I have a Yamaha 2800 inverter generator. It runs the 13,500 AC fine. I have yet to try it on the 15,000 AC. Since the bigger AC is about 8 years newer, I think it is probably more efficient and I expect the generator will run it fine.
When I used it on last TT, it ran the 13.5 AC, a few lights and the TV fine at the same time. You would obviously have to turn off AC to run microwave, coffee maker, or hair dryer.
I would not buy less than 2800 watts if I wanted to make sure the AC ran. I know the 2400 watt Yamaha is hit and miss on running AC based on forum reading. Hope this helps.