Question

A 3-phase induction motor draws 1000 kVA at power factor of 0.8 lag. A synchronous condenser is connected in parallel to draw an additional 750 kVA at 0.6 power factor leading. Then the power factor of the total load supplied by the mains is

• A. Reactive power absorbed by supply is 600 kVAR.
• B. Reactive power delivered by supply is 600 kVAR.
• C. Supply power factor is unity.
• D. Supply power factor is 0.9 lagging.

Answer 1

The correct option is C Supply power factor is unity.

Complex power can be represented as,

${\overline{S}}_{IM}=1000\times 0.8+j1000\times 0.6=800+j600$
${\overline{S}}_{SC}=750\times 0.6-j750\times 0.8$
$=450-j600$

$\therefore$ ${\overline{S}}_{Total}={\overline{S}}_{IM}+{\overline{S}}_{SC}$
= $800+j600+450-j600$
${\overline{S}}_{Total}=1250kW$
Total load supplied by the mains is only real power
$\therefore$ $pf=1$