$1)$ Consider a three$-$phase series capacitance of $0\mathrm{.}5$ pu for the $20-$km line and a three$-$phase series capacitance of $0\mathrm{.}3$ pu for the $10-$km line. Calculate the following values by using the $25$ kV$/575$ V transformer$$s base values: $12$ MVA and $25$ kV:

Impedance base value: Capacitance $0\mathrm{.}5$ pu Capacitance $0\mathrm{.}3$ pu

$2)$ Consider a three$-$phase shunt capacitance of $0\mathrm{.}5$ pu at the $120$kV$-$bus $$B$120$ Calculate the following values by using the base values: $12$ MVA and $120$ kV: Impedance base value Capacitive reactive power Qc

$3)$Consider a three$-$phase shunt capacitance of $0\mathrm{.}5$ pu at the $25$kV$-$bus $$B$25$ Calculate the following values by using the base values: $12$ MVA and $25$ kV:Impedance base value Capacitive reactive power Qc

$4)$calculate the subsynchronous resonance frequency for the case with series compensation for both lines $($note: the $120$ kV$/25$ kV and reactance $0\mathrm{.}08$ for both windings are specified w$.$r$.$t$.$ a base value of $47$ MVA, whereas all the previous impedance are calculated based on a base value of $12$ MVA$).$