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.


On 15/03/2019 10:20, paul dove via EV wrote:
Peukert's law was developed for Lead-Acid batteries, and works well in that 
application.

It does not necessarily apply to other battery chemistries, especially 
Lithium-Ion batteries. Lithium-Ion batteries tend to self-heat during rapid 
discharge, and the Nernst Equation predicts battery voltage will increase with 
temperature. Thus, the effect of increased resistance is offset by the 
self-heating effect. This advantage of Lithium-Ion batteries is a well-known 
advertised feature. In a research paper, a 50Ah lithium-ion battery tested was 
found to give about the same capacity at 5A and 50A; this was attributed to 
possible Peukert loss in capacity being countered by the increase in capacity 
due to the 30◦C temperature rise due to self-heating, with the conclusion that 
the Peukert equation is not applicable.

https://www.google.com/amp/s/www.researchgate.net/publication/245106038_A_critical_review_of_using_the_Peukert_equation_for_determining_the_remaining_capacity_of_lead-acid_and_lithium-ion_batteries/amp

Sent from my iPhone

On Mar 14, 2019, at 10:19 PM, Lee Hart via EV <ev@lists.evdl.org> wrote:

Michael Ross via EV wrote:
I am not sure about previous discussions and you may know this: Peukert's
Law is not applicable to Li ion cells in any way. It only relates to lead
acid cells.
I agree with the rest of what you said, but not with this. Peukert's law says 
nothing about the chemistry involved; it applies to *all* types of batteries 
and all chemistries.

Peukert's equation applies to any battery or cell that has internal resistance, and that has a 
minimum "cutoff" voltage below which it is harmed. It simply states that the higher the 
load current, the lower the apparent amphour capacity. High currents cause a larger voltage drop, 
so you reach the "cutoff" voltage before the cell is truly dead.

The amphours are not "missing"; you just can't get them without reducing the 
load current, or pulling its voltage below the safe minimum. If you're willing to shorten 
the life of the cell, you can still get it.

Peukert matters more for lead-acids because they typically have a higher 
internal resistance. In particular, lead-acid internal resistance goes up a lot 
as the cell approaches dead. Most other chemistries do not have this large 
change in internal resistance as a function of state of charge.

--
Any intelligent fool can make things bigger, more complex, and more
violent. It takes a touch of genius, and a lot of courage, to move
in the opposite direction. -- Albert Einstein
--
Lee Hart, 814 8th Ave N, Sartell MN 56377, www.sunrise-ev.com
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