Delta Coil Currents with Unbalanced Load

[wwhitney]

Say we have a transformer with a 480V delta secondary, and we apply a 48 ohm resistance across lines A and B as the only load. So the line currents | Ia |= | Ib | = 10A, and Ic=0A.

Let's call the coil currents Iab, Ibc, and Ica, where (1) Ia = Iab - Ica, Ib = Ibc - Iab, and Ic = Ica - Ibc, as phasors. How do we determine the actual coil currents from the loading? The 3 equations (1) are not invertible.

I'm thinking for an ideal transformer we can't determine the coil currents, so we'll have to consider the impedance of the coils to figure out how the current divides between Iab vs Ibc plus Ica. If so, what is the typical phase angle and order of magnitude for these impedances?

Cheers, Wayne

P.S. This question is a prelude to trying to answer https://forums.mikeholt.com/threads/current-flow-with-l-l-autotransformer-fault-to-n.2576343/

 

[wwhitney]

I'm thinking for an ideal transformer we can't determine the coil currents, so we'll have to consider the impedance of the coils to figure out how the current divides between Iab vs Ibc plus Ica.

I'm thinking the above is correct. If the transformer secondary is balanced so that each coil has identical impedance, we don't need to know the actual impedance to determine how the 10A line current divides between the two paths Iab vs Ibc = Ica. As the path through 2 coils would have twice the impedance, so the current through it would be half the current through the single coil path.

In other words with Ia = Ib = 10A (two line currents) and Ic=0, with equal coil impedances we'd expect Iab = 20/3 A and Ibc=Ica = 10/3 A.

Is the above correct as far as it goes, and is this equal coil impedance model sufficiently accurate in practice for real transformers?

Thanks,
Wayne