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# Circuits of different voltages physically in parallel

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There is plenty of information out there on modeling the impedance matrix of two parallel lines of the same voltage. I'm having a hard time finding any information on a scenario in which we have two circuits of different voltages in the same corridor. Can anyone point me to a reference, text book, or just give an explanation of how an equivalent impedance matrix is created?

For example, I'm thinking specifically of a 12.47kV line on the same pole as a 34.5 or 69kV line. I'm interested in modeling the 12.47kV line, but how do I take the effect of the 34.5 or 69kV coupling into account?

Thank you

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I poor understand you... Do you mean such a circuit?

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I think the OP is referring to mutual inductance of lines that are not electrically connected in parallel, just located near each other. The connection shown in the diagram above would cause a fault. When studying for the PE exam I ran across this a bit in the Camara book, but had to get some info from the older Yarbrough version. I don't have either with me right now, but you may be able to do it with the ACSR conductor chart (with the bird names).

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I poor understand you... Do you mean such a circuit?

Unless V1=V2=V3 I think this circuit would violate the laws of physics as drawn.

Can't remember how to model it, wouldn't this inducance be more dependent on the current in the conductor than the voltage? (not much help, i know)

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I finally did find an answer buried away in one of my old text books. It is indeed dependent upon the current.

If anyone happens upon this post looking for an answer, I found it in "Power Systems Modelling and Fault Analysis" by Tleis. I don't recommend this book actually... but it does explain how you model my problem.