On the Roles and Interactions of the MMC Internal Energy Balancing Degrees of Freedom for Three-Wire Three-Phase Connections

This paper proposes a comprehensive analysis of the modular multilevel converter (MMC) focusing on the different arm applied voltage components, that this paper will refer as degrees of freedom (DOFs), which must be considered in order to perform the internal energy balancing of the converter. The analysis relies on the commonly used differential and additive reference frames. By means of a steady-state analysis, the different voltages components applied and currents components flowing through the converter are studied and an in-depth discussion of the roles of each DOF in the converter is presented. Furthermore, the mathematical expressions of the power exchanged between the AC/DC networks and within the converter, between the arms (vertical) and among phase-legs (horizontal), are derived considering all the DOFs of the MMC, revealing potential interactions among the differential and additive quantities. Finally, the theoretical analysis is validated through comparisons between the values obtained with the mathematical expressions and the simulation results assuming different case scenarios.