after verifying to myself (using pspice) that a balancing transformer with high mutual inductance between both halves of the winding (without being a particualarly high inductance, even) gives an incredible reduction on circulating current when used with 2 varaics in parallel ( 2 uncoupled chokes also reduces Icirc...but the coupling reduces it yet further), can anyone give me a nice explanation of what's going on. I've tried it myself but seem to be stuffing up somewhere.
Your problem is similar to that found in power production when two or more generators are paralleled. While the flow of real power from/between generators is controlled by frequency/prime-move controls, the sharing of reactive load is done by voltage regulation.
The 'circulating currents' you speak of are a form of reactive load. Ideally, with identical output voltages and identical internal impedances, any reactive load supplied by the system is split equally between the sources. And if there is no reactive load at all, then their would be no reactive current (i.e. 'circulating current') flowing between the units.
In power generation, one generator can actually become a reactive load for another generator if its output voltage is reduced below the line voltage. Its power factor will decrease but the current will be leading the voltage reference instead of the usual lagging. The result is large 'circulating currents' between the two machines.
If you model the variacs as ideal adjustable AC sources with a series inductive reactance, you can see the voltage drop in the internal reactance for a given load. Because this reactance is inductive, the variac's final output voltage is not always exactly in phase with the output of other variacs, even though the supply voltage is common to both and the ideal transformer's secondaries are in phase.
So if the two transformer secondaries are slightly different voltages, and the final output voltage of both circuits must be the same (they are directly connected), then the voltage drop in the internal reactances must be different. For that to be true, the two variacs' internal reactances must have different current flows, hence 'circulating currents'.
By putting a balancing transformer in series with both variacs, any phase difference in variac output voltages cause circulating currents as before. But the currents themselves cause the final output voltages to match through both the internal reactance drop as before, but now also the balancing transformer. The transformer forms a sort of 'proportional feedback' such that a much smaller current is needed to bring the two final outputs equal.
Of course, if you hook up the transformer backward, well look out ;-)
Chokes have the disadvantage that the final output voltage has poorer regulation. That is, as load on the bank increases, the voltage drop on the chokes causes the output voltage to drop more than if they weren't there. A balancing transformer can have low inductance (as you noted) so the voltage won't drop as much with applied load, yet still limit circulating currents.
Many thx Daestrom for ur reply. I'm slowly starting to understand, I think. A major stumbling block is the significance of the mutual inductance. Why does this mutual inductance make such a difference to the effectiveness of the circuit?
The variacs have slightly different output voltages. The final outputs are tied together (i.e. shorted together) so the variac voltage difference has to be 'made up' in the choke/balance transformer.
With a choke, the only way to get a voltage drop is by having circulating currents. But with a transformer, the 'voltage drop' on one side is reflected as a 'voltage rise' on the other (transformer action if you want to call it that).
Careful connections electrically means a small circulating current in one direction can not only provide a voltage drop for that variac's output, but also induce a voltage of opposite phase in the other variac's circuit to 'raise' it. So the amount of circulating current needed to 'balance' the various voltages from variac to common output to other variac is much smaller.
Ur absolutely correct. Thanks for a very nicely worded and thought out reply. I ploughed in and did the maths for 3 cases. A balanced Tx, Chokes, and the case of no balancing coils at all.
After making some assumptions in the 1st case as follows:
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