The total power delivered to a balanced threephase load when operating at a line voltage

Chapter 11, Problem 11.39

(choose chapter or problem)

The total power delivered to a balanced three-phase load when operating at a line voltage of \(2500 \sqrt{3} \mathrm{~V}\) is 900 kW at a lagging power factor of 0.6. The impedance of the distribution line supplying the load is \(1+j 3 \Omega / \phi\). Under these operating conditions, the drop in the magnitude of the line voltage between the sending end and the load end of the line is excessive. To compensate, a bank of Y-connected capacitors is placed in parallel with the load. The capacitor bank is designed to furnish 1125 kVAR of magnetizing reactive power when operated at a line voltage of \(2500 \sqrt{3} \mathrm{~V}\).

a) What is the magnitude of the voltage at the sending end of the line when the load is operating at a line voltage of \(2500 \sqrt{3} \mathrm{~V}\) and the capacitor bank is disconnected?

b) Repeat (a) with the capacitor bank connected.

c) What is the average power efficiency of the line in (a)?

d) What is the average power efficiency in (b)?

e) If the system is operating at a frequency of 60 Hz, what is the size of each capacitor in microfarads?