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A Solution to the RWP for Exam 1 – Stealing Power (2006)

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Re: A Solution to the RWP for Exam 1 – Stealing Power (2006)

#11

Post by usr1106 »

amluto wrote: post #4

A major missing detail is accounting for the other phase conductors in the transmission line. They will tend to cancel the field, and the ability of this scheme to work will depend on getting the coil to collect much more flux from one phase than the other two. Real devices based on this principle exist: current transformers, Rogowski coils, and lights! The latter looks like this: https://pr-tech.com/product/spanlite…

> A major missing detail is accounting for the other phase conductors in the transmission line.

Good point. So for the customary 3-phase power lines the UNC exam is confusing and the given sample solution wrong. In reality you could steal much less than the already ridiculous amount in the exam.

The German railways operate a 1-phase power grid. (After all 3-phase transmission makes only sense if you are able to balance the consumption of the 3 phases at a single place (small area in real life). With relatively few trains using 1 phase at uncoordinated locations that's not the case. And they cannot use the public grid because for historical reasons they operate on a different frequency.

A 1-phase transmission line needs 2 conductors. With my high school physics, I can't tell what that means. Isn't it so that when the max current flows in one direction in one conductor it will flow in the opposite direction in the other one? So what you can steal is determined by d1^2 - d2^2 where dn is your stealing coil's distance from conductor n? Orders of magnitudes worse than in the exam once again.

Re: A Solution to the RWP for Exam 1 – Stealing Power (2006)

#13

Post by hilbert42 »

I love stories like this. As the article shows, stealing very low frequency mains power (60Hz) this way is highly inefficient as practical considerations would reduce the coupling efficiency to ridiculously low levels.

However, I do recall a method that was apparently 'much' more efficient (at least from a theoretical perspective). That said, it was still inefficient in absolute terms.

Some decades ago I read a report that someone who lived very nearby to a Navy high power (~1MW) low-frequency RF transmitter used to communicate with submarines stole power by building a suitable antenna to pick up RF energy broadcast from the transmitter (I think he put the antenna coil in his roof but that may just be hearsay).

Note: I used 'low frequency' twice here so I must clarify, the RF TX was indeed very low frequency by radio standards (needed to communicate through seawater) but it was still many times higher than mains frequency. Assuming the transmitter's frequency was somewhere between say 12kHz and 35kHz then it would be between ~200 and 500 times higher than mains frequency, thus coupling the energy would be that much easier. This combined with both an antenna especially built to radiate as well as having a proper ground counterpoise/earthing system would have provided the transmitting station's neighbor with a much better opportunity to steal power.

The report was so long ago I've forgotten most of the pertinent details but it seems that the guy got caught because they discovered an unexpected notch in the antenna's radiation pattern.

If I recall this happened in Florida sometime in the 1960s. Seems the guy powered all his fluorescent lights from the RF.

Would someone with a much better recollection of the facts please clean up the details. Thanks.

Re: A Solution to the RWP for Exam 1 – Stealing Power (2006)

#16

Post by hilbert42 »

usr1106 wrote: post #11
amluto wrote: post #4

A major missing detail is accounting for the other phase conductors in the transmission line. They will tend to cancel the field, and the ability of this scheme to work will depend on getting the coil to collect much more flux from one phase than the other two. Real devices based on this principle exist: current transformers, Rogowski coils, and lights! The latter looks like this: https://pr-tech.com/product/spanlite…

> A major missing detail is accounting for the other phase conductors in the transmission line. Good point. So for the customary 3-phase power lines the UNC exam is confusing and the given sample solution wrong. In reality you could steal much less than the already ridiculous amount in the exam. The German railways operate a 1-phase power grid. (After all 3-phase transmission makes only sense if you are able to balan…

"A 1-phase transmission line needs 2 conductors"

Right, but for many single phase installations a ground/earth return is often employed. This often simplifies things and saves a lot of infrastructure costs.

Whether it's single or 3-phase, calculating the coupling efficiency will, at best, only be a rough guesstimate unless great care is taken to accurately collect and collate all physical and electrical parameters. Not only will interline coupling be relevant so will the fact that three phases are involved and we'd have to take into account standing waves etc. (mind you at 50/60Hz the wavelength is enormous (thousands of kms) so the transmission line effect is likely be trivial at the local level - see note).

I reckon this article deliberately avoided the transmission line/multiphase effect to avoid that controversy or complicatlation.

__

PS: ignoring the transmission line velocity factor and ground effects, the wavelength at 60Hz is 5000km and it's 6000km at 50Hz; therefore the first voltage maxima (lambda/4) will, in both instances, only ocurr at over a thousand km from the source. Standing wave effects due to the presence of three phase will reduce this but it's still a big distance - too big to have much of an effect to vary much over a single farmer's land.

The solution therefore would be to calculate the various vectors for any given point on the line (here, at any area on the farmer's land and take that as constant for calculating the coupling to the secondary (pickup) inductor). It seems to me the most practical way would be to just measure the field strength empirically or to look up the various tables and monographs readily available in power engineering.

Re: A Solution to the RWP for Exam 1 – Stealing Power (2006)

#18

Post by amluto »

usr1106 wrote: post #11
amluto wrote: post #4

A major missing detail is accounting for the other phase conductors in the transmission line. They will tend to cancel the field, and the ability of this scheme to work will depend on getting the coil to collect much more flux from one phase than the other two. Real devices based on this principle exist: current transformers, Rogowski coils, and lights! The latter looks like this: https://pr-tech.com/product/spanlite…

> A major missing detail is accounting for the other phase conductors in the transmission line. Good point. So for the customary 3-phase power lines the UNC exam is confusing and the given sample solution wrong. In reality you could steal much less than the already ridiculous amount in the exam. The German railways operate a 1-phase power grid. (After all 3-phase transmission makes only sense if you are able to balan…

> Isn't it so that when the max current flows in one direction in one conductor it will flow in the opposite direction in the other one? So what you can steal is determined by d1^2 - d2^2 where dn is your stealing coil's distance from conductor n?

There are two wires because of Kirchoff's current law -- if the current goes out in one direction, it has to come back somehow. There are "single wire earth return" systems that use the ground as the return wire, for better or for worse.

If you replace d^2 by d^-2 in your equation, you'll be closer. Although, as noted in the OP, the magnetic field around a wire is proportional to distance^-1.

Re: A Solution to the RWP for Exam 1 – Stealing Power (2006)

#19

Post by hilbert42 »

ggm wrote: post #10

This was discussed in the squatting community I was in, London, 1984. The coil approach would get you lighting. I never had to do it, we had power. We argued about the wisdom of theft, when the electricity company would actually re-connect you to an illegally occupied house anyway. Why compound your problems with the law?

Years ago for a laugh I tried to stop the rotating aluminum disk in my power meter from rotating by holding a powerful ex-magnetron magnet near the one in the meter.

It made not one iota of difference to the disk's rotation speed as the poles of the meter's magnet are so close to the disk that there was no way to alter the strength of the magnetic field that was at right angles on to the disk.

Electricity utilities have been in the game a long time, they already know all the tricks and design their systems accordingly.

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