I tried real hard a couple of years back to get my EU2000i to run my 13,500BTU air conditioner on the roof of my OFF-ROAD POPUP trailer.
Always tripped the breaker connecting the shore power cable of the trailer directly to the 120V RECEPTACLE on the generator using a RV30-15A adapter.
I even tried to run the air conditioner directly since I could get to the a/c 20AMP power cord plug. Same deal - always tripped the breaker. I did start the fan on the air conditioner first and did get the compressor to run a couple of time doing this. But as soon as the A/C would cycle it would trip the breaker...
NOTE that my 2KW Honda Generator 120VAC receptacles is rated at 13.3AMPS