Just finished mine today----
I went through 3 iterations of inverters-

. I started out just trying to run a small 120v fridge/freezer in a basement bay.
#1- Zantex 1500w modified sine wave inverter. It ruined the fridge/freezer and ruined itself. It was kinda funny because the box that the inverter came in showed a fridge/freezer just like I have. It was tied directly into a dedicated freezer outlet.
#2- Then I installed a 1000w pure sine wave Cotek (Samplex) inverter. It ran the freezer well.
Then I decided to tie the inverter into one house circuit that would power up the TV's, the computer, and the fridge/freezer. When shore power was applied it would trip the GFCI inverter load side receptacle. The Samplex engineer said it had something to do with the motor home neutrals. This would always require me to turn on/turn off the inverter before/after shore power was applied. The engineer suggested I bypass the GFCI and hot wire it- I said "NOPE". I asked- What do you have that has no GFCI load output?-Hence, a 2000w Coket pure sine wave inverter which can be wired directly into my additional Automatic Transfer Switch and to the TV circuit.
#3- Just installed the SK2000-112 Cotek. Everything is working normally, and well now

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It's only taken 2+ years to get this far and a heck of a lot of aggrevation.
Why don't they install pure sine wave inverters in all motor homes at the factory-- Heck, forget it- I know the answer to that one

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Samplex service is surperb- If your interested the phone number is 604-525-3836. They are in Coquitlam BC. I only paid the difference between the 1000 and the 2000 at the 2 year point

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I only have two 6 volt golf cart batteries (as you do), in series, and no room for more. The 1000w inverter would have sufficed okay if it wasn't for the tripping of the inverter GFCI load receptacle. I fortunately had wired the first inverters with 2/0 gauge wire so the switch to the new (today) 2000 watt inverter was a piece of cake. I also installed a remote switch (CR-8) in the bedroom so that I don't have to go to the bay to turn it on/off.
I guess you know what I suggest/recommend you do-start where I ended up today

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Oh, they want the inverter mounted no more than 6 feet from your battery power supply.