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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter3, Single Phase Controlled Rectifiers"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.3.1: page 3-11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import symbols, simplify\n",
      "from math import pi, sin, cos, sqrt\n",
      "#form factor,ripple factor ,transformation utilization factor and peak inverse voltage\n",
      "Vm=1 #assume\n",
      "R=1 #assume\n",
      "alfa = pi/3 # radian\n",
      "Vm = symbols('Vm', real = True)\n",
      "Vldc = Vm/2/pi*(1+cos(alfa))\n",
      "Vlrms = Vm*sqrt(1/4/pi*(pi-pi/3)+1/4/pi*sin(2*pi/3))\n",
      "ff=Vlrms/Vldc\n",
      "print \"part (a):\"\n",
      "print \"form factor is\",round(ff,3),\"or\",round(ff*100,1),\"%\"\n",
      "#form factor is calculated wrong in the textbook\n",
      "print \"part (b)\"\n",
      "rf=sqrt(ff**2-1) #\n",
      "print \"ripple factor is\",round(rf,2),\"or\",round(rf*100),\"%\"\n",
      "#ripple factor is calculated wrong in the textbook\n",
      "Vs=Vm/(sqrt(2)) #rms secondary voltage\n",
      "Is=Vlrms/R #\n",
      "TUF=((Vldc**2)/R)/(Vs*Is) #\n",
      "print \"part (c)\"\n",
      "print \"transformation utilization factor is\",round(TUF,3),\"or\",round(TUF*100,1),\"%\"\n",
      "#transformation utilization factor is calculated wrong in the textbook\n",
      "R=1 #assume\n",
      "Vm=1 #assume\n",
      "print \"part (d)\"\n",
      "print \"PIV=Vm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a):\n",
        "form factor is 2.033 or 203.3 %\n",
        "part (b)\n",
        "ripple factor is 1.77 or 177.0 %\n",
        "part (c)\n",
        "transformation utilization factor is 0.166 or 16.6 %\n",
        "part (d)\n",
        "PIV=Vm\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.4.1: page 3-25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "% matplotlib inline\n",
      "from numpy import array, sqrt, pi, nditer, cos, sin\n",
      "#plot the variation\n",
      "vsrms=230 #volts\n",
      "vm=sqrt(2)*vsrms #volts\n",
      "alpha=array([0,30, 60, 90, 120, 150, 180]) #degree\n",
      "x=array([0,(30*(pi/180)),(60*(pi/180)),(90*(pi/180)),(120*(pi/180)),(150*(pi/180)),(180*(pi/180))])\n",
      "\n",
      "def cur(alpha,x):\n",
      "    it = nditer([alpha,x,None, None])\n",
      "    for a,b,c,d in it:\n",
      "        c[...]=(vm/pi)*(1+cos(a*pi/180)) #\n",
      "        d[...]=vsrms*((1/pi)*(pi-b+(sin(2*b))/2))**(1/2) \n",
      "    return it.operands\n",
      "vldc = cur(alpha,x)[2]\n",
      "vlms = cur(alpha,x)[3]\n",
      "from matplotlib.pyplot import subplot, xlabel, ylabel, title, plot, ylim, show\n",
      "%matplotlib inline\n",
      "subplot(1,3,1)\n",
      "xlabel(\"alpha\") #\n",
      "ylabel(\"Vldc\") #\n",
      "title('(a) Variation of average load voltage')\n",
      "plot(alpha,vldc) #\n",
      "subplot(1,3,3)\n",
      "xlabel(\"alpha\") #\n",
      "xlabel(\"Vlrms\") #\n",
      "title('(b) Variation of RMS load voltage')\n",
      "plot(alpha,vlms) #\n",
      "ylim(40,250)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:14: RuntimeWarning: invalid value encountered in double_scalars\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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wK3cfHv/uBjCzLYAjgC3ia35nZjX3+QcPhmHDwiHmIpItxx0H11wDn36adiRS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\nERGREqhgioiIlEAFU0REpAT/H/mNE3klMROZAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f1219c765d0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.4.5: page 3-38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import pi, sqrt, degrees, acos\n",
      "from numpy import arange\n",
      "#delay angle,rms , averae output current ,average and rms thyristor current\n",
      "Vrms=120 #RMS VOLTAGE \n",
      "R=10 #in ohms\n",
      "Vldc= (0.25*(2*sqrt(2)*Vrms))/pi #in volts\n",
      "csd= (Vldc*pi)/(sqrt(2)*Vrms) #\n",
      "alpha= degrees(acos(csd-1)) #\n",
      "print \"part (a)\"\n",
      "print \"delay angle = %0.2f degree\" %alpha\n",
      "Vrms=120 #RMS VOLTAGE \n",
      "Vm=sqrt(2)*Vrms #assume\n",
      "t=arange(2*pi/3,pi,0.1) \n",
      "Vlms=((Vm/(sqrt(2)))*(((1/pi)*((pi-(2*pi)/3)+sin(4*pi/6*pi/180))))**(1/2)) \n",
      "Vldc= (0.25*(2*sqrt(2)*Vrms))/pi #in volts\n",
      "Ildc=Vldc/R #average load current in ampere\n",
      "Ilms=Vlms/R # rms load current in ampere\n",
      "print \"part (b)\"\n",
      "print \"rms load current = %0.2f A\" %Ilms\n",
      "print \"average load current = %0.2f A\" %Ildc\n",
      "#rms load current is calculated  wrong in the textbook\n",
      "Im=Vm/R #\n",
      "from sympy.mpmath import quad, sin\n",
      "f1 = lambda omega_t : Im*sin(omega_t)\n",
      "Ith = (1/(2*pi)*(quad(f1,[alpha*pi/180,pi]))) # A (calculating integration)\n",
      "f2 = lambda omega_t : (Im*sin(omega_t))**2\n",
      "Ithrms = sqrt(1/(2*pi)*(quad(f2,[alpha*pi/180,pi]))) # A (calculating integration)\n",
      "print \"part (c)\"\n",
      "print \"average thyristor current = %0.2f A\" %Ith\n",
      "print \"rms thyristor current = %0.2f A\" %Ithrms"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a)\n",
        "delay angle = 120.00 degree\n",
        "part (b)\n",
        "rms load current = 7.05 A\n",
        "average load current = 2.70 A\n",
        "part (c)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "average thyristor current = 1.35 A\n",
        "rms thyristor current = 3.75 A\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.6.1: page 3-69 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#average load voltage,rms load voltage,average and rms load currents ,form factor and ripple factor\n",
      "R=10 #IN OHMS\n",
      "r=10 #IN OHMS\n",
      "Vi=230 #in volts\n",
      "alpha=60 #fiirng angle in degree \n",
      "Vm=Vi*sqrt(2) #in voltas\n",
      "Vldc=((Vm)/pi)*(1+cos(alpha*pi/180)) #average load voltgae\n",
      "print \"part (a)\"\n",
      "print \"average load voltage = %0.2f Volts\" %Vldc\n",
      "print \"part (b)\"\n",
      "r=10 #IN OHMS\n",
      "Vi=230 #in volts\n",
      "alpha=60 #fiirng angle in degree \n",
      "Vm=Vi*sqrt(2) #in voltas\n",
      "Vlms=((Vm/(sqrt(2)))*(((pi-pi/3)+(sin(2*pi/3*pi/180))/2)/pi)**(1/2)) #\n",
      "print \"rms load voltage = %0.2f V\" %Vlms\n",
      "#rms voltage is calculated wrong in the textbook\n",
      "print \"part (c)\"\n",
      "Ildc=Vldc/R # in amperes\n",
      "Irms=Vlms/R # in amperes\n",
      "print \"rms load current = %0.2f A\" %Irms\n",
      "print \"average load current = %0.2f A\" %Ildc\n",
      "#rms load current is wrong in the textbook\n",
      "print \"part (d)\"\n",
      "ff=Vlms/Vldc \n",
      "print \"form factor is =\",round(ff,2),\"or\",round(ff*100,2),\"%\"\n",
      "rf=sqrt(ff**2-1) #\n",
      "print \"ripple factor =\",round(rf,2),\"or\",round(rf*100,2),\"%\"\n",
      "#form factor and ripple factor is calculated wrong in the textbook"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a)\n",
        "average load voltage = 155.30 Volts\n",
        "part (b)\n",
        "rms load voltage = 188.61 V\n",
        "part (c)\n",
        "rms load current = 18.86 A\n",
        "average load current = 15.53 A\n",
        "part (d)\n",
        "form factor is = 1.21 or 121.45 %\n",
        "ripple factor = 0.69 or 68.91 %\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7.1: page 3-72"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import array, nditer, sqrt, pi, cos\n",
      "from __future__ import division\n",
      "#device ratings\n",
      "Io=25 #in amperes\n",
      "Vsrms=120 # in colts\n",
      "Vm=sqrt(2)*Vsrms # in volts\n",
      "alpha=array([0,60,90,135,180])\n",
      "\n",
      "def volt(alpha):\n",
      "    it = nditer([alpha, None])\n",
      "    for a,b in it:\n",
      "        \n",
      "        b[...]=Vm/pi*(1+cos(a*pi/180))\n",
      "    return it.operands[1]\n",
      "vldc = volt(alpha)\n",
      "print \"alpha :   \",\n",
      "for a in nditer([alpha]):\n",
      "    print a,'\\t',\n",
      "print \"\"\n",
      "\n",
      "print \"VLdc(V) : \",\n",
      "for a in nditer([vldc]):\n",
      "    print a,'\\t',\n",
      "print \"\"\n",
      "\n",
      "PIV=Vm #peak inverse voltage\n",
      "Iascr=Io/2 #scr average currentin ampere\n",
      "Iadod=Io #average diode current in amperes\n",
      "Ipscr=Iascr #peak current rating for SCR in amperes\n",
      "Ipdod=Iadod #peak current rating for diode in amperes\n",
      "print \"scr average current = %0.2f A\" %Iascr\n",
      "print \"Average diode current = %0.2f A\" %Iadod\n",
      "print \"Peak current rating for SCR = %0.2f A\" %Ipscr\n",
      "print \"Peak current rating for diode = %0.2f A\" %Ipdod"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "alpha :    0 \t60 \t90 \t135 \t180 \t\n",
        "VLdc(V) :  108 \t81 \t54 \t15 \t0 \t\n",
        "scr average current = 12.50 A\n",
        "Average diode current = 25.00 A\n",
        "Peak current rating for SCR = 12.50 A\n",
        "Peak current rating for diode = 25.00 A\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7.2: page 3-73"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin\n",
      "#Vldc,Vn,Vlrms,HF,DF and PF\n",
      "Vsrms=120 #in volts\n",
      "alpha=pi/2 #\n",
      "vm=sqrt(2)*Vsrms #\n",
      "vldc=((sqrt(2)*Vsrms)/(pi))*(1+cos(alpha)) #in volts\n",
      "vldcm=(2*vm)/(pi) #in volts\n",
      "vn=vldc/vldcm #normalised average output voltage in volts\n",
      "x=((1/pi)*((pi-alpha)+(sin((2*alpha)))/2))**(1/2) #\n",
      "vlrms=((vm/sqrt(2))*x) #RMS load voltage in volts\n",
      "Io=1 #assume\n",
      "Isrms=Io*(1-(alpha/pi))**(1/2) #in amperes\n",
      "Is1rms=((2*sqrt(2))*Io*cos(alpha/2))/(pi) #in amperes\n",
      "HF=((Isrms/Is1rms)**2-1)**(1/2) #Harmonic Fator is\n",
      "DF=cos(alpha/2) #Displacement factor\n",
      "PF=(Is1rms/Isrms)*(DF) #power factor\n",
      "print \"average output voltage, Vldc = %0.2f V\" %round(vldc)\n",
      "print \"Normalised average output voltage, Vn = %0.2f V\" %vn\n",
      "print \"RMS load voltage, Vlrms = %0.2f V\" %vlrms\n",
      "print \"Harmonic factor, HF = %0.2f %%\" %(HF*100)\n",
      "print \"Displacement factor, DF = %0.2f %%\" %(DF*100)\n",
      "print \"Power factor, PF = %0.4f lagging\" %PF"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "average output voltage, Vldc = 54.00 V\n",
        "Normalised average output voltage, Vn = 0.50 V\n",
        "RMS load voltage, Vlrms = 84.85 V\n",
        "Harmonic factor, HF = 48.34 %\n",
        "Displacement factor, DF = 70.71 %\n",
        "Power factor, PF = 0.6366 lagging\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7.5: page 3-77"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import degrees, acos\n",
      "#alpha\n",
      "print \"part (a)\"\n",
      "vc=135 #in volts\n",
      "vs=220 #in vlts\n",
      "rl=0.5 #in ohms\n",
      "io=10 #in ampeeres\n",
      "vm=sqrt(2)*vs #\n",
      "vldc=io*rl+vc #\n",
      "alpha=degrees(acos((vldc*pi)/(2*vm))) #\n",
      "print \"alpha = %0.f degree \"%alpha\n",
      "print \"part (b)\"\n",
      "vc=145 #in volts\n",
      "vs=220 #in vlts\n",
      "rl=0.5 #in ohms\n",
      "io=10 #in ampeeres\n",
      "vm=sqrt(2)*vs #\n",
      "vldc=io*rl-vc #\n",
      "alpha=degrees(acos((vldc*pi)/(2*vm))) #\n",
      "print \"alpha = %0.f degree \"%(alpha)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a)\n",
        "alpha = 45 degree \n",
        "part (b)\n",
        "alpha = 135 degree \n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 3.7.6: page 3-79"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#average output voltage,supply rms current ,\n",
      "#supply fundamental current current,displacement factor,supply factor and supply harmonic factor\n",
      "Vsrms=220 #in volts\n",
      "alpha=pi/3 #\n",
      "vm=sqrt(2)*Vsrms #\n",
      "vldc=((2*vm)/(pi))*(cos(alpha)) #in volts\n",
      "vldcm=(2*vm)/(pi) #in volts\n",
      "vn=vldc/vldcm #normalised average output voltage in volts\n",
      "x=((1/pi)*((pi-alpha)+(sin((2*alpha)))/2))**(1/2) #\n",
      "vlrms=((vm/sqrt(2))*x) #RMS load voltage in volts\n",
      "Io=1 #assume\n",
      "Isrms=Io*(1-(alpha/pi))**(1/2) #in amperes\n",
      "Is1rms=((2*sqrt(2))*Io*cos(alpha/2))/(pi) #in amperes\n",
      "HF=((Isrms/Is1rms)**2-1)**(1/2) #Harmonic Fator is\n",
      "DF=cos(alpha/2) #Displacement factor\n",
      "PF=(Is1rms/Isrms)*(DF) #power factor\n",
      "print \"part (a)\"\n",
      "print \"average output voltage, Vldc = %0.2f V\" %round(vldc)\n",
      "print \"part (b)\"\n",
      "print \"due to exact 50% duty cycle the rms value of supply current Isrms=Io\"\n",
      "Io=1 #assume\n",
      "Isrms=Io #in amperes\n",
      "Is1rms=((2*sqrt(2))*Io)/(pi) #in amperes\n",
      "print \"part (c)\"\n",
      "print \"supply fundamental current =\",Is1rms,\"Io \"\n",
      "print \"part (d)\"\n",
      "DF=cos(alpha) #\n",
      "print \"displacement factor =\",DF\n",
      "print \"part (e)\"\n",
      "SPF=Is1rms*DF #\n",
      "print \"supply power factor = %0.2f lagging \" %SPF\n",
      "print \"part (f)\"\n",
      "HF=(((Isrms/Is1rms)**2)-1)**(1/2) #\n",
      "print \"supply harmonic factor = %0.2f %%\" %(HF*100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a)\n",
        "average output voltage, Vldc = 99.00 V\n",
        "part (b)\n",
        "due to exact 50% duty cycle the rms value of supply current Isrms=Io\n",
        "part (c)\n",
        "supply fundamental current = 0.900316316157 Io \n",
        "part (d)\n",
        "displacement factor = 0.5\n",
        "part (e)\n",
        "supply power factor = 0.45 lagging \n",
        "part (f)\n",
        "supply harmonic factor = 48.34 %\n"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}