Question

Two 800 kVA, 3-phase alternator are operating in parallel and supply a load of 1200 kVA at 0.8 lagging power factor. If one of the machines is operating at 0.9 lagging power factor and supplying 750 kVA, the power factor (lagging) at which the other machine operating is______lagging.

• A. 0.58

Answer 1

The correct option is A 0.58
$S_{load}=1200\angle -co{s}^{-1}\left(0.8\right)=960-j720$

$S_A=750\angle -co{s}^1\left(0.9\right)=675-j326.9$

$Now,S_A+S_B=S_{load}$

$\therefore$ $S_B=S_{load}-S_A$

$=960-j720-675+j326.9$

$=285-j393.1$

$S_B=485.54\angle -{54.05}^{\circ }$

$cos{\varphi }_B=cos(-{54.05}^{\circ })=0.587\left(lagging\right)$