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HVDC grids demand the fast and reliable operation of the protection system. The failure of any protection element should initialize a backup protection almost immediately in order to assure the system's stability. This paper proposes a novel backup strategy that covers the failure of the primary protection including the malfunctioning of the HVDC circuit breaker. Only local voltage measurements are employed in the proposed backup protection and the voltage derivative is calculated at both sides of the limiting inductor. Consequently, the speed and reliability of the protection system are enhanced, since no communication channel is needed. This paper contains a thorough specification of the proposed protection strategy. This strategy is validated in a four-terminal HVDC grid with various fault case scenarios, including high-resistance fault cases. The operation of the backup protection is reliable and remarkably fast. [ABSTRACT FROM AUTHOR]