基于Maxwell方程和R-L分数阶导数的高频激励条件下纳米晶材料磁滞特性预测模型  

Hysteresis Characteristics Prediction Method of Nanocrystalline Materials Under High-frequency Excitation Based on Maxwell’s Equation and R-L Fractional Derivative

作　　者：姬俊安 赵志刚[2] 张时 杜振斌 翟志强[3] 贾慧杰 JI Jun’an;ZHAO Zhigang;ZHANG Shi;DU Zhenbin;ZHAI Zhiqiang;JIA Huijie(State Key Laboratory of Reliability and Intelligence of Electrical Equipment(Hebei University of Technology),Beichen District,Tianjin 300401,China;Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province(Hebei University of Technology),Beichen District,Tianjin 300401,China;Hebei Provincial Key Laboratory of Electromagnetic&Structural Performance of Power Transmission and Transformation Equipment(Baoding Tianwei Baobian Electric Co.,Ltd.),Baoding 071056,Hebei Province,China)

机构地区：[1]省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学),天津市北辰区300401 [2]河北省电磁场与电器可靠性重点实验室(河北工业大学),天津市北辰区300401 [3]河北省输变电装备电磁与结构性能重点实验室(保定天威保变电气股份有限公司),河北省保定市071056

出　　处：《中国电机工程学报》2024年第13期5431-5440,I0035,共11页Proceedings of the CSEE

基　　金：国家自然科学基金项目(面上基金项目)(52077053)。

摘　　要：准确预测高频激励条件下纳米晶材料的磁滞特性,对电力电子变压器等高频电力设备磁性元件的优化设计具有重要意义。该文基于Maxwell方程和Riemann-Liouville(R-L)分数阶导数,建立高频激励下纳米晶材料磁滞特性预测模型。首先,根据Maxwell方程,首次推导出计及趋肤效应影响的涡流磁场强度解析式;其次,针对现有静态磁滞特性和异常效应建模方法未考虑趋肤效应影响的问题,依据R-L型分数阶导数理论,建立有效描述带材内部磁通密度分布不均时纳米晶静态磁滞特性与异常效应综合预测模型,并提出一种考虑频率效应的阻尼系数ρ和非整数阶n的解析计算方法;最后,基于磁场分离理论,建立高频激励下纳米晶材料磁滞特性预测模型。通过与纳米晶材料1K107B在高频激励下实测磁滞回线进行对比,验证该文所建预测模型的有效性。相较于经典模型,该文所建模型对磁滞回线的预测精度提升了35.8%。Accurate prediction of hysteresis characteristics of nanocrystalline at high frequency is of great significance to the optimization design of magnetic components of power electronic transformers.Based on Maxwell’s equation and Riemann-Liouville(R-L)fractional derivative,a prediction method of hysteresis loop considering skin effect is established in this paper.First,based on Maxwell’s equation,the prediction method of eddy current considering the skin effect is deduced and established.Second,in response to the problem that existing methods for static hysteresis characteristics and excess effects do not consider the influence of skin effect,based on the R-L fractional derivative,a prediction method of static hysteresis and excess effects considering skin effect is established.A parameter calculation method for damping coefficientρand non-integer order n is proposed.Finally,based on the magnetic field separation theory,a prediction method for the magnetic properties of nanocrystalline is established at high frequency.Compared with the measured results of nanocrystalline 1K107B at high frequency,the effectiveness of the proposed method is verified.Compared with the traditional method,it enhances prediction accuracy by 35.8%.

关 键 词：MAXWELL方程 Riemann-Liouville(R-L)分数阶导数 趋肤效应 磁滞回线 

分 类 号：TM433[电气工程—电器]