$3\mathrm{.}23$ Figure $3\mathrm{.}32$ shows the oneline diagram of a three$-$phase power system. By selecting a common base of $100$ MVA and $22$ kV on the generator side, draw an impedance diagram showing all impedances including the load impedance in per$-$unit. The data are given as follows:

$\backslash$table$[[$G:$,90$ MVA,$22$ kV$,x=0\mathrm{.}18$ per unit$],[T_1$:$,50$ MVA,$\frac{22}{220}kV,x=0\mathrm{.}10$ per unit$],[T_2$:$,40$ MVA,$\frac{220}{11}kV,x=0\mathrm{.}06$ per unit$],[T_3$:$,40$ MVA,$\frac{22}{110}kV,x=0\mathrm{.}064$ per unit$],[T_4$:$,40$ MVA,$\frac{110}{11}kV,x=0\mathrm{.}08$ per unit$],[$M:$,66\mathrm{.}5$ MVA,$10\mathrm{.}45$ kV$,x=0\mathrm{.}185$ per unit$]]$

Lines $1$ and $2$ have series reactances of $48\mathrm{.}4$ and $65\mathrm{.}43,$ respectively. At bus $4,$ the three$-$phase load absorbs $57$ MVA at $10\mathrm{.}45$ kV and $0\mathrm{.}6$ power factor lagging.

FIGURE $3\mathrm{.}32$

Problem $3\mathrm{.}23$