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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:603160d56b04457665b7cf5381387c06e4c52903d6f85f1c61a983bdc3c14ebc"
+ },
+ "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",
+ "%matplotlib 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": [
+ "The required plots are shown below:\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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DAABNDU1McpmEPensHQ/k6valsCYwderUXWfPnh326uu5ublW58+fD+zevftD6WsZGRmO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\npnpxYRhQmerFBS3V6/z98xi1dxR7YRp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E1o2PO1DUm6B7AhRFUWqM7glQFEWpMdoEKIqi\n1BhtAhRFUWqMNgGKoig1RpsARVGUGvt/5i5yreN7pjkAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x25c1f10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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IACiKYs2SmJj4Yr9+/W44OztnRkZGrmA6HjYsvXr1ynJzc7sql8vT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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x3529b90>"
+ ]
+ }
+ ],
+ "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",
+ "%matplotlib 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": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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YmBReuHBhxLsE8a+gOmhCkIYhqQDQnuR+L6PGxkb1uLi4MS1tZPz48SfeJYDO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\npcyJEyce7tu37592dnYZ165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+ "text": [
+ "<matplotlib.figure.Figure at 0x2ce0f10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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45aJ1zp49O4KiKDJ79uyIEydOfEI/V1hYqEv/vGbNmvU7d+5c2Nhx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\ng8APAMAwCPwAAAyDwA8AwDD/DxR4tH4eP493AAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x33b4a90>"
+ ]
+ }
+ ],
+ "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",
+ "%matplotlib 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": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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LPuhJW/DhLpBJ2C8sZzJJ1NbWypYuXfrRsGHD8ocNG5a/fPny9Xfv3u1j6ve4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\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x2594cd0>"
+ ]
+ },
+ {
+ "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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/wb59+xYzUTkkHtQEKFeXeUA9kav6kshVfZEw4DwJxAm4xwS/4R4T3Gez/SRa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\nYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x37f8250>"
+ ]
+ }
+ ],
+ "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": {}
+ }
+ ]
+} \ No newline at end of file