Impedance Modeling of Modular Multilevel Converter in D-Q and Modified Sequence Domains

Modular multilevel converters (MMCs) are characterized by the multiharmonic coupling interactions among internal dynamics. In this work, multiple $d$ - $q$ references and multiharmonic frames, which are developed through dynamic phasor and harmonic state space, are used to derive the generalized impedance models of MMC in the $d$ - $q$ and modified sequence domain, respectively. Although some previous studies have been devoted to revealing the equivalence of different impedance models, this article attempts to elaborate the relation of different multifrequency modeling approaches and provide a more comprehensive review of MMC impedance models. A rigorous comparison of modeling procedure, impedance response, and stability analysis result between different MMC models is conducted. It is demonstrated that the MMC impedance models in the two domains can be related by a generic linear transformation matrix. Furthermore, the stability analysis results given by the generalized Nyquist criterion are identical in these two domains. Application recommendations for different impedance models are given as well. The developed impedance models and their effectiveness for stability and resonance analysis are validated by a 501-level aggregated model in MATLAB/SIMULINK.