Single Phase Load on Delta Transformer

[Voltzz]

What is calculation for delta winding currents IAB, ICA, IBC when single phase load is connected between line A and B. Line current will be IA=Vab/Z=-IB, IC=0. But how can winding current be calculated?

 

[xnuke]

Create a 3x3 matrix M = [1/3, -1/3, 0; 0, 1/3, -1/3; -1/3, 0, 1/3]. Create a column vector of line currents I = [IA; IB; IC]. Multiply M*I to get vector of phase currents [IAB; IBC; ICA].

The derivation of M was a little painful; it's the pseudoinverse of the non-invertible transformation matrix [1, 0, -1; -1, 1, 0; 0, -1, 1] that transforms a vector of delta phase currents to a vector of line currents. I modeled an example circuit in both LTSpice and Octave as well as doing a hand calculation, and got the same results for all three, so I'm pretty sure my method is correct. Hopefully, someone else will tackle the derivation and confirm my result. My solution works for three-phase unbalanced line currents of any values.