The Kelvan Empire was a significant power in the Andromeda Galaxy, including the Kelvan homeworld and acquired territories. The Kelvan ethos called for expansion through the conquest and control of 'inferior' species, rather than traditional colonization.
Kelvans predicted rising radiation levels in Andromeda would render their galaxy uninhabitable to their species within 10 millennia. Around the 20th century, the Kelvan Empire dispatched multi-generational starships to their neighboring galaxies, searching for new territories suitable for conquest and occupation. A Kelvan expedition arrived in the Milky Way Galaxy in 2268.
The military power and influence of the Kelvan Empire, in relation to other Andromedan civilizations, is unclear. Kelvans encountered by the USS Enterprise possessed highly advanced technology, and did not regard the Federation as a significant impediment to conquest. (TOS: "By Any Other Name")