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Question

A 3-phase induction motor draws 1000 kVA at power factor of 0.8 lag. A synchronous condenser is connected in parallel to draw an additional 750 kVA at 0.6 power factor leading. Then the power factor of the total load supplied by the mains is

A
Reactive power absorbed by supply is 600 kVAR.
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B
Reactive power delivered by supply is 600 kVAR.
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C
Supply power factor is unity.
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D
Supply power factor is 0.9 lagging.
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Solution

The correct option is C Supply power factor is unity.
Complex power can be represented as,

¯¯¯¯SIM=1000×0.8+j1000×0.6=800+j600
¯¯¯¯SSC=750×0.6j750×0.8
=450j600

¯¯¯¯STotal=¯¯¯¯SIM+¯¯¯¯SSC
= 800+j600+450j600
¯¯¯¯STotal=1250 kW
Total load supplied by the mains is only real power
pf=1

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