Cheap inverters have dirty sinewave output, and are not reliable.
I did a lot of research about inverters about 4 years ago. Theres plenty of people who buy cheap inverters only to have them break or damage items because the output is not a clean sinewave.
One of my brotherd bought a cheap inverter so his wife could use an electric blanket in his F150 when they travel. But its dirty sinewave output fried the control for that electric blanket.
I bought a 2,200 W output with very clean sinewave output, made by MeanWell. They ain't cheap, and few electronic supply companies rep them ( carry their products ).
MeanWell inverters are very high quality and cost a lot more. Their output is a very clean sinewave. Likley even cleaner than most house power. Their inverters are used big yachts, and the reliability and sine wave purity, though not advertised as such, are medical grade.
I had to call MeanWell to find who to purchase it from. If I rember correct it was Digital Electronic in Texas.
I upgraded my 2016 CR-V with a 350 Amp alternator from Apex, that can put out 185 A at idle, upgraded the battery from the original 51R to a 24F, and bought 350 A anderson low voltage high current quick connectors, and had a local stereo shop install zero ga. wire upgtade from the 24F battery + and gnd. to the new alternator + and block, and then a 350 fuse and ran + and gnd. into the vehicles cabin through the firewall behind the glovebox, ran that through trim in the vehicle by passengers door, and out under front passengers seat with about 14 inches of slack and terminates with an Anderson 350 A connector. Inverter had mating Anderson 350 A connector wired to the inverter. All zero ga. wire. Marked both of the all red Anderson connectors with a lot of big black sharpie on the gnd. side of both.
Stereo shop also put velcro on the bottom of the inverter so it sticks to the carpet of the floor of the vehicle.
Bought 100 ft. of 12 - 3 outdoor extension and riged an access hole behind the front passengers seat.
I also had to change the serpentine belt to a Continental number 4070562 that is 56.2 inches long ( 0.3 inches shorter than the original ) to take up the slack because the Apex high current alternator has a slightly smaller puley so it spins faster.
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My PAYNE forced air furnace detected that the neutral was not tied to GND. the first time I test ran it from the inverter. I ran the combustion air draft inducer fan but then shut down and would not run the main forced air fan, and would not run the igniter and gas.
I made up a short cord that ties neutral to GND. and connected that in series between the extension cord female and the male plug

I added to the furnace, and with that, the furnace runs fine when powered by the inverter.
All of this cost my around $2,400.00
The vehicle gets about 2.75 hours per gallon when idling continous to power the furnace and a few other small items.
We had 2 outages when I used it so far.
Be sure to run the vehicles AC if it not a very cold day so the inverter stays cool. If its is a cold day, be sure to set the venting to outside and cold and fan to max.
Its nice to be able to sleep through the night knowing that the vehicles 15.6 gallon fuel tank will run this setup long enough. Compared to putting gas in a generator in cold weather every few hours.
Apex said they did not make a high Amp alternator for the 1.5 L turbo Hondas. So another time that I was happy I went for the normally asperated 2.4 L with the 2016 instead of a 2018 the sales man tried to get me to buy.
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MeanWell sell smaller and larger inverters besides the 2,200 Watts. They also have a line of inverters that have ability to run AC power through and the inverter monitors the AC and very quickly takes over to supply the AC if the AC power fails, so the output is not interrupted by AC power failures.
They make these systems in 12, 24, and 48 VDC inputs.
They also make battery management systems.
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Quality cost. If you want quality MeanWell is one place to look.
Be sure any install has plenty of ventilation. And clean air filtration often.
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Here's a picture of the power cord from a bad window ac unit I added to my furnace and a plug I added to plug the furnace into.
That bottom wire from the furnace to the box is a GND. only so the house GND. is still tied when using the inverter.
To run from the inverter, I unplug it, adde the short lengh of extension cord I made that ties N to GND. to the end of the 100 ft. cord, and connect to the inverter.