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Biggest Issue would be the ability to sustain a 2000w output. My alternator can output 1900 some watts at around 3000rpm (im told). You would need at least 1 (or more) deep cycle batteries to run the invertor from, and an isolator from the main van battery to keep from discharging it too much.
This setup is very similar to an RV, where is is used to run TV's and Microwave, gotta watch how much you discharge the battries, small power tools would not be a real problem, a large power saw would. It is all a matter of the size of the invertor and Amp-Hours of the battries.
As far as invertor type, most power tools will run fine on the cheeper inverters (which use a square wave often called a "modified sine wave").
If you are looking at a significant load for more than 30 min. I would consider a Honda 2000i generator. Thye are very very very quiet and efficient. Just another idea.
Inverters are fine if you have significant battery storage - 4D or or a couple of 6Volt Golf cart batteries for a 2000W inverter, and your usage is limited to short periods of time between charges.
you will be drawing a constant 166 amps from the battery, if you plan on pulling 15a at 120 volts. there is no way your electrical could handle that. you better get a generator.
It really depends on what you want to run and how often you're going to run it. I bought a 1500W inverter to put in my van. I chose that one because I wanted to be able to run a small microwave or coffee maker (not at the same time) while camping. Even at that, I planned to install a dual battery set-up with the second battery being a deep cycle RV battery.
If you want the inverter for charging drill batteries, it'll probably be fine. Maybe it'll work for occasional use of a small power saw. Maybe. Anything more than that and you're better off looking at a generator.
Power tools don't usually require 2000W continuous. You need a high peak rating to get the tool started and keep it from getting stuck in a cut.
The Motorcraft 3G alts put out 130 amps or more. That can keep any tool going, and if a higher peak is really necessary the battery can pick up the slack.
A deep cycle is necessary for any extended tool use without the vehicle running.
The key here is wiring and quality connections. An inverter will shut down if the voltage it gets drops below 10.5v. If you have the engine running and a fully charged battery at 14.6v and try to draw 200 amps, a poor connection and/or thin cable will drop the voltage to a point where the inverter will shut down even though there's power available, the wire won't overheat, the inverter's rated for it. The exact gauge needed depends on how long the wire is. The wire's current capacity- where it will overheat- is not likely to be the issue, we're worried about losing too much voltage here which is a separate thing. Making quality connections that don't drop substantial voltage under high current is almost an art form.
DannyM here above me said it as good as I could have. I'm an electrician and I have a 3000 watt inverter running on my van. I do have a second battery that came with the van. The second battery is on a relay to keep it isolated until the truck is running so you don't kill the primary battery. As an electrician I drill around 500 holes per house with a 7.5 amp hole hawg drill and I have no issues as long as I use a 12 gauge extension cord. On the inverter I have 0 gauge wire running from the second battery about 4 feet away for the inverter. Anything less would be uncivilized.
Keep in mind
amps X volts = watts(inverter size)
In my case 7.5 amps X 110 volts=825 watts(I know mine is overkill but sometimes I run 2 drills at once, radio, chargers, you name it)
You can get 1/0 wire cheap from flea market vendors too. The only problem is it's all for naught if you don't do proper connections. The ones where you put stranded wire in a hole and a screw presses into it directly is the worst kind, even if it's gold plated and expensive.
The stainless screw posts with wing nuts on top of my deep cycle marine battery turned out to be terrible after awhile. Under load, I could read 1v between the stainless and the lead terminal it was mounted into.
I've gotten the best results with ring terminals that I soldered onto the cable after crimping. Doesn't oxidize and strands don't slip out one by one.