Here is an initial analysis and a recommended configuration for your proposed system:
(1)
ENERGY CONSUMPTION
(1.1) The LED string consumes 12V * 50mA = 0.6W
(1.2) You would like to power the LED string for 6 hours per 24 hour day, so the LEDs will consume 6 hours * 0.6W =
3.6 Watt/hours (W/h) per day.
(2)
ENERGY STORAGE
(2.1) Assuming your 18650 Lithium Ion (LiIon) batteries each have a 2A/Hr capacity (2,000 mA/h), each battery can store 3.6V * 2A/h =
7.2 W/h of energy.
(3)
ENERGY SOURCE
Assuming that you get 4 hours sunlight a day- only a very rough estimate which will be pessimistic if you live in Florida and optimistic if you live in Alaska.
(3.1) The 12V 3W solar panel will produce 4 hours * 3W =
12 W/h each day.
(3.2) The 5V 2.5W solar panel will produce 4 hours * 2.5 Watts =
10 W/h each day.
(4)
SUGGESTED SYSTEM
(4.1) One 18650 battery which will store sufficient energy to power your LED string for (7.2 W/h)/ 0.6W = 12 hours.
(4.2) Say the 12V solar panel, but one of the 5V solar panels would do, if you prefer.
The suggested system passes the acid test because the energy input and energy storage are greater than the energy consumption.
You may ask why I have suggested a LiIon battery and dismissed the lead acid battery:
(1) The lead acid battery has an energy storage capacity way in excess of your needs at, 12 *18W/h = 216 W/h.
(2) A LiIon battery is much easier to charge and and has a far better defined cut off voltage.
(3) A LiIon battery maintains its charge much longer
(4) LiIon batteries are smaller and much lighter for a given energy storage
(5) The charging efficiency of LiIon batteries in much higher than lead acid batteries.
(6) You can use much more of the stored energy
(5) I do not like lead acid batteries (but they are necessary in some applications).
Give the suggested system above some thought and let us know if it fits in with your plans.
The rest of your requested functions: charging, battery cut off voltage, automatic switching on and off of the LEDs, etc can then be sorted at the detailed design stage.
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