No Paul, Lee is indeed referring to the rate of discharge chart,
however, he has chosen the cut-off to be _*3 volts*_, rather than the
customary cut-off of_*2.5 volts*_. (No one uses a cut-off of 3 volts,
that I am aware of. All the charts note that 2.5v cut-off is the
standard for comparison. If we picked 3.5 volts as the cut-off, we would
get a huge spread in the apparent capacity, but that would be silly.)
You are correct that the 12 minute discharge (0.2C rate), the 0.5C rate,
and the 1C rate all show the same capacity, 3.25 mA-hr. While the 2 hour
discharge (2C rate) shows a slightly elevated capacity of 3.350 mA.
I suspect that the faster rates had some unavoidable internal
heating, (even though the case temperature was held at a constant 25
degrees Celsius,) which tends to decrease the internal resistance, and
tends to raise the terminal voltage under load, especially when the
impedance rises near the end. Thus, the apparent capacity shift is quite
likely due to increased internal temperature rather than ion diffusion.
Lead acid curves would have shown a much greater sensitivity to the
discharge rate. Much greater. As I said earlier, the ions can diffuse
perhaps 100 times more quickly in Li-Ion cells than in lead-acid cells,
which makes the Puekert exponent very close to unity in Li_ion. Puekert
is not really useful in Li_ion because the diffusion is so fast in Li-Ion.
Bill D.
On 3/17/2019 12:40 AM, paul dove via EV wrote:
That’s not what the spec sheet says. You are reading the graph for temperature
variations. There is almost no difference due to discharge rates. 2C is 3250
and 0.5C is 3350 according to your spec sheet.
And lead acid batteries have a Puekert coefficient as low as 1.08.
Sent from my iPhone
On Mar 15, 2019, at 9:14 AM, Steve Heath via EV <[email protected]> wrote:
Peukert's law is not an actual law but an empirical formula that is based on
actual physical measurements. It gives an approximate estimate of how much
capacity can be obtained. The way that it is used is that the capacity is
measured at different discharge rates to give a co-efficient that can then be
applied to other batteries. This is where the difficulty lies. The coefficient
is taken by measurement and providing another battery is the same then the
coefficient is applicable. If not and it isn't.
The key point is that the discharge curves for li ion batteries do vary significantly
depending on the load in real life according to the manufacturer data. At the 0% soc end
point, the capacities are the same (give or take). This is why the Peukerts coefficient
is close to 1 rather than 1.2 or higher for a lead acid battery. Hence the comment that
it is not applicable. It is there but very small to be accurate. However at a typical
self preservation point e.g cutoff voltage used by BMS, the capacities are different.
As a result, there is a "Peukerts" effect where the amount of capacity that can
be obtained is different depending on the discharge current. It is not the same Peukerts
effect but the end result is the same. Discharge more, less capacity...
The data sheet for a Panasonic 18650 shows this effect very well (
https://www.batteryspace.com/prod-specs/NCR18650B.pdf ) where a cut off voltage
of 3v gives a capacity of 2400mAh at 2c and 3300 mAh at 0.2C . At the 0% soc
point they all come out at 3300 and 3400. So discharging to 0% soc, the
discharge current is more or less irrelevant. Interestingly these results are
taken at constant cell temperature where any overheating advantage is not
applicable. Without seeing the complete paper that was referred to, it is
difficult to know if any comparison with manufacturer data was made or whether
tests were done at constant temperature and what the results were.
Discharging to a lower 15-20% level to protect the battery, there is a big
difference. If you want to get the best capacity out of a li ion battery with a
BMS, either reduce the discharge rate or change the BMS to accept a lower
cutoff voltage and risk battery damage.
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