Reconsideration of Nonphysical Solution in Jiles–Atherton Model for Real-Time Hysteresis Estimation

The Jiles–Atherton (JA) model is widely used in real-time hysteresis estimation for its better physical understanding and less experimental efforts. However, the inherent defects of JA model may lead to some nonphysical solutions, including negative differential permeability, non-closure of minor loops, and asymmetry of centered minor loops. To deal with such problems, a limiter for differential permeability and a scaling factor for loop closure are generally adopted. However, the existing methods may cause loops’ edges overlapping and cannot solve the asymmetry of centered minor loops. Therefore, a new equation for irreversible magnetization is proposed to solve the negative differential permeability and the edges overlapping. Also, to improve the fitting performance, the JA coefficients are adjusted for different fields and different loops’ turning points. In addition, a scaling factor for centered minor loops is developed to deal with the asymmetry. The factor only needs prior knowledge of minor loops’ starting points. Besides, a modified stack model is proposed, which can extract enough information for coefficients lookup and scaling factors calculation and can realize real-time hysteresis estimation for arbitrary field. Finally, the estimation results are verified by experiments on a toroidal transformer.