# Lithium - Mixing Capacities



## green caveman (Oct 2, 2009)

Is there any reason why you shouldn't mix different capacities in parallel in a lithium pack?

So, for example, could I mix 2x40ah in parallel with 1x80ah (or a 60 and a 20 with an 80 or any other combination)?


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## WarpedOne (Jun 26, 2009)

Because you are throwing your money through the window. Yes, it would work and yes, it would fail soon.

A string of batteries is strongest when all the cells have exact internal resistance and voltage so the load gets divided into equal pieces. If one cell is weaker or stronger, the stronger cells get *less* of a load and the weaker one *more*. The poor cell is already weaker but it also has to bear a bigger load so it can only fail much sooner.

Your scenario would be OK if two smaller cells had exactly the same capacity and voltage and the bigger one would had exactly double the capacity of two smaller cells and exactly the same voltage. Bigger the differences, sooner to fail.


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## green caveman (Oct 2, 2009)

WarpedOne said:


> Because you are throwing your money through the window. Yes, it would work and yes, it would fail soon.


Just to be clear, your suggesting that a set of (4x20ah) cells in a pack will fail faster than one 80ah cell. Is this just statistics, 4x the number of cells so 4x the likelihood that there will be an imbalance, or is there something about wiring these in parallel that make the failure more likely than the statistics would suggest?


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## Guest (Nov 19, 2011)

If you mix and match your best bet would be to be sure your bottom balanced on your cells. Be sure to not fully charge or discharge. That will give you some good wiggle room just in case. I don't really see a huge problem but it could. The capacity is more of an issue than the internal resistance. So two of the 40ah cells may actually have a total of like 88 ah when connected together and the 80ah cell may only have like 82 ah so you have a 4ah difference. With that type of difference it would be wise to keep off the bottom and top and be sure your cells are bottom balanced. 

Pete


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## EVfun (Mar 14, 2010)

I wouldn't mix capacities because you will paralleling cells of different internal resistances. The current out of the cells under load will follow the internal resistance, the cell with the lowest will supply the most current, the cell with the highest the least. The things is, as the cell capacity gets smaller the internal resistance does not rise in proportion. A 40 amp hour cell will not have 4.5 times the internal resistance of the 180 amp cell, but perhaps only 2.5 times the internal resistance (that is a rough estimate based on some reports that 180 amp hour cells have slightly less than 1 milliohm of internal resistance and my 60 amp hour cells about 1.5 milliohms.)

To be simple, consider the case of 1, 180 AH cell and 1, 40 AH cell under a 500 amp load:

I estimate the internal resistance of the 180 AH cell to be 0.0008 ohms and internal resistance of the 40 AH cell to be 0.0022 ohms.
The internal resistance of the 2 cells in parallel is 0.0005867 ohms.
Under a 500 amp load the voltage of the pair should sag to 3.007 volts.
The little 40 amp hour cell will be supplying 133.3 amps.
It is supplying 26.7% of the load but only has 18.2% of the total capacity.
It will get down to a low state of charge where the voltage under load gets soft far before the 180 amp hour cell gets low.
It is seeing 3.3C draws at 500 amps while the 180 amp hour cell is delivering 1.5C. 
The small cell will have a much tougher cycle life I would expect it to not last nearly as long.


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## Guest (Nov 19, 2011)

The comparison is between two 40AH cells in parallel and one 80AH cell. How do you estimate on paper? You need to test it. Putting two cells in parallel it seems logical that the internal resistance would be shared between the two. Sure each one maybe .0022 ohms but each would only require half that since the two are truly now only considered as a single cell? What makes the resistance different if you parallel two cells or not? All cells are internally parallel as you all know. The issue is not going to present him with a large problem. 

Its not fair to compare an 80AH cell or 40AH cell with a 180Ah cell.


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## green caveman (Oct 2, 2009)

EVfun said:


> I wouldn't mix capacities because you will paralleling cells of different internal resistances.


Argh! This would need some hard numbers to know whether it's a real issue or not, especially since there's the 1/R stuff going on for parallel cells.

If you say that a 180Ah cell is a little less than 1 mOhm and a 60Ah is about 1.5mOhm, then three 60Ah in parallel would be 0.5. So if the 180Ah cells are always 0.99 then 0.5 is significantly different, but if your 1.5 and 1 is off by a little it would make a big difference.

Also, what's the variation? If 180Ah cells vary between 0.75 and 1.25 then it's unlikely that the parallel cells will have much bigger variation. If the tolerances are much tighter, then you have the potential for a much more significant percentage variation. So you need the mean and SD to really know what's going on (I haven't searched for either of these so they may be out there).

So I think you point is valid, but without more accurate numbers it would be hard to tell if it's significant.


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## Jozzer (Mar 29, 2009)

2 Lithium cells in parallel behave as one, so you won't have problems paralleling.
You may have problems with differing capacities in series (ie, 2 x 40AH may not have the same the same capacity as 1 x 80AH cell, if yout hen run these 2 in series one may run out before the other).


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## green caveman (Oct 2, 2009)

Jozzer said:


> (ie, 2 x 40AH may not have the same the same capacity as 1 x 80AH cell, if yout hen run these 2 in series one may run out before the other).


That's the real question. I'm not sure either way. If you took the cases off the 2x 40Ah and stuffed all the parts you got out into an 80Ah case (this is a thought experiment, not something I'm advocating) what would the difference be? If nothing, then the presence or absence of the (extra) case is irrelevant. As was pointed out, all the cells are parallel internal to the case, so why would it make a difference whether they are parallel within one case or within two?

If the manufacturing controls (or just the nature of the chemistry) mean that the capacity of a 40Ah cell varies, does it vary by more than half an 80Ah cell? If it did, a pack of parallel 40Ah cells would also not work because there would be a capacity variation between the 2x40Ah=80Ah components.


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## Jozzer (Mar 29, 2009)

Well, the fact is, EVERY cell will have a slightly different capacity, if you fit a cell level Low Voltage Cutoff circuit (or use bottom balancing and only 80% capacity if that's your thing) then there will be no noticeable difference between the 2 setups..


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## green caveman (Oct 2, 2009)

Jozzer said:


> Well, the fact is, EVERY cell will have a slightly different capacity, if you fit a cell level Low Voltage Cutoff circuit (or use bottom balancing and only 80% capacity if that's your thing) then there will be no noticeable difference between the 2 setups..


I'm tending to think that I agree with you that the two setups are the same. I suppose that if I was really concerned I could research a BMS that would give me the best feedback (and the saving from being "creative" on the pack would easily cover the extra cost).


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## EVfun (Mar 14, 2010)

green caveman said:


> Argh! This would need some hard numbers to know whether it's a real issue or not, especially since there's the 1/R stuff going on for parallel cells.
> 
> If you say that a 180Ah cell is a little less than 1 mOhm and a 60Ah is about 1.5mOhm, then three 60Ah in parallel would be 0.5. So if the 180Ah cells are always 0.99 then 0.5 is significantly different, but if your 1.5 and 1 is off by a little it would make a big difference.
> 
> ...


The variation between cells in series shouldn't be a big issue because they will supply the same current, though at slightly different voltages under load. Cells in parallel will be at the same voltage, but supplying different current. There is no reason to believe that current will be proportional to the cells capacity -- it will be proportional to the cells internal resistance.

The exact resistance numbers would make a big difference. I toss the example out there because by many reports the smaller capacity cells sag less under a given C load than larger cells of the same type. I have considered putting a string of 8 amp hour Headway cells in parallel with my 60 amp hour Thunder Sky cells to stiffen the pack and allow my to pull higher peak currents (with respectable voltage.) The 38120P cells have 8 AH and about 3 mohm of internal resistance. My 60 AH TS cells have about 1.5 mohm internal resistance. I could pull 400 amps from my cells and 200 amps from the Headway cells for a total of 600 amps. This is an extreme case but at 3C for the TS cells (180 amps) the Headway cells would deliver another 90 amps. At that rate the Headway cells would have been dead in about 5 minutes but the TS can put out 180 amps for about 20 minutes. At some point much of the load will fall back onto the TS cells as the Headway cells get low and begin sagging under much lower loads.

If the cell sizes are closer, perhaps 40 and 80 amp hours is close enough, and if the peak currents are kept pretty low then you should be able to get away with different cells in parallel. The higher the peak currents and the greater the cell difference the worse they will share the load.


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## EVfun (Mar 14, 2010)

gottdi said:


> The comparison is between two 40AH cells in parallel and one 80AH cell. How do you estimate on paper? You need to test it. Putting two cells in parallel it seems logical that the internal resistance would be shared between the two.


1/R[1] + 1/R[2] + 1/R[3] ... = 1/R

We can determine the total resistance of cells in parallel if we know the internal resistance of each cell. Since we know cells in parallel will have the same voltage we can estimate how will share the load. It will be based on resistance, not capacity. I somehow doubt we are going to invalidate Ohm's law. I=VR

I saw the 1x80 and saw 180. The issue will be much smaller between 40 and 80 amp hour cells, still, I wouldn't encourage paralleling different cells.


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## MN Driver (Sep 29, 2009)

I'm going to clip this quote because I agree with everything that EVfun has said so far in regards to simple math surrounding internal resistance, capacity, and running cells in parallel. Everything except for a detail that I think was missed in this quote below.


EVfun said:


> To be simple, consider the case of 1, 180 AH cell and 1, 40 AH cell under a 500 amp load:
> 
> I estimate the internal resistance of the 180 AH cell to be 0.0008 ohms and internal resistance of the 40 AH cell to be 0.0022 ohms.
> The internal resistance of the 2 cells in parallel is 0.0005867 ohms.
> ...


They will begin with the smaller cell providing a large amount of the load but remember that the voltage sag(internal resistance) changes at different SOC levels so once the 40Ah cell pushing out 133.3 amps is getting exhausted it will quickly be putting less current and the 180Ah cell will be outputting more current. In the end if the output is moderate to where the current can be sustained without cell the cell being overloaded that things will be fine and they will balance out.

I think that as far as an internal heat limit standpoint that if you keep the total amp draw below the max that the smallest capacity cell could take on its own that you would be more than safe doing this as long as every parallel pair is set up the same. In the OPs example of a 40Ah with an 80Ah, let's say the 40Ah cell can take 400 amps for 10 seconds(CALB spec), if your load was less than 400 amps and you knew your cell could handle it, you'd know for sure that a 40Ah could be mixed with an 80Ah cell.

Now if you draw a 500 amp load, you'd still be fine because the 80Ah cell will still take some load but finding out the max load you could draw would require a clamp meter around the battery connections to watch how much current is coming from which cells in a sample setup running the full expected load for a short duration at high, medium, and low SOCs to see how much current is coming from each cell.

I've considered the idea of a booster setup when I was considering a worn out set of old LiFePO4 cells that the previous owner said would sag to 3.25-3.5vpc at 300 amps, these were 100Ah cells that were old, used, and abused a bit. They were an older version of a 1C continuous cell that isn't as powerful as currently available cells and the abuse caused them to sag more. I considered buying them for their low price of 65 cents/Ah but didn't make my decision in time. I had plans of paralleling however many Headway cells directly to the better cells out of the whole group(discarding the weaklings) to allow them to handle the load better and running a higher voltage system(plenty of cells available) to make it work well. It's an extreme setup to bolster the pack and would require testing to see how everything would really behave but that was my plan. In the end I'd probably if it came down to paralleling strong small cells with big cells to bolster them it would have probably not been worth it but if those cells weren't that bad then I missed out on a killer deal for a very lightweight conversion.


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## green caveman (Oct 2, 2009)

MN Driver said:


> the smallest capacity cell could take on its own that you would be more than safe doing this as long as every parallel pair is set up the same. In the OPs example of a 40Ah with an 80Ah, let's say the 40Ah cell can take 400 amps for 10 seconds(CALB spec), if your load was less than 400 amps and you knew your cell could handle it, you'd know for sure that a 40Ah could be mixed with an 80Ah cell.


Now I'm confused. We're not talking about, say, mixing 40's and 80's but, say, a parallel pair of 40's with an 80. And I'm actually considering similar cells, not used vs new or CALB vs Headway, etc. 

Now, to a first approximation, if the 80 can source, say 500A, then, presumably, a 40 can source 250, so 500A for two in parallel (assuming the internal resistance of the two 40's is the same, etc. etc. etc.).

I think the real question is, what's the difference between two 40's and an 80. So far, I haven't seen anything that says it's anything other than the case configuration - you get a bonus case with the two 40Ah (but they are a little smaller ).


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## EVfun (Mar 14, 2010)

I agree with you MN Driver that the current split will change as the SOC goes down faster in the small cells. The thing is, I only see about a 10% increase in internal resistance between 99% charged and some point around 30% charged. Once I see the sag get to that point the pack is about to go down fast (a lot like charging, the voltage under load holds with just a slow change up to a point where is shoot off.)

So I ran the numbers for what I was considering at 2 points. Paralleling a 60 AH TS with a 8 AH HW P cell. 600 amps is 400 and 200 at full charge. When the HW cell gets down to about 30% SOC its internal resistance should go up to about 3.3 mohms. That only cuts its load to 187 amps out of 600. Some point after that it is either going to start charging at a significant current from the TS cell every time my foot lets up on the throttle or quickly contribute less and less of the total peak current. Once the HW cell is to the SOC where the sag under load has doubled (0.006 ohm internal resistance) it would still be carrying 120 amps out of the 600 amps total. Sharing "fairly" (in proportion to capacity) is only 71 amps for the HW cell. 

It would be interesting to try and if I did it with 2 packs in parallel (32S2P, where the 2P are a 60 AH pack and an 8 AH pack) I could pretty easily measure average current sharing both directions. I could also fit that pack under the back seat of the buggy on the right side, and it would be a pretty cheap experiment (well, less than $750 all included.) The regular HW cell interconnection straps are even smaller than 1/0 so that would help hold its current contribution down a little. Hmmm...


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## EVfun (Mar 14, 2010)

I originally saw 2x40 and 180 ("1x80") and was concerned. If the cells are the same brand, same age, and paralleled first then in series I suspect you will be fine so long as your current expectations are reasonable. What I mean is, if you don't pull more than 150% of what the 40 amp hour cells can provide there should be little cause for concern. If you want to pull more you should do some load tests of cells in parallel with equal shunts on each cell to see how they actually share current at different states of charge.

The series circuit is always at the same current (naturally.) It is only sharing differences in the paralleled groups within it that could be a concern.


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## green caveman (Oct 2, 2009)

EVfun said:


> I originally saw 2x40 and 180 ("1x80") and was concerned. If the cells are the same brand, same age, and paralleled first then in series I suspect you will be fine so long as your current expectations are reasonable. What I mean is, if you don't pull more than 150% of what the 40 amp hour cells can provide there should be little cause for concern. If you want to pull more you should do some load tests of cells in parallel with equal shunts on each cell to see how they actually share current at different states of charge.
> 
> The series circuit is always at the same current (naturally.) It is only sharing differences in the paralleled groups within it that could be a concern.


I'm not sure why you're concerned about current, assuming that the 40's are identical,in parallel they'll carry half the current, so it should be possible to pull, say 3C, 240A, from either the 80 or the 2x40. Each of the 40's will also see 3C, 120A. 

I could see a little concern as to whether they are identical, but I can't think that would be more than, say, 5%.


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## EVfun (Mar 14, 2010)

If you look at the manufacturers spec sheet for cells of different capacities you often find that the internal resistance does not scale down with capacity. The 40 amp hour cell may capable of higher C rate discharges and the internal resistance of the the 40 amp hour cell may be less double that of the 80 amp hour cell. The cells will share the load based on their internal resistance, not their nameplate capacity.

Are you by chance talking about making an 80 amp hour pack where some of the cells are 80 amp hour cells and others are 2, 40 amp hour cells in parallel? If that is the case the paralleling of cells shouldn't be an issue. The actual capacity of cells could be an issue on deeper cycles (the 40's might really be 45 and the 80's might really be 82 amp hours.) The internal resistance differences between 2, 40 AH cells and 1, 80 AH cell could be an issue for setting an appropriate minimum pack voltage under load. I had the impression you where trying to make a 160 amp hour pack by paralleling an 80 amp hour cell and 2, 40 amp hour cells.


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## green caveman (Oct 2, 2009)

EVfun said:


> If you look at the manufacturers spec sheet for cells of different capacities you often find that the internal resistance does not scale down with capacity. The 40 amp hour cell may capable of higher C rate discharges and the internal resistance of the the 40 amp hour cell may be less double that of the 80 amp hour cell. The cells will share the load based on their internal resistance, not their nameplate capacity.


They'll share it on some inverse of the resistance inversed, it's the 1/R=1/R1+1/R2... problem.



EVfun said:


> Are you by chance talking about making an 80 amp hour pack where some of the cells are 80 amp hour cells and others are 2, 40 amp hour cells in parallel? If that is the case the paralleling of cells shouldn't be an issue. The actual capacity of cells could be an issue on deeper cycles (the 40's might really be 45 and the 80's might really be 82 amp hours.) The internal resistance differences between 2, 40 AH cells and 1, 80 AH cell could be an issue for setting an appropriate minimum pack voltage under load. I had the impression you where trying to make a 160 amp hour pack by paralleling an 80 amp hour cell and 2, 40 amp hour cells.


That's the gist of it. There's possibly some cost saving, because as the price of cells come down there are some deals showing up on low-Ah cells, but never enough to make a pack, and usually different Ah. If you can mix-and-match you have some flexibility, so if you shoot for 80 you can use 1x80, 2x40, 20+60, 4x20... Or your 160 example.

Now I'm starting to wonder about different manufactures. I should go and look at the difference in resistance specs.


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