The global development of high-voltage direct-current (HVDC) systems in fields such as renewable energy sources, interconnection of asynchronous grids or power transmission over great distances, is unquestionably important. Though widely used, the modular multilevel converter with half-bridge cells is sensitive to DC pole-to-pole faults and the time-response of the protections is critical. Reliability and availability are paramount: circuit-breakers must minimize the effects of any fault on the converter, while ensuring rapid restart. This paper focuses on the modelling aspects to analyse the behaviour of HVDC stations during DC pole-to-pole faults, using either AC or DC circuit-breakers, with different parameters. The proposed model can represent the main issues met by the converter cells during DC faults, such as semiconductor overcurrents and overvoltages, allowing a proper design of the cells.