Eddy-current losses scale with f²: transformers and motors under HF

Core loss in motors and transformers is commonly separated into three parts (Bertotti):

$$P_{\text{core}}=P_{\text{hyst}}+P_{\text{eddy}}+P_{\text{exc}}$$

The classical eddy-current term is

$$P_{\text{eddy}}=K_e\cdot B_{\max }^2\cdot f^2\cdot t^2$$

Relative classical eddy-loss factor (f/50 Hz)² at constant flux density — thin-lamination assumption; at very high frequencies field penetration into the lamination limits the real increase.

What the research reports

• Distribution transformers: inverter harmonics raise eddy-current losses by up to +33% and accelerate insulation ageing by about 22% (Yaghoobi et al., 2020).
• Induction motors: iron losses rise by +29% under load and +86% at no load, with temperature rises up to +13 °C (Ding & Mi, 2011).

Reading the curve correctly

The $f^2$ term is a scaling law for a given flux density in thin laminations. HF components carry far less flux than the fundamental, and at MHz frequencies the field no longer penetrates the full lamination thickness. The point is not the absolute number — it is that HF content is disproportionately lossy compared with its share of the current.

References

1. Physics — core losses
2. Bertotti, 1988
3. Yaghoobi et al., 2020 — transformer losses under harmonics
4. Ding & Mi, 2011 — iron losses under PWM