I've heard of powerless ebb n flo systems. well powerless in that they don't rely on electricity. you basically raise the reservoir so the tray floods, then lower it to drain.
I may be mistaken, but I believe it was greystoke who spoke of it.

We use Autopots. I believe this system is called sub-surface irrigation. It uses gravity only and, of course, light. This sytem uses no power if you can grow with just sunlight. You can find more info if you're interested by googling autopots.

Water does not flow uphill without power...you may not pay for it, but there's power.

Aeration of nutrients also requires power.

I've made a powerless, manual, system for my cold crops that live indoors next to the patio door.
I simply took a dish tub & filled with one gallon of nutrient water, filled a small window-box that fits inside of the tub (all the way) with a mix of vermiculite & perlite. Twice a day I lower it into the solution for a while (sometimes I forget about it for hours on end....no ill effects thus far. LMAO), then pull it out to rest it on a plastic coat hanger that sits on top of the tub.
A very simplified, very human-powered, ebb & flow. I wanted to see how simplified a system could get. I dunno if it could get any more simplified! LOL

Here is a link that might be useful: That Tub set-up

Have you tried a Google search on "non-circulating hydroponics"? Dr. Kratky of the University of Hawaii wrote the original articles about this simple, low-tech system in the 1990's. I purchased a booklet and VHS tape from the university several years ago and found the system to be very simple, effective and cost efficient. There is a new book listed on Amazon.com ("The Secret of Non-Circulating Hydroponics: An Instructional Manual for Entrepreneurs & Hobbyists" by Terry Moore Cadle) that may be of interest to you. I have not read the book.