So you want to go for 7 to 14 days on battery without using a generator.
You figure that the most solar you can have is 180 watts. 180 watts will provide max 15 amps per hour (amp hour) (180w/12v=15A). Unfortunately, you will likely never see the full 15A - more like 8-10A for maybe 8-10 hours = 70 to 100Ah total incoming. But for fun - let's use 15Ah.
For a fridge to use only 30 amp hours per day (on battery alone without using solar) - it would draw only 1.5 amps on average. That is a pretty low number. I would recommend that you verify the fridge draw. If you have a battery monitor - such as a Victron 712 - you can use it to estimate useage. For fun - let's use 30Ah per day.
So - let's do the math for the fridge only.
30Ah per day x 7 days = 210Ah.
30Ah per day x 14 days = 420Ah
Odds are you will use twice that.
15Ah per day x 7 days = 105Ah
15Ah per day x 14 days = 210Ah.
Odds are you will get less.
So in 7 days the minimum draw will be 210Ah (no lights, no radio, no TV, just fridge) and the maximum charge will be 105Ah leaving you with a minimum battery discharge of 105Ah.
Now, let's talk batteries.
Lead acid batteries are only good for 50% of rated amp hours if you want them to last. Otherwise, expect to replace them every few years. Buy a quality battery like Lifeline or Trojan. A Group 27 12v
battery is 80Ah, a Group 31 12V battery is 105Ah. So based on the math, you will need (2) 105Ah G31 12V batteries to last 7 days.
A couple of issues to consider:
1. Flooded lead acid (FLA) or AGM need to be brought to 90-100% charge daily or they will develop lead sulfate crystals on the plates (sulfation) which will reduce capacity (less amp hours). So you will need to figure this into how many amp hours you want in the bank.
2. FLA/AGM are nominal 12V which means when you see 12V you have used 50% of the battery capacity.
3. Motors and compressors (water pumps, fridges, etc.) work harder, hotter and less efficient at lower voltages.
4. FLA/AGM batteries charge slowly. The bulk stage (up to 80%) allows higher voltage and higher amps to charge. The last 20% (absorption) reduces voltage and amps. It can take 8-10 hours to fully charge due to internal battery resistance and reduced voltage/amps so not to boil off the electrolyte. There is also a 15% efficiency loss - for every 100 watts charge, 15 watts is lost to chemical energy conversion and only 85 watts is absorbed by the battery.
5. FLA/AGM both require maintenance. FLA should be charged to 90-100% daily and should be equalized monthly. FLA need to have the electrolyte water level monitored. AGM should be charged 90-100% daily.
6. FLA/AGM batteries have cycle life between 300-1000 cycles depending on the manufacturer. This cycle life is is based on 100% maintenance and ideal temperature conditions. This never happens. A cycle life is a 100% discharge based on discharging only 50%. Discharging a FLA/AGM will kill the battery quickly.
Lithium Iron Phosphate (LiFePO4) batteries are good for 100% rated amp hours. However, it is recommended that only 80-90% be discharged. Purchase only lithium batteries with a BMS (battery management system). The BMS protects the battery. BMS come in different amp ratings. The most common is the 100A BMS. That allows 100 amp discharge and 100 amp charge ability. Some batteries offer 150A, 200A, 300A BMS which allow for higher discharge rates and less BMS stress.
So, based on the math, you need (1) 105Ah lithium battery to last 7 days.
A couple of issues to consider:
1. Lithium batteries are 1/2 to 1/3 the weight of FLA/AGM.
2. Lithium batteries are available from 100Ah to 400Ah and all weigh less than 100lbs.
3. Lithium batteries are nominal 12.8V. This means that you still see around 12.8V at 50% capacity and beyond.
4. Lithium batteries require no maintenance.
5. Lithium batteries can stay at a partial state of charge indefinitely without damage to the battery. Lithium batteries can be 100% discharged without damage to the battery.
6. Lithium batteries have 99% charge efficiency. Basically, every watt that the solar panel produces will be stored in the battery. This is important especially on low sun or short days.
7. Lithium batteries have a cycle life of 3000-5000 cycles depending on depth of discharge. The lower DOD, the longer the cycle life. A 25% average discharged battery will have longer cycle life than an 100% average discharged battery. In real terms - if you discharge the battery 100% on a daily basis, 3000 cycle life/365 days = 8.2 years. 50% daily discharge = 16.4 years. At the "end of life" a lithium battery still holds 80% of capacity. That means a 100ah battery still has 80Ah of usable energy.
You have a lot of LFePO4 options.
Potential suppliers include: