Analytical Inverse Preisach Model and Its Comparison With Inverse Jiles–Atherton Model in Terms of Accuracy and Computational Speed

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 issues of electrical equipment in terms of magnetic vector potential or with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed has a broader range of applications. However, the well-known classical Preisach hysteresis model is formulated with the forward form, and has the double integration of its distribution function, making it inconvenient and impractical in electrical engineering. In this article, an analytical inverse Preisach model is proposed for the first time. First, the analytical expressions of permeability of the initial magnetization curve, descending and ascending branches of the hysteresis loop are derived using one closed form of the Everett integral function. Subsequently, the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that the 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 the widely used inverse Jiles–Atherton (J–A) hysteresis model.