Modular multilevel converters (MMCs) have the advantages of high-power density and small-harmonic distortion because of their modularity and flexibility, thus providing a new avenue for research into scalable superconducting magnetic energy storage (SMES) in renewable energy generation. This study presents coordinated control for a three-phase four-wire (3P4W) MMC-based SMES system under unbalanced voltage applications. First, the positive- and negative-sequence mathematical models and the port-controlled Hamiltonian with dissipation model of the 3P4W MMC-SMES system are established by introducing an additional path for zero-sequence current. Second, a multi-objective passivity-based control strategy that can effectively improve the power quality and system robustness and eliminate both double-frequency active and reactive power fluctuations or double-frequency active power fluctuation and negative-sequence current is proposed. The simulation results based on MATLAB/Simulink demonstrate the effectiveness of the proposed topology of the SMES and its control strategy.