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Minus whatever the car consumes... I doubt they installed a 3kw inverter if they only need a fraction of that. Also, be careful that the power you're tapping into has access to all of what you are trying to suck out of it. There's a BMS (charger) between the DC-DC and the battery, for example, and some electrical switching (not necessarily relays and heavy wiring) to the "Accessory" outlets. Each has their limits. On my car, the Accessory outlet is fused to 8 A, even though there's supposedly over 10x that elsewhere in the system, and some folks have reported damaging the car's 12v DC switching circuitry when running a simple tire inflation pump from it.

Remember, 2kw is something like 166 Amps. This isn't alligator clips stuff.

Correct. An inverter of that size would need to be wired into the battery properly. You couldn't just plug it into a 12 volt outlet in the car and expect it to work.
 
Correct. An inverter of that size would need to be wired into the battery properly. You couldn't just plug it into a 12 volt outlet in the car and expect it to work.
Mmm, it may not be quite that simple. In an ICE, you've got everything running from the alternator - it's the only source of DC power - and the 12v battery charger is essentially the voltage regulator that's built into it. It is possible that the charger for the 12v battery in an EV is one leg of that DC-DC converter, possibly different than other parts of the car, and so the battery may (likely) not have access to the entire 3kw of DC-DC current. Why would they build a 3kw charge regulator for a relatively little 12v battery? To tap into the battery itself, without draining the battery, you'd need to know what the current capacity of the charger circuit is, not the overall DC-DC conversion capacity.

In my Roadster, I measure 13.8v at the battery, 13.5v at the Accessory outlet, and the in-dash AV/Nav unit tells me 12.0v. Definitely separate circuits in use . The Fiat 500e is a different car, of course. I'd be very curious to measure the actual "12v" voltages around the car, to see if they track the battery voltage or not. Since it is somewhat an ICE conversion, they may have left much of the ICE's single-bus wiring in place, in which case, your plan might work. But be sure to understand what's upstream of wherever you pull current from.