[Power] Sizing a solar array for the one laptop per child program

[Richard A. Smith]

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> Greetings,
>
> I am a first year grad student at UMASS Lowell and I am working on a
> project to size a solar array capable of providing power to 4
> One-Laptop-per-Child PCs for 5 hours per day 5 days a week during the
> months from April through December. The arrays are to be installed in
> a remote village in Peru.
>
> I have been reviewing the specs online and I am having trouble sizing
> the load. The XO-1.5 laptops are shown to draw power limited to 25W.
> Does this imply that I should size my array to provide 25 Watts to
> the laptop at all times during operation (25W*5 hours)? Also, the
> battery capacity is 16.5 Watt-hours (NIMH) and 22 Watt-hours (LiFeP).
> What is the difference between NIMH and LeFeP? If the laptop is
> pulling 25 Watts, and the battery capacity is 22 Watt-hours, does
> this mean that the battery can only provide a little less than one
> hour worth of capacity??
>
> My system voltage will be 12 volts DC. We will most likely be using
> 50 watt panels that were donated to the program, and I have the
> irradiation data for the location. How should I size my load for four
> PC’s operating 5 hours a day?
>
> I appreciate any help you can give me.
>
> Respectfully,
> Joe

When sizing the system you need 2 numbers:

1) is peak power draw.
2) is the amount of energy your system needs to source under worst case 
conditions to meet your needs.

You can ignore all the info about the NiMH batteries.  NiMH was only 
used in some of the larger test runs of XO-1.  Only LiFePO4 batteries 
have been used since we went into mass production.

#1 is easy.  The 25W number you see listed is the peak power draw for 
the laptop at any given time.  With 4 laptops the peak power draw is 100 
watts.  This means that all the components in your system need to be 
sized such that they could (if demanded) handle 100W of power.  For a 
12V system this means 8.3 amps.  10 amp rating on things will be easy to 
get.  This peak number will only be reached when charging a low battery.

#2 is a bit more difficult since it depends on a model of your expected 
laptop usage.

I usually size the load in number of battery recharge cycles per day. ie 
the laptop starts the day with an empty battery, gets charged and then 
used back to empty.  It assumes the laptop is powered off during 
charging. Its not a perfect model but it makes the math easy.
When I look at my battery charge logs I typically see 20 - 22 watt-hours 
of energy used.  Bruce Baikie who is doing a DC solar setup for Haiti is 
using 25.5 watt-hours per charge as his base unit.  I think 25Wh is a 
good number to use.

Therefore if you want to completely charge 4 empty XO batteries you will 
need a system that will supply you with 100 watt-hours of energy (4 
units * 25Wh/charge).  On a full battery the average workload will get 
2.5-3 hours of use without power management.  If your workload allows 
for power management to periodically put the XO into low power modes 
then you can get much longer operation times but you would need to do 
testing with your workload get a runtime to use.  If you don't have that 
then you need to assume zero power management.

You desire 5 hours of operation so in the simplistic model thats 2 
recharges per day.  So your total energy estimate would be 200 
watt-hours per day.

The more complex model would be to assume that your are not going to 
completely exhaust the batteries all the time but instead have them 
normally connected to DC power.  Then your daily requirements depend on 
how much power your workload will use.  Sitting idle (no power 
management) the XO-1.5 average draw is about 5 watts.  Going full out 
its about 10 watts.  So your daily usage for 5 hours would be somewhere 
between 25Wh and 50Wh.  Putting your usage for 4 between 100Wh and 
200Wh.  If the laptops go home with the kids at night and come in with 
empty batteries then you need to add an extra 25Wh per battery.  So your 
usage could be 200 - 300Wh.

Hope this helps.

-- 
Richard A. Smith  <richard at laptop.org>
One Laptop per Child