The ratings of a three-phase three-winding transformer are 

Primary (1): Y connected, \(66 \mathrm{kV}, 15\) MVA
Secondary (2): Y connected, \(13.2 \mathrm{kV}, 10\) MVA
Tertiary (3): A connected, \(2.3 \mathrm{kV}, 5 \mathrm{MVA}\)

Neglecting winding resistances and exciting current, the per-unit leakage reactances are

\[
\begin{aligned}
& X_{12}=0.08 \text { on a } 15-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\
& X_{13}=0.10 \text { on a } 15-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\
& X_{23}=0.09 \text { on a } 10-\mathrm{MVA}, 13.2-\mathrm{kV} \text { base }
\end{aligned}
\]

(a) Determine the per-unit reactances \(X_{1}, X_{2}, X_{3}\) of the equivalent circuit on a \(15-\mathrm{MVA}, 66-\mathrm{kV}\) base at the primary terminals.

(b) Purely resistive loads of \(7.5 \mathrm{MW}\) at \(13.2 \mathrm{kV}\) and \(5 \mathrm{MW}\) at \(2.3 \mathrm{kV}\) are connected to the secondary and tertiary sides of the transformer, respectively. Draw the perunit impedance diagram, showing the per-unit impedances on a 15-MVA, \(66-\mathrm{kV}\) base at the primary terminals.