I want to design a solar powered system but I am puzzled by the type of battery which I should use. I am aware that for solar applications special batteries are available but I could not find any in my locality. Please guide me as to what differentiates a solar battery from a normal battery. And in what way the characteristics of charging and discharging circuit differ for both batteries.
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Batteries have a lot of properties. For example, some batteries need to be fully discharged before charging. Some batteries (car starter batteries) are designed for supplying short bursts of high current and then be recharged and are not designed for a deep discharge. Usually the "usual" battery is a plain old car starter battery and the "solar" battery is a deep-cycle lead-acid battery which is more or less a variation of a car starter battery.
What you obviously will want is a battery that allows for partial discharge and allows for deep slow discharge - those are deep cycle lead-acid batteries, Ni-MH batteries and varieties of Li-Ion batteries (people say that shallow discharge is best for Li-Ion, but in professional power tools they work quite well with deep discharge unless it goes beyond some super low level and the latter is guarded against with control electronics).
The three will largely vary in price, weight per stored energy, discharge capabilities, charging requirements and control electronics requirements. Unless you need your power supply to be very portable (like for carrying in a bag) the usual choice is a deep-cycle lead-acid battery - it is relatively cheap and provides decent performance. A very important property of lead-acid batteries is they can't be stored partially discharged - that leads to sulphation and permanent damage, so you'll have to take care of the battery being fully charged after each discharge.
The best way to do this might be to charge the laptop battery directly from the solar panel/s by using a voltage regulator. If you get way more energy from the panels then you should probably use deep discharge lead-acid batteries, preferably AGM ones. They are quite easy to find and they do not have any problem with reasonably high or low temperatures. You can also deep discharge them without any serious harm.
We model a solar cell as a current source but not as a voltage source. For a example 10V solar panel output 3V-15V depending on level of intensity of the light.
There is a solution for this, Just use a joule theft, it will ramp up whatever input voltage to a voltage where you could push energy into a lead acid battery.