电工装备硅钢磁心静态磁滞改进模拟方法

doi:10.11930/j.issn.1004-9649.202503012

中国电力 ›› 2025, Vol. 58 ›› Issue (7): 137-146.DOI: 10.11930/j.issn.1004-9649.202503012

电工装备硅钢磁心静态磁滞改进模拟方法

刘任¹(), 曾宇²(), 胡安龙³(), 唐波¹^,²()

1. 湖北省输电线路工程技术研究中心（三峡大学），湖北宜昌　443002
2. 三峡大学电气与新能源学院，湖北宜昌　443002
3. 国网甘肃省电力公司经济技术研究院，甘肃兰州　730050

收稿日期:2025-03-07 发布日期:2025-07-30 出版日期:2025-07-28
作者简介:
刘任（1990），男，通信作者，博士，讲师，从事电工装备电磁综合特性分析与优化设计，E-mail：liu_remail@sina.com
曾宇（1999），女，硕士研究生，从事软磁材料磁滞与损耗建模，E-mail：zengyu9865@163.com
胡安龙（1991），男，硕士，工程师，从事电力设备优化设计与电网规划研究，E-mail：505129963@qq.com
唐波（1978），男，教授，博士生导师，从事超特高压输电技术与输变电系统电磁环境研究，E-mail：tangboemail@sina.com
基金资助:
国家自然科学基金资助项目（52407009）；湖北省自然科学基金青年基金资助项目（2023AFB037）。

Modified Static Hysteresis Simulation Method for Electrical Equipment with Silicon Steel Core

LIU Ren¹(), ZENG Yu²(), HU Anlong³(), 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. State Grid Gansu Electric Power Company Economic and Technological Research Institute, Lanzhou 730050, China

Received:2025-03-07 Online:2025-07-30 Published:2025-07-28
Supported by:
This work is supported by National Natural Science Foundation of China (No.52407009), Natural Science Foundation of Hubei Province Youth Science Fund Program (No.2023AFB037).

摘要/Abstract

摘要：

微磁学Landau-Lifshitz-Gilbert（LLG）方程相比于传统Preisach、J-A等磁滞模型具有物理意义清晰、模拟精度高等优点，但由于计算量、存储空间等问题的限制，其难以应用于实际电工钢片的宏观静态磁滞模拟。首先根据电工钢片结构特征，基于代表性体积单元法（representative volume element，RVE）提出了LLG方程的几何模型离散方法，继而构造了毫米级范围内总吉布斯自由能中各能量项的简化表达式，并提出了相关参数的快速辨识方法，从而推导出一种用于电工钢片宏观静态磁滞模拟的简化LLG方程。最后基于该简化LLG方程模拟了产品级取向及无取向硅钢片样品在不同工况下的静态磁滞回线，发现其吻合度均较高，并在模拟精度上与广泛应用的Preisach、J-A磁滞模型进行对比，验证了所提模型及方法的优势。

关键词: 微磁学, LLG方程, 电工钢片, 代表性体积单元法, 静态磁滞

Abstract:

Compared to traditional hysteresis models like Preisach and Jiles-Atherton (J-A), the micromagnetic Landau-Lifshitz-Gilbert (LLG) equation offers advantages such as clearer physical interpretation and higher simulation accuracy. However, its application to macroscopic static hysteresis simulation of electrical steel sheets has been limited due to computational intensity and memory constraints. This paper first proposes a geometric model discretization method for the LLG equation based on the Representative Volume Element (RVE) approach, tailored to the structural characteristics of electrical steel sheets. Subsequently, simplified expressions for the energy terms within the total Gibbs free energy are developed for the millimeter scale. A rapid parameter identification method for the relevant parameters is also introduced. This leads to the derivation of a simplified LLG equation specifically for macroscopic static hysteresis simulation in electrical steel sheets. Finally, the proposed simplified LLG equation is used to simulate static hysteresis loops of industry-grade grain-oriented (GO) and non-oriented (NO) silicon steel sheet samples under various operating conditions. The simulations exhibit strong agreement with measurements. Comparisons in simulation accuracy with the widely applied Preisach and J-A hysteresis models further validate the superiority of the proposed model and methodology.

Key words: micromagnetics, LLG equation, electrical steel sheet, representative volume element, static hysteresis

刘任, 曾宇, 胡安龙, 唐波. 电工装备硅钢磁心静态磁滞改进模拟方法[J]. 中国电力, 2025, 58(7): 137-146.

LIU Ren, ZENG Yu, HU Anlong, TANG Bo. Modified Static Hysteresis Simulation Method for Electrical Equipment with Silicon Steel Core[J]. Electric Power, 2025, 58(7): 137-146.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202503012

https://www.electricpower.com.cn/CN/Y2025/V58/I7/137

图/表 16

图 1 磁矩磁化强度Mi绕有效场Heff_i旋转、进动示意

Fig.1 Schematic of magnetisation vector Mi of magnetic moment around an active field Heff_i

图 2 LLG方程的分析对象和分析空间

Fig.2 Analysis subject and analysis space of the LLG equation

图 3 LLG方程参数与磁滞回线形状的关系

Fig.3 Relationship between the parameters of the LLG equation and the shape of the hysteresis return line

图 4 基于所提简化LLG模型模拟磁滞回线过程

Fig.4 Flow of hysteresis loop simulation based on the proposed improved simplified LLG model

图 5 电工钢片磁特性测量平台

Fig.5 Measurement platform for the magnetic properties

表 1 取向及无取向硅钢片样品参数

Table 1 Parameters of oriented and non-oriented silicon steel samples

类型	牌号	长度/ mm	宽度/ mm	厚度/ mm	密度/ (kg·m^–3)
取向硅钢样品	23QG100	300	30	0.23	7650
无取向硅钢样品	35W233	300	30	0.35	7650

表 2 无取向硅钢样品在高磁密区域（Bm=1.3~1.5 T）的简化LLG方程参数

Table 2 Parameters of the simplified LLG equation for the non-oriented silicon steel samples in high magnetic flux density regions (Bm=1.3~1.5 T)

M_s/T		h_Zee/T		μ_ani/(A·m^–1)		b₂/J		b₄/J		b₆/J		b₈/J		b₁₀/J		b₁₂/J
1.52		2.58		93.53		26.6		116		–625.9		1610.1		–1870.2		866.7

表 3 取向硅钢样品在高磁密区域（Bm=1.2~1.8 T）的简化LLG方程参数

Table 3 Parameters of the simplified LLG equation for the grain oriented silicon steel samples in high magnetic flux density regions (Bm=1.2~1.8 T)

M_s/T		h_Zee/T		μ_ani/(A·m^–1)		b₂/J		b₄/J		b₆/J		b₈/J		b₁₀/J		b₁₂/J
1.82		3.17		28.33		31.8		32.9		–125.7		281.3		–337.4		185.6

表 4 取向及无取向硅钢样品J-A模型固定参数

Table 4 Fixed parameters of J-A models of the oriented and non-oriented silicon steel samples

参数	取向硅钢片	无取向硅钢片
饱和磁化强度M_s/(A·m^–1)	1.21×10⁶	1.45×10⁶
形状参数a/(A·m^–1)	26.924	15.284
可逆磁化参数c	0.3081	0.5825

图 6 基于简化LLG方程计算的无取向硅钢片静态磁滞回线与实测值对比

Fig.6 Comparison of static hysteresis loops calculated based on simplified LLG equation for non-oriented silicon steel wafers with measured values

图 7 基于简化LLG方程计算的取向硅钢片静态磁滞回线与实测值对比

Fig.7 Comparison of static hysteresis loops calculated based on simplified LLG equation for oriented silicon steel wafers with measured values

图 8 基于Preisach模型、J-A模型和简化LLG方程模拟的静态磁滞回线与相应实测磁滞回线

Fig.8 Simulated static hysteresis loops based on Preisach model, J-A model and simplified LLG equation respectively and the measured ones

表 5 基于简化LLG方程模拟的无取向硅钢片样品静态磁滞损耗的仿真值与测量值

Table 5 Simulated and measured values of static hysteresis loss of unoriented silicon steel wafer samples simulated based on simplified LLG equations

磁密幅值B_m/T	计算值W_i,calc/(J·m^–3)	实测值W_i,meas/(J·m^–3)	相对误差σ/%
1.5	271.95	278.14	2.96
1.4	219.64	229.47	4.28
1.2	153.68	153.68	1.31
1.0	116.04	107.23	4.41
0.8	74.00	73.99	0.01
0.6	46.62	46.67	0.08
0.4	23.34	24.20	3.52
0.2	6.38	6.54	2.30

表 6 基于简化LLG方程模拟的取向硅钢片样品静态磁滞损耗的仿真值与测量值

Table 6 Simulated and measured values of static hysteresis loss in samples of oriented silicon steel wafers simulated based on simplified LLG equations

磁密幅值B_m/T	计算值W_i,calc/(J·m^–3)	实测值W_i,meas/(J·m^–3)	相对误差σ/%
1.8	138.46	150.25	7.84
1.7	86.75	98.18	11.88
1.5	47.87	55.42	13.62
1.3	37.51	34.91	10.78
1.1	26.63	26.38	0.95
0.9	16.46	17.32	4.96
0.7	10.58	10.31	2.66
0.5	5.35	4.94	8.41
0.3	2.29	1.87	18.33

表 7 基于Preisach、J-A模型与简化LLG方程模拟无取向硅钢样品静态磁滞回线的平均相对误差

Table 7 Mean relative errors of non-oriented silicon steel sample based on Preisach model, J-A model and simplified LLG equation

模型		平均相对误差/%
LLG方程		2.36
Preisach模型		8.44
J-A模型		9.57

表 8 基于Preisach、J-A模型与简化LLG方程模拟取向硅钢样品静态磁滞回线的平均相对误差

Table 8 Mean relative errors of oriented silicon steel sample based on Preisach model, J-A model and simplified LLG equation

模型		平均相对误差/%
LLG方程		8.82
Preisach模型		12.51
J-A模型		14.65

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电工装备硅钢磁心静态磁滞改进模拟方法

Modified Static Hysteresis Simulation Method for Electrical Equipment with Silicon Steel Core

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