A three-phase \(138 \mathrm{kV} \Delta / 13.8 \mathrm{kV} \mathrm{Y}\) distribution substation transformer rated \(40 \mathrm{MVA}\) OA/50 MVA FA/65MVA FOA has an 9\% 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 \(100 \mathrm{MVA}\) and \(13.8 \mathrm{kV}\) on the primary distribution side of the transformer.

(c) Calculate the shortcircuit 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 \(13.8 \mathrm{kV}\).