基于广义状态空间平均的LLC谐振变换器建模及稳定性分析

LLC谐振变换器在航空航天领域中广泛应用，但LLC谐振变换器固有的非线性特性及输出“小纹波”易造成系统失稳。为准确分析LLC谐振变换器非线性特性及输出“小纹波”问题，引入广义状态空间平均(generalized state space averaging, GSSA)理论对LLC谐振变换器进行建模，将时域非线性状态空间模型转化为GSSA模型。并推导基于GSSA理论的闭环系统小信号模型。通过特征值分析法及Nyquist曲线对元件参数、控制参数及参数耦合对系统稳定性影响进行分析，再利用仿真对模型及理论分析进行验证。仿真结果表明，建立的广义状态空间平均模型可以考虑到系统中“小纹波”因素，具有更高的精度。稳定性理论分析结果与稳定性分析仿真验证结果一致。

Modeling and stability analysis of an LLC resonant converter based on generalized state space averaging

An LLC resonant converter has wide application in aerospace, but it is easy for its inherent nonlinear characteristics and small ripple output problem to cause system instability. To accurately describe these problems of the LLC, this paper introduces the generalized state space averaging (GSSA) theory to model the LLC resonant converter system. It transforms the time-domain nonlinear state space model into a GSSA model, and derives the small-signal model of the closed-loop system based on GSSA theory. From eigenvalue analysis and Nyquist curve theory, the effects of component and control parameters and parameter coupling are determined for stability analysis for the LLC resonant converter system. The model and theoretical analysis are verified by simulation. The results of simulation show that the GSSA model has higher accuracy, and can take into account the small ripple factor in the system. Theoretical analysis result and simulation verification result for stability are consistent.