As stated a 2000 watt is pushing it.
I wouldn't recommend it.
A 13.5k a/c draws about 16-20 amps during start up then runs about 12-14 amps while running.
Your converter is always running and it sees about 3-5 amps continuously.
A 3500 watt continous watt gennie would in my opinion be your minimum.
Generators can sometimes be misleading.
I seen one listed at "2000" watts but in small print it said "surge" watts.
Running watts was around 1650.
Don't do it, not enough output to keep things in check. This is why most people who have a 2K generator have two 2K generators and a parallel cord to tie them together making the total output at 4K.
As for why many of these folks to two 2K generators is that if a/c is not needed one generator may meet their needs for dry camping. Or that two 2K generators is much lighter to move around than the weight of a 4K generator
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