# Power line inductance on an electric fence

1. May 23, 2010

### Creini

Hi,

Hope this is the right forum to ask this question.

I have an electric fence running parallell to an electrified railway (25kV@50Hz, varying current). I'm trying to figure out how to calculate the induced voltage on the fence to figure out how long the fence can be before it becomes dangerous.

As far as I can make out this will be dependant on how well the fence is earthed, how far away from the current carrying conductor(s) and the permeability of the material in the fence?

Most of the examples I can find is on how to calculate the inductance between two (or more) current carrying conductors.

Should I consider my fence as a conductor? And then calculate the mutual inductance between the two? To calculate the mutual inductance I should calculate the flux linkages$$\varphi$$?

I think the flux linkages per meter is the same as the flux per meter as there is only one link (N=1). Which would give me:

d$$\phi$$=($$\mu$$*I)/(2$$\pi$$x) dx Wb/m = $$\varphi$$

in this case(?). Do I then integrate $$\varphi$$ from the current carrying conductor to the fence? e.g. if the fence is 5m from the conductor, would I integrate from the outside of the conductor (e.g. 0.05m) to 5m?

$$\varphi$$cond,fence = ($$\mu$$*I)/(2$$\pi$$)*ln(5/0.05)

Or do I integrate just around the fence? E.g. from 4.95 to 5.05?

Or am I completely wrong?

/Mattias

2. May 23, 2010

### DeveshB

weird .... the magnetic field acts along the height of the fence. the induced current has to oppose that magnetic field so the current must flow parallel to the railway line in opp. direction inside the fence , but its grounded hence.....

3. May 24, 2010

### Bob S

Interesting question. First, the magnetic field from a single power line drops off at 1/r, and only the magnetic field between R (the separation to the electric fence) and ∞ will couple to the electric fence (ignoring ground effects). Second, there are one or two additional power lines carrying the return current (so the sum current = zero), so the magnetic field from all the conductors is proportional to the separation of the power lines, and drops off faster with r, probably 1/r2. This is actually a directional coupler, as pointed out by the previous post, so in ideal situations, the induced signal in the electric fence is in the opposite direction to the power flow in the power line. I recall two papers written in the 1950's, one by Firestone, and another by Barney Oliver (who moved to HP ~1952). See references listed in

http://portal.acm.org/citation.cfm?id=1463947&dl=GUIDE&coll=GUIDE&CFID=89460559&CFTOKEN=84801571

Bob S

Last edited: May 24, 2010