GATE EE 2016 Set 2 — Question 51
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Electric Circuits → AC Power & Three-Phase → Power Factor Correction
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Question
The power consumption of an industry is 500 kVA, at 0.8 p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is 100 kW, the p.f. of the motor is _____________
Correct answer
0.31 to 0.33
Solution
Step 1: Calculate the real and reactive power of the industry.
kVA, (lagging)
kW
kVAR (lagging)Step 2: Determine the required reactive power from the motor to achieve unity power factor.
For unity power factor, the total reactive power .
kVAR (leading)Step 3: Calculate the motor's apparent power and power factor.
kW
kVA
Motor p.f. (leading)The power factor of the motor is approximately 0.316, which falls within the range [0.31, 0.33].
kVA, (lagging)
kW
kVAR (lagging)Step 2: Determine the required reactive power from the motor to achieve unity power factor.
For unity power factor, the total reactive power .
kVAR (leading)Step 3: Calculate the motor's apparent power and power factor.
kW
kVA
Motor p.f. (leading)The power factor of the motor is approximately 0.316, which falls within the range [0.31, 0.33].
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