In operation of the modular multilevel converter (MMC)-based battery energy storage system (BESS), different submodules (SMs) may be required to provide a different amount of active power, which is defined as inter-SM active power disparity in this paper. This happens in various conditions, for example, when some SMs have faulty batteries and thus, cannot process any active power. This paper proposes a general analysis of the inter-SM active power disparity limits of the modular multilevel converter-based battery energy storage systems. An analytical method is provided to derive the maximum/minimum power that any subset of SMs in one arm can provide. Based on the derived results, the active power limits of SMs are nonlinear with the number of SMs. Both simulation and experimental results are provided, which verify the proposed analysis and method. The proposed analysis facilitates the design and operation of the MMC-based BESSs.