State estimation and iterative strategy for nonlinear differential control in modular multilevel converters

• Particle filtering is applied to estimate states in nonlinear and non-Gaussian MMC systems. • An iterative control strategy reduces nonlinear problems to linear subproblems for real-time use. • Lyapunov-based analysis guarantees global convergence and robustness of the proposed method. • Simulations confirm strong control performance under disturbances and observation noise. This paper presents a novel nonlinear differential control framework for modular multilevel converter (MMC) systems, integrating particle filter-based state estimation with a continuous iteration strategy. The proposed method addresses the challenge of strong nonlinearities, external disturbances, and non-Gaussian observation noise, which conventional control strategies such as PI and LQR fail to handle effectively. The particle filter ensures accurate state estimation under noisy and nonlinear conditions, while the iteration strategy transforms complex nonlinear dynamics into a sequence of linear subproblems, enabling real-time solvability. Compared to existing methods, this hybrid approach offers enhanced robustness, convergence, and control precision. Theoretical analysis using Lyapunov stability theory and Barbalat’s lemma proves global convergence and bounded error. Extensive simulations under HVDC and renewable energy scenarios validate the method’s superiority in handling dynamic disturbances, making it a practical solution for advanced power electronics systems.