中文摘要：

针对含有大规模子模块的模块化多电平换流器（modular multilevel converter, MMC）直流电容电压平衡问题，提出一种基于改进排序的电容电压平衡方法。基于传统排序电压平衡方法中的排序环节要求对桥臂内所有子模块电容电压进行排序，计算延时严重影响电压平衡控制的动态响应。以避免投入组和切除组组内元素排序为目的改进快速排序算法，每趟排序均选择第m个位置的记录作为基准值，通过判断使下一趟排序只在被划分后的一个区域上递归；采用数学归纳法证明改进快速排序算法的时间复杂度为O（n）。考虑MMC子模块电容电压连续两个控制周期变化规律后，提出采用改进的快速排序算法排序之前按照上个控制周期的排序结果排列电容电压能够进一步减少比较次数。最后，通过计算机随机实验验证改进快速排序算法的时间复杂度并搭建两端401电平MMC-HVDC仿真模型验证所提电压平衡方法的可行性和有效性。

英文摘要：

Aiming at the DC capacitor voltage balancing problem of a modular multilevel converter （MMC） with large-scale sub-modules, a novel balancing method based on modified sorting was proposed. The sorting link of the capacitor voltage balancing method based on traditional sorting required sorting all the capacitor voltages, whose computation delay seriously influenced the dynamic response of the voltage balancing control. The quick sort algorithm was modified by avoiding sorting the elements in on-group and off-group, selecting the record of the m-th position as the reference for each rank and with only one region for the next rank by judging. The time complexity of the modified quick sort algorithm was proved to be O（n） by mathematical induction. After considering the MMC sub-modules＇ capacitor voltages variation law in continuous two control cycle, it is presented that the comparison times can be further reduced if the capacitor voltages are arranged according to the results in the last control cycle. Finally, the time complexity of the modified quick sort algorithm is verified by the computer random experiment, and the 401 level MMC-HVDC simulation model is built to verify the feasibility and effectiveness of the proposed voltage balancing method.