Simplified Backflow Power Model and Parameter Optimization for Frequency-Controlled Full-Bridge LLC Converters
Wang Hang1, An Shaoliang1, Jiao Qian1, Sun Xiangdong1, Wu Hongfei2
1. School of Electrical Engineering Xi’an University of Technology Xi’an 710048 China; 2. College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211106 China
Abstract：In renewable energy generation, electric vehicles, and communication power supplies, the LLC resonant converter has become a mainstream topology for high-performance power supply design due to its simple circuit structure, excellent soft-switching capability, and favorable electromagnetic interference characteristics. However, under wide voltage or light-load conditions, the converter is subjected to a significant backflow power issue, where the resonant current lags the input voltage, leading to increased conduction losses, core losses, and current stress, thereby severely limiting system efficiency improvement. Existing research on backflow power mitigation falls into two main categories: control method optimization and hardware parameter optimization. The former, including multiple phase-shift or hybrid frequency-phase-shift control, reduces backflow power but suffers from high control complexity and limited practicality. The latter, such as fundamental harmonic analysis (FHA) based parameter design or topology modifications with additional resonant components, faces issues such as large gain calculation errors, high hardware cost, or increased control freedom. Moreover, existing studies only consider the impact of parasitic capacitance on soft switching, ignoring its relationship with backflow power through charge/discharge behavior. Additionally, parasitic capacitance is commonly treated as a linear constant equivalent without accounting for its nonlinear voltage-dependent characteristics, which degrades the accuracy of zero-voltage switching (ZVS) boundary determination and backflow power optimization. A simplified linear calculation model for backflow power and a parameter optimization method for the LLC converter are proposed, adopting direct frequency control and considering the nonlinear charge/discharge effect of the switching-device parasitic capacitance. Based on the time-domain analysis model of the full-bridge LLC converter, a time-domain expression of backflow power is established. Leveraging the linear characteristics of the resonant tank current during the backflow power generation interval, the calculation coefficients in the time-domain expression are simplified, thereby streamlining the backflow power calculation process. The nonlinear parasitic capacitance is modeled as a voltage-dependent capacitor and incorporated into the backflow power calculation. The backflow power is decomposed into dead-time and resonant intervals, yielding a linear approximate model that reduces the time for qualitative judgment and quantitative calculation of backflow power. Based on the simplified backflow power model and incorporating ZVS conditions and voltage gain constraints, a multi-objective parameter optimization method is constructed. By optimizing key parameters such as the magnetizing inductance and resonant capacitance, the method minimizes backflow power and reduces system losses while ensuring ZVS over the entire load range. The calculation program was tested in Matlab under identical conditions. The simplified calculation model reduces computation time by 57% while maintaining the same accuracy. On a 1200W experimental prototype, the simulation and experimental errors under rated conditions are less than 10% and 7.5%, respectively. The resonant parameters designed using the proposed optimization method achieve a peak efficiency of 96.2%. Simulation and experimental results show that the proposed method reduces backflow power and improves operating efficiency under light-load and wide-voltage conditions, with low computational cost.
汪航, 安少亮, 焦茜, 孙向东, 吴红飞. 频率控制型全桥LLC变换器的回流功率简化模型与参数优化[J]. 电工技术学报, 2026, 41(18): 6186-6200.
Wang Hang, An Shaoliang, Jiao Qian, Sun Xiangdong, Wu Hongfei. Simplified Backflow Power Model and Parameter Optimization for Frequency-Controlled Full-Bridge LLC Converters. Transactions of China Electrotechnical Society, 2026, 41(18): 6186-6200.
[1] 王哲, 李驰, 郑泽东, 等. 一种基于耦合电感的高增益软开关谐振变换器[J]. 电工技术学报, 2024, 39(1): 194-205. Wang Zhe, Li Chi, Zheng Zedong, et al.A high step-up ZVS/ZCS resonant converter based on coupled inductor[J]. Transactions of China Electro- technical Society, 2024, 39(1): 194-205. [2] 纪国盛, 吴红飞, 杨帆, 等. 磁集成三相LLC谐振变换器共模激磁电流产生机理及其抑制方法[J]. 中国电机工程学报, 2025, 45(18): 7316-7324, I0024. Ji Guosheng, Wu Hongfei, Yang Fan, et al.Generation mechanism and suppression of common mode magnetizing current in magnetic integrated three-phase LLC resonant converter[J]. Proceedings of the CSEE, 2025, 45(18): 7316-7324, I0024. [3] 姜盟瀚, 伍群芳, 王勤, 等. 一种考虑损耗与寄生参数的LLC四元平面矩阵变压器集成优化设计[J]. 电工技术学报, 2025, 40(10): 3195-3208. Jiang Menghan, Wu Qunfang, Wang Qin, et al.Integrated optimization design of LLC four-element- matrix planar transformer considering loss and parasitic parameters[J]. Transactions of China Elec- trotechnical Society, 2025, 40(10): 3195-3208. [4] 张宇鑫, 陈捷, 王简, 等. 基于简化时域模型的LLC谐振变换器同步整流在线驱动策略[J]. 电工技术学报, 2025, 40(8): 2615-2629. Zhang Yuxin, Chen Jie, Wang Jian, et al.Syn- chronous rectifier on-line driving strategy for LLC resonant converter based on a simplified time domain model[J]. Transactions of China Electrotechnical Society, 2025, 40(8): 2615-2629. [5] 赵永秀, 刘泽伟, 王崇杰, 等. 变模态倍压型LLC谐振变换器多目标参数优化[J]. 电工技术学报, 2024, 39(22): 7139-7153. Zhao Yongxiu, Liu Zewei, Wang Chongjie, et al.Multi objective parameter optimization of variable mode voltage doubling LLC resonant converter[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7139-7153. [6] 陈杰, 刘昌咏, 邓文明, 等. 四开关三电平半桥LLC变换器的控制策略与效率优化[J]. 电工技术学报, 2024, 39(24): 7833-7845. Chen Jie, Liu Changyong, Deng Wenming, et al.Control improvement and efficiency optimization of four switch three-level half-bridge LLC converter[J]. Transactions of China Electrotechnical Society, 2024, 39(24): 7833-7845. [7] 钱秋晓, 陈美喜, 郭睿, 等. 自适应高效混合输出切换线路[J]. 电气技术, 2024, 25(9): 38-41, 45. Qian Qiuxiao, Chen Meixi, Guo Rui, et al.Adaptive high efficiency hybrid output switching circuit[J]. Electrical Engineering, 2024, 25(9): 38-41, 45. [8] 董汉菁, 谢小高. 基于相间有源阻抗平衡单元的多相交错并联LLC谐振变换器均流策略研究[J]. 中国电机工程学报, 2024, 44(3): 1117-1132. Dong Hanjing, Xie Xiaogao.A current sharing scheme of multiphase interleaved LLC resonant converter based on phase-to-phase active impedance balance unit[J]. Proceedings of the CSEE, 2024, 44(3): 1117-1132. [9] 康薇, 肖飞, 任强, 等. 双有源桥DC-DC变换器三移相调制及其死区效应分析和补偿[J]. 电工技术学报, 2024, 39(6): 1907-1922. Kang Wei, Xiao Fei, Ren Qiang, et al.Three-phase- shift modulation and its dead band effect analysis and compensation of dual-active-bridge DC-DC converter[J]. Transactions of China Electrotechnical Society, 2024, 39(6): 1907-1922. [10] 范恩泽, 李耀华, 葛琼璇, 等. 基于优化移相的双有源串联谐振变换器前馈控制策略[J]. 电工技术学报, 2022, 37(20): 5324-5333. Fan Enze, Li Yaohua, Ge Qiongxuan, et al.Feed- forward control strategy of dual active bridge series resonant converter based on optimized phase shift[J]. Transactions of China Electrotechnical Society, 2022, 37(20): 5324-5333. [11] 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. [12] Wang Yichen, Wang Feng, Zhuo Fang, et al.Analysis of high performance synchronous rectified CLLC resonant converter with reactive power optimi- zation[J]. IEEE Transactions on Power Electronics, 2023, 38(12): 15253-15271. [13] Kan Jiarong, Xie Shaojun, Tang Yu, et al.Voltage-fed dual active bridge bidirectional DC/DC converter with an immittance network[J]. IEEE Transactions on Power Electronics, 2014, 29(7): 3582-3590. [14] 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. [15] Shi Zhe, Tang Yu, Guo Yingjun, et al.Optimal design method of LLC half-bridge resonant converter con- sidering backflow power analysis[J]. IEEE Transa- ctions on Industrial Electronics, 2022, 69(4): 3599-3608. [16] 黄何伟, 曹太强, 潘光绪, 等. 考虑回流功率因素的全桥CLL谐振变换器参数优化设计[J]. 电工技术学报, 2023, 38(20): 5503-5514. Huang Hewei, Cao Taiqiang, Pan Guangxu, et al.Parameter optimal design of full-bridge CLL resonant converter considering backflow power factor[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5503-5514. [17] 杨超, 许海平, 张祖之, 等. PWM与移相结合控制下的混合三电平隔离型双向DC-DC最小回流功率控制研究[J]. 电工技术学报, 2019, 34(15): 3186-3197. Yang Chao, Xu Haiping, Zhang Zuzhi, et al.Minimum backflow power control of the hybrid three level isolated bi-directional DC-DC converters based on PWM-phase-shifting control[J]. Transactions of China Electrotechnical Society, 2019, 34(15): 3186-3197. [18] Lin R L, Huang L H.Efficiency improvement on LLC resonant converter using integrated LCLC resonant transformer[J]. IEEE Transactions on Industry Applications, 2018, 54(2): 1756-1764. [19] Jiang Peng, Feng Hao, Ran Li.ZVS analysis and a design method for unidirectional medium-voltage LLC-DCX with high step-up ratio[J]. IEEE Transa- ctions on Power Electronics, 2024, 39(3): 2948-2953. [20] Liu Xinbo, He Shuiyuan, Ma Ruiqi, et al.An LLC DCX converter parameter design method considering junction capacitances and current phase angle of dead-time high-frequency resonance[J]. IEEE Journal of Emerging and Selected Topics in Power Elec- tronics, 2025, 13(3): 3817-3830. [21] 张俊涛, 林国庆. 多模态超宽输出双LLC谐振变换器拓扑及控制策略[J]. 电工技术学报, 2025, 40(24): 8052-8065, 8079. Zhang Juntao, Lin Guoqing.A variable-mode ultra- wide output voltage gain dual LLC resonant converter and control method[J]. Transactions of China Elec- trotechnical Society, 2025, 40(24): 8052-8065, 8079. [22] 高祎韩, 周子航, 张欣, 等. 双有源桥串联欠谐振变换器的最小回流电流控制[J]. 电工技术学报, 2024, 39(14): 4480-4494. Gao Yihan, Zhou Zihang, Zhang Xin, et al.Minimum backflow current control of under-resonant-dual- bridge-series-resonant converter[J]. Transactions of China Electrotechnical Society, 2024, 39(14): 4480-4494. [23] Wang Zhixuan, Sun Xiangdong, Song Weizhang, et al.Reducing turn-OFF losses in DAB converters by minimizing voltage-current overlap under ZVS operation[J]. IEEE Transactions on Power Electronics, 2025, 40(11): 16611-16625. [24] Liu Jianqiang, Zhang Jiepin, Zheng T Q, et al.A modified gain model and the corresponding design method for an LLC resonant converter[J]. IEEE Transactions on Power Electronics, 2017, 32(9): 6716-6727.
2026, Vol. 41 
