Dynamic modeling of modular multilevel converters

Theory for the dynamics of modular multilevel converters is developed in this paper. It is shown that the sum capacitor voltage in each arm often can be considered instead of the individual capacitor voltages, thereby significantly reducing the complexity of the system model. A selection of the so-called insertion indices, which compensates for the sum-capacitor-voltage ripples, is considered. The system which results for this selection is analyzed, and is shown to be asymptotically stable. Finally, explicit formulas for the steady-state sum-capacitor-voltage ripples are derived.