The Modular Multilevel Converter is very likely to operate in a grid-connected mode under asymmetric conditions. Such a converter features several unique characteristics, which make its analysis different from other types of power converters in similar cases. The existence of three independent capacitive phase legs rather than a common DC-link capacitor requires special attention, in terms of stability and component dimensioning. This paper investigates the impact of unbalanced grid conditions on the operation of the Modular Multilevel Converter. The expressions for the branch energy variation are derived assuming that the grid-related quantities can be modeled by means of symmetrical components. Moreover, the effect of circulating current control for capacitive storage reduction as well as DC-link oscillation elimination is also studied. Finally, a control system is proposed and simulation results verify its discrete-time implementation.