Yes - The Everhot was designed to run on renewable power!
Originally conceived to run from a small amount of spare power from his water turbine (in the days before generating your own power was as accessible as it is now) a Gloucestershire mill owner designed the Everhot to heat using small elements with a low power input and then gently emit the warmth whilst conserving the remaining energy.
It's equally happy just plugging in to the mains though! (Everhots just use a 13amp socket - no big 32amp or 45 amp cooker circuit needed.)
'Domestic' Solar and Wind Power
If you have a solar array on your roof, or your own wind turbine it's likely that it'll be a 'grid-connected' system that adapts itself to feed back to the grid when you're generating more power than you're using and to draw in from the grid when demand outstrips supply.
In this case it's best to plug the Everhot in to your home's electrical system in the normal way. You could use the 'ECO' mode to make best use of your own power and 'time' the cooker to heat up in the middle part of the day (and send it to 'sleep' overnight when you're not generating). You may need to compromise slightly when programming to make sure the cooker's at full heat for when you want to cook but overall it can integrate well with this type of system.
Generally, over a year the Everhot will consume a similar amount of power to that generated by most domestic '4kWp' systems - you could say that it'll run 'for free' on your own power if you think of it that way!
Solar power isn't all that predictable, this is Great Britain don't forget! Wind power is even less so. Again it's best to run a grid-connected system with the Everhot plugged in in the normal way and let the import/export electrics look after things.
The Everhot has a maximum power draw of 2.8kW (that's with all hotplate and oven elements on at once, or 2.5kW with the grill on [the control won't allow any other elements on when the grill is on]).
If you're in 'ECO' mode (reduced heat) another handy feature for off-grid users is that the power draw is then limited to 2kW (it does mean that the grill can't be used, and the maximum temperatures for the ovens and hot-plates is lower than 'normal mode' to help reduce consumption).
Note for 'Induction' models - the induction hob plugs in separately to the 'heat-storage' side of the cooker and its maximum power demand is also 2.8kW.