Generalized Preisach model for the description of hysteresis and eddy current effects in metallic ferromagnetic materials

We discuss a generalization of the Preisach model, based on the assumption that each point (α,β) of the Preisach plane corresponds to a small correlation region of the system cross section, inside which magnetic flux reverses at a rate Φ̇ ∝ Ha − α (or Ha − β) when the applied field Ha exceeds the threshold α (or β). When the magnetizing frequency f is low, the model reduces to the conventional Preisach model. When f is increased, the model predicts that the area of the hysteresis loop should increase with f according to the law C0 + C1f + C2√f, where C1 is related to the so-called classical loss and C2 is expressed directly in terms of the Preisach function, p(α,β). The prediction of the existence of the excess loss term C2√f is in agreement with experiments. The fact that the coefficient C2 is calculated from p(α,β) implies that one can predict dynamic losses directly from quasistatic hysteresis losses, a remarkable conclusion which is also confirmed by recent investigations with electrical steels.