This paper presents a detailed theoretical analysis and performance assessment of the capacitor voltage balancing strategies for staircase modulated modular multilevel converters (MMC) in terms of the algorithm structures, voltage balancing effect, and switching frequency. A constant-frequency redundancy selection (CFRS) method with minimal switching loss is proposed and the function realization of specific modules of the algorithm is given. This method is simple and efficient in both switching frequency and regulation capacity. Laboratory results show very good agreement with the theoretical analysis and numerical simulations.