Like what kryo said, they provide a bonus to industry production (factories become better). At some point, adding a power plant is like adding another factory (the increase to industry from the bonuses is about the same as adding another factory). Any point after that, the bonus industry make the power plant a useful addition. Basically a power plant becomes more powerful with every factory it can power, too few and they're worthless, and with enough, they are a must have (it would be a waste not to use them).


-A fusion power plant has a +10% bonus, so 10 industry structures would be needed before it would be useful.

-An anti-matter power plant has a +20% bonus, so 5 industry structures would be needed before it would be useful.

-A quantum power plant has a +30% bonus, so 4 industry structures would be needed before it would be useful.

Don't forget that initial colonies, and civ capitals also provide industry points, so you probally require less factories than what was stated for power plants to be useful. It depends on what industry structures you are currently using.

If you're into total maximizing, don't forget to count input from asteroid mines if you've got 'em.