A new Energy Management Strategy to save hydrogen is proposed for the Hybrid Power Systems based on Renewable Energies Sources and Proton Exchange Membrane Fuel Cell system used as additional energy sources and backup energy source, respectively. The Power Following control of the Fuel Cell boost converter compensates the requested power on the DC bus in order to mitigate the DC power dynamics due to variability of load demand and uncertainty about available power from renewable sources. Also, two optimization loops based on the Global Extremum Seeking algorithm are used to find the global optimum of the optimization function by real-time control of both fueling rates. The Static Feed-Forward strategy with the same Power Following control is implemented and used as reference in order to compare the hydrogen savings considering the same scenarios for the DC power dynamics (variable or constant load, without or with power from renewable sources).