Calculating induced voltage in two parallel conductors

In summary: The voltage on the ground check conductor will be equal to the RMS voltage of the powered conductor multiplied by the square of the distance between the ground check conductor and the powered conductor.
  • #1
Steve Wetzel
11
1
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
 
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  • #3
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?
 
  • #4
Steve Wetzel said:
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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?
 
  • #8
Can anyone help with this?
 

1. How do you calculate the induced voltage in two parallel conductors?

The induced voltage in two parallel conductors can be calculated using the formula V = μ0I1I2L / 2πd, where V is the induced voltage, μ0 is the permeability of free space, I1 and I2 are the currents in the two parallel conductors, L is the length of the conductors, and d is the distance between them.

2. What is the significance of the distance between the parallel conductors in calculating induced voltage?

The distance between the parallel conductors plays a crucial role in determining the induced voltage. As the distance increases, the induced voltage decreases, and vice versa. This is because the closer the conductors are, the stronger the magnetic field between them, resulting in a higher induced voltage.

3. Can the induced voltage be negative in two parallel conductors?

Yes, the induced voltage can be negative in two parallel conductors. This occurs when the currents in the conductors are in opposite directions, and the magnetic fields they produce cancel each other out, resulting in a net negative induced voltage.

4. What factors affect the induced voltage in two parallel conductors?

The induced voltage in two parallel conductors is affected by various factors, including the currents in the conductors, the distance between them, the length of the conductors, and the permeability of free space. Any changes in these factors can result in a change in the induced voltage.

5. How can the induced voltage in two parallel conductors be increased?

The induced voltage in two parallel conductors can be increased by increasing the currents in the conductors, decreasing the distance between them, or increasing the length of the conductors. Additionally, using a material with a higher permeability of free space between the conductors can also increase the induced voltage.

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