Rechargeable electrical energy storage system comprising: • a plurality of rechargeable electrical energy storage devices (100 1 -100 n), arranged in parallel with one another, each rechargeable electrical energy storage device comprising: - a storage module comprising at least one rechargeable battery; - at least one controllable contactor, said main contactor, for connecting, or not, said storage module to an electrical circuit; - a bypass branch of said main contactor, said bypass branch comprising, connected in series: ▪ at least one controllable contactor, said secondary contactor, for closing or opening said bypass branch, and ▪ at least one diode conducting current only in the discharge direction of said storage module; and • a single control module for controlling the at least one main contactor, respectively the at least one secondary contactor, common to a plurality of, in particular to all of, the storage devices (100 1 -100 n); characterized in that the single control module is designed to perform: • first, within a first storage device, a shift of the discharge toward the bypass branch of said storage device, by controlling: - first the closure (or the holding in the closed position) of the secondary contactor, - then the opening of the at least one main contactor; • then switching of the discharge from said first storage device to a second storage device by controlling: - first the closure of the at least one main contactor (108 2) of the second storage device (100 2), - then the opening of the secondary contactor (112 1) of said first storage device (100 1). • a plurality of rechargeable electrical energy storage devices (100 1 -100 n), arranged in parallel with one another, each rechargeable electrical energy storage device comprising: - a storage module comprising at least one rechargeable battery; - at least one controllable contactor, said main contactor, for connecting, or not, said storage module to an electrical circuit; - a bypass branch of said main contactor, said bypass branch comprising, connected in series: ▪ at least one controllable contactor, said secondary contactor, for closing or opening said bypass branch, and ▪ at least one diode conducting current only in the discharge direction of said storage module; and - a storage module comprising at least one rechargeable battery; - at least one controllable contactor, said main contactor, for connecting, or not, said storage module to an electrical circuit; - a bypass branch of said main contactor, said bypass branch comprising, connected in series: ▪ at least one controllable contactor, said secondary contactor, for closing or opening said bypass branch, and ▪ at least one diode conducting current only in the discharge direction of said storage module; and ▪ at least one controllable contactor, said secondary contactor, for closing or opening said bypass branch, and ▪ at least one diode conducting current only in the discharge direction of said storage module; and • a single control module for controlling the at least one main contactor, respectively the at least one secondary contactor, common to a plurality of, in particular to all of, the storage devices (100 1 -100 n); • first, within a first storage device, a shift of the discharge toward the bypass branch of said storage device, by controlling: - first the closure (or the holding in the closed position) of the secondary contactor, - then the opening of the at least one main contactor; - first the closure (or the holding in the closed position) of the secondary contactor, - then the opening of the at least one main contactor; • then switching of the discharge from said first storage device to a second storage device by controlling: - first the closure of the at least one main contactor (108 2) of the second storage device (100 2), - then the opening of the secondary contactor (112 1) of said first storage device (100 1). - first the closure of the at least one main contactor (108 2) of the second storage device (100 2), - then the opening of the secondary contactor (112 1) of said first storage device (100 1).