中文摘要：

子模块电容电压均衡控制策略是保证模块化多电平换流器（modular multilevel converter，MMC）正常运行的重要环节。对于每相桥臂含有大规模数量子模块的模块化多电平换流器高压直流输电（modular multilevel converter based high voltage direct current，MMC-HVDC）系统，减小排序复杂度对 MMC-HVDC 工程控制器设计难度以及硬件需求的降低具有重要意义。该文基于质因子分解法提出一种优化的混合排序法，通过引入希尔排序算法大幅度降低排序次数，从而降低仿真时间，降低了对系统硬件的要求。推导适用于MMC-HVDC系统的希尔排序步长的时间复杂度，给出基于混合排序法的排序次数计算公式，分析分组层数对系统降低频率的影响，得到分组层数与混合排序法优化效率成反比例关系的结论。最后在PSCAD/EMTDC中搭建两端401电平 MMC-HVDC 模型进行仿真，仿真结果验证了混合排序法及分组层数对优化效率影响的分析的有效性与正确性。

英文摘要：

Equalization of sub-module voltage is the important guarantee for the normal operation of the modular multilevel converter （MMC）. For the MMC based high voltage direct current （MMC-HVDC） with large amount of submodules per arm, it is of great significance to cut down the complexity of sorting process for the reduction of the design of controllers and hardware requirement of MMC-HVDC projects. An optimized mixed sorting method was presented based on the prime factorization method, the sort number was substantially reduced owing to the introduction of Shell sorting algorithm. Thus the sort time and the requirement for the hardware of the system are reduced. Time complexity of the Shell algorithm applied to the MMC-HVDC was deduced and the calculation formula was proposed for the sort number of the mixed sorting algorithm. Impacts on the reduction of the frequency by the grouping layers were analyzed. Conclusion that the optimizing efficiency of the mixed sorting method is in inversely-proportional relationship with the grouping layers is acquired. Finally, simulation was carried out based on the 401-level two-terminal MMC-HVDC system in PSCAD/EMTDC. The efficiency and correctness of the mixed sorting method and the impact of the grouping layers on the optimizing efficiency are proved.