An electrical power supply system for an electric vehicle, such as a rail vehicle, including: a fuel cell, an electric battery, a first power conversion element, a second power conversion element and a transformer, wherein an input of the first power conversion element is configured to receive a charge current or to deliver a traction current, characterized in that the transformer includes a primary winding, a first secondary winding and a second secondary winding, the primary winding being connected to an output of the first power conversion element and the secondary windings (12, 14) being connected to an input of the second power conversion element, and in that the battery is connected to the terminals of an output of the second power conversion element, and in that the fuel cell is connected in series with an inductance at a midpoint of the transformer between the first secondary winding and the second secondary winding, the electrical power supply system further including a diode connected in series with the inductance in a branch of the second conversion element, said diode preventing the current from circulating toward the fuel cell; and in that the second power conversion element is a bridge converter including a first transistor connected to a first arm of the second power conversion element between the first secondary winding and a common ground, and a second transistor connected to a second arm of the second power conversion element between the second secondary winding and the common ground, the inductance being configured to accumulate energy supplied by the fuel cell when the first and second transistors (S2, S4) are both in their closed state, and in that the electrical power supply system comprises a control device configured to control the electrical power supply system so as to operate at least in a first operating mode in which the battery is electrically charged from an electric voltage applied at the input of the first power conversion element, or in a second operating mode in which the battery is recharged by the fuel cell, the control device being configured to simultaneously switch the first and second transistors into the second operating mode so that the latter act as voltage step up clipper at the output of the fuel cell. wherein an input of the first power conversion element is configured to receive a charge current or to deliver a traction current, characterized in that the transformer includes a primary winding, a first secondary winding and a second secondary winding, the primary winding being connected to an output of the first power conversion element and the secondary windings (12, 14) being connected to an input of the second power conversion element, and in that the battery is connected to the terminals of an output of the second power conversion element, and in that the fuel cell is connected in series with an inductance at a midpoint of the transformer between the first secondary winding and the second secondary winding, the electrical power supply system further including a diode connected in series with the inductance in a branch of the second conversion element, said diode preventing the current from circulating toward the fuel cell; and in that the second power conversion element is a bridge converter including a first transistor connected to a first arm of the second power conversion element between the first secondary winding and a common ground, and a second transistor connected to a second arm of the second power conversion element between the second secondary winding and the common ground, the inductance being configured to accumulate energy supplied by the fuel cell when the first and second transistors (S2, S4) are both in their closed state, and in that the electrical power supply system comprises a control device configured to control the electrical power supply system so as to operate at least in a first operating mode in which the battery is electrically charged from an electric voltage applied at the input of the first power conversion element, or in a second operating mode in which the battery is recharged by the fuel cell, the control device being configured to simultaneously switch the first and second transistors into the second operating mode so that the latter act as voltage step up clipper at the output of the fuel cell.