Fractional derivatives for the core losses prediction: State of the art and beyond

Abstract

The core losses prediction in laminated magnetic circuits has generated relentless scientific research efforts. In this domain, the almost forty years old Statistical Theory of Losses (STL) is still prevailing. Modern electrical energy conversion exposes laminated magnetic circuits to higher frequencies and larger excitation fields. STL, which requires a full flux penetration, poorly considered these intense stimuli. Recent studies proposed upgrading STL by modifying the classical eddy current loss term using fractional derivative operators. Excellent predictions were observed, but the lumped aspect inherent to STL means working with averaged quantities which constitutes a limitation. Alternatively, local predictions and good simulation trajectories were obtained for the frequency dependence of hysteresis by replacing the classic magnetic diffusion equation with a fractional one. Still, the physical origin of the fractional diffusion equation remains questionable. In the light of these results, we propose in this new study to review the use of the fractional derivative operators for the core losses prediction. We eventually revealed an alternative way to combine the classic diffusion equation to a fractional material law, leading to the ultimate fractional method, with physical fundaments, few parameters, and accurate results on significant frequency bandwidths.