Design of an observer-based super-twisting algorithm for three-phase single-stage grid-connected photovoltaic systems

The present paper proposes a nonlinear control strategy for a single-stage, three-phase grid-connected photovoltaic (PV) system. The system architecture is relatively simple, consisting of PV arrays connected to the utility grid via a three-phase voltage source inverter (VSI) and an LCL filter, which attenuates current harmonics at the inverter output. The control objectives are: (i) maximizing the extracted power from the PV arrays, (ii) injecting the harvested power into the grid with unity power factor (UPF), and (iii) ensuring global asymptotic stability of the closed-loop system. To achieve these goals, a control law based on the Super-Twisting Algorithm (STA) is designed, using state estimates provided by a High-Order Sliding Mode Observer (HOSMO), thereby reducing sensor requirements and implementation costs. The controller relies only on measurements of grid voltage and current, along with PV voltage and current. Closed-loop stability is rigorously established via Lyapunov theory, explicitly considering parametric uncertainties in the LCL filter and any bounded external disturbances. Extensive MATLAB/Simulink simulations under variable irradiance and temperature profiles, LCL filter parameter variations, grid voltage sags, and harmonic distortions demonstrate the superior performance of the HOSMO in state estimation compared to a conventional SMO, with reduced steady-state errors and fast convergence. Furthermore, the STA-based control achieves rapid and reliable maximum power point tracking, improved power quality with lower harmonic distortion, reduced reactive power injection, and robust operation under adverse conditions, outperforming a Backstepping controller in all tested scenarios.