In a battery energy storage system (BESS) based on the cascaded H-bridge (CHB) converter or modular multilevel converter (MMC), the active power distribution among the submodules (SMs) can be highly unbalanced, especially when batteries with different power ratings are used. Meanwhile, there are certain limits for the unbalanced power distribution among the SMs. It is a challenge to determine whether the active power distribution is viable for cascaded multilevel converters with unequal capacitor voltages because the complexity grows exponentially as the number of SMs increases. This paper proposes a generalized analytic solution to this problem, which reduces the complexity significantly and is readily applicable to converters with large number of SMs. The validity of this method is proved theoretically and verified with simulation and experimental results on both the MMC and CHB converter.