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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. Two selections of the so-called insertion indices, which both compensate for the sum-capacitor-voltage ripples, are considered. The dynamic systems which respectively result from these selections are analyzed. An effective dc-bus model, which takes into account the contribution from the submodule capacitors, is obtained. Finally, explicit formulas for the stationary sum-capacitor-voltage ripples are derived.
Harnefors et al. (Wed,) studied this question.