NOVELTY - The system (3) has a rechargeable supplying device i.e. motor supplying battery (31), for electrically supplying an electrical motor, and an energy recharging device i.e. supercapacitor (32), charged by an external power source (2) e.g. recharge station, and for recharging the rechargeable supplying device. The supercapacitor has charge power load higher than charge power of the rechargeable supplying device, and is connected to the electrical motor supplying battery by a direct current/direct current converter (33).    USE - System for storing electrical energy in a battery supplying recharging system to supply an electrical motor of a motor vehicle e.g. electric motor vehicle and hybrid motor vehicle (all claimed).    ADVANTAGE - The battery supplies the energy to the electrical motor of the motor vehicle, and is recharged by the supercapacitor with limited storage energy for supporting very high recharge power, thus rapidly recharging the supercapacitor to transfer the electrical energy to the motor vehicle, even when the motor vehicle is in a running state. The system limits immobilization time of the vehicle by rapid recharging of the supercapacitor, and avoids polluting the availability of the vehicle. The system maintains the charge of the battery in urban areas to facilitate the battery management for the driver, and reduces the complete charging time of the battery with the completely immobilized vehicle.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for the following:    (1) a battery supplying recharging system comprising an external electric supply source    (2) a method for storing electrical energy to supply an electrical motor of a motor vehicle.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of a battery recharging system for a electric or hybrid motor vehicle.'(Drawing includes non-English language text)'    External power source (2)    Electrical energy storing system (3)    Motor supplying battery (31)    Supercapacitor (32)    Direct current/direct current converter (33)    Connection unit (34)