A Two-Piece Sigmoid Model for High-Order Power Electronics Converters and an Analysis of Their Dynamic Behaviors

High-order power electronics converters are switching systems with multiple switching conditions and multiple operating modes. It is challenging to analyze their dynamics and stability based on traditional models because of their multimodal nature. To address this issue, a sigmoid function-based two-piece switching system model is proposed in this article. Using the voltage-controlled series-series inductive wireless power transfer (SS-IWPT) system as an example, this study adopts the sigmoid function to construct a two-piece switching system model for the system. Filippov’s theory and the Floquet method were used to analyze the dynamic behavior of such systems. Floquet multipliers were employed to compute the stable domains of the system’s parameter space, which can be used to guide parameter design. Theoretical analysis based on the proposed model indicates that SS-IWPT systems could exhibit Neimark-Sacker bifurcation under certain conditions and that their dynamic behaviors can range from periodic states to quasiperiodic states. These findings are consistent with the time-domain waveforms obtained from circuit simulation and an experimental prototype. Both simulation and experimental results validate the accuracy of the proposed model, which can significantly reduce the difficulty of analyzing high-order power electronics systems dynamics.