We use a 200ah lifepo4 battery pack (equivalent to 2, 100ah lifepo4 batteries in parallel) and a 2000w inverter to power our 1050w (line input power) microwave and 11k btu a/c unit. Get about 85-90 min of continuous runtime when we're powering the a/c (similar runtime for microwave--although we rarely run it for more than 10-15 min.). When we're on the road we recharge the lifepo4 with a 40a dc to dc charger. It's all been working flawlessly now for almost 2 years.
Choosing a capable 2000w inverter is important. Not all 2000w inverters are created equal. Although most inverters can supply their continuous current rating, many fall short providing suitable amounts of inrush current. Inrush current is necessary to successfully start a/c units and microwaves. Unfortunately, very few manufacturers provide inrush current specs for their inverters.
Proper gauge wiring and quality connections are important, too. It can take 110-150a of 12vdc to power a typical microwave or RV a/c unit. That's a lot of current. It's one thing to simply power a microwave and/or a/c unit for a few minutes---it's another thing to do it continuously for an hour or so. Improper wiring and/or bad connections can cause significant voltage drop (and heat). Best case, you won't obtain full power from your inverter---worst case you could start a fire. Don't scrimp on the wiring.
Good luck!
