Either go with an electric battery, or go with a hydrocarbon like kerosene or methane or so.
I made the original comment contemporary batteries ain't good for electric planes. And I would not bet on batteries becoming good enough anytime soon.
But I don't think physics prohibits anything here?
Things that involve metal-air reactions are basically fuel cells and don't count. If you go down that route, you'll quickly find yourself working with some kind of chemical fuel. They will suddenly look a lot like existing airplanes in terms of basic concept.
Ok, that definition works.
I would have gone with 'whatever people (in the future or now) use for powering their phones, laptops and electric cars' is by definition 'conventional' at that point in time.
Energy density is steadily increasing. Hydrogen will be a short-term solution for medium/long haul flights, but will eventually be replaced by batteries.