This work deals with the development of an economic supervisory predictive control method for the management of a hybrid renewable energy system. The hybrid cell integrates solar panels, a gas microturbine and a storage unit. Tuning the predictive controller is easy: the optimal criterion encom- passes the environmental, fuel, energy delivery and storage costs. Short time predictions of the solar power are embedded in the supervisor which yields smoother battery control and better power management. Real-time experiments are driven in a Hardware-in-the-Loop framework illustrating the relevance of the proposed supervisory predictive control design.