Most controllers have an screen that shows the voltage. It should be north of 13v if charging. That or just check the battery voltage on a sunny day and it should be north of 13v.
If its just the fridge and you run almost nothing else 12v, it's likely OK for a night or two of boondocking with 100w. A second battery would be more useful than more solar. This assumes a 12v compressor fridge...an absorption fridge (also runs on propane) will easily use 10 times as much when running on electricity. It also assumes it's not killer hot out and you leave the door open a lot.
If you want to run more 12v stuff (lights, fans, furnace, etc...) and boondock for multiple days, an energy audit is the way to go. Simplified a bit:
- How long will each 12v device be run per day, then mulitply the wattage by the hours it is on to get total amp-hours @ 12v.
- How many "usable" amp-hours does your battery bank have (lead-acid batteries should only use 50% of the rated amp-hr and lithium should only use 80% of the rated amp-hr...using more can prematurely age the batteries). Convert to watt-hours by multiplying by 12.
- Divide usable watt-hours by how many watt-hours you estimate you will use. This will give you an estimate of how long the batteries will last in days. Discount this by 20-30% to cover items you missed or aging of batteries eventually reducing usable amp-hr.
- Solar is really about longer term boondocking. If you are stopping for a night or two, solar is mostly a bonus. If boondocking longer term, you want enough solar to cover your daily consumption. Take the rating of the solar panels and multiply by 4 to get an estimate of how many watt-hours it will generate (100w panel would be 400watt-hour generated each day). In reality it will vary based on time of year and weather (clouds are a big impact) but 4 times the rating is a good starting point.