Solution Electrical Numerical 20

Numerical 20: Two 10 MVA 3 phase Alternator operate in parallel to supply at 0.8 power factor with lagging load of 15 MVA. If the output of one Alternator is 8 MVA at 0.9 lagging. 1. Calculate the output of second Alternator. 2. Calculate the value of Power factor of second Alternator.

Solution: we need to calculate active and reactive components for the further calculation: 

Parallel operation:

Load = 15 MWA

p.f = cosф = 0.8

thus, sinф = 0.6

Active load =  15 x 0.8 = 12 MW

Reactive load = 15 x 0.6 = 9 MVAr

Alternator One:

Load  = 8 MVA

p.f = cosф = 0.9

thus, sinф = 0.4358

Active load = 8 x 0.9 = 7.2 MW

Reactive load = 8 x 0.4358 = 3.4864 MVAr

Alternator Two:

Active load = 12 - 7.2 = 4.8 MW

Reactive load = 9 - 3.4864=5.5136 MVAr

$\displaystyle \mathrm{Load = \sqrt{Active\ load ^2 +\ Reactive\ load^2 }}$ 

$\displaystyle \mathrm{Load = \sqrt{4.8 ^2 +\ 5.5136^2 }}$ 

Load = 7.317 MVA

$\displaystyle \mathrm{cos\phi = \frac{MW}{MVA}\ =\ \frac{4.8}{7.317}\ =\ 0.656}$