Richard A. Smith richard at laptop.org
Tue Jul 22 15:49:55 EDT 2008

```mianeil2 at yahoo.com wrote:

> I was also wondering if you could give me feedback on this table. The
> table shows how much kWh is needed a year to power a xo based on
> different scenarios. If you think I should add or change anything

As I often state in my discussions on laptop power, calculations like
this are actually pretty complex and the simplistic approach while good
for ballpark estimations can have a large amount of error.

First as others pointed out you units are wrong.  You need to substitute
Watts every where you have kW.

The next issue is that you are assuming a perfect conversion on the
recharge half of your cycle.  Which is not correct.  The avg power draw
of 5-7 watts for the XO is measured internally either via the battery
sensor or by our instrumented XO.  It does not take into account the
efficiency of the DC/DC converter when recharging the XO from external
power.
It also does not take into consideration the charge efficiency of the
battery.  It takes more power charge a battery than just the usable
capacity of the battery.

The DC/DC converter's efficiency is affected by the difference between
the input voltage and the output voltage.  We don't really have any
numbers on the exact range of efficiency for the XO @ 12V but typically
your average DC/DC converter is around 85%. The 88% number pops into
mind from when I was last looking at such things.

Then there is the charge efficiency.  Which is more complex because its
actually 2 numbers. One for constant current (CC) charge mode and then
another for constant voltage (CV) charge.  The batteries start off in CC
mode and then switch to CV mode after certain criteria are reached the
criteria happens around the same time but is a bit different for each
battery and much more different between the 2 types of batteries.

I don't have numbers for these efficiencies.  The EC code has comments
with magical constants that suggest certain numbers for these values but
I've learned that a lot of those comments may be wrong or apply to
earlier versions of the batteries.   The range suggested is 80 - 90%.

The only way to know exactly what a good average for charge efficiency
is would be to measure and compare the power in with power out across
several batteries of each type (remember we have 2 chemistries).

Thats possible in the case where the XO is powered up and you can read
the battery sensor, but when the XO is off its not so easy.  Guess what?
Your %'s will be different in the 2 cases because the charge rate is
much faster when the XO is off.

Buts lets just say for a quick ball park that DC/DC is 88% and average
battery CE is 85%.  Now your recharge numbers are off by about 25%.

Listing things in "cranking hours" may also be problematic.   If you
really were cranking some human power device your output would be so
variable that the only way to get meaningful data is to measure it and
develop some sort of profile for what the average person can really do.

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

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