Question

Two similar 400 V, 3-phase alternators share equal kW power delivered to a balanced three phase, 50 kW, 0.8 p.f. lagging load. If the power factor of one machine is 0.9 lag, then the current supplied by other machine is _____A.

• A. 51.47

Answer 1

The correct option is A 51.47
Active power supplied to load = 50 kW

Reactive power supplied to load,
$Q=Ptan\varphi$
$=50\tan \left({\cos }^{-1}0.8\right)$
$=37.5kVAR$

Active power supplied by one generator $=\frac{50}{2}=25kW$
Power factor of generator 1 $=cos{\varphi }_1=0.9lag$

Reactive power supplied by generator 1
$=25\times \tan \left({\cos }^{-1}0.9\right)=12.10kVAR$

Reactive power supplied by generator 2
$=37.5-12.10$
$=25.4kVAR$
${\varphi }_2={\tan }^{-1}\left(\frac{25.4}{25}\right)={45.45}^o$
cos${\varphi }_2=0.701$ lagging


Current supplied by machine 2 is ,

$I_2=\frac{P_2}{\sqrt{3}{V}_L\cos {\varphi }_2}=\frac{25\times {10}^3}{\sqrt{3}\times 400\times 0.701}$

$=51.47A$