How to calculate Li-Ion battery charging rate?

[LightForce]

Hi!

I have a charger circuit, which terminates charging process after 3 hours. It is permanently programmed by manufacturer and I can't simply turn it off. I want to synchronise charging termination with a moment, when battery reaches a full charge. So what C-rate should I choose? How to calculate it? I want to recharge three 18650 cells connected in parallel with total capacity of 6600 - 7800 mAh. Charger's current capability is a strong 4A.

If charging rate turn out to be too high for this pack, I can go for 2 x 3 hrs of charging time.

Cheers,

Damian

 

[SilverFox]

Hello Damian,

Is the charge circuit designed for charging Li-Ion chemistry? Does it utilize a constant current/constant voltage charge algorithm? Does it clamp the voltage at 4.200 volts?

It looks like you have cells in the range of 2200 mAh to 2600 mAh, is this correct?

Tom

 

[LightForce]

Hi Tom,

Don't worry, everything is OK. This unit is specialised, stand-alone Li-Ion charger with total voltage error lower than 0.75%. Internally set to 4.200 V voltage limit. It interrupts charging process and disconnects the cells, when current lows to C/10 rate, if time is shorter than 3 hrs.

These are LG ICR18650S2 or B2 cells.

 

[SilverFox]

Hello Damian,

In that case, if you hook up 3 of the 2200 mAh cells in parallel, you end up with the equivalent of a 6600 mAh cell. Charging at around 0.7C will give you a complete charge, if the cells are completely empty, in around 3 hours. 0.7 * 6600 = 4.62 amps. Use your charger at the 4 amp rate and you should be good to go.

If the cells are only partially discharged, the charging time will be reduced. If that is the norm for you, you may be able to add a couple of more cells in parallel and, while the charge rate will be lower, they should end up fully charged in the 3 hours. You may have to play with this a little to get the proper number of cells to charge at one time.

Tom

 

[LightForce]

Thanks Tom!

I decided to use a charger which recharges each 3.7V section of 14.8V pack independently in order to keep the pack perfectly balanced, without need of additional balancer setup.

I appreciate your knowledge about all the batteries and commitment here on CPF, great work:goodjob:

 

[MrAl]

Hi,

I never recommend charging cells like this in parallel with a hefty charger and
here is why...

If i understand you correctly, your charger puts out 4 amps max, and
the cells are 18650 cells.

Since the cells are 18650 they have a max charge current of about 1 amp each.

Now if you charge one cell alone, the max safe current is 1 amp, so if you were
to try to charge it at 4 amps you would be risking damaging the cell or worse.
So you connect three cells in parallel. Ok, now each cell can take a max of 1 amp
but 4/3 equals 1.333 amps so as soon as you hook it up you are already charging
the cells at too high of a current.
But lets say they can take the 1.333 amps for now. What happens if one cell
charges up before the other two? What happens is that now that one cells
gets a low current like 100ma while the other two have to split 3.9 amps.
This means now two of the cells get 1.95 amps each, which is almost twice
the rated current for charging safely. But that's not the worst...
Once a second cell charges up there is only one cell left being charged.
Now if the first cell gets 100ma and the second cell gets 100ma that leaves
3.8 amps going to the last cell ! Clearly that's way too high unless you can
find cells that can take almost 4 amps continuously as there is no way to
estimate the time that one cell will be charging on its own.

To understand this a bit better, consider that each cell has it's own
characteristic, where its current draw is totally dependent on its
terminal voltage:
i=f(v)
where
i is the charge current and
v is the terminal voltage and
f is it's characteristic function.
Note that every cell has its own function, so for three cells we have
three *different* functions:
f1, f2, and f3.
Using the functional equivalent for each cell, this gives rise to three
*different* current levels:
i1=f1(v)
i2=f2(v)
i3=f3(v)
where v is the same for all three cells.
This of course means the total current divides up as:
I=i1+i2+i3
but I is always a constant, so we replace I with 4:
i1+i2+i3=4
From this it's clear to see that if any two cells currents goes to
zero the remaining cell takes the full current until it too charges up.
After say i2 and i3 get close to zero we have approximately this:
i1=4
which means the first cell gets four amps!


It's better to charge these cells individually and not in parallel unless maybe
you set the current down to the limit of one cell (about 1 amp or so).

 

[Supernam]

I believe that this would never actually happen, because say you have 2 cells that are unequal in initial charge. The higher charged cell will not necessarily finish charging before the lower charged cell because charge will flow more easily to the lower charged cell. That's why we can charge in parallel and still get a full charge in all the cells. If one cell finished charging before the others, then that one cell would have hit 4.2 volts making the whole charger switch to constant voltage mode, which means that current would start to fall.

Silverfox, is this right?

 

[SilverFox]

Hello Al,

The smallest 18650 cells that Damian has are 2200 mAh cells that are rated at a maximum charge rate of 1C. So, each cells maximum charge rate is 2.2 amps. Hook three cells in parallel and the maximum charge rate for the 3 cells is 6.6 amps.

When you parallel Li-Ion cells, they equalize in voltage and state of charge. Paralleling Li-Ion cells is one of the best ways to balance them. Please note that this does not work for Nickel chemistry, but works very well for Li-Ion chemistry.

When Li-Ion cells are connected in parallel, one cell can not charge up faster than the others. The state of charge is directly related to its voltage. If all the cells are at the same voltage, they are all at the same state of charge.

This holds true even if the cells are different capacities.

You can take a 1000 mAh cell that is at a resting open circuit voltage of 3.5 volts and parallel it with a 2600 mAh cell that is also at a resting open circuit voltage of 3.5 volts and hook them up to a charger and charge at 2 amps and they will both end up at 4.200 volts, fully charged, balanced, and without doing any damage to either of the cells due to high charging currents.

It may be possible to end up with cells that are slightly out of balance if you introduce additional resistance when paralleling the cells. I am opposed to using magnets for connections because of this. However, the additional resistance will also have an effect on the actual charging current, lowering it from what was selected on the charger.

I should also throw in that we are talking about cells that have at least 80% of their initial capacity. It may be possible to have an imbalanced situation develop if one cell has a substantially higher internal resistance than the others. However, I have connected cells with 0.050 ohms with a cell of 0.320 ohms and did not have any problems with high current going to the lower resistance cell. At the end of the charge the high resistance cell would not rest at 4.200 volts, but dropped down to 4.012 volts. Please note that the charge was terminated when the current dropped to below 0.050 mA. On a side note, this is where I believe you will run into problems with your charger set up. You would continue to trickle charge this cell and are dangerously close to the lithium plating occurrence area. I understand that your voltage is clamped at 4.2 volts, but with aged cells the current dwindles down at the minimum level for a long time.

Unfortunately, I can not find any documentation on the effects of extremely low current charging at a lower voltage with aged cells. Once you exceed 4.200 volts, you're in trouble, but below 4.200 volts, there isn't much documentation available.

The real question is if lithium plating is voltage dependent or available electrode dependent.

At any rate, parallel charging Li-Ion cells is safe. You end up with fully charged, balanced cells. To determine the charge rate, you add the capacities of the cells, divide it by the number of cells in parallel, and check to make sure that number does not exceed 1C for any of the cells. The one caution is to check the voltage of the cells you are connecting in parallel to make sure they are within 0.5 volts of each other. This minimizes the surge current when they are hooked up together.

Tom

 

[SilverFox]

Hello Supernam,

No.

When you parallel the cells, they equalize in voltage and state of charge. In the worst case, with one cell completely full and the other completely empty, this equalization process takes about 30 minutes (assuming 2200 mAh cells). Usually it only takes about 5 minutes.

Tom

 

[LuxLuthor]

Always great to keep getting additional details about parallel charging of Li-Ion cells.

 

[MrAl]

Hi again,


Tom, what you are saying in effect is that EVERY li-ion cell has the same
voltage current characteristic, and i find this very hard to believe, especially
with two cells that are different base capacity, and there is an easy way
to illustrate this...

Suppose we have two cells (simpler than considering three) in parallel and
one of the cells is defective such that it is almost an open circuit. Guess
which cell gets all the current until it reaches near 4.2 volts? It doesnt
matter what the defective cell voltage is because it will never draw much
current, therefore the good cell will always get the bulk of the max current.
This of course means there must be at least *some* degree of cell
matching, and that match must last until the entire pack dies. This has got
to be impossible.

To say that two cells of different capacity share the current equally is also
just not going to work out. If you put a cell that is 1Ahr in parallel with
a cell that is 2Ahr and even if they share current equally the 2Ahr cell gets
2 amps (probably ok considering the specs you quoted in your last post),
but the 1Ahr cell also gets 2 amps, which is probably too much for that one.
This doesnt work out even when we consider equal current distribution.
In real life it's not going to work out.

There is nothing mysterious about this circuit to me. It's simply just another
parallel circuit, and all the components are known to be variable so some
degree. I saw the same thing a long time ago with the paralleling of LEDs.
Yes, it does work sometimes...but then sometimes it doesnt...depending
on how well the LEDs are matched *and* how well they *stay* matched
over time and temperature. This could and does sometimes mean failure.
If the LEDs are especially durable, they might last, but this isnt something
that should be taken for granted.

Could this be why all the computer packs have been burning up recently?

A good idea to check for an imbalance of cells is to put a resistor in series
with each cell in order to measure the charge current for each cell.
This is rather easy to do with home built chargers, but with store bought
ones it may be difficult.

Another idea would be to check the temperature rise of each cell as it charges.
If the temperature rise acts to raise the characteristic voltage of a cell it may
help to regulate charge current. To understand this better a resistor in series
with each cell to measure current and a temperature probe on each case to
measure temperature. The cell current and temperature could then be
compared to see how the effective series resistance changes with temperature.
I dont have any info in front of my at this time to indicate if this change in R
is positive or negative with temperature, but i would bet it's positive, meaning it
will aid the parallel charging process...but just how good it helps remains to be
seen...if it does at all. Anyone up to performing an experiment?
Of course the question then arises as to whether or not we want to subject
the cell to a temperature rise in the first place, and how high it gets.

 

[SilverFox]

Hello Al,

Hmm, I am not sure I understand your logic...

To say that two cells of different capacity share the current equally is also
just not going to work out. If you put a cell that is 1Ahr in parallel with
a cell that is 2Ahr and even if they share current equally the 2Ahr cell gets
2 amps (probably ok considering the specs you quoted in your last post),
but the 1Ahr cell also gets 2 amps, which is probably too much for that one.
This doesnt work out even when we consider equal current distribution.
In real life it's not going to work out.

It almost sounds like you are suggesting that if you have a charging current of 2 amps available and are delivering it to 2 cells, each cell is receiving 2 amps. That just doesn't add up.

Each cell gets half of the current.

I believe the same goes for discharging. If you have two batteries in parallel and are drawing 2 amps from them, each cell sees 1 amp of load.

Are you really suggesting that charging is different from discharging as far as current division between cells goes?

Here is a test you can do to confirm this. Take two Li-Ion cells and discharge them. Make sure that they are within 0.5 volts of each other when measuring their resting open circuit voltage. Hook them up in parallel and set your charger for a 1C charge rate for one of the cells. If you are correct, your charge time should be around 1.5 hours. If I am correct, your charge time will be almost double that.

Tom

 

[VidPro]

here is some logic along the lines of Mr. ALs concerns.

what if , lets say in the world of Murphey, after 400 charges or 3 years, 2 of the cells in the parellel set FAIL completly.
they open up and anode disconnect, now you would be pumping 6 amps into the last one in the bunch and because it to is Aged, and old and suseptable, you end up with a possible issue.

if the cell CAN charge in 2 hours, and you only NEED it in 6 hours, then charge this parellel set at 1/3c and remain much safer, and still achieve overnight charge.

because when you finnaly set up a great system like this, fully balanced series sets of good capacity by parelleling multiples, it is likly that you will use it, and use it, and use it, and years later, it will still work that you will completly forget to throw it away because its aged, and out of service.

you still have your huge parelleled capacity, you still can charge it overnight, and top it off in a really short time, but you never have a "laptop fire"

 

[LightForce]

Hi there

I've never thought, that I start such a heated discussion

Taking an opportunity and not starting next unecessary thread I want to ask one question about this:

Is this correct setup? Each switching buck-mode charger module works from 4.7V input and charges cells with 4A current. Each 3.7V battery module is connected in series with separate 3.7, 7.4, 11.1 and 14.8V leads to the chargers. Will it work?

Nice Paint work, isn't it?

Thanks,
Damian

 

[SilverFox]

Hello VidPro,

I believe I understand Al's concerns, I just don't agree with his assessment of how current flows in a parallel circuit involving batteries.

As I see it, Al has two concerns. The first is that he does not believe that Li-Ion cells equalize when they are connected in parallel, and thus he believes that it is possible for one cell to charge up faster than another cell in the same parallel circuit. The second is a warning that if a cell in the parallel pack fails during the charging process, it is possible to damage the other cells in parallel with it.

I have never had any problems with cells remaining unbalanced when paralleled, nor have I had any cells fail in an open condition. I have had a few short out, but that is a different story...

Theoretically, it is possible for a cell to go open, so I think we need to explore this.

It would seem that this would favor charging more than two cells. If we take 3 cells with 2200 mAh capacity and hook them in parallel, we end up with a battery with a capacity of 6600 mAh. Charging at 0.7C would mean a current of 4.62 amps. If one cell went open, we would have 2.31 amps going into the other two cells. This is very close to a 1C charge, so everything would be OK.

Now, if two cells suddenly go open, that would leave one cell charging at a little over 2C. While this is not recommend for long cell life, it would greatly reduce the CV portion of the charge and the current would drop off during the CC portion.

This scenario becomes acute if we have more than 10 cells in parallel, are charging at 1C, and all but 1 cell go open at the same time. The people working with Li-Ion cells for Electric Vehicle use have discovered that Li-Ion cells, when empty, can handle up to 10C charge rates for a short period of time. This scenario would probably overheat the cell receiving the charge to where the PTC would shut things down, however I think it is highly unlikely that this would happen.

Let's look at some numbers. If we parallel 10 cells of 2200 mAh capacity, we end up with a 22 Ah battery. To charge at 1C we need to supply 22 amps. I don't believe there are any consumer chargers capable of 22 amps at 4.2 volts, so we would have to use a regulated power supply.

If I were setting this large a pack up for charging, I would make sure I could check the current going to the various cells, or at least groups of cells. If a bunch of cells went open during the charge, I am sure it would be detected while attending to the charge.

Tom

 

[MrAl]

Hi Tom,

Vidpro helped to explain my concerns very well.


QUOTE
It almost sounds like you are suggesting that if you have a charging
current of 2 amps available and are delivering it to 2 cells, each
cell is receiving 2 amps. That just doesn't add up.
END QUOTE

I thought we were talking about a charger that can put out 4 amps total?

Also, i was saying that each cell has its own characteristic. Part of this
characteristic is the internal (series) resistance. For two cells with
EXACT characteristics other than their internal resistance, and when this
internal resistance is different for each cell, when these are wired in
parallel and charged with a charger that can put out 4 amps, each cell
does not get 2 amps. One cell gets more current than the other.
Note that if we leave out the internal resistance we can model the two
cells as voltage sources. If both are at the same state of charge
(supposedly ideal conditions) and they both have the same characteristic
(also supposedly ideal) then both voltages will be the same. Now we
didnt say the internal resistance was going to be the same, in fact
lets say one cell (cell 1) has 0.05 ohms internal R and the other cell
(cell 2) has 0.1 ohms internal R. The charger is modeled as a constant
current current source that puts out 4 amps total. Now if the charge
equalizes, then both cells should get 2 amps each.
What actually happens however, because of the difference in series R
of the two cells is that the current can not divide equally (this is
similar to two unequal resistors in parallel), is that cell 1 will drawn
2.66 amps and cell 2 will draw 1.33 amps. How can i be so sure? I used
a simulation program and modeled all the devices as stated above.
Interestingly, when the terminal open circuit voltage of each of these
cells is measured they will both measure 4.0 volts. This is because
the internal resistance does not affect the open circuit voltage
measurement (im sure you know this already...just mentioning it for
completeness in this discussion).

I mentioned the LEDs in parallel before because that is a similar
situation, where you dont really know the character of all of
the LEDs and they will most likely be different.

Note that if the internal R of both cells above were the same, then
the current would share equally. I dont know any way to make sure
this is always going to be the case however, especially over long
periods of time.


One thing i should also mention here...
After i posted my previous post i read up a little on the protection
circuits sometimes employed in the cells. These circuits open
the cell up (open circuit it) under extreme conditions (im sure
you know this too). What i am wondering now is what happens if
we are charging two 'protected' cells and one gets a higher current
and the protection circuit 'opens up' and takes that cell out of
the circuit (temporarily) and so the other cell gets the full 4
amps, then that cell opens up, then the first cell circuit closes
and brings it back in so it gets 4 amps, then opens again, etc.
I see a situation where the protection circuits might be switching
on and off repeatedly in an attempt to protect the cells.
This could in fact help to regulate current to the cells, but you
have to realize that these protection circuits were not put in
place to 'regulate' current. Instead they were put in place to
'protect' the cell. There is a big difference from a design
standpoint. A circuit that 'protects' only has to meet certain
criteria that is often much simpler in concept than a circuit
that has to 'regulate', and of course this means 'regulation'
means taking much more into account than with simple 'protection'.
To design a protection circuit usually means a comparator that
detects some fault condition based on a voltage comparison, and
if detected, it opens the circuit. Just how long it stays open
is hard to say. Once the fault goes away, the circuit is then
closed. For an overcurrent this condition may come and go, and
just how fast it switches depends on the circuit.
A regulator, however, takes all the dynamics into account, so
that if it is desired to get 2 amps to the cell max, then the
regulator will no doubt handle this task well with no question.
I guess a good question then is did the designers take this into
account? Did they actually design a regulator or a simple
protection circuit? My guess goes to the protection circuit,
which is cheaper, and does actually protect the cell. It was not
made to protect the other cells in a pack however.
What else i dont like is that im not sure if most protection
circuits were made to be used in this manner.
After all, the cell will be constantly banged with a 4 amp pulse,
and close to the end voltage (4.2 volts) this is sure to push
the voltage above the max voltage spec of 4.200 volts
on a repeated basis.

We also have to consider that there are many packs out there
and they are probably being charged in parallel. The problem
is we dont know what the max charger current is. Is it equal
to 1C, or higher? If it is 1C then it doesnt matter if there
are 2 cells in parallel because the max current for any one
cell will always be 1C, even if one cell goes bad and opens up.

Now to get back to the original application...
If someone is going to use a 4 amp charger on three cells in parallel
and one cell has 0.05 ohms R and the other two have 0.3 ohms R
(quite a difference i know) then once cell could get as much
as 3 amps, while the other two share 1 amp between them (500ma each).
Again, all three cells open circuit voltage reads 4.0 volts.

What can be done about this?
The safest thing to do is charge at 1C.
The other possibility is to measure the current going to each
cell and if there is a big enough difference, add some series
R to the cell that draws the most current.
If we add 0.2 ohms to cell 1 in the three cell pack mentioned above,
the charge currents look like this:
cell 1: 1.5 amps
cell 2: 1.25 amps
cell 3: 1.25 amps

One thing we have going for us is that the cell with the lowest
characteristic voltage (open circuit voltage) will see its voltage
rise to meet the other two cells, whereas the other two cells
voltage will increase more slowly. This at least eventually
equalizes the characteristic voltages.


Finally, it would be a good idea to investigate the nature of
the protection circuits used for these cells to try to determine
its ability to regulate the charging current. Of course this
wont apply to unprotected cells, nor will it help in the case
where the protection circuits cutoff point happens to be a bit
higher than we would like it to be (im sure they dont build it
for exactly 2 amps on a 2Ah cell, but of course higher).

What i cant help but think about the recent recall is that perhaps
they were charging in parallel with a current that was too high,
and it eventually damaged one or more of the cells, although they
did blame the mass extinction (he he) on contamination, so its
hard to say for sure.

If anyone can find more info on the protection circuit, that would
be good too so maybe we can look into this a bit further.

Tom:
If you still dont agree on the flow of current in parallel battery
banks i can post a circuit somewhere and we can discuss it more
if you like...no problem. If i made a mistake in my analysis
i want to know about it, as to what caused it.

One big source of info is contained on the ieee site, which i
dont have access to at this time. The info is on a pseudo electrical
model of an Li-ion cell that supposedly can be used to determine
all sorts of nice information about the cells. If anyone can
get access to this, this would help everyone using Li-ion cells.

 

[LuxLuthor]

This is a great exchange of questions. I now see that Al (among other things) is raising the question about what happens when there is different levels of resistance in the individual cells in parallel. I don't know if that has been examined like this before. I am not smart enough about all this to answer, but I do see the questions Al is asking.

 

[SilverFox]

Hello Al,

So, your main concern has to do with the current supplied to each cell, and that current is dependent on the cells internal resistance.

First of all, lets get back to the original calculations.

Originally, we were charging 3 cells of 2200 mAh capacity, and came up with 4 amps as an acceptable charging rate.

Let's rework this for 2 cells of 2200 mAh capacity. When we parallel the two cells we end up with a battery of 4400 mAh capacity. Keeping our charge rate at 0.7C we would select a charging current (for 2 cells) of around 3 amps.

Your choice of cell internal resistance is about the limit of the range we can expect to see, so let's say that cell 1 has an internal resistance starting at 0.100 ohms and cell 2 has an internal resistance starting at 0.050 ohms. Please note that the internal resistance is dynamic throughout the charge and aged cells have a higher swing than newer cells.

As you have indicated cell 2 will start off charging at a higher rate, but it is still under the 1C recommendation. If I did the math correctly, cell 1 will be charging at around 1.0 amp and cell 2 will be charging at around 2.0 amps. Keep in mind that the constant current portion of the charge is only 20 - 30% of the total charge time. Once the cells get up to 4.2 volts, the current drops off.

Now, if we went for the 4 amp charging rate with cells starting at these internal resistances, we have a 2200 mAh cell charging at 2666, or at roughly 1.2C. Although this is a little high, it is still manageable. I don't think there would be any issues charging at this rate, but it is above the "recommended" rate.

0.100 ohms is about as high as you can get and still have a cell that is capable of delivering 80% of its initial capacity, so that is a good extreme to work with.

I took stock of the Li-Ion cells that I have been charging in parallel. The impedance of those cells runs between 0.056 ohms and 0.062 ohms. With these values, and with a 4 amp charge rate, I come up with charge rates ranging from 1.88 amps to 2.12 amps. Hardly any difference at all.

I guess I should advise people that if they have "crap" Li-Ion cells, they should recycle them. If they insist on trying to use them, they should charge them individually.

The notebook battery problem is an interesting one. I believe that the balance protection used in these packs checked the voltage of the serial stacks to make sure they were equal. This does not check the cells that are in series.

My original computer battery pack is a 4S2P set up using 1900 mAh cells. This works out to a 14.8 volt 3800 mAh battery pack. The charging rate is 3.5 amps. I also have a replacement pack that has upped the capacity to 4460 mAh, so it must have 2230 mAh cells in it.

Keeping each serial string in balance helps, but unless there is individual cell balancing, there still can be the possibility of a cell getting out of balance.

I think the "issues" with the battery packs involved contamination in the electrolyte of the cells being aggravated by series cell imbalances. As a cell approaches or goes over 4.200 volts, it has the possibility of aggressively attacking the electrodes and plating metal lithium out. Add a good healthy dose of heat, and you are on your way to thermal runaway.

At any rate, I still maintain that parallel charging is safe, serial charging is where you run into problems, and individual charging is the best way to go.

Tom

 

[LightForce]

Hi,

I don't want to go into details of your discussion, becouse my knowledge is way to little to compete with you. But guys.. Please, don't left my question without response.

Damian

 

[SilverFox]

Hello Damian,

You may find this thread informative.

Here is another one.

Tom