DC MicroGrids with the integration of renewable energy sources (renewables) and energy storage systems can improve the performance of power systems, ensuring safe operation of a local network, where the MicroGrid control is responsible to assure stability and power quality of the system. This paper proposes a distributed nonlinear control strategy for a DC MicroGrid composed of a PV, a battery storage and a supercapacitor to properly supply a local AC load, where a complete stability analysis in conducted using Lyapunov techniques. The MicroGrid is connected to an AC grid by a VSC converter, which injects the right amount of active and reactive power according to the AC load demand. The supercapacitor's duty is to control DC bus voltage dealing with transient stability while the battery fulfills long term power flow, where the energy is controlled to assure power flow balance, ensuring proper operation for the MicroGrid. Simulation results illustrate the performance of the proposed control and the system's operation.