Transmission lines can be modeled as some inductance per unit length and some capacitance to ground per unit length with some resistance to account for losses. The equations to model this behavior can be found in these lecture notes.
The "residual power" is the stored electric charge in the capacitive section of the transmission line. This is a potentially dangerous charge that exists even after the power has been removed. Similar to the charge found in the capacitors in old TV sets and the flash section of cameras.
The amount of time it takes for the charge to decay depends on atmospheric conditions (mainly humidity):
The decay time of residual DC charge in a 500kV transmission line had
once been measured during five fine and dry days of winter season. The
results showed a large scattering without depending on the
simultaneously observed weather conditions, such as temperature or
relative humidity. Then the authors have performed an additional
experiment in a laboratory to discuss the factors that affect the
residual dc charge leakage in a dry condition focusing on the moisture
in the air and the dusts floating in the atmosphere. It is shown that
absolute humidity alone decides the decay time without scattering
under clean and calm condition. The floating dusts blown up by the
wind, however, reduce the decay time and bring a large scattering.
The dusts should be a charge carrier moving freely in the atmosphere.
“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.
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:
Best Answer
High-voltage partial discharges across the insulators.