An infinite bus, which is a constant voltage source, is connected to the primary of the three-winding transformer of Problem 3.53. A 7.5-MVA, 13.2-kV synchronous motor with a subtransient reactance of 0.2 per unit is connected to the transformer secondary. A \(5-\mathrm{MW}, 2.3-\mathrm{kV}\) threephase resistive load is connected to the tertiary. Choosing a base of \(66 \mathrm{kV}\) and 15 MVA in the primary, draw the impedance diagram of the system showing per-unit impedances. Neglect transformer exciting current, phase shifts, and all resistances except the resistive load.

Problem 3.53

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

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

Neglecting resistances and exciting current, the leakage reactances are:

\[
\begin{aligned}
& \mathrm{X}_{\mathrm{PS}}=0.09 \text { per unit on a } 15-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\
& \mathrm{X}_{\mathrm{PT}}=0.08 \text { per unit on a } 15-\mathrm{MVA}, 66-\mathrm{kV} \text { base } \\
& \mathrm{X}_{\mathrm{ST}}=0.05 \text { per unit on a } 10-\mathrm{MVA}, 13.2-\mathrm{kV} \text { base }
\end{aligned}
\]

Determine the per-unit reactances of the per-phase equivalent circuit using a base of \(15 \mathrm{MVA}\) and \(66 \mathrm{kV}\) for the primary.