Grid faults are common in power systems and can have a severe impact on the operation of the converters in the system. In this paper, the operation of a Modular Multilevel Converter (MMC)-based Static Synchronous Compensators (STATCOM) is investigated during grid faults. The study focuses on the challenging internal control of the converter to allow the independent control of the energy levels of each arm, with the goal to maintain internal balancing of the MMC during contingencies. Extensive experimental results highlight the need for a sophisticated internal control. Moreover, the experimental analysis verifies that, by using the proposed control structure, the MMC can effectively ride through a fault on the AC side without tripping, while injecting the necessary positive and negative sequence reactive current levels according to the most recent grid codes.