An electrical power supply system for an electrically powered motor vehicle, said vehicle including an electric motor, and a transmission device for transmitting energy between the drive wheels and the motor, said vehicle further including electrical accessories, in particular an air-conditioning device. Said system comprises a first rechargeable battery serving to power the electric motor and a second rechargeable battery serving to power the electrical accessories of the vehicle, the batteries being connected in parallel to the motor. The invention also relates to a method for controlling such a system.