Do nearby lines affect the impedance of a transmission line?

[Iancol]

Hi There! I have a bit of a 2-part question. I have been working on model transmission lines for the past few weeks and wanted to get a few things straight.

Part 1:
If two lines from different systems or different parts of the system share the same structure, or are at least located close to each other, do they affect each other's impedance? See Picture for clarification.

Part 2:
Calculating the total impedance of a double circuit transmission line is relatively standard. I am wondering how you calculate the impedance of just one of the circuits from the double circuit line. This picture demonstrates the protection of the line (both lines share the same tower and thus make a double circuit). We have relays that 'look' at the impedance from each direction to detect faults. So when calculating the impedance to program the relays, would I simply calculate the total of the double circuit and divide by 2? or does the other line not affect the impedance?

Any clarification would be great!
Thanks for reading

 

[davidbeach]

Yes, they affect each other. See Anderson's Analysis of Faulted Power Systems for detail on how to calculate the impedances. Don't omit the grounded neutral of any nearby distribution feeders.

 

[odlanor]

part 2- firstly, search for mutual inductance at relay manual!

 

[odlanor]

part 2- firstly, search for mutual inductance at relay manual!
sometimes relay guide has an easier solution for settings.

 

[Iancol]

Thanks for the replies guys!
I couldn't find a copy of "Anderson's Analysis of Faulted Power Systems" for free, but I did manage to find a great paper by SEL that describes the exact models I am trying to calculate. It does make some approximations when dealing with carson's formulas that aren't explained in full. However I imagine these equations are "close enough" since trying to calculate ground impedance is a bit of an art of approximation itself.

Is there a standard or respected method out there for numerically approximating carson's formulas? Right now it seems to be "whatever works for you" and searches can turn up a multitude of different ways to approximate carson's formulas.

Thanks!

 

[juleselec]

The appropriate approximation for Carson's equations will depend on your application. For short lines, it is common to use an approximation that simply neglects the series expansion terms (P and Q). Apparently there is around a 3% error when you do this (can't find the reference for that unfortunately), but the simplified equations do not consider the height of the conductors above the ground.

For longer lines, the series expansion terms should be taken into account. There are plenty of approaches to consider these terms (as you've found in your searches). A common approach (and one taken by quite a few software packages) is to simply calculate the first n terms of the series expansion (e.g. n=8).

In any case, I wouldn't worry too much about getting the series expansion terms perfectly right. The value you choose for earth resistivity will likely have a more significant effect, and this will probably be a rough estimate anyway.