# Chapter 6 - REPRESENTATION AND PERFORMANCE OF LONG TRANSMISSION LINES¶

## Example E1 - Pg 168¶

In [1]:
#calculate A,B,C,D
import math
import cmath
import numpy
#Given data :
r=0.22##ohm
x=0.45##ohm
g=4.*10.**-9##S
b=2.53*10.**-6##S
f=50.##Hz
l=1000.##Km
#Using Convergent series of complex angles
z=r+1j*x##ohm
y=g+1j*b##ohm
Z=z*l##ohm
Y=y*l##ohm
YZ=Y*Z##ohm
Y2Z2=YZ**2.##ohm
Y3Z3=YZ**3.##ohm
A=1.+YZ/2.+Y2Z2/24.+Y3Z3/720.##ohm
D=A##oh,m
B=Z*(1.+YZ/6.+Y2Z2/120.+Y3Z3/5040.)##ohm
C=Y*(1.+YZ/6.+Y2Z2/120.+Y3Z3/5040.)##ohm
print '%s' %("Auxiliary Constants by using Convergent series of complex angles : ")#
print "A = ",A#
print "B = ",B#
print "C = ",C#
#Using Convergent series of real angles
A=cmath.cosh(cmath.sqrt(YZ))##ohm
D=A##ohm
B=cmath.sqrt(Z/Y)*cmath.sinh(cmath.sqrt(YZ))##ohm
C=cmath.sqrt(Y/Z)*cmath.sinh(cmath.sqrt(YZ))##ohm
A=cmath.cosh(cmath.sqrt(YZ))##ohm
print '%s' %("Auxiliary Constants by using Convergent series of real angles : ")#
print '%s %.2f %s %.2f' %("A, magnitude is ",abs(A)," and angle in degree is ",cmath.phase(A)*180/math.pi)#
print '%s %.2f %s %.2f' %("B, magnitude is ",abs(B)," and angle in degree is ",cmath.phase(B)*180/math.pi)#
print '%s %.4f %s %.2f' %("C, magnitude is ",abs(C)," and angle in degree is ",cmath.phase(C)*180/math.pi)#
print '%s' %("We obtain same result by both of the methods.")
Auxiliary Constants by using Convergent series of complex angles :
A =  (0.471555198201+0.229032046676j)
B =  (142.776787567+386.558406193j)
C =  (-0.000206399312625+0.00207114180387j)
Auxiliary Constants by using Convergent series of real angles :
A, magnitude is  0.52  and angle in degree is  25.90
B, magnitude is  412.08  and angle in degree is  69.73
C, magnitude is  0.0021  and angle in degree is  95.69
We obtain same result by both of the methods.

## Example E2 - Pg 169¶

In [2]:
#calculate Sending end line voltage in kV,Sending end current in A, magnitude is
import math
import cmath

#Given data :
Z=200.*(math.cos(80.*math.pi/180.) + 1j*math.sin(80.*math.pi/180.))##ohm
Y=0.0013*(math.cos(90.*math.pi/180.) + 1j*math.sin(90.*math.pi/180.))#S/phase
P=80.*10.**6##W
pf=0.8##power factor
VRL=220.*1000.##V
VR=VRL/math.sqrt(3.)##V
IR=P/math.sqrt(3.)/VRL/pf##A
fi=math.acos(pf)*180/math.pi##degree
IR=IR*(math.cos(-fi*math.pi/180.) + 1j*math.sin(-fi*math.pi/180.))##A
YZ=Y*Z##ohm
Y2Z2=YZ**2##ohm
Y3Z3=YZ**3##ohm
A=1.+YZ/2.+Y2Z2/24+Y3Z3/720##ohm
D=A##oh,m
B=Z*(1.+YZ/6.+Y2Z2/120.+Y3Z3/5040.)##ohm
C=Y*(1.+YZ/6.+Y2Z2/120.+Y3Z3/5040.)##mho
VS=A*VR+B*IR##V
VSL=math.sqrt(3.)*abs(VS)##V
print '%s %.2f' %("Sending end line voltage in kV : ",VSL/1000.)#
IS=C*VR+D*IR##
print '%s %.2f %s %.2f' %("Sending end current in A, magnitude is ",abs(IS)," and angle in degree is ",cmath.phase(IS)*180/math.pi)#
Sending end line voltage in kV :  263.59
Sending end current in A, magnitude is  187.48  and angle in degree is  7.66

## Example E3 - Pg 176¶

In [4]:
#calculate Constant A0,Constant B0,Constant C0,Constant D0
import math
import cmath
#Given data :
VRL=220.##kV
VR=VRL/math.sqrt(3.)##V
P=10.*10**6##VA
Z=1.+1j*8.##ohm(in %)
Zse=Z/100.*VRL**2./100.##ohm/phase
A=0.9*(math.cos(0.6*math.pi/180.) + 1j*math.sin(0.6*math.pi/180.))##Auxiliary constant
D=A ##Auxiliary constant

B=153.2*(math.cos(84.6*math.pi/180.) + 1j*math.sin(84.6*math.pi/180.))##Auxiliary constant
C=0.0012*(math.cos(90*math.pi/180.) + 1j*math.sin(90*math.pi/180.))##Auxiliary constant
A0=A+C*Zse##constant
B0=B+D*Zse##ohm#constant
C0=C##mho or S#constant
D0=A##constant
print '%s %.4f %s %.2f' %("Constant A0, magnitude is ",abs(A0)," and angle in degree is ",cmath.phase(A0)*180/math.pi)#
print '%s %.f %s %.2f' %("Constant B0(ohm), magnitude is ",abs(B0)," and angle in degree is ",cmath.phase(B0)*180/math.pi)#
print '%s %.4f %s %.2f' %("Constant C0(S), magnitude is ",abs(C0)," and angle in degree is ",cmath.phase(C0)*180/math.pi)#
print '%s %.1f %s %.2f' %("Constant D0, magnitude is ",abs(D0)," and angle in degree is ",cmath.phase(D0)*180/math.pi)#
Constant A0, magnitude is  0.8536  and angle in degree is  1.02
Constant B0(ohm), magnitude is  188  and angle in degree is  84.39
Constant C0(S), magnitude is  0.0012  and angle in degree is  90.00
Constant D0, magnitude is  0.9  and angle in degree is  0.60

## Example E4 - Pg 177¶

In [9]:
#calculate Constant A0,Constant B0,Constant C0,Constant D0
import math
import cmath
#Given data :
A=0.98*(math.cos(2.*math.pi/180.) + 1j*math.sin(2.*math.pi/180.))##Auxiliary constant
D=A##Auxiliary constant
B=28.*(math.cos(69.*math.pi/180.) + 1j*math.sin(69.*math.pi/180.))##Auxiliary constant
Zse=12.*(math.cos(80.*math.pi/180.) + 1j*math.sin(80.*math.pi/180.))##ohm
C=(A*D-1)/B##Auxiliary constant
A0=A+C*Zse##constant
B0=B+2.*A*Zse+C*Zse**2.##ohm#constant
C0=C##mho or S#constant
D0=A0##constant
print '%s %.2f %s %.2f' %("Constant A0, magnitude is ",abs(A0)," and angle in degree is ",cmath.phase(A0)*180/math.pi)#
print '%s %.2f %s %.2f' %("Constant B0(ohm), magnitude is ",abs(B0)," and angle in degree is ",cmath.phase(B0)*180/math.pi)#
print '%s %.2f %s %.f' %("Constant C0(S), magnitude is ",abs(C0)," and angle in degree is ",cmath.phase(C0)*180/math.pi)#
print '%s %.3f %s %.2f' %("Constant D0, magnitude is ",abs(D0)," and angle in degree is ",cmath.phase(D0)*180/math.pi)#
Constant A0, magnitude is  0.96  and angle in degree is  3.53
Constant B0(ohm), magnitude is  50.89  and angle in degree is  75.24
Constant C0(S), magnitude is  0.00  and angle in degree is  53
Constant D0, magnitude is  0.958  and angle in degree is  3.53

## Example E5 - Pg 177¶

In [11]:
#calculate
import math
import cmath
#Given data :
A=0.92*(math.cos(5.3*math.pi/180.) + 1j*math.sin(5.3*math.pi/180.))#Auxiliary constant
D=A##Auxiliary constant
B=65.3*(math.cos(81*math.pi/180.) + 1j*math.sin(81*math.pi/180.))##Auxiliary constant
ZT=100*(math.cos(70*math.pi/180.) + 1j*math.sin(70*math.pi/180.))##ohm
YT=0.0002*(math.cos(-75.*math.pi/180.) + 1j*math.sin(-75.*math.pi/180.))##S
C=(A*D-1)/B##Auxiliary constant
A0=A*(1+2*YT*ZT)+B*(YT)+C*ZT*(1+YT*ZT)##constant
B0=2.*A*ZT+B+C*ZT**2##ohm#constant
C0=2.*A*YT*(1.+YT*ZT)+B*YT**2.+C*(1.+YT*ZT)**2.##mho or S#constant
D0=A0##constant
print '%s %.5f %s %.2f' %("Constant A0, magnitude is ",abs(A0)," and angle in degree is ",cmath.phase(A0)*180/math.pi)#
print '%s %.2f %s %.2f' %("Constant B0(ohm), magnitude is ",abs(B0)," and angle in degree is ",cmath.phase(B0)*180/math.pi)#
print '%s %.6f %s %.1f' %("Constant C0(S), magnitude is ",abs(C0)," and angle in degree is ",cmath.phase(C0)*180/math.pi)#
print '%s %.2f %s %.2f' %("Constant D0, magnitude is ",abs(D0)," and angle in degree is ",cmath.phase(D0)*180/math.pi)#
Constant A0, magnitude is  0.84340  and angle in degree is  26.45
Constant B0(ohm), magnitude is  233.85  and angle in degree is  84.30
Constant C0(S), magnitude is  0.003442  and angle in degree is  50.9
Constant D0, magnitude is  0.84  and angle in degree is  26.45

## Example E6 - Pg 178¶

In [15]:
#calculate
import math
import cmath
#Given data :
A=0.945*math.cos(1.02*math.pi/180.) + 1j*math.sin(1.02*math.pi/180.)##Auxiliary constant
D=A##Auxiliary constant
B=82.3*math.cos(73.03*math.pi/180.) + 1j*math.sin(73.03*math.pi/180.)##ohm#Auxiliary constant
C=0.001376*math.cos(90.4*math.pi/180.) + 1j*math.sin(90.4*math.pi/180.)##S#Auxiliary constant
#part (i)
Y=C##S
Z=2.*(A-1)/C##ohm
print '%s' %("For equivalent T-network : ")#
print '%s %.6f %s %.1f' %("Shunt admittance in S, magnitude is ",abs(Y)," and angle in degree is ",cmath.phase(Y)*180/math.pi)#
print '%s %.2f %s %.1f' %("Impedance in ohm, magnitude is ",abs(Z)," and angle in degree is ",cmath.phase(Z)*180/math.pi)#
print '%s' %("For equivalent pi-network : ")#
Z=B##ohm
print '%s %.2f %s %.2f' %("Series Impedance in ohm, magnitude is ",abs(Z)," and angle in degree is ",cmath.phase(Z)*180/math.pi)#
Y=2.*(A-1)/B##S
print '%s %.6f %s %.2f' %("Shunt admittance in S, magnitude is ",abs(Y)," and angle in degree is ",cmath.phase(Y)*180/math.pi)#
#For T-Network Value of Z is wrog in the book.
For equivalent T-network :
Shunt admittance in S, magnitude is  0.999976  and angle in degree is  90.0
Impedance in ohm, magnitude is  0.12  and angle in degree is  72.1
For equivalent pi-network :
Series Impedance in ohm, magnitude is  24.04  and angle in degree is  2.28
Shunt admittance in S, magnitude is  0.004821  and angle in degree is  159.83