Thanks Paul. I thought it was a simple misunderstanding.

On 16/03/2019 21:07, Bill Dube via EV wrote:
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.)
It's Steve actually but no offence taken. I selected 3 v as it has a nice horizontal line  with which to visually drop the perpendiculars. And yes 3v is a bit high for a cut off voltage. The BMS I use is set at 2.85v but some will go lower or higher. The actual voltage will depend on the battery cutoff voltage itself which does vary from manufacturer to manufacturer. Some quote2.5v but others higher like 2.8 or 2.9. The end result is that the more current you discharge at the less capacity you will get. The BMS needs to be set at a high enough point to stop discharge to 0% but low enough to get a reasonable capacity.

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.

To be honest Peukert is not a law but an empirical formula that is specific to the battery type and conditions which makes its use not very accurate at all. It does describe an effect (but not explains why it happens) and the coefficient gives an indication of the depth or severity of the effect. Yes you can do the calculations to as many decimal points as you want but the error still might be +/- 20% or more!

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 <> 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 ( ) 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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