# Transformer Losses and Efficiency

There are broadly two sources of losses in transformers on load, these being copper losses and iron losses.

Copper losses are variable and result in a heating of the conductors, due to the fact that they possess resistance. If R1 and R2 are the primary and secondary winding resistances then the total copper loss is I21 R1 + I22 R2

Iron losses are constant for a given value of frequency and flux density and are of two types hysteresis loss and eddy current loss.

Hysteresis loss is the heating of the core as a result of the internal molecular structure reversals which occur as the magnetic flux alternates. The loss is proportional to the area of the hysteresis loop and thus low loss nickel iron alloys are used for the core since their hysteresis loops have small areas.

Eddy current loss is the heating of the core due to e.m.f.’s being induced not only in the transformer windings but also in the core. These induced e.m.f.’s set up circulating currents, called eddy currents. Owing to the low resistance of the core, eddy currents can be quite considerable and can cause a large power loss and excessive heating of the core.

Eddy current losses can be reduced by increasing the resistivity of the core material or, more usually, by laminating the core (i.e. splitting it into layers or leaves) when very thin layers of insulating material can be inserted between each pair of laminations. This increases the resistance of the eddy current path, and reduces the value of the eddy current.

Transformer efficiency,

$\eta=\frac{\text { output power }}{\text { input power }}=\frac{\text { input power }- \text { losses }}{\text { input power }}$

$\quad \eta=1-\frac{\text { losses }}{\text { input power }}$

and is usually expressed as a percentage. It is not uncommon for power transformers to have efficiencies of between 95% and 98%

Output power = V2I2 cosΦ2
Total losses = copper loss + iron losses,
and input power = output power + losses   