Capacitor That Serve For Domestic Appliances

There aren't any for you particular applications. Capacitors have low storage but generally high charge and discharge rates (and high cost), pointless for storing energy for powering home appliances.

What you are after is a battery powered inverter made up of batteries and an inverter, and possibly solar panels. Alternatives also include a diesel generator or perhaps a bicycle with an electric generator connected to it (with or without batteries and an inverter), although you will probably only be able to power one or two appliances (if any).

The only way to go is deep cycle batteries something like forklift or submarine batteries hooked up to a combined charger/inverter, You can supply this by way of mains electrics or wind generator or if your lucky enough to have a stream on your land, a water driven generator. If you look on a site for a company called Victron energy they have all the information you could wish for,But how or what you use is up to you. you should be able to generate enough power during the night & early in the day to allow you to do all your cooking,washing etc without going onto mains or running a generator. If you also install a solar water heater for hot water you could become totally independent of energy company's. You would need to change your lights to 12v.

Bazzer

If you need hours of back up look into a battery/inverter back up product (UPS). If you need continuous back up look into a gasoline or PL gas generator back up product. Cost will depend on how much power (KW) is needed and for how long.