Maximizing power transfer from 50Hz AC line via toroidal current transformer

Question

This paper looked at ways of achieving high power-to-weight ratio for harvesting power from a 50Hz overhead line. https://findresearcher.sdu.dk/ws/portalfiles/portal/250674676/EPE_2023_Advanced_Magnetic_Energy_Harvester_for_Charging_Drones_from_Overhead_Powerlines_final_version_.pdf

It clamped a toroidal current transformer to the line and used power electronics to convert to DC for charging.

It used synchronous methods to maximize the power draw taking into account the saturation characteristics of the core.

To me, it seems power-to-weight ratio might also be increased by having an intermediate high voltage DC bus that is stepped down. The high voltage of the DC bus would allow for a higher power output given the magnetic field / current limitations. For this setup:

1. Is it advisable to avoid core saturation?
2. Would power factor correction on the secondary side significantly increase the throughput, and if so, is it advisable to use AC capacitors with the pickup to create a tank (at 50Hz....), or use an intelligent H-bridge to phase-lock the voltage and current (like this: https://www.ijert.org/research/simulation-of-closed-loop-ac-dc-converter-for-power-quality-improvement-IJERTV4IS031036.pdf)
3. Is kW range power transfer feasible without degrading the power-to-weight ratio significantly, even if only for a short time (<1min)?
4. How do I properly calculate the CT equivalent circuit parameters based on the physical parameters (number of turns, wire details, core material, toroid dimensions, air gap length) and model in something like LTSpice?

Some parameters (let's say for a target charging power = 200-300W):

• approx 1kg toroidal air-gapped pickup as per above study.
• line current ranges from 50 to 200A.
• let's say a 600VDC bus so that 1200V semiconductors can be selected.

I am not asking you to design my circuit. I am not 'being lazy'. The purpose of this project is not academic / commercial, or even hobby. It can be assumed that the power harvesting is legal. I don't care if this question is 'bad' in some way - I've spent enough time trawling through the net and trying to excavate knowledge from my BE (EEE). If you would like to help, then please do :)

Answer 1

Minimum line current 50A means we need to drop maximum 20V to deliver 1kW. I assume we have no way of looping a wire around (power lines are generally solid wire, coated with rigid insulation, and tensioned fairly highly), nor obtaining a loop "in nature", so the primary turns count must be 1.

Voltage should be sine wave to maximize power transfer: downside, this does require a converter stage, which will itself cost some weight. The next easiest option is the square wave, which can extract more power from a given current, and wouldn't require a conversion stage -- but takes more flux. This is justified because the peak flux of a square wave is \$\frac{V_{pk}}{4 F}\$, and of a sine, \$\frac{V_{rms}}{\sqrt{2} \pi F}\$, and the power delivered as a sine current and square voltage is \$\frac{2\sqrt{2} V_{pk} I_{rms}}{\pi}\$, and sine/sine, \$V_{rms} I_{rms}\$; thus the power per flux is \$\frac{8\sqrt{2} I_{rms}F}{\pi}\$ for sine/square and \$\sqrt{2} \pi I_{rms} F\$ for sine/sine. Reducing common factors, we find \$\pi \gt \frac{8}{\pi}\$ and sine/sine wins.

(Note that excess power into a square wave, can be dumped by simply shorting out the transformer. A switching converter could also be used, but then the converter could simply be controlled for PFC operation, and you're back to the first case.)

1 kg of steel is v_e = 127k mm³, and we can take any proportion of that to make core parameters effective area A_e and magnetic path length l_e multiply to that quantity. For GOSS, B_max = 1.8 T is probably just feasible at this current, so we need $$ A_e = \frac{V_{rms}}{\sqrt{2} \pi F B_{max} N} $$ or for V_rms = 20 V, F = 50 Hz and B_max = 1.8 T and N = 1, A_e = 50k mm².

That's a pretty big core, in general, but notice it only leaves 2.5 mm of length, but we need to somehow curl that enormous cross-section around at least a, oh, 12 mm diameter wire, plus the secondary. Needless to say, l_e under 50 mm or so, ain't gonna happen.

A minimum-mass design still needs to account for secondary mass (copper is heavy -- or, do we stretch the core some more to fit larger but lighter aluminum instead?), and there is some back-and-forth to be had on power dissipation and heatsinking: efficiency isn't important, past a certain point anyway, as quite a lot of power can be dissipated into the rapid air streams around the unit; and heatsinking doesn't need to be a pure waste mass, it might be used to carry structural load as well.

Speaking of efficiency, if the props for example are producing huge amounts of tip vorticity, that's a huge waste of power that should be spent purely on lift instead. Props with winglets, or in shrouds, with director blades, etc. might prove far more successful in extending the range of the unit than sapping some power from a line could.

On a separate note, I wonder how effective the radio is in presence of corona discharge. The unit will take on most of the potential of the line it's attached to (probably 10s kV), and any projections on the unit will concentrate electric field, leading to corona discharge and RF emissions. These emissions can extend quite high indeed (100s MHz), and I wonder if it would impair a typical ~GHz band radio.

Answer 2

Thought I'd better answer my own question.

After reading further, The paper mentioned at the top of the question, re-linked here, represents the state of the art in regard to magnetically extracting power from overhead lines.

The most efficient methods hinge on selecting an optimal transformer core, and then either control the window during which the transformer is shorted, as in the above paper, or manipulate the magnetization via an additional control coil (for example, here). They all yield about 40-60% improvement over an optimally saturated core, which indicates to me that this is the best that physically can be achieved for a given line frequency.

Answering my own questions specifically:

1. Is it advisable to avoid core saturation? No. The core permeability in the most efficient methods is deliberately overrated to allow for the above manipulations.

2. Would power factor correction on the secondary side significantly increase the throughput? No, because we are operating at and beyond saturation. It is the limiting factor. However, it is important to control the effective resistance of the charging circuit to maximize power throughput

3. Is kW range power transfer feasible without degrading the power-to-weight ratio significantly, even if only for a short time (<1min)? No. The limit is the core properties, plus the above mentioned manipulations. There aren't magnetic materials that can achieve this yet, at least common and affordable ones