Chapter 3, Problem 3.51P

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

Primary(1): Y connected $\text{66}\text{kV,}\text{15}\text{MVA}$

Secondary (2): Y connected, $\text{13}.\text{2 kV},\text{ 1}0\text{ MVA}$

Tertiary (3): A connected, $2.3\text{ kV},5\text{ MVA}$

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

$X_{12}=0.08$ on a $\text{15-MVA,}\text{66-kV}$ base

$X_{13}=0.10$ on a $\text{15-MVA,}\text{66-kV}$ base

$X_{23}=0.09$ on a $\text{10-MVA,}\text{13}\text{.2-kV}$ base

(a) Determine the per-unit reactances $X_1,X_2,X_3$ of the equivalent circuit on a $\text{15-MVA,}\text{66-kV}$ base at the primary terminals. (b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3kV 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 $\text{15-MVA,}\text{66-kV}$ base at the primary terminals.