Muttley600 said:
I'm more curious now as to what will happen with too big a cap
In a practical sense, too "big" a cap is not a problem.
What you look for is a filtering network that keeps the AC "noise" caused by inadequate filtering from expressing itself on the power supply's DC output, given the power requirements of your "end-using" circuit's purpose(s).
Why, you ask?
The AC ripple riding on a DC level can, in certain circuits, "contaminate" the so-called "DC bus"; the main power for the circuit components. That being the case, this
ripple can (especially in biasing or reference sub-circuits) cause premature triggering, false rise times and even phase/frequency shifting errors. In strictly "on/off" situations it can cause "chatter" in the switching circuits which can have totally unacceptable responses from many digital devices.
Or more simply it would result in an annoying 60 (or 50) Hz hum from an amplifier's speakers.
The point being that the "cleanliness" of a DC source (a battery being the ideal, for the most part) is predicated by the circuit design purpose
and your expected output.
Looks like where we can go from here is to "mate" your AC generator to the rectifying/filtering network and make a DC to DC converter.
It may end up looking over-engineered (some may even say
crude) and impracticable, but it'll be something you created.
CBB