A power system network operating at $60$Hz has a generator operating at the sending end per phase voltage of $$The transmission line has per phase parameters as $,$The line is connected to a wye connected $100$MW load at $0\mathrm{.}9$ lagging power factor and line voltage of $215$kV$.$

a$)$ Find the apparent power in the power system.$(15)$

b$)$ Suppose a shunt capacitor bank of $$is inserted before the load, repeat computations in a$)$ and,$(8)$

c$)$ Make a conclusive observation on the effect of the shunt capacitor bank on the power system.