I would read the reviews on Amazon. There are some comments about people running 15000 BTU ACs on their travel trailers. Evidently not with propane unless you install a "hard start capacitor".
Cut from one comment on amazon.
"generator could barely handle my 15000 btu air conditioner right out of the box. It would not start the compressor at all while using propane, but would start it most of the time using gas only when all of the other breakers were turned off. Even then, when the compressor turned on, the overload light would blink. After reading other reviews, I installed the Supco SPP6 hard start capacitor and it changed everything. I can now start and run everything (ac, fridge, microwave, outdoor fridge) at the same time while using propane!! I even turned the electric hot water on for a few minutes while ac was running. It worked, but it was maxed out. Wouldn't recommend running both hot water heater and ac at the same time.
