Various topologies of the Direct Current (DC) microgrid have been proposed in the literature by considering practical requirements. One of the important criteria in topology selection is the availability of a well-functioning protection scheme. A significant part of the DC microgrid protection system literature considers differential protection schemes for various topologies. However this scheme doesn’t work satisfactorily with noisy measurements. Noisy measurements are a reality and can not be avoided for any real engineering system. This article proposes a robust protection scheme to alleviate some problems associated with topology selection. The proposed scheme considers noisy current measurements and works by estimating the time derivative of line currents. The proposed approach uses continuous finite-time convergent differentiator to estimate the derivative. The gains of the differentiator were tuned through Firefly algorithm-based optimization technique. Matlab/Simulink ®-based simulations verified the effectiveness of the proposed approach over the existing differential current scheme.