrt(3/2)*Va_peak\n",
      "\n",
      "#Results:\n",
      "print \"(a) Frequency:\",fc,\"Hz\"\n",
      "print \"\\n    Synchronous speed:\",ns,\"r/min\"\n",
      "print \"\\n(b) Rms amplitude of line-to-line voltage:\",round(Vll_rms,0),\"V\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Frequency: 50.0 Hz\n",
        "\n",
        "    Synchronous speed: 1500.0 r/min\n",
        "\n",
        "(b) Rms amplitude of line-to-line voltage: 191.0 V\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 10.13, Page number: 547"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "Vo=48                               #Load voltage(V)\n",
      "R=3.7                               #Resistance of load(ohm)\n",
      "L=.32                               #Inductance of laad(H)\n",
      "D=0.8                               #Duty cycle\n",
      "f=1000                              #Hz\n",
      "\n",
      "#Calculations:\n",
      "iL_avg=(2*D-1)*Vo/R\n",
      "T=1/f\n",
      "tau=L/R\n",
      "iL_min=((-Vo/R)*(1-2*exp(-T*(1-D)/tau)+exp(-T/tau)))/(1-exp(-T/tau))\n",
      "iL_max=(Vo/R)*(1-2*exp(-D*T/tau)+exp(-T/tau))/(1-exp(-T/tau))\n",
      "\n",
      "#since T/tau << 1, so using 10.32 in e.g. given.\n",
      "del_iL=(2*Vo)*T*D*(1-D)/(R*tau)\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Avg load current:\",round(iL_avg,2),\"A\"\n",
      "print \"Minimum load current:\",round(iL_min,2),\"A\"\n",
      "print \"Maximum load current\",round(iL_max,2),\"A\"\n",
      "print \"Current ripple:\",round(del_iL,2),\"A\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Avg load current: 7.78 A\n",
        "Minimum load current: 7.76 A\n",
        "Maximum load current 7.81 A\n",
        "Current ripple: 0.05 A\n"
       ]
      }
     ],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}