These answers are all valid but no one has given you a practical solution, unless you happen to be an electrician. I do like that small Jackery for 300 dollars. I doubt you'll be experimenting wiring a battery to your fan. You would need someone that knew about that. You could get something fixed in the house for about 350 but you said you wanted a portable solution. Again going back to that Jackery box like Lurker posted up$1000 usd? I don't even own that much cash
An electronics UPS won't last anywhere near the duration of an outage here.