Modeling and Shaping of the DC-Side Admittance of a Modular Multilevel Converter under Closed-Loop Voltage Control

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this article, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation, which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model.