Oh my, well this is indeed a difficult subject. Command Center power generation, eh? Alright then...
I've done some research, and according to Outpost 1(.5), "the Command tile [OP1.5 Command Center] has its own battery power supply". According to Outpost 2, the Command Center is "equipped with a small power plant".
There was not, to say the least, a vast amount of information available to me.
Therefore, using the limited data I could acquire, I have developed this hypothesis:
The Command Center uses Gnome-Power.
There are hundreds of shafts dug hundreds of miles below the surface under the Command Center. Within these shafts are thousands of hampster wheels with gnomes on them, running all day long. The running of the gnomes causes the wheel to spin, thus generating electric power. Also, the cost of building the cages, digging the shafts, and cloning the gnomes is why the Command Center costs so much to build another one. Also, this hypothesis has led to speculation on what the purpose of the fourth worker needed by the Command Center is. Many believe that he makes sure the gnomes receive proper rations and cleans up the dead gnomes.
And there's your answer!