Peukerts Law Based on Manufacturer Information

[DodgeViperEvilTwin]

So I have been trying to derive peukerts exponent based on assumptions I know this won't be accurate but I am curious about the data. So I don't know the time to discharge the battery so I guessed 3 Hours the capacity at a 20 hour rate is 40Ah meaning the manufacturer rated discharge current was 2A. However I ran into an issue with this because I get log(3)=log((40/(2*20))^k) then when I take log base 2 of 1 I get 0. Mathematically I see this but I am not sure why trying to find for k this way won't work. I know assuming some random discharge time makes no sense but let's say experimentally I found that to be 3 when using a discharge current of 2A then could I use the equation in this way? I still could not because I would still get a 0 on the other side. So I guess my question actually is why can't I use this equation in the manner I am trying? It must be because they are inherrrent losses in the battery and so the capacity listed in the numerator won't be exactly as rated.

 

[anorlunda]

So I have been trying to derive peukerts exponent based on assumptions I know this won't be accurate but I am curious about the data.

I'm confused by your question. Are you trying to derive it based soley on a curve fit where the single input is discharge time?

I'm not sure if you'll get a better answer here or in the Chemistry forum. If no good answers appear, I'll try moving this thread to chemistry.

Lead-acid batteries are complicated. Thinking "I put energy in, so I'll get energy out (minus some percent loss)" is far too simplified.

Have you read https://en.wikipedia.org/wiki/Peukert's_law ?
Also this http://www.smartgauge.co.uk/peukert_depth.html

 

[DodgeViperEvilTwin]

I'm confused by your question. Are you trying to derive it based soley on a curve fit where the single input is discharge time?

I'm not sure if you'll get a better answer here or in the Chemistry forum. If no good answers appear, I'll try moving this thread to chemistry.

Lead-acid batteries are complicated. Thinking "I put energy in, so I'll get energy out (minus some percent loss)" is far too simplified.

Have you read https://en.wikipedia.org/wiki/Peukert's_law ?
Also this http://www.smartgauge.co.uk/peukert_depth.html

I just mean based on the equation on the Wikipedia page you linked how can I find k if I know t, H,C, and I? This is for a LiFePO4 based battery not that it matters but I wanted an exact number I didn't just want to pull typical numbers that's why I am trying to figure this out I am hoping with this number I can somehow arrive at an approximate number for reserve capacity

 

[CWatters]

If I've understood correctly...

The formula uses the rated capacity and (indirectly) the actual capacity from I and t.

If you feed it data that implies these are the same then I believe you will indeed get k=0 because anything to the power 0 is equal to 1.

I think K=0 implies an ideal battery where the capacity doesn't change with current draw.

Sorry if I have this wrong but I'm getting interrupted.

 

[DodgeViperEvilTwin]

I just mean based on the equation on the Wikipedia page you linked how can I find k if I know t, H,C, and I? This is for a LiFePO4 based battery not that it matters but I wanted an exact number I didn't just want to pull typical numbers that's why I am trying to figure this out I am hoping with this number I can somehow arrive at an approximate number for reserve capacity

I ordered an electronic load tester so that way I can draw a constant 10A and read the capacity at that draw. Which if I time the point at which I fully drain the battery then I can find k.

 

[DodgeViperEvilTwin]

If I've understood correctly...

The formula uses the rated capacity and (indirectly) the actual capacity from I and t.

If you feed it data that implies these are the same then I believe you will indeed get k=0 because anything to the power 0 is equal to 1.

I think K=0 implies an ideal battery where the capacity doesn't change with current draw.

Sorry if I have this wrong but I'm getting interrupted.

I think I understand where the issue comes from I am trying to use the manufacturers rated current not necessarily the load they applied. Therefore I don't have the actual number that the equation called for.

 

[anorlunda]

The second link I provided says that the coefficient must come from the manufacturer. Presumably, you could do the experiments yourself, but it might be a lot of work.

What is the value of an exact number for k? There are a number of other factors including temperature, and sulphation of the plates, and current-versus-time-profile that significantly change performance more significantly than small changes in k.

 

[DodgeViperEvilTwin]

The second link I provided says that the coefficient must come from the manufacturer. Presumably, you could do the experiments yourself, but it might be a lot of work.

What is the value of an exact number for k? There are a number of other factors including temperature, and sulphation of the plates, and current-versus-time-profile that significantly change performance more significantly than small changes in k.

I was hoping to get it so I could play with some calculations to determine if this battery holds an advantage of its lead acid counterparts in terms of capacity.

 

[anorlunda]

I'm not sure that LiFePO4 even follow the same shaped curve.

 

[DodgeViperEvilTwin]

The second link I provided says that the coefficient must come from the manufacturer. Presumably, you could do the experiments yourself, but it might be a lot of work.

What is the value of an exact number for k? There are a number of other factors including temperature, and sulphation of the plates, and current-versus-time-profile that significantly change performance more significantly than small changes in k.

I see batteries in the same group size but they indicate higher Ah rating yet I always thought LiFePO4 batteries were better. So I was curious to find the true k value so I could do a proper comparison. I have the reserve capacity of the other but it is unlisted for the battery I am messing with and the manufacturer does not know.

 

[DodgeViperEvilTwin]

I'm not sure that LiFePO4 even follow the same shaped curve.

I am still learning about all of this they may well not however I assumed they might be close as they have somewhat similar cell voltages when at 12V. So they have 12.8 nominal and the lead acid has 12.6V I know that is trivial but I am thinking they would then have similar charge profiles as the top voltage on lead acid is 14.4V and 14.6V for LiFePO4.

 

[anorlunda]

The Wikipedia article says

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, see [1]. 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.[3]

 

[DodgeViperEvilTwin]

The Wikipedia article says

Well that answers that then I did not even see that.