I agree with @MrSoftware. Read the specs. Slow charging is not the problem, not as long as the batteries have enough charge every time you want to fire off the solenoid. One question you haven't yet answered concerns the solenoid. How often it will be used and for what duration?

If you're charging at 10 watts per day and using the solenoid at 9 watts per day then you're golden. But if you're hoping to use it 12 watts per day then your recharging system will need to be upgraded to handle the higher load. Now - I'm using these numbers purely as a reference, and this isn't really the way you measure things. The point is that if the solenoid is using more energy than the batteries are storing then the system will fail to operate when needed. The most likely weak spot in the system would be the solar panel(s). Full direct daylight occurs only when the panel is directly facing the sun. As the sun moves off of "Direct Facing" the voltage will drop. At first it drops slightly, but as the day goes on the drop becomes more prominent. Then there's obstructions concerns; clouds, smoke from fires, trees and building shadows. That's why I focus on the daily production of the panel. Also, summertime sunlight is longer and more direct. Winter is shorter and less direct. Unless you're planning on moving the panel to capture the most possible sunlight. These are the factors that need to be figured into the equation.

So again, how much use is the solenoid going to get? How much energy does it use? How long will it be energized every time it's used?

 

In post #18 is mentioned it was a demo unit, so maybe the daily use isn't well defined yet. ?

 

In post #18 is mentioned it was a demo unit, so maybe the daily use isn't well defined yet. ?

Sorry I misunderstood the question, there isn't much of its daily use, as it is a project that I intend to do to understand how to charge a battery from a solar panel and supply power to a variety of several components connected to the same battery.

 

Let us assume average SP output as 3W for 8 hr. or 24Wh. or 1440 Ws. Load 2 A @ 12 V & 1 s = 24 Ws, so should be able to complete 60 cycles
per day. If demand is less then should be able to keep battery charged, if demand is greater, the a larger SP is needed.
Open circuit V might be about 18V , so if charge V is between 12 & 18 V then SP should be able to charge the battery.
As always, we need more information.

 

IMHO; if it's a learning project, take your best guess at it and build it. Don't fall victim to analysis paralysis. You'll probably make some mistakes, it may or may not work perfect on your first shot, but you will learn something guaranteed.