Edge-Shifted Variable On-Time Modulation for Bidirectional LLC Converter with Zero Circulating Current on the Low-Voltage Side
Li Yong1,2, Bao Junyang1,2, Liu Bangyin1,2, Duan Shanxu1,2
1. State Key Laboratory of Advanced Electromagnetic Technology Wuhan 430074 China;
2. School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China
The bidirectional LLC converter, valued for its high efficiency and power density, is a prime candidate for low-voltage, high-current applications such as battery optimizers. Traditional modulation, however, is hampered by asymmetrical gain characteristics, difficult bidirectional switching, and significant circulating currents.
To address these problems, this chapter proposes the edge-shifted variable on-time (ESVOT) modulation. This new modulation introduces two additional control degrees of freedom—a phase-shift angle and the on-time of the low-voltage side (LV-side) switches—to optimize the LV-side circulating current and ensure perfectly symmetrical forward and reverse operating characteristics.
Since the ESVOT modulation complicates the converter's operating modes, the conventional fundamental harmonic analysis (FHA) method is no longer adequate for accurately modeling its steady-state characteristics. Therefore, to precisely calculate the phase-shift angle and LV-side switch on-time required to achieve zero circulating current under various load and gain conditions, this paper employs exact time-domain analysis (ETDA) for the steady-state analysis. Based on the characteristics of the resonant tank waveforms, eight operating patterns are identified. The mode analysis and a soft-switching characteristic evaluation are then conducted for each pattern. Among these, four patterns are selected as feasible operating patterns due to their excellent soft-switching performance and their ability to achieve zero circulating current on the LV-side. The ETDA is also used to derive the steady-state voltage gain characteristics and the boundary conditions for each pattern. Building on this analysis, a bidirectional control scheme that integrates the ESVOT modulation with a two-dimensional look-up table (2D-LUT) is developed. This scheme utilizes a 2D-LUT-based feedforward controller to provide the feedforward values for the switching frequency, phase-shift angle, and LV-side switch on-time, thereby ensuring zero circulating current on the transformer's LV-side in the steady state. Concurrently, a closed-loop controller adjusts the switching frequency to regulate the power.
The proposed ESVOT modulation and bidirectional control scheme has been validated on a 2.5 kW prototype. The 2D-LUT based feedforward controller requires a minimum of just 10 kB of memory, offering advantages such as simple implementation and low hardware requirements. Dynamic experimental results demonstrate that the prototype can complete smooth and rapid transitions between forward and reverse operation within 8 ms. Furthermore, steady-state experimental results indicate that, compared to the conventional modulation, the ESVOT modulation successfully eliminates the circulating current on the transformer's LV-side. This boosts the prototype's efficiency under forward and reverse light-load conditions by up to 5.8% and 4.5%, respectively. Finally, the prototype achieved a peak efficiency of 98.67% and a power density of 46 W/in³, while also exhibiting perfectly symmetrical forward and reverse operating characteristics.
李勇, 包浚炀, 刘邦银, 段善旭. 双向LLC变换器低压侧零环流的边沿偏移型变导通时间调制[J]. 电工技术学报, 0, (): 20251200-20251200.
Li Yong, Bao Junyang, Liu Bangyin, Duan Shanxu. Edge-Shifted Variable On-Time Modulation for Bidirectional LLC Converter with Zero Circulating Current on the Low-Voltage Side. Transactions of China Electrotechnical Society, 0, (): 20251200-20251200.
[1] Chen S, Zhang G, Yu S S, Mei Y, Zhang Y.A review of isolated bidirectional DC-DC converters for data Centers[J]. Chinese Journal of Electrical Engineering, 2023, 9(4): 1-22.
[2] Khan I, Rahman S, Ayaz M A, Amir M, Shehada H.Review of isolated DC-DC converters for application in data center power Delivery[J]. IEEE Transactions on Industry Applications, 2024, 60(4): 5436-5446.
[3] 姜盟瀚, 伍群芳, 王勤, 孙志峰, 吕晖. 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 Menhan, Wu Qunfang, Wang Qin, Sun Zhifeng, Lü Hui.Integrated Optimization Design of LLC Four-Element-Matrix Planar Transformer Considering Loss and Parasitic Parameters[J]. Transactions of China Electrotechnical Society, 2025, 40(10): 3195-3208.
[4] 赵永秀, 刘泽伟, 王崇杰, 雷鸣, 晏铭. 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, Lei Ming, Yan Ming.Multi Objective Parameter Optimization of Variable Mode Voltage Doubling LLC Resonant Converter[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7139-7153.
[5] Ma Y, Wu X, Li R.Hybrid modulation strategy for dual active bridge LLC resonant Converter[C/OL]//2024 CPSS & IEEE International Symposium on Energy Storage and Conversion (ISESC). November 2024.
[6] Gao B, Zhang X, Lin C, Jiang K, Ye Z, Li R. Circuit design and control of Independent-input, parallel-output DC/DC converters for modular battery Balancing[C/OL]//2024 CPSS & IEEE International Symposium on Energy Storage and Conversion (ISESC). November2024. Xi’an, China.
[7] Wu X, Li R, Cai X.A novel current Self-balancing method for high-gain and high-frequency Converter[J]. IEEE Transactions on Industrial Electronics, 2023, 70(5): 4922-4930.
[8] 江添洋, 张军明, 汪槱生. 同步控制双向LLC谐振变换器[J]. 电工技术学报, 2015, 30(12): 87-96.
Jiang Tianyang, Zhang Junming, Wang Yousheng.Bidirectional LLC Resonant Converter with Synchronous Control Method[J]. Transactions of China Electrotechnical Society, 2015, 30(12): 87-96.
[9] Jiang T, Zhang J, Wu X, Sheng K, Wang Y.A bidirectional LLC resonant converter with automatic forward and backward mode Transition[J]. IEEE Transactions on Power Electronics, 2015, 30(2): 757-770.
[10] 陶文栋, 王玉斌, 张丰一, 曲增彬, 潘腾腾. 双向LLC谐振变换器的变频-移相控制方法[J]. 电工技术学报, 2018, 33(24): 5856-5863.
Tao Wendong, Wang Yubin, Zhang Fengyi, Qu Zengbin, Pan Tengteng.Pulse Frequency Modulation and Phase Shift Combined Control Method for Bidirectional LLC Resonant Converter[J]. Transactions of China Electrotechnical Society, 2018, 33(24): 5856-5863.
[11] 李浩, 郭海洋, 帅康, 周鑫恒. 基于变频-移相的双向L-LLC谐振变换器混合调制策略[J/OL]. 电力电子技术, 2025.
Li Hao, Guo Haiyang Shuai Kang, Zhou xinheng. Minimum Resonant Current Strategy of Bidirectional L-LLC Resonant Converters with Hybrid Frequency-Shift and Phase-Shift Modulation[J/OL]. Power Electronics, 2025.
[12] Liu J, Ai Y, Chen S, Zhang Z, Shi Y.A hybrid pulse frequency modulation control strategy for L-LLC resonant Converter[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2022, 10(6): 6960-6972.
[13] 鲁静, 同向前, 尹军, 申明. L-LLC谐振型双向DC-DC变换器轻载优化控制策略研究[J]. 电工技术学报, 2022, 37(17): 4458-4465.
Lu Jing, Tong Xiangqian, Yin Jun, Shen Ming.The Optimal Control Strategy for L-LLC Bi-Directional Resonant DC-DC Converter under Light Load[J]. Transactions of China Electrotechnical Society, 2022, 37(17): 4458-4465.
[14] 孙晓东, 董纪清, 张永祥. L-LLC谐振型双向DC/DC变换器轻载效率优化研究[J]. 电力电子技术, 2025, 59(9): 25-31.
Sun Xiaodong, Dong Jiqing, Zhang Yongxiang.Research on Optimization of Light Load Efficiency of L-LLC Resonant Bi-directional DC/DC Converter[J]. Power Electronics, 2025, 59(9): 25-31.
[15] 张树炜, 李堂, 张彬意, 毛行奎. 混合式L-LLC谐振变换器数字同步整流控制策略研究[J]. 电力电子技术, 2025, 59(7): 15-24.
Zhang Shuwei, Li Tang, Zhang Binyi, Mao Xingkui.Research on Digital Control Strategy of Synchronous Rectification for Hybrid L-LLC Resonant Converter[J]. Power Electronics, 2025, 59(7): 15-24.
[16] Chen Q, Wang H, Wu K, Zhuang J, Zhang Y.A Bi-directional LLC topology with symmetrical gain and anti-DC bias Ability[J]. IEEE Transactions on Industry Applications, 2025, 61(2): 3329-3336.
[17] Li H, Wang S, Zhang Z, Zhang J, Zhu W, Ren X, Hu C.A bidirectional synchronous/asynchronous rectifier control for wide battery voltage range in SiC bidirectional LLC Chargers[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 6090-6101.
[18] 李浩然, 崔超辉, 王生东, 张之梁, 胡存刚. 基于二阶拟合模型的SiC双向LLC数字同步整流控制[J]. 电工技术学报, 2022, 37(24): 6191-6203.
Li Haoran, Cui Chaohui, Wang Shengdong, Zhang Zhiliang, Hu Cungang.Two-Order Fitting Model-Based Digital Synchronous Rectifier Control for SiC Bidirectional LLC Converter[J]. Transactions of China Electrotechnical Society, 2022, 37(24): 6191-6203.
[19] 张宇鑫, 陈捷, 王简, 佘焱, 王勇. 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, She Yan, Wang Yong.Synchronous 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.
[20] Kalayci K, Demirel O, Arifoglu U, Hizarci H.Analysis of Three-level T-type LLC resonant isolated bidirectional DC-DC converter under three-degrees-of-freedom Modulation[J]. IEEE Access, 2023, 11: 60605-60625.
[21] Zhang J, Liu J, Yang J, Zhao N, Wang Y, Zheng T Q.An LLC-LC type bidirectional control strategy for an LLC resonant converter in power electronic traction Transformer[J]. IEEE Transactions on Industrial Electronics, 2018, 65(11): 8595-8604.
[22] Xu J, Yang J, Xu G, Jiang T, Su M, Sun Y, Wang H, Zheng M.PWM modulation and control strategy for LLC-DCX converter to achieve bidirectional power flow in facing with resonant parameters Variation[J]. IEEE Access, 2019, 7: 54693-54704.
[23] Su M, Ouyang Q, Deng G, Xu G, Sun Y, Xiong W.Modified topology and PWM modulation for bidirectional LLC-DCX converter with center-tapped Transformer[J]. IEEE Transactions on Transportation Electrification, 2022, 8(3): 3907-3920.
[24] Sun Y, Deng Z, Xu G, Deng G, Ouyang Q, Su M.ZVS analysis and design for half bridge bidirectional LLC-DCX converter with consideration of nonlinear capacitance and different load under synchronous turn-on and turn-off Modulation[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2429-2443.
[25] Luo S, Liu W, Peng T, Wang Y, Duan S. Research on hybrid modulation strategy of bidirectional LLC resonant converter in distributed energy storage System[C/OL]//2022 IEEE 3rd China International Youth Conference on Electrical Engineering (CIYCEE). November2022. Wuhan, China.
[26] Li Y, Bao J, Wang F, Duan S. Constant On-time modulation and control for bidirectional LLC converter with flux-Balancing[C/OL]//2024 Energy Conversion Congress & Expo Europe (ECCE Europe). September2024. Darmstadt, Germany.
[27] Fang X, Hu H, Shen Z J, Batarseh I.Operation mode analysis and peak gain approximation of the LLC resonant Converter[J]. IEEE Transactions on Power Electronics, 2012, 27(4): 1985-1995.
[28] Yu R, Ho G K Y, Pong B M H, Ling B W-K, Lam J. Computer-aided design and optimization of high-efficiency LLC series resonant Converter[J]. IEEE Transactions on Power Electronics, 2012, 27(7): 3243-3256.
[29] Li Z, Zhang S, Chen D, Sun P, He Y, Luo Q, Liu J, Wei Y.An accurate, universal and fast time domain model for different types of resonant converters by considering parasitic capacitors and Deadtime[J]. IEEE Transactions on Power Electronics, 2024: 1-16.
[30] 王志刚, 董长城, 侯凯, 高鹏飞. 全桥LLC电路时域模型及其分析[J]. 电力系统自动化, 2018, 42(20): 138-143, 164.
Wang Zhigang, Dong Changcheng, Hou Kai, Gao Pengfei.Time Domain Model of Full Bridge LLC Circuit and Its Analysis[J]. Automation of Electric Power Systems, 2018, 42(20): 138-143, 164.
[31] Kasper M, Burkart R M, Deboy G, Kolar J W.ZVS of power MOSFETs Revisited[J]. IEEE Transactions on Power Electronics, 2016, 31(12): 8063-8067.
[32] Wei Y, Wang Z, Luo Q, Alan Mantooth H.MATLAB GUI based steady state Open-loop and closed-loop simulation tools for different LLC converters with all operation Modes[J]. IEEE Open Journal of Industry Applications, 2021, 2: 320-336.