The high uncertainty associated with renewable power production limits renewable energy penetration in off-grid systems. Advanced control strategies allow for a more effective exploitation of non-dispatchable sources. This paper presents a two-layer predictive management strategy for an off-grid hybrid microgrid featuring controllable and non-controllable generation units and a storage system. The upper layer deals with the unit commitment, while the second layer regulates real-time operation, applying a response filter to smooth out genset load variation. The algorithm is tested on data from a real rural microgrid in Somalia, performing minute-by-minute simulations. Results are compared to the currently deployed management strategy and to a new improved heuristic algorithm. The two new methods attain a fuel consumption reduction with respect to the previous management system of about 15%. Finally, a new configuration for the Somalian microgrid is evaluated, in the two cases where the predictive or heuristic management strategies are adopted. The comparison of the two optimal solutions demonstrates that the adoption of the proposed predictive strategy leads to a 6.5% cut of the overall system cost, ensuring at the same time a 24.1% fuel consumption reduction with respect to the best heuristic solution and attaining a renewable penetration as high as 65.1%. (C) 2019 Elsevier Ltd. All rights reserved.