If you have a medium size off grid power budget, there is some good news in the refrigerator department. (more on creating your power budget).
Traditionally, we used a small propane refrigerator that was a pain. It was only 8 cubic feet in size. The pilot light would go yellow and 
you’d have to clean and dust it to restore its normal performance. When in need of maintenance, it would also offer up a stinky propane type smell from the incomplete burning at the pilot light. We were really glad to replace it with a small, low power unit I found at Lowes.
The Replacement was a 10 cubic foot Magic Chef unit with an important rating. The compressor was rated at 130 Watts! The Energy Star estimate was 386KWh per year. That meant the power was relatively low when running, and nothing at other times. This unit cost around $300 compared to $600 or $700 for a new, small propane unit. Keeping the door closed as much as possible helps quite a bit.
Also, it helps to place this unit in the coldest part of your home, to minimize power consumption during winter months when the available solar power is lower.
Refrigerator Tips 2 and 3. Please leave your comments below!
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I know some boaters put cold drinks and frequently accessed items in a top loading cooler instead of the fridge that has a front opening door. The boaters who anchor out (off grid) even go so far as to limit door opening to once per meal times. This done to limit the time the compressor runs and uses energy. A bag of ice placed in the cooler helps keep things cool and if it is ice cubes can be added to drinks if desired.
If buying a new fridge is not in your budget at the moment, adding insulation around the shell will help as will adding a computer fan to blow air across the radiator. Such cooling fans can be powered by the smaller size solar panel often sold in automotive stores as a battery top up charger for when the vehicles is left parked in the sun for extended periods of time. Fans can be salvaged from computer in the dump or scrap heap.
Thanks for the comment Arild, and you are one step ahead of me on the adding insulation.
This summer when the room temperature goes up, I’m planning on re-visiting our Fridge’s power consumption and measuring real power differences with added insulation. Current measurements for 65-70F room temp are here.
I have a Kenmore compact fridge. I plugged it into an 800 watt inverter to a deep cycle battery. It ran for about 10 minutes. Then the inverter light went from green to red. I would really appreciate any advice. Thanks!!!
What is the UL amp rating on the unit? I’ve seen many ‘small’ fridges on the showroom floor that use the same compressor as the larger units. It sounds like you got past the starting surge of power for startup. Its possible that the inverter is too small. I’d suggest one that is rated as follows: UL rated amps * 120 Volts * 1.25 In other words, you want a 25-30% margin for the inverter to operate with to cover losses with modified sine wave designs.