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This paper proposes a novel control scheme to regulate the capacitor voltages in a multi modular converter (MMC) topology which is suitable for HVDC transmission systems. The scheme is based on the use of the active positive sequence current component, to maintain balance between the AC-side and DC-side powers, and the active and reactive negative sequence components, to exchange energy from the capacitors of one phase to those of another phase. The latter equalizes the stored energy amongst the valves and it is useful during asymmetrical AC system faults, or during fast system disturbances, which generally charge/discharge capacitors of each valve in a very different way. Performance of the proposed controller is tested on an example HVDC system which comprises an MMC inverter and an MMC rectifier station connected via a DC-link cable. The MMC topology considered is a standard three-phase bridge and uses H-bridge modules to implement converter valves. Compared to the standard MMC, which uses half-bridge modules, the H-bridge MMC offers the capability to ride-through DC system faults. Proposals are verified through detailed simulations of the example system under fault conditions. This includes: a three-phase to ground fault, a single-phase to ground fault and a pole-to-pole fault on the DC-link. Results confirm the converter capability to ride-though not only AC system faults but also DC system faults. However, system functionality is limited by the capacity of cell capacitors to store/deliver energy during the fault. Nevertheless, an H-bridge MMC HVDC terminal, even with a small storage capacity (20 ms at rated power), is still able to manage severe AC and DC system outages without assistance of auxiliary elements (e.g. break resistor, fault current limiter).