[RE-wrenches] Fwd: discharging Rolls batteries

[Michael Welch]

Forward from non-member Julie Haugh:
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Hugh Piggot writes:
> According to Peukert's law (and manufacturers' data bears this out 
> well) the capacity of a battery depends on the rate of discharge. 
> Everyone who knows anything about batteries knows that the capacity 
> is specified at a certain rate whether it be C20 for a 20 hour 
> discharge or whatever. And the capacity at 100 hours (C100) is about 
> 33% higher than the capacity at the 20 hour rate. If you look at the 
> way this is measured though, it is based on running the battery down 
> to a chosen 'discharge limit' voltage. And I have not heard anything 
> from Wrenches nor seen anything in the literature to suggest that the 
> battery discharged in 20 hours has actually lost any amphours 
> compared to the 100 hours one. So it appears to me that if you give 
> it a rest and then start discharging it again, but now at the 100 
> hour rate you could still get another 33% extra capacity.

The amp-hours that are not produced at the higher discharge rates
are lost until the next charge / discharge cycle.  You can't get them
back by discharging at a lower rate after the battery is fully
discharged.
You can increase the remaining capacity by lowering the discharge rate,
but that only applies to any remaining capacity, not to the energy that
was removed.

The proper way to calculate remaining capacity is to add up all of
the Peukert-corrected amp-hours that are removed, using the Peukert
amp-hour capacity.  Unlike regular amp-hour ratings (load for X number
of hours that produces a given terminal voltage), Peukert is calculated
using a 1 amp load, and then the number of hours it takes to produce
some voltage.  Here's a Peukert calculator --

http://www.smartgauge.co.uk/calcs/peukert.xls

(There are other calculators on the web, but many of them seem to
confuse "rated amp-hours" with Peukert-corrected amp-hours, or expect
you to calculate the Peukert capacity to start with.  This spreadsheet
allows you to work with capacity the way you normally do.)

To give an example, consider a T-105 battery which is typically
rated around 225 amp-hours at the 20 hour rate.  If it is an FLA
battery, a good value for Peukert's exponent is 1.3.  Fill in those
3 boxes.  To calculate the Peukert capacity, use the spreadsheet above,
then in the pink "Discharge Rate" box, enter "1".  Under "Total Amp
Hours Available", you'll have the Peukert capacity -- 465 amp-hours.
That is, if you discharged the battery at a constant rate of 1 amp,
at the end of 465 hours, the battery would be dead (ignoring all
of the self-discharge that would have happened in 465 hours).

Now, in the same pink box, enter 225 / 20 = 11.25 amps as the
discharge rate.  You'll get 20 hours as the discharge time and
225 amp-hours as the number of amp-hours that are available.

To see an example of why this matters, consider a 112.5 amp load
for 6 minutes (C/2 at a 10% duty cycle).  Enter "112.5" in the
same pink discharge rate box and you see that the "hours" drops
from 20, to 1 rather than 2.  Those "Peukert corrected amps" is
the amount of capacity that the battery's chemistry "thinks" has
been removed, and it can't be restored without recharging the
batteries.

Thus, you could discharge for 20 hours with a C/20 load at a 100%
duty cycle, or 10 hours with a C/2 load at a 10% duty cycle.  If
you can control load and duty cycle, go for higher duty cycles
at lower loads.  Even though watts-hours per hour remains
constant (100 watts for 1 hour, versus 1000 watts for 0.1 hour),
as you can see, one solution allows you to run for 20 hours,
while the other only allows you to run for 10 hours.

To use the bank teller analogy, when you ask the bank teller to
give you more money faster, they get nervous and some of the
money falls onto the floor and they have to get more out of the
drawer.  They aren't allowed to stop and pick the money up
until the next day when the cash drawer is filled up again.

This URL will allow you to calculate the Peukert exponent if
you have two different discharge rates --

http://www.smartgauge.co.uk/calcs/peukert_2.xls

If you fill that in for the T-105, you'd see that the Peukert
exponent is about 1.3 -- a T-105 will (typically) deliver 225Ah
at the C/20 rate, or 75 Amps for 105 minutes.  Enter 225 for C1,
1.75 for R2 (105 minutes / 60), and 156 for C2 (1.75 hours x 75
amps = 131Ah).  The answer I get is 1.29

> Well now. I don't expect to get away with saying that. But why not? 
> I can't find any evidence that it is not true.

This will be covered whenever the discussion of Peukert happens.

The short answer is that the chemical reactions aren't always
productive, in the sense that the electrons go where you want
them to go -- out the battery posts and into your loads.
--
Julie Haugh
Senior Design Engineer
greenHouse Computers, LLC // jfh at greenhousepc.com // greenHousePC on
Skype