Dynamic Magnetostatic Energy Correction Based on Domain Area Evolution for Mesoscopic Hysteresis Modeling

In mesoscopic domain energy models of electrical steel sheets, the demagnetizing field Hd is usually held constant at its domain-wall-complete value throughout magnetization. This treatment overestimates the magnetostatic energy at intermediate states and distorts the simulated hysteresis loop. We introduce a field-dependent coefficient υH that scales the magnetostatic energy at each field step. The coefficient is calculated from the aligned-domain area measured by magneto-optical Kerr microscopy and is anchored at the negative coercivity point H = −Hc, where the macroscopic magnetization vanishes and the aligned-domain area S0 is minimal. The definition follows from the linear relation Hd ≈ Nd·M that holds during domain-wall motion. Measurements in two observation zones of a grain-oriented steel give consistent υH curves, confirming the repeatability of the method. When the correction is incorporated into an Assembly Domain Structure Model, the coercivity error drops from 113% to 9–22% relative to the experimental average, with the predicted value falling inside the experimental range, and the remanence error drops from 39.9% to 15–17%. The same correction, applied to a second grain-oriented steel of a different grade, likewise reduces the coercivity and remanence errors (to about 23% and 18%, respectively), confirming that the method is applicable across grades.