Modern refers are very efficient and often give a yearly power usage. As an example use 364kWh. For 1 day 364kWh/364 = 1000Wh for 1 day.
Per hour it's 1000Wh/24h = 42W. Assuming it cycles on 50% of the time it then draws 42/.50 = 84W while running.
For 120V AC operation that's 84/120 = 0.7A when running.
Using a multiplier of 11 for battery/inverter usage that's 0.7A*11 = 7.7A DC when running.
Also for battery/inverter usage it would use (for 1 day) 1000W/12.0V = 83AH from the batteries. For 2x GC2 batteries at 230AH that’s 83/230 = 36% discharge for just the batteries.
Actual power usage will vary depending upon usage and ambient temperatures
Also some modern refers use variable speed motors and have very little additional start up amp surge.
Dutch’s Haier HA10TG31SB refer above is rated at 330kWh and the 2A and 6A label may suggest a worst case scenario.
Basically with a A/C, TV, lights and refer you should be OK on 30A as a typical 10 cu ft refer AC draw is 1-2A possibly with a higher startup surge.