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| 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 |
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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.
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Received: 25 March 2026
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2026, Vol. 41 
