GATE 2016 EE – Question 50
A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz, the capacitance per phase of the bank, expressed in microfarads, is ________.
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Correct answer: 47 to 49
Explanation
The cable heat loss depends on the current, so the apparent power must stay at the original $\sqrt{800^2 + 600^2} = 1000$ kVA. With 900 kW of real power, the reactive power the cable may carry is $\sqrt{1000^2 - 900^2} = 435.9$ kVAr. The capacitors must therefore supply $600 - 435.9 = 164.1$ kVAr. For a star-connected bank, $Q_c = V_L^2 \omega C$, so $C = \frac{164.1 \times 10^3}{3300^2 \times 2\pi \times 50} = 48 \ \mu\text{F}$.