So, as you know, you need a Pure Sine inverter generator. And, while 1000 watts will do, 2000 watts isn't much more and will give you some margin of error. I have a WEN 2000w inverter generator, and some others on here do as well. It supposedly has the same engine as the Yamaha. It's very quiet, 51db on Eco, and uses very little fuel, 14+hrs on light load on 1gal, in my experience. It doesn't weigh all that much so you can move it around, less than 60lbs. And, it's super-easy to pull-start. I don't like how you have to remove the side panel to fill or check the oil, but thankfully, you don't have to do it often, and it has a low-oil shutoff.
And best thing: it's on sale today, ONLY! $359 on special at Home Depot, shipped.
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Since it's 9:30p now, you only have until 3am ET, to order it!
Harman approves of a UPS that sends a square, clipped wave to the stove that it recognizes, which then starts the shutoff procedure. Lots of UPSes send a square, clipped wave and should work. However, if you want your Harman to run and not auto-shutoff, then you want a PureSine UPS, like the CyberPower that is in my sigfile. APC too, but last I checked it cost alot more than the CyberPower which goes on sale quite often at NewEgg for about $150 for the 1500 model.
I installed an outdoor outlet that I plug the generator to. Then, I run a 12-2 wire to a quad outlet in my kitchen. It's only for the generator. In the kitchen is my pellet stove and fridge, etc. I can then plug appliances into that outlet.
As for how you run it, you could have the UPS plugged into your digital inverter generator, and plug your stove into the UPS. Then, when your generator runs out of fuel, you can then refill it, while the stove runs on UPS power. For a 1500VA sized UPS, and if your Harman draws about 100 watts, it could run for 45m to an hour. So, you should have plenty of time to refill your generator. No, I don't let my generator cool off between refueling.