Abstract: Under the demand of high-proportion renewable energy grid integration and weak power grid support, the modular multilevel converter(MMC) based on virtual synchronous generator(VSG) exhibits a large peak value of AC-side impedance resonance due to fixed control parameters and insufficient parameter coordinated regulation. This easily triggers system oscillation, restricting the grid-connected stability and dynamic support performance. To address the above issues, this paper constructs a discrete state-space model of VSG based on model predictive control, and proposes a multi-objective optimization control method for grid-side MMC of offshore wind turbines that balances active power tracking speed, virtual speed response, and overshoot suppression. A Pareto weight allocation mechanism is introduced, and the adaptive reshaping of the amplitude-phase characteristics of MMC equivalent output impedance at the grid connection point is realized through online coordinated predictive optimization of VSG inertia J, damping D, and reactive loop integral coefficient K_q. Meanwhile, impedance frequency sweep analysis of VSG-MMC is carried out to extract positive-sequence impedance and complete frequency-domain comparison, so as to quantitatively evaluate the change of impedance robustness before and after the proposed method. Simulation results show that compared with the fixed-parameter control method, the proposed method significantly suppresses resonant impedance in key frequency bands, improves anti-disturbance capability and stability margin, and achieves the coordinated improvement of dynamic response and small-disturbance impedance stability. It provides theoretical support for the stable control of grid-forming wind turbines connected to MMC.

Key words: offshore wind turbines, modular multilevel converter, model predictive control（MPC）, impedance reshaping