Many types of crops still require power tillers and other types of power implements. I think a wind turbine and/or (but preferably both) a solar photo voltaic (or csp) station can service many acres, cuz there is often wind and/or sun. Provided one keeps tillers and other equipment small (ie: walk behind).
I'm no electrical engineer, but here's how I see it possibly working. Restricting tillers, mowers and such to 5 hp or so (possible higher though - up to 10 or even more), the extension cords can remain reasonable thin. (They will grow in necessary thickness as horsepower requirements rise.)
I see a reel cart accompanying the tiller, so that when you travel away from the power source the cord is unreeling and lying on the ground. When you travel back towards the power source, the reel is activated (powered electrically) to reel up the cord.
For the power source, the place where this extension cord is plugged in, I see a large buried cable going in a line down a field, with plug-in outlets above ground on posts every 60 feet or whatever.
The idea is to till the land which is within 200 feet or whatever of this main power line, on both sides of it. So, if you have buried half a mile (or whatever) of main line and provided outlets along the way, you will be able to do quite a few acres. 400 feet x 2640 feet. I make that to be 24 acres.
For many people that will be enough or more than enough. But one can also run multiple lines off one wind/solar station, so the acreage covered can also go much higher.
But obviously, this also all hinges on having a good medium sized wind turbine and/or solar pv array. In medium winds and reasonable sunlight you need enough watts to achieve your desired horsepower. Also, Ithink there will be some voltage drop along the cords.