Due to a dramatic increase in grid-connected renewable energy resources, energy storage systems are interesting and important for future power systems, among which the modular multilevel converter (MMC)-based battery energy storage systems (BESSs) are one of the most modular, efficient, and flexible topologies. Uneven active power distribution among submodules (SMs) in the arms of an MMC-based BESS is necessary for certain applications. The main contribution of this article is to present a general analysis of the inter-SM active power disparity problem which incorporates the inherent operational constraints of the MMC converter. An analytical method to derive inter-SM active power disparity limits is introduced. The proposed analysis can help facilitate the design of MMC-based BESS for applications such as recycled batteries and hybrid battery chemistries, which can both require significant inter-SM active power disparity. The analysis formulates a criteria vector and criterion value that describes whether an MMC-based BESS is capable of supplying demanded output powers while subject to inter-SM active power disparity. Simulation and experimental results are obtained on a single-phase system with varying numbers of SMs per arm, which verifies the feasibility and generality of the proposed analytical method.