Starting with the simple devices first.
I want to be very specific in general terms, that the following definitions are specifically, in general mostly accurate, except specifically when manufactures in general, specifically play fast and loose specifically in general with their general specific terminology and advertising claims, generally speaking.
Would a manufacturer do that? :scratch2::scratch2:
Basic surge protectors try to limit voltage spikes in the AC power line and do not provide any type of voltage regulation. And while some may have filtering to help remove unwanted electrical noise, this filtering may be of only the most basic kind.
Power filters, usually include surge protectors and add additional, more sophisticated filtering to help remove unwanted electrical noise.
Power conditioners may run a range of devices depending on marketing by the manufacture. The basic ones are simple power filters. The more sophisticated units may contain more comprehensive filtering to clean up the AC power.
They may include some form of voltage regulation, and be called an AVR (automatic voltage regulator) device and to be clear they will not function correctly if the voltage drops below a certain level.
Whether or not an AVR will meet the needs of the end user depends on the specific situation, the quality of the device and the actual range of voltage variation.
The ones that may have an issue with making a clicking sound use a simple stepped auto transformer to compensate for various windows or ranges of low and high voltage. They contain circuitry to sense the AC power voltage and direct the unit to select the appropriate voltage on the auto transformer to provide the most appropriate amount of voltage correction.
The clicking sounds that are heard are the relays used to select the voltage taps on the auto transformer. These devices are not uninterruptible power supplies and will shut down if the AC power line voltage goes low enough and or will not have enough regulation range to keep your voltage in the needed range.
Due to design and quality some will produce more noise and not all of them will have the same voltage adjustment windows or steps.
Under the category of locally regenerating (at the end user’s location) the sine wave AC power, are cheap UPS (uninterruptible power supplies) devices.
Since the sine wave AC power is locally regenerated it should be a clean and stable source of power, unaffected by unwanted noise on the AC power line and unwanted voltage fluctuations including the total interruption of the incoming AC power line.
One can move up the quality ladder to devices such as The Tripp-Lite SU1000RTXL2Ua as mentioned by N8Nagel. His post, #9 in this tread, contains good information.
Basic surge protector devices and power line filter devices are usually rated for a 15 amp load (all though not all are) and as such should handle a refrigerator, but UPS devices and some devices similar to the Tripp-Lite device may not have the capacity to handle a high current device such as a refrigerator. It is important to consider the power and current ratings of these devices.
As you can see, you have received many suggestions, unfortunately several have not addressed your specific situation (too much fluctuation) in voltage, possibly because they do not understand your situation or they do not understand the functionality of the various devices.
If you are having AC power voltage fluctuations that are outside of normal operating voltages, that by definition eliminates the basic surge protectors and AC power line filters and some so called power conditioners. While they may help protect against voltage spikes and help to remove unwanted electrical noise, they will do nothing to stabilize varying AC line voltages.
For this you will need one of the devices that help to regulate the voltage. Some, as already mentioned do this in steps and not all steps are created equal. These are the devices that may produce the clicking sounds, some worse than others. To be clear some power conditioners, as defined by the manufacture, may contain an AVR.
Then there are devices that regenerate the AC power sine wave such as cheap UPS devices and the higher quality Tripp-Lite SU1000RTXL2Ua type devices. These devices provide AVR, (automatic voltage regulation), spike protection and filtering of unwanted electrical noise and they do it mostly silently, although as N8Nagel mentioned there may be some cooling fan noise. The specifications for these device, may in some cases, specific there operating noise level.
To help you keep the terminology straight, it may help if you refer a specific device by its highest level of functionality. For instance the device referenced by N8Nagel is a a high quality UPS, not a surge protector that includes automatic voltage regulation.
As you move up the ladder of functionality for these devices, each higher level device usually contains (with some variation) the functionality of the devices below it.
While not everyone needs the full functionality of devices such as the Tripp-Lite SU1000RTXL2Ua and other similar devices, and some of the other devices mentioned above may be adequate depending on the situation, it is hard to go wrong using a device like the Tripp-Lite above.
However you have added an additional requirement of supplying your refrigerator with clean, stable power and that adds the need to pay particular attention to the power and current rating of the device.
