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What's the formula to calculate Columbic efficiency for LFP cell / battery pack both for chg and dchg?

linuxnewbie

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Hi all

I want to calculate CE (Coloumbic eff) of a battery for discharging and for charging but I am struggling to find the right formula for both cases. I do know the basic one i.e. Qdchg / Qchg * 100 .

here I also want to know whether I should keep my chg and dchg rate fixed . is it important to have let's say Qchg @ 0.2C and Qdch also @ 0.2C or they can be diff too? I am working on SOC estimation of a battery using Coloumb counting so I want to know the right way to getting those numbers both for chg and dchg stages. thanks a bunch :)
 
AFAIK Li-ion and LFP coulombic efficiency is so high that you can probably ignore it if you operate mostly between the voltage knees(10% to 90% charge-discharge). Or it would be difficult to measure. Or dominated by self-discharge.
Maybe order of 99.5% to 99.9%
Cycling once per day at 99.9% CE you would lose 3% in a month due to CE.
Self-discharge rate for LFP is usually given somewhere around 5% per month.

If I would attempt to measure the coulombic efficiency I'd probably test over several cycles:
Charge to x.xxx volts, (discharge 100Ah, Charge 100Ah)*repeat 10x and on last charge cycle charge again to x.xxx volts and note how much over 100Ah you have to put in the battery to reach same voltage as you had 10 cycles earlier.
 
You should use the same charge and discharge Amps. Then you should run different sets of data to determine if Coulombic efficiency varies.
what do you mean here by different sets of data ? do you mean I repeat the test at different C-rates for eg one time at 0.1C , next time 0.5C and so on or do you mean repeat the same test but multiple times at a fixed rate?

also will this be my charging Coloumbic eff or dicharging Coloumbic eff ?
 
I mean use one discharge rate per set of data.
The formula you posted used quantities for charge and discharge as a function. Isn't that what definition of Coulombic efficiency measures? Since Coulombic efficiency is so high for Lithium cells I honestly do not know know much about the process of measuring it.
 
Are you just going to ask this question different ways until you get the answer you are looking for ?

As said in the other threads you started, you need to include battery temperature/charge rate/SOC range in your formula. I have never seen an accurate SOC meter for LiFePO4, not saying it can’t be done - but i gave up many years ago..
 
Are you just going to ask this question different ways until you get the answer you are looking for ?

As said in the other threads you started, you need to include battery temperature/charge rate/SOC range in your formula. I have never seen an accurate SOC meter for LiFePO4, not saying it can’t be done - but i gave up many years ago..
with due respect if you read this particular thread you will understand what I am really after, CE is a completely different topic and it has got its own complexities. saying temp , C-rates , shunt is very easy but telling the right procedure and steps arent. if it was that simple , I would have gotten the right formula with the right procedure by now ;). well if it isnt done in the past dosent mean its impossible to achieve. let see how far I can pull this off ?
 
Can we agree that this definition from Google is a fair statement:
"Coulombic efficiency (CE), also called faradaic efficiency or current efficiency, describes the charge efficiency by which electrons are transferred in batteries. CE is the ratio of the total charge extracted from the battery to the total charge put into the battery over a full cycle."
That would be the same formula (Qdchg / Qchg * 100 ) as @linuxnewbie posted at the beginning of this thread. That answers the question in the title of this thread about how to calculate it.
With all due respect to @linuxnewbie the question has been answered. It does not sound like anyone on this forum is interested in writing your paper for you. Hopefully, during your college education you have acquired the critical thinking skills to design a process to do that. Perhaps that is what your professor is looking for.
 
Sure, your questions were all slightly different - probably could have all been covered in the one thread.

I’m in a position where my cells often go for many months without getting fully charged, so i’ve been using coulomb counting to determine pack capacity for close to a decade.

An individual cell will not always have the same efficiency. The main difference is charge rate, but temperature and level of charge are also factors.

To be useful, your calculation error will have to be less than 0.1%.

I don’t think you will be able to implement a SOC only algorithm that will remain accurate over a 12month period on a LiFePO4 cell that is never taken into either voltage knee.

Very happy to be proven wrong - i will buy one of your SOC monitors :)
 
Thank you both @Ampster and @toms for your valuable replies to this thread . I really appreciate it.

In reply to @Ampster statement, I would like to highlight again that I asked for CE formula both for discharging and charging stages. I created this thread after coming from google's general definition. Nevertheless, let's keep sharing knowledge and improve more and more.

@toms , I really value your comment here since I can already see that you have a fair amount of experience with handling batteries, it was nice to know your point of view. thanks :)
 
I would like to highlight again that I asked for CE formula both for discharging and charging stages.
I would like to highlight that the Coulombic efficiency formula uses data from the discharging and charging stages. It is what is is. There is no efficiency to be measured for those stages separately since the formula is a relationship between the Amphours going into and going out of a battery. Hence you will not find the formula you are searching for.

There are losses in the charging circuitry but those losses are not related to Coulombic efficiency.
Where is the "beating a dead horse" emoticon?
 
Last edited:
I would like to highlight that the Coulombic efficiency formula uses data from the discharging and charging stages. It is what is is. There is no efficiency to be measured for those stages separately since the formula is a relationship between the Amphours going into and going out of a battery. Hence you will not find the formula you are searching for.

There are losses in the charging circuitry but those losses are not related to Coulombic efficiency.
Where is the "beating a dead horse" emoticon?
just for your own info, I have found the formula for both stages in a research paper and they are quite a diff from each other :)
 
You can't have separate Coulombic efficiencies for both charging and discharging by definition. To be 100% correct, the definition of Coulombic efficiency is:

1634118036902.png

Thus, the ratio of the discharged capacity to the capacity needed to be charged to the initial state before discharge. Note that you can only get the average Coulombic efficiency this way, since this efficiency changes depending on state of charge.
If you find separate formulas for both charge and discharge, this is by definition not a formula for Coulombic efficiency.

You can also calculate the energy efficiency:

1634118422575.png
This is more complex since you introduce the voltages, which are dependent on the rate of current flow, as well as state of charge, temperature, age, etc. However, here again we're talking ratios between charge and discharge.
 
<snip>
I am working on SOC estimation of a battery using Coloumb counting so I want to know the right way to getting those numbers both for chg and dchg stages. thanks a bunch :)
There are 3 commonly used factors in Coloumb counting. Efficiency, Temperature compensation, and Peukert exponent. Temperature compensation is by how much efficiency changes with temperature, and Peukert how much capacity changes with rate of discharge. At higher rates of discharge, the capacity of a battery is reduced.

For Lithium chemistries the effects are small and often ignored, or just combined and expressed with an efficiency of ~99%. For Lead acid, the values are provided by manufactures to enter into the meter.

This article on programming a colomb counter explains them.
 
<snip>

There are 3 commonly used factors in Coloumb counting. Efficiency, Temperature compensation, and Peukert exponent. Temperature compensation is by how much efficiency changes with temperature, and Peukert how much capacity changes with rate of discharge. At higher rates of discharge, the capacity of a battery is reduced.

For Lithium chemistries the effects are small and often ignored, or just combined and expressed with an efficiency of ~99%. For Lead acid, the values are provided by manufactures to enter into the meter.

This article on programming a colomb counter explains them.
thanks alot for this , yes I have gone to that article before and for Li chem the Peukert effect is quite non-existent
 
You can't have separate Coulombic efficiencies for both charging and discharging by definition. To be 100% correct, the definition of Coulombic efficiency is:

View attachment 68631

Thus, the ratio of the discharged capacity to the capacity needed to be charged to the initial state before discharge. Note that you can only get the average Coulombic efficiency this way, since this efficiency changes depending on state of charge.
If you find separate formulas for both charge and discharge, this is by definition not a formula for Coulombic efficiency.

You can also calculate the energy efficiency:

View attachment 68632
This is more complex since you introduce the voltages, which are dependent on the rate of current flow, as well as state of charge, temperature, age, etc. However, here again we're talking ratios between charge and discharge.
thank you for the correction so if I decide to lets sat do 5 cycles complete chg / dchg on 0.1C
then 0.2C ... all the way to 1C with increments of 0.1 here .. later have them averaged and put them in a table so I know if the battery is in this rate I choose that respective value of CE. would that make sense ?

why I am asking this way is because lets say I do 0.5C test but in real application what if I use 1C then for sure with double the C-rate there must be some significant effect on efficiency value , I mean not that much but still some change , would it then make sense to proceed the way I just mentioned up or thats completely irrelevant and waste of time
 
thanks alot for this , yes I have gone to that article before and for Li chem the Peukert effect is quite non-existent
It is *NOT* non-existent. It is around 1.03-1.05
It is often ignored, but it is still there, and some Lifepo4 manufactures will provide a number to program into a meter. Note this spec sheet from Lithionics. Charge eff. 98%, Temp comp 0%, Peurkert 1.05.
 
It is *NOT* non-existent. It is around 1.03-1.05
It is often ignored, but it is still there, and some Lifepo4 manufactures will provide a number to program into a meter. Note this spec sheet from Lithionics. Charge eff. 98%, Temp comp 0%, Peurkert 1.05.
this was very useful for me to have an overview of how its done practically , also one question what does this temp compensation 0 mean here?
 
this was very useful for me to have an overview of how its done practically , also one question what does this temp compensation 0 mean here?
It means that as temperature changes, the efficiency of the battery does not change. With other chemistries (lead acid) as the temperature gets warmer the battery is less efficient. Efficiency would be given at a certain temperature (ex 95% @ 70 degrees) and the temp compensation (ex 0.4) would be subtracted from the efficiency for every degree over the baseline temp. In this example, 93%
 
It means that as temperature changes, the efficiency of the battery does not change. With other chemistries (lead acid) as the temperature gets warmer the battery is less efficient. Efficiency would be given at a certain temperature (ex 95% @ 70 degrees) and the temp compensation (ex 0.4) would be subtracted from the efficiency for every degree over the baseline temp. In this example, 93%
so can I then say that for a LFP battery temp change on Columbic Eff is non-existent or can be neglected?
 
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