Question

Two 550 kVA alternators operate in parallel to supply the following loads:
(i) 250 kW at 0.6 p.f lagging
(ii) 100 kW at 0.5 p.f. leading
If one machine supply 200 kW at 0.9 p.f lagging, the p.f. of other machine is _____ lagging.

• A. 0.92

Answer 1

The correct option is A 0.92
Real power,

$P=P_{L1}+P_{L2}$

$Q=Q_{L1}+Q_{L2}$

$=P_{L1}\times \tan {\varphi }_1+P_{L2}\times \tan {\varphi }_2$

$Q=250\times \frac{0.8}{0.6}-\frac{100\times \frac{\sqrt{3}}{2}}{1/2}=160.128kVAR\left(lagging\right)$

$P_{G1}=200kW$

$Q_{G1}=\frac{\sqrt{1-{0.9}^2}}{0.9\times 200}\times 200=96.86kVAR$

$Q_{G2}=160.128-96.86=63.26kVAR$

$P_{G2}=350-200=150kW$

$p.f.=\frac{150}{\sqrt{{150}^2+{63.26}^2}}=0.922lag$