Abstract Temperature rise calculation is a complex problem in modeling high-power high-frequency transformers (HFT). An accurate and fast thermal model is significant for the optimal design and stable operation of HFT. At present, lumped parameter thermal network model is usually built through dimensionality reduction, and its calculation precision is easily affected by structural parameters. It is difficult to achieve accurate hot spot prediction in optimizing a wide parameter range. A three-dimensional thermal model of HFT considering anisotropic thermal conductivity is constructed based on the finite difference method (FDM). The discretization error of the three-dimensional thermal model is quantitatively analyzed, which is mainly affected by the loss density, thermal conductivity, and size of the finite difference element. In order to minimize the number of finite differential elements while ensuring the calculation accuracy of the thermal model, three-dimensional sizes of the differential element are adjusted actively according to the discretization error expression. For HTF with nanocrystalline core and litz wire winding, the element sizes in the direction along the width, height of winding and the thickness of core are the key parameters affecting the accuracy of temperature rise calculation. The parameter adaptability of the proposed thermal model is verified in detail with finite element simulation, including structural parameters, loss density, and heat dissipation conditions. The results show that the maximum error of the model is less than 10% in a wide range of parameters. However, the error of the traditional lumped parameter thermal network model is significantly affected by the structural parameters, and the error varies in the range of 10%~80% within the same parameter variation range. Based on the proposed thermal model, the efficiency-power density optimal design of a 10 kHz 150 kW transformer was carried out with the parameter scanning method. The upper limit of temperature rise was set to 100 K, and the differential element sizes were adjusted according to the error of less than 5 K. The optimization design program calculated 500 000 design points within 371 s with parallel computing, and the average time of three-dimensional thermal model calculation for a single design point was 2.8 ms. The temperature rise calculation results of the design points on the optimal design boundary were verified, and the error was less than 5.5%. Compared with finite element simulation and the lumped parameter thermal network model, the proposed three-dimensional thermal model based on FDM balances calculation accuracy and calculation speed. On the optimal design boundary, with the increase of power density, the transformer efficiency gradually decreases, and the temperature rise gradually increases. The maximum power density to meet the 100 K temperature rise requirement was about 9 kW/L, and the transformer efficiency was about 99.82%. A 150 kW transformer prototype was processed according to the optimized design point with maximum power density, and the maximum temperature rise was 103 K under rated working conditions.
Luo Rensong,Wang Tao,Wen Jifeng等. Three-Dimensional Temperature Calculation and Optimization Design Method for High Power High-Frequency Transformer[J]. Transactions of China Electrotechnical Society, 2023, 38(18): 4994-5005.
[1] 赵晓君, 张纯江, 柴秀慧, 等. 串并联架构区域电能路由器柔性运行与功率流控制策略[J]. 电工技术学报, 2021, 36(7): 1480-1491. Zhao Xiaojun, Zhang Chunjiang, Chai Xiuhui, et al.Flexible operation and power flow control strategies for series-parallel architecture region electric power router[J]. Transactions of China Electrotechnical Society, 2021, 36(7): 1480-1491. [2] 高范强, 李子欣, 李耀华, 等. 面向交直流混合配电应用的10kV-3MV·A四端口电力电子变压器[J]. 电工技术学报, 2021, 36(16): 3331-3341. Gao Fanqiang, Li Zixin, Li Yaohua, et al.10kV-3MV·A four-port power electronic transformer for AC-DC hybrid power distribution applications[J]. Transactions of China Electrotechnical Society, 2021, 36(16): 3331-3341. [3] 周兵凯, 杨晓峰, 张智, 等. 能量路由器中双有源桥直流变换器多目标优化控制策略[J]. 电工技术学报, 2020, 35(14): 3030-3040. Zhou Bingkai, Yang Xiaofeng, Zhang Zhi, et al.Multi-objective optimization control strategy of dual-active-bridge DC-DC converter in electric energy router application[J]. Transactions of China Electro-technical Society, 2020, 35(14): 3030-3040. [4] Leibl M, Ortiz G, Kolar J W.Design and experimental analysis of a medium-frequency transformer for solid-state transformer applications[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2017, 5(1): 110-123. [5] 孙凯, 卢世蕾, 易哲嫄, 等. 面向电力电子变压器应用的大容量高频变压器技术综述[J]. 中国电机工程学报, 2021, 41(24): 8531-8546. Sun Kai, Lu Shilei, Yi Zheyuan, et al.A review of high-power high-frequency transformer technology for power electronic transformer applications[J]. Pro-ceedings of the CSEE, 2021, 41(24): 8531-8546. [6] 靳艳娇, 乔光尧, 邓占锋, 等. 全环氧固封高频变压器散热优化设计研究[J]. 电网技术, 2022, 46(7): 2531-2537. Jin Yanjiao, Qiao Guangyao, Deng Zhanfeng, et al.Heat dissipation optimization design of epoxy resin sealing high frequency transformer[J]. Power System Technology, 2022, 46(7): 2531-2537. [7] Scoltock J, Wang Yiren, Calderon-Lopez G, et al.Rapid thermal analysis of nanocrystalline inductors for converter optimization[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(3): 2276-2284. [8] Shafaei R, Ordonez M, Ali Saket M.Three-dimensional frequency-dependent thermal model for planar transformers in LLC resonant converters[J]. IEEE Transactions on Power Electronics, 2019, 34(5): 4641-4655. [9] 李永建, 闫鑫笑, 张长庚, 等. 基于磁-热-流耦合模型的变压器损耗计算和热点预测[J]. 电工技术学报, 2020, 35(21): 4483-4491. Li Yongjian, Yan Xinxiao, Zhang Changgeng, et al.Numerical prediction of losses and local overheating in transformer windings based on magnetic-thermal-fluid model[J]. Transactions of China Electrotech-nical Society, 2020, 35(21): 4483-4491. [10] 唐钊, 刘轩东, 陈铭. 考虑流体动力学的干式变压器热网络模型仿真分析[J]. 电工技术学报, 2022, 37(18): 4777-4787. Tang Zhao, Liu Xuandong, Chen Ming.Simulation analysis of thermal network model of dry-type transformer considering fluid dynamics[J]. Transa-ctions of China Electrotechnical Society, 2022, 37(18): 4777-4787. [11] Yuan Shuai, Zhou Lijun, Gou Xiaofeng, et al.Modeling method for thermal field of turbulent cooling dry-type on-board traction transformer in EMUs[J]. IEEE Transactions on Transportation Elec-trification, 2022, 8(1): 298-311. [12] Chen Yifan, Yang Qingxin, Zhang Changgeng, et al.Thermal network model of high-power dry-type trans-former coupled with electromagnetic loss[J]. IEEE Transactions on Magnetics, 2022, 58(11): 1-5. [13] Gao Yucheng, Sankaranarayanan V, Dede E M, et al.Modeling and design of high-power, high-current-ripple planar inductors[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 5816-5832. [14] 陈彬, 梁旭, 唐波, 等. 大功率中频三相变压器优化设计方法[J]. 中国电机工程学报, 2021, 41(8): 2877-2890. Chen Bin, Liang Xu, Tang Bo, et al.Optimization method of high-power medium-frequency three-phase transformer[J]. Proceedings of the CSEE, 2021, 41(8): 2877-2890. [15] Booth K, Subramanyan H, Liu Jun, et al.Parallel frameworks for robust optimization of medium-frequency transformers[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(4): 5097-5112. [16] Mogorovic M, Dujic D.100 kW, 10 kHz medium-frequency transformer design optimization and experimental verification[J]. IEEE Transactions on Power Electronics, 2019, 34(2): 1696-1708. [17] Bahmani M A, Thiringer T, Kharezy M.Optimization and experimental validation of medium-frequency high power transformers in solid-state transformer applications[C]//2016 IEEE Applied Power Electro-nics Conference and Exposition (APEC), Long Beach, CA, USA, 2016: 3043-3050. [18] Wrobel R, Mellor P H.A general cuboidal element for three-dimensional thermal modelling[J]. IEEE Transa-ctions on Magnetics, 2010, 46(8): 3197-3200. [19] 孙志忠, 袁慰平, 闻震初. 数值分析[M]. 3版. 南京: 东南大学出版社, 2011. [20] 王佳宁, 邹强, 胡嘉汶, 等. 一种中压绝缘大功率中频变压器的优化设计方法[J]. 电工技术学报, 2022, 37(12): 3048-3060. Wang Jianing, Zou Qiang, Hu Jiawen, et al.An optimal design method for medium-voltage insulated high-power medium-frequency transformer[J]. Transa-ctions of China Electrotechnical Society, 2022, 37(12): 3048-3060. [21] Lu Rui, Yu Jianxiong, Feng Dingyi, et al.Modeling and design of a medium frequency transformer with high isolation and high power-density[C]//2021 IEEE Applied Power Electronics Conference and Expo-sition (APEC), Phoenix, AZ, USA, 2021: 1694-1700. [22] Jaritz M, Hillers A, Biela J.General analytical model for the thermal resistance of windings made of solid or Litz wire[J]. IEEE Transactions on Power Elec-tronics, 2019, 34(1): 668-684. [23] Liu Xiaomei, Gerada D, Xu Zeyuan, et al.Effective thermal conductivity calculation and measurement of Litz wire based on the porous metal materials structure[J]. IEEE Transactions on Industrial Elec-tronics, 2020, 67(4): 2667-2677. [24] Salinas López G, Expósito A D, Muñoz-Antón J, et al.Fast and accurate thermal modeling of magnetic components by FEA-based homogenization[J]. IEEE Transactions on Power Electronics, 2020, 35(2): 1830-1844. [25] 汪涛, 骆仁松, 文继峰, 等. 基于辅助绕组的高频变压器绕组损耗测量方法[J]. 电工技术学报, 2022, 37(10): 2622-2630, 2655. Wang Tao, Luo Rensong, Wen Jifeng, et al.A measurement method of winding loss for high-frequency transformer based on auxiliary winding[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2622-2630, 2655. [26] Wu H H, Hsiao Y Y, Huang H S, et al.A practical plate-fin heat sink model[J]. Applied Thermal Engineering, 2011, 31(5): 984-992.
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