The electric power grid is undergoing significant changes and updates nowadays, especially on a production and transmission level. Initially, the move towards a distributed generation in contrast to the existing centralized one implies a significant integration of renewable energy sources and electricity storage systems. In addition, environmental awareness and related concerns regarding pollutant emissions have given rise to a high interest in electrical mobility. Advanced power electronics interfacing systems are expected to play a key role in the development of such modern controllable and efficient large-scale grids and associated infrastructures. During the last decade, a global research and development interest has been stimulated in the field of modular multilevel conversion, due to the well-known offered advantages over conventional solutions in the medium- and high-voltage and power range. In the context of battery energy storage systems, the Modular Multilevel Converter (MMC) family exhibits an additional attractive feature, i.e., the capability of embedding such storage elements in a split manner, given the existence of several submodules operating at significantly lower voltages. This thesis deals with several technical challenges associated with Modular Multilevel Converters as well as their enhancement with battery energy storage elements. Initially, the accurate submodule capacitor voltage ripple estimation for a DC/AC MMC is derived analytically, avoiding any strong assumptions. This is beneficial for converter dimensioning purposes as well as for the implementation improvement of several control schemes, which have been proposed in the literature. The impact of unbalanced grid conditions on the operation and design of an MMC is then investigated, drawing important conclusions regarding the choice of line current control and required capacitive storage energy during grid faults. [...]