On the Dynamics of Inherent Balancing of Modular Multilevel DC–AC–DC Converters

Modular multilevel dc-ac-dc converters (MMDACs) serve as an enabler for dc distribution systems. The modular structure enables flexible voltage transforms, but raises issues over balancing of the submodule (SM) capacitor voltages. This letter focuses on dynamics inherent MMDACs under circulant modulation. We provide invariance-like result using a variant Barbalat's Lemma and prove that SM voltages converge to kernel switching matrix, which is intersection invariant sets each state. further interpret permuted linear time-invariant system envelop trajectories governed by eigenvalues state-transition matrix. extends previous full-rank criterion in steady state provides new insight into dynamic behavior MMDACs.