The most common "power saver" switch on an ice box turns off (or reduces) the electrical resistance heating of the cabinet around the door seal. The cheap and dirty way to reduce power is for the maker to wire a diode across the switch contacts. Essentially the power is only on 1/2 the time.
The purpose of the heater is to keep water vapor from the room air from condensing and then dripping on the floor. The door seals are not as effective they were in the "bad old days" because the seal pressure is only from the flexible magnet that's in the plastic seal. In the old days the door latch maintain the pressure but ice boxes tended to trap little kids inside and most consumer ice boxes just don't have a mechanical latch anymore.
Some units provide some/most/all of the cabinet heat from the high pressure line from the compressor which will loop around the door(s) opening(s). This saves the power the heater would consume and reduces (and may eliminate) the need for a fan for the refrigerant condenser.
I am actually looking for a device that is fitted by utility companies to restrict use of mainly refrigerators during peak load hours. In essence they switch off and switch on at predetermined times daily without any human intervention.
The systems I have seen switch off the A/C unit and the water heater. Switching the fridge has too many legal implications, I doubt any utility wants to do that. The systems work by sending a signal along the power line to shut down the equipment you agreeto lose. For that you get a little break on your bill. It is OK for people who are not at home during the day and don't miss the A/C or hot water. When it is a problem is when they have a loading problem on the weekend, you have a house full of people and the PoCo turns off the A/C.
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