Abstract：Grain-oriented electrical steel sheets are widely used in high power transformers because of their good magnetic properties in the rolling direction. However, the core of transformer will be affected by mechanical stress during assembly and operation, resulting in significant changes in the hysteresis characteristics of electrical steel sheets. The Sablik-Jiles-Atherton (S-J-A) hysteresis model is widely used to simulate the hysteresis characteristics under mechanical stress because of its simple calculation and clear physical meaning. Due to the crystal orientation of the grain-oriented electrical steel sheets, its magnetic properties exhibit strong anisotropic characteristics, and the anisotropic energy has a strong dependence on the applied external stress. The original S-J-A model doesn't consider the influence of anisotropic energy, which makes the S-J-A model significantly inaccurate in modeling the hysteresis return of grain-oriented electrical steel sheets laminations. To solve these problems, this paper proposes an improved S-J-A model that takes into account the anisotropic energy and the stress dependence of the model parameters. In this paper, the anisotropic energy is considered in the anhysteretic magnetization., including the anisotropic energy of the material itself as well as the anisotropic energy due to mechanical stress. At the same time, the magnetostriction and pinning coefficient k are regarded as the result of the joint action of the magnetization M and the applied mechanical stress σ. In addition, in the relevant literature, only the parameter k is considered to be dependent on the mechanical stress, and other parameters are not affected by the mechanical stress. In the actual simulation of the model, it is found that the shape parameter of anhysteretic magnetization a is also dependent on the mechanical stress, so an improved s-j-a model is obtained. The simulation results show that the improved S-J-A hysteresis model fits better under tensile stress and smaller compressive stress, and the mean square error does not exceed 3A/m, which proves the accuracy and reasonableness of the model in this paper. When the compressive stress is greater than 7.14 MPa, the error becomes larger, reaching a maximum of 8.21 A/m, but the overall fit is acceptable. Comparing this method with the original S-J-A hysteresis model, it is found that the mean square error of the original model increases with the increase of compressive stress, reaching 162.91 A/m at σ = -10.63 MPa, which is too large to be acceptable. Under the condition of tensile stress, the mean square error of the original model is also larger than that of the proposed method under the same tensile stress. Through the above analysis, it can be seen that the fitting accuracy obtained by this method is higher than that of the original S-J-A hysteresis model, which proves the superiority of the proposed method. The following conclusions are obtained from the simulation of the hysteresis line under stress: (1) The simulation results of the improved model and the original S-J-A model for electrical steel sheets are compared and analyzed. The results show that the simulation accuracy of the improved model is higher, which proves its superiority. (2) The model parameters under different mechanical stresses are extracted, and the results show that the average anisotropic energy density Kan, the pinning coefficient k and the shape parameter of anhysteretic magnetization a in the S-J-A model have obvious dependence on the mechanical stresses, and these parameters have different dependence on the compressive and tensile stresses.
朱育莹, 李琳. 考虑各向异性和模型参数应力依赖关系的改进Sablik-Jiles-Atherton磁滞模型[J]. 电工技术学报, 2023, 38(17): 4586-4596.
Zhu Yuying, Li Lin. An Improved Sablik-Jiles-Atherton Hysteresis Model Considering Anisotropy and Stress Dependence of Model Parameters. Transactions of China Electrotechnical Society, 2023, 38(17): 4586-4596.
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2023, Vol. 38 
