Solution Electrical Numerical 14

Numerical 14: 72 KVA transformer supplies a heating and lighting load of 12 KW at unity power factor and a motor load of 70 kVA at 0.766 (lagging) power factor; Calculate the minimum rating of the power-factor improvement capacitors which must be connected in the circuit the ensure that the transformer does not become overloaded.

Solution: 

Motor:-

KVA = 70

CosΦ = 0.766

∴ Φ = 40°

SinΦ = 0.6428

KVAr = KVA X SinΦ = 70 x 0.6428 = 44.996

KW = KVA x CosΦ = 70 x 0.766 =53.62

Transformer:-

KVA = 72

KW = Total Load applied = 12 + 53.62 =65.62

$\displaystyle \mathrm{KVAr = \sqrt{72^{2}-65.62^{2}}}$ 

=29.63

Capacitor 

KVAr = 44.996 - 29.63 =15.4