Transmission Line Impedances in Matrix format 3

[Uquresh1]

A customer provided me transmission line impedance for a 69KV line in matrix format. He got it from ETAP. I am used to of getting impedances in R1+jX1 and Ro+jXo format which is exactly what I input into ASPEN. Can someone please help me with reading or decyphering these matrices to obtain my impedances for ASPEN modeling.

R Matrix (ohms)

A B C
A 0.72 0.404 0.368
B 0.404 0.762 0.386
C 0.368 0.386 0.689

0 1 2
0 1.496 -0.029 0.026
1 0.026 0.338 -0.002
2 -0.029 -0.001 0.338


X Matrix (ohms)

A B C
A 2.539 1.158 1.19
B 1.158 2.502 1.136
C 1.19 1.136 2.566

0 1 2
0 4.858 -0.017 0.045
1 0.045 1.374 -0.024
2 -0.017 -0.024 1.374

 

[wroggent]

Well, if you assume the line is completely transposed:

Z0=Z'aaeq+2Z'abeq
Z1=Z2=Z'aaeq-Z'abeq

where

Z'aaeq=1/3(Zaaeq+Zbbeq+Zcceq)
Z'abeq=1/3(Zabeq+Zaceq+Zbceq)

From your numbers:

Zaaeq=0.72+j2.539
Zab=0.404+j1.158

etc...

Going through this calculation arrives at basically what the matrix for the sequence impedance you gave shows...

Z0=1.49567+j4.85833
Z1=0.337667+j1.37433

 

[juleselec]

It really depends on what kind of study you will be doing and the level of accuracy you are interested in.

When you enter R1 + jX1, R0 + jX0, etc into ASPEN, you are actually using a single-phase equivalent model of the transmission line (i.e. ignoring mutual coupling). So if you simply want to do balanced load flows with short and/or fully transposed lines, then using the sequence impedances as wroggent described will work perfectly well.

But the customer has provided you with partial data for a multi-conductor three-phase line model, which includes the mutual couplings between phase conductors. The mutual couplings become more important for unbalanced systems and long untransposed lines. I said partial data because you should usually get the shunt admittance matrices as well (i.e. shunt capacitance and conductance).

In any case, these matrices are calculated from geometric layouts of the transmission line using a LINE CONSTANTS program. I'm pretty sure ASPEN has one so if you want to model the line in detail, then you should ask the customer for the geometric layout of the transmission line and the type of conductors used, and then plug them into the ASPEN line constants program.