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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摘要高频变压器漏感是影响电力电子变压器运行可靠性和功率传输特性的一个至关重要的参数。利兹线绕组复杂的绞合结构使得变压器漏感精确计算面临挑战。由于高频变压器优化设计过程中对漏感计算速度和准确性要求较高,传统有限元法需要对利兹线绕组进行精细化建模,对计算机硬件成本要求高,计算耗时长,因此目前常采用解析计算法。基于一维磁场假设的解析计算法虽然能快速计算变压器漏感,但忽略了绕组端部效应和内、外磁心窗口磁场强度分布差异的影响,导致计算误差较大。为此该文建立一种基于镜像原理的双二维利兹线绕组高频变压器漏感解析计算模型,在考虑内、外磁心窗口磁场强度分布差异的同时,兼顾绕组的端部效应和频变特性。最后,绕制了三台不同型号的样机,并进行实验验证与对比分析。实验结果表明,所建立的模型能够实现圆形和矩形利兹线绕组高频变压器漏感的精确、高效计算。

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关键词 ：高频变压器, 利兹线, 漏感, 双二维模型, 镜像法, 频变特性

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

收稿日期: 2024-07-17

PACS:

TM433

作者简介: 赵志刚男,1981年生,教授,博士生导师,研究方向为电工磁材料磁性能模拟与工程电磁场数值仿真及应用。E-mail: zhaozhigang@hebut.edu.cn

引用本文:

赵志刚, 王凯, 陈天缘, 苏楠, 巩业超. 利兹线绕组高频变压器漏感双二维镜像法计算模型[J]. 电工技术学报, 2025, 40(18): 5715-5727. Zhao Zhigang, Wang Kai, Chen Tianyuan, Su Nan, Gong Yechao. Model for Calculating Leakage Inductance of High-Frequency Transformer with Litz-Wire Winding by Double-2-D Image Method. Transactions of China Electrotechnical Society, 2025, 40(18): 5715-5727.

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