GATE 2017 EE (EE2) – Question 62

Power Systems · Voltage and Frequency control, Power factor correction · 2 marks · Numerical answer

A 3-phase 50 Hz generator supplies a balanced inductive load of 3 MW at 17.32 kV through an overhead line. Per-phase line resistance and reactance are 0.25 Ω and 3.925 Ω. Generator terminal voltage is 17.87 kV. The load power factor is ________.

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Correct answer: 0.75 to 0.85

Explanation

Take receiving phase voltage $V_R=17320/\sqrt3$ V as reference. Real current component is $I\cos\phi=P/(3V_R)\approx100$ A. Let t=tanφ, so current is approximately 100(1−jt) A.

The sending voltage phasor is $V_S=V_R+(0.25+j3.925)I$. Equate its magnitude to 17870/√3 V and select the positive t for an inductive load.

The resulting t is about 0.728, giving **pf≈0.8085 lagging**, within the official 0.75–0.85 interval. The usual approximate voltage-drop calculation gives about 0.80 as well.

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