Question

A generating station is connected with following loads:
1. A lighting load of 200 kW
2. An induction motor of 200hp, 0.7 p.f. lagging and efficiency 80%.
3. A synchronous motor of 100 hp, efficiency 90%.
If the combined p.f. is unity, then the p.f. of synchronous motor is __________ leading. (1 hp = 735.5 W)

• A. 0.4

Answer 1

The correct option is A 0.4
Active power consumed by induction motor,
$=\frac{200\times 735.5}{0.8}=183.875kW$
$p.f.,cos{\varphi }_{IM}=0.7lagging\Rightarrow {\varphi }_{IM}={45.57}^{\circ }$
Active power consumed by synchronous motor,
$=\frac{100\times 735.5}{0.9}=81.722kW$



Reactive power consumed by IM
$=183.875\times tan\left({45.57}^{\circ }\right)$
= 187.57 kVAR

So reactive power supplied by synchronous motor
= 187.57 kVAR

$\varphi =ta{n}^{-1}\left(\frac{187.57}{81.722}\right)={66.458}^{\circ }$

$Thep.f.ofsynchronousmotor=cos\left({66.458}^{\circ }\right)$
$\cong 0.4leading$