I'd like to build an uninterruptable power supply for an AC (110V) fan so that when the power goes out, the fan can continue running intermittently (say, 5 min every 2 hours, for 10 hours, for a total of 25 min). The fan is roughly 1/4 horsepower (186 W). Therefore, to run for 25 min requires 186 * 60 * 25 = 279,000 J of energy.
I'm thinking about using a bunch of 18650 batteries to provide enough energy. I also need an inverter of some sort to convert it to AC. Some kind of logic would also be needed to run the fan intermittently.
Can you give a high level guidance on what else I need and the general feasibility of this?