At just after 8.30pm last night (Thursday, March 1) firefighters from East and West Sussex tackled the blaze, which broke out in an auxiliary building at the site which is not used to generate electricity.
Scottish Power, which manages the site, said power supplies would not be affected by the fire.
A small number of workers were on site when the fire started, but there were no reports of any injuries.
Firefighters wearing breathing apparatus used a firefighting system in the building, which put out most of the fire.
Six fire engines and an aerial ladder platform were sent to the fire, plus support vehicles.
Firefighters left the scene at 3.45am.
Sussex Police provided an overview of the fire with footage taken from the south east air support unit helicopter hotel 900.
A cordon was set up around the site for public safety but there was no need for nearby homes to be evacuated.
The cause of the fire is under investigation.