Global asymptotic stabilization of a grid-connected modular multilevel converter via Lyapunov function

This paper presents a new control method based on Lyapunov function approach for simultaneous control of grid currents, circulating currents and modules voltages of a modular multilevel converter. Unlike existing methods that use nested and multi-loop control structures, the proposed method has a single-loop structure and ensures the global asymptotic stability of the closed-loop system. In this regard, first, the dynamic equations of the converter and the grid are extracted using the averaging technique, and then the coordinates of the steady-state operating point are calculated. Next, using the obtained operating point coordinates and the dynamic equations of the main system, the error dynamics are computed. Finally, these equations and the Lyapunov function, based on the error signals, are used for the analytic calculation of the control inputs. The simulation results confirm the efficiency of the proposed control method.