Sorry I'm late to the party.
I have a similar problem with my 15A Sears compressor, it has to be plugged into an outlet next to the breaker box and it still dims the lights when it starts. That compressor (as noted previously) draws 15A at 120v, that is 3000Watts, but that is the baseline running power. It might draw 2 or three times that when starting.
So what happens is that you get the generator running and it runs based on load, so its running at low power (no load) maybe making 2000-3000W out of 5500W. You turn on the compressor which wants 3000x2 or x3 to start so it tries to draw 6KW or 9KW, which it can't because the Watts aren't being made, so the voltage drops and the current spikes and your wiring gets fried. Then the genny picks up to match the load and and the thing runs for a while, but you essentially gave it a heart attack and then it jogged around the block a few times before it falls over dead.
A) a smaller compressor. You just need one to fill the tires. Use hand tools like the rest of us awesome mechanics or get cordless electric impact guns and charge the spare batteries from your genny, which is a nice low constant load. Or get a couple corded electric guns and they will run off the genny, Or
B) as noted, get a lot bigger genny, or
C) get a gas/diesel powered compressor if you really want to stick with air powered tools, or
D) Start the Genny and override the govenor by pulling on the govenor/throttle linkage to have the genny running at max RPM when the compressor starts. You'll need to do this each time the compressor starts or you'll be back to having a dead compressor.
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