List of standardized internal resistances

[swbluto]

Maybe you've heard, but bearing has come up with a formula for directly calculating a comparable form of internal resistance which basically means you can directly compare the performance of the underlying cells from one battery pack to another! His explanation is at his thread . Basically, the "standardized" internal resistance has units of millihour or what I've suggested should be named after bearing and that unit's name currently pending(I suggested bearing, but bearing might have a better last name). So, this post is basically to provide a list that directly compares different cells. The formula for a given battery or cell is R*Ah/V and a lower number is better - Using numbers harvested from several sources, here they are. The formula for R = (V_1-V_2)/(I_2-I_1) and those values should be extracted when the battery is half full. Also, the voltage of the battery in the R*Ah/V formula is determined by a "standard voltage per cell" multiplied by the number of cells in series. This standard voltage per cell is the open circuit voltage of the cell when it's 50% full and this will be the same number for a given chemistry. I haven't verified these values yet, but I'm guessing 3.2 volts for lifepo4, 3.7 volts for LiPo and 1.2 volts for Nimh sounds good. So, for example, a 48V battery with 16 in series would have a 50% half-full open circuit voltage of 3.2volts/cell*16cells = 51.2 volts. The purpose for this standard voltage is to ensure that cells and batteries from different chemistries can be compared.

Update: bearing has come up with a new insight - This formula is basically a straightforward way of finding how long a short-circuited standardized cell would take to drain, in theory when its internal resistance remains constant. The higher the C value, the lower the internal resistance and so you'd expect it to completely drain in a shorter amount of time. He is calling this the cell's SDT or shortest discharage time. To convert from millihours to seconds, we just multiply by 3.6.

(units in bearings = millihours)
LiFePO4(Each cell having 3.2 volts):

A123 M1 LiFePO4: 10 milli ohm * 2.3 Ah / 3.2 V = 7 millihours or 25.2 seconds.
Ping V.1 5Ah cell: .065 ohm*5Ah/3.2 V = 101 millhours
(Measured by DoctorBass) Headway's blue cell: 0.009 Ohm * 10Ah / 3.2V = 28.125 millihours or 101.25 seconds
LiPo(Each cell having 3.7 V):

Zippy Flightmax 5ah 20C cell LiPo: 5 milli ohm * 5 Ah / 3.7 V = 7 milli hours or 25.2 seconds

Nimh(Each cell having 1.2V):

Sanyo RC-3600HV NiMH: 4 milli ohm * 3.6 Ah / 1.2 V = 12 milli hours or 43.2 seconds.
Vectric Nimh: 12 mOhm * 30Ah / 1.2V = 30 milli hours or 108 seconds.


Some observations, lead acid batteries couldn't be immediately based on this formula. A much better comparison is their peukert's constant since their internal resistance is exponential with increasing current. Also, you'd notice that the ping has a corrected internal resistance of about 7 times higher suggesting that if an a123 can be called a "30c cell", than a ping cell could be called a 30/7 = 4.2 c battery. But, what determines a "C" rating is more often based on its 85% capacity cycle lifetime rather than its comparable amount of voltage-drop/battery-heating, and the 85% capacity cycle lifetime is dependent on many more factors than simply internal resistance and the heating of the cell and the relationship is obviously not linear / easily-accurately-predictable.

Feel free to chime in with your own battery's measurements or a cell's data! It'd be nice to have a list to which direct comparisons could be made. Basically, to calculate the value, all you need is the voltage(3.2 volts/cell for lifepo4, an arbitrarily standardized lifepo4 voltage to ensure comparability), capacity(in Ah) and the internal resistance when the battery is half full and you're set to go! If you don't want to do the calculation, just provide the above data and I'll calculate it and add it to the list.

 

[voicecoils]

As I understand, Doctorbass has measured the Headway blue 3.2v10Ah cell to be 9 milliohms of internal resistance.

∴ 0.009 Ohm * 10Ah / 3.2V = 28.125 Bearings

 

[docnjoj]

So if the battery gets really hot, do we state it has "boiled Bearings" Sorry in advance!
otherDoc

 

[voicecoils]

Will come back with better data from my 36v10Ah Headway packs I have (I run two in series, each has its own BMS) to get an idea of the internal resistance and 'SDT' of running each I present the following.

 

[monster]

so for my parallel ping packs @ 48v 24ah a rough guess of the bearings would be

(53v-48v)/(33a)= 151 milliohm (for high discharge?)

151 x 24ah / 48v = 76 millihour

does this look right?

 

[swbluto]

Using a personally observed data point from my 36v10Ah Headway packs I have (I run two in series, each has its own BMS) to get an idea of the internal resistance and 'bearings unit' of running each I present the following:

Using the formula: Ri=(V1-V2)/(I2-I1), under these conditions:

Ri = (Resting Voltage - Voltage under I_Load)/(I_Load) where each parameter is committed to memory glancing at my CA while traveling up a hill!

(79V - 71V)/(21A) = 381 milliohms (observed near end of pack discharge when voltage drop would be most severe)

∴ (381 * 10) / 76.8 = 49.61 Bearings

The BMS's in series and interconnect wiring will introduce some additional resistance of course. Ideally, 9 milliohms * 24 cells = 216 milliohms internal resistance. I will try to simulate the same situation at the beginning of a pack discharge when it is fresh and voltage drop is lower.

Oh dear, that's quite the discrepancy. Is the pack constructed of the same type of blue cells that doctor bass tested? I suppose headway's BMS and wiring could seriously introduce losses, but I don't think it should be on the order of 150 mOhms or nearly the total internal resistance of the cells.

 

[bearing]

(79V - 71V)/(21A) = 381 milliohms (observed near end of pack discharge when voltage drop would be most severe)

But was the resting voltage really 79 V near end of discharge? that sounds like a a fully charged value.
Since the unloaded voltage changes as the cell discharges the calculation of internal resistance should be done at the same state of charge. I think you didn't do that, and that is the reason you got a high value.

Ideally the internal resistance measurement should be done with two different load currents and at 50% state of charge.

 

[voicecoils]

Ah crap. I've looked through my ride notes and I've made an error. Those values came from a ride where I discharged 391Wh (5.35Ah). The final resting voltage at the end of the ride was 78.8V. The observed voltage drop would have been a bit before the end in that case.

The pack is made of new blue cells (tabbed not screw). I have only fully discharged the pair once and packs combined provided 790Wh (more then their rating) or 10.90Ah with current limited to 22A max.

I will delete my above posts and hope to come back with a better test. Bearing, when you say two different loads then what we are looking for a voltage at one load (V1, I1) and then a second lower voltage at a second higher current (V2, I2) correct?

So if we have (just for example) a pack at a resting voltage of 10V then we put a 10A load on it and it sags to 8V, then we take the same pack and put a load of 20A on it and get a sag down to 6V. Our values for the IR calculation would be: V1=8V, I1=10A, V2=6V, I2=20A.
Ri=(V1-V2)/(I2-I1)
Ri=(8-6)/(20-10)
Ri= 200 milliohms for this example.

I just want to double check so I can carry the tests out appropriately and will try to do so at a ~50% discharge.

 

[bearing]

Yes, voicecoils, that is just what I meant. Seems like good current points for your battery.

 

[bearing]

Nice initiative to start this thread swbluto. I don't have the equipment (yet) to be able to contribute though.

The formula:

SDT = 3.6 * Ri * Capacity / Nominal Voltage
Ri in milliohms
Capacity in Ah
Nominal Voltage in Volts
SDT in seconds.

 

[Mr. Mik]

For Vectrix NiMH cells:

0.0012Ohm * 30Ah / 1.2V = 0.030h

I still fail to see how all this helps, though!

A cell which is identical to another except for higher capacity has a "worse" result with this formula - why should that be the case?

For example, the damaged cells in my Vectux still have the same low resistance, but maybe 16Ah capacity instead of 27Ah capacity (at 20A to 1.1V cutoff).

According to the explanations given by others above, the damaged cells are supposedly better than the good ones!

 

[liveforphysics]

For a given Ri, the lower the capacity means that an equal energy pack made of those cells would yield higher performance.

This is a specific battery performance indicator number. A pack of equal energy made from your lower capacity cells would yield higher performance. However, in my experience, Ri and capacity fall directly proportionate with each other as a battery degrades/fails. Your cell design must be something unique to the batteries I have played with.

 

[ZapPat]

For Vectrix NiMH cells:

0.0012Ohm * 30Ah / 1.2V = 0.030h

I still fail to see how all this helps, though!

A cell which is identical to another except for higher capacity has a "worse" result with this formula - why should that be the case?

For example, the damaged cells in my Vectux still have the same low resistance, but maybe 16Ah capacity instead of 27Ah capacity (at 20A to 1.1V cutoff).

According to the explanations given by others above, the damaged cells are supposedly better than the good ones!

Well if you were comparing new cells to purchase, and wanted to know which cell has the best performance no matter what capacity you are comparing, then it does make sense. If you have two cells with the same resistance, but one is twice as big as the other, then you would conclude that the smaller cell is potentially more powerfull than the larger cell.

Of course in your case your cells are the same physical size, which does make the result look odd, but this is not usually the case when looking at new cells. However, this does make me think that cell size might be an important thing to consider in such a comparative equation. I mean if you have two cells with the same amp-hour ratings, but one has a 50% higher Ri but also is only 2/3 the size of the other, then they actually have the same Ri per volume. On top of this the seemingly worse Ri cell actually would have more capacity per volume, so ends up being superior for energy storage.

 

[swbluto]

However, in my experience, Ri and capacity fall directly proportionate with each other as a battery degrades/fails. Your cell design must be something unique to the batteries I have played with.

Yes, that is interesting. The Ri generally increases as the capacity is reduced - If the Ri is constant, than lower capacity Vectrix cells might be a better performer if you were to base your battery buying decision on the capacity you plan to buy. Of course, depleted cells won't fare as well for volumetric comparison/energy-density and then there's the expected cycle life which would likely be an unknown since data of cycle life past 85% of original capacity seems to be particularly scarce.

 

[swbluto]

Ok, just added a verified ping test to the list. It turns out that Headway's cells actually appear to be 100/30 ~= 3.3333 times better than Ping's, so if Ping's claim of "2C max continuous" is true, then "5C continuous max" of headway's cells actually sounds fairly accurate, if not an underestimate.