Abstract：The rapid development of industries such as aerospace, electric vehicles, and green data centers requires low-power, non-isolated buck-switching power supplies to achieve high efficiency, high power density, and lightweight miniaturization. The converter adopts a topology structure of multi-phase interleaved Buck to reduce the current ripple. However, magnetic components usually occupy more than 30% of the total volume of the power supply, which affects the power density and dynamic characteristics of the power output. Power magnetic integration technology has been studied to reduce magnetic components' footprint, volume, and losses and improve switching power supplies’ efficiency. This paper proposes a multi-dimensional modeling and multi-objective optimization method based on a two-phase interleaved Buck converter for the negative-coupling magnetic devices with improved core structure and winding layout. Firstly, based on the electrical parameter model of the converter and the magnetic circuit characteristics of the negative-coupling inductor, the magnetic core structure and winding layout are improved and optimized. Secondly, multi-dimensional models of the converter are established regarding the winding turns, magnetic column air gap, magnetic column edge length, and switching frequency. Combining the model and constraint conditions, a multi-objective optimization process is designed to obtain non-dominated solutions for the transformer efficiency, magnetic device footprint and volume under different winding turns. Finally, the optimal parameters are selected, and integrated magnetic devices are manufactured. A 28 V/12 V, 168 W experimental prototype has been built. Compared to independent inductors, the optimized magnetic device had a footprint reduction rate of 45.48%, a volume reduction rate of 43.66%, an increase in the rated efficiency of the converter by 0.9%, and a magnetic device power density of 8 020 W/in3. Simultaneously changing the input voltage of the converter and the air gap of the integrated magnetic device allows the converter to operate under different working conditions. By operating the converter and integrated magnetic devices at different switching frequencies and observing the efficiency of the converter, the feasibility of the multi-objective optimization process can be verified. The following conclusions can be drawn. The equivalent steady-state inductance should be the same as the independent inductance value to keep the current ripple constant. The new magnetic device extends the magnetic core and plates in the circumferential direction, improving the magnetic shielding performance and reducing interference with other components. Negative-coupling reduces the AC magnetic flux in the magnetic core and offsets the DC magnetic flux in the magnetic plates. It is beneficial for reducing the magnetic plates’ thickness and the magnetic device’s volume, thereby improving the converter’s power density.
刘泽, 周国华, 何英杰, 徐能谋. 两相交错并联Buck变换器集成磁器件多维度建模与多目标优化[J]. 电工技术学报, 2025, 40(24): 8039-8051.
Liu Ze, Zhou Guohua, He Yingjie, Xu Nengmou. Multidimensional Modeling and Multi-Objective Optimization of Integrated Magnetic Device for Two-Phase Interleaved Buck Converter. Transactions of China Electrotechnical Society, 2025, 40(24): 8039-8051.
[1] 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. [2] 倪硕, 吴红飞, 陈君雨, 等. 交错并联临界导通模式Buck电感高密度集成与优化[J]. 电工技术学报, 2022, 37(18): 4688-4696. Ni Shuo, Wu Hongfei, Chen Junyu, et al.Integration and optimization of a high power density inductor for an interleaved critical conduction mode Buck converter[J]. Transactions of China Electrotechnical Society, 2022, 37(18): 4688-4696. [3] Lee F C, Wang Shuo, Li Qiang.Next generation of power supplies: design for manufacturability[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 9(6): 6462-6475. [4] 程鹤, 徐恺, 李朋圣, 等. 三相CLLC谐振变换器磁集成平面变压器设计与优化[J]. 电工技术学报, 2024, 39(12): 3774-3786. Cheng He, Xu Kai, Li Pengsheng, et al.Design and optimization of three-phase CLLC resonant converter with magnetic integrated planar transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3774-3786. [5] 高圣伟, 王浩, 刘晓明, 等. 新型磁集成双频DC/ DC变换器[J]. 中国电机工程学报, 2020, 40(24): 8131-8144, 8250. Gao Shengwei, Wang Hao, Liu Xiaoming, et al.A novel double frequency DC/DC converter with magnetic integration[J]. Proceedings of the CSEE, 2020, 40(24): 8131-8144, 8250. [6] Li Mingxiao, Wang Chang, Ouyang Ziwei, et al.Optimal design of a matrix planar transformer in an LLC resonant converter for data center applications[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2023, 11(2): 1778-1787. [7] Lee F C, Li Qiang, Nabih A.High frequency resonant converters: an overview on the magnetic design and control methods[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(1): 11-23. [8] Liu Yue, Wu Hongfei, Ni Shuo, et al.Lower-height- oriented magnetic integration design for onboard power converter of electric vehicles[J]. IEEE Transa- ctions on Transportation Electrification, 2024, 10(1): 163-173. [9] 苏冰, 王玉斌, 王璠, 等. 基于耦合电感的多相交错并联双向DC-DC变换器及其均流控制[J]. 电工技术学报, 2020, 35(20): 4336-4349. Su Bing, Wang Yubin, Wang Fan, et al.Multi-phase interleaved bidirectional DC-DC converter with coupled inductors and current sharing control strategy[J]. Transactions of China Electrotechnical Society, 2020, 35(20): 4336-4349. [10] Naseem N, Cha H.Triple-active-bridge converter with automatic voltage balancing for bipolar DC distribution[J]. IEEE Transactions on Power Elec- tronics, 2022, 37(7): 8640-8648. [11] 高圣伟, 王博, 孙醒涛. 一种交错并联双向DC-DC变换器的新型磁集成技术[J]. 中国电机工程学报, 2023, 43(9): 3538-3549. Gao Shengwei, Wang Bo, Sun Xingtao.A novel magnetic integration technology for interleaved parallel bidirectional DC-DC converters[J]. Pro- ceedings of the CSEE, 2023, 43(9): 3538-3549. [12] Wang Shuo, Pham P H, Li Qiana, et al.PCB winding-based coupled inductor for a high-frequency DC/DC converter with 99% efficiency[C]//2023 IEEE Applied Power Electronics Conference and Expo- sition (APEC), Orlando, FL, USA, 2023: 420-425. [13] 马小勇, 王萍, 王议锋, 等. 基于交错并联Boost变换器的耦合电感综合建模与多目标优化方法[J]. 电工技术学报, 2022, 37(24): 6399-6410. Ma Xiaoyong, Wang Ping, Wang Yifeng, et al.Comprehensive modeling and multi-objective opti- mization method for coupled inductors of interleaved Boost converters[J]. Transactions of China Electro- technical Society, 2022, 37(24): 6399-6410. [14] Zhu Feiyang, Li Qiang.Coupled inductors with an adaptive coupling coefficient for multiphase voltage regulators[J]. IEEE Transactions on Power Elec- tronics, 2023, 38(1): 739-749. [15] 刘越, 吴红飞, 邹军, 等. CRM-PFC矩阵式低高度平面电感优化设计[J]. 中国电机工程学报, 2021, 41(19): 6760-6769. Liu Yue, Wu Hongfei, Zou Jun, et al.Optimal design of CRM-PFC matrix low-height planar inductor[J]. Proceedings of the CSEE, 2021, 41(19): 6760-6769. [16] Gadelrab R, Lee F C.PCB-based magnetic integration and design optimization for three-phase LLC[J]. IEEE Transactions on Power Electronics, 2023, 38(11): 14037-14049. [17] 高圣伟, 李永宵, 田金锐, 等. 双频DC-DC变换器的磁集成技术[J]. 电工技术学报, 2024, 39(13): 4025-4036. Gao Shengwei, Li Yongxiao, Tian Jinrui, et al.Magnetic integration of double frequency DC-DC converter[J]. Transactions of China Electrotechnical Society, 2024, 39(13): 4025-4036. [18] Stratta A, Gottardo D, Di Nardo M, et al.Optimal integrated design of a magnetically coupled inter- leaved H-bridge[J]. IEEE Transactions on Power Electronics, 2022, 37(1): 724-737. [19] Li Zheqing, Hsieh E, Li Qiang, et al.High-frequency transformer design with medium-voltage insulation for resonant converter in solid-state transformer[J]. IEEE Transactions on Power Electronics, 2023, 38(8): 9917-9932. [20] Kimura S, Itoh Y, Martinez W, et al.Downsizing effects of integrated magnetic components in high power density DC-DC converters for EV and HEV applications[J]. IEEE Transactions on Industry Appli- cations, 2016, 52(4): 3294-3305.
2025, Vol. 40 
