Parameter Analysis and Optimization of Virtual Impedance for Grid-Forming MMC Based on GWO Algorithm

Modular multilevel converters (MMCs) are widely used in high-voltage direct current transmission, renewable energy integration, and rail transit. However, most existing MMCs adopt grid-following control, which performs well in strong power grids but easily induces broadband oscillation when interacting with weak power grids, threatening system stability. To address the voltage support and stability issues of weak power grids caused by high-proportion renewable energy integration, grid-forming MMCs are increasingly being adopted, but their stability analysis remains insufficient. To fill this gap, this paper establishes the impedance model of grid-forming MMCs using a multi-harmonic linearization method and analyzes system stability based on the Nyquist stability criterion. To suppress broadband oscillation, a virtual impedance control strategy is introduced, where the parameter selection of virtual impedance directly determines the control performance. Therefore, the grey wolf optimization algorithm is employed to optimize the virtual impedance parameters, achieving effective oscillation suppression and stable system operation.