Eigenvalue Optimization of the Energy-Balancing Feedback for Modular Multilevel Converters

Research output: Contribution to journalResearch articleContributedpeer-review



Despite its potential impact on the balancing performance, current literature on the modular multilevel converter (MMC) energy-balancing feedback gain design and tuning process seem incomplete. In order to close this research gap, the energy-balancing feedback gain tuning of an ac current controlled MMC with half-bridge cells and isolated star point is considered in this paper. The tuning is difficult, because each energy error adds its own dedicated component to the circulating current reference that leads to a strong coupling that evades common tuning approaches. This problem is solved in two steps: at first, the relevant error dynamics is extracted and validated to model the time domain behavior of the energy balancing. Second, a theorem from Wu (1975) is invoked to easily calculate the closed-loop eigenvalues that finally allow for an easy optimization of the energy-balancing performance. Despite the radical simplifications during the modeling and error dynamics extraction, the acquired model is able to adequately reproduce the energy errors and the balancing circulating current of the converter. Simulation and measurement results on a grid-side MMC demonstrate a considerable performance improvement in contrast to the traditional gain estimation on the open loop. This is verified with and without a second harmonic in the circulating currents.


Original languageEnglish
Article number8648292
Pages (from-to)11482-11495
Number of pages14
JournalIEEE transactions on power electronics
Issue number11
Publication statusPublished - Nov 2019


ASJC Scopus subject areas


  • Control systems, energy balancing, modeling, modular multilevel converter (MMC)