I think the timeframe of AI War is set so far into the future that speculating on power sources is unnecessary. For reference, when asked about what year the game is set in, the response was 'this is set so far into the future that the humans wouldn't even know what the Gregorian calendar system is'.
However, if you do want to speculate on power sources, I think I can state with certainty that solar power will not be the technology used. It can't even provide enough power for our dinky little spacecraft that want to travel beyond mars, it certainly can't power neutronium-melting antimatter bombs. Given what is known about human technology in AI War, likely power sources would be direct matter conversion, antimatter-matter reactions, or perhaps fusion if the ships are really low tech.
If you want to discuss power generation in general, starting a thread in the off-topic board would be a really great way of hearing some diverse, well thought out opinions on the subject. It's a subject I've learned a fair bit about myself, so I would certainly welcome the opportunity!