The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium-voltage distribution systems. Inherent balance of submodule (SM) capacitor voltages is considered as an ideal property, which avoids a complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This article extends the inherent balance concept previously shown for square-wave modulation to a multilevel version for MMDCs. A switching duty matrix d_U is introduced: it is a circulant matrix of preset multilevel switching patterns with multiple stages and multiple durations. Inherent voltage balance is ensured with a full-rank d_U . Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A nonfull rank d_U causes clusters of SM voltage rather than a single common value, with the clusters indicated by the kernel of the matrix. A generalized coprime criterion is developed into several deductions that serve as practical guidance for design of multilevel circulant modulation. The theoretical development is verified through full-scale simulations and downscaled experiments. The effectiveness of the proposed circulant modulation in achieving SM voltage balance in an MMDC is demonstrated.

中文翻译：

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模块化多电平 DC-DC 转换器中多电平循环调制的固有 SM 电压平衡

模块化多电平直流转换器 (MMDC) 的模块化使其对中压配电系统具有吸引力。子模块 (SM) 电容器电压的固有平衡被认为是一种理想的特性，它避免了基于许多测量的复杂分类过程，从而降低了成本并提高了可靠性。本文将之前针对方波调制显示的固有平衡概念扩展到用于 MMDC 的多级版本。开关占空比矩阵d _U被引入：它是一个预置的多级和多持续时间的多级切换模式的循环矩阵。全等级确保固有电压平衡d _ü 。循环矩阵理论表明，这相当于一个简化的公因子准则。非满级d _U导致 SM 电压的簇而不是单个公共值，簇由矩阵的内核指示。一个广义的互质标准被发展成几个推论，作为多级循环调制设计的实际指导。理论发展通过全尺寸模拟和缩小实验得到验证。证明了所提出的循环调制在实现 MMDC 中的 SM 电压平衡方面的有效性。