Processing math: 100%
电工技术学报  2023, Vol. 38 Issue (10): 2567-2576    DOI: 10.19595/j.cnki.1000-6753.tces.220467
电工理论 |
解析逆Preisach磁滞模型
刘任1,2, 杜莹雪3, 李琳4, 唐波1,2
1.湖北省输电线路工程技术研究中心(三峡大学) 宜昌 443002;
2.三峡大学电气与新能源学院 宜昌 443002;
3.华为技术有限公司北京研究所 北京 100085;
4.新能源电力系统国家重点实验室(华北电力大学) 北京 102206
Analytical Inverse Preisach Hysteresis Model
Liu Ren1,2, Du Yingxue3, Li Lin4, Tang Bo1,2
1. Hubei Provincial Engineering Technology Research Center for Power Transmission Line China Three Gorges University Yichang 443002 China;
2. College of Electrical Engineering and New Energy China Three Gorges University Yichang 443002 China;
3. Huawei Beijing R&D Centre Beijing 100085 China;
4. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China
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摘要 如何在保证模拟精度的基础上,提升逆磁滞模型的计算速度一直以来是国际电磁场领域研究的热点问题。然而,现有所提逆磁滞模型难以兼顾精度与速度的双重要求。解析形式的逆磁滞模型具有较快的求解速度,如何提出高精度的此类模型是解决上述问题的关键所在。为此,该文利用课题组所提基于解析Everett函数推导而得的解析正Preisach磁滞模型,分别推导了初始磁化曲线、磁滞回线下降支与上升支的磁导率的解析表达式,继而利用差分法,推导得到了目前唯一一个解析的逆Preisach磁滞模型。通过对比仿真与实验结果,验证了所提解析逆Preisach磁滞模型的模拟精度,并在模拟精度与计算速度两方面将其与广泛应用的逆J-A磁滞模型进行对比,发现它的平均相对误差比逆J-A磁滞模型小10 %以上,且其计算速度约为逆J-A磁滞模型的2.67倍。
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刘任
杜莹雪
李琳
唐波
关键词 软磁材料磁滞模型解析逆Preisach模型    
Abstract:The complex nonlinear hysteresis characteristics of soft magnetic materials significantly impact the energy losses, multi-physics field, and other properties of electrical equipment. Thus, it is crucial to accurately simulate the hysteresis loops of the soft magnetic materials. Under this circumstance, many hysteresis models, such as the well-known Preisach and Jiles-Atherton (J-A) models, have been developed. As the FEA problem of the electrical equipment is usually formulated by magnetic vector potential, making the magnetic flux density B the output of the differential equations, the inverse hysteresis models are more in demand. The inverse Preisach model is usually viewed as the most accurate among all the inverse hysteresis models. However, it involves complex integral operations, so its computation cost is high. As a result, it is not practical in electrical engineering, which makes the accurate analytical inverse Preisach model inheriting low computation cost more desired.
In this paper, to our knowledge, an analytical inverse Preisach model, the only one among all of the Preisach models, is developed and proposed. Firstly, the analytical expressions of permeability of the initial magnetization curve, ascending and descending segments of the hysteresis loop are obtained using our proposed analytical forward Preisach hysteresis model based on the analytical Everett function. The analytical inverse Preisach hysteresis model, as shown in Eq.(1), is derived with the difference method. A grain-oriented silicon steel sample and a non-oriented silicon steel sample are selected to measure their hysteresis loops at different flux density levels. The simulated hysteresis loops and the measured ones are compared. It is shown that the predicted hysteresis loops agree with the measured ones. Additionally, each calculated hysteresis loss (the area enclosed by the corresponding simulated hysteresis loop) is compared with the measured one, which also tests the accuracy of our proposed model. Besides, the average relative error of the analytical inverse Preisach model is smaller than that of the inverse J-A model by more than 10%, and its computation speed is approximately 2.67 times faster than that of the inverse J-A model.
H(t+Δt)={H(t)+B(t+Δt)B(t)ni=12α2ieβiH(t)βiγi(1+γieβiH(t))2(11+γieβiH(t)11+γieβiH(t))+k1+k2k3[1tanh2(H(t)k3)]Hm=0 and Bm=0H(t)+B(t+Δt)B(t)ni=12α2ieβiH(t)βiγi(1+γieβiH(t))2(11+γieβiH(t)11+γieβiHm)+k1+k2k3[1tanh2(H(t)k3)]HHmH(t)+B(t+Δt)B(t)ni=12α2ieβiH(t)βiγi(1+γieβiH(t))2(11+γieβiHm11+γieβiH(t))+k1+k2k3[1tanh2(H(t)k3)]HHm (A1)
where αi, βi, γi, k1 ,k2, k3 are the model coefficients, n is the number of items in Everett function, Hm and Bm are the last reversal magnetic field intensity and magnetic flux density, respectively.
Key wordsSoft magnetic materials    hysteresis model    analytical inverse Preisach model   
收稿日期: 2022-03-29     
PACS: TM464  
基金资助:湖北省教育厅科学技术研究计划青年人才项目(Q20221205)和宜昌市科技计划项目(A23-4-09)资助
通讯作者: 刘 任 男,1990年生,博士,硕士生导师,主要研究方向为电工软磁材料的宽频磁化与损耗机理及其建模方法和电工装备的电磁综合特性分析与全局结构优化设计。E-mail: liu_remail@sina.com   
作者简介: 杜莹雪 女,1994年生,硕士,研究方向为电工软磁材料的磁滞及损耗建模方法。E-mail: 18222243479@163.com
引用本文:   
刘任, 杜莹雪, 李琳, 唐波. 解析逆Preisach磁滞模型[J]. 电工技术学报, 2023, 38(10): 2567-2576. Liu Ren, Du Yingxue, Li Lin, Tang Bo. Analytical Inverse Preisach Hysteresis Model. Transactions of China Electrotechnical Society, 2023, 38(10): 2567-2576.
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