Analytic Discrete State-Space Model of LLC Resonant Converter

The LLC resonant converter has widely been used for having high-frequency soft-switching capability which could lead to high power density power electronic solutions, and higher power conversion efficiency at lower costs. However, the presence of excessive non-linearity resulting from power conversion through the resonant tank has led to a lack of accurate and reliable large-signal and small-signal models which limits the performance optimization. This paper presents a theoretical analysis of the LLC converter using the sampled-data modeling approach to accurately convert the continuous-time-variant state equations to discrete-time-invariant state equations and solve them using switching time-segmented boundary conditions to obtain the discrete large-signal model. The small-signal model is obtained by perturbation and linearization of the steady-state model in the vicinity of the cyclic equilibrium states of the converter. Theoretical analysis results are validated by simulating a 650W LLC converter in Matlab Simulink. Based on the provided results, the proposed steady-state and small-signal models can accurately predict the dynamic behavior of the LLC converter in different operational conditions.