An Improved Bouc-Wen Based Hysteresis Model under Harmonic Magnetization
Li Yongjian1,2, Li Yating1,2, Lin Zhiwei1,2, Cheng Zhiguang3, Tian Yakun1,2, Chen Ruiying1,2
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China; 2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300130 China; 3. Hebei Provincial Key Laboratory of Electromagnetic & Structural Performance of Power Transmission and Transformation Equipment Baoding 071056 China;
Abstract：The excitation current of electrical equipment is distorted by harmonic components, which causes a significant increase in iron loss. This paper analogizes the complicated energy change and minimization of total energies during the domain wall motion to the driving force and simplifies the pinning force hindering the domain wall motion as viscous friction. Therefore, the nonlinear hysteretic mechanics Bouc-Wen model is adopted to characterize the hysteresis phenomenon. The initial model is modified by adding new terms that characterize the rotation of domain magnetization. The modified model is used to simulate the hysteresis loops under quasi-static magnetization. The model is further modified to a dynamic model by taking account of the resistance caused by the eddy current, then the loops under sinusoidal excitation with different frequencies and high order harmonics are simulated. The variation and frequency effect of parameters representing the damping coefficients under different excitations are discussed. Finally, the comparison between the measured and calculated results shows good agreement, and the accuracy of the proposed model is validated.
李永建, 利雅婷, 林志伟, 程志光, 田亚坤, 陈瑞颖. 基于改进Bouc-Wen模型的谐波激励条件下电工钢片磁滞特性模拟与验证[J]. 电工技术学报, 2022, 37(17): 4259-4268.
Li Yongjian, Li Yating, Lin Zhiwei, Cheng Zhiguang, Tian Yakun, Chen Ruiying. An Improved Bouc-Wen Based Hysteresis Model under Harmonic Magnetization. Transactions of China Electrotechnical Society, 2022, 37(17): 4259-4268.
[1] 杨庆新, 李永建. 先进电工磁性材料特性与应用发展研究综述[J]. 电工技术学报, 2016, 31(20): 1-12. Yang Qingxin, Li Yongjian.Characteristics and developments of advanced magnetic materials in electrical engineering: a review[J]. Transactions of China Electrotechnical Society, 2016, 31(20): 1-12. [2] Cossale M, Kitzberger M, Goldbeck G, et al.Local degradation in soft magnetic materials: a simplified modeling approach[J]. IEEE Transactions on Industry Applications, 2019, 55(6): 5897-5905. [3] Reinert J, Brockmeyer A, De Doncker R W A A. Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation[J]. IEEE Transactions on Industry Applications, 2001, 37(4): 1055-1061. [4] 刘刚, 孙立鹏, 王雪刚, 等. 正弦及谐波激励下的铁心损耗计算方法改进及仿真应用[J]. 电工技术学报, 2018, 33(21): 4909-4918. Liu Gang, Sun Lipeng, Wang Xuegang, et al.Improvement of core loss calculation method and simulation application under sinusoidal and harmonic excitations[J]. Transactions of China Electrotechnical Society, 2018, 33(21): 4909-4918. [5] Li Yongjian, Chen Ruiying, Cheng Zhiguang, et al.Dynamic hysteresis loops modeling of electrical steel with harmonic components[J]. IEEE Transactions on Industry Applications, 2020, 56(5): 4804-4811. [6] 赵小军, 王瑞, 杜振斌, 等. 交直流混合激励下取向硅钢片磁滞及损耗特性模拟方法[J]. 电工技术学报, 2021, 36(13): 2791-2800. Zhao Xiaojun, Wang Rui, Du Zhenbin, et al.Hysteretic and loss modeling of grain oriented silicon steel lamination under AC-DC hybrid magnetization[J]. Transactions of China Electrotechnical Society, 2021, 36(13): 2791-2800. [7] Mayergoyz I D, Friedman G.Generalized Preisach model of hysteresis[J]. IEEE Transactions on Magnetics, 1988, 24(1): 212-217. [8] Sudo M, Mifune T, Matsuo T, et al.A simplified domain structure model exhibiting the pinning field[J]. IEEE Transactions on Magnetics, 2013, 49(5): 1829-1832. [9] 赵志刚, 刘佳, 郭莹, 等. 非正弦励磁环境磁性材料改进损耗模型的研究[J]. 电工技术学报, 2019, 34(13): 2693-2699. Zhao Zhigang, Liu Jia, Guo Ying, et al.Investigation on the improved loss model of magnetic materials under non-sinusoidal excitation environment[J]. Transactions of China Electrotechnical Society, 2019, 34(13): 2693-2699. [10] 李阳. 基于动态J-A磁滞模型直流偏磁下的变压器铁损计算[D]. 天津: 天津工业大学, 2018. [11] 段娜娜, 徐伟杰, 李永建, 等. 一种考虑温度和压力影响的磁滞模型及其实验验证[J]. 电工技术学报, 2019, 34(13): 2686-2692. Duan Nana, Xu Weijie, Li Yongjian, et al.A temperature and stress dependent hysteresis model with experiment validation[J]. Transactions of China Electrotechnical Society, 2019, 34(13): 2686-2692. [12] 刘任, 李琳, 王亚琦, 等. 基于随机性与确定性混合优化算法的Jiles-Atherton磁滞模型参数提取[J]. 电工技术学报, 2019, 34(11): 2260-2268. Liu Ren, Li Lin, Wang Yaqi, et al.Parameter extraction for Jiles-Atherton hysteresis model based on the hybrid technique of stochastic and deterministic optimization algorithm[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2260-2268. [13] 赵志刚, 马习纹, 姬俊安, 等. 谐波激励条件下铁心动态Energetic建模与验证[J]. 电工技术学报, 2020, 35(20): 4241-4250. Zhao Zhigang, Ma Xiwen, Ji Junan, et al.Dynamic Energetic modeling and verification of core under harmonic excitation[J]. Transactions of China Electrotechnical Society, 2020, 35(20): 4241-4250. [14] 赵志刚, 马习纹, 姬俊安. 基于Energetic模型的直流偏磁条件下电工钢片磁特性模拟及实验验证[J]. 中国电机工程学报, 2020, 40(14): 4656-4665, 4743. Zhao Zhigang, Ma Xiwen, Ji Junan.Simulation and experimental verification of magnetic characteristics of electrical steel sheet under DC bias based on Energetic model[J]. Proceedings of the CSEE, 2020, 40(14): 4656-4665, 4743. [15] Bertotti G.General properties of power losses in soft ferromagnetic materials[J]. IEEE Transactions on Magnetics, 1988, 24(1): 621-630. [16] Ismail M, Ikhouane F, Rodellar J.The hysteresis Bouc-Wen model, a survey[J]. Archives of Computational Methods in Engineering, 2009, 16(2): 161-188. [17] Makris N, Palios X, Moghimi G, et al.Pressurized sand damper for earthquake and wind engineering: design, testing, and characterization[J]. Journal of Engineering Mechanics, 2021, 147(4): 04021014. [18] Zhu Wei, Wang Daihua.Non-symmetrical Bouc-Wen model for piezoelectric ceramic actuators[J]. Sensors and Actuators A: Physical, 2012, 181: 51-60. [19] Ikhouane F, Rodellar J.Systems with hysteresis: analysis, identification and control using the Bouc-Wen model[M]. Chichester: John Wiley & Sons, 2007. [20] Sues R H, Mau S T, Wen Y K.Systems identification of degrading hysteretic restoring forces[J]. Journal of Engineering Mechanics, 1988, 114(5): 833-846. [21] 钟文定. 铁磁学-下册[M]. 2版. 北京: 科学出版社, 2017. [22] Bertotti G.Hysteresis in magnetism: for physicists, materials scientists, and engineers[M]. San Diego: Academic Press, 1998. [23] Charalampakis A E, Dimou C K.Identification of Bouc-Wen hysteretic systems using particle swarm optimization[J]. Computers & Structures, 2010, 88(21-22): 1197-1205.
2022, Vol. 37 
