A battery module including a plurality of battery cells and a cell balancing system having a respective battery cell monitoring module attached to each battery cell and a module carrier having second connection means for connection of a positive terminal of the battery cell to a negative terminal of an adjacent battery cell and for an electrical connection of a negative terminal of the battery cell to a positive terminal of another adjacent battery cell. The battery cell monitoring modules are connected to one another by a balancing bus for transmitting data and electrical current. The electronic battery cell monitoring modules are connected to the positive and negative terminals of the battery cell. The module carrier has two electrical lines and an energy storage module for storing electrical energy. The energy storage module is connected to the two electrical lines to take up or output electrical energy over them.