Losses, Regulation and Efficiency

• Copper loss — I²R in the windings. Rises with the square of load current.
• Iron loss — hysteresis plus eddy currents. Depends on flux, which is set by the applied voltage, so it is essentially constant from no load to full load.

A distribution transformer energised all year burns iron loss the entire time, whether it is supplying anything or not. That is a real operating cost, and it is why no-load loss is a specified quantity.

Hysteresis

Energy spent reversing magnetic domains each cycle — proportional to the B-H loop area and to frequency. Reduced with silicon steel, which has a narrow loop.

Eddy currents

The core is itself a conductor, so the changing flux drives currents in it. Loss goes as the square of lamination thickness, so laminating the core into thin insulated sheets attacks it directly.

Both scale with frequency, which is why a 400 Hz aircraft transformer can be far smaller than a 50 Hz one of the same rating — and why switched-mode supplies at tens of kilohertz are smaller still.

1. 1Open-circuit test. Rated voltage, secondary open. Rated flux means full iron loss, while the tiny magnetising current makes copper loss negligible — so the wattmeter reads iron loss.
2. 2Short-circuit test. Secondary shorted, voltage raised until rated *current* flows — about 5% of rated volts. Flux and iron loss are then negligible while copper loss is full — so the wattmeter reads copper loss.

Each test suppresses one loss so the meter can read the other alone. It is how a 500 MVA transformer's efficiency is established with a supply of a few kilowatts.

At light load the constant iron loss is a large share of a small output, so efficiency is poor. It rises to a maximum where copper loss equals iron loss, then falls again as copper loss grows with the square of current.

Maximum efficiency at variable loss = constant loss is a general result for machines. Since the designer chooses the winding resistance, they choose the load fraction at which the peak occurs — and a distribution transformer is deliberately designed to peak near half load, because that is where it spends its life.

For distribution work the meaningful figure is all-day efficiency: energy out over energy in across 24 hours, which properly weights the many hours spent lightly loaded.

Regulation is the voltage sag from no load to full load, caused by winding resistance and leakage reactance — typically 2–8%, and lower is better.

It depends on the load's power factor, and a leading power factor can make it negative, so the output voltage *rises* under load. Efficiency and regulation also conflict: lowering impedance improves regulation and raises the fault current the switchgear must interrupt.