A $3-$ph$,100$ km long transmission line has resistance $0\mathrm{.}05/$km$,$ inductive reactance $0\mathrm{.}5/$km$,$ capacitive

susceptance $5\mathrm{.}5$x$10-6$ mho$/$km$.$ The line delivers power to a Y connected $400$ MW load at $0\mathrm{.}9$ lead power factor at

$345$ kV$.$ Use the T model to represent the transmission line and calculate the following.

$($a$)$ The phase voltage across the shunt capacitor of the model.

$($b$)$ The current, line$-$to$-$line voltage and power factor at the sending end.

$($c$)$ Does the sending end power factor lag or lead.

$($d$)$ The transmission efficiency.