Effect of Bundling on Transmisson Line Inductance

[shivad]

Hi everyone!
I am new to this forum.
Can anyone help me to find any reference about this question:
"What is the effect of bundling on decreasing the inductance of a transmission line?"
I will be very grateful for any help.

 

[wildman]

Gee, that is an interesting question that I never thought of before. Could the capacitance between the wires in the bundle have an affect?

 

[Astronuc]

It's not capacitance since the conductors in the bundle have the same electric potential.

See slides 3-8 and 15 of this PowerPoint presentation
courses.ece.uiuc.edu/ece476/lectures/ECE4762005Lect5.ppt (use save target as)

For a bundled conductor of mean geometric radius R_b,

the inductance is given by \frac{\mu_0}{2\pi}\,ln(\frac{D}{R_b}),

and the inductance decreases as R_b increases. Compare this result with L for a single conductor.

There is more theory with the same notes on bundling in
courses.ece.uiuc.edu/ece476/lectures/ECE4762005Lect6.ppt

These course notes may be time limited, i.e. the links will be invalid at some point in the future.

 

[wildman]

More questions

I see in the case of like a power line, but I thought it was a bundling of Insulated wires carrying different signals at high frequency. So the potentials in that case will not be the same. What happens then? Does capacitance make any difference in that case? Would inductance be reduced? Or is it only in the "power line" case where all the wires are at the same potential that we get reduced inductance?

Thanks in advance for your answers!

 

[Astronuc]

I see in the case of like a power line, but I thought it was a bundling of Insulated wires carrying different signals at high frequency. So the potentials in that case will not be the same. What happens then? Does capacitance make any difference in that case? Would inductance be reduced?

As far as I know, the cables in the bundles are not insulated from each other, and are at the same potential for a particular phase (in a 3 phase system). Also, the cables in the bundle are at the same AC frequency, 50 Hz or 60 Hz depending on country, and each of 3 phases is at the same frequency.

Certainly if the cables in the bundles were at different potentials, there would be some capacitance, and then there would be the effect of the "LC" in the circuit, which is a matter for power lines anyway during transients such as lightning strikes or rapid load changes. The phases certainly have differences in potential among each other and with the ground (neutral).

Or is it only in the "power line" case where all the wires are at the same potential that we get reduced inductance?

If one reads the notes to which I linked, one sees that bundling creates an effectively larger hollow conductor, which has the effect of reducing inductance.