$3\mathrm{.}25$ Consider a single$-$phase electric system shown in Figure $3\mathrm{.}33.$ Transformers are rated as follows:

$X-Y15$MVA,$\frac{13\mathrm{.}8}{138}kV,$ leakage reactance $10\%$

$Y-Z15$MVA,$\frac{138}{69}kV,$ leakage reactance $8\%$

With the base in circuit Y chosen as $15$MVA,$138kV,$ determine the perunit impedance of the $500$ resistive load in circuit $Z,$ referred to circuits Z$,$ Y$,$ and X$.$ Neglecting magnetizing currents, transformer resistances, and line impedances, draw the impedance diagram in per unit.

FIGURE $3\mathrm{.}33$

Single$-$phase electric system for Problem $3\mathrm{.}25$