Transformer Efficiency

Method 1:

Efficiency = Output / Input
= (Input - Losses) / Input
= 1- (Losses / Input) ; input = VI cos θ ; (say, losses/ VI = x)

Efficiency = 1 - (x/ (cos θ+x))
= 1 - ((x/cos θ)/(1+ x/cos θ)
Method 2:

Efficiency = (VA * cos θ) / ((VA * cos θ) + Losses) * 100

Example:

Transformer KVA = 1000 KVA; 11 KV/ 433 V, Full loadLosses measured = 12.5 KW
calculate efficiency in full load at .8 PF, .9 PF and UPF.

method 1:
Eff at .8 PF = 800/ (800+12.5) * 100 = 98.46%
Eff at .9 PF = 900/912.5 * 100 = 98.63%
Eff at UPF = 100/ 1012.5 * 100 = 98.76%

Method 2:
x= 12.5 / 1000= 0.0125 Eff= 1- (x / x+ cos θ)
Eff at .8 PF = 1- (0.0125/(.8+.0125))= 1- (0.0125/.8125) = 98.46%
Eff at .9 PF = 1- (0.0125/(.9+.0125)) = 1- (0.0125/.9125) = 98.63%
Eff at UPF = 1- (0.0125/1+ .0125) = 1- (0.0125/1.0125) = 98.76%