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 multilevel structure enables flexible voltage transforms, but raises issues over balancing of the submodule (SM) capacitor voltages. This letter focuses on the dynamics of inherent balancing...

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Bibliographic Details
Published in:IEEE transactions on power electronics 2021-01, Vol.36 (1), p.34-40
Main Authors: Xiang, Xin, Gu, Yunjie, Chen, Kaiwen, Astolfi, Alessandro, Green, Timothy C.
Format: Article
Language:English
Subjects:
Balancing
Barbalat's lemma
Capacitors
circulant modulation
Eigenvalues
Electric converters
inherent balancing
invariance principle
Modular structures
Modular systems
Modulation
Multilevel
permuted linear time-invariant (LTI) systems
Sorting
Steady-state
Switches
Switching
Time invariant systems
Trajectory
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Summary:Modular multilevel dc-ac-dc converters (MMDACs) serve as an enabler for dc distribution systems. The modular multilevel structure enables flexible voltage transforms, but raises issues over balancing of the submodule (SM) capacitor voltages. This letter focuses on the dynamics of inherent balancing of MMDACs under circulant modulation. We provide an invariance-like result using a variant of Barbalat's Lemma and prove that the SM capacitor voltages converge to the kernel of the circulant switching matrix, which is the intersection of the invariant sets for each switching state. We further interpret the balancing dynamics as a permuted linear time-invariant system and prove that the envelop of the balancing trajectories is governed by the eigenvalues of the permuted state-transition matrix. This result extends previous full-rank criterion for inherent balancing in a steady state and provides new insight into the dynamic behavior of MMDACs.
ISSN:0885-8993
1941-0107
DOI:10.1109/TPEL.2020.3001431