It was considered in this work the connection of a photovoltaics (PV) solar plant to the main grid through a Direct Current (DC) MicroGrid and a hybrid storage system, composed of a battery and a supercapacitor, in order to satisfy constraints of grid connection (the so-called Grid-Codes). The objective, and main contribution of this paper, is to stabilize the DC MicroGrid voltage in spite of large variations in production and consumption, using a nonlinear hierarchical easy-to-implement control strategy. Here it is presented the MicroGrid's control design based on detailed models of the photovoltaic energy sources and the storage systems. Such DC grids may present an unstable behavior created by the PV's intermittent output power, by switching ripples from the power converters and their power electronics, and oscillatory currents produced by some types of loads. Therefore the system is subject to both fast and slow variations, and its stabilization is based on different technologies of storage, such as battery and supercapacitor, and control algorithms designed thanks to the use of time-scale separation between different components of the storage systems. The obtained nonlinear results are stronger than current linear controllers, allowing to keep operating margins around the voltage reference. At the same time in this work, insights from power systems practice have been used, aiming to obtain a very simple and easy-to-implement control scheme. Detailed simulation results are provided to illustrate the behavior and effectiveness of the proposed stabilization technique.