I will try to explain all of this in fairly simple terms.
If you want to try and use the old battery, you should do a capacity test. Properly charge it to 13.8 volts, and then connect a known load to it, maybe a car headlight. Measure how much power it is putting out and how long it runs for. Is it holding enough energy to be worth the space it takes up? Also measure the voltage under the load. If it is falling below 12 volts, it will take energy away from the other parallel batteries. Batteries in parallel need to have matching voltage. If your old battery has one week cell, it is now a lower voltage and won't work well.
Charge controllers. There are a few different types of PV (photo voltaic) solar charge controllers. The super cheap ones are called PWM for Pulse Width Modulation. It looks that the one you have is this type. They are basically just a semi smart switch. It directly connects the solar input to the battery. Solar panels act like a current source, so the voltage of the solar panel(s) will be pulled down to the battery voltage and you will get a current hopefully close to the solar panel IMP current going into the battery. As the battery charges, the voltage rises. At some point, the charge controller will see the voltage hit it's pre-set voltage limit. For a "12 volt" controller, this should be about 13.5 to 14 volts. It will then turn oiff the current from the solar panels and let the battery voltage fall. It only has to drop a small amount. If there is any load on the system, like running lights or the inverter, the voltage will fall quickly and the PWM charge controller will turn back on. Each on off cycle is a pulse, and the width of each pulse is "modulated" to make the average current match your loads. If you are pulling 5 amps, but the solar panels are pushing 10 amps, it will be on about half the time. It works, but it is not efficient. The amp rating is how much current it can switch. Most PWM systems use "12 volt" panels to "12 volt" batteries. So you run the panels all in parallel. The current of each panel adds up. And use the ISC or I(current) Short Circuit. That is the maximum current the panels is expected to produce. My 100 watt panels are each rated at about 6 amps. So I could put 5 of those on a 30 amp controller. But 30 amps at 12 volts is only 360 watts. And that is where PWM loses energy.
The other most common type of charge controller is MPPT. They do cost more, but they are well worth the extra cost. Using the same 5 x 100 watt 12 volt panels, you would get the full 500 watts in the same conditions. You typically get 30% more energy with an MPPT controller, even when the PWM is doing it's best. Once the battery is full, then it no longer matters. So for a small system to run a few lights, where the battery s filled up easily, PWM works just fine, but if you want the most power to run things like an air conditioner, then you really want to go MPPT. MPPT stands for Maximum Power Point Tracking. The amount of power a solar panel produces varies directly with the amount of light hitting the panels face. The MPPT will constantly measure what the panel is producing a load the panel to the most power possible at any given moment. But that voltage will be constantly changing. So the MPPT uses a DC to DC voltage converter to put that energy into the battery. The maximum power point of my 100 watt panels is up at 18 volts VMP at 5.5 amps IMP. Running 3 of them in parallel is 16.5 amps at 18 volts. The PWM would only produce 17 amps x 13 volts = 221 watts, where the MPPT will produce 16.5 x 18 = 297 watts. 34% more power. And since the MPPT can convert the voltage, you can run the panels in series. Then you get 54 volts at just 5.5 amps. You can use smaller wire and have far less losses on a long wire run to the panels.
MPPT controllers do have current and voltage limits. The current limit is typically on the output side as most reduce the voltage down to the battery, so that current is higher. The voltage limit is on the input side because that is the higher voltage. Victron controllers are a bit expensive, but I ended up changing out my perfectly good working BougeRV MPPT charge controller, and the Victron is better in many ways. Their model numbers are pretty easy. I got the "Smart Solar 150-35" 150 is the input voltage limit and 35 is the output current limit. You set your battery type and it just works.
When trying to run larger loads over time, you need to figure out how much peak power and total energy you are working with. You mention a 680 watt air conditioner. You currently have 3 x 100 watt panels. Assuming you get pretty good sun exposure, let's say you get an honest 5 sun hours per day. 300 watt x 5 = 1,500 watt hours. 1,500 / 680 = 2.2 hours. 300 watts of solar panel on a good day could run the air conditioner for just 2.2 hours. If you add more battery, it may run longer from fully charged, but then what is going to charge the batteries again? You can only get out the energy that is put in. How many hours do you want the air conditioner to run for in a single day? "Sun Hours" may be a little odd to understand, so I will try to explain it here. This is the energy plot from my larer Enphase AC PV solar power system.
I have a total of 4,800 watts of panels on that. On that day (March 14, 2024) the system produced 25.9 kilowatt hours.
25,900 watt hours / 4,800 watts of solar panels = 5.4 "Sun Hours" of daylight hit the panels. That is a very good day for late winter/early spring here in southern California. Now the sun was shining, and it was daylight from 7 am to 6:30 pm, or 11.5 hours, but the energy hitting my fixed angle panels started low, ramped up, peaked about 1 pm, then ramped back down over those 11.5 hours. I got about the same energy as if it was perfect noon time sun for just 5.4 hours. That is "Sun Hours" also called solar insolation. You will see there are 2 other lines in the graph. The higher one has a few dips in it, that is clouds going by. That is the trace from the day before. Those clouds dropped the total energy to 23.3 KWHs. That is a loss of 2.6 KWHs just from a few clouds. The lower trace was the same day but from last year. We had a storm with heavy clouds and that really reduced production. Only making 3.3 KWHs, or less than 1 sun hour over the entire 11 hours of daylight.
If you want to run a 680 watt air conditioner for 10 hours of the day, you need 10 x 680 = 6,800 watt hours. Let's say you can get a fairly consistent 4 sun hours per day. 6,800 watt hours / 4 hours = 1,700 watts. Yes, you would need 1,700 watts of solar panels to produce the energy needed to run the air conditioner for 10 hours a day. On a good sunny day, it may run longer, on a cloudy day, it may not run as long.
If you are only going to run it while the sun is up, you don't need a whole lot of battery, but you do still need more than you might think. Let's say it is high noon and the panels are making 1,700 watts. Great! The 680 watt air conditioner is using those 680 watts right now, but that leaves 1,020 watts coming from the panels. That needs to go into the batteries. At 12 volts that is 1,020 watts / 12 volts = 85 amps of charge current. OUCH! that is a lot for a battery. Lead acid can typically only charge at 0.1 C or just 10 amps for a 100 amp hour battery. Even a good Lithium Iron Phosphate (LFP) battery should only be 0.5 C or 50 amps to a 100 amp hour battery. Some will take a full 1.0C 100 amps, but check with the manufacturer. And when a cloud goes by, if the solar panel output dropped to zero, the full 680 watts needs to come from the battery to keep the AC running. 680 / 12 = 57 amps. The battery needs to supply 57 amps when the sun is not hitting the panels. That should not be too hard. But since the solar panels are not making peak power most of the time, the battery needs to flatten it out. Also keep in mind that I did not even bother to calculate any efficiency losses, or the compressor start surge from the AC. I would suggest having enough battery to store a full day of solar production. Let's call it 7,000 watt hours at 12 volts = 583 amp hours of battery capacity.
It adds up pretty fast when you want to run a decent amount of power for several hours.
The best way to design a system is always to start from the amount of energy you need to provide. Power x time for everything you want to run. When it is all added up, you can see how much battery and solar panel is needed.
I have a total of 6,800 watts of solar panels now, and 36,000 watt hours of battery (720 amp hours at 50 volts) and a 6,800 watt inverter that can run virtually everything in my house. But I am still grid tied as I run out of power from time to time.
