Whirlpool, 110V, 6.5 amp refridgerator

For a standard, modern, energy star refrigerator, generally a 1.2 to 1.5 kWatt (1,200 to 1,500 Watt) AC inverter is recommended... It will generally also run a few lights, radio, cell phone charger, etc...

What you do need is to measure the amount of energy per day (Watt*Hours) using a Kill-a-Watt or similar meter:

https://www.solar-electric.com/kiacpomome.html

Nominally, for an off grid energy efficient home, I would suggest around 3.3 kWH per day (3,300 Watt*Hour) system. If you really only want to run a refrigerator, lets assume that it draws around 548 kWH per year or (547kWH/365 days per year=) ~ 1.5 kWH per day. A full time off-grid "reliable" system may look like (loss of guesses here about your specifics). First sizing the battery bank:

• 1,500 WH per day * 1/0.85 AC inverter eff * 1/24 volt battery bank * 2 days storage * 1/0.50 max battery discharge (for long life) = 294 AH @ 24 volt battery bank

Say you start with 6 volt @ 200 AH "golf cart" flooded cell batteries. That would be 4x in series for (4x6volt=) 24 volts, and 2x strings in parallel for (2x 200 AH=) 400 AH.

Note: A 400 AH @ 24 volt battery bank will support a suggested maximum ~2,000 Watt AC inverter and ~2,000 Watt solar array. Larger AC inverters typically waste power and will empty the battery bank very quickly if heavy loads are used.

We suggest 5% to 13% rate of charge, with 5% good for weekend/emergency usage in sunny weather, to 10%+ for full time off grid:

• 400 AH * 29.0 volts charging * 1/0.77 panel+controller deratings * 0.10 rate of charge = 1,506 Watt array "nominal"
  

Then there is sizing the array for your loads and amount of sun... Say you are near Tuscon with a fixed array:
http://www.solarelectricityhandbook.com/solar-irradiance.html

Tucson
Average Solar Insolation figures

Measured in kWh/m2/day onto a solar panel set at a 58° angle from vertical:
(For best year-round performance)

Jan	Feb	Mar	Apr	May	Jun
4.95	5.63	6.61	7.07	6.91	6.56
Jul	Aug	Sep	Oct	Nov	Dec
5.77	5.66	6.09	5.84	5.30	4.76

Based on hours of sun, seasons, and 1,500 WH per day, and a derating of 0.75 (you do not want to use 100% of your predicted power per day--Unless you have a backup AC genset for some days of less than clear weather):

• 1,500 WH per day * 1/0.52 off grid system AC eff * 1/0.75 "no genset" fudge factor * 1/4.76 December average hours of sun = 808 Watt array minimum for "nominal" December usage
  

So, somewhere between an 808 Watt and 1,506 Watt array would work. (solar panels are historically cheap, and battery prices are rising--Tending towards the 1,506 Watt array would be "very nice"--Especially if you do not want a genset).

The above is a quick back of the envelope calculation for a "reliable" off grid system to run a standard Energy Star Refrigerator. Hot weather, using the ice maker, etc. can cause a fridge to use significantly more energy.

You can, of course, go with a smaller system (like just one string of golf cart batteries and an ~808 Watt array)--But that does mean you will have to monitor the system more closely during hot or cloudy weather. Also note that I am using "accurate" numbers like "808" so you can follow me where the numbers come from... For solar power, +/- 10% (i.e., and array that is 800 Watts +/- 80 Watts in size) are pretty much "the same". Solar power numbers are "estimates"--Not etched in stone.

-Bill