Solve in paper $...($b$)$ A single line diagram of a four$-$bus system is shown in Figure Q$3($b$),$ for which $Z_{\text{B}\text{U}\text{s}}$ is given below. Assume the pre$-$fault voltage at bus $2$ to be $V_2(0)=1\mathrm{.}0+j0\mathrm{.}0pu,$ and neglect all pre$-$fault currents.

Let a $3-$phase fault occur at bus $2$ of the network. Calculate

$($i$)$ The fault current $I_2(F).$

$[2$ marks$]$

$($ii$)$ The voltages $V_1(F),V_3(F),V_4(F),$ during the fault at buses $1,3$ and $4.$

$[6$ marks$]$

$($iii$)$ Find the current flow in the line from bus $3$ to bus $1,I_{31}(F).$

$[2$ marks$]$

$Z_{\text{B}\text{U}\text{S}}=j\left[\begin{array}{cccc}0\mathrm{.}25& 0\mathrm{.}2& 0\mathrm{.}16& 0\mathrm{.}14\\ 0\mathrm{.}2& 0\mathrm{.}23& 0\mathrm{.}15& 0\mathrm{.}151\\ 0\mathrm{.}16& 0\mathrm{.}15& 0\mathrm{.}196& 0\mathrm{.}1\\ 0\mathrm{.}14& 0\mathrm{.}151& 0\mathrm{.}1& 0\mathrm{.}195\end{array}\right]$ per unit

Figure Q$3($b$)$ Single line diagram of a $4-$bus power system