In this paper the analytical solution for the submodule voltage ripple equations of a Modular Multilevel Converter (MMC) is derived, based on the knowledge of the external voltage/current magnitudes, and enhancing a concept previously presented in literature. In order to achieve high accuracy, all passive elements of the converter, common-mode voltage injection as well as intentionally imposed circulating current harmonics are taken into consideration. The natural charge level mechanism of the capacitor voltages is also explained. As application examples, the three- as well as the two-phase grid-connected Modular Multilevel Converter cases are chosen. The control of line and circulating currents is also discussed and two respective independent feedback loops are formed. The concept of Fictive-Axis Emulation (FAE) is tailored for the two-phase MMC case, in order to achieve vector control of the line current and therefore straightforward desired injection of active and reactive power. Finally, the development of a reduced-scale laboratory prototype is presented and a full set of experimental results are provided, verifying the aforementioned concepts.