A three$-$phase transmission line is shown in one$-$line format in Figure $11\mathrm{.}8.$ The buses at each end, represented as voltage sources, haye the same voltage magnitude; $138$ kV $,$ RMS$,$ line$-$line. For now, model the line as having an impedance to balanced currents of $Z_1=j40.$ Assume the sending end has a plase advance over the receiving end of angle $.$

$($a$)$ What is real power flow through the line for $8=10?$

$($b$)$ What is real power flow through the line for $8=30?$

$($c$)$ What angle $ results in a real power flow of $100$ MW $?$

$($d$)$ With $100$ MW tlowing through the line, what is reactive power at the sending and receiving ends?