A device (10) for the electric power supply of a load (11), includes at least two energy storage elements (13, 14), elements for determining the power needs of the load (11), elements (16, 17) for monitoring each energy storage element (13, 14), which are able to provide information about a maximum instantaneous power of each energy storage element (13, 14), a calculation body (19) for determining a maximum secured power according to the electromotive force (Ebat(t)) and the resistance (Rbat(t)) of the Thévenin model, a maximum specified current and a maximum specified voltage, and elements (Cbat(t), Csc(t)) for controlling each energy storage element (13, 14), the elements being adjusted over time according to the power needs of the load (11) and the maximum secured power of each energy storage element (13, 14).