The Ratings of a Three-Phase Three-Winding Transformer Are:
Primary (1) $\quad$

The ratings of a three-phase three-winding transformer are:
Primary (1): $\quad$ Y connected, $66 \mathrm{kV}, 20$ MVA
Secondary (2): $\quad$ Y connected, $13.2 \mathrm{kV}, 15$ MVA
Tertiary (3): $\quad \Delta$ connected, $2.3 \mathrm{kV}, 5$ MVA
Neglecting winding resistances and exciting current, the per-unit leakage reactances are:
$\begin{aligned}& \mathrm{X}_{12}=0.08 \text { on a } 20-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\& \mathrm{X}_{13}=0.10 \text { on a } 20-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\& \mathrm{X}_{23}=0.09 \text { on a } 15-\mathrm{MVA}, 13.2-\mathrm{kV} \text { base }\end{aligned}$
(a) Determine the per-unit reactances $\mathrm{X}_{1}, \mathrm{X}_{2}, \mathrm{X}_{3}$ of the equivalent circuit on a 20-MVA, $66-\mathrm{kV}$ base at the primary terminals. (b) Purely resistive loads of $12 \mathrm{MW}$ 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 per-unit impedance diagram, showing the per-unit impedances on a $20-\mathrm{MVA}, 66-\mathrm{kV}$ base at the primary terminals.