How to Calculate Transmission Line Coefficients?

[Jason-Li]

Homework Statement

Figure shows a 50 Hz, high-voltage, transmission line. The relationships between the sending and receiving end voltages and currents are given by the complex ABCD equations:

where 'S' stands for sending-end and 'R' stands for receiving-end

(a) Given the parameter values in TABLE C and an open-circuit received voltage measured as 88.9 kV, calculate the values of

and

and hence the power

absorbed from the supply by the transmission line on open circuit.

(b) If the line is modeled by the T-circuit of FIGURE 3(b), see if you can estimate the primary line coefficients R, L, G and C. The line is 50 km long.

The Attempt at a Solution

I am currently doing part (b), if

[ A B ] = [ 1+Z1*Y2 Z1+Z3+Z1*Y2*Z3 ]
[ C D ] = [ Y2 1+Y2*Z3 ]

Then Y2 = C =j0.001349S
Also A=1+Z1*Y2
Z1= (A-1)/Y2
Z1=(0.8698+j0.03542-1) / j0.001349
Z1= 26.268+j96.558 Ω
Z1=Z3
So as Z1 & Z3 in series:
R+jXL = Z1*2
R+jXL = 52.536+j193.116 Ω
R coefficient = R / 50 = 1.051Ω/km
L= XL / 2πf = 193.116 / 2π*50 = 0.614707H
L coefficient = 0.614707 / 50 = 12.294mH/km
G coefficient = 0 as Y2 branch is not resistive only 'imaginary'
XC = 1 / Y2 = -j741.290 which is capacitive
C= 1/ XC*2πf = 1 / j741.290*2π*50 = 4.29μF
C coefficient = 4.29μF / 50 = 85.88pF/km

How does that look to you smarter people?

 

[Babadag]

In my opinion Z3 is parallel with 1/Y2 and the total Z [if VR=0] has to be Z1+Z3||1/Y2

 

[Babadag]

Sorry, it could be better using D=IS/IR =Z3||1/Y2 divided by Z3

 

[Jason-Li]

Hi Babadag,

I would've likely said the same however in my learning materials the below is stipulated. I then equated that each as appropriate. Any ideas?

 

[Babadag]

It is o.k. and for the record Z1=Z3 indeed.