Method for supplying energy in a local energy supply network, in particular after a power outage, wherein the local energy supply network can be connected to a higher-level energy supply network via a connection point and connects a plurality of participants (6a, 6b), in particular households, wherein at least one of the participants comprises an energy supply device with an inverter (10a, 10b) for feeding into the local energy supply network and the method comprises the following steps: i) Disconnecting the local energy supply network from the higher-level energy supply network using an electrical switch; ii) Disconnecting all participants (6a, 6b) from the local energy supply network with the help of further switches, which are located at the participants (6a, 6b); iii) Determining a master inverter and at least one slave inverter among the participants with an energy supply device if there are several participants with an energy supply device; otherwise, determining the inverter of the only participant with an energy supply device as the master inverter; iv) Connecting those participants comprising energy supply devices to the local energy supply network via the respective further switches, so that the master inverter and, if present, the at least one slave inverter can feed into the local energy supply network; v) output of an alternating voltage by the master inverter and, if present, the at least one slave inverter, the frequency (f), voltage amplitude and phase angle (φ) of the alternating voltage being predetermined by the master inverter; vi) determining the total electrical energy (E ges) and/or the total electrical power (P ges) available in the local energy supply network provided by the at least one energy supply device; vii) connecting at least one participant without an energy supply device to the local energy supply network after step v) as a function of at least the total energy (E ges) available, the total electrical power (P ges) available, the expected power consumption of the at least one participant without an energy supply device and/or the expected energy demand (Ee) of the at least one participant without an energy supply device; viii) Disconnecting participants (6a, 6b), in particular participants without an energy supply device, from the local energy supply network as required, so that the grid stability of the local energy supply network is maintained. i) Disconnecting the local energy supply network from the higher-level energy supply network using an electrical switch; ii) Disconnecting all participants (6a, 6b) from the local energy supply network with the help of further switches, which are located at the participants (6a, 6b); iii) Determining a master inverter and at least one slave inverter among the participants with an energy supply device if there are several participants with an energy supply device; otherwise, determining the inverter of the only participant with an energy supply device as the master inverter; iv) Connecting those participants comprising energy supply devices to the local energy supply network via the respective further switches, so that the master inverter and, if present, the at least one slave inverter can feed into the local energy supply network; v) output of an alternating voltage by the master inverter and, if present, the at least one slave inverter, the frequency (f), voltage amplitude and phase angle (φ) of the alternating voltage being predetermined by the master inverter; vi) determining the total electrical energy (E ges) and/or the total electrical power (P ges) available in the local energy supply network provided by the at least one energy supply device; vii) connecting at least one participant without an energy supply device to the local energy supply network after step v) as a function of at least the total energy (E ges) available, the total electrical power (P ges) available, the expected power consumption of the at least one participant without an energy supply device and/or the expected energy demand (Ee) of the at least one participant without an energy supply device; viii) Disconnecting participants (6a, 6b), in particular participants without an energy supply device, from the local energy supply network as required, so that the grid stability of the local energy supply network is maintained.