{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 4 : Performance of Lines" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.1, Page No 65" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "R=0.496\t\t# resistance\n", "X=1.536\n", "Vr=2000.0\n", "\n", "#Calculations\n", "Z=(10*2*2/(11*11)) + complex(30)*2*2/(11*11)\n", "Zt=(.04+(1.3*2*2/(11*11))) + complex(0.125,(4.5*2*2/(11*11)))#Transformer impedence\n", "Il=250*1000.0/2000\t# line current(amps.)\n", "Pl=Il*Il*R\t\t\t#line loss(kW)\n", "Po=250*0.8\t\t\t# output(kW)\n", "cosr=0.8\t\t\t# power factor\n", "sinr=0.6\n", "n=200*100.0/(200+7.7)\n", "Vs=(Vr*cosr+Il*R)+complex(Vr*sinr+Il*X)\n", "V=math.sqrt((1662**2)+ (1392**2))\n", "\n", "#Results\n", "print(\"efficiency= %.1f percent \" %n)\n", "print(\"Sending end voltage,|Vs|=%.0f volts\" %V)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency= 96.3 percent \n", "Sending end voltage,|Vs|=2168 volts\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.2, Page No 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "print(\"when load is star connected\")\n", "Vln=400/math.sqrt(3.0)\t\t# Line to neutral voltage(V)\n", "Z=complex(7,11)\t\t\t\t\t#Impedence per phase\n", "Il=231/Z\t\t\t\t\t\t# line current(amp.)\n", "I=abs(231/Z)\n", "Pi=3*I*I*7\n", "Po=3*I*I*6\n", "\n", "#Calculations\n", "print(\"power input =%.0f watts\\n\" %Pi)\t\t#Answers don't match due to difference in rounding off of digits\n", "print(\"power output=%.0f watts\\n\" %Po)\t#Answers don't match due to difference in rounding off of digits\n", "print(\"when load is delta connected\\n\")\n", "Ze=complex(2,3)\t\t# equivalent impedence(ohm)\n", "Zp=complex(3,5)\t\t# impedence per phase\n", "il=231/Zp\t\t\t#Line current(amps.)\n", "IL=abs(il)\n", "pi=3*IL*IL*3\n", "po=3*IL*IL*2\n", "\n", "#Results\n", "print(\"power input=%.1f watts\" %pi)\t\t\t#Answers don't match due to difference in rounding off of digits\n", "print(\"power output = %.0f watts \" %po)\t\t#Answers don't match due to difference in rounding off of digits" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "when load is star connected\n", "power input =6592 watts\n", "\n", "power output=5650 watts\n", "\n", "when load is delta connected\n", "\n", "power input=14125.0 watts\n", "power output = 9417 watts \n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.3, Page No 66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "a=100/.5\n", "Xl=2*(10**-7)*math.log(100/.5)\t\t#inductance(H/meter)\n", "XL=20*(1000)*Xl\t\t\t\t\t\t# inductance of 20 km length \n", "R=6.65\t\t\t\t\t\t\t\t# resistance(ohm)\n", "Rc=20*1000/(58.0*90)\t\t\t\t# resistance of copper(ohm)\n", "I=10*1000/(33*.8*math.sqrt(3))\t\t# the current(amps.)\n", "\n", "#Calculations\n", "Pl=3*I*I*Rc/(10**6)\t\t\t\t\t#loss (MW)\n", "n=10.0/(10+Pl)\n", "print(\"Efficiency=%.4f percent \" %n)\n", "Vr=19052\n", "cosr=.8\t\t\t\t#power factor\n", "sinr=.6\n", "Vs=abs(((Vr*cosr+I*Rc) +complex(Vr*sinr+ I*R)))\n", "\n", "#Results\n", "print(\"Vs =%.0f volts\\n\" %Vs)\t#Answer don't match due to difference in rounding off of digits\n", "Reg=(Vs-Vr)*100/Vr\n", "print(\"Regulation =%.2f percent\" %Reg)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency=0.9479 percent \n", "Vs =28965 volts\n", "\n", "Regulation =52.03 percent\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.4 Page No 67" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "IR=(400)/((math.sqrt(3)*complex(6.3,9)))\n", "\n", "#Calculations\n", "IY=231*complex(math.cos(math.radians(-120)),math.sin(math.radians(-120)))/8.3\n", "IB=231*complex(math.cos(math.radians(120)),math.sin(math.radians(120)))/complex(6.3,-8)\n", "In=abs((IR +IY +IB))\t\t#Neutral current\n", "print(\"Neutral current =%.2f amps\\n\" %In)\n", "VR=abs(IR*complex(6,9))\n", "VY=abs(IY*(8))\n", "VB=abs(IB*complex(6,-8))\n", "\n", "#Results\n", "print(\"Voltage across Phase R =%.1f volts \\n\" %VR)\n", "print(\"Voltage across Phase Y =%.2f volts \\n\" %VY)\n", "print(\"Voltage across Phase B =%.0f volts \\n\" %VB)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Neutral current =45.18 amps\n", "\n", "Voltage across Phase R =227.4 volts \n", "\n", "Voltage across Phase Y =222.65 volts \n", "\n", "Voltage across Phase B =227 volts \n", "\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.5, Page No 73" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "R=100*.1\t\t#Resistance of line (ohm)\n", "Xl=2*(10**-7)*100*1000*math.log(200/.75)\t#inductance of line\n", "X2=Xl*314\t\t\t\t\t\t\t\t\t#inductive reactance\n", "C=2*(math.pi*100)*8.854*(10**-12)*100*1000*(10**6)/(math.log(200/.75))\t# capacitance per phase (micro farad)\n", "\n", "#Calculations\n", "print(\"Using Nominal-T method\\n\")\n", "Ir=20*1000.0/(math.sqrt(3)*66*.8)\n", "Vr=66*1000/math.sqrt(3)\n", "Vc=complex((38104*.8+ Ir*5),(38104*.6+ Ir*17.55))\t# voltage across condenser\n", "Ic=complex(314*(Vc)*.9954*(10**-6))\n", "ise=Ir+Ic\n", "Is=abs(Ir+Ic)\n", "Vs=abs(Vc + (ise*complex(5,17.53)))\n", "VR=abs(Vs*complex(-3199)/complex(5,-3181))# no load recieving end voltage\n", "Reg=(VR-Vr)*100.0/Vr\n", "Pl=3*(Ir*Ir*5 + Is*Is*5)/1000000\n", "n=20*100/(20+Pl)\n", "print(\"percent regulation=%.1f \" %Reg)\n", "print(\"percent efficiency=%.1f \\n\" %n)\n", "print(\"Using Nominal-pi method\\n\")\n", "Ir1=218.68*complex(.8,-.6)\n", "Ic1=complex(314*.4977*(10**-6)*Vr)\n", "Il=Ir1+Ic1\n", "vs1=Vr+Il*complex(10,35.1)\n", "Vs1=abs(vs1)\n", "Vr1=Vs1*complex(-6398)/complex(10,-6363)\n", "VR1=abs(Vr1)\t\t\t# no load recieving end voltage\n", "Reg2=(VR1-Vr)*100/Vr\n", "IL=abs(Ir1+Ic1)\n", "Loss=3*IL*IL*10\n", "n=20*100/21.388\n", "\n", "#Results\n", "print(\"percent regulation=%.2f \" %Reg2)\n", "print(\"percent efficiency=%.1f \" %n)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Using Nominal-T method\n", "\n", "percent regulation=18.2 \n", "percent efficiency=93.0 \n", "\n", "Using Nominal-pi method\n", "\n", "percent regulation=18.23 \n", "percent efficiency=93.5 \n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.6, Page No 78" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import cmath\n", "#initialisation of variables\n", "R=0.2\n", "L=1.3\n", "C=0.01*(10**-6)\n", "\n", "#Calculations\n", "z=complex(R,(L*314.0*(10**-3)))\t\t# serie impedence\n", "y=complex(314.0*C)\t\t# shunt admittance\n", "Zc=cmath.sqrt(z/y)\t\t# characterstic impedence\n", "Y=cmath.sqrt(y*z)\n", "Vr=132*1000/math.sqrt(3.0)\n", "Ir=0\n", "Vin=(Vr + Ir*Zc)/2\t\t\t# incident voltage to neutral at the recieving end\n", "\n", "#Results\n", "print(\"Vr =%.3f volts \\n\" %Vr)\t\t#Answer don't match due to difference in rounding off of digits\n", "print(\"(i)The incident voltage to neutral at the recieving end {0:.5f}+{1:.5f}i\".format(Vin.real, Vin.imag))\t#Answer don't match due to difference in rounding off of digits\n", "Vin2=(Vr - Ir*Zc)/2\t\t\t\t\t\t# The reflected voltage to neutral at the recieving end\n", "print(\"(ii)The reflected voltage to neutral at the recieving end{0:.5f}+{1:.5f}i\".format(Vin2.real, Vin2.imag))\t\t#Answer don't match due to difference inrounding off of digits\n", "Vrp=Vr*cmath.exp(.2714*120*(10**-3))*cmath.exp(complex(1.169*120*(10**-3))/1000.0)#Taking Vrp=Vr+\n", "Vrm=Vr*cmath.exp(-0.0325)*cmath.exp(complex(-.140))/1000\t\t\t#Taking Vrm=Vr-\n", "v1=Vrm/2\t\t\t\t # reflected voltage to neutral at 120 km from the recieving end\n", "phase_v1=math.degrees(math.atan(v1.imag/v1.real))\n", "v2=Vrp/2\t\t\t #incident voltage to neutral at 120 km from the recieving end\n", "phase_v2=math.degrees(math.atan(v2.imag/v2.real))#Phase angle of v2\n", "print(\"(iii) reflected voltage to neutral at 120 km from the recieving end =%.2f at angle of %.2f\" %(abs(v1),phase_v1))\n", "print(\"incident voltage to neutral at 120 km from the recieving end = %.2f at angle of %.2f\" %(abs(v2),phase_v2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Vr =76210.236 volts \n", "\n", "(i)The incident voltage to neutral at the recieving end 38105.11777+0.00000i\n", "(ii)The reflected voltage to neutral at the recieving end38105.11777+0.00000i\n", "(iii) reflected voltage to neutral at 120 km from the recieving end =32.07 at angle of 0.00\n", "incident voltage to neutral at 120 km from the recieving end = 39372.08 at angle of 0.00\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.7 Page No 79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "Ir=40.0*1000/(math.sqrt(3)*132*.8)\n", "Vr=132.0*1000/math.sqrt(3)\n", "\n", "#Calculations\n", "Zc=380*complex(math.cos(math.radians(-13.06)),math.sin(math.radians(-13.06)))\n", "IR=Ir*complex(math.cos(math.radians(-38.8)),math.sin(math.radians(-38.8)))\n", "Vsp=(Vr+IR*Zc)*(1.033*complex(math.cos(math.radians(8.02)),math.sin(math.radians(8.02))))/2\n", "Vsm=(Vr-IR*Zc)*(0.968*complex(math.cos(math.radians(8.02)),math.sin(math.radians(8.02))))/2\n", "vs=Vsp+ Vsm\n", "Vs=abs(vs)\n", "ise=(Vsp-Vsm)/Zc\n", "Is=abs(ise)\n", "P=3*Vs*Is*math.cos(math.radians(33.72))/10**6\n", "n=40*100/P\n", "\n", "#Results\n", "print(\"efficiency=%.1f\" %n)\t\t#Answer don't match due to difference in rounding off of digits" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "efficiency=92.3\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.8, Page No 80" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import cmath\n", "#initialisation of variables\n", "yl=complex(0.2714,1.169)*120*(10**-3)\n", "Ir=40*1000/(math.sqrt(3)*132*.8)\n", "A=cmath.cosh(yl)\n", "\n", "#Calculations\n", "phase_A=math.degrees(math.atan(A.imag/A.real)) #Phase angle of A\n", "IR=Ir*complex(math.cos(math.radians(-38.8)),math.sin(math.radians(-38.8)))\n", "Vr=132*1000/math.sqrt(3)\n", "Zc=380*complex(math.cos(math.radians(-13.06)),math.sin(math.radians(-13.06)))\n", "B=Zc*cmath.sinh(yl)\n", "phase_B=math.degrees(math.atan(B.imag/B.real)) #Phase angle of B\n", "Vs=(A*Vr+B*IR)\n", "f=abs(B)\n", "d=abs(Vs)\n", "C=cmath.sinh(yl)/Zc\n", "phase_C=math.degrees(math.atan(C.imag/C.real)) #Phase angle of C\n", "D=cmath.cosh(yl)\n", "phase_D=math.degrees(math.atan(D.imag/D.real))\t\t#Phase angle of D\n", "\n", "#Results\n", "print(\"A=%.2f at an angle of %.2f \" %(abs(A),phase_A))\n", "print(\"B=%.1f at an angle of %.0f \" %(abs(B),phase_B))\n", "print(\"C=%.2f at an angle of %.2f \" %(abs(C),phase_C))\n", "print(\"D=%.2f at an angle of %.2f \" %(abs(D),phase_D))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "A=0.99 at an angle of 0.26 \n", "B=54.6 at an angle of 64 \n", "C=0.00 at an angle of -89.92 \n", "D=0.99 at an angle of 0.26 \n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.9 Page No 81" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "Ir=218.7*complex(0.8,-0.6)\n", "Ic1=complex(314)*0.6*(10**-6)*76200\n", "Il=Ic1+Ir\n", "Vs=76200 + Il*complex(24,48.38)\n", "\n", "#Calculations\n", "phase_Vs=math.degrees(math.atan(Vs.imag/Vs.real))\n", "Pl=3*24*abs(Il)*abs(Il)/1000000.0 #The Loss(MW)\n", "n=40*100/(40+Pl)\n", "print(\"Using Nominal- pi method\")\n", "print(\"Vs=%.0f volts at an angle of %.2f \\n\" %(abs(Vs),phase_Vs))\n", "print(\"efficiency=%.2f percent\" %n)\n", "print(\"\\nUsing Nominal-T method\")\n", "Vc=76200*complex(0.8,0.6)+218.7*complex(12,24.49)\n", "Ic=complex(314)*1.2*(10**-6)*complex(63584,51076.0)\n", "Is=complex(199.46,23.95)\n", "Vs=(Vc + Is*complex(12,24.49))/1000.0\n", "phase_Vs=math.degrees(math.atan(Vs.imag/Vs.real))\t#Phase angle of Vs\n", "Pl1=3*12*((200.89**2)+ 218.7**2)/1000000 #The loss(MW)\n", "n1=40*100/(40+Pl1)\n", "\n", "#Results\n", "print(\"Vs=%.2f at an angle of %.2f \" %(abs(Vs),phase_Vs))\n", "print(\"efficiency=%.2f percent\\n\" %n1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Using Nominal- pi method\n", "Vs=87299 volts at an angle of 3.95 \n", "\n", "efficiency=91.28 percent\n", "\n", "Using Nominal-T method\n", "Vs=86.25 at an angle of 40.70 \n", "efficiency=92.65 percent\n", "\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4.10 Page No 92" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import cmath\n", "#initialisation of variables\n", "R=0.1557*160\n", "GMD=(3.7*6.475*7.4)**(1.0/3)\n", "Z1=2*(10**-7)*math.log(560/0.978)*160*1000\n", "XL=63.8\n", "\n", "#Calculations\n", "C=(10**-9)*2*(10**6)*math.pi*160*1000.0/(36*math.pi*math.log(560/.978))\n", "Z=math.sqrt((0.1557**2)+.39875**2)*complex(math.cos(math.radians(68.67)),math.sin(math.radians(68.67)))\n", "jwC=complex(314)*1.399*(10**-6)/160.0\n", "Zc=cmath.sqrt(Z/jwC)\n", "y=cmath.sqrt(Z*jwC)\n", "yl=y*160\n", "A=cmath.cosh(yl)\n", "B=Zc*cmath.sinh(yl)\n", "C=cmath.sinh(yl)/Zc\n", "Ir=50000/(math.sqrt(3)*132)\n", "Vs=(A*76.208) +(B*(10**-3)*Ir*complex(math.cos(math.radians(-36.87)),math.sin(math.radians(-36.87))))\n", "VS=152.34\n", "Is=C*76.208*(10**3) +(A*Ir*complex(math.cos(math.radians(-36.87)),math.sin(math.radians(-36.87))))\n", "Ps=3*abs(Vs)*abs(Is)*math.cos(math.radians(33.96))\n", "pf=math.cos(math.radians(33.96))\n", "Vnl=abs(Vs)/abs(A)\n", "reg=(Vnl-76.208)*100/76.208\n", "n=50000*.8*100/abs(Ps)\n", "\n", "#Results\n", "print(\"Vs line to line =%.2f kV\\n\" %VS)\n", "print(\"sending end current Is(A){0:.5f}+{1:.5f}i\".format(Is.real, Is.imag)) #Answer don't match due to difference in rounding off of digits\n", "print(\"sending end power=%.0f kW\" %Ps)\n", "print(\"sending end p.f =%.3f\" %pf)\n", "print(\"percent regulation=%.1f \" %reg)\n", "print(\"percent efficency=%.1f \" %n)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Vs line to line =152.34 kV\n", "\n", "sending end current Is(A)211.28696+-129.31797i\n", "sending end power=55350 kW\n", "sending end p.f =0.829\n", "percent regulation=17.2 \n", "percent efficency=72.3 \n" ] } ], "prompt_number": 10 } ], "metadata": {} } ] }