Modular Multilevel Converters (MMCs) have been popular in high voltage power conversion applications because they use a number of modules with relatively low voltage ratings to be cascaded to achieve high voltage operation. In HVDC transmission, for instance, a large number of modules are required to reach the desired operating voltage. Recent research has focused on using MMCs in medium voltage applications to interface renewable energy sources to the distribution grid at voltage levels of up to 35kV. Asymmetric voltages have been used with great success in conventional multilevel inverter topologies to lower the total device count, thereby resulting in a lower total system cost and complexity. MMCs with asymmetric voltages in a 2:1 ratio have been proposed but require complex voltage balancing schemes. Asymmetric multilevel inverters with other voltage ratios (such as 3:1) have been shown to have potentially lower device counts than topologies with 2:1 ratios. However, conventional modulation schemes do not scale to MMCs with 3:1 voltage ratios. This paper presents a generalized analytical model and control scheme for asymmetric MMCs using space-vectors. Capacitor voltages are balanced by a combination of common-mode and differential-mode offsets in the modulating signal. A scalable, level-shifted carrier based modulation scheme is used which eliminates recursive timing calculations. The proposed scheme is modeled in MATLAB/Simulink and the simulation results are presented.