A Fast and High-Accuracy Multiscale Computational Method for Eddy-Current Loss Assessment in Transformer Laminated Cores

MA Xinyu; DUAN Nana; MU Xiaobin

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A Fast and High-Accuracy Multiscale Computational Method for Eddy-Current Loss Assessment in Transformer Laminated Cores

更新时间：2026-06-23

- A Fast and High-Accuracy Multiscale Computational Method for Eddy-Current Loss Assessment in Transformer Laminated Cores
- JOURNAL OF XI’AN JIAOTONG UNIVERSITY (2026)
- 作者机构：
  
  1.西安交通大学电气工程学院，710049，西安
  2.中国电力科学研究院有限公司先进输电技术全国重点实验室，102209，北京
- 作者简介：
- 基金信息：
- DOI：
  CLC： TM153
- Received：08 May 2026，
  
  Revised：2026-06-23，
  
  Accepted：23 June 2026，
- 稿件说明：
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MA Xinyu, DUAN Nana, MU Xiaobin. A Fast and High-Accuracy Multiscale Computational Method for Eddy-Current Loss Assessment in Transformer Laminated Cores[J/OL]. JOURNAL OF XI’AN JIAOTONG UNIVERSITY, 2026.
DOI：

MA Xinyu, DUAN Nana, MU Xiaobin. A Fast and High-Accuracy Multiscale Computational Method for Eddy-Current Loss Assessment in Transformer Laminated Cores[J/OL]. JOURNAL OF XI’AN JIAOTONG UNIVERSITY, 2026. DOI：

摘要

为满足高效节能变压器设计中叠片铁心涡流损耗快速、准确评估的需求，针对传统有限元法精细建模计算量大、现有多尺度有限元法因富集函数缺乏物理针对性而导致局部涡流场及损耗计算误差较大的问题，提出一种基于本征函数先验知识的变压器叠片铁心涡流损耗快速高精度多尺度计算方法。首先，根据矢量磁位在叠片区域内满足的双曲余弦分布特征，提取能够反映叠片内部场量变化规律的本征函数，并将其作为先验信息引入多尺度有限元框架。然后，结合水平集函数与单位分解法，构造能够刻画材料交界面及边缘集肤效应区域非线性场量变化的富集函数，实现叠片铁心局部涡流场的低自由度求解；在此基础上，根据涡流密度分布计算局部涡流损耗密度及单位长度涡流损耗。最后，以模拟变压器局部叠片铁心电磁行为的二维线圈-叠片模型进行验证。结果表明：以传统有限元法在精细剖分下的计算结果为基准，所提方法在网格节点数和自由度分别减少97.99%和97.41%的条件下，计算时间由628 s降至51 s，缩短91.88%；与原有多尺度有限元法相比，在相同粗网格条件下，所提方法使矢量磁位平均相对误差降低98.80%，单位长度涡流损耗相对误差降低96.77%。研究结果表明，所提方法能够在极低网格密度下同时降低计算规模、缩短计算时间并提高局部场量与涡流损耗计算精度，可为变压器叠片铁心涡流损耗评估及精细化电磁分析提供高效计算工具。

Abstract

To meet the demand for fast and accurate eddy-current loss assessment in laminated cores for energy-efficient transformer design

this paper proposes a fast and high-accuracy multiscale computational method based on eigenfunction-informed prior knowledge. The method addresses the high computational cost of refined modeling in the conventional finite element method (FEM)

as well as the relatively large errors in local eddy-current field and loss calculations caused by the lack of physical relevance in the enrichment functions used in existing multiscale finite element methods (MSFEMs). First

according to the hyperbolic-cosine distribution characteristic satisfied by the magnetic vector potential in the laminated region

an eigenfunction capable of representing the field variation inside the laminations is extracted and introduced into the MSFEM framework as prior information. Then

by combining the level-set function with the partition of unity method

an enrichment function is constructed to characterize the nonlinear field variation near material interfaces and edge skin-effect regions

enabling a low-degree-of-freedom solution of the local eddy-current field in the laminated core. On this basis

the local eddy-current loss density and the eddy-current loss per unit length are calculated from the eddy-current density distribution. Finally

the proposed method is validated using a two-dimensional coil-lamination model that represents the local electromagnetic behavior of a transformer laminated core. The results show that

using the fine-mesh FEM result as the reference

the proposed method reduces the number of mesh nodes and degrees of freedom by 97.99% and 97.41%

respectively

while reducing the computational time from 628 s to 51 s

corresponding to a reduction of 91.88%. Compared with the original MSFEM under the same coarse-mesh condition

the proposed method reduces the average relative error of the magnetic vector potential by 98.80% and the relative error of the eddy-current loss per unit length by 96.77%. These results demonstrate that the proposed method reduces the computational scale and time while improving the accuracy of local field calculation and eddy-current loss assessment under an extremely low mesh density

providing an efficient computational tool for eddy-current loss assessment and refined electromagnetic analysis of transformer laminated cores.

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references

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