Question

A 3-phase induction motor draws 1 MVA at a p.f of 0.8 lag. A synchronous condenser is connected in parallel to draw an additional 750 kVA at 0.6 p.f lead. The p.f of the total load supplied by the mains is _______.

• A. 1

Answer 1

The correct option is A 1
The given condition can be explained with phasors,

Active power consumed by induction motor,
$=1MVA\times 0.8=800kW$

Reactive power consumed by induction motor :
$=800kW\times \tan \left({36.87}^{\circ }\right)$
$=600kVAR$

Active power consumed by synchronous condenser
$=450kW\times \tan \left({53.13}^{\circ }\right)$
$=600kVAR$

$Q_{net}=0i.e.,\varphi =0^{\circ }$

$cos\varphi =1$

$\therefore \text{The power factor of the total load is unity}$