What is the efficiency formula used?

Efficiency is output power divided by input power: η = (S × loadFraction × PF) / (S × loadFraction × PF + W0 + loadFraction² × Wk). W0 is the constant no-load core loss and Wk is the full-load copper loss, which scales with the square of the load fraction.

Why does copper loss scale with load squared?

Copper (load) loss is I²R heating in the windings. Current is proportional to load, so the loss rises with the square of the load fraction. At half load the copper loss is only a quarter of its full-load value, while core loss stays constant.

What is no-load loss and when does it occur?

No-load or core loss is the energy lost magnetizing the iron core. It is essentially constant whenever the transformer is energized, even with no load connected, so it runs 8,760 hours a year and dominates the losses on lightly loaded transformers.

At what load is a transformer most efficient?

Peak efficiency occurs where copper loss equals core loss, which happens at a load fraction equal to the square root of W0 divided by Wk. Most distribution transformers are designed to peak near 35 to 50 percent load, matching typical duty.

How do I estimate annual no-load energy?

Multiply the no-load loss in watts by 8,760 hours and divide by 1,000 to get kWh per year. A 100-watt core loss costs 876 kWh a year regardless of load, which is why low-no-load designs under DOE and TP-1 standards save money on lightly loaded units.

Transformer Efficiency & No-Load Loss Calculator

A transformer wastes energy two ways: a constant core loss whenever it is energized and a load-dependent copper loss that grows with current squared. This calculator combines the nameplate no-load and full-load loss figures to give efficiency at any operating point and the annual energy quietly burned as no-load loss.

How it works

Efficiency at a given load fraction x and power factor PF:

output  = S × x × PF                          (kW, S in kVA)
losses  = W0 + x² × Wk                         (W0 core, Wk full-load copper)
η       = output / (output + losses/1000) × 100
peak η at x = sqrt(W0 / Wk)                     (where copper loss = core loss)
annual no-load energy = W0 × 8760 / 1000       (kWh per year)

Core loss W0 is constant, so on a lightly loaded transformer it dominates and runs every hour of the year. Copper loss Wk only matters near full load because it scales with x².

Example and tips

A 100 kVA transformer with 200 W core loss and 1,200 W copper loss, running at 40 percent load and 0.95 PF, makes about 38 kW output against roughly 392 W of total loss — about 98.97 percent efficient. Its no-load loss alone costs about 1,752 kWh a year. Peak efficiency sits near 41 percent load (sqrt(200/1200)). When sizing, avoid oversizing units that will sit lightly loaded, since their constant no-load loss runs 8,760 hours regardless of duty.