A 300-MVA, 13.8-kV, three-phase, \(60-\mathrm{Hz}\), Y-connected synchronous generator is adjusted to produce rated voltage on open circuit. A balanced three-phase fault is applied to the terminals at \(t=0\). After analyzing the raw data, the symmetrical transient current is obtained as

\[
i_{\mathrm{ac}}(\mathrm{t})=10^{4}\left(1+\mathrm{e}^{-\mathrm{t} / \tau_{1}}+6 \mathrm{e}^{-\mathrm{t} / \tau_{2}}ight) \quad \mathrm{A}
\]

where \(\tau_{1}=200 \mathrm{~ms}\) and \(\tau_{2}=15 \mathrm{~ms}\).

(a) Sketch \(i_{\mathrm{ac}}(\mathrm{t})\) as a function of time for \(0 \leq \mathrm{t} \leq 500 \mathrm{~ms}\).

(b) Determine \(\mathrm{X}_{d}^{\prime \prime}\) and \(\mathrm{X}_{d}\) in per unit based on the machine ratings.