A Method for the Calculation of the AC-Side Admittance of a Modular Multilevel Converter

Connecting a modular multilevel converter to an ac grid may cause stability issues, which can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. This paper presents a method for calculating the ac-side admittance of modular multilevel converters, analyzing the main frequency components of the converter variables individually. Starting from a time-averaged model of the converter, the proposed method performs a linearization in the frequency domain, which overcomes the inherent nonlinearities of the converter's internal dynamics and the phase-locked loop used in the control. The ac-side admittance obtained analytically is first validated by simulations against a nonlinear time-averaged model of the modular multilevel converter. The tradeoff posed by complexity of the method and the accuracy of the result is discussed, and the magnitude of the individual frequency components is shown. Finally, experiments on a down-scaled prototype are performed to validate this study and the simplification on which it is based.