An AC-to-AC modular multilevel converter (MMC) is configured to be connected between a three-phase AC system and a single-phase AC system. The MMC includes a number of converter arms connected in a ring to allow a circulating current to be circulated in the ring through each of the converter arms. Each converter arm includes series-connected converter cells. Phase terminals are arranged in the ring between the converter arms such that each of the converter arms is separated from neighboring converter arms by at least one of the phase terminals. The phase terminals include respective terminals for each of a first phase, a second phase and a third phase of the three-phase AC system and respective terminals for each of a positive conductor and a negative conductor of the single-phase AC system.