Battery Model and charging

Mr Al and I have been having some discussion about how to model a battery in a charging circuit.

This discussion came about from a previous discussion I was having with some non CPF people. Newbie and I were also having a discussion on pulse width modulated charging and its effects on heating up the cells while charging.

Newbie sent me this link, which gives a model for a battery.

The discussion started by wondering if PWM charging would tend to heat cells more than constant current charging.

Energizer, in their data sheet, gives a 0.030 ohm value for internal resistance of their NiMh cells, but also show a value of 0.012 ohms of impedance.

My original question was wondering how internal resistance and impedance enter into the cell heating equation.

My impedance meter utilizes a frequency of 1 kHz. I am measuring internal resistance by observing the change in voltage of a cell with different loads applied. I believe Al is measuring internal resistance in a way that is similar to the way I am doing it.

My interest in this subject comes from trying to understand how batteries age. "Crap" cells heat up more than healthy cells, and this may give us an idea of what is going on.

Unfortunately, my hope that an impedance measurement would give us the answer did not pan out. In some cases impedance comes close to internal resistance, but there seems to be a lot more to it. I have cells with high internal resistance that seem to have normal impedance. I also have cells with "elevated" impedance that have normal internal resistance. This observation has led me to dig deeper.

I will let Al jump in here and talk about the model.

Tom

Tom:

How are you measuring resistance? Using the CBA-II method?

One could compare a RC type charger like the Triton or ICE to the MAHA C808M since it's electronics are housed outside the cell holder, so that generated heat won't affect it.

Hello Bill,

Yes, I am using the change in voltage divided by the change in current to get internal resistance. The CBA is used for accurate loading.

The original question that Al and I were discussing went something like this...

If we have a cell with 0.030 ohms of resistance and charge it on a constant current charger at 1 amp, the cell generates around 0.03 watts of heat. Now, if we take the same cell and use a PWM charger that charges at 2 amps at a 50% duty cycle, we now have 0.06 watts going to heat the cell.

If the impedance of the cell was more influential, with a cell impedance of 0.018 ohms, perhaps the cell would not heat up as much.

However, this paper that I listed has a battery model that uses a combination of both the resistance and the impedance of the cell.

Tom

This is definitely an interesting topic to explore, I'm curious to find out where this leads.

I have some background from hobby in speaker building/modeling and small generator building/designing.

When thinking of say- a capacitor, impedance is lower as you increase frequency, the reverse for an inductor.. I would have to imagine that the internals of a modern battery cell probably have reactive loads in both directions, I guess the trick would be finding a sweet spot. Some frequency, that the cell has the lest reactive load overall. My thinking may be way off base here... (so jump in and correct me, lol)... but might be worth having a "tone generator(square wave rectified to DC no buffer cap)" of sorts that you could adjust the frequency on the fly with an ohm meter connected to the cell. See where you get the lowest resistance, then try a test charge at that frequency and measure heat and energy waste.

There is a good possibility that I am totally babbling and have no idea what I am talking about here.

I think the chemistry involved would make an electrical model of a cell extremely non-linear. My guess would be that the impedence/resistance would depond not only on the charge/discharge current and the duty cycle, but also the temperature of the cell, the condition of the electrolites, and how the crystals have formed (previous charging conditions).

If need be, I can do a discharge on my Competition Electronics Turbo 35 GFX and get an actual internal resistance reading...

Hi there,

Here is a drawing of this new model so it can be easily viewed and talked about...

Be sure to take a look at the simplified model also (scroll down far)
to see how much simpler it will make understanding how the resistances
will affect charging with a constant current or with a pulse charge.
With this simplified model the NiMH cell shown in the original paper
will have the following values converted from the original values:

RS=0.10 ohms
RT=0.09 ohms
CT=40 farads

and note almost all of the complexity has been removed in order to
make it easier to see what is happening with a pulse and constant charge,
as we are left with two resistors and a single capacitor.

From this we can see that most of us would be measuring RS alone when
we do a RS=(change in voltage)/(change in current) method to determine
RS in a typical cell. This means that constant current charging would
produce more power than we would expect when we assume RS alone.
With RT, the power would be 1.9 times as much (almost twice that of
RS alone). Without considering RT estimates for the power saved
by pulse charging could be way off.
I'll get back to this after you guys have had a chance to view the
simplified model in the diagram below.

Hello Al,

Thanks for drawing that up.

In reviewing the paper, I find the Rseries behavior for Li-Ion to be as expected, however, the NiMh values are a little harder to understand.

The graph indicates that Rseries increase 3 to 4 times at 0.2C and 0.4C discharge rates, when comparing to 0.67C and 1.0C rates. The Rseries is also low at 0.1C and 0.13C rates.

Could this increase in resistance at those rates contribute to the difficulty in determining the end of charge signal? This may be an additional reason why battery manufacturers warn us to stay away from using those rates for charging.

It is also interesting that the lowest Rseries is observed at 1C.

Tom

Hi Tom,

I havent looked carefully at how any of the values change with SOC
(or at least by any significant amount) because first
i wanted to find some useful info about charging overall and how the RS and other
R's are going to affect this. In other words, to start with i will hold SOC constant.
For the NiMH data, i set SOC=0.57 just because it was convenient.

I feel this is the most important thing to look at first because a problem came
up even when taking this simplified approach to start with.
It turns out that the following seems to be true:

1. The RS that we measure is done with 1kHz AC so we are measuring
the RS of the model directly (due to the long time constant of RT and CT).
2. The Energizer data shows an impedance (Ze) of 0.012 at a frequency of 1kHz, yet
their 'series resistance' (RSe) is shown as 0.030 to 0.040.

Now from (2) above since RSe is greater than Ze this implies RSe is not RS of the
model, but rather RS of the model *plus* the impedance of RT and CT.
The problem here is that if RS is in series with an impedance, the minimum impedance
will be RS. Thus, Energizer should have measured a value for Ze of greater than
0.030 (or 0.040).
The only rational explanation is that they put this small Ze in series with RS, but
then again you could not use a test frequency of 1kHz to find this value, and they
state that they use 1kHz.

This means something is wrong here, and we would have to find out what it is
before we can conclude anything that would be of any use.

In other words, there may be a parallel capacitance somewhere that is not
shown in any of the models. If we dont know what it is, it's going to be
very hard to come up with any useable results.
The other possiblity is that Energizer is using some other method of measuring
the internal Ze, but i dont see how if they state 1kHz. According to the model,
1kHz would be a silly frequency to use for determining anything to do with RT
and CT.

The other contradition is that i have measured the internal R of several NiMH cells
myself and have found much less variation in |dV|/|dI| with frequency than i would
expect to get if the impedance was varying that much.

Thus, there is some discrepancy between what the model looks like and what
Energizer is reporting.
Note there is no discrepancy between my own measurements and the model, however,
in that i got what i would expect from a cell that looks like that model at the
frequencies i used to test it at...which is interesting.

Could it be Energizer fudged the readings or something?

Do you have any 'impedance' measurements to post here?

Here's a impedance graph thread of mine which didn't generate much interest: Graphs

Hello Al,

Here is a set of numbers to play with...

Sanyo lists 0.025 ohms of impedance at 1 kHz for their 2500 mAh cells. Mine come in at 0.022 ohms on my impedance meter. Checking the internal resistance, I come up with 0.050 ohms.

GP lists 0.006 ohms of impedance at 1 kHz for their 3300 mAh SC cells. Mine come in at 0.0057 ohms on my impedance meter. The internal resistance for these cells comes in at 0.008 ohms.

Tom

Bill,
Thanks for the link, i'll take a look. BTW, how did you measure
impedance, with a special tester or some other way?


Tom,
Thanks for the data. It still adds to the mystery that is
now developing however

I think i found part of the problem, and that is the Energizer
model shows that the 'internal resistance' is the effective
resistance, and that is the sum of what they are calling Rh
and Rd, Rd being called the "delayed resistance".
If we sum Rh and Rd as they do, we get:
Re=Rh+Rd
and this is what they call the internal resistance or effective
resistance (Re). This could explain why Z is lower than R as
per our previous discussions. Since Re is higher than either
Rh or Rd, we could say that the total Z (we'll call ZTotal) is:
ZTotal=Rh+Zi, where Zi is made from the parallel Rd and Cp
(Cp is equivalent to my 'simplified model' drawings CT, and
Rd is equivalent to that drawings RT, and Rh is equiv to RS).
Their model is essentially the same as the simplified model
i drew, but they include a constant voltage source in series
with it to provide for the 'open circuit voltage' which i didnt
feel was important (yet) for understanding the effect of
these internal resistances and capacitances. This of course
means if we refer to the simplifed model and compare it to
the Energizer model, we end up with the following equivalences:
RT=Rd
CT=Cp
Rh=RS

Now all this works out very nicely, except for one problem that
still remains...
That is, if you look at either the simplifed model or the new
'full' model presented by Chen-Rincon-Mora, and we try to use
it to determine the impedance of 0.010 ohms or similar (Energizer
and apparently by your measurements) we will quickly find that
1kHz is a terrible frequency to use to try to determine this
impedance. The reason for this is because CT is so darn huge
it doesnt show much response at 1kHz. In fact, if we do a quick
estimate of the reactance to a 40 farad cap at 1kHz we get:
Xc=3.98e-6 ohms. This goes up as frequency goes down, so at
100Hz we would get Xc=39.8e-6 ohms, and at 10Hz we would get
Xc=398e-6 ohms. It's only when we go down to 1Hz that we get
something that seems useful: ZT would be 0.004 ohms, which would
get close to what we are actually seeing. They all state
1 kHz however so i cant say this frequency is valid.

The question remains then, what is Energizer and apparently other
manufacturers using to measure what they are calling the
"impedance at 1kHz" ?

Note that, given the models so far (including the Energizer one),
if we were to apply a frequency of 1kHz and measure the change
in voltage over the change in current we would get not the impedance,
but the internal resistance Rh (Energizer model) or RS (simple model).
If we instead look at the voltage, current, and phase shift between
current and voltage (as would be the true method to determine
the impedance) then we find a surprise: the phase shift is so
darn close to zero degrees we are not able to extract any additional
information. This is because the cap is so large relative to
the test frequency. If we had super super equipment that could actuall
see the small, or should i say tiny, phase shift, and then did
the calculation, we would get a complex impedance of:
ZT=0.1-0.000004j, where ZT is the total impedance. From this we can
see that it is mostly real, and the value of the real part is
0.1 and it is ohms, which is 0.1 ohms and is the resistance we
have been calling Rh (Energizer) or RS (simple model).
Note the imaginary part, 0.000004, is so darn small that it bears
little part in all of this. The impedance, as read on a meter
that could detect these small small changes in phase shift, would
read "0.100 ohms Impedance", and certainly not "0.010 ohms".
Just for the record, the RT and CT part create a complex impedance that
is very small at 1kHz:
Z(RT,CT)=1.58e-10 -4e-6j
and this would read "0.000004 ohms" on a meter that could do
something this small.

Thus, no way of looking at ANY of the models produces ANY
impedance that is around 0.010 ohms, unless we ignore the
so called "test frequency" of 1kHz, and set it to get the
value we want. To do this, we would have to reduce the
frequency to below 1Hz, like 0.3 to 0.5 Hz or around there.

There is another possibility, and that is that the 1 amp
test current (Energizer) produces some sort of change in
the resistance Rh itself, but the problem with this idea
is that each cell, depending on its Ah rating, would require
a different test current in order to produce the same
degree of change.

The other possibility is that there is a parallel capacitance,
which none of the models cared to show. If this is true,
depending on where the cap is placed in the model would make
a very big difference in how the cell reacts to constant vs
pulse charging. But then why would those two guys go
through all the trouble of making up that new model if they
didnt want to consider this parallel cap? I guess it could be
that they didnt feel it would affect the model in a way that
would help to show what they wanted their model to show.

Another possibility is that the nonlinear voltage dependent
voltage source, controlled by VSOC (which is really SOC from 0 to 1)
causes what looks like a change in impedance at a somewhat higher
current like 1 amp. The only problem here is that CCAP is so
INCREDIBLY huge that even a current of 1 amp isnt going to
do much for the short time period of 0.5ms (one half cycle of
a 1kHz wave). Perhaps i'll take a closer look at this anyway.

Any other ideas anyone?

Hello Al,

Here is Energizers paper on internal resistance.

I will add, just as a point of reference, that I have never been able to come close to the 0.012 ohms of impedance that is listed in the Energizer specification sheet. I usually get much higher values.

Tom

Hi again,

Tom, thanks for that new link. I'll take a look at that right away.

I made a slight error when i reported 40 farads for the CT capacitor, when
that was for the Li-ion model, however the real value would be around 1000
farads, which makes matters look ever worse.

What i am considering now is that the resistance RS is really around 0.010
ohms and the other resistor RT is around 0.020 ohms. This would make the
effective DC resistance 0.030 ohms while at 1kHz we would only see the
0.010 resistance. To call this 'impedance' however, is probably a bad idea,
because it's a voltage and current that are almost exactly in phase with
each other. In fact, using the correct cap value of 1000 farads the phase
shift is so small i doubt it can be measured. This means the 'impedance'
measurement equipment must really be measuring "resistance when subjected
to an ac current", which sort of can be called impedance.
This only problem now with this idea is that when i measured the series R
in my cells, i was seeing much higher values for what Energizer would call the
'impedance'. I never saw anything that small either.

I'll take a look at this new link and see what info it might provide.

Hello again,

Tom, that paper doesnt help at all because although they go into detail about
the alkaline cell they dont even bother to mention how they are measuring
'impedance'. They simply state that "impedance is often lower than resistance"
but they dont bother to say how they measure it.
They go into detail about measuring the internal R of the alkaline cell, and
that is what we are doing (just about) for measuring the internal R of our
NiMH cells, but unfortunately they dont give any data for the NiMH cells like that,
but (in a different paper) give a very general description. It's almost like
they are trying to avoid saying how they measure internal impedance.

The do however mention that "the impedance is the resistance to AC current"
which implies that they are measuring the impedance of a cell as we would
measure any other two terminal device which is what i was assuming all along.
Trouble is, this leads to too many conflicts between what they report
(and apparently what your impedance tester measures) and the models
presented in the paper on the new model and also models presented in other
places on the web, and also with what i have measured independently.

So far we are back to square one where:

The models indicate that constant current charging is the best way to keep
heat at a minimum in an NiMH cell, while the Energizer data indicates
that there could be some benefit from pulse charging.

So far i have to go with the models because they represent what i have
measured myself and the Energizer data seems to say nothing about the
cell that can be demonstrated experimentally.
Of course this could change if we can get ahold of the procedure Energizer
uses to measure internal impedance...any ideas how we can get this?

Al:

I used a Extech BT100 Battery Tester which logs.

Hello Al,

It is very difficult to find anyone within Energizer that knows anything technical. The standard procedure is to send them an email with your question. You then receive a boiler plate response telling you that it is normal for cells to heat up at the end of a charge. When you press further, they thank you for being an Energizer customer and tell you that if you have any further questions to be sure to contact them...

I have gone this route several times with them, and still can't find anyone that knows anything beyond the basics.

GP also lists their internal resistance at 1 kHz. They may be a better choice to send an email to. I will check some standards that I have to see if they mention anything official about impedance measurement methods.

Tom

Hi Tom,

Thanks for doing that. I think it will be very worthwhile to find out what is going on
here. BTW, i checked the idea that maybe the large cap CCAP (which would have
a huge value of 7200 farads for a 2Ah cell) was affecting the impedance in some
way and i verified that the 'voltage' across this theoretical capacitance does
not change significantly at 1kHz even with a 1 amp AC test current, which means
so far the impedance 'measurements' still dont add up.
Note also that in all of Bills measurements (with what i gather is a rather expensive
test meter) none of them reach as low as 0.012 ohms as Energizer claims.
I had measured something like 0.050 ohms, but since i didnt attempt to get
any super accuracy i would admit to Z as low as 0.030 if someone where to argue
that value, but nothing like 0.010 ohms...and the cells are still very new (10 cycles
max).

I was also going to talk about a model i found that contains parallel caps, and
parallel caps would make the impedance look lower than the resistance. The
only problem with this is that this model makes the impedance go down to
0.010 ohms for example, then i have to figure out why i didnt measure that
when i tested at 1kHz. The other problem is that this model is for large Li-ion
and not NiMH cells.

Al:

The tests I ran in that thread I had to use a clamp of sorts which introduced a bit more impedance and I had to rotate the cell looking for a low point before starting each test. Using the tester alone the lowest value I saw was about .015 ohms on PowerEx 2Ah cells.

Hello Al,

Duracell lists an internal resistance for their NiMh cells of 0.170 ohms, however they don't give any details on how it was measured.

Tom