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

• Published in: IEEE transactions on magnetics 2023-11, Vol.59 (11), p.1-1
• Main Authors: Liu, Ren, Gu, Chaoyang, Sun, Jiangdong, Shu, Fandi, Tang, Bo
• Format: Article
• Language: English
• Subjects: Accuracy; Analytical models; Computational modeling; Distribution functions; Electric equipment; Electrical engineering; Exact solutions; Flux density; Hysteresis; Hysteresis loops; Hysteresis models; inverse Preisach model; Magnetic fields; Magnetic flux; Magnetic hysteresis; Magnetic vector potentials; Magnetism; Magnetization; Magnetization curves; Mathematical analysis; Model accuracy; Preisach's theory; Silicon; Silicon steels; soft magnetic materials; Steel
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2023.3281779

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 both has 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 unpractical in the electrical engineering. In this paper, an analytical inverse Preisach model is proposed for the first time. Firstly, the analytical expressions of permeability of initial magnetization curve, descending and ascending branches of the 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 the widely used inverse Jiles-Atherton hysteresis model.