The power generator was a device that can produce a type of power (electricity, plasma, etc.) for use in other devices. Some power generators can be portable, others can be quite large. They ran on various fuels (including dolamide). A primary generator was also called a main generator.
In 2268, Starfleet Intelligence agent Bridget McLellan had disabled a containment field at the Klingon research station on Zeta Aurigae IV by destroying the main power generator with her phaser. (VAN - Declassified novella: The Stars Look Down)