That's reducing the facts to the essential, @Mechta, thanks!
Now I agree that it is desirable, at the very least, to have the engine(s) operative without any dependency on the aircraft electrical system. Still, every petrol engine requires sparks so some kind of electricity is required; yet some meet this requirement. The Rotax 912 family at least, and I think a good many US engines too, those that run from magneto's. Thinking along the lines of the 912, why couldn't a fadec get electrical power from a completely separate circuit, with its own generator coils? Does it require a lot of power, perhaps?