MMC is an emerging topology which is able to handle high voltage and power ratings. Such converters are necessary for VSC-HVDC transmission system as it provides several advantages. Being a complex topology, several challenges are needed to be investigated. The purpose of this thesis is to analyze one of those challenges: unbalance conditions in the system which are created internally and during asymmetrical grid faults. Sorting and selection methods with variants: NLC, CTB and RSS has been explained and implemented. Unequal energy storage in the arms and phases of the converter is found to be an important consequence of unbalances in the system. Energy controllers are proposed in order to eliminate the unequal energy distribution among the converter. Since HVDC is required to remain connected during grid fault, an output current injection strategy under fault conditions is presented and simulated with the aim of complying with the grid codes. A systematic approach has been introduced for the effective reduction of the sum capacitor voltage ripple in an MMC application. Finally, a small prototype has been built and experimental results are presented.