Dear all,

I hope you are doing well.

This semester, I have a power system analysis course; I am now teaching the chapter devoted to unbalanced operation modeling of power systems.

Using the book by Dr. Elgerd as one of my references, I have seen something strange in his book. Before applying the symmetrical components transformation to the voltage-current relation of a synchronous generator, he states that the equations in the abc domain are as follows:

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with the impedance matrix Z to be in this form:

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This matrix, as is evident, is NOT symmetrical but cyclic symmetrical. This means that Z12 is different from Z21. That is, the mutual impedance from phase b to phase a is different from the mutual impedance from phase a to phase b!

It seems that he is taking a non-salient pole generator into account (as all the diagonal elements are equal). Under such conditions, all the off-diagonal terms should seemingly be equal in opposition to this textbook!

Am I missing something? This is really strange as in physical sense, the mutual impedances should be reciprocal (please take into account that we have still not applied any abc==>dq0 transformation).

I humbly ask you to help me in this regard.

For the sake of completeness, I give you the link to the full text of the book, as follows:

https://handoutset.com/wp-content/uploads/2022/07/electric-energy-system-theory-an-introduction-olle-i.-elgerd.pdf

Please go to page 228/291.

Best wishes