利兹线绕组高频变压器漏感双二维镜像法计算模型

doi:10.19595/j.cnki.1000-6753.tces.241280

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Abstract High-frequency transformer leakage inductance is an important parameter that affects the operational reliability and power transfer characteristics of power electronic transformers. The complex stranded structure of the Litz-wire winding makes it challenging to calculate transformer leakage inductance accurately. The difference in magnetic field strength between the transformer's inner and outer core windows introduces errors in the single 2-D calculation model, which only considers the magnetic field strength of the inner core window. Additionally, the complex structure of the Litz-wire makes it difficult to extract the magnetic field strength accurately. Therefore, this paper establishes a leakage inductance analytical calculation model that considers the difference in magnetic field distribution between the inner and outer core windows of a high-frequency transformer with a Litz wire winding, as well as the eddy current effect and edge effect of the transformer with a Litz wire winding at high frequencies.
Firstly, this paper proposes a double-2D leakage inductance calculation model, which calculates the transformer leakage energy through two planes. Then, the mirror method is employed to analyze the two-dimensional magnetic field and extract the leakage energy of the inner and outer core windows. The two-dimensional magnetic field distribution of the core window can be obtained using the mirror principle, avoiding the complex solution of the Poisson equation while considering the edge effect. Secondly, to assess the frequency-variable characteristics of the leakage magnetic energy in the conductor region, two frequency-dependent factors are introduced to evaluate the skin and proximity effects. Finally, three prototypes of different models are verified.
The following conclusions are drawn. (1) This paper analyzes the difference in the distribution of magnetic field strength between the inner and outer core windows, thereby improving the accuracy of transformer leakage energy calculations by separately extracting the magnetic field strengths of the inner and outer core windows. (2) The mirror method extracts the leakage energy of the static magnetic field from the inner and outer core windows to account for the edge effect of the windings. The introduction of two normalization factors accounts for the conductor skin effect and proximity effect at high frequencies, enabling the accurate prediction of high-frequency transformer leakage inductance in Litz-wire windings across a wide frequency range. (3) Compared with the measurement results, the average relative error of the prototypes is no more than 6%. Compared with the 2-D finite element (FEM), the proposed model saves the calculation time by avoiding the complex modeling and simulation process.

Key words： High-frequency transformer Litz wire leakage inductance double-2-D models image method frequency-variable characteristic

Received: 17 July 2024

PACS:

TM433

Fund:国家自然科学基金（52077053, 52377008）和中央引导地方科技发展基金（226Z1601G）资助项目

Corresponding Authors: 王凯男,1998年生,硕士研究生,研究方向为高频变压器优化设计与工程电磁场数值仿真及应用。E-mail: 202221401108@stu.hebut.edu.cn

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	Zhao Zhigang
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	Chen Tianyuan
	Su Nan
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Zhao Zhigang,Wang Kai,Chen Tianyuan等. Model for Calculating Leakage Inductance of High-Frequency Transformer with Litz-Wire Winding by Double-2-D Image Method[J]. Transactions of China Electrotechnical Society, 2025, 40(18): 5715-5727.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.241280 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I18/5715

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