Sequence Impedance Modeling of Modular Multilevel Converters

This paper presents the development of sequence impedance models for modular multilevel converters (MMC). The intended applications of the models include stability and resonance analysis of high-voltage dc transmission, static synchronous compensation, and other systems that use MMC. The basis of the modeling method is harmonic linearization that has been applied to other types of converters, but a new formulation is presented to allow the inclusion of harmonic effects. This generalization, called multiharmonic linearization, is necessary for MMC because of the significant second harmonics present in the arm currents, capacitor voltages, and control signals. To accommodate multiple harmonics in the linearization process, a matrix formulation is introduced and used to model both the converter power stage and its control. The developed sequence impedance models are validated by point-by-point simulation of detailed converter circuit models, and used to understand the effects of harmonics and control on MMC frequency-domain characteristics.