Let the three-phase lossless transmission line of Problem 5.31 supply a load of 1000 MVA at 0.8 power factor lagging and at \(500 \mathrm{kV}\).

(a) Determine the capacitance/phase and total three-phase Mvars supplied by a three-phase, \(\Delta\)-connected shunt-capacitor bank at the receiving end to maintain the receiving-end voltage at \(500 \mathrm{kV}\) when the sending end of the line is energized at \(500 \mathrm{kV}\).

(b) If series capacitive compensation of \(40 \%\) is installed at the midpoint of the line, without the shunt capacitor bank at the receiving end, compute the sending-end voltage and percent voltage regulation.

Problem 5.31

A \(500-\mathrm{kV}, 300-\mathrm{km}, 60-\mathrm{Hz}\), three-phase overhead transmission line, assumed to be lossless, has a series inductance of \(0.97 \mathrm{mH} / \mathrm{km}\) per phase and a shunt capacitance of \(0.0115 \mu \mathrm{F} / \mathrm{km}\) per phase.