Why not to use batteries? Of different kinds.
This is the essence of the question; I don't see it's impossible, and if it's possible, then why nuclear? I agree that as society we grow our needs in power, but solar and wind sources are relatively easy to distribute, and it's rare when a lot of installations doesn't get light and wind, and distribution grid alone - without fossil fuel plants or nuclear power plants - can help. So the need in nuclear fission power is questionable.