What's the internal resistance of your battery?

[swbluto]

Hey, I just derived an easy to use formula for calculating the internal resistance of your battery(I didn't know of it until now, so I apologize for any redundancy this information might contain) just from knowing the resting voltage(the voltage when there's no throttle for some period of time which is like 5-25 seconds), and the "working"/"draining" voltage at a given "working/draining" current, all of which the cycle analyst sees.

Where R_b is the internal resistance, I the current, V_0 the resting voltage and V the drain voltage...

So, what battery are you using and what did you calculate? Make sure to mention the nominal voltage and capacity.

I did a "rough" calculation on my battery(I just recalled values that I seem to see, which might be off by a couple of volts and, thus, several tens of milli-ohms), and it seems my Ping 1.0 10AH 48V battery has an internal resistance of 200 mOhms which comes to 12.5 mOhms for each 10AH 2-cell group. I think that's possibly a little high, but I don't know what the "standards" are.

 

[Link]

IIRC, 12.5mΩ isn't too bad, actually, especially considering the price of the cells.

 

[Anonymous]

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[swbluto]

That seems like it might be true. It appears the original headway 10AH cells at http://endless-sphere.com/forums/viewtopic.php?f=14&t=3374&start=255 had internal resistances ranging from 9-17 mOhms(Do you use something else besides charmap to get the uncapitalized omega symbol?), with a seemingly realistic median of 14 mOhms so it sounds about right for the money. Plus, ping's comes with a BMS, it's pre-constructed and it comes with a charger. His sounds like a real deal for its rough specs: The company he's obtaining these cells from seem to be of a "higher quality" than most chinese cells, just from the measured specs.

 

[swbluto]

:wink:

 

[Anonymous]

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[olaf-lampe]

To get a precise result you have to measure volt and ampere at the same time and you should also do this with a half-empty battery. Also it is important to know how much current you draw. It should be as much as possible depending on the given max constant discharge rate (and constant too). The voltage drop over the BMS is also important. Measure the voltage right across the battery not at the BMS power outlet.

-Olaf

 

[Link]

(Do you use something else besides charmap to get the uncapitalized omega symbol?)

alt+234 for Ω. 230 for µ. Also occasionally useful is 248, or °. I use 253 (which is ²) sometimes, too.

 

[John in CR]

I can't see the image, which must contain the formula needed.

John

 

[Anonymous]

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[Mr. Mik]

Are my maths too rusty, or can you express this formula a bit simpler, like this:

No matter it this is correct or not, I think you will get more accurate results if you compare voltages at a low and a medium current load, not no current vs. medium current.

As described in the procedure for internal resistance in the CBA2 owners manual:

Charge the pack, set the CBA, for example, to 11 A; assuming the battery is safe at that level. Run the test
for 30 seconds and record the voltage at the end of this test. Run a test again at perhaps 1 amp for another
30 seconds and record the voltage again. If the battery has .5 volts less at 11 A than it does at 1 A use
Ohms law: R=E/I. R being resistance in Ohms, E is voltage in volts and I current in amperes. The internal
resistance of the pack, in this example, would be: R = .5/10 or .05 ohms. Note that we used the difference
in current between the two tests of 10 A.

This formula might be better:

 

[ZapPat]

That's exactly right, Mr Mik; R = (V2 - V1) / (I2 - I1).

Using the no-load voltage for one of your operation points is not good and will result erroneous resistance readings (sometimes more, sometimes less). So as Mr Mik points out, always use two operation points for more precision.

Also follow Olaf's advice, all good. The only thing I might add to Olaf's info is that tests should be done at about half discharge (standard way as Olaf suggests), but for us it would also be usefull to have the test also done towards the end of discharge (maybe around 20% DOD) to make sure that the battery's performance does not get too bad as it pushes out the last of it's juice. Of course this might be my info-hungry tech mind talking, pushing me into wanting to compare everything too thouroughly...

Check out these theads for info about resistance checking:
The LiFePO4 Headway cell 38120P TEST REPORT inside (check mostly the last pages of this thread)
Nuts&Volts post

 

[swbluto]

Are my maths too rusty, or can you express this formula a bit simpler, like this:

That seems to be right. A rough "calculation" seems to put the figure in the ball-park.

This formula might be better:

Yes, that seems to be another formula. In fact, it seems as if the one above that you simplified from my calculation is a special case where I_o = 0 amps. In that case, one of the I values on the bottom disappears and you're left a mathematically equivalent statement. Nice work. It's also nice to see a more generalized statement.

I think you got one of subscripts mixed up, though, on one of the lines unless a negative resistance is intended.

 

[Jonathan]

Too Much math for this old brain.

My A123 M1 have < 1mOhms resistance as bare cells
Build into packs it's 4mOhms resistance mostly due to the tap/balancing wires (cell-cell is stilll < 1mOhms)
My one bad cells exhibit >3mOhms resistance.

Now these are all resting state with > 50% SOC.