To power your mines, you need power plants. When your Energy Output indicator at the top-right of the Menu Bar is in the red, it’s time to build more power facilities. There are three types of power production facilities: Solar Plants, Fusion Reactors, and Solar Satellites. Each has its strengths and weaknesses, and deciding just what mix of them to build is a big part of the game’s strategy; your build method will evolve as your empire grows.
Solar Plants use no additional resources beyond their initial construction. Their efficiency is affected by the proximity to the sun; on a planet in slot 1, a Solar Plant will produce significantly more power than a plant located on a slot 8 planet. Initially, Solar Plants are cheap and can be built very quickly. Eventually, however, new Solar Plants become extremely expensive.
Fusion Reactors produce power by fusing deuterium, and require a continuous supply of deuterium to fuel them. In the beginning, they are not as efficient as Solar Plants. But as you continue to research higher levels of Energy Technology, their efficiency increases. The benefit of this grows exponentially when you have multiple planets. A single increase in Energy Tech research will increase the efficiency and power output of ALL your fusion reactors on ALL of your planets at once. At higher efficiency levels, Fusion Reactors produce much more power than Solar Plants, and some players eventually destroy their Solar Plants in favor of Fusion Reactors to free up fields for building other things.
Note: Another source for power is the Solar Satellite, a stationary orbital spacecraft.