Impedance modeling of modular multilevel converters

The impedance modeling of modular multilevel converters (MMCs) is a prerequisite for applying the impedance-based stability analysis method to an MMC-based high-voltage direct current (MMC-HVDC) transmission system. The objective of this paper is to develop impedance models of a three-phase MMC in order to assess its stability. The analytical ac-side and dc-side impedance models of the three-phase MMC with and without circulating current control (CCC) are derived separately with consideration of the MMC internal dynamics. In doing that, a control strategy for the MMC in an application of wind power integration through MMC-HVDC is taken into consideration when calculating the ac-side impedances. The analytical impedance models derived for the MMC are verified by the method based on injecting a small-signal perturbation in the detailed nonlinear time-domain simulation model of the MMC.