Transmission Line Coefficients

  • #1
57
8

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:

mimetex-cgi-20v_s-v_r-a_1-ja_2-i_r-b_1-jb_2-gif.gif


mimetex-cgi-20i_s-v_r-c_1-jc_2-i_r-d_1-jd_2-gif.gif


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
mimetex-cgi-20v_s-gif.gif
and
mimetex-cgi-20i_s-gif.gif
and hence the power
mimetex-cgi-20p_-so-gif.gif
absorbed from the supply by the transmission line on open circuit.

(b) If the line is modelled 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.

upload_2019-3-4_11-6-3.png



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?
 

Attachments

Answers and Replies

  • #2
430
119
In my opinion Z3 is parallel with 1/Y2 and the total Z [if VR=0] has to be Z1+Z3||1/Y2
 
Last edited:
  • #3
430
119
Sorry, it could be better using D=IS/IR =Z3||1/Y2 divided by Z3
 
  • #4
57
8
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?

upload_2019-3-6_20-32-20.png
 

Attachments

  • #5
430
119
It is o.k. and for the record Z1=Z3 indeed.
 

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