A power generator was a means of generating power on planets, starships, and other fixed installations, such as starbases. It provided power for shields, phasers, replicators, and other on-board devices.
While James T. Kirk and Spock were searching for a duplicate of Kirk in 2266, engineering aboard the USS Enterprise featured two large power generators. Kirk's double initially climbed atop one of the generators in an attempt to evade the two searchers, who walked around the units, which the duplicate soon moved off. (TOS: "The Enemy Within")
When Major Kira Nerys tried to confiscate a shipment of dolamide from a Valerian transport in 2369 for proof they wanted to ship it to the Cardassians for their weapons, Commander Benjamin Sisko refused. According to Sisko, dolamide was also used for power generators, reactors, and in short-range transports. (DS9: "Dramatis Personae")
To get the help of Captain Miller, Kathryn Janeway told him that she located the power generator which contributes to the Nazi facility and offered a plan to destroy it. (VOY: "The Killing Game, Part II")