The invention relates to an electrical energy storage device comprising a plurality of flat storage cells for storing and discharging electrical energy, having opposing flat current collectors, a plurality of frame elements for maintaining the storage cells, and a clamping means for clamping the cells with the frame elements into a stack. Each storage cell carries at least one measurement or sensor element for measuring at least one physical variable, to which at least one respective cable for transmitting the measurement data is fixed. The frame elements comprise first recesses for receiving the measurement or sensor elements and second recesses connected to the first recesses, the second recesses of the frame elements together forming at least one channel extending over the length of the device for receiving the cables.