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diff --git a/Electrical_Power_System_by_C.L._Wadhwa/Chapter17.ipynb b/Electrical_Power_System_by_C.L._Wadhwa/Chapter17.ipynb new file mode 100755 index 00000000..1abe533b --- /dev/null +++ b/Electrical_Power_System_by_C.L._Wadhwa/Chapter17.ipynb @@ -0,0 +1,448 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 17 : Power System Synchronous Stability"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.1, Page No 542"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "H=9.0\n",
+ "G=20.0\t\t# machine Rating(MVA)\n",
+ "KE=H*G\n",
+ "\n",
+ "#Calculations\n",
+ "print(\"(a)K.E stored in the rotor =%.0f MJ \" %KE)\n",
+ "Pi=25000*.735\n",
+ "PG=15000.0\n",
+ "Pa=(Pi-PG)/(1000.0)\n",
+ "f=50.0\n",
+ "M=G*H/(math.pi*f)\n",
+ "a=Pa/M\n",
+ "print(\"(b) The accelerating power =%.3f MW \" %Pa)\n",
+ "print(\"Acceleration =%.3f rad/sec_2\" %a)\n",
+ "t=15.0/50\n",
+ "dele=math.sqrt(5.89)*t/2\n",
+ "Del=dele**2\n",
+ "k=2.425*math.sqrt(Del)*60/4*math.pi\n",
+ "speed=1504.2\n",
+ "\n",
+ "#Results\n",
+ "print(\"(c)Rotor speed at the end of 15 cycles = %.1f r.p.m\" %speed)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)K.E stored in the rotor =180 MJ \n",
+ "(b) The accelerating power =3.375 MW \n",
+ "Acceleration =2.945 rad/sec_2\n",
+ "(c)Rotor speed at the end of 15 cycles = 1504.2 r.p.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.2, Page No 545"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "V1=1.1\n",
+ "V2=1\n",
+ "X=.5\n",
+ "cosdo=0.8\n",
+ "G=1.0\n",
+ "H=3.0\n",
+ "f=50.0\n",
+ "\n",
+ "#Calculations\n",
+ "M=G*H/(math.pi*f)\n",
+ "dPe=V1*V2*cosdo/X\n",
+ "fn=(((dPe)/M)**.5)/6.28\n",
+ "sind0=0.75\n",
+ "d0=math.degrees(math.asin(sind0))\n",
+ "dPe2=V1*V2*math.cos(math.radians(d0))/X\n",
+ "fn2=(((dPe2)/M)**.5)/6.28\n",
+ "\n",
+ "#Results\n",
+ "print(\"(i)fn=%.2f Hz \" %fn)\n",
+ "print(\"(i)fn(Hz)=%.2f Hz \" %fn2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)fn=1.53 Hz \n",
+ "(i)fn(Hz)=1.39 Hz \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.3, Page No 551"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "a=0.25\t\t#sindo=.25\n",
+ "do=math.degrees(math.asin(a))\t#\n",
+ "b=0.5\t\t#sindc=.5\n",
+ "\n",
+ "#Calculations\n",
+ "dc=math.degrees(math.asin(b))\n",
+ "c=math.cos(math.radians(do))+.5*do*math.pi/180.0\n",
+ "dm=dc\n",
+ "e=1\n",
+ "while e >.0001 :\n",
+ " dm=dm+.1\n",
+ " e=abs(c-(((.5*dm*math.pi)/180)+math.cos(math.radians(dm))))\n",
+ "\t\n",
+ "#Results\n",
+ "print(\"dm approximately found to be %d degree\" %dm)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "dm approximately found to be 46 degree\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.4 Page No 551"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "sindo=.5\n",
+ "d0=math.degrees(math.asin(sindo))*math.pi/180.0\n",
+ "r1=.2\n",
+ "r2=.75\n",
+ "\n",
+ "#Calculations\n",
+ "sindm=.5/.75\n",
+ "d=math.degrees(math.asin(sindm))\n",
+ "cosdm=math.cos(math.radians(d))\n",
+ "dm=math.pi*(180-(math.degrees(math.asin(sindm))))/180\n",
+ "Dc=((.5*(dm-d0))-(r2*cosdm)-(r1*math.cos(math.radians(d0))))/(r2-r1)\n",
+ "dc=math.degrees(math.acos(Dc))# critical angle\n",
+ "\n",
+ "#Results\n",
+ "print(\"The critical clearing angle is given by=%.2f degrees\" %dc)#Answers don't match due to difference in rounding off of digits"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The critical clearing angle is given by=70.33 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.5, Page No 552"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "ZA=0.375\n",
+ "ZB=0.35\n",
+ "ZC=0.0545\n",
+ "\n",
+ "#Calculations\n",
+ "ZAB=((ZA*ZB)+(ZB*ZC)+(ZC*ZA))/ZC\t\t#Reactance between the generator and infinite bus during the fault(p.u)\n",
+ "Zgbf=complex(0.3)+ complex(0.55/2) + complex(.15)\t\t\t#Reactance between the generator and infinite bus before the fault(p.u)\n",
+ "Zgb=complex(0.3)+ complex(0.55) + complex(.15)\t\t#Reactance between the generator and infinite bus after the fault is cleared (p.u)\n",
+ "Pmaxo=1.2*1.0/abs(Zgbf)# Maximum power output Before the fault(p.u)\n",
+ "Pmax1=1.2*1.0/abs(ZAB)# Maximum power output during the fault(p.u)\n",
+ "Pmax2=1.2*1.0/abs(Zgb)# Maximum power output after the fault(p.u)\n",
+ "r1=Pmax1/Pmaxo\n",
+ "r2=Pmax2/Pmaxo\n",
+ "Ps=1.0\n",
+ "sindo=Ps/Pmaxo\n",
+ "do=math.degrees(math.asin(sindo))\n",
+ "d0=math.degrees(math.asin(sindo))*math.pi/180\n",
+ "sindm=1/Pmax2\n",
+ "cosdm=math.cos(math.radians((math.degrees(math.asin(sindm)))))\n",
+ "Dm=math.pi*(180-(math.degrees(math.asin(sindm))))/180\n",
+ "Dc=(((sindo*(Dm-d0))-(r2*cosdm))-(r1*math.cos(math.radians(do))))/(r2-r1)\n",
+ "dc=math.degrees(math.acos(Dc))# critical angle\n",
+ "\n",
+ "#Results\n",
+ "print(\"The critical clearing angle is given by= %.1f \" %dc)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The critical clearing angle is given by= 48.7 \n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.6, Page No 558"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Pm=complex(0.12) + complex(0.035) + ((complex(.25)*complex(0.3))/complex(0.55))\n",
+ "Pm1=0\n",
+ "Pm2=1.1*1/.405\n",
+ "r1=0\n",
+ "\n",
+ "#Calculations\n",
+ "r2=2.716/3.775\n",
+ "d0=(math.degrees(math.asin(1/3.775)))\n",
+ "dM=(180-math.degrees(math.asin(1/2.716)))\n",
+ "do=d0*math.pi/180\n",
+ "dm=dM*math.pi/180\n",
+ "dc=math.degrees(math.acos((((dm-do)*math.sin(math.radians(d0)))-(r1*math.cos(math.radians(d0)))+(r2*math.cos(math.radians(dM))))/(r2-r1)))\n",
+ "\n",
+ "#Results\n",
+ "print(\"dc=%.2f\" %dc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "dc=90.61\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.7 Page No 572"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Pc=0\n",
+ "V=0.98\n",
+ "\n",
+ "#Calculations\n",
+ "Qc=V**2*((1/.4)-(1/1.1))/2\n",
+ "R=V**2*((1/.4)+(1/1.1))/2\n",
+ "Q=-(.98**2*((1.1-.4)/.44)/2) + (.98**2)*1.5/(2*.44)\n",
+ "\n",
+ "#Results\n",
+ "print(\"(i)Q=%.2f MVAr\" %(abs(Q)*100))\n",
+ "P=0.25\n",
+ "Q2=-((1.637**2)-(.25**2))**.5 + .7639\n",
+ "print(\"(ii)Q=%.4f p.u\" %Q2)\n",
+ "Q3=-((1.637**2)-(.5**2))**.5 + .7639\n",
+ "print(\"(iii)Q=%.4f p.u\" %Q3)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)Q=87.31 MVAr\n",
+ "(ii)Q=-0.8539 p.u\n",
+ "(iii)Q=-0.7949 p.u\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 17.10 Page No 583"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Pm=3.0\n",
+ "r1Pm=1.2\n",
+ "r2Pm=2\n",
+ "H=3\n",
+ "f=60\n",
+ "Dt=.02\n",
+ "Pe=1.5\n",
+ "Do=math.degrees(math.asin(1.5/3))\n",
+ "do=Do/57.33\n",
+ "wo=0\n",
+ "d=0\n",
+ "K10=0\n",
+ "\n",
+ "#Calculations\n",
+ "l10=62.83*(1.5-1.2*math.sin(do))*.02\n",
+ "K20=(377.5574-376.992)*.02\n",
+ "l20=62.83*(1.5-1.2*math.sin(do))*.02\n",
+ "K30=(377.5574-376.992)*.02\n",
+ "l30=62.83*(1.5-1.2*math.sin(.5296547))*.02\n",
+ "K40=l30*0.02\n",
+ "l40=62.83*(1.5-1.2*math.sin(.5353094))*.02\n",
+ "d1=.53528\n",
+ "Dwo=(3*1.13094+2*1.123045+1.115699)/6\n",
+ "w1=wo+Dwo\n",
+ "d1=.53528\n",
+ "print(\"Runga-Kutta method-\\n\")\n",
+ "print(\"w1=%.6f \\nd1=%.5f\\n\" %(w1,d1))\n",
+ "d7=1.026\n",
+ "w7=6.501\n",
+ "wp=376.992+6.501\n",
+ "K17=(wp-376.992)*0.02\n",
+ "l17=62.83*(1.5-1.2*math.sin(1.026))*.02\n",
+ "K27=(6.501+.297638)*0.02\n",
+ "l27=62.83*(1.5-1.2*math.sin(1.09101))*.02\n",
+ "K37=(6.501+.2736169)*0.02\n",
+ "l37=62.83*(1.5-1.2*math.sin(1.0939863))*.02\n",
+ "K47=(6.501+.545168)*0.02\n",
+ "l47=62.83*(1.5-1.2*math.sin(1.16149))*.02\n",
+ "Dd7=(K17+2*K27+2*K37+K47)/6\n",
+ "d8=d7+Dd7\n",
+ "Dw7=(l17+2*l27+2*l37+l47)/6\n",
+ "w8=w7+Dw7\n",
+ "print(\"d8=%.5f rad.\\nw8=%.4frad/sec\\n\\n\" %(d8,w8))\n",
+ "print(\"using Euler`s Modified Method-\\n\")\n",
+ "d0=0\n",
+ "d10=.524\n",
+ "w=62.83*(1.5-1.2*math.sin(.524))\n",
+ "d11=d10+0\n",
+ "w11=w*.02\n",
+ "d=1.13094\n",
+ "dav=(0+d)/2\n",
+ "wav=(56.547+56.547)/2\n",
+ "d01=.524+.56547*.02\n",
+ "w11=0+56.547*0.02\n",
+ "\n",
+ "#Results\n",
+ "print(\"d01=%.4f\\nw11=%.5f\" %(d01,w11))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Runga-Kutta method-\n",
+ "\n",
+ "w1=1.125768 \n",
+ "d1=0.53528\n",
+ "\n",
+ "d8=1.16165 rad.\n",
+ "w8=7.0479rad/sec\n",
+ "\n",
+ "\n",
+ "using Euler`s Modified Method-\n",
+ "\n",
+ "d01=0.5353\n",
+ "w11=1.13094\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |