Local-measurement-based algorithms are relevant as primary protection for high voltage direct current (HVdc) grids due to the restriction in operation speed. The communication time delay significantly affects communication-based algorithms, therefore, they are mostly implemented as backup protection or for high-resistance fault detection. This article proposes a local derivative-based protection scheme for HVdc grids. Primary protection is based on the voltage derivative. Conversely, the backup and busbar protections are based on the current derivative. The proposed system is evaluated against low- and high-resistance fault case scenarios via simulation in PSCAD software. The voltage derivative-based algorithm provides a fast and accurate primary protection. On the other hand, the current derivative-based algorithm is implemented to operate when a failure is produced in the primary protection. The parallel operation of these two algorithms saves time when it comes to backup operation after primary protection's failure. Likewise, the busbar protection operates rapidly and selectively. Influence of the limiting inductor's size, sampling frequency, fault resistance, and noise disturbance on the performance of the proposed protection scheme are also analyzed. The presented protection scheme is capable of rapidly and selectively detecting faults up to 200 omega while covering primary, backup and busbar protections. Moreover, only common local derivative-based algorithms are employed in addition to typical limiting inductor's sizes and relatively low sampling frequencies.