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Powering an air conditioner from an inverter is not only possible, it's done all the time. However, it’s not easy. The math is simple.
Aims inverters are rated up to 3X instantaneous power, which means it can supply up to 9,000 watts for a few seconds to start the A/C. However, just do the math and see how many Amps it takes to produce 9,000 Watts at 12 Volts. Fortunately, most newer A/Cs don’t need 9,000 Watts during start-up, but if inverter had to supply that much due to other loads, you’d be looking at needing close to 1,000 Amps during lock-rotor A/C start-up.
Anyway, once running, the best 13,500 BTU/hr air conditioners use just over 1,000 watts at standard operating temperatures, so need to figure on at least 1,200 watts feeding inverter. That’s 100 Amps from battery.
So if you want 3 hours of air conditioning, you need at least 300 Amp-hours of useable battery capacity. At 50% discharge, that’s much more than 600 Amp-hours of battery capacity because it’s being discharged way faster than standard 20-hour rate.
Solar recharging of batteries if running A/C all day are for the most part academic discussions. You’d need something crazy like about 5,000 Watts of solar panels to run a 1,000-Watt A/C round the clock. It’s so much I’ve never wasted the time estimating it.
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