The dc impedance model of a modular multilevel converter (MMC) is the basis for analyzing harmonic resonances of MMC-based dc systems. As an MMC typifies a multiple harmonic response system, its internal dynamics and controls significantly influence its external characteristics. In this paper, a dc impedance model of an MMC is developed by harmonic transfer function method that considers the internal dynamics and typical controls of MMCs. The internal dynamics mainly include capacitor voltage fluctuation and multi-harmonic response characteristics, while typical controls consist of dc voltage control, positive-negative sequence separation-based phase current control, circulating current control, and some other linear controls. As a result, the proposed impedance model can be used not only to analyze the harmonic stability of an MMC-based dc system, but also to investigate the influence of additional controls in an MMC on system stability. Furthermore, the proposed model makes up for the deficiencies in harmonic stability analysis of MMC-based dc systems. The results of both the hardware-in-the-loop RT-LAB digital simulation and the physical experimentation validate the proposed impedance models and analyses.
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Ji et al. (2019) studied this question.
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