Estimate primary line coeffiecients

[billyray]

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.

Homework Equations

From the table I am using C as 0 + j.001349s = Y2
A as 0.8698 + j 0.03542
so
(1+Z1Y2) = A
(.8698 + .03542 j - 1)/(.001349 j)= Z1
= 26.26 - j644.75
I am using an online calculator for this. I have looked at other posts and my answer is different am I doing something wrong to get Z1. I was then going to use the equation Z1 = 0.5 (R +jωL) x length of line. am I on the right track.

The Attempt at a Solution

Attempted above

 

[Babadag]

Apart from the fact that Z1 = 26.2565+j96.516 the calculation is correct.

 

[billyray]

Hi Babadag

Thanks for the help again. You mean they were wrong and mine is correct?
so Z1 = 26.26 - j644.75

 

[Babadag]

0.8698-1=-0.1302; -0.1302/j0.001349=-j0.1302/(j^2.0.001349)=j96.516 it does not?
j0.03542/j0.001349)=26.256

 

[billyray]

oh
that means Z1 = 26.256
how would I go about getting Z1 = 0.5 (R +jωL)x line length ?
would L be 0?

 

[Babadag]

I am sorry, billyray. Your division it is wrong.
Let’s say you have to divide a+jb by jc (a+jb)/jc=a/jc+b/c=ja/(jxj)c+b/c=b/c-ja/c
a=0.8698-1=-0.1302
b=0.03542
c=0.001349
Then the result will be: b/c=0.03542/0.001349=26.2565;ja/c=-j(-0.1302/0.001349)=+96.516 does not it?

 

[billyray]

ah ok I see thank you for the time and effort Babadag its most appreciated.
R would then be 26.2565 and L j96.5901 / 2 x pi x 50
would Cs just be j 0.001349 /2x pi x 50 and G = 0

 

[billyray]

I am a little confused about C as 0 + j.001349s = Y2
Y2 = (G + jωC) x length of line
would g just be 0 and Capacitance be j.001349/2xpix50

 

[billyray]

I have looked at another post and they say:
Shunt element = 1/C
would my capacitance be 1/j.001349/w

 

[billyray]

i have my capacitance as 4.294 x 10 to the power -6 does that seem correct?

 

[Babadag]

Reactance : inductive XL= Lxꞷxlength; capacitive XC=1/(Cxꞷxlength) but Y2=length/Rair+j/XC=Gxlength+jCxꞷxlength.
All these parameters are direct proportional with the length.

 

[billyray]

Thanks Babadag
so if I use Y2 = (0 + j.001349ꞷ )x length
I can use 0 = G
ꞷ=2xpix50Hertz
and j0.001349/ꞷxlength
=4.294 x 10^6 xlength for capacitance
thanks again for helping

 

[billyray]

=4.294 x 10^-6 I mean sorry

 

[Babadag]

Sorry.G- the shunt conductance- it is not actually the air resistance but the insulator creepage resistance- something about 1-2/10^9 S [S=Siemens=1/ohm]

 

[billyray]

how do I work the G part out?

 

[billyray]

thanks for help anyway Babadag