I think that a basic issue with Aurora invasions is that it's very one note, in that there are really only three things you can attack on a colony: it's population, it's ground troops and its shipyards. Shipyards are sort of separate issue because they can be attacked from space or by STOs. The electricity idea is interesting because it could offer a way to attrit a colony's ability to function and defend itself from the ground (or air!) without having to land troops or kill a couple tens of millions of people.
Maybe a mechanic where planets have some kind of ground unit capacity that can be increased by relatively inexpensive "transport infrastructure," or "garrison infrastructure," which requires electricity. When the electricity shuts off, troops over that cap experience "disorganization" or whatever other term is most appropriate, which makes them less effective. This would both make stacking huge ground forces on a planet by both players and NPRs less practical and give a vector of attack that isn't just spending more minerals then the other guy, which is essentially the current ground dynamic (with the notable exception of the terrain bonuses, the recent changes to which are really nice.)
If incorporated, as others say, into a CAS fighter rework that would allow selecting specific installation types to target, this could create some very interesting situations. Say you have 3 NPRs you're neighboring. Two are at war with you and another is likely to join in. A raid using light carriers on the third would make a lot of sense in this situation, the space superiority fighters destroying shipyards and isolated warships and your atmospheric craft crippling the electrical infrastructure, which hampers the NPR's ability to rebuild. You wouldn't have to commit huge amounts of ground troops or drop a couple hundred nukes and make it not worth conquering later. Not only that, but with the ability to target installation types you could also blow up ground force construction facilities to stop a buildup, or the mines on a mining colony, so on and so forth. The decision space increases a lot.
I also think that having multiple types of electricity sources with different use-cases and drawbacks, upkeep requirements etc would be really interesting on it's own merits, and a solid opportunity to use the existing reactor techs more then they currently are. Making the decision between, say, a sorium power plant that needs minerals but is cheap as opposed to a fusion reactor or solar arrays with less upkeep seems like it could be a relatively simple but compelling addition.
P.S, while on the subject of ground combat I think heavy and long range artillery should degrade the fortification rating of any unit they hit. Would give them a much stronger use case.