On DC-side impedance frequency characteristics analysis and DC voltage ripple prediction under unbalanced conditions for MMC-HVDC system based on maximum modulation index

In this study, we first briefly introduce the effect of circulating current control on the modulation signal of a modular multilevel converter (MMC). The maximum modulation index is also theoretically derived. According to the optimal modulation index analysis and the model in the continuous domain, different DC-side output impedance equivalent models of MMC with/without compensating component are derived. The DC-side impedance of MMC inverter station can be regarded as a series xR + yL + zC branch in both cases. The compensating component of the maximum modulation index is also related to the DC equivalent impedance with circulating current control. The frequency characteristic of impedance for MMC, which is observed from its DC side, is analyzed. Finally, this study investigates the prediction of the DC voltage ripple transfer between two-terminal MMC high-voltage direct current systems under unbalanced conditions. The rationality and accuracy of the impedance model are verified through MATLAB/Simulink simulations and experimental results.