A breakthrough in battery tech that results in small but very long lasting batteries will result in the invention of a bunch of obvious things that are currently impossible or impractical given current tech.
I am not sure if those would strictly qualify as inventions or innovations/improvements. We already have a list of designs to build and power once we have significantly better batteries, or significantly better ways of harnessing other energy source (e.g. nanorobots powered by body heat). I do think that those "significantly better" batteries, will need to be completely new ways of thinking about the battery, which would be the disruptive part. But once we have one, the rest is "let's put that to good use, and into every house" kind of thing.