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The grid-connected modular multilevel converter (MMC) is very likely to operate under asymmetric grid conditions. Such a converter features several unique characteristics, which make its analysis different from other types of power converters in similar cases. In this paper, the three well-established control techniques, i.e., balanced current and negative sequence current injection for active/reactive power oscillation elimination, are tailored for the MMC case taking into account grid current limitation under fault conditions. Since the focus is laid on the MMC design impact during grid asymmetries, the three methods are compared in terms of branch energy variation increase as well as maximum achievable active power transfer. Moreover, the effect of circulating current second-order harmonic injection for capacitive storage reduction as well as dc-link oscillation elimination is also studied. Finally, experimental results from a downscaled laboratory prototype verify the theoretical studies. [ABSTRACT FROM PUBLISHER]