Question

A 3-phase synchronous motor absorbing 50 kW is connected in parallel with a factory
load of 200 kW having a lagging power factor of 0.75. If the combined load has a p.f of
0.95 lagging, what is the kVA rating of synchrnous motor ? Also calculate the power
factor at which the synchrnous motor is working.

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Answer 1

Answer:

The power factor at which the synchrnous motor is workingp.f. of motor is kW/kVA = 50/57.8 = 0.865

Explanation:

From the above question:

A 3-phase synchronous motor absorbing 50 kW is connected in parallel with a factory load of 200 kW having a lagging power factor of 0.75. If the combined load has a p.f of 0.95 lagging,

Load kVA = 200/0.8

Load kVA  = 250  

Load kVAR = 250 × 0.6

Load kVAR = 150 (lag) [cos φ = 0.8 sin φ = 0.6]  

Here we need to find the kVA rating of synchrnous motor

Also we have to calculate the power factor at which the synchrnous motor is working.

Total combined load = 50 + 200

Total combined load = 250 kW  

kVA of combined load = 250/0.9

kVA of combined load = 277.8  

Combined kVAR = 277.8 × 0.4356

Combined kVAR = 121 (inductive) (combined cos φ = 0.9, sin φ = 0.4356)  

Hence, leading kVAR supplied by synch, motor = 150 – 121 = 29 (capacitive)

kVA of motor alone = √(kW2 + kVAR2) = √(502 + 292) = 57.8

p.f. of motor = kW/kVA = 50/57.8 = 0.865

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