Electricity access in developing countries, where the availability of public distribution grids is still poor, is considered a key factor for improvement of people life conditions. In these situations, the lack of a reliable grid can be mitigated by the introduction of stand-alone DC microgrids, including small Photovoltaic (PV) generators and storage devices. This paper focuses on optimal energy management and power supply reliability of such a microgrid. In particular, a Model-Predictive-Control (MPC) - based control system is introduced to optimally manage storage devices and coordinate load shedding actions. Additionally, an Artificial-Neural-Network (ANN) - based predictor is introduced to manage unpredictable solar irradiance and temperature variations. The availability of reliable adaptive forecasts provided by the ANN-based predictor increases the efficiency of the optimization performed by the MPC-based control over the prediction horizon, avoiding the well-known issues related to optimization performed on unreliable forecast. In this paper, the proposed control approach is detailed for a specific case study and its advantages with respect to traditional controller algorithms are highlighted by comprehensive numerical simulations. The presented results highlight that the proposed MPC controller provides a substantial increment in power supply reliability with respect to standard controls, especially for priority loads. This is obtained at the expense of an increased battery stress, which is acceptable for electricity access applications where power supply reliability is usually the foremost need.