A Modular Multilevel Converter With Self-Voltage Balancing Part I: Mathematical Proof

The modular feature of the modular multilevel converter (MMC) distinguishes itself from other topologies for medium-/high-voltage applications. However, as the count of submodules increases, the control complexity of voltage balancing for each submodule sharply increases. Conventionally, the MMC is deemed to have no inherit voltage balancing property without voltage monitoring and control. This paper mathematically proves that MMC capacitor voltage is self-balanced by nature if considering certain submodule patterns. This implies that MMC could achieve the submodule capacitor voltage balancing without any monitoring or control. The mathematical proof starts from observing the two- and three-level MMCs. Mathematically, two- and three-level MMCs are proved to be self-balanced. Then, a similar observation is extended to N-level MMC. And N-level MMC is proven to be self-balanced mathematically. The modulation which utilizes this MMC merit and secures the self-voltage balancing for MMC will be fully explained in Part II.