Question $1$

$(10$ marks$)$

The one$-$line diagram of a simple three$-$bus power system is shown in Figure below. Each generator is represented by an emf behind the transient reactance. All impedances are expressed in per unit on a common $100$ MVA base, and for simplicity, resistances are neglected. The following assumptions are made:

Shunt capacitances are neglected, and the system is considered on no$-$load.

All generators are running at their rated voltage and rated frequency with their emfs in phase.

Determine the fault current, the bus voltages, and the line currents during the fault when a balanced three$-$phase fault with a fault impedance $Zf=0\mathrm{.}12$ per unit occurs on:

$($a$)$ Bus $3$

$($b$)$ Bus $2$

$($c$)$ Bus $1$