With the increasing penetration of renewables, low voltage (LV) distribution networks face rising demands to accommodate an increasing range of renewable energies. Low voltage direct current (LVDC) distribution networks are considered as a viable approach to alleviate the strain on existing distribution networks. Nonetheless, establishing reliable and selective protection solutions is recognized as crucial challenges to facilitate the wide adoption of LVDC. Several existing protection algorithms focus on significant fault currents, fixed threshold settings, and high sampling frequency to establish effective coordination. However, these approaches are either constrained in low fault current scenarios or require expensive data acquisition techniques. To address such issues, this paper develops a novel self-adjusting based protection scheme. The method only utilizes the inherent post-transient voltage derivative (PTVD) sign and value with a self-adjusting mechanism to distinguish faults. The proposed method overcomes the selectivity limitations of existing voltage-based solutions when a lower sampling frequency is employed. The effectiveness is validated on an LVDC test network constructed in PSCAD/EMTDC and an RT-Box-based hardware test bed. Results under injected noise signals further demonstrate the robustness of the proposed method.