Abstract: When the grid voltage is unbalanced, power quality problems such as fluctuations in active and reactive power, grid current distortion, and DC bus voltage fluctuation easily occur on the AC side of the AC/DC hybrid distribution network with flexible multi-state switch (FMSS) under traditional voltage-current control strategies. Based on this, this paper first analyzes the topology and characteristics of voltage unbalance in the AC-DC hybrid distribution network with FMSS and proposes a multi-objective control strategy for FMSS based on supercapacitor energy storage. The method enables flexible switching of FMSS between different control objectives, such as output current balance and the constancy of active and reactive power, by adjusting the regulation coefficient D. The method also utilizes the supercapacitor storage on the DC side to control the FMSS. Concurrently, the DC-side supercapacitor energy storage system is used to absorb the unbalanced power and stabilize the DC bus voltage, thereby achieving multi-objective control of FMSS under grid voltage unbalance conditions. Finally, a hybrid AC-DC distribution network model with FMSS is constructed using MATLAB/Simulink simulation software and a hardware-in-the-loop experimental platform, which verifies the validity and feasibility of the proposed strategy and ensures the safe and reliable operation of the AC-DC interconnection system.