Normal household refrigerators use a lot of power.  

The more often you open the door the more the refrigerator has to run to maintain temperature.  In a situation with emergency power this will deplete batteries or fuel supplies very quickly.

There are some simple steps you can take to save a lot of energy based on this simple fact: freezing water into ice is a very efficient way to store energy.

This may seem crazy since to freeze water you are removing energy.  However, temperature differences represent potential to extract useful energy.  In this case you are using the temperature difference to cool something down, which is also very efficient. 

These easy steps will save lots of emergency power and still provide you with emergency refrigeration: 

•  When the power fails take the ice and perishables from the refrigerator and put them into ice chests
• Turn the thermostat in the main (not freezer) part to the warmest setting and don't open it again 
• Use your backup power source to run the refrigerator only long enough to freeze bags or bottles of water (2 liter soda bottles work great)
• Use the ice you make to replace the melted ice in the ice chests
  

All you need to do this is a few ice chests and bags or bottle to use to make blocks of ice.  Avoid using ice cubes because they will melt too fast.

The reason this saves so much power is that you are only opening the door of the freezer a couple of times per day and using ice to store energy.  

You can also combine these steps with a termoelectric cooler like this one to extend how long the ice lasts.