A Lyapunov-Based Model Predictive Control Approach for Photovoltaic Microgrid Integration via Multilevel Flying Capacitor Inverter

Abstract

In this study, we introduce a Model Predictive Control (MPC) approach based on a Lyapunov energy function, ensuring global asymptotic stability for a single-phase multilevel flying capacitor inverter (FCI) that interfaces with photovoltaic systems and microgrids. The defined cost function is derived from the Lyapunov energy function, harnessing the stored energy within the capacitor and inductor. This choice is rooted in the principle that as long as total energy is continuously dissipated, the system’s states will eventually reach the equilibrium point. Moreover, this cost function eliminates the need for tuning the weighting factors, a process that can be cumbersome and time-consuming due to the lack of clear guidelines. To assess the efficacy of the proposed control strategy, we conducted simulations using MATLAB/Simulink under varying weather conditions. The results obtained demonstrate that the MPC strategy not only ensures overall stability but also delivers high-quality sinusoidal current with minimal total harmonic distortion (THD), practical low steady-state error in the grid current, and rapid dynamic response, even in the face of changing weather conditions.