Peter Bennett is absolutely correct. Inverter/Chargers run at .5 to .7 power
factor which means that the AC current supplied to them will be as much as
double what the calculation of DC volts * DC amps= DCwatts/115 AC volts
gives you. It is current which trips out a genset. It is power (watts) that
overloads its engine.

The Honda EU1000i is only rated for 850 watts continuous, so it could just
barely (as Larry notes) run a 5000 BTU, 7 amp Carry On. I am rather
surprised that it even starts it, as the inrush current is at least double
the 7 amp running current. Chalk that up to the excellent electronics in the
little Honda. I had a 2800 watt Coleman generator that would barely start a
Carry On. And as Larry noted with the Honda, it wouldn't restart it unless
the freon circuit stabilized its pressure over quite a while to eliminate
the high head pressure start up condition.

A better solution is a larger generator or a very efficient charger. IOTA
makes a fairly efficient charger- about .8 power factor as I recall. Even
so, the Honda EU1000i will be limited to supporting a 40 amp DC charging
rate at best.

David