Calculating induced voltage in two parallel conductors

[Steve Wetzel]

Say I have two parallel conductors that are both L long and d distance apart (center to center). I run AC power of frequency f and RMS voltage V through one conductor. That current will create a fluctuating magnetic field which will pass through the the other conductor and generate a voltage. How do I calculate what that voltage is?
We know:
V = RMS voltage of powered conductor
L = length of the two conductors
d = center to center distance of the conductors
f = frequency of the ac current on the powered conductor

 

[berkeman]

Welcome to the PF.

A changing magnetic field can induce a voltage and current in a conducting loop, so you need to define where the 2nd wire goes to connect back to itself.

https://en.wikipedia.org/wiki/Faraday's_law_of_induction

 

[Steve Wetzel]

That makes sense. I am wondering how to model this exactly. The reason I am asking is I am working with a mine that that is having a problem which I have seen come up before. The cable is a medium voltage cable with 3 copper braid shielded conductors and 2 ground wires in two interstices and one ground check wire in the third. With long cable runs the ground check gets enough voltage on it to cause problems in the ground check circuit. The ground check circuit simply checks for continuity on the ground conductors so I think we could assume that the 2 ground conductors in the cable are in parallel with the ground check conductor and create the loop.

Is this making any sense?

 

[berkeman]

Is this making any sense?

Yes, absolutely. Sounds like a problem that we can help you with.

We need a sketch of the total system, with the lengths of the wiring runs, the cable separations, and the loop areas of all the power wiring runs.

Also, if you used twisted pair wiring runs, that would eliminate magnetic field coupling. That may not be an option in your installation, though.

 

[Steve Wetzel]

Thank you. This specific case is for 3900m of 25kV rated cable. I will find out the actual operating voltage and conductor size. But I would like to know how to calculate this for various cabe sizes, voltage ratings and cable lengths. As I said, this will be a three conductor cable with three conductors in the interstices, two uncovered grounds and one ground check. The phase conductors are shielded with copper wires. Would it be safe to make the following assumptions: Could I consider the three phase conductors to be point sources and ignore the actual diameter of the conductor and could I ignore the copper braid shield over each of the insulated conductors? I need to find out the conductor size to determine the distances between each of the centers of each of the conductors.

 

[Steve Wetzel]

I did determine the relative distances. If R is the diameter over the large insulated conductor and r is the diameter over the insulated ground check and the ground wires (that not exact but usually close) than the center of each ground and ground check is R+r away from 2 phases and the distance to the third phase is:
( ( 4( R + r )^2 - ( 4R^2 )^.5 ) / 2 + R ( 3 ) ^2

Still working on getting the exact size, hopefully I can do that next week.

 

[Steve Wetzel]

OK, I have the dimensions.
500 kcmil fine stranded Conductor OD: 0.736 inches
Diameter over Insulation and shield: 1.45 inches
Current on each phase conductor: 590A , voltage 25kV (we don't need voltage right, just current)
Diameter over Ground Conductor: 0.423 inches
Cable Length 3600 meters. (11,811 ft)

The ground check and ground wires are connected together through a monitoring device The ground wires are connect to ground so they will see no voltage but the ground check conductor will see a voltage. What voltage will it see if we assume a high impedance between the ground check and ground?

MORE IMPORTANTLY, what is the formula to calculate this?

 

[Steve Wetzel]

Can anyone help with this?