There are 2W poly-silicon based panels that are designed as "battery maintainers" for storage of cars. They work well even in winter at latitudes of 40+ and a rainy environment behind a windshield (direct experience). So very low insolation and lots of light reduction going on. This basically offsets leakage and keeps the battery from going flat which can be bad for longevity.
Most panels are rated for an insolation that corresponds to mid-latitude US and summertime conditions this is known as STC (Standard Test Conditions) so that little 2W panel mentioned above may have been producing ~ only 1W peak at best. Keep in mond that was only ensuring that the battery is charged for the next spring.
In equatorial Kenya, especially at higher elevations the insolation will be 3 - 4X of the scenario above. So closer to 2.5 W for much longer during the day. The total Energy (W*Hr) in Kenya vs. winter temperate example will be much much higher simply because the light will be available for longer in the day. Insolation maps for the all areas are available.
Is your 5W sufficient? well more than sufficient to keep the battery charged. If it's enough for all the units (like lights etc.) that need supplying is another thing because that depends upon demand. I would recommend that you look at that side of the equation first to allow you to supply parameters for the design.
Since cost is so extremely constrained, here is one approach to consider.
The smaller the panel the better. With a small panel your charging becomes almost an non-issue and is safe. But then the issue shifts to how do I prevent the battery from being overdrawn so that the small panel has a chance to recharge it the next day. the design shifts to having a simple monitoring circuit that allows only so much power to be drawn and then protects the battery (with an over-ride for emergency).
Of course there are other ways of doing this with different balances of panels, batteries and circuit sophistication and cost. The social elements are probably the main area where your project is going to fail or win.
Here are some numbers:
- Nokia feature phone uses a BL-5CB battery 800mAh @ 3.7 V -> 3 W*h -> call it 4W*h with inefficiencies.
- White LED lamp draws 10W @ ~ 1000 Lumens (60w incandescent = ~1000 Lumens) at 4 hours/night = 40 Wh -> 50 Wh with inefficiencies.
- note this is totally un-realistic, as this LED would be very very expensive.
- a reading light need not be ~ 1000 lumens either.
- so lets cut this in 1/2 -> 25 Wh needed
- worst case scenarion 25 Wh + 5 Wh = 30 Wh might well be doable with a 5W panel and 6 hours a day of sunlight.
It is a long question, but better than a short one, as you've shown your own research.
1) Solar cells. If you're stacking your own ones, stack 9 of them and get the 4.5V of the original circuit.
2) Battery charging. Batteries are the only thing you've left out of your spec. This is an area where the circuit design relies on cutting a lot of corners. In theory it might be out of spec, if you were to put 4.5V at 280ma through AA NiMH cells indefinitely. In practice, you don't get full sun all day, you'll be using it indoors, and you're not going to get optimal power transfer from the cells, so this isn't going to cause problems.
3) Diode. It's just a regular diode, not a zener. Current through it is actually determined by the battery and right hand side circuit, not the solar panel - the transistor is off when the panel is generating electricity. The original 1N914 will be fine. 1N4004 will also be fine.
4) Resistors: not a precision component here, use whatever meets your cost constraint. 5.1k for 5k is fine.
5) Wire: not critical. Your ebay link looks suitable. Thinner is better for the toroid.
6) Transistors: stick with the exact part numbers. Design may rely on specific parameters.
7) LED: again, this circuit relies on cheating. Normally a white LED won't run from two NiMH cells. The joule thief part provides a boost converter that gives small pulses of higher voltage. It doesn't have the capacity to provide a lot of current at that voltage. In combination with the pulsing this means there should be no risk of damaging it.
(A proper analysis of this circuit would be good, if nobody else supplies one I'll do it in a few days).
Best Answer
If you are thinking about using just one of those panels and a standard incandescent house bulb - forget about it ! -. That panel only produces 0.6 watts of power, and that's likely only in fullest sunlight.
You may be able use a very small DC bulb from a flash light (torch) with that panel. If using a small 3V 200ma incandescent bulb you could connect it directly to the leads of the solar panel. Of course with no other components (like a battery), when a cloud goes by the light goes bye-bye.
Another option would be to hook up 10 red or yellow LEDs in parallel (with a 51 ohm resistor in series with each LED). That allows about 20ma per LED. This could also be connected directly to the panel output (observing polarity of the LEDs).
The 3V output would not quite be enough to directly drive most white LEDs as they tend to need 3v or more. There are booster circuits available that could increase the voltage to drive a white LED, but with only one solar panel you would still be limited to 0.6w (or less depending on the efficiency of the booster). - Here is one example of a voltage booster that might be used - http://www.icstation.com/icstation-mt3608-step-booster-power-apply-module-p-3448.html
To get any significant light output you would need to buy several panels and place them in series or parallel to get higher power levels.