Analytical Derivation of the AC-Side Input Admittance of a Modular Multilevel Converter With Open- and Closed-Loop Control Strategies

This paper deals with the derivation of the ac-side input admittance of a grid-connected modular multilevel converter (MMC) under both open- and closed-loop ac-side current control strategies. The contribution of the internal dynamics of the MMC on the input admittance depends on the type of ac-side controllers implemented. For this reason, the input admittance is first derived with the MMC operating in open loop on the ac side. The results are then modified to include various ac-side controllers in order to analyze the impact of the internal dynamics of the MMC on the total input admittance. Based on the findings, recommendations are given on modeling the input admittance of the MMC. Finally, the derived analytical models are verified using a detailed switching model of the MMC in the frequency domain.