$($a$)$ The bus impedance matrix for a three$-$bus power system is

Zbus $5$ j $30\mathrm{.}120\mathrm{.}080\mathrm{.}04$

$0\mathrm{.}080\mathrm{.}120\mathrm{.}06$

$0\mathrm{.}040\mathrm{.}060\mathrm{.}084$ per unit

where subtransient reactances were used to compute Zbus. Prefault volt$-$

age is $1\mathrm{.}0$ per unit and prefault current is neglected. $($a$)$ Draw the bus

impedance matrix equivalent circuit $($rake equivalent$).$ Identify the per$-$

unit self$-$ and mutual impedances as well as the prefault voltage in the

circuit. $($b$)$ A three$-$phase short circuit occurs at bus $2.$ Determine the

subtransient fault current and the voltages at buses $1,2,$ and $3$ during

the fault