$1-)$ Consider the $3-$bus power system shown, where the values marked are impedances in per$-$unit.

$($a$)$ Construct the bus impedance matrix $Z_{\text{b}\text{u}\text{s}}$ of the system using the $Z_{\text{b}\text{u}\text{s}}$ modification methods.

$($b$)$ Given the generator internal voltages

$E_1=E_2=1\mathrm{.}36+j0\mathrm{.}69pu$

determine the bus voltages $V_1,V_2$ and $V_3.$