A three-phase \(138 \mathrm{kV} \Delta /13.8\mathrm{kV}\) Y distribution substation transformer rated 40 MVA OA/50 MVA FA/65MVA FOA has an \(8 \%\) impedance.

(a) Determine the rated current on the primary distribution side of the transformer at its OA, FA, and FOA ratings.

(b) Determine the per unit transformer impedance using a system base of 100 MVA and \(13.8 \mathrm{kV}\) on the primary distribution side of the transformer.

(c) Calculate the short-circuit current on the primary distribution side of the transformer for a three-phase bolted fault on the primary distribution side. Assume that the prefault voltage is \(13.8 \mathrm{kV}\).