I am trying to calculate the Sequence Impedance/Zero Sequence Impedance of couple of lines, but Im not sure if the calculation are right, and besides there are some tricky things on the data provided.

  • Tower (in meters)

enter image description here

  • • PS30

• Nominal voltage 34.5 kV

• Circuits 1

• Conductors p/phase 1

• 60 Hz

• terrain resistivity 100Ohm/m

• Ground wires No

• ACSR, 266.8 KCM, 26/7

• MGR/ 6.61416 mm=0.260400141inch=0.021700001ft

• rac 0.23426 Ohm/km (0.350ohm/mi) • wk=0.12134

Then in the calculations
\$ \large{}D_{e}=2160\sqrt{\frac{\rho}{f}}=2160\sqrt{\frac{100}{60Hz}}=2788.5480ft \$
\$ \textbf{$r_{ac}=0.23426\Omega/km=0.37692434\Omega/mi$} \$
At 60Hz
\$r_{d}=0.09528\Omega/mi;\omega k=0.12134\$
Distance between wires
\$ D_{ab}=3.76804ft D_{ac}=6.10236ft D_{bc}=3.76804ft D_{abc}=4.42493ft \$
Mutual inductances

\$Z_{aa}=Z_{bb}=Z_{cc}\$\$=r_{a}+r_{d}+j\omega kln\frac{D_{e}}{D_{s}}\$


\$Z_{ab}=r_{d}+j\omega kln\frac{D_{e}}{D_{ab}}\$






\$Z_{abc}\$=\begin{array}{ccc} 0.4722+j1.427409 & 0.09528+j0.8016595 & 0.09528+j0.743159\\ 0.09528+j0.8016595 & 0.4722+j1.427409 & 0.09528+j0.8016595\\ 0.09528+j0.743159 & 0.09528+j0.8016595 & 0.4722+1.427409 \end{array} $

My questions are
*if this is correct since in the data provided the value of \$ rac =0.23426 Ohm/km\$ was used (converted to Ohms/miles) or should it be used the tables value of 0.350Ohm/mile.

  • then how can be calculated the zero sequence? Does it need to be transposed and apply \$[A]^{-1} [Zabc] [A]\$.

Note: I am using the book of Anderson, Analysis of Faulted Power Systems, but if there is another way to do so please tell it. The main concern is if the values are ok, since the notation sometimes are referred in different way.

  • 2
    \$\begingroup\$ It would help if you added some descriptions about your steps, don't just rely on short-hand notations and expect them to be known, because there are many schools all over the world, and each may learn them differently. It would help with the clarity, too. I've upvoted because it looks like you've done your research before asking. \$\endgroup\$ Jun 14, 2021 at 19:18

1 Answer 1


Yes, once you have calculated the impedance matrix for the line, \$Z_{abc}\$, you need to pre-multiply it with \$A^{-1}\$ and post-multiply it with \$A\$.

$$Z_{012}=\begin{pmatrix}Z_{00} & Z_{01} & Z_{02} \\\ Z_{10} & Z_{11} & Z_{12} \\\ Z_{20} & Z_{21} & Z_{22} \end{pmatrix} =A^{-1}Z_{abc}A$$

Turan Gönen called this equation the "similarity transformation" in his excellent text, Electric Power Transmission System Engineering: Analysis and Design.

If your line is perfectly transposed you will find the resulting matrix \$Z_{012}\$ will be a square diagonal matrix (no coupling between the sequence networks). But, since your line is not transposed, their will be off-diagonal terms. This means that their will be coupling between the sequence networks (e.g. zero-sequence current flow could/would produce positive and negative sequence voltage etc.).

Yes, use the \$rac\$ presented as input data. Why wouldn't you?

You can verify your calculations with commercial programs like this one or free ones like ATP or OpenDSS.


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