Question

Two 550 kVA alternators operate in parallel to supply the following load.
(i) 250 kW at 0.6 pf lagging. (ii) 100 kW at 0.5 pf leading.
If one machine is supplying 200 kW at 0.9 pf lagging. The power factor angle in degree of other machine is______leading.

• A. -22.86

Answer 1

The correct option is A -22.86
$P=P_{L1}+P_{L2}$

$=250+100=350kW$

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

$=P_{L1}tan{\varphi }_1+P_{L2}tan{\varphi }_2$
$Q=250\times \frac{0.8}{0.6}-\frac{100\times \frac{\sqrt{3}}{2}}{\frac{1}{2}}=160.128kVAR\left(lagging\right)$

$P_{G1}=200kW$

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

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

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

$\text{Power factor angle}=ta{n}^{-1}\left(\frac{63.26}{150}\right)lagging={22.86}^{\circ }lagging$

$\text{or Power factor angle}=-{22.86}^{\circ }\text{leading}$