A Direct Current (DC) microgrid is a concept derived from a smart grid integrating DC renewable sources. The DC microgrids have three particularities: (1) integration of different power sources and local loads through a DC link; (2) on-site power source generation; and (3) alternating loads (on-off state). This kind of arrangement achieves high efficiency, reliability and versatility characteristics. The key device in the development of the DC microgrid is the power electronic converter (PEC), since it allows an efficient energy conversion between power sources and loads. However, alternating loads with strictly-controlled PECs can provide negative impedance behavior to the microgrid, acting as constant power loads (CPLs), such that the overall closed-loop system becomes unstable. Traditional CPL compensation techniques rely on a damping increment by the adaptation of the source or load voltage level, adding external circuitry or by using some advanced control technique. However, none of them provide a simple and general solution for the CPL problem when abrupt changes in parameters and/or in alternating loads/sources occur. This paper proposes a mathematical modeling and a robust control for the basic PECs dealing with CPLs in continuous conduction mode. In particular, the case of the low voltage residential DC microgrid with CPLs is taken as a benchmark. The proposed controller can be easily tuned for the desired response even by the non-expert. Basic converters with voltage mode control are taken as a basis to show the feasibility of this analysis, and experimental tests on a 100-W testbed include abrupt parameter changes such as input voltage.