Calculating phase currents from line currents in an unbalanced delta

[DaveE]

Transformers are passive; do you mean resistive, as post #1 described?

No, I meant no induced voltages/currents. No coupling to an energy source. Inductors are OK, coupled inductors are OK as long as they don't couple to an energy source. Honestly "passive" is the best adjective I've got. In my world "passive" means energy is conserved, or dissipated, not created.

If we add 1 to each current (this is adding a circulating current of 1) we have another solution

You have a different unique solution to a different network. The OP needs one more piece of information to fully specify the network. Your "min norm" requirement functions as that piece of information.

So, I remain unsatisfied by your two examples since each defines a different network. You can't just add a constant "circulating current" as a solution to the original network. It is a solution for a member of the set of networks defined in the OP. But, as soon as you add that current you must change the load impedances accordingly to satisfy KVL/KCL. Go back in those examples and finish the problem, calculate each of the phase impedances.

For a single well defined passive load network, I would like a definition of what the circulating currents in that load network are.

As an aside , can you answer Baluncore's question in post #23: "Why do you deny the existence of circulating currents in reactive AC systems ?"

I think either he's wrong or he has a different idea of what a circulating current is than what you will see in this simple example. The real world is much more complicated than this example. In any case, I would ask for his definition as well.

I don't deny that people talk of circulating currents, or that they exist (given a good definition). Most often as "wasted" currents in distribution systems with multiple transformers (like magnetizing currents), multiple sources, and/or induced current from magnetic coupling. For example this, with paralleled inverters.

I don't claim they don't exist anywhere. Just not in this particular problem set. I also am genuinely curious about what y'all think they are. As you can see from my previous posts, I've been a bit confused about this until I thought about it some more and realised the the "solution set" was actually more like a set of separate networks, each with a unique solution. OTOH, I'm getting tired of words and would prefer clear technical explanations.

Based on some brief web searches (like this), I think it is often a pretty ill-defined thing; one of those garbage collection sort of concepts, like "parasitic". In general, current flow that you don't want. I don't seek an answer as much as a definition; the answer will then follow.