<p>The modular multilevel converter-battery energy storage system (MMC-BESS) is a converter system that has the potential to enhance grid stability. The conventional control methodology, which relies on carrier phase shift and double closed-loop techniques, is prone to a multitude of parameters and exhibits a relatively slow rate of state of charge (SOC) equalization. In light of the aforementioned considerations, this paper proposes an enhanced SOC equalization strategy based on reduced computational burden voltage level model predictive control (RCBVL-MPC). This strategy retains only two coefficients for interphase and intraphase SOC equalization, thereby markedly reducing the number of control parameters. Concurrently, the equivalent computational complexity of each phase is diminished from N + 4 to N/2 + 5 in the RCBVL-MPC component through a progressive optimization search methodology, thereby reducing the computational burden. In the SOC equalization section, a SOC equalization strategy combining fixed circulating current and fixed coefficients is put forth. This strategy employs the fixed circulating current method for equalization when the SOC difference is considerable, thereby enhancing the equalization velocity of interphase and intraphase SOCs. The interphase SOC equalization time is reduced by a minimum of 57%, and the bridge arm SOC equalization time is reduced by a minimum of 64.3%. Conversely, the fixed coefficients method is adopted when the SOC difference is minimal, thus guaranteeing a superior equalization precision. The efficacy of the proposed method is corroborated by both simulation and experimental results.</p>