Self cleaning pond for ducks?

Ducks like to poop.
Ducks love pond.
I like pond to be clean.
I don't like to clean every month.

Is there a solution to this equation that doesn't require some complex power hungry contraption?

Get rid of the ducks.  Otherwise, learn to live with it.

Geoff Lawton has kept ducks near a swale which floods periodically, flushing away the poop.  This will only work in a wet climate with frequent biggish rain events.  I think it is shown in this video:  

In this video he shows a small duck pond that drains by gravity to provide fertilizer water:  

My pond was green because of fish poop. I made a system with an air lift pump into a reservoir filled with puzzolane. On the bottom of the reservoir a pipe going up and back into the pond. I put heliphytes in, plants that create an aerobic climate in the pouzelane, which makes the bacteria living in it create plant food out of algae. Put it on for 5/10 min a day. Chrystal clear after 5/6 weeks.

Always thinking permaculture, as I travel back and forth through Kitsap and Mason coutys here in Washington state I see theses timber company tracts that have large shallow ponds surrounded by second growth trees that need to be thinned. Seems like they would be Ideal for some one that wanted to homestead with ducks. If one set up a rotational system in these ponds they theoretically should improve with disturbance and regrowth.  Get grass to grow in the area that they trample and manure then nesting pairs of Brant geese will come and raise there young there.
Most new homesteaders are trying to raise ducks in feedlot conditions which means you have to dispose of the waist instead of it cycling naturally.
If you are interested in the land mccormick-land-company-port-orchard