Yes, with the right model, and for less time than you are hoping. Be clear about which of the two numbers is stopping you.
Power versus capacity
Two separate specifications decide this.
Power, in watts, is whether the station can supply the draw at all. A 13,500 BTU rooftop air conditioner draws roughly 1,300 to 1,700W while running, with a much larger spike at startup.
Capacity, in watt-hours, is how long it lasts. This is almost always the binding constraint, and it is the one people skip.
Which Jackery can do it
The HomePower 3600 Plus listing states 3,600W continuous with 7,200W surge. That covers the running draw with room to spare and the surge covers a typical compressor start. Its 3,584Wh of capacity, against roughly 1,500W of draw, works out at about two hours with nothing else running.
The Explorer 5000 Plus listing states 7,200W continuous and 14,400W surge with 5,040Wh, so it starts a larger unit more comfortably and lasts nearer three hours at the same draw.
Anything in the 1kWh to 2kWh class will, at best, run a rooftop unit for well under an hour. That is not a useful night's sleep.
Making it last longer
Three levers, in order of how much they help.
- Expansion batteries. The HomePower 3600 Plus takes up to five Battery Pack 3600 units for 21kWh, which changes the answer from two hours to an overnight.
- Solar, sized properly. A 500W folding array is a meaningful daily contribution to a station this size. It will not keep pace with an air conditioner in real time, but it refills between uses.
- Run the air conditioner less. Pre-cool on shore power before you unplug, shade the rig, and use it in the evening rather than through the afternoon.
The honest recommendation
If air conditioning off-grid is the main goal, a portable power station is an expensive way to get a few hours. People who genuinely cool a trailer off-grid are running a large fixed battery bank with a substantial roof array, or they are running a generator, or they have a soft-start kit and modest expectations.
If the goal is a quiet night with the fridge, fan and lights running and the air conditioner as an occasional luxury, the HomePower 3600 Plus is a good fit. Tell us the BTU rating on your unit and whether it has a soft start, and we will check the numbers with you.