We've got two kinds of power going on in The City of Ember, and while they couldn't be more different on the surface, the more we dig, the more we realize they're intertwined. First, there's the power of energy—the river, the generator, and the electricity that lights the city. But that power is controlled by the people in power, mainly, the mayor. That gives him a whole lot of control over the citizens of Ember, since he's in charge of supplies and information. But while Lina and Doon may seem like just a pair of powerless kids, over the course of the novel, they learn that sometimes having power means taking matters into your own hands, no matter what The Powers That Be might do to you.
The mayor only has power because people agree to give it to him.
It was pretty stupid of the Builders to leave the population of Ember without any idea of how their city is powered. That just goes to show that more than anything, knowledge is power.