A device balancing overall levels of electrical charge in plural blocks of cells in a battery. The blocks can be connected in a circuit during a charging phase of the cells accumulating charge, and during a discharging phase of the cells giving back charge. The device includes one series switch and one parallel switch. The series switch can, when closed and the parallel switch is open, connect a block to the circuit, in series with the other blocks, so that the block is connected during the charging and discharging phases. The parallel switch can, when closed and the series switch is open, disconnect the block from the circuit, so that the block is disconnected if discharging disconnection conditions are met during the discharging phase or if charging disconnection conditions are met during the charging phase. The block includes a mechanism locally balancing charge levels of its cells when disconnected.