Hysteretic and Loss Modeling of Silicon Steel Sheet under the DC Biased Magnetization Based on the Preisach Model
Zhao Xiaojun1, Liu Xiaona1, Xiao Fan1, Liu Yang2
1. School of Electrical and Electronic Engineering North China Electric Power University Baoding 071003 China; 2. State Key Laboratory of Advanced Transmission Technology Global Energy Interconnection Research Institute Co. Ltd Beijing 102211 China
Abstract:Based on the Preisach model, a parameter identification method for simulating asymmetric hysteresis loops is proposed and applied to the simulation of static and dynamic hysteresis characteristics of grain-oriented (GO) silicon steel sheet. Due to the asymmetry of curves under the DC bias, an algorithm was presented to create asymmetrical first order reversal curves (FORCs) according to the experimental data of major hysteresis loop measured in DC-bias condition, and the corresponding Everett function was established. The static hysteresis curves were simulated by the Preisach model. The consistency between the simulated results and the measured ones verified the proposed method. Finally, the DC-biasing dynamic hysteresis model was constructed considering the influence of DC bias magnetic field and AC magnetic flux peak on excess loss. In addition, the loss characteristics of GO silicon steel sheet under DC bias condition were simulated. The influence of DC bias on different types of losses was analyzed.
赵小军, 刘小娜, 肖帆, 刘洋. 基于Preisach模型的取向硅钢片直流偏磁磁滞及损耗特性模拟[J]. 电工技术学报, 2020, 35(9): 1849-1857.
Zhao Xiaojun, Liu Xiaona, Xiao Fan, Liu Yang. Hysteretic and Loss Modeling of Silicon Steel Sheet under the DC Biased Magnetization Based on the Preisach Model. Transactions of China Electrotechnical Society, 2020, 35(9): 1849-1857.
[1] 程志光, 高生, 李琳. 电气工程涡流问题的分析与验证[M]. 北京: 高等教育出版社, 2000. [2] 江鹏, 李敬, 张群, 等. 基于A-λ 混合单元法的静磁场数值求解[J]. 电工技术学报, 2018, 33(5): 1167-1176. Jiang Peng, Li Jing, Zhang Qun, et al.Numerical simulation for magnetostatic problems based on A-λ mixed finite element method[J]. Transactions of China Electrotechnical Society, 2018, 33(5): 1167-1176. [3] 胡静竹, 刘涤尘, 廖清芬, 等. 基于有限元法的变压器电磁振动噪声分析[J]. 电工技术学报, 2016, 31(15): 81-88. Hu Jingzhu, Liu Dichen, Liao Qingfen, et al.Analysis of transformer electromagnetic vibration noise based on finite element method[J]. Transactions of China Electrotechnical Society, 2016, 31(15): 81-88. [4] 赵小军, 李琳, 程志光, 等. 应用谐波平衡有限元法的变压器直流偏磁现象分析[J]. 中国电机工程学报, 2010, 30(21): 103-108. Zhao Xiaojun, Li Lin, Cheng Zhiguang, et al.Analysis of the DC bias phenomenon in transformers based on harmonic-balanced finite element method[J]. Proceedings of the CSEE, 2010, 30(21): 103-108. [5] 王佳音, 白保东, 刘宏亮, 等. 直流偏磁对变压器振动噪声的影响[J]. 电工技术学报, 2015, 30(8): 56-61. Wang Jiayin, Bai Baodong, Liu Hongliang, et al.Research on vibration and noise of transformers under DC bias[J]. Transactions of China Electro- technical Society, 2015, 30(8): 56-61. [6] 康丽, 张艳丽, 唐伟, 等. 基于变系数Steinmetz公式的直流偏磁下铁心损耗计算[J]. 电工技术学报, 2019, 34(增刊1): 1-6. Kang Li, Zhang Yanli, Tang Wei, et al.Calculation of core loss under DC bias based on the variable coefficient steinmetz formula[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 1-6. [7] 陈彬, 李琳, 赵志斌. 典型非正弦电压波激励下高频磁心损耗[J]. 电工技术学报, 2018, 33(8): 1696-1704. Chen Bin, Li Lin, Zhao Zhibin.Magnetic core losses under high-frequency typical non-sinusoidal voltage magnetization[J]. Transactions of China Electro- technical Society, 2018, 33(8): 1696-1704. [8] 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 deter- ministic optimization algorithm[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2260-2268. [9] Beatrice C, Appino C, De La Barrière O, et al. Broadband magnetic losses in Fe-Si and Fe-Co laminations[J]. IEEE Transactions on Magnetics, 2014, 50(4): 1-4. [10] Hamada S, Louai F Z, Nait-Said N, et al.Dynamic hysteresis modeling including skin effect using diffusion equation model[J]. Journal of Magnetism & Magnetic Materials, 2016, 410: 137-143. [11] 白保东, 赵晓旋, 陈德志, 等. 基于J-A模型对直流偏磁条件下变压器励磁电流的模拟及实验研究[J]. 电工技术学报, 2013, 28(增刊2): 162-166. Bai Baodong, Zhao Xiaoxuan, Chen Dezhi, et al.Simulation and experiment research on transformer excitation current under DC magnetic bias based on J-A model[J]. Transactions of China Electrotechnical Society, 2013, 28(S2): 162-166. [12] 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. [13] 刘任, 李琳. 基于场分离技术与损耗统计理论的动态Energetic磁滞模型[J]. 中国电机工程学报, 2019, 39(21): 6412-6419. Liu Ren, Li Lin.Dynamic Energetic hysteresis model based on field separation approach and statistical theory of losses[J]. Proceedings of the CSEE, 2019, 39(21): 6412-6419. [14] Hauser H.Energetic model of ferromagnetic hysteresis 2: magnetization calculations of (110)[001] FeSi sheets by statistic domain behavior[J]. Journal of Applied Physics, 1995, 77(6): 2625-2633. [15] 刘洋, 张艳丽, 谢德馨, 等. 考虑硅钢片二维矢量磁特性的复数E&S模型[J]. 中国电机工程学报, 2012, 32(3): 144-149, 3. Liu Yang, Zhang Yanli, Xie Dexin, et al.A complex E&S model considering 2D vector magnetic pro- perties of silicon steel sheet[J]. Proceedings of the CSEE, 2012, 32(3): 144-149, 3. [16] Enokizono M, Shimoji H, Horibe T.Loss evaluation of induction motor by using magnetic hysteresis E&S model[J]. IEEE Transaction on Magnetic, 2002, 38(5): 2379-2381. [17] Dlala E.Efficient algorithms for the inclusion of the Preisach hysteresis model in nonlinear finite-element methods[J]. IEEE Transaction on Magnetic, 2011, 47(2): 395-408. [18] Hussain S, Lowther D A.An efficient implementation of the classical Preisach model[J]. IEEE Transaction on Magnetic, 2018, 54(3): 1-4. [19] 段娜娜, 徐伟杰, 李永建, 等. 基于极限磁滞回线法的软磁复合材料磁特性模拟[J]. 电工技术学报, 2018, 33(20): 4739-4745. Duan Nana, Xu Weijie, Li Yongjian, et al.Elec- tromagnetic property modeling of the soft magnetic composite material based on the limiting loop method[J]. Transactions of China Electrotechnical Society, 2018, 33(20): 4739-4745. [20] Mayergoyz I D.Mathematical model of hysteresis and their applications[M]. New York: Academic Press, 2003. [21] 赵小军. 基于谐波平衡有限元法的变压器直流偏磁特性研究[D]. 北京: 华北电力大学, 2011. [22] Zirka S E, Moroz Y I, Harrison R G, et al.Inverse hysteresis models for transient simulation[J]. IEEE Transactions on Power Delivery, 2014, 29(2): 552-559. [23] Bertotti G.Hysteresis in magnetism[M]. San Diego: Acedemic, 1998. [24] Dlala E.A simplified iron loss model for laminated magnetic cores[J]. IEEE Transaction on Magnetic, 2008, 44(11): 3169-3172. [25] 刘任, 李琳. 基于损耗统计理论与J-A磁滞模型的直流偏磁下磁性材料损耗计算方法[J]. 高电压技术, 2019, 45(12): 4062-4069. Liu Ren, Li Lin.Loss prediction of magnetic material under DC bias based on the statistical theory of losses and Jiles-Atherton hysteresis model[J]. High Voltage Engineering, 2019, 45(12): 4062-4069. [26] Wang Xiaohui, Thomas D W P, Sumner M, et al. Characteristics of Jiles-Atherton model parameters and their application to inrush current simulation[J]. IEEE Transaction on Magnetic, 2008, 44(3): 340-345.