【好文推荐】容错式磁通切换永磁电机的磁场精确建模

容错式磁通切换永磁电机的磁场精确建模Modeling of Fault-tolerant Flux-switching Permanent-magnet Machines for Predicting Magnetic and Armature Reaction FieldsAuthors：Ying Fang; Jinghua Ji; Wenxiang Zhao

DOI：10.30941/CESTEMS.2022.00053

https://ieeexplore.ieee.org/document/10004929

01

摘要

本文建立了容错式磁通切换永磁电机永磁磁场和电枢磁场分布的精确子域解析模型。整个求解区域被划分为五个子域，其中外气隙的引入是为了考虑漏磁。通过调整线圈匝数和永磁体剩磁来保持电机的电负荷和磁负荷不变。用分离变量法求解偏微分方程确定每个区域的通解表达式，通过应用相邻子域的连续性边界条件，进一步得到磁场分布。和空载情况下相比，仅电枢磁场作用下一些场解析式的形式会发生变化，仿真验证了解析模型的准确性。

02

创新点

• 将子域解析应用于容错式磁通切换永磁电机中。由于容错齿的引入，且容错齿与电枢齿不等宽，相邻定子槽中心距离不等，定子槽的子域定义更复杂，也增加了编程求解的难度。引入外气隙考虑漏磁，且通过调整线圈匝数、电流幅值及永磁体剩磁，将槽及永磁体等效为规则的扇形区域，给出了等效前后参数的变化。
• 分别预测了空载和仅电枢磁场作用下电机的磁场分布，两种情况下某些子域场解析式的形式会发生变化，对磁矢位方程变化的区域进行理论推导。

03

主要内容

1.子域的划分及等效

首先，根据电机的拓扑结构，划分了五种子域并在图中标注出了相应的角度及径向长度的定义，如图1所示。然后，根据保持电机的电负荷及磁负荷不变的原则，调节线圈匝数、电流幅值及永磁体剩磁，将槽和永磁体等效为规则的扇形区域，具体参数如表1所示。

 (a)电机拓扑结构

（b）区域参数定义

图1. 子域的划分

表1. 参数的调整

2.各区域磁矢位方程及通解

对有源区域列写泊松方程，对无源区域列写拉普拉斯方程，分离变量法求出磁矢位方程的通解，再根据边界条件求解相应的系数。仅电枢磁场作用下，相比于空载情况，此时定子槽区域变为有源场,永磁体区域变为无源场，两个区域磁矢位方程通解的形式会发生变化。拉普拉斯方程和泊松方程如下式所示：

式中，m₀是真空磁导率，M是永磁体磁化强度，J是电流密度矩阵。

3.数据对比

•  气隙磁密对比

(a)径向磁密对比

(b)切向磁密对比

图2. 空载气隙磁密对比

(a) 径向磁密对比

(b) 切向磁密对比

图3. 仅电枢磁场作用下气隙磁密对比

•  反电势与转矩对比

(a) 反电势对比

(b) 电磁转矩对比

图4. 反电势及转矩对比

04

结论

本文建立了容错式磁通切换永磁电机的子域解析模型，计算的气隙磁密及谐波组成具有较高的准确性，用以精确分析电机电磁性能，亦可以指导该类电机的设计与优化。

引用本文

Y. Fang, J. Ji and W. Zhao, "Modeling of Fault-tolerant Flux-switching Permanent-magnet Machines for Predicting Magnetic and Armature Reaction Fields,"  CES Transactions on Electrical Machines and Systems, vol. 6, no. 4, pp. 413-421, December 2022, doi: 10.30941/CESTEMS.2022.00053.

本文作者

Ying Fang received the B.Sc. degree in electrical engineering in 2020 from Jiangsu University, Zhenjiang, China. She is currently working toward the M. Sc. degree in control science and engineering at Jiangsu University.

Her current research interests include modeling and eddy current loss analysis for permanent magnet machine.

Jinghua Ji received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from Jiangsu University, Zhenjiang, China, in 2000, 2003, and 2009 respectively.

Since 2000, she has been with the School of Electrical and Information Engineering, Jiangsu University, where she is currently a Professor in Electrical Engineering. From 2013 to 2014, she was a Visiting Scholar with the Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, U.K. Her areas of interest include motor design and electromagnetic field computation. She has authored and co-authored over 100 technical papers in these areas.

Wenxiang Zhao (M’08-SM’14) received the B.Sc. and M.Sc. degrees from Jiangsu University, Zhenjiang, China, in 1999 and 2003, respectively, and the Ph.D. degree from Southeast University, Nanjing, China, in 2010, all in electrical engineering. He has been with Jiangsu University since 2003, where he is currently a Professor with the School of Electrical Information Engineering.

From 2008 to 2009, he was a Research Assistant with the Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong. From 2013 to 2014, he was a Visiting Professor with the Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, U.K. His current research interests include electric machine design, modeling, fault analysis, and intelligent control. He is the author or co-author of more than 150 papers published in various IEEE TRANSACTIONS.

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