I have a 3650 watt generator from Home Depot and a lot of extension cords. When the tornadoes came through several years ago it saved everything. I ran the return pumps, refrigerator, microwave, phone, router, modem, televisions, and computers. We cooked on the gas grill and microwave. It was about this time of year so it was not hot or cold. We also took some of my son's in-law's frozen food for safekeeping. We had to send to Birmingham to get gas for the first day or so and then one of the convenience stores near us got a big generator so we had gas. I had to refill the gas tank twice every 24 hours. It is noisy but nobody complained (at least not to me). I've got about 25 gallons of gas on storage now just in case. Had I not had the generator there's no telling what I would have lost, as it was I lost nothing.
I wouldn't worry about the HOA. Whatever penalty they assess would be less than you would have if you didn't have a generator.
Good luck.