An energy storage device for storing energy for a stationary AC voltage grid includes a control device; and at least two switching units. Each switching unit includes multiple storage elements for storing a part of the energy, a converter having an AC voltage connection for connection to the AC voltage grid and a DC voltage connection, and a multiplexer switching device electrically connected with the DC voltage connection of the converter and with one of the storage elements via a respective storage connection. The multiplexer switching device is configured to select one of the storage connections in dependence on a selection signal generated by the control device and to electrically connect only the one storage connection selected by multiplexer switching device with the DC voltage connection of the converter. The control device is configured to control the converter of each of the at least two switching units so as to gradually reduce an energy flow between the AC voltage grid and a first one of the switching units and to correspondingly increase an energy flow between the DC voltage grid and at least one second one of the switching units until the energy flow between the AC voltage grid and the first switching unit is reduced to zero.