Transformer losses and efficiency expression

Types of losses

1. Core (iron) losses occur in the core and are practically constant from no-load to full load (since V1 and f are constant).

• Hysteresis loss: Pₕ = ηₕ Bm^1.6 f V, reduced by using silicon steel / CRGO.
• Eddy current loss: Pₑ = kₑ Bm² f² t² V, reduced by thin insulated laminations.

2. Copper (I²R) losses occur in the primary and secondary windings and vary as the square of the load current: Pcu = I1² R1 + I2² R2 = I1² R01.

3. Stray and dielectric losses (small): leakage-flux losses in the tank and structure, and insulation losses (insignificant at normal voltages).

Since a transformer has no moving part, there are no friction or windage losses, so efficiency is very high (95–99 %).

Efficiency expression

Efficiency η = output power / input power = output / (output + losses).

Let the transformer have rating S (VA), secondary voltage V2, and let a fraction x of full load be supplied at a load power factor cos φ.

Output power           = x S cos φ
Iron loss              = Pi  (constant)
Copper loss at x load  = x² Pcu   (Pcu = full-load copper loss)

η = x S cos φ / ( x S cos φ + Pi + x² Pcu )

At full load (x = 1):

η = S cos φ / (S cos φ + Pi + Pcu)

Equivalent form using currents: η = V2 I2 cos φ2 / (V2 I2 cos φ2 + Pi + I2² R02).

Observations:

• Efficiency depends on the power factor; it is lower for lower power factor.
• For a given power factor, efficiency is highest at the load where Pi = x² Pcu.
• All-day efficiency matters for distribution transformers, which are on 24 hours but loaded only part of the day.

Example: 100 kVA, Pi = 1 kW, Pcu = 1.5 kW at unity pf, full load: η = 100/(100 + 1 + 1.5) = 97.6 %.