In a factory, a three-phase, 4-kV, 400-kVA synchronous machine is installed along with other induction motors. The following are the loads on the machine: (i) Induction motors: 500 kVA at 0.8 power factor lagging (ii) Synchronous motor: 300 kVA at unity power factor

In a factory, a three-phase, 4-kV, 400-kVA synchronous machine is installed along with other induction motors. The following are the loads on the machine: (i) Induction motors: 500 kVA at 0.8 power factor lagging (ii) Synchronous motor: 300 kVA at unity power factor Determine the overall power factor of the factory loads.

Right Answer is:

7/5√8 lagging

SOLUTION

(a) Induction motors:

Power = 500 × 0.8 = 400 kW

Reactive Power = 500 × 0.6 = 300 kVAR

(b)Synchronous motor:

Power = 300 kW

Reactive Power = 0.0

Factory :

Power = 400 + 300 = 700 kW

Reactive Power = 300 + 0 = 300 kVAR

Complex Power = √(7002 + 3002) = 100√58  = 762 kVA

Power factor = 700/(100√58) = 7/√58 = 0.92 lagging

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