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Cooking and heating water with electricity off-grid is usually impractical but there are exceptions. In some cases the relatively large power loads can be used without affecting house battery1) state of charge:
In general DC power3) is used for warming or very slow cooking. Part of this is due to the limits of cigarette lighter outputs, typically 120w (10A x 12v). The “catch-22” is that most people don't drive their vehicle sufficient hours to do real cooking off DC.
Higher power is common with AC devices but one must have the power to run it, and to recharge the battery bank afterwards.
Analog cooking appliances (knobs, not electronics) run fine off inexpensive MSW inverters.
see the dedicated crockpot and instant pot pages
see this article
Power/time saving
Cleaning