Analytical Inverse Preisach Model and Its Comparison With Inverse J-A Model in Terms of Accuracy and Computational Efficiency

Inverse hysteresis model with magnetic flux density and magnetic field intensity as input and output respectively is more preferred, compared with the forward one, for resolving the electromagnetic problems of the electrical equipment in terms of magnetic vector potential, or for analyzing the electromagnetic issues of electrical equipment with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed both has broader range of applications. However, the classical Preisach hysteresis model that is well known is formulated with the forward form, and involves the double integration of its distribution function, making it inconvenient and unpractical in the electrical engineering. In this paper, an analytical inverse Preisach model is proposed in this paper for the first time. To derive it, the analytical expressions of permeability for the initial magnetization curve, descending and ascending branches of hysteresis loop are derived using one closed form of Everett integral function. Subsequently the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that classical Preisach model cannot simulate with an odd function analytically. The experiment of one grain oriented silicon steel sample and one non-oriented silicon steel sample, under different magnetic excitation levels is conducted, and the accuracy and efficiency of the proposed analytical inverse Preisach model are confirmed by comparing its simulated hysteresis loops with the experimental ones and that computed with widely used inverse Jiles-Atherton hysteresis model.