Problem $2.(25$ points total$)$

For the power system whose single line diagram is shown below along with the negative and zero$-$sequence reactances the $\backslash (\backslash$Delta$-$Y $\backslash )$ transformers are solidly grounded. The motor neutral is grounded through a reactance $\backslash ($ X$\_\{$n$\}=0\mathrm{.}05\backslash$mathrm$\{$pu$\}\backslash )$ on the motor base.

Neglect pre$-$fault load current and $\backslash (\backslash$Delta$-$Y $\backslash )$ phase shifts for transformers.

Calculate:

a$)$ the subtransient fault current in per$-$unit and in kA for a bolted double line to ground fault from phase b to c to ground at bus $2,$ if pre$-$fault voltage is $\backslash ($ V$\_\{$F$\}=1\mathrm{.}05\backslash$mathrm$\{$pu$\}\backslash ),$

b$)$ the neutral fault current, and

c$)$ the contributions to the fault current from the motor and from the transmission line sides.