The modular multilevel converter of the battery energy storage system (MMC-BESS) not only is suitable for the large-scale energy storage and dispatching of AC and DC grids, but also has a strong ability to suppress power fluctuations caused by the new energy output or grid failures. When an asymmetric voltage or a sudden change in DC load occurs in the AC grid, in order to compensate for the power difference between AC and DC sides, the energy storage submodule of the MMC-BESS will have a large unbalanced charging and discharging current, destroying the equalization state of SOC and seriously affecting energy storage capacity utilization and battery service life. In order to deal with the above problems, in this paper, the characteristics of the power difference between the MMC-BESS phase unit and the upper and lower bridge arms are analyzed. It is found that when considering the fluctuation of the submodule capacitor voltage, the phase unit power has the fundamental frequency AC circulating current component, and the power difference between the upper and lower bridge arms has the DC circulating current component. Therefore, the three-level SOC equalization correction control strategy is proposed based on interphase, upper and lower bridge arms, and submodules, and the feedforward sliding window integral method is introduced into the SOC equalization correction control layer of upper and lower bridge arms, so as to achieve the purpose of more balanced and accurate power distribution among phases and among upper and lower bridge arms of each phase. The simulation results show that the MMC-BESS has effective compensation ability when there is a large power difference in the AC and DC power grid. Under the unbalanced working conditions of the three-phase power grid, the three-phase AC current can quickly reach equalization, and the total harmonic content is 1.38%, and the unbalance degree is 2.4%. Under the same operating conditions, compared with the traditional optimal one-third average method, the SOC equalization correction control strategy proposed in this paper has smaller submodule capacitor voltage fluctuation rate, harmonic distortion rate, and three-phase system circulating current. And the SOC of each phase has a faster equalization convergence speed.