{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 23 : State Estimation In Power Systems" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 23.1, Page No 148" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "C1=0.02*100\n", "C2=0.05\n", "Fs=100\n", "S1=complex(0.41,-0.11)\n", "S2=complex(-0.4, 0.10)\n", "S3=complex(-.105,0.11)\n", "S4=complex(-.105,.11)\n", "S5=complex(0.14,-.14)\n", "S6=complex(-0.7,.35)\n", "Z12=complex(0.08,.24)\n", "Z23=complex(0.06,.18)\n", "Z31=complex(0.02,.06)\n", "Z21=Z12\n", "Z32=Z23\n", "Z13=Z31\n", "\n", "#Calculations\n", "W1=(50*10**(-6))/((C1*abs(S1)+(C2*(Fs)))**2)\n", "W2=(50*10**(-6))/((C1*abs(S2)+C2*(Fs))**2)\n", "W3=(50*10**(-6))/((C1*abs(S3)+C2*(Fs))**2)\n", "W4=(50*10**(-6))/((C1*abs(S4)+C2*(Fs))**2)\n", "W5=(50*10**(-6))/((C1*abs(S5)+C2*(Fs))**2)\n", "W6=(50*10**(-6))/((C1*abs(S6)+C2*(Fs))**2)\n", "print(\"W1= %.2f\" %W1)\t\t\t#Answers for W1,W2,W3,W4,W5,W6 in the book is wrongly Calculated\n", "print(\"W2= %.2f\" %W2)\t\n", "print(\"W3= %.2f\" %W3)\t\n", "print(\"W4= %.2f\" %W4)\t\n", "print(\"W5= %.2f\" %W5)\t\n", "print(\"W6= %.2f\" %W6)\t\n", "a1=W1/(abs(13)**2)\n", "[D]=diag([W1/(abs(Z13)**2)W2/(abs(Z31)**2)W3/(abs(Z12)**2)W4/(abs(Z21)**2)W5/(abs(Z23)**2)W6/(abs(Z32)**2)])\n", "A=[-1 0 11 0 -11 -1 0-1 1 00 1 -10 -1 1]\n", "B=[-1 01 01 -1-1 10 10 -1]\n", "b=[1-100-11]\n", "C=(B')*D#Assuming Transpose(B)D=C\n", "F=(B')*D*B#Assuming Transpose(B)*D*B=F\n", "G=(inv(F))*C#Assuming(BTDB)-1*(BT)*D=F\n", "E1=1.05\n", "E2=E1\n", "E3=E1\n", "invH=diag([Z31/E3Z13/E1Z12/E1Z21/E2Z23/E2Z32/E2])\n", "Sm=[.41+%i*.11-.4-%i*.1-.105-%i*.11.14+%i*.14.72+%i*.37-.7+%i*.35]\n", "EMo=invH*Sm\n", "a=EMo-b*E1\n", "E=G*a\n", "\n", "#Results\n", "print(E,\"E=\") #Answers differs due to wrong calculation of W1,W2,W3,W4,W5,W6" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i) For p.f unity , Eth= 1.34000+0.00000i\n", "(i) For p.f .8 , Eth= 1.59500+0.00000i\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 22.3, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "X=.625\n", "P=1.0\n", "Q=0.6\n", "V=1.0\n", "\n", "#Calculations\n", "Eth=V+(Q*X/V)+complex(P*X/V)\n", "Phase_Eth=math.degrees(math.atan(Eth.imag/Eth.real))\n", "\n", "#Results\n", "print(\"Eth=%.2f at an angle %.0f degrees\" %(abs(Eth),Phase_Eth))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Eth=2.00 at an angle 0 degrees\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 22.4, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "P=0.5\n", "toff=4.0\n", "\n", "#Calculations\n", "ton=(P*toff-0*toff)/(0.8-P)\n", "\n", "#Results\n", "print(\"Toff= 4min .\")\n", "print(\"ton(min.)=%.3f min.\" %ton)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Toff= 4min .\n", "ton(min.)=6.667 min.\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 22.6 Page No 150" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "V=1.0\n", "Qload=1.0*V\n", "Qcap=-0.75*V**2\n", "\n", "#Calculations\n", "Qnet=Qload+Qcap\n", "VS=1-0.75*2*V # voltage sensitivity\n", "\n", "#Results\n", "print(\"Voltage sensitivity=%.3f\" %VS)\n", "print(\"since the voltage sensitivity is negative,\\nvoltage regulation by tap changing will reduce net reactive load and improive voltage stability \")" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Voltage sensitivity=-0.500\n", "since the voltage sensitivity is negative,\n", "voltage regulation by tap changing will reduce net reactive load and improive voltage stability \n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 22.7, Page No 151" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "Y=complex(-10)\n", "n=1+0.1\n", "\n", "#Calculations\n", "Y1=n*(n-1)*Y\n", "Y2=(1-n)*Y\n", "\n", "#Results\n", "print(\"Y1= {0:.2f}+{1:.2f}i\".format(Y1.real, Y1.imag))\n", "print(\"Y2= {0:.2f}+{1:.2f}i\".format(Y2.real, Y2.imag))\n", "print(\"The shunt elements equal to a reactor of 1.1V1^2 size oin the primary side and a capacitive of sixe 1V2**2 on the secondary side\")" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Y1= -1.10+0.00i\n", "Y2= 1.00+-0.00i\n", "The shunt elements equal to a reactor of 1.1V1^2 size oin the primary side and a capacitive of sixe 1V2**2 on the secondary side\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 22.8, Page No 152" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "P=1.0\t\t#assuming\n", "S1=P/.95\t#For pf .95\n", "S2=P/.8\t\t#For pf .8\n", "\n", "#Calculations\n", "dMVA=(S2-S1)*100.0/P\t\t#Increase in MVA rating \n", "Q1=P*math.tan(math.radians(math.degrees(math.acos(0.95))))\t\t#Q for pf .95\n", "Q2=P*math.tan(math.radians(math.degrees(math.acos(0.8))))\t\t#Q for pf .8\n", "dPc=(Q2-Q1)*100.0/Q1\t\t#Percent additional Reactive Power Capability \n", "\n", "#Results\n", "print(\"Percent additional Reactive Power Capability is %.2f\" %dPc)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Percent additional Reactive Power Capability is 128.18\n" ] } ], "prompt_number": 17 } ], "metadata": {} } ] }