Memristive Characteristics and Extreme Multistability of LLC DC-DC Resonant Converters

The characteristics of a power electronic circuit composed of a rectifier bridge and passive filter correspond with the basic characteristics of extended memristors. Using the PI control system of an
LLC
resonant dc–dc converter as an example, this article establishes an equivalent memristor model for the system and investigates its dynamics. The Floquet theory, bifurcation diagram, and Poincaré map are used to investigate the dynamics of the system. The correctness of the established model and analysis results were verified through a simulation and experiments. The study results show that it is a system with no equilibrium, and the attractors generated by it are all hidden attractors. Similar to general converters,
LLC
resonant converters produce various types of bifurcations, such as Neimark–Sacker, boundary-collision, and topological equivalence bifurcations with the change in parameters, exhibiting ordinary nonlinear phenomena such as periods, quasi-periods, and chaos.
LLC
resonant converters also rely significantly on initial values to produce transient periods and extreme multistability, thereby increasing the uncertainty of the system. Therefore, to ensure the safe and reliable operation of the system, the dynamical characteristics of power electronics systems should be studied from the perspective of transient transition and multistability, which is a new problem worth investigating.