I have had a tiny solar system at our hunting cabin, starting with a single deep-cycle flooded lead-acid battery like you would use for a trolling motor (rated at 74 Ah) from the local farm supply store and a 100W polycrystalline solar panel from a big box store,. Our first inverter ran my husband's CPAP all night long the first year, but since the panel was wired direct, it continued shoving voltage in after the battery was fully charged, so it hydrolysed electrolyte, not so good for long life, and wouldn't run the CPAP all night the next year, so I added a second battery. Time passed, I bought a charge controller (
Bogart Engineering SC-2030) that is still sitting in the box. My current setup has 2 100W panels and 3 of the same batteries (one of which I managed to boil dry-it took over half a gallon of distilled water to bring it back up), but when I bought a new, larger inverter (not even pure sine), it would alarm after a couple hours. Rearranging cable connections did not help. Finally for whatever reason, when I put the CPAP on an extension cord with no other changes, it worked fine. So there is something about the way the inverter draws current from the battery that makes it dip into a state it thinks is low voltage, and maybe the cord sort of evens things out so the draw isn't as deep. I suppose if I dragged my $10 used oscilloscope up there I could find out...
The other thing is, the SLA and AGM batteries I have had experience with are not robust when it comes to solar or other practical uses. We have replaced my husband's AGM ATV battery at least 3 times, and he has only run the ATV a handful of times. PITA. But he got it cheap, used, so that met his standards.
If you really want to learn about making a solar system and how it responds to loads, you can get far with just your multimeter, with the caveat that VOLTS only tell half or less of the story. You must know the amp draw in order to correctly understand your battery state of charge. And to measure amps, you need a known resistance to measure voltage across, so you can use our old friend V= I*R. A Radio Shack 1/4 watt resistor will not do the job, for that you need a "shunt" (see
this page for description. Other places sell them too). All a shunt is, is a resistor that can pass all the current while not heating up or reducing the voltage drop very much, and you put it in line with the positive line from your battery, so all the current passes through it. A good analogy is a water meter-water comes from the supply, all of it passes through the meter, and then to the various loads. Every amp you use has to be replaced, AND a little more, by your charger. Put in the shunt, measure the amps going into the battery from the charger, and out to your loads.
The other key thing to understand about lead-acid batteries is that the temperature affects the voltage. And for the long-term life of your battery, you should not discharge deeper than 50% state of charge. According to
this chart, 11V is 10% state of charge, and this is not too good for the life of your battery. Make sure you understand, though, that the chart shows OPEN CIRCUIT voltage (no loads) and you can't measure this accurately until after AT LEAST an hour has passed since you drew a load.
It seems like a lot to learn, but you can really get very far indeed with good, concise information. I highly recommend
Handy Bob Solar, as this guy is a retired electrical engineer who has written pages about setting up a usable solar system for RVing or small off-grid cabins, and he shares his actual experience with the components he recommends. I haven't found any information there that did not work as he said it would.
Good luck, and enjoy your system!