Hybrid feedback control of PMSG-based WECS with multilevel flying-capacitor inverter enhanced by fractional order extremum seeking

• A new hybrid control strategy is introduced for multilevel FCI in WECS application. • The controller design uses Lyapunov theory and an invariance principle, ensuring asymptotic stability. • An MPPT-based Fractional-Order Extremum Seeking (FO-ES) control is proposed to extract maximum power from wind. • The fractional-order calculus is used in the FOESC algorithm to improve the convergence speed and system performance. This paper proposes an original hybrid control strategy for a three-phase multilevel flying capacitor inverter (FCI) used in wind energy conversion system (WECS). A state feedback law, computed using a Lyapunov function and an invariance principle, is designed to manage grid current control and capacitor voltage balancing, guaranteeing the asymptotic stability of the closed-loop system. Additionally, a fractional-order extremum seeking control (FOESC) algorithm for Maximum Power Point Tracking (MPPT) is introduced, which optimizes power capture by adjusting turbine speed from the DC side without requiring a detailed system model (model-free approach). The use of fractional-order calculus leads to improved convergence and more seamless performance while preserving the robust characteristics of the system. The proposed control strategies are validated through simulation, demonstrating improved transient response and stability under varying wind conditions and parameter uncertainties. These results highlight the potential of advanced control algorithms to enhance the efficiency and reliability of wind energy systems, contributing to global efforts to achieve sustainable energy goals.