Commonly the control and safety equipment (PLCs etc) at the very least. Maybe a few lights.
A lot depends on how reliable your emergency generator is and what size it is.
It's often a bit of a fight between the safety team who want all sorts of things hanging off the UPS and the electrical team trying to keep it to a manageable size.
Basically just enough to allow the FPSO to shut down safely and then if all else fails go into a full power down with everything else vented / flared or shut off.
Loose bulk power you shutdown.
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