An energy storage system, comprising one or more local energy storage systems (4, 41, 42, 43) with a respective local storage capacity and local output suitable for absorbing (En) and emitting (Ep) energy to connected power supply grids (5, 6, 61, 62, 63, 64), with the one or more local energy storage systems (4, 41, 42, 43) each being connected directly to a non-local power supply grid as a public power supply grid and also to one or more local power supply grids (6, 61, 62, 63, 64) as in-house power supply grids or a power supply grid within a house or building complex or power supply grids of a wind farm or solar power plant, the connection to the power supply grids (5, 6, 61, 62, 63, 64) being configured such that, simultaneously and independently of each other, the local and non-local power supply grids can be supplied with energy by the energy storage system, or energy can be absorbed from the power supply grids, and comprise at least one local control unit (41-1, 42-1, 43-1), which is intended at least for control of the respective energy storage system (41, 42, 43) for localised regulating and system tasks to improve a local power supply quality for the one or more respective local power supply grids (6, 61, 62, 63, 64), and the energy storage system further comprising a central control unit connected via a communication network to the respective local control units (41-1, 42-1, 43-1), which is intended for the control of the absorbing (En) and emission (Ep) of energy by the one or more local energy storage systems (4, 41, 42, 43) to the non-local power supply grid, with the central control unit being equipped for having at its disposal all available portions of the local storage capacities (LSKg) and of the local output (LLg) of the one or more energy storage systems (4, 41, 42, 43) for non-localised regulating and system tasks (NLRS), such as e.g. a provision of primary and secondary control power or support of a black start, a storage of output peaks, a reactive power compensation or an increase in transmission output in the non-local power supply grid, which have been submitted by the respective local control units (41-1, 42-1, 43-1) to the central control unit via the communication network as not needed for the localised regulating and system tasks, characterised in that the local energy storage system (4, 41, 42, 43) comprises a regulating unit (41-3, 42-3, 43-3) with a regulating box with a regulating element and separate disconnection switches for each of the connected power supply grids (5, 6), wherein the local control unit is connected to the regulating element via a data connection to submit configuration data according to a regulation function (KD-R) for control of energy flows, wherein the one or more local power supply grids (6, 61, 62, 63, 64) and the non-local power supply grid are connected to the regulating unit (41-3, 42-3, 43-3), wherein the regulating unit (41-3, 42-3, 43-3) is configured to regulate the energy flow between the connected power supply grids (5, 6, 61, 62, 63, 64) and the energy storage system (4, 41, 42, 43), wherein the regulating element, based on the configuration data of the regulating function (KD-R), controls the distribution of the energy flow incoming from the connection point to the connected power supply grids (5, 6) as energy flow for the local power supply grid and as energy flow (EFg) for the non-local power supply grid.