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diff --git a/Elements_of_Power_system/Chapter_7.ipynb b/Elements_of_Power_system/Chapter_7.ipynb new file mode 100755 index 00000000..fba9cc63 --- /dev/null +++ b/Elements_of_Power_system/Chapter_7.ipynb @@ -0,0 +1,454 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:7a4739840eca82c1ce9eed121a54d5060bb7d710089eb77f452cc47ec3867eee"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 7 - CORONA"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E1 - Pg 189"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Line Voltage for comencing of corena(in kV)\n",
+ "import math\n",
+ "#Given data :\n",
+ "r=1.##cm\n",
+ "d=4.##meter\n",
+ "g0=30./math.sqrt(2.)##kV/cm\n",
+ "LineVoltage=math.sqrt(3.)*g0*r*math.log(d*100./r)##kV\n",
+ "print '%s %.2f' %(\"Line Voltage for comencing of corena(in kV) :\",round(LineVoltage))#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Line Voltage for comencing of corena(in kV) : 220.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E2 - Pg 190"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Disruptive critical voltage from line to line(kV rms)\n",
+ "import math\n",
+ "#Given data :\n",
+ "Ph=3.##phase\n",
+ "V=220.##kV\n",
+ "f=50.##Hz\n",
+ "r=1.2##cm\n",
+ "d=2.##meter\n",
+ "mo=0.96##Irregularity factor\n",
+ "t=20.##degree C\n",
+ "T=t+273.##K\n",
+ "b=72.2##cm\n",
+ "go=21.1##kV rms/cm\n",
+ "dela=3.92*b/T##Air density factor\n",
+ "Vdo=go*dela*mo*r*math.log(d*100./r)##in kV\n",
+ "Vdo_line=math.sqrt(3.)*Vdo##in kV\n",
+ "print '%s %.2f' %(\"Disruptive critical voltage from line to line(kV rms) : \",round(Vdo_line))#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Disruptive critical voltage from line to line(kV rms) : 208.00\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E3 - Pg 190"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Spacing between conductors in meter\n",
+ "import math\n",
+ "#Given data :\n",
+ "V=132.##kV\n",
+ "r=2./2.##cm\n",
+ "Vexceed=210.##kV(rms)\n",
+ "go=30000./math.sqrt(2.)##Volts/cm\n",
+ "go=go/1000.##kV/cm\n",
+ "Vdo=Vexceed/math.sqrt(3.)##Volt\n",
+ "mo=1.##assumed \n",
+ "dela=1.##assumed air density factor\n",
+ "#Formula : Vdo=go*del*mo*r*log(d*100/r)##in kV\n",
+ "d=math.exp(Vdo/go/dela/mo/r)*r##cm\n",
+ "print '%s %.2f' %(\"Spacing between conductors in meter : \",d*10**-2)#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Spacing between conductors in meter : 3.04\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E4 - Pg 190"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Minimum Diameter of conductor by Hit & Trial method(cm)\n",
+ "import math\n",
+ "import numpy\n",
+ "#Given data :\n",
+ "Ph=3.##phase\n",
+ "V=132.##kV\n",
+ "f=50.##Hz\n",
+ "d=3.##meter\n",
+ "d=d*100.##in cm\n",
+ "go=21.21##kV/cm : assumed\n",
+ "mo=0.85##assumed \n",
+ "dela=0.95##assumed air density factor\n",
+ "Vdo=V/math.sqrt(3.)##kV\n",
+ "#Formula : Vdo=go*del*mo*r*log(d*100/r)##in kV\n",
+ "#r*log(d/r)=Vdo/go/del/mo: solving\n",
+ "#Implementing Hit & Trial method\n",
+ "w=numpy.zeros(200)\n",
+ "\n",
+ "w[0]=.1\n",
+ "for i in range (1,200):\n",
+ "\tw[i]=.1+w[i-1];\n",
+ "\n",
+ "for r in w:\n",
+ " if round(r*math.log(d/r))==round(Vdo/go/dela/mo):\n",
+ " print '%s %.2f' %(\"Minimum Diameter of conductor by Hit & Trial method(cm) : \",2*r)#\n",
+ " break"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Minimum Diameter of conductor by Hit & Trial method(cm) : 1.20\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E5 - Pg 191"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate g1max(kV/cm)\n",
+ "import math\n",
+ "#Given data :\n",
+ "r=2.5/2.##cm\n",
+ "epsilon_r=4.##constant\n",
+ "r1=3./2.##cm\n",
+ "r2=9./2.##cm\n",
+ "V=20.##kV(rms)\n",
+ "#Formula : gmax=q/(2*epsilon*r)\n",
+ "g2maxBYg1max=r/epsilon_r/r1##unitless\n",
+ "#Formula : V=g1max*r*log(r1/r)+g2max*r1*log(r2/r1)\n",
+ "g1max=V/(r*math.log(r1/r)+g2maxBYg1max*r1*math.log(r2/r1))##in kV/cm\n",
+ "print '%s %.2f' %(\"g1max(kV/cm) = \",g1max)#\n",
+ "print '%s' %(\"Corona will be present.g1max > go\")#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "g1max(kV/cm) = 35.01\n",
+ "Corona will be present.g1max > go\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E6 - Pg 192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Line to line visual critical voltage for local corona(kV-rms),Line to line visual critical voltage for general corona(kV-rms)\n",
+ "import math\n",
+ "#Given data :\n",
+ "Ph=3.##phase\n",
+ "r=10.4/2##mm\n",
+ "r=r/10.##in cm\n",
+ "d=2.5##meter\n",
+ "d=d*100.##in cm\n",
+ "t=21.##degree C\n",
+ "T=t+273.##K\n",
+ "b=73.6##cm-Hg\n",
+ "mo=0.85# \n",
+ "mv_l=0.7#\n",
+ "mv_g=0.8#\n",
+ "go=21.21##kV/cm : assumed\n",
+ "dela=3.92*b/T##Air density factor\n",
+ "#Formula : Vdo=go*del*mo*r*log(d*100/r)##kV\n",
+ "Vdo=go*dela*mo*r*math.log(d/r)##kV\n",
+ "Vdo_line=math.sqrt(3.)*Vdo##kV\n",
+ "Vvo=go*dela*mv_l*r*(1+.3/math.sqrt(dela*r))*math.log(d/r)##kV\n",
+ "Vvo_line_local=Vvo*math.sqrt(3.)##kV(rms)\n",
+ "print '%s %.1f' %(\"Line to line visual critical voltage for local corona(kV-rms) : \",Vvo_line_local)\n",
+ "Vvo_line_general=Vvo_line_local*mv_g/mv_l##kV(rms)\n",
+ "print '%s %.f' %(\"Line to line visual critical voltage for general corona(kV-rms) : \",Vvo_line_general)\n",
+ "#Note : Answer in the book is not accurate.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Line to line visual critical voltage for local corona(kV-rms) : 115.1\n",
+ "Line to line visual critical voltage for general corona(kV-rms) : 132\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E7 - Pg 193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Corona Loss at 113 kV in kW ,Disruptive critical voltage between lines(kV)\n",
+ "#Given data :\n",
+ "import math\n",
+ "Pc1=53.##in kW\n",
+ "V1=106.##in kV\n",
+ "Pc2=98.##in kW\n",
+ "V2=110.9##in kV\n",
+ "Vph1=V1/math.sqrt(3.)##in kV\n",
+ "Vph2=V2/math.sqrt(3.)##in kV\n",
+ "#Formula : Pc=3*244/del*(f+25)*sqrt(r/d)*(Vph-Vdo)**2*10**-5##kW/Km\n",
+ "print '%s' %(\"Using proportionality : Pc is proportional to (Vph-Vdo)**2\")#\n",
+ "print '%s' %(\"We have, Pc1/Pc2 = (Vph1-Vdo)**2/(Vph2-Vdo)**2\")#\n",
+ "Vdo=(Vph1-math.sqrt(Pc1/Pc2)*(Vph2))/(1-math.sqrt(Pc1/Pc2))#\n",
+ "V3=113.##in kV\n",
+ "Vph3=V3/math.sqrt(3.)##in kV\n",
+ "Pc3=Pc2*(Vph3-Vdo)**2./(Vph2-Vdo)**2##in kW\n",
+ "print '%s %.1f' %(\"Corona Loss at 113 kV in kW : \",Pc3)#\n",
+ "VLine=math.sqrt(3.)*Vdo##in kV\n",
+ "print '%s %.1f' %(\"Disruptive critical voltage between lines(kV): \",VLine)#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Using proportionality : Pc is proportional to (Vph-Vdo)**2\n",
+ "We have, Pc1/Pc2 = (Vph1-Vdo)**2/(Vph2-Vdo)**2\n",
+ "Corona Loss at 113 kV in kW : 121.5\n",
+ "Disruptive critical voltage between lines(kV): 92.4\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E8 - Pg 194"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Total corona loss under foul weather condition using Peek formula in kW,Total corona loss under foul weather condition using Peterson formula in kW \n",
+ "import math\n",
+ "#Given data :\n",
+ "f=50.##Hz\n",
+ "l=160.##km\n",
+ "r=1.036/2.##cm\n",
+ "d=2.44*100.##cm\n",
+ "g0=21.1##kV/cm(rms)\n",
+ "m0=0.85##irregularity factor\n",
+ "mv=0.72##roughness factor\n",
+ "b=73.15##cm\n",
+ "t=26.6##degree C\n",
+ "dela=3.92*b/(273.+t)##air density factor\n",
+ "Vd0=g0*dela*m0*r*math.log(d/r)##kV(rms)\n",
+ "print '%s %.2f' %(\"Critical disruptive voltage(rms) in kV : \",Vd0)#\n",
+ "Vv0=g0*dela*mv*r*(1+0.3/math.sqrt(dela*r))*math.log(d/r)##kV\n",
+ "print '%s %.1f' %(\"Visual Critical voltage(rms) in kV : \",Vv0)#\n",
+ "Vph=110./math.sqrt(3.)##in kV\n",
+ "Pc_dash=d/dela*(f+25)*math.sqrt(r/d)*(Vph-0.8*Vd0)**2*10**-5##kW/km/phase\n",
+ "T_Corona_loss=l*3*Pc_dash##kW\n",
+ "print '%s %.f' %(\"Total corona loss under foul weather condition using Peek formula in kW : \",T_Corona_loss)#\n",
+ "VphBYVd0=Vph/Vd0/0.8#\n",
+ "K=0.46##constant\n",
+ "Corona_loss=21*10**-5*f*Vph**2*K/(math.log10(d/r))**2##kW/km/phase\n",
+ "T_corona_loss=Corona_loss*3*l##kW\n",
+ "print '%s %.1f' %(\"Total corona loss under foul weather condition using Peterson formula in kW : \",T_corona_loss)#\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical disruptive voltage(rms) in kV : 54.73\n",
+ "Visual Critical voltage(rms) in kV : 66.1\n",
+ "Total corona loss under foul weather condition using Peek formula in kW : 1645\n",
+ "Total corona loss under foul weather condition using Peterson formula in kW : 1308.7\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example E9 - Pg 195"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate Power loss due to corona for fair weather condition,Total corona loss using Peek formula in kW,Total corona loss under foul weather condition using Peterson formula in kW \n",
+ "import math\n",
+ "#given data :\n",
+ "f=50.##Hz\n",
+ "l=175.##km\n",
+ "r=1./2.##cm\n",
+ "d=3.*100.##cm\n",
+ "g0=21.1##kV/cm(rms)\n",
+ "m0=0.85##irregularity factor\n",
+ "mv=0.72##roughness factor\n",
+ "mv_dash=0.82##roughness factor\n",
+ "b=74.##cm\n",
+ "t=26.##degree C\n",
+ "Vph=110./math.sqrt(3.)##kV\n",
+ "dela=3.92*b/(273.+t)##air density factor\n",
+ "Vd0=g0*dela*m0*r*math.log(d/r)##kV(rms)\n",
+ "Vvo=g0*dela*mv*r*(1.+0.3/math.sqrt(dela*r))*math.log(d/r)##kV rms\n",
+ "Vvo_dash=Vvo*mv_dash/mv##kV rms\n",
+ "Pc=244./dela*(f+25.)*math.sqrt(r/d)*(Vph-Vd0)**2.*10.**-5##kW/Km/phase\n",
+ "T_CoronaLoss=Pc*l*3.##kW\n",
+ "print '%s' %(\"Power loss due to corona for fair weather condition : \")#\n",
+ "print '%s %.f' %(\"Total corona loss using Peek formula in kW : \",T_CoronaLoss)#\n",
+ "K=0.0713##constant for Vph/Vdo=1.142\n",
+ "Pc=21.*10.**-5*f*Vph**2./(math.log10(d/r))**2.*K##kW/Km/phase\n",
+ "T_CoronaLoss=Pc*l*3##kW\n",
+ "print '%s %.1f' %(\"According Peterson formula, Total corona loss for 175 km 3-phase line(kW): \",T_CoronaLoss)#\n",
+ "print '%s' %(\"Power loss due to corona for stormy weather condition : \")#\n",
+ "Vd0=0.8*Vd0##kV\n",
+ "Pc_dash=l*3.*244./dela*(f+25.)*math.sqrt(r/d)*(Vph-Vd0)**2.*10.**-5##kW/Km/phase\n",
+ "print '%s %.f' %(\"Total corona loss using Peek formula in kW : \",Pc_dash)#\n",
+ "K=0.395##constant for Vph/Vdo=1.42\n",
+ "Pc=21.*10.**-5*f*Vph**2./(math.log10(d/r))**2.*K##kW/Km/phase\n",
+ "T_CoronaLoss=Pc*l*3.##kW\n",
+ "print '%s %.f' %(\"According Peterson formula, Total corona loss for 175 km 3-phase line(kW): \",T_CoronaLoss)#\n",
+ "#Answer is wrong in the book for corona loss fair weather condition using Peek formula.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Power loss due to corona for fair weather condition : \n",
+ "Total corona loss using Peek formula in kW : 249\n",
+ "According Peterson formula, Total corona loss for 175 km 3-phase line(kW): 205.4\n",
+ "Power loss due to corona for stormy weather condition : \n",
+ "Total corona loss using Peek formula in kW : 1457\n",
+ "According Peterson formula, Total corona loss for 175 km 3-phase line(kW): 1138\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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