Accurate calculation of the hysteresis characteristics of magnetic materials is of great significance for the optimal design of electrical equipment. In previous studies, the Preisach model based on the centered cycle method is widely used for the simulation of hysteresis characteristics as this method uses data that can be easily obtained 1. However, the existing centered cycle method model cannot correctly consider the influence of reversible magnetization and leads to a large error when calculating the small major hysteresis loops 2. In this paper, an improved centered cycle method for identifying the Preisach distribution function (PDF) considering the reversible magnetization is proposed, which can improve the accuracy of predicting the symmetrical minor loops.
II Method and Discussion
As shown in Figure 1, an improved PDF identification method considering the reversible magnetization is proposed, which is consistent with the principle of the magnetization process. The reversible relative permeability is obtained by derivation at the reversal points of the centered cycles with different measured magnetic flux densities and obtained parametric equation, which is integrated to obtain the reversible magnetization. Four centered cycles of different magnetic flux densities are used to discretize the Preisach plane, and the values of the PDF are calculated through the modified magnetic flux densities. The irreversible magnetization is obtained by accumulating the values of the PDF. The final output value is obtained by superposing the irreversible magnetization and the reversible magnetization. The simulation results of grain-oriented silicon steel based on B30P105 are shown in Fig. 2, and the expected accuracy can be achieved.
III Conclusion
In this paper, a modified Preisach model with centered cycle method under the magnetization principle is developed. Obtained results show that the accuracy of the simulated symmetrical minor loops can be improved.

References
1 Bernard Y, Mendes E, Ren Z. Determination of the distribution function of Preisach’s model using centred cyclesJ. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2000. 2 Peng D, Sima W, Ming Y, et al. An Improved Centered Cycle Method for Identifying the Preisach Distribution FunctionJ. IEEE Transactions on Magnetics, 2018, PP(11):1-5.

Fig.1. (a) Discretized Preisach Plane. (b) Numerical discrete calculation process of improved Preisach Model.

Fig.2. Comparison of simulation results of B30P105 silicon steel. (a) B_p=0.2T. (b) B_p=0.5T. (c) B_p=0.7T. (d) B_p=1.1T.