Problem $5\mathrm{.}31$

A $500$ kV$,300$ km$,60$ Hz$,$ three$-$phase overhead transmission line, assumed to be lossless, has

a series inductance of $0\mathrm{.}97$ mH$/$km per phase and a shunt capacitance of $0\mathrm{.}0115$ F$/$km per

phase. The receiving$-$end load is $800$ MW at $0\mathrm{.}8$ power factor lagging and at $500$ kV$.$ Determine

the following:

$($a$)$ Determine the phase constant $,$ the surge impedance ZC$,$ the velocity of propagation $,$

and the wavelength of the line.

$($b$)$ Calculate the voltage, current, real, and reactive power at the sending end.