Transformer Losses and Efficiency

$\eta = \frac{x S \cos\phi}{x S\cos\phi + P_{core} + x^2 P_{cu,fl}}$

where $x$ is the fraction of full load. Maximum efficiency occurs when copper loss equals core loss:

$x = \sqrt{\frac{P_{core}}{P_{cu,fl}}}$

Large transformers reach 98–99.5 % efficiency.

All-day efficiency = energy out / energy in over 24 h — important for distribution transformers that are energised continuously but lightly loaded much of the time.