# Transmission Line Transposition - Conceptual Question

• Marcin H

#### Marcin H

This is more of a conceptual question and not a homework question. I am having a hard time understanding why we have to transpose transmission lines and how physically moving them changes anything. Do we only transpose in 3 phase transmission lines when we have 3 wires? Does the orientation matter like equilateral triangle or just 3 next to each other?

I understand that current from one wire can cause a disturbance in the other wire through magnetic flux linkage, but I am having trouble understanding how and why and the details behind it. and why transposing them can solve this issue. I just started learning this material so sorry if I am not making sense.

Moderator: edited to remove the homework template.

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• John FD
Ideally, all phases in a 3 phase network should be equal and balanced. Balanced in load, and balanced in impedance.

Since the locations of the 3 conductors on the pole are not a perfect triangle, the impedances are not exactly balanced. Transposing the conductors once in a while tries to cancel that so that the end-to-end impedance really is balanced.

Does that make sense?

• John FD and Fisherman199
Ideally, all phases in a 3 phase network should be equal and balanced. Balanced in load, and balanced in impedance.

I understand that we want our 3 phase network to be balanced in load and impedance, meaning we want the same current flowing through each line and the same impedance on each line. Just to clarify one point there the impedance from the wire is coming from the resistance of the wire and the mutual coupling/flux linkage of the wires? Or is that wrong? Where does the impedance come from?

Since the locations of the 3 conductors on the pole are not a perfect triangle, the impedances are not exactly balanced.

And why would a NOT perfect triangle make the impedances not balanced? Is it because the wires could have different amounts of flux linkage or coupling? I feel like I'm also getting a bit confused in the terminology here.

Transposing the conductors once in a while tries to cancel that so that the end-to-end impedance really is balanced.

Also, what does once in a while mean? How often do we have to transpose our wires on a transmission line of length d or something?

I understand that we want our 3 phase network to be balanced in load and impedance, meaning we want the same current flowing through each line and the same impedance on each line. Just to clarify one point there the impedance from the wire is coming from the resistance of the wire and the mutual coupling/flux linkage of the wires? Or is that wrong? Where does the impedance come from?

Not the resistance, but the reactance is what is significant. There are two sources, mutual inductive reactance between the lines, and capacitive reactance between each line and ground.

And why would a NOT perfect triangle make the impedances not balanced? Is it because the wires could have different amounts of flux linkage or coupling? I feel like I'm also getting a bit confused in the terminology here.

Because not all corners of the triangle can be the same height above the ground.

Also, what does once in a while mean? How often do we have to transpose our wires on a transmission line of length d or something?

There's no set formula. Transpose once every 50 to 100 miles is what I'm used to. The loads are also slightly unbalanced, so there the balance of the transmission line needs to be good, not perfect.

For the benefit of those who don't know what we're talking about, this is a transpose. #### Attachments

• John FD, dlgoff, Marcin H and 2 others
This is more of a conceptual question and not a homework question. I am having a hard time understanding why we have to transpose transmission lines and how physically moving them changes anything. Do we only transpose in 3 phase transmission lines when we have 3 wires? Does the orientation matter like equilateral triangle or just 3 next to each other?

I understand that current from one wire can cause a disturbance in the other wire through magnetic flux linkage, but I am having trouble understanding how and why and the details behind it. and why transposing them can solve this issue. I just started learning this material so sorry if I am not making sense.

Moderator: edited to remove the homework template.

The location matters because the mutual inductance and capacitance changes with regard to the orientation of the conductors in space (or in the ground). The mutual inductance of three parallel conductors is different than the mutual inductance of 3 conductors oriented equilaterally. By this, Transposing will keep the impedance close enough to being equal on each phase. Transposing one of the phases will also result in one of the phases being slightly longer than the other two, affecting the self-inductance (very) slightly (not really considered).

If you're taking your Electromagnetics class now it would be a good exercise to create a general mathematical model for the effect each Transposing scheme has on a circuit's inductance and capacitance. Also, make some changes to the GMD (Geometric mean distance) to help solidify concepts. I'll do it as well once I get some spare time. I'll post it here when (and if) I get it done.

I understand that we want our 3 phase network to be balanced in load and impedance, meaning we want the same current flowing through each line and the same impedance on each line. Just to clarify one point there the impedance from the wire is coming from the resistance of the wire and the mutual coupling/flux linkage of the wires? Or is that wrong? Where does the impedance come from?
Every conductor will have a self-inductance and shunt-capacitance to the return. Every grouping of conductors will have a mutual inductance and capacitance. Every conductor will have a resistance, though usually ignored at high voltages (lower currents). Resistance of a conductor does not depend on magnetic or electric field phenomena so has no change when sharing close proximity with other conductors.

The impedance of a wire is derived from the conductance of it's material, construction details (cross-section, etc.), and it's behavior when exposed to changing magnetic and electric fields (also affected by material and construction details, but also including frequency). So: Z=R+iX and X=i2π⋅f⋅L or X=i2π⋅f⋅(1/C). (Where Inductance (L) and Capacitance (C) describe the conductor's behavior in response to changing Magnetic fields and changing Electric fields respectively). Understanding that, it should follow that the reactive part of impedance will change with orientation of conductors in space relative to other conductors and the phase conductor's length; whereas, the resistive part of the impedance will change only with length.

And why would a NOT perfect triangle make the impedances not balanced? Is it because the wires could have different amounts of flux linkage or coupling? I feel like I'm also getting a bit confused in the terminology here.
I think what you meant is, "how could a non-perfect triangle (equilateral?) make the impedances balanced." (I say this since, given how you phrased your original questions, the answer should have been clear to you at that point. Correct me if I'm wrong.). As mentioned, shunt capacitance and mutual inductance both change with the orientation of conductors. Put three conductors in a line. Calculate mutual inductance and capacitance. Place them then in an equilateral triangle. Recalculate. Place them in a right triangle. Recalculate. What changed? Increase the distances between conductors. Recalculate everything. What changed? Decrease the distances between conductors. Recalculate everything. What changed?

( @anorlunda , @berkeman , @jim hardy, @Baluncore please correct me where I've misspoken)

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• Marcin H
Not the resistance, but the reactance is what is significant. There are two sources, mutual inductive reactance between the lines, and capacitive reactance between each line and ground.

Because not all corners of the triangle can be the same height above the ground.

There's no set formula. Transpose once every 50 to 100 miles is what I'm used to. The loads are also slightly unbalanced, so there the balance of the transmission line needs to be good, not perfect.

For the benefit of those who don't know what we're talking about, this is a transpose.
View attachment 230892
Oh, ok. We just go to the part where we can model transmission lines as RLC circuits connected together. As for the capacitative reactance between the wires and the ground, is the difference really that big? In a horizontal arrangement of the transmission lines you wouldn't have this problem. So would you still have to transpose to deal with the inductive reactance? Just maybe less often?

And for and equilateral triangle arrangement the wires are still fairly close to each other so is the difference in capacitative reactance still large enough to have an impact? Or does it just add up for the hundreds of miles of transmission line that is being used? Even tho per unit the value might be small?

And another thing how does transposing fix this problem exactly. I'm having a hard time understanding why moving the wire physically changes things. Does it only change the capacitative reactance when you change the height for example? I guess we haven't gotten that far in class, but how big of a factor is height in transmission lines? In your picture I see we have a horizontal arrangement, but change the height in the middle and then we go back to horizontal arrangement just in different positions. Which part is helping us keep balance impedance in the system? The changing heights part in the middle or in general changing the position of every wire?

• John FD
The location matters because the mutual inductance and capacitance changes with regard to the orientation of the conductors in space (or in the ground). The mutual inductance of three parallel conductors is different than the mutual inductance of 3 conductors oriented equilaterally. By this, Transposing will keep the impedance close enough to being equal on each phase. Transposing one of the phases will also result in one of the phases being slightly longer than the other two, affecting the self-inductance (very) slightly (not really considered).

If you're taking your Electromagnetics class now it would be a good exercise to create a general mathematical model for the effect each Transposing scheme has on a circuit's inductance and capacitance. Also, make some changes to the GMD (Geometric mean distance) to help solidify concepts. I'll do it as well once I get some spare time. I'll post it here when (and if) I get it done.

Every conductor will have a self-inductance and shunt-capacitance to the return. Every grouping of conductors will have a mutual inductance and capacitance. Every conductor will have a resistance, though usually ignored at high voltages (lower currents). Resistance of a conductor does not depend on magnetic or electric field phenomena so has no change when sharing close proximity with other conductors.

The impedance of a wire is derived from the conductance of it's material, construction details (cross-section, etc.), and it's behavior when exposed to changing magnetic and electric fields (also affected by material and construction details, but also including frequency). So: Z=R+iX and X=i2π⋅f⋅L or X=i2π⋅f⋅(1/C). (Where Inductance (L) and Capacitance (C) describe the conductor's behavior in response to changing Magnetic fields and changing Electric fields respectively). Understanding that, it should follow that the reactive part of impedance will change with orientation of conductors in space relative to other conductors and the phase conductor's length; whereas, the resistive part of the impedance will change only with length.

I think what you meant is, "how could a non-perfect triangle (equilateral?) make the impedances balanced." (I say this since, given how you phrased your original questions, the answer should have been clear to you at that point. Correct me if I'm wrong.). As mentioned, shunt capacitance and mutual inductance both change with the orientation of conductors. Put three conductors in a line. Calculate mutual inductance and capacitance. Place them then in an equilateral triangle. Recalculate. Place them in a right triangle. Recalculate. What changed? Increase the distances between conductors. Recalculate everything. What changed? Decrease the distances between conductors. Recalculate everything. What changed?

( @anorlunda , @berkeman , @jim hardy, @Baluncore please correct me where I've misspoken)
Thank you for the lengthy response. This actually cleared up a lot. I think after a few more classes and examples I will have a much better understanding of this. Could you explain what geometric mean distance (GMD) is exactly and how it's used? Is it only used if the distance between our wires is different? For example if we don't have a perfect equilateral triangle or if we don't have an equally spaced horizontal transmission line?

Also, do you have a good source for derivations or proofs for varies transmission line orientations? I have the equations in my notes with a proof using superposition, but I had a hard time follwoing that proof. Specifically I had a hard time understanding where the (D/r') come from in the formula for each wire when superposed and the sign they get. Some wires had a negative sign but I wasn't sure where it came from.

The formula I am talking about is per unit length inductance of a wire: Edit*** that equation was for the case of a 2 conductor line. Before that we found the per unit length inductance at a distance R on some long flat sheet, so that D in the equation above would be an R. I didn't fully understand that derivation either. I have R labeled as the distance between the wire and it's return path. Which reminds me... Is the return path just the neutral wire? Do we always have a neutral wire on a transmission line?

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• John FD
Which reminds me... Is the return path just the neutral wire? Do we always have a neutral wire on a transmission line?

Now you're rambling. We prefer one question per thread.

When you study three phase systems, you'll learn that no separate return path is needed.

Now you're rambling. We prefer one question per thread.

When you study three phase systems, you'll learn that no separate return path is needed.
Sorry. Once I get one question my brain just floods with 1000 other ones. I'll hold off for a bit and see if things clear up in class. Thanks for the help thus far.

• John FD
Once I get one question my brain just floods with 1000 other ones.
Good for you! That's called curiousity, required for an interesting and productive life. Keep it up!

Cheers,
Tom

p.s. The reason for the one-subject-per-thread is there are many 10's of thousand readers worldwide, and you may notice that the serial numbers for the posts are in the 6 000 000 range. If a several questions are under one thread title, it makes it hard for readers to find things.
(note, I just checked and there are over 3 000 readers online right now as I write this) So we try to keep access simple. (even if some of the questions, and answers, are not so simple. )

• John FD, dlgoff, Greg Bernhardt and 1 other person