The high harmonic content and fluctuation of electrical parameters of a modular multilevel converter- distributed energy storage (MMC-DES) system affect the life of the battery, and endanger the safe and stable operation of MMC-DES. To reflect the operating rules of the system directly and analyze the factors affecting the fluctuation of the capacitor voltage and battery current, a time-domain analytical model of MMC-DES based on modal division is established. The switching function, average value method and component volt-ampere characteristics are combined to write and derive the analytical expression in the time domain by coupling different working states and modes of sub-modules. By analyzing the temporal analytical expression of the explicit function, the fluctuation characteristics and influencing factors of the electrical parameters in the sub-module are reflected. Finally, comparisons between theoretical calculation and simulation obtained from PSCAD/EMTDC show that the proposed mathematical model of MMC-DES has an acceptable calculation accuracy, and verifies the relationship between the fluctuation of capacitor voltage and battery current and capacitance value, energy storage inductance value, amplitude and phase angle of circulating current, battery charge/discharge power, modulation ratio and other parameters. This work is supported by the Beijing Municipal Natural Science Foundation (No. 32220259).