Unified Nonlinear Backstepping Control of a Single-Stage Grid-Tied PV-MMC for Coordinated Arm Current Regulation, MPPT, and Voltage Balancing

Abstract This paper presents the modeling and nonlinear control of a single-stage grid-connected photovoltaic (PV) system based on a modular multilevel converter (MMC) interfaced with the utility grid through an RL filter. The proposed control strategy is designed to simultaneously achieve efficient solar energy extraction, accurate grid current tracking, and stable MMC operation. A cascaded nonlinear control scheme based on the backstepping technique is developed, in which the inner loop regulates the MMC arm currents, while the outer loop governs the PV-side dynamics. In particular, the differential component of the arm currents is controlled to ensure accurate grid current tracking and unity power factor operation (UPF), whereas the outer loop simultaneously performs maximum power point tracking (MPPT) and capacitor voltage balancing. To facilitate the controller design and stability analysis, a nonlinear averaged model of the PV--MMC system is first derived. The main contribution is a unified nonlinear control framework that integrates arm current regulation, MPPT, and capacitor voltage balancing within a single-stage PV--MMC architecture, without an additional DC--DC conversion stage. This approach also explicitly accounts for the coupling between the PV source dynamics and the MMC submodule capacitor voltages. The proposed strategy is validated through detailed simulations using a switched model implemented in the \textsc{MATLAB/Simscape Power Systems} environment. The results demonstrate fast dynamic response, accurate PV voltage regulation, effective capacitor voltage balancing, and high-quality grid current injection under varying operating conditions.