There probably are ways to do it, permaculturally, but I can't come up with a sure fire trick that would work everywhere. There is the heating and then there is the pumping. You might be able to use a compost system to heat your pond system. You might be able to use a solar panel to pump your water. it would depend on your situation. At my place, I would consider maybe a gravity feed system that runs creek water into a large compost system thus heating the water and at the same time dumping the water into a hot tank that cools slightly and drops it into the fish tank, the overflow from the fish pond going into aquatic plant tanks and then outside into other systems. Feeding the fish might not be too big a problem permaculture style: Black Soldier Fly, Compost Worms, meal worms... there are options.
I can conceive of a system that, like Sepp's, looks more like aquaculture than aquaponics, but has some characteristics of the latter and could certainly be called aquaponics. Since Aquaponics can be broken down to hydroponics and aquaculture combined, and hydroponics can simply be defined as growing plants in nutrient rich water, there is no reason that aquaponics need be constrained to systems which involve high tech pumps, plastics, or grid electricity, which seem to be things that permaculturalists might want to minimize if they plan to follow the ethics.
It occurs to me that most people are responding to the question with the notion that the system will be used in a rural or off grid situation.
However in an urban setting aquaponics would seem to really find it's stride permaculturally. You could recycle/scrap together most of the materials for a home system and commercial systems could make good use of the existing resources (grid power, commercial structures, larger and wealthier market for outputs, etc...) to make a more resilient urban system. For most people on this forum I'd imagine aquaponics in the more technical sense (self contained, recirculating, run by pumps) won't ever hold much appeal beyond a hobby type thing
Freaky neat, actually, in my humble opinion.
it has been running continualy uncovered outside for 6 years and the original foam matt has been entirely consumed by a massive root mass that has begun to gather detritus and build soil and there are now earthworms and these gameris shrimp that appeared without human introduction along with a couple other macroarthropods that we haven't identified. Pretty neat.
Certainly grid power is not going to reduce in price
I suspect that grid power pricing is going to become variable, and you will have programmable devices that go with it.
E.g. when the wind is blowing on a sunny day, and the windmills are spinning fast, power goes down to 3c/kWh. On a cold still winter night it may be 20c/kWh
At 3c/kWh it becomes economical to electrolyze hydrogen from water, and store it, then later burn it in combine cycle MHD/gas turbine to generate power. You lose about half the energy doing this, so power has to down to half the price to make it worth while.
Similarly the generating equipment doesn't get used much, so you have to amortize that out over fewer kWh's So the sales price will tend to be higher. As more devices are made, the gap between times of surplus and times of deficit get smaller.
Even now, at the utility level, companies are putting in industrial sized batteries. (Move with a crane...) At present they are used where by putting in a 100 MWh (megawatt hours) battery they can save rebuilding a powerline. The existing line can cope with the average power demeand, but not the peak.
Battery and remote small plants along with smart monitoring are stabilizing forces on the grid.