A model for the calculation of excess losses in a nanocrystalline ribbon

A dynamic constitutive relation incorporating a fractional-order temporal derivative is introduced to model excess magnetic losses in nanocrystalline ferromagnetic ribbons. The formulation extends the static hysteresis law by accounting for inter–domain wall correlations responsible for anomalous frequency dependence, in accordance with Bertotti’s statistical theory of losses. The resulting non-linear field problem is solved in the frequency domain using a harmonic balance approach, enabling an efficient treatment of fractional operators without time-domain convolutions. The method is applied to a thin nanocrystalline ribbon and validated through detailed comparisons with experimental hysteresis measurements over a wide range of frequencies and flux densities. Good agreement is obtained without parameter readjustment beyond a single identification point. Although high-frequency predictions could not be experimentally verified, the model provides physically consistent trends suitable for the preliminary dimensioning and optimization of electrical machines and magnetic components.