Current in Delta Winding Phases

If I have line current magnitudes and angles for A, B, and C phase current, how can I calculate the current flowing through the individual windings in a delta winding?

Put another way, I’m just confused on how we can assume that Iab = Ia - Ib when there’s another parallel path. How do we know how much current is flowing through Iab and how much is flowing through the series combination of Iac and Icb in an unbalanced load?


It will be your line to line current. Winding AB has Iab = Ia - Ib and so on.
Assuming you have a Delta-wye grounded transformer, analyse the transformer using sequence components. If you have your load currents, convert them to sequence currents. This gives you Load: ISa1,ISa2, ISa0.

The positive and negative components are by definition balanced.

Use the transformer tap ratio and phase shift and convert the positive sequence load currents to the high side.

This gives you IPa1, IPa2, IPa0

Do the same for the negative sequence components but phase shift them the opposite of the positive sequence phase shift.

assuming abc rotation

a = 1<120 deg

IPb1 = a^2IPa1
IPc1 = a
IPb2 = aIPa2
IPc2 = a^2

This gives you high side:

IPa = IPa1+IPa2
IPb = IPb1+IPb2
IPc =IPc1+IPc2

This is what you get when if you measured at the high side.

Total with circulating zero sequence currents =

Winding Iab = (IPa1 + IPa2) - (IPb1 + IPb2) + I0P
Ibc = (IPb1 + IPb2) - (IPc1 + IPc2) + I0P
Ica = (IPc1 + IPc2) - (IPa1 + IPa2) + I0P

IP0 = ISa0*TransformerRatio

So, basically you take what you would see with the positive and negative components in the winding and just add the circulating zero sequence currents to it. Or, just not look at the components.

Above is a snippet.