Improved Finite Element Method of Winding Loss and Leakage Inductance for Planar Transformer Used in LLC Converter
Zhao Zhigang1,2, Zhang Xuezeng1,2
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300401 China; 2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300401 China
Abstract：The finite element method is often used to accurately calculate the performance parameters such as winding loss and leakage inductance of planar transformers. However, due to high storing and calculating costs, in the case of a tight design cycle, the number of design schemes that can be accurately calculated is limited, which increases the risk of selecting the local optimum point as the final design scheme. Therefore, the process of constructing and solving linear equations that occupy many resources is improved. Firstly, by analyzing the magnetic field intensity distribution of the planar transformer, according to the strength of the edge effect, the solution region of the planar transformer is divided into the strong edge effect region and the weak edge effect region. Secondly, a one-dimensional linear element that is more suitable for the weak edge effect region is introduced to reduce the number of nodes and elements necessary to describe the solution region’s field, saving computing and storing resources. Thirdly, by restricting the distribution of adjacent element nodes, the problems of element compatibility and coefficient matrix construction caused by the introduction of one-dimensional linear elements are solved. Finally, planar transformer models are built. The winding loss and leakage inductance of calculated and experimental values, as well as the calculating and storing costs of the proposed method and the finite element method, are compared, which verifies the proposed method.
赵志刚, 张学增. LLC平面变压器绕组损耗与漏感改进有限元计算方法[J]. 电工技术学报, 2022, 37(24): 6204-6215.
Zhao Zhigang, Zhang Xuezeng. Improved Finite Element Method of Winding Loss and Leakage Inductance for Planar Transformer Used in LLC Converter. Transactions of China Electrotechnical Society, 2022, 37(24): 6204-6215.
[1] 吕正, 颜湘武, 孙磊. 基于变频-移相混合控制的L-LLC谐振双向DC-DC变换器[J]. 电工技术学报, 2017, 32(4): 12-24. Lü Zheng, Yan Xiangwu, Sun Lei.A L-LLC resonant bidirectional DC-DC converter based on hybrid control of variable frequency and phase shift[J]. Transactions of China Electrotechnical Society, 2017, 32(4): 12-24. [2] Shahabi A, Lemmon A N.Modeling of ZVS transi- tions for efficiency optimization of the phase-shifted full-bridge topology[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(1): 529-544. [3] Fei Chao, Li Qiang, Lee F C.Digital implementation of light-load efficiency improvement for high- frequency LLC converters with simplified optimal trajectory control[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2018, 6(4): 1850-1859. [4] Qian Ting, Qian Chenghui.A combined topology with coupled LLC resonance for wide-range operation[J]. IEEE Transactions on Power Electronics, 2019, 34(7): 6593-6600. [5] 丁超, 李勇, 姜利, 等. 电动汽车直流充电系统LLC谐振变换器软开关电压边界分析[J]. 电工技术学报, 2022, 37(1): 3-11. Ding Chao, Li Yong, Jiang Li, et al.Analysis of soft switching voltage boundary of LLC resonant con- verter for EV DC charging system[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 3-11. [6] Li Guangdi, Xia Jin, Wang Kun, et al.Hybrid modulation of parallel-series LLC resonant converter and phase shift full-bridge converter for a dual-output DC-DC converter[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2019, 7(2): 833-842. [7] Wu Hongfei, Li Yuewei, Xing Yan.LLC resonant converter with semiactive variable-structure rectifier (SA-VSR) for wide output voltage range application[J]. IEEE Transactions on Power Electronics, 2016, 31(5): 3389-3394. [8] Wu Liang, Xiao Long, Zhao Jun, et al.Modelling and optimisation of planar matrix transformer for high frequency regulated LLC converter[J]. IET Power Electronics, 2020, 13(3): 516-524. [9] 刘晓东, 董保成, 吴慧辉, 等. 基于并联变压器切换的LLC谐振变换器宽范围效率优化控制策略[J]. 电工技术学报, 2020, 35(14): 3018-3029. Liu Xiaodong, Dong Baocheng, Wu Huihui, et al.Wide range efficiency optimization control strategy for LLC resonant converter based on parallel trans- former switching[J]. Transactions of China Electro- technical Society, 2020, 35(14): 3018-3029. [10] 汤欣喜, 邢岩, 吴红飞, 等. 兼顾稳态效率和暂态升压能力的LLC变换器[J]. 电工技术学报, 2020, 35(4): 767-774. Tang Xinxi, Xing Yan, Wu Hongfei, et al.An improved LLC converter considering steady-state efficiency and transient boost capability[J]. Transa- ctions of China Electrotechnical Society, 2020, 35(4): 767-774. [11] 李彬彬, 王志远, 张丙旭, 等. 采用辅助变压器的可调压谐振零电压零电流开关变换器[J]. 电力系统自动化, 2022, 46(7): 160-169. Li Binbin, Wang Zhiyuan, Zhang Bingxu, et al.Voltage-regulatable resonant zero-voltage zero-current switching converter with auxiliary transformer[J]. Automation of Electric Power Systems, 2022, 46(7): 160-169. [12] 袁宇波, 史明明, 舒良才, 等. 基于混频调制的电力电子变压器设计方法及实验验证[J]. 电力系统自动化, 2020, 44(22): 176-183. Yuan Yubo, Shi Mingming, Shu Liangcai, et al.Design method and experimental verification of power electronic transformer based on mixed- frequency modulation[J]. Automation of Electric Power Systems, 2020, 44(22): 160-169. [13] Rouhollah S, Martin O, Ali S M.Three-dimensional frequency-dependent thermal model for planar trans- formers in LLC resonant converters[J]. IEEE Transa- ctions on Power Electronics, 2018, 34(5): 4641-4655. [14] Zhang Zhiliang, He Binghui, Hu Dongdong, et al.Multi-winding configuration optimization of multi- output planar transformers in GaN active forward converters for satellite applications[J]. IEEE Transa- ctions on Power Electronics, 2018, 34(5): 4465-4479. [15] 林聪智, 何铭协, 任小永, 等. 基于矩阵变压器的1MHz GaN LLC变换器[J]. 南京航空航天大学学报, 2018, 50(5): 695-700. Lin Congzhi, He Mingxie, Ren Xiaoyong, et al.1MHz GaN LLC resonant converter with matrix trans- former[J]. Journal of Nanjing University of Aero- nautics & Astronautics, 2018, 50(5): 695-700. [16] Ho G K Y, Pong B M H. Multilayer flexible printed circuitry planar transformer with integrated series capacitance for an LLC converter[J]. IEEE Transa- ctions on Power Electronics, 2019, 34(11): 11139-11152. [17] Zhang Zhiliang, Hu Dongdong, Ren Xiaoyong, et al.Multi-winding configuration optimization of multi- output planar transformers in GaN active forward converters for satellite applications[J]. IEEE Transa- ctions on Power Electronics, 2019, 34(5): 4465-4479. [18] Cove S R, Ordonez M, Luchino F, et al.Applying response surface methodology to small planar trans- former winding design[J]. IEEE Transactions on Industrial Electronics, 2013, 60(2): 483-493. [19] Li J, Water W, Zhu Boyuan, et al.Integrated high- frequency coaxial transformer design platform using artificial neural network optimization and FEM simulation[J]. IEEE Transactions on Magnetics, 2015, 51(3): 1-4. [20] Lotfi A W, Lee F C.Two dimensional field solutions for high frequency transformer windings[C]//Pro- ceedings of IEEE Power Electronics Specialist Conference-PESC '93, Seattle, 1993: 1098-1104. [21] Fei Chao, Gadelrab R, Li Qiang, et al.High-frequency three-phase interleaved LLC resonant converter with GaN devices and integrated planar magnetics[J]. IEEE Transactions on Power Electronics, 2019, 7(2): 653-663. [22] Shafaei R, Perez M C G, Ordonez M. Planar trans- formers in LLC resonant converters: high-frequency fringing losses modeling[J]. IEEE Transactions on Power Electronics, 2020, 35(9): 9632-9649. [23] Spro O C, Mauseth F, Peftitsis D.High-voltage insulation design of coreless, planar PCB trans- formers for multi-MHz power supplies[J]. IEEE Transactions on Power Electronics, 2021, 36(8): 8658-8671. [24] 王议锋, 刘瑞欣, 韩富强, 等. CLTLC多谐振变换器的磁集成方法[J]. 电工技术学报, 2021, 37(2): 380-388. Wang Yifeng, Liu Ruixin, Han Fuqiang, et al.Magnetic integration method for CLTLC multi- resonant converter[J]. Transactions of China Electro- technical Society, 2021, 37(2): 380-388. [25] 王泽忠, 全玉生. 工程电磁场[M]. 北京: 清华大学出版社, 2021. [26] IEC 63093-9, Ferrite cores - guidelines on dimensions and the limits of surface irregularities - part 9: planar cores[S]. Brussels: CEN-CENELEC Management Centre, 2020.
2022, Vol. 37 
