Flexible multi-state switch （FMSS） is a new type of power electronic device that replaces traditional tie switches and is applied to modern distribution networks. It can optimize the consumption and regulation of distributed power sources in modern distribution networks. The FMSS controlled by VSG is not affected by the deterioration of phase-locked loop performance in weak power grid environments，it can provide frequency support to the grid at low grid strength，thus enhancing the stability of the system. As a device connected to the distribution network，FMSS，when there is three-phase imbalance in the grid voltage，the output current of FMSS under traditional VSG control will become unstable，and the power will also fluctuate significantly，greatly reducing the efficiency of the grid connection point. To address this issue，based on the modular multilevel converter （MMC） structure and the traditional VSG control strategy，positive and negative sequence current compensation was introduced to achieve the stability of FMSS output current，active power，and reactive power under unbalanced power grids. Finally，a four terminal FMSS model was built using Matlab/Simulink，and the effectiveness of the proposed control strategy was verified through the simulation.