Be careful of the inrush current on some of these air cons.
It's the same sort of deal as to why you do not put a laser printer on a UPS.
General load, it should be fine, but inrush current is huge - it will trip the UPS.
I suspect when the compressor turns on there would be a rather large inrush current and your generator may die.
We had a 2KVA petrol generator a while ago. We used it during blackouts.
We were lucky to get maybe 1.5KVA out of it before it became unstable (not to mention hot).
Personally - i wouldn't run an air con on a small generator. If you have a 5KVA or so, then go for it.
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