Electronic – Length of high voltage power transmission in different countries

“Persons were charged with stealing electricity by placing a large coil, somehow, near high voltage AC transmission lines.”

Is this feasible or was it perhaps an April fool’s article that I swallowed hook line and sinker in my youthful naivety.

Entirely feasible.
Farmers were occasionally charged with power theft in this country (New zealand) in the past. I haven;'t heard of a case in a decade or few - maybe they are getting cleverer at it :-).

This is the same principle as used for "IPT" / "Inductive Power Transfer as seen in phone chargers, industrial monorail powering, electric vehicle charging and much more.

I started to say that if the pickup coil was symmetrical with respect to two phases that were perfectly balanced that you'd get zero pickup, and then suddenly realised that I've always done IPT with essentially a single phase, and that with a 3 phase system with 120 degrees phase separation you should get the advantage of the full load current even if the two phases were fully balanced.

You are essentially getting fields produced by the current, not the voltage, and the voltage is essentially irrelevant as long as you observe the normal conventions that apply to any other dealing with xxx kV.

Energy Harvesting from Electromagnetic Energy Radiating from AC Power Lines - FAR more energy can be obtained than they achieve.

Worked example - I suspect some of the conclusions are suspect A Solution to the RWP for Exam 1 - Stealing Power

Low technical content - high relevance

Directly relevant but low technical value Electromagnetic Harvesters: Free Lunch or Theft!

Several related stack exchange questions with variably useful content.

• How would an electric company detect wireless theft of electricity?

• https://skeptics.stackexchange.com/questions/3520/is-it-possible-to-obtain-current-indirectly-from-power-lines

• Stealing energy from radio towers or power lines

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Online vehicle transfer - I do not have access to this paper but it is probably at least relevant as it will have examples of dual linear conductors and a pickup coil.

Mythbusters getting it wrong

Related:

Industrial monorail

Maximising transfer

Capacitive - but impressive:

Short answer

The maximum power transfer theorem tells you how to maximise the power delivered to the load given a source impedance. In you scenario the load would be transmisión line + \$ Z_L = Z_{in} \$ which can be equal \$ Z_t^*\$ regardless of what the value of \$ \tau \$ is. but in order minimice the power dissipated by the lossy transmission line (or maximice the one dissipated by the load) you also have to match this impedances to get no reflected wave.

Long answer

Let me first consider the lossless transmission line case. this is $$real \ Z_0, \quad Z_{in} = \frac{Z_L +Z_0 j tan(\beta d)}{Z_0 +Z_L j tan(\beta d)} $$ Since the line is lossless, all the power that enters into it will be dissipated by the load at the end, so in order to maximice this power entering to the transmission line we use the maximum power transfer theorem, which states that, given an internal impedance of a voltage source, in order to maximise the power transfer the impedance seen by the system (voltage source + internal impedance) should be equal to the source internal impedance, this means $$Z_{in} = Z_t $$ Given a load \$Z_L \$ there are two scenarios in where this is achieved:

1. Finding a combination of Z_0 and \$d\$ that ends up with \$Z_in = Z_t \$ at the other side of the transmission line (an example of this would be the quarter-wave impedance transformer)
2. choosing \$Z_0 = Z_L = Z_t\$

Both will guarantee maximum power transfer for a lossless transmission line. note that in the first case, you won't get \$\tau = 1 \$, there will be reflection at the line/load interface.

That been said, now we can address the problem of a lossy transmission line as the one you described. The problem remains essentially the same, the only way of extracting the maximum power from the source is getting \$Z_{in} = Z_t^* \$ as before, so both scenarios seem to be the same. Nevertheless, now it isn't true that all this power will be entirely dissipated by the load, you have to take into account the losses of the transmission line. In order to minimice this losses, you have eliminate the reflected wave. So the second scenario would be optimal $$Z_0 = Z_L = Z_t^* $$.