Abstract：LLC resonant converters are widely used in low-voltage, high-current applications because of their wide soft-switching range, high efficiency, and superior power density. Owing to the finite current-handling capability of a single module, multiple LLC resonant converters are usually interleaved in parallel to increase system capacity. When the modules are operated at the same switching frequency, the phase-shifted output currents partially cancel each other. Accordingly, the total output-current ripple is reduced, and the volume and cost of the output filter are minimized. Nevertheless, even under identical manufacturing processes, unavoidable tolerances in the resonant components lead to mismatches in resonant parameters. A deviation as small as 5% between two modules can result in a current imbalance exceeding 50%, making current-sharing control a critical design issue in paralleled LLC systems. Current-sharing techniques for LLC resonant converters are generally classified into two categories. The first relies on additional hardware to enforce current balance, such as switch-controlled capacitors to equalize the resonant tanks or magnetic coupling between modules. Although strong regulatory capabilities can be provided, interdependencies among modules and complex hardware exist. The second employs fully digital control without any hardware modification, preserving modularity and scalability. However, it requires inter-module communication and imposes a high computational burden. Thanks to the rapid advancement of digital controllers, digitally implemented current-sharing strategies have become increasingly attractive. Among digital methods, pulse-frequency modulation (PFM) is commonly used to equalize the voltage gain across modules. Unfortunately, PFM forces the modules to operate at different switching frequencies, which degrades the ripple-cancellation benefit inherent to interleaving. Consequently, a fixed-frequency strategy is preferred, with phase-shift modulation (PSM) used to adjust the effective duty cycle of the higher-gain module to achieve current sharing without frequency deviation. In most interleaved systems, the phase displacement among n modules is rigidly set to 180°/n. When resonant-parameter mismatches exist, the phase shifts introduced for current sharing distort the individual current waveforms, rendering the fixed interleaving angle suboptimal for ripple minimization. To determine the optimal interleaving angle, an accurate representation of the resonant-tank current is essential. Time-domain analysis (TDA) divides the LLC operation into several topological modes and solves exact differential equations in each mode to obtain precise current and voltage waveforms. The computational intensity of TDA and the absence of closed-form solutions usually necessitate look-up-table-based implementations. Alternatively, state-plane analysis (SPA) captures the geometric relationships among the resonant state variables, yielding a concise and intuitive graphical representation of converter behavior. By avoiding the simultaneous solution of differential equations, SPA significantly simplifies the derivation while preserving sufficient accuracy for control purposes. This paper applies geometrically simplified SPA to a full-bridge LLC resonant converter under hybrid PFM-PSM control to locate the instants of peak output current under various operating modes. Subsequently, a two-module interleaved LLC system is investigated, and an adaptive interleaving-angle strategy applicable to n modules is proposed. In this strategy, PFM regulates the output voltage, while PSM balances the currents and deliberately offsets the peak-current instants of the two modules by 180°/n. Thus, the peak-to-peak output-current ripple is minimized. Simulation and experimental results show that, compared with the conventional fixed 180°/n interleaving approach, the proposed adaptive scheme markedly reduces the output-current ripple.
聂铭志, 唐海国, 陈捷, 石稀元, 王勇. 基于状态轨迹分析的交错并联LLC型谐振变换器自适应输出电流纹波优化控制[J]. 电工技术学报, 2026, 41(14): 4852-4866.
Nie Mingzhi, Tang Haiguo, Chen Jie, Shi Xiyuan, Wang Yong. Adaptive Output Current Ripple Reduction Control of Interleaved LLC Resonant Converter Based on State Plane Analysis. Transactions of China Electrotechnical Society, 2026, 41(14): 4852-4866.
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2026, Vol. 41 
