{
"metadata": {
"name": "",
"signature": "sha256:a3dcc0814e961bf1cd3db74adc66300f1f3d1872ea1c97bd01480f29b5cfe9db"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 10: Performance of Transmission\n",
"Lines"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.1, Page Number: 233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration:\n",
"pf = 0.8 #power factor\n",
"Z = 10+15j #load impedance(ohm)\n",
"magVr = 33000 #receiving end voltage(V)\n",
"P = 1100 #poweer delivered(kW)\n",
"\n",
"#Calculation:\n",
"magI = P*1000/(magVr*pf) #line current(A)\n",
"phy = math.acos(pf)\n",
"Vr = magVr+0j #V\n",
"I = magI*(math.cos(phy)-math.sin(phy)*1j) #A\n",
"Vs = Vr + I*Z\n",
"\n",
"#Angle between Vs and Vr is\n",
"alpha = math.atan(Vs.imag/Vs.real)\n",
"phys = phy+alpha\n",
"pfs = math.cos(phys)\n",
"Pl = magI**2*Z.real/1000\n",
"Pi = P+Pl\n",
"n = P/Pi*100\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) Sending end voltage is\",round(abs(Vs)),\"V\"\n",
"print \"(ii) sending end power factor is\",round(pfs,4),\"lagging\"\n",
"print \"(iii)Transmission efficiency is\",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Sending end voltage is 33709.0 V\n",
"(ii) sending end power factor is 0.7955 lagging\n",
"(iii)Transmission efficiency is 98.45 %\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.2, Page Number: 235"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"a = 0.775 #cross-section of conductor(cm**2)\n",
"n = 0.9 #transmission efficiency\n",
"Pr = 200000 #receiving end power(W)\n",
"pf = 1 #power factor\n",
"V = 3300 #line voltage(V)\n",
"ro = 1.725 #specific resistance(micro_ohm-cm)\n",
"\n",
"\n",
"#Calculation:\n",
"Ps = Pr/n #sending end power(W)\n",
"Pl = Ps-Pr #line loss(W)\n",
"I = Pr/(V*pf) #line current(A)\n",
"R = Pl/(2*I**2) #resistance of 1 conductor(ohm)\n",
"l = R*a/(ro*10**-6) #length of conductor(cm)\n",
"\n",
"\n",
"#Result:\n",
"print \"The conductor length is\",round(l*10**-5,1),\"km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The conductor length is 13.6 km\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.3, Page Number: 235"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"pf = 0.8 #power factor\n",
"Pr = 5000 #receiving end power(kW)\n",
"Vr = 22 #receiving end voltage(kV)\n",
"Z = 4+6j #impedance of each conductor(ohm)\n",
"\n",
"#Calculation:\n",
"phy = math.acos(pf)\n",
"magVrp = Vr*1000/3**0.5 #sending end voltage/phase(kV)\n",
"magI = Pr*1000/(3*magVrp*0.8) #Line current(A)\n",
"Vr = magVrp+1j \n",
"I = magI*(math.cos(phy)-math.sin(phy)*1j)\n",
"\n",
"#(i)Sending end voltage per phase:\n",
"Vs = magVrp+I*Z\n",
"Vsl = abs(Vs)*3**0.5 #V\n",
"\n",
"#(ii)\n",
"reg = (abs(Vs)-magVrp)/magVrp*100 #voltage regulation(%)\n",
"#(iii)\n",
"Pl = 3*abs(I)**2*Z.real/1000 #line loss(kW)\n",
"n = Pr/(Pr+Pl)*100 #transmission efficiency(%)\n",
"\n",
"#Result:\n",
"print \"(i) Sending end voltage is\",round(abs(Vsl)/1000,3),\"kV\"\n",
"print \"(ii)Percentage regulation is\",round(reg,3),\"%\"\n",
"print \"(iii)Transmission efficiency\",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Sending end voltage is 23.942 kV\n",
"(ii)Percentage regulation is 8.825 %\n",
"(iii)Transmission efficiency 93.93 %\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.4, Page Number: 236"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"\n",
"#Variable declaration:\n",
"Pr = 15000 #power delivered(kW)\n",
"Vl = 132 #line voltage(kV)\n",
"Ro = 1 #line resistance(ohm/km)\n",
"pf = 0.8 #power factor\n",
"\n",
"#Calculation:\n",
"I = Pr/(3**0.5*Vl*pf) #line current(A)\n",
"#the loss in the transmission is to be 5%.\n",
"Pl = 5*Pr/100 #kW\n",
"R = Pl*1000/(3*I**2) #line resistance(ohm)\n",
"d = R/Ro #line length(km)\n",
"\n",
"#Result:\n",
"print \"Length of line is\",round(d,2),\"km\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length of line is 37.17 km\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.5, Page Number: 236"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"pf = 0.8 #power factor\n",
"Pr = 3600 #sending end power(kW)\n",
"magVs = 33 #receiving end voltage(kV)\n",
"Z = 5.31+5.54j #impedance of each conductor(ohm)\n",
"\n",
"\n",
"#Calculation:\n",
"R = Z.real #ohm\n",
"X = Z.imag #ohm\n",
"phy = math.acos(0.8)\n",
"magVsp = magVs*1000/(3**0.5) #V/phase\n",
"magVr = symbols('magVr') #Receiving end voltage(V/phase)\n",
"magI = Pr*1000/(3*magVr*pf) #line current(A)\n",
"\n",
"#(i)Using approximate expression for magVsp,\n",
"magVr1 = solve((magVr+magI*R*pf+magI*X*math.sin(phy))-magVsp,magVr)[1]\n",
"\n",
"#(ii)line current:\n",
"magI1 = Pr*1000/(3*magVr1*pf) \n",
"\n",
"#(iii)Efficiency\n",
"Pl = 3*magI1**2*R/1000 #kW\n",
"n = Pr/(Pr+Pl)*100\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) The receiving end voltage \",round(magVr1*3**0.5/1000,2),\"V\"\n",
"print \"(ii) Line current is\",round(magI1,2),\"A\"\n",
"print \"(iii)Transmission efficiency is\",round(n,2),\"%\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The receiving end voltage 31.93 V\n",
"(ii) Line current is 81.36 A\n",
"(iii)Transmission efficiency is 97.15 %\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.6, Page Number: 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"import math\n",
"\n",
"#Variable declaration:\n",
"Z = 6+8j #line impedance(ohm)\n",
"magVs = 120 #sending end voltages(kV)\n",
"magVr = 110 #receiving end voltaes(kV)\n",
"pf = 0.9 #power factor\n",
"\n",
"\n",
"#Calculation:\n",
"R = Z.real #ohm\n",
"X = Z.imag #ohm\n",
"magVsp = round(120*1000/3**0.5) #V/phase\n",
"magVrp = round(110*1000/3**0.5) #V/phase\n",
"phy = math.acos(pf)\n",
"magI = symbols('magI') #line current(A)\n",
"magI1 = solve(magVrp+magI*R*math.cos(phy)+magI*X*math.sin(phy)-magVsp,magI)[0]\n",
"\n",
"#(i):\n",
"Po = 3*magVrp*round(magI1)*math.cos(phy)/1000 #kW\n",
"\n",
"#(ii):\n",
"pfs = (magVrp*math.cos(phy)+magI1*R)/magVsp\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) Power output is\",round(Po),\"kW\"\n",
"print \"(ii)Sending end power factor\",round(pfs,2),\"lagging\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Power output is 111458.0 kW\n",
"(ii)Sending end power factor 0.88 lagging\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.7, Page Number: 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"Z = 1.5+4j #impedance of the line(ohm)\n",
"magVr = 11000 #receivig end voltage(V)\n",
"pf = 0.8 #power factor\n",
"Pr = 5000 #power delivered()\n",
"\n",
"\n",
"#Calculation:\n",
"R = Z.real #ohm\n",
"X = Z.imag #ohm\n",
"magVrp = magVr/3**0.5 #V/phase\n",
"phy = math.acos(pf)\n",
"magI = Pr*1000/(3*magVrp) #line current(A)\n",
"magVsp = magVrp+magI*R*pf+magI*X*math.sin(phy) #Volt\n",
"reg = (magVsp - magVrp)/magVrp*100 #voltage regulation(%)\n",
"Pl = 3*magI**2*R/1000 #line losses(kW)\n",
"Po = Pr*pf #output power(W)\n",
"Pi = Po + Pl #Input Power(kW)\n",
"n = Po/Pi*100 #efficiency(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"The % regulation is\",round(reg,2),\"%\"\n",
"print \"The efficiency is\",round(n,1),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The % regulation is 14.88 %\n",
"The efficiency is 92.8 %\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.8, Page Number: 238"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration:\n",
"Pr = 1000 #power delivered(kW)\n",
"pf = 0.8 #power factor\n",
"r = 0.03 #line resistance per phase(ohm/km)\n",
"L = 0.7 #line inductance per phase(mH)\n",
"l = 16 #line length(km)\n",
"magVr = 11000 #receiving line voltage(V)\n",
"f = 50 #power frequency(Hz)\n",
"\n",
"#Calculation:\n",
"R = r*l #line resistance(ohm)\n",
"X = 2*3.14*f*L/1000*l #line reactance(ohm)\n",
"magVrp = round(magVr/3**0.5) #receiving end (v/phase)\n",
"phy = math.acos(pf)\n",
"magI = round(Pr*1000/(3*magVrp*math.cos(phy)),1) #line current(A)\n",
"magVsp = magVrp+magI*R*math.cos(phy)+magI*X*math.sin(phy)\n",
"reg = (magVsp-magVrp)/magVrp*100 #Volt\n",
"Pl = round(3*magI**2*R/1000,1) #line losses(kW)\n",
"Pi = Pr + Pl #Input Power(kW)\n",
"n = Pr/Pi*100 #efficiency(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"The % regulation is\",round(reg,2),\"%\"\n",
"print \"The efficiency is\",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The % regulation is 2.58 %\n",
"The efficiency is 99.38 %\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.9, Page Number: 238"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
"#Variable Declaration:\n",
"Pr = 2000 #load power(kVA)\n",
"pf = 0.8 #power factor\n",
"l = 20 #line length(km)\n",
"r1 = 7.5; x1 = 13.2 #resistance & reactance of transformer primary(ohm)\n",
"r2 = 0.35; x2 = 0.65 #resistance & reactance of transformer secondary(ohm)\n",
"r = 0.4; x = 0.5 ##resistance & reactance of line(ohm/km)\n",
"Vp = 33*1000 #voltage at primary side(kV)\n",
"Vs = 6.6*1000 #voltage at secondary side(kV)\n",
"\n",
"\n",
"\n",
"#Calculation:\n",
"R = l*r #resistance of each conuctor(ohm)\n",
"X = l*x #reactance of each conductor(ohm)\n",
"phy = math.acos(pf)\n",
"#Let us transfer the impedance of transformer secondary\n",
"#to high tension side i.e., 33 kV side.\n",
"#Equivalent resistance of transformer referred to 33 kV side:\n",
"R1 = r1 + r2*(Vp/Vs)**2 #ohm\n",
"\n",
"#Equivalent resistance of transformer referred to 33 kV side:\n",
"X1 = x1+ x2*(Vp/Vs)**2 #ohm\n",
"\n",
"\n",
"Rt = R+R1 #Total resistance of line and transformer(ohm)\n",
"Xt = X+X1 #Total reactance of line and transformer(omh)\n",
"Vr = Vp/3**0.5 #receiving end voltage(V/phase)\n",
"I = round(Pr*1000/(3**0.5*Vp)) #line current(A)\n",
"Vs = Vr+I*Rt*math.cos(phy)+I*Xt*math.sin(phy) #sending end voltage(V)\n",
"Vsl = 3**0.5*Vs #sending end line voltage(V)\n",
"pfs = (Vr*pf+I*Rt)/Vs #sending end power factor\n",
"Pl = 3*I**2*Rt/1000 #line loss(kW)\n",
"Po = Pr*pf #output power(kW)\n",
"n = Po/(Po+Pl)*100 #transmission efficiency(%)\n",
"\n",
"#Result:\n",
"print \"Sending end line voltage is\",round(Vsl/1000,1),\"V\"\n",
"print \"Sending end power factor is\",round(pfs,4)\n",
"print \"Transmission efficiency is\",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Sending end line voltage is 35.6 V\n",
"Sending end power factor is 0.7826\n",
"Transmission efficiency is 94.72 %\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.10, Page Number: 241"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration:\n",
"r = 0.25 #resistance of line(ohm/km)\n",
"l = 100 #line length(km)\n",
"x = 0.8 #Reactance(ohm/km)\n",
"y = 14*10**-6 #susceptance(siemen/km)\n",
"magVr = 66000 #Receiving end line voltage(V)\n",
"Pr = 15000 #power delivered(kW)\n",
"pf = 0.8 #power factor(lagging)\n",
"\n",
"\n",
"\n",
"#Calculation:\n",
"R = r*l #ohm\n",
"X = x*l #ohm\n",
"Y = y*l #siemen\n",
"magI = Pr*1000/(pf*magVr) #line current(A)\n",
"phy = math.acos(pf) #phasor angle\n",
"Vr = magVr+0j #Volt\n",
"Ir = round(magI*pf)-round(magI*math.sin(phy))*1j #load current(A)\n",
"Ic = 1j*round(Y*magVr)\n",
"\n",
"#(i):\n",
"Is = Ir+Ic #Sending end current(A)\n",
"\n",
"#(ii):\n",
"delV = Is*(R+X*1j) #voltage rop(V)\n",
"Vs = Vr+delV #sending end voltage(V)\n",
"reg = (abs(Vs)-magVr)/magVr*100 #voltage regulation(%)\n",
"\n",
"#phase angle between Vr & Ir:\n",
"theta1 = math.atan(Is.imag/Is.real)\n",
"\n",
"#phase angle between Vr & Is:\n",
"theta2 = math.atan(Vs.imag/Vs.real)\n",
"\n",
"phys = abs(theta1)+theta2\n",
"pfs = math.cos(phys) #supply power factor\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) The sending end current is\",round(abs(Is)),\"A\"\n",
"print \"(ii) The sending end voltage is\",round(abs(Vs)),\"V\"\n",
"print \"(iii)Regulation is\",round(reg,2),\"%\"\n",
"print \"(iv) Supply power factor is\",round(pfs,2),\"lagging\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The sending end current is 240.0 A\n",
"(ii) The sending end voltage is 79583.0 V\n",
"(iii)Regulation is 20.58 %\n",
"(iv) Supply power factor is 0.86 lagging\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.11, Page Number: 244"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration:\n",
"l = 100 #line length(km)\n",
"r = 0.1 #resistance/km/phase(ohm)\n",
"xl = 0.2 #reactance/km/phase(ohm)\n",
"b = 0.04*10**-4 #Capacitive susceptance/km/phase(siemen)\n",
"Pr = 10000 #power delivered(kW)\n",
"Vrl = 66000 #sending end line volt(V)\n",
"pf = 0.8 #power factor(lagging)\n",
"\n",
"\n",
"#Calculation:\n",
"R = r*l #Total resistance/phase(ohm)\n",
"Xl = xl*l #Total reactance/phase(ohm)\n",
"Y = b*l #Capacitive susceptance(siemen)\n",
"magVr = round(Vrl/3**0.5) #Receiving end voltage/phase(V)\n",
"magIr = round(Pr*1000/(3**0.5*Vrl*pf)) #Load current(A)\n",
"phy = math.acos(pf)\n",
"Z = R+Xl*1j #Impedance per phase(ohm)\n",
"#(i) Taking receiving end voltage as the reference phasor,\n",
"Vr = magVr+0j\n",
"Ir = magIr*(pf-math.sin(phy)*1j) #A\n",
"V1 = Vr+Ir*Z/2 #Voltage across C(V)\n",
"Ic = 1j*Y*V1 #Charging current(A)\n",
"Is = Ir+Ic #sending end current(A)\n",
"\n",
"\n",
"#(ii) Sending end voltage,\n",
"Vs = V1+Is*Z/2 #V\n",
"magVsl = 3**0.5*abs(Vs) #Line value of sending end voltage(V)\n",
"\n",
"#(iii) Referring to phasor diagram (iii),\n",
"theta1 = math.atan(Vs.imag/Vs.real) #angle between Vr & Vs\n",
"theta2 = math.atan(abs(Is.imag/Is.real)) #angle between Vr & Is\n",
"phys = theta1+theta2 #angle b/w Vs & Is\n",
"\n",
"pfs = math.cos(phys) #Sending end power factor\n",
"\n",
"#(iii):\n",
"Ps = 3*abs(Vs)*abs(Is)*pfs/1000 #Sending end power(kW)\n",
"n = Pr/Ps*100 #Efficiency(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) The sending end current is\",round(abs(Is)),\"A\"\n",
"print \"(ii) Sending end voltage is\",round(magVsl/1000,3),\"kV\"\n",
"print \"(iii)Sending end power factor is\",round(pfs,3),\"lagging\"\n",
"print \"(iv) Transmission efficiency is\",round(n,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The sending end current is 100.0 A\n",
"(ii) Sending end voltage is 69.532 kV\n",
"(iii)Sending end power factor is 0.853 lagging\n",
"(iv) Transmission efficiency is 97.12 %\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.12, Page Number: 245"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
"#Variable declaration:\n",
"l = 100 #line length(km)\n",
"r = 0.2 #resistance/km/phase(ohm)\n",
"xl = 0.4 #reactance/km/phase(ohm)\n",
"b = 2.5*10**-6 #Capacitive susceptance/km/phase(siemen)\n",
"Pr = 20000 #power delivered(kW)\n",
"Vrl = 110000 #sending end line volt(V)\n",
"pf = 0.9 #power factor\n",
"\n",
"\n",
"#Calculation:\n",
"R = r*l #Total resistance/phase(ohm)\n",
"Xl = xl*l #Total reactance/phase(ohm)\n",
"Y = b*l #Capacitive susceptance(siemen)\n",
"magVr = round(Vrl/3**0.5) #Receiving end voltage/phase(V)\n",
"magIr = round(Pr*1000/(3**0.5*Vrl*pf)) #Load current(A)\n",
"phy = math.acos(pf)\n",
"Z = R+Xl*1j #Impedance per phase(ohm)\n",
"\n",
"#(i) Taking receiving end voltage as the reference phasor,\n",
"Vr = magVr+0j\n",
"Ir = magIr*(pf-(math.sin(phy))*1j) #A\n",
"V1 = Vr+Ir*Z/2 #Voltage across C(V)\n",
"Ic = 1j*Y*V1 #Charging current(A)\n",
"Is = Ir+Ic #sending end current(A)\n",
"Vs = V1+Is*Z/2 #V\n",
"magVsl = 3**0.5*abs(Vs) #Line value of sending end voltage(V)\n",
"\n",
"#(ii):\n",
"Pl = 3*abs(Is)**2*R/2+3*magIr**2*R/2 #line loss(W)\n",
"n = Pr/(Pr+Pl/1000)*100 #efficiency\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) The current and voltage at the sending end is\",round(magVsl/1000,2),\"kV\"\n",
"print \"(ii)Efficiency of transmission is\",round(n,2),\"%\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) The current and voltage at the sending end is 116.75 kV\n",
"(ii)Efficiency of transmission is 96.26 %\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.13, Page Number: 247"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"l = 150 #line length(km)\n",
"r = 0.1 #resistance/km/phase(ohm)\n",
"xl = 0.5 #reactance/km/phase(ohm)\n",
"b = 3*10**-6 #Capacitive susceptance/km/phase(siemen)\n",
"Pr = 50000 #power delivered(kW)\n",
"Vrl = 110000 #sending end line volt(V)\n",
"pf = 0.8 #power factor\n",
"\n",
"\n",
"#Calculation:\n",
"R = r*l #Total resistance/phase(ohm)\n",
"Xl = xl*l #Total reactance/phase(ohm)\n",
"Y = b*l #Capacitive susceptance(siemen)\n",
"magVr = round(Vrl/3**0.5) #Receiving end voltage/phase(V)\n",
"magIr = round(Pr*1000/(3**0.5*Vrl*pf)) #Load current(A)\n",
"phy = math.acos(pf)\n",
"Z = R+Xl*1j #Impedance per phase(ohm)\n",
"\n",
"Vr = magVr+0j\n",
"Ir = magIr*(pf-(math.sin(phy))*1j) #A\n",
"Ic1 = Vr*1j*Y/2 #Charging current at the load end(A)\n",
"Il = Ir+Ic1 #line current(A)\n",
"Vs = Vr+Il*Z #Sending end voltage(V)\n",
"magVsl = abs(Vs)*3**0.5 #Line to line sending end voltage(V)\n",
"Ic2 = 1j*Vs*Y/2 #Charging current at the sending end(A)\n",
"Is = Il+Ic2 #Sending end current(A)\n",
"\n",
"\n",
"#Result:\n",
"print \"The sending end voltage is\",round(magVsl/1000,2),\"V\"\n",
"print \"The sending end current is\",round(abs(Is),1),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The sending end voltage is 143.56 V\n",
"The sending end current is 306.3 A\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.14, Page Number: 248"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"\n",
"#Variable Declaration:\n",
"l = 100 #line length(km)\n",
"r = 0.1 #resistance/km/phase(ohm)\n",
"xl = 0.5 #reactance/km/phase(ohm)\n",
"b = 10*10**-6 #Capacitive susceptance/km/phase(siemen)\n",
"Pr = 20000 #power delivered(kW)\n",
"Vrl = 66000 #sending end line volt(V)\n",
"pf = 0.9 #power factor\n",
"\n",
"\n",
"#Calculation:\n",
"R = r*l #Total resistance/phase(ohm)\n",
"Xl = xl*l #Total reactance/phase(ohm)\n",
"Y = b*l #Capacitive susceptance(siemen)\n",
"magVr = round(Vrl/3**0.5) #Receiving end voltage/phase(V)\n",
"magIr = round(Pr*1000/(3**0.5*Vrl*pf)) #Load current(A)\n",
"phy = math.acos(pf)\n",
"Z = R+Xl*1j #Impedance per phase(ohm)\n",
"\n",
"Vr = magVr+0j\n",
"Ir = magIr*(pf-(math.sin(phy))*1j) #A\n",
"Ic1 = round(magVr*Y/2)*1j #Charging current at the load end(A)\n",
"Il = Ir+Ic1 #line current(A)\n",
"Vs = Vr+Il*Z #Sending end voltage(V)\n",
"magVsl = abs(Vs)*3**0.5 #Line to line sending end voltage(V)\n",
"Ic2 = 1j*Vs*Y/2 #Charging current at the sending end(A)\n",
"Is = Il+Ic2 #Sending end current(A)\n",
"\n",
"#(i):\n",
"theta1 = math.atan(Vs.imag/Vs.real) #angle between Vr & Vs\n",
"theta2 = math.atan(abs(Is.imag/Is.real)) #angle between Vr & Is\n",
"phys = theta1+theta2 #angle b/w Vs & Is\n",
"pfs = math.cos(phys) #Sending end power factor\n",
"\n",
"#(ii):\n",
"reg = (abs(Vs)-magVr)/magVr*100 #voltage regulation(%)\n",
"\n",
"#(iii):\n",
"Ps = 3*abs(Vs)*abs(Is)*pfs/1000 #sending end power(W)\n",
"n = Pr/Ps*100 #transmission efficiency(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"(i) Sending end power factor is\",round(pfs,3),\"lagging\"\n",
"print \"(ii) Regulation is\",round(reg,2),\"%\"\n",
"print \"(iii)Transmission efficiency is\",round(n),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Sending end power factor is 0.906 lagging\n",
"(ii) Regulation is 15.15 %\n",
"(iii)Transmission efficiency is 95.0 %\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
" Example 10.15, Page Number: 254"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import cmath\n",
"\n",
"#Variable Declaration:\n",
"l = 200 #line length(km)\n",
"r = 0.16 #resistance/km/phase(ohm)\n",
"xl = 0.25 #reactance/km/phase(ohm)\n",
"b = 1.5*10**-6*1j #Capacitive susceptance/km/phase(siemen)\n",
"Pr = 20000 #power delivered(kW)\n",
"Vrl = 110000 #sending end line volt(V)\n",
"pf = 0.8 #power factor\n",
"\n",
"#Calculation:\n",
"R = r*l #Total resistance/phase(ohm)\n",
"Xl = xl*l #Total reactance/phase(ohm)\n",
"Y = b*l #Capacitive susceptance(siemen)\n",
"Z = R+Xl*1j #Series Impedance/phase(ohm)\n",
"magVr = Vrl/3**0.5 #Receiving end voltage per phase(V)\n",
"magIr = round(Pr*1000/(3**0.5*Vrl*pf)) #Receiving end current(A)\n",
"Vs = magVr*cmath.cosh((Y*Z)**0.5)+magIr*(Z/Y)**0.5*cmath.sinh((Z*Y)**0.5) #sending end voltage(V/phase)\n",
"Is = magVr*(Y/Z)**0.5*cmath.sinh((Y*Z)**0.5)+magIr*cmath.cosh((Y*Z)**0.5)\n",
"\n",
"\n",
"#Result:\n",
"print \"Sending end line-to-line voltage is\",round(3**0.5*abs(Vs)/1000,1),\"V\"\n",
"print \"Sending end current is\",round(abs(Is),1),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Sending end line-to-line voltage is 117.0 V\n",
"Sending end current is 131.5 A\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.16, Page Number: 258"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import cmath\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"Z = 20+52j #Series line impedance/phase(ohm)\n",
"Y = 315*10**-6*1j #Shunt admittance/phase(siemen)\n",
"pf = 0.85 #power factor\n",
"Pr = 30000 #receiving end power(kW)\n",
"magVrl = 132000 #receiving end voltage(V)\n",
"\n",
"\n",
"#Calculation:\n",
"#(i) Generalised constants of line,\n",
"A = 1+Z*Y/2\n",
"D = A\n",
"B = Z*(1+Z*Y/4)\n",
"C = Y\n",
"\n",
"#(ii) Sending end voltage,\n",
"magVr = magVrl/3**0.5 #V/phase\n",
"magIr = Pr*1000/(3**0.5*magVrl*pf) #line current(A)\n",
"phy = math.acos(pf)\n",
"Vr = magVr+0j\n",
"Ir = magIr*(math.cos(phy)-1j*math.sin(phy))\n",
"Vs = A*Vr+B*Ir\n",
"magVs = abs(Vs) #sending end voltage(V/phase)\n",
"magVsl = 3**0.5*magVs #Sending end line-to-line voltage(V)\n",
"\n",
"\n",
"#(iii) Regulation:\n",
"#At no load, Ir = 0,\n",
"magVro = abs(Vs/A)\n",
"reg = (magVro-magVr)/magVr*100 #regulation(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"(i)The A, B, C and D constants of the line are\"\n",
"print \" A =\",complex(round(A.real,3),round(A.imag,5))\n",
"print \" B =\",complex(round(B.real,2),round(B.imag,2))\n",
"print \" C =\",complex(round(C.real,6),round(C.imag,6))\n",
"print \" D =\",complex(round(D.real,3),round(D.imag,5))\n",
"\n",
"print \"(ii) Sending end voltage is\",round(magVs*3**0.5/1000),\"kV\"\n",
"print \"(iii)Regulation of the line is\",round(reg,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)The A, B, C and D constants of the line are\n",
" A = (0.992+0.00315j)\n",
" B = (19.84+51.82j)\n",
" C = 0.000315j\n",
" D = (0.992+0.00315j)\n",
"(ii) Sending end voltage is 143.0 kV\n",
"(iii)Regulation of the line is 9.25 %\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.17, Page Number: 259"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import cmath\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"A = cmath.rect(0.95,math.radians(1.4))\n",
"B = cmath.rect(96,math.radians(78))\n",
"C = cmath.rect(0.0015,math.radians(90))\n",
"D = cmath.rect(0.95,math.radians(1.4))\n",
"Pr = 50000 #receiving end power(kW)\n",
"pf = 0.8 #power factor\n",
"magVrl = 132000 #receiving end voltage(V)\n",
"\n",
"\n",
"#Calculation:\n",
"magVr = magVrl/3**0.5 #Receiving end voltage/phase(V)\n",
"magIr = Pr*1000/(3**0.5*magVrl*pf) #line current(A)\n",
"phy = math.acos(pf)\n",
"Vr = magVr+0j\n",
"Ir = magIr*(math.cos(phy)-1j*math.sin(phy))\n",
"Vs = A*Vr+B*Ir #Sending end voltage per phase\n",
"Is = C*Vr+D*Ir #Sending end current\n",
"Ic = Is-Ir #Charging current\n",
"#At no load, Ir = 0,\n",
"magVro = abs(Vs/A)\n",
"reg = (magVro-magVr)/magVr*100 #regulation(%)\n",
"\n",
"\n",
"#Result:\n",
"print \"Charging current is (\",round(abs(Ic)),round(math.degrees(angle(Ic)),1),\") A\"\n",
"print \"Regulation is\",round(reg),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Charging current is ( 128.0 93.2 ) A\n",
"Regulation is 30.0 %\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 10.18, Page Number: 260"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import cmath\n",
"import math\n",
"\n",
"#Variable Declaration:\n",
"A = cmath.rect(0.98,math.radians(3))\n",
"B = cmath.rect(110,math.radians(75))\n",
"C = cmath.rect(0.0005,math.radians(80))\n",
"D = cmath.rect(0.98,math.radians(3))\n",
"MVA = 50 #receiving end power\n",
"pf = 0.8 #power factor\n",
"magVrl = 110 #receiving end voltage(kV)\n",
"\n",
"\n",
"#Calculation:\n",
"Pr = MVA*pf*10**6\n",
"magVr = round(magVrl/3**0.5,1) #Receiving end voltage/phase(V)\n",
"magIr = round(MVA*10**6/(3**0.5*magVrl*1000),1) #line current(A)\n",
"phy = math.acos(pf)\n",
"Vr = magVr*1000+0j\n",
"Ir = magIr*(math.cos(phy)-1j*math.sin(phy))\n",
"#(round(Ir.real)+1j*round(Ir.imag))\n",
"V1 = round((A*Vr).real)+math.ceil((A*Vr).imag)*1j\n",
"V2 = round((B*Ir).real)+math.ceil((B*Ir).imag)*1j\n",
"Vs = V1+V2 #Sending end voltage per phase\n",
"theta1 = math.atan(Vs.imag/Vs.real)\n",
"Is = C*Vr+D*Ir #Sending end current\n",
"theta2 = math.atan(Is.imag/Is.real)\n",
"phys = theta2-theta1\n",
"Ps = 3*abs(Vs)*abs(Is)*math.cos(phys) #Sending-end power(W)\n",
"n = Pr/Ps*100 #efficiency(%)\n",
"\n",
"#Result:\n",
"print \"(i) Sending end voltage is\",round(abs(Vs)),\"V\"\n",
"print \"(ii) Sending end current is\",round(abs(Is)),\"A\"\n",
"print \"(iii)Sending-end power is\",round(Ps/10**6,1),\"MW\"\n",
"print \"(iv) Transmission efficiency is\",round(n,1),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Sending end voltage is 87429.0 V\n",
"(ii) Sending end current is 246.0 A\n",
"(iii)Sending-end power is 48.7 MW\n",
"(iv) Transmission efficiency is 82.2 %\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}