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 H_d 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 υ_H 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 = -H_c, where the macroscopic magnetization vanishes and the aligned-domain area S₀ is minimal. The definition follows from the linear relation H_d ≈ N_d·M that holds during domain-wall motion. Measurements in two observation zones of a grain-oriented steel give consistent υ_H 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.