We are assuming here that you are asking about a regular residential refrigerator. At the other end of the scale is the smaller compressor type fridges that many of us use in a truck, van or SUV. Power requirements for these are vastly less. I have a typical Chinese made 52 qt model for the Casa that runs off of a Jackery 1000. The Jackery will run it for at least 4 days which usually gives an opportunity for solar to recharge the unit.
Since my electrical needs are relatively modest 1000w is plenty for fridge, phone, fans, etc and I have a single Renogy 100 watt solar panel that feeds the battery. I had planned to buy a second 100 watt panel but so far have never needed it.
The bigger units like Wanderingrichard posted have a lot more capacity and may be reaching the point that they can power a real refrigerator for a while. The beauty of these units-although big and relatively heavy-is that they are self contained.They have the long life battery, the charge controller and inverter all in one package without all of the attendant wiring and fusing required in building a piece by piece system. Just hook up to a solar panel and plug in.
Old 406 Kid is our resident solar expert owning a home that I believe is about 15 miles from the nearest electricity. He has used solar for years.
