During the operation of a generator (10) in an electrical system (1), particularly in a stand-alone system, such as an onboard power supply system on a ship or an offshore platform, wherein the electrical system (1) comprises a first subsystem (2) having a first rated voltage (UN1) and at least one second subsystem (3) having a second rated voltage (UN2), wherein the first rated voltage (UN1) is higher than the second rated voltage (UN2), wherein the generator (10) has a field winding (11) which, in a normal mode of the generator (10), in which it supplies current to the first subsystem (2), has a first field current applied to it which matches the first rated voltage (UN1) of the first subsystem (2), and wherein the generator (10) comprises a cooling device (12) for cooling the field winding (11), the aim is to keep down-times or impairments in the electrical system (1) in the event of failure of the cooling device (12) as low as possible without the need for additional emergency power supply devices. The invention allows this by virtue of the generator (10) being switched, following failure of the cooling device (12), from the normal mode to an emergency mode, in which it supplies current to the second subsystem (3), wherein in the emergency mode the field winding (11) has a second field current applied to it which is lower than the first field current and which matches the second rated voltage (UN2) of the second subsystem (3).