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This work aims to investigate the behaviour of an electric arc for passive resonance HVDC circuit breakers. DC circuit breakers are needed to protect future HVDC grids by selectively clearing DC fault currents. This minimises fault impact, assuring the correct operation of the rest of the HVDC grid. Due to lack of current zero-crossings compared to AC grids, DC circuit breakers need to create artificial current zero-crossings. The switching arc of a gas-insulated circuit breaker interacts with a resonant circuit, creating an oscillating current superimposed on the fault current, consequently causing current zero-crossings. Different arc models, including Cassie-Mayr and TP KEMA, are implemented to simulate switching arc behaviour. Subsequently a DC circuit breaker is modelled, using different arc models, to analyse the influence of the resonant circuit parameters. Cassie-Mayr model leads to a decaying resonant current without zero-crossings, because of a preset constant arc voltage as model parameter. While a DC circuit breaker model using KEMA or TP KEMA arc model, simulates current zero-crossings. A larger capacitance and a smaller inductance in the resonant circuit cause quicker current zero-crossings, resulting in a shorter time to interruption. Furthermore, the influence of the TP KEMA model parameters on the arc-circuit resonance is analysed. A larger cooling parameter P results in shorter time to current zero-crossings. A smaller time constant T benefits the interruption capability. The rate of change of the arc current in a DC circuit breaker is large because of the superimposed high frequency resonant current. This makes current interruption more challenging. Vacuum circuit breakers have a high dielectric recovery strength. Therefore, a composite DC circuit breaker topology is investigated, combining a gas-insulated and a vacuum circuit breaker model in series. The vacuum circuit breaker enhances the interruption capability at current zero-crossing, while leaving the time to current zero-crossing almost unaffected.