Question

DO IT To receive credit for this assignment, each problem must be computed using a MATLAB script. Do not hard-code computations. Define variables for the parameters given in the problem, and use MATLAB to calculate necessary intermediate and final output variables. Inlcude the MATLAB Code. A 200-mi. transmission line has the following parameters at 60 Hz: Resistance, r = 0.24 Ω/mi. per phase Series Reactance, x = 0.71 Ω/mi. per phase Shunt Susceptance, b = 5.42 × 10−6 S/mi. per phase Determine the signal wavelength λ and the propagation constant γ, attenuation constant α, phase constant β, and characteristic impedance Zc of the transmission line at 60 Hz using the general expressions in terms of Z and Y parameters valid for conductance G = 0 S/mi. Next, calculate the “convenient” artificial value for conductance G = RC/L and α, β, and Zc using this approximation. Finally, determine the sending-end voltage and current if the line is open-circuited and the receiving-end voltage is 100 kV line-to-line.

Answer 1

Matlab program
clc;
clear all;
.......Calculations when G=0............
l=200;
r=0.24;
R=l*r;
x=0.71;
X=l*x;
z=r+j*x;
Z=z*l;
b=5.42*10^(-6);
B=b*l;
g=0;
y=g+j*b;
Zc=sqrt(z/y)
gama=sqrt(z*y)
alpha=real(gama)*l
beta=imag(gama)*l
lambda=(2*pi)/beta
.......Calculations when G=RC/L............
G=(R*B)/X
Y=G+j*B
Zc1=sqrt(Z/Y)
gama1=sqrt(Z*Y)/l
alpha1=real(gama1*l)
beta1=imag(gama1*l)
.....Sending end voltage and current when G=0............
VR=100
IR=0
Vs=VR*cosh(gama*l)
Is=VR*(sinh(gama*l)/Zc)
.....Sending end voltage and current when G=(R*C)/L.....
Vs1=VR*cosh(gama1*l)
Is1=VR*(sinh(gama1*l)/Zc1)
Calculations:
Zc = 366.929 - 60.339i
gama = 3.2704e-04 + 1.9888e-03i
alpha = 0.065408
beta = 0.39775
lambda = 15.797
G = 3.6642e-04
Y = 3.6642e-04 + 1.0840e-03i
Zc1 = 3.6193e+02 + 8.1267e-15i
gama1 = 6.6310e-04 + 1.9617e-03i
alpha1 = 0.13262
beta1 = 0.39234
VR = 100
IR = 0
Vs = 92.3907 + 2.5353i
Is = -9.2565e-04 + 1.0564e-01i
Vs1 = 93.2156 + 5.0856i
Is1 = 0.033957 + 0.106571i

Note: Voltages are in KV and currents are in KA.