A three-phase grounded wye-delta connected transformer

Question

A three-phase grounded wye-delta connected transformer supplies a load. The load voltage is 480 V (line-to-line), the loads are:

            Phase AB is 25 kW with power factor 0.8 lagging;

            Phase BC is 10 kVA with power factor 0.75 lagging; and

            Phase CA is 47 kW with power factor 0.85 lagging.

The transformer is rated 50 kVA, 12.47 kV / 480 V, 9.2%. Calculate:

(a) the unbalanced delta currents in each phase (I_AB, I_BC, I_CA)

(b) the unbalanced wye currents (I_a, I_b, I_c)

(c) the required supply voltages per phase (both line-to-line and line-to-neutral)

(d) the ground current at the wye side. Hint: place the transformer impedance at the wye side in series in each phase.