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Correct way to calculate battery pack capacity?


esaj

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@Michael Vu had posted this in the Facebook-group:

11666304_10106334366849930_1395312502748

It's the BMS-containing battery pack of Firewheel F779 (779Wh), but if you look at the pack, it says 60V  11.6Ah. Now, that would mean that

60V * 11.6Ah = 696Wh

But, if you calculate it with the maximum voltage of the cells used (Sony US18650V3, max voltage 4.2 +- (0.05V?), nominal 3.7V, minimum 2.5V), you get

16 * 4.2V = 67.2V

67.2V * 11.6Ah = 779.52Wh

...which they've then rounded down, maybe they thought F779 sounds better than F780. :P

And if they had used the ACTUAL nominal voltages and not rounded it UP, it would have been

16 * 3.7V = 59.2V

59.2V * 11.6Ah = 686.72Wh

 I was looking through some cell options for custom packs, and noticed that the largest available cells are around 3400mAh (3.4Ah) at 3.7V nominal / 4.2 max, so that would be either

59.2V * 3.4Ah = 201.28Wh

Or

67.2V * 3.4Ah = 228.48Wh

per pack of 16 cells.

Which one is the correct way to calculate Watthour-capacity, nominal or maximum voltage? Does it really even matter? Can you ever really use up all the capacity, considering that the cells aren't discharged even nearly to the minimal voltage? Most discharge curves seem to cut the 3.5V line (Firewheel mainboard stops you from riding at this point) maybe around halfway through the "actual" charge, if you compare to discharging them way more closer to the minimal voltage (but that of course could damage the cells).

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According to http://batteryuniversity.com/learn/article/confusion_with_voltages this is just another way to cheat the customer ahhh "get a market advantage"...

"The nominal voltage of lithium-ion is 3.60V/cell and represents three nickel-based batteries connected in series (3 x 1.20V = 3.60V). Some cell manufacturers mark their Li-ion as 3.70V/cell or higher. This offers a marketing advantage because the higher voltage boosts the watt-hours on paper (voltage times current equals watts). The 3.70V/cell rating also creates unfamiliar references of 11.1V and 14.8V when connecting three and four cells in series rather than the more familiar 10.80V and 14.40V respectively. Equipment manufacturers adhere to the nominal cell voltage of 3.60V for most Li-ion systems."

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According to http://batteryuniversity.com/learn/article/confusion_with_voltages this is just another way to cheat the customer ahhh "get a market advantage"...

​Ok, so probably nominal voltage should be used for calculating capacity. But using 3.6V or 3.7V nominal voltage to calculate the Watthours vs. using the maximum voltage gives far greater numbers... so 779Wh Firewheel is actually probably closer to 

16 * 3.6V = 57.6V

57.6V * 11.6Ah = 668,16Wh

A "slight" difference of around 110Wh or about 15% vs. the so-called 779Wh  :D

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Yes - the nominal voltage is the average voltage during discharge.

This marketing advantage/cheat is maybe exactly what hobby16 writes about the battery packs when he encounters the difference of the marketed capacity and what he measures with his charge doctor.

With the charge doctor you could also get the usable capacity for wheels the stop already at about 3.5V - so if you ride until the wheel stops and then measure the capacity which gets charged with the charge doctor, you should know exactly how much was used while riding.

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Yes - the nominal voltage is the average voltage during discharge.

This marketing advantage/cheat is maybe exactly what hobby16 writes about the battery packs when he encounters the difference of the marketed capacity and what he measures with his charge doctor.

​Yeah, this also might make comparing ranges and Wh between different EUCs a bit tricky, as some wheels might discharge the batteries to a lower voltage than others... Here's for example the discharge curve @ 3.5A (1C) of one of the cells I was looking into for the possible custom packs (LG INR 18650 MJ1 3500 mAh / 10A LiNiCoAlO2): 

http://powercartel.com/2015/02/test-results-for-lg-inr18650-mj1-3500mah-18650-li-ion-battery/194415tm9m6t1grzzmjjjx-2/

If the wheel stops you from riding around 3.5V, you get about 1.7Ah out of the battery. On the other hand, if another wheel would let you discharge it down to 3.3V, you'd get something like 2.5Ah out of it! Of course, personally I'm more interested in how far it can take me / how long the charge lasts than the actual numeric Ah/Wh amount...

Btw, does anyone know if using LiNiCoAl (NCA) is safe in wheels, as it seems to be one of the more volatile chemistries: http://batteryuniversity.com/learn/article/types_of_lithium_ion ? :P

Lithium Nickel Cobalt Aluminum Oxide battery, or NCA, has been around since 1999 for special application and shares similarity with NMC by offering high specific energy and reasonably good specific power and a long life span. These attribute made Elon Musk choose NCA for the Tesla EV’s. Less flattering are safety and cost. 

The energy densities and the battery tests seem tempting, but I'd rather not ride on top of a bomb ready to go off any moment...  ;) 

 

With the charge doctor you could also get the usable capacity for wheels the stop already at about 3.5V - so if you ride until the wheel stops and then measure the capacity which gets charged with the charge doctor, you should know exactly how much was used while riding.

True, might be a good idea to order one from hobby16. :)

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I always use 3.7V

This marketing advantage/cheat is maybe exactly what hobby16 writes about the battery packs when he encounters the difference of the marketed capacity and what he measures with his charge doctor.

​no no, the difference between nameplate Wh (what is marked on the pack's label) and real Wh was due to cheating by Gotway, I don't have such discrepancies with Firewheel.

The convention everybody can use to translate Ah to Wh is to take a nominal voltage of 3.6V or 3.7V and that's consistent throughout batteries.

Example: 2.2Ah cells in a 16S1P pack => 16x 2.2Ah x 3.7V = 130Wh.

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Which one is the correct way to calculate Watthour-capacity, nominal or maximum voltage? Does it really even matter? Can you ever really use up all the capacity, considering that the cells aren't discharged even nearly to the minimal voltage? Most discharge curves seem to cut the 3.5V line (Firewheel mainboard stops you from riding at this point) maybe around halfway through the "actual" charge, if you compare to discharging them way more closer to the minimal voltage (but that of course could damage the cells).

​The Wh value is the best way to caracterise energy. Some are used to Ah (or mAh), a more popular indicator with bikelec users but it's less reliable since voltage varies.

Two days ago, I tried to discharge the Gotway the most I could for my capacity check. Its voltage, measured by the bluetooth app had dropped down to 3.1V/cell and I could still ride, at 5km/h with the buzzer beeping all along the last km (the most embarrassing km I've ever made). That's was a sure way to wear the battery, with Firewheel, it wouldn't be possible but with Gotway, well, you can. I suppose it's one more of GW's cheating, to get an inflated range (without saying that you can do that, but causing a huge stress to the battery).

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​The Wh value is the best way to caracterise energy. Some are used to Ah (or mAh) but it's less reliable since voltage varies.

Two days ago, I tried to discharge the Gotway the most I could for my capacity check. Its voltage, measured by the bluetooth app had dropped down to 3.1V/cell and I could still ride, at 5km/h with the buzzer beeping all along the last km (the most embarrassing km I've ever made). That's was a sure way to wear the battery, with Firewheel, it wouldn't be possible but with Gotway, well, you can. I suppose it's one more of GW's cheating, to get an inflated range (without saying that you can do that, but causing a huge stress to the battery).

For cell lifetime, it's probably a good thing that FW won't let you discharge the cells deeper than 3.5V. But wouldn't that mean that if you had a wheel that lets you discharge them to a lower voltage, and the wheel was otherwise similar (weight, power etc) and ridden in same way, you'd actually get far more range on that wheel than the other which stops you at 3.5V? I better stop quoting FW ranges and Wh when talking to people about range vs. Wh  :P

At first I though I could pick just a cell with some chemistry I want and as large Ah -capacity as possible, but looking at the discharge curves, it's not that simple... And I don't even know the average discharge current I use while riding... :rolleyes:  If the motor's rated at 550W / 1350W peak, I could take a guess of using around 300-400W power on average, then considering around 60V nominal voltage, the discharge current I'm using could be around... 300W/60V = 5A, 400W/60V = 6.666..A. Maybe. Or maybe not. :D  Would need some sort of telemetry device attached to the power lines during riding to know for sure ;)

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For cell lifetime, it's probably a good thing that FW won't let you discharge the cells deeper than 3.5V. But wouldn't that mean that if you had a wheel that lets you discharge them to a lower voltage, and the wheel was otherwise similar (weight, power etc) and ridden in same way, you'd actually get far more range on that wheel than the other which stops you at 3.5V? ;)

​well, less and no, esaj :P

When the voltage drops below 3.5V, there is not much juice left, I would say less that 5% of the full capacity and the voltage drop is quite stee so you'll let a bit more range, not "far more range". The steep drop is a bit less true for LiIon but for LiPo, the drop is really really steep. And LiFePo is still different, with different thresholds.

Not simple indeed. I'll write a post to explain more about all this for users to take care of their wheel's battery. It would have been simpler too if seller didn't cheat on the capacity.

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Are you sure about that? In most battery discharge tests I've seen, the cut-off value is 2.5v. Under, say a 10A load, the voltage quickly drops to 3.5v within a matter of minutes, even though the cell has more than 80% capacity remaining. 

559-green%20vs%20blue%20at%2020A.png 

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Are you sure about that? In most battery discharge tests I've seen, the cut-off value is 2.5v. Under, say a 10A load, the voltage quickly drops to 3.5v within a matter of minutes, even though the cell has more than 80% capacity remaining. 

I am pretty sure your curves are for LiFePo, which has lower voltage values.

For LiIon, curves are like below (source : http://www.ibt-power.com/Battery_packs/Li_Ion/Lithium_ion_tech.html ). The cut-off values on my wheels can be seen by the voltage at the beginning of the charge, around 57V, that is 3.5V/cell.

Li_Ion_DiscGph.JPG

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I am pretty sure your curves are for LiFePo, which has lower voltage values.

For LiIon, curves are like below (source : http://www.ibt-power.com/Battery_packs/Li_Ion/Lithium_ion_tech.html ). The cut-off values on my wheels can be seen by the voltage at the beginning of the charge, around 57V, that is 3.5V/cell.

Li_Ion_DiscGph.JPG

​Any idea what type of cell that actually is, the ones I've been looking at usually have the 3.5V point much earlier in the curve (at least on higher discharge current)? Like this:

http://lygte-info.dk/pic/Batteries2012/Efan IMR18650 3200mAh (Purple)/Efan IMR18650 3200mAh (Purple)-Capacity.png

 

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But GotWay does not cheat?

​Oh yes, it does ! I just have confirmation from 2 other users from our bulk order.

We have batteries labelled "340Wh", but in fact, no more than 300Wh can be crammed in, which correspond to 280Wh batteries.

Gotway, stop the joke !

 

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​Any idea what type of cell that actually is, the ones I've been looking at usually have the 3.5V point much earlier in the curve (at least on higher discharge current)? Like this:

http://lygte-info.dk/pic/Batteries2012/Efan IMR18650 3200mAh (Purple)/Efan IMR18650 3200mAh (Purple)-Capacity.png

 

​IMR reference must be from Samsung batteries. The mean continuous discharge rate on our wheels is around 2A (eg 120W, remember it must be consistent with the fact that you can ride a 130Wh wheel during one hour), with the corresponding curve on the graphs.

There is a lot of different references of 18650 batteries even from the same manufacturer with the same nominal capacity, some are "current rated" others are "capacity rated". I know much less about the naming of thoses batteries than I should (as a hobbyist, I'm more with LiPo, a fast evolving field too). You can look up good information from this site : http://www.powerstream.com/18650-high-discharge-rate.htm

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​IMR reference must be from Samsung batteries. The mean continuous discharge rate on our wheels is around 2A (eg 120W, remember it must be consistent with the fact that you can ride a 130Wh wheel during one hour), with the corresponding curve on the graphs.

There is a lot of different references of 18650 batteries even from the same manufacturer with the same nominal capacity, some are "current rated" others are "capacity rated". I know much less about the naming of thoses batteries than I should (as a hobbyist, I'm more with LiPo, a fast evolving field too). You can look up good information from this site : http://www.powerstream.com/18650-high-discharge-rate.htm

​I don't know the real capacity the current batteries have left (they've been used for something like 300-400 cycles, so not peak capacity anymore), that's why I probably should buy a Charge Doctor from you, but that's actually a pretty good point... If I knew the current capacity, and I usually ride it to empty in about an hour or a little more, I could calculate the estimated average wattage used and thus discharge current from that and then use it with the curves to find the best possible cells :)

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​I don't know the real capacity the current batteries have left (they've been used for something like 300-400 cycles, so not peak capacity anymore), that's why I probably should buy a Charge Doctor from you, but that's actually a pretty good point... If I knew the current capacity, and I usually ride it to empty in about an hour or a little more, I could calculate the estimated average wattage used and thus discharge current from that and then use it with the curves to find the best possible cells :)

​I must tell you, I don't believe the 300, 400 cycle wear-out is true on our wheels, because the mean current is not so high. It's possible the batteries are wearing out at slower pace than stated, because big manufacturers like Samsung or Panasonic prefer to state conservative values for legal reasons.

Why ? because I have had more than 100 cycles on my Firewheel and I see no decrease in capacity whatsoever (and its not based on hearsay or some others' "experience", it based on precise curves made with the Charge Doctor).

It's too soon to know for sure but let's hope I'm right :P

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That discharge graph was from the Samsung 25R, it's the extreme 25A discharge graph, so yes, not your typical leisurely EU ride :)  
http://www.dampfakkus.de/akkutest.php?id=559

However, even at 2A, which is well within the operating range of cruising on your Wheel, the voltage reaches 3.5v when there's still 50% left in the tank. It would seem pretty crazy if the manufacturer left 50% capacity as a 'reserve', 2.8v maybe, 3.0v possibly, but 3.5v doesn't make any sense. 

http://www.dampfakkus.de/akkuvergleich.php?akku1=498&akku2=99&akku3=&akku4=&akku5=&akku6=&a=2

Battery_Testing.thumb.png.95d7e3edd4c94b

Almost all Li-ion chemistries (NiCoAl, NiMnCo, etc) are rated to 2.5v discharge. What we need to do is test all the major brands to see how low their control-boards allow the voltages to get. 

P.S. Dampfakkus besides updating cells more frequently than lygte-info.dk, also has this terrific feature that allows you to compare the discharge curves of up to 6 different cells!

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@hobby16, definitely agree that there are likely to be huge variations on the life-span of the battery-pack between vendors. Empirically, I think there is data to show that the anemic <16 cell Wheels, besides being taxed more severely than those with parallelization, also suffer proportionally more when in regen mode during hard braking & descents. Good quality testing required to put the theory to test...  

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Another (maybe stupid) question: if the cells were rated below the discharge current the motor can pull at peak power, does it mean the cells get damaged, or that they simply won't give as much power, and the peak power will be lower? Just wondering if I have to have cells with really high discharge currents (like around 20A, considering that 1350W/60V = 22.5A)? Of course with more packs I'd expect the current to flow from each pack in proportion to the amount of packs (ie. 22.5A with two packs = 22.5A/2 = 11.25A per pack)?

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In most Wheels, the BMS &/or control-board will regulate current to the motor. In the case you described, the output for the cell would be about 10A (residual is because that 1350W peak figure probably uses the mfg's disconnected-from-the-wall 4.2v cell rating, rather than the nominal 3.6-3.7v). Something like the MSuper 850Wh monster has 6 (I think) parallel packs, 6p16s, at which point the battery-pack isn't going to be a bottleneck in providing continuous power. 

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However, even at 2A, which is well within the operating range of cruising on your Wheel, the voltage reaches 3.5v when there's still 50% left in the tank. It would seem pretty crazy if the manufacturer left 50% capacity as a 'reserve', 2.8v maybe, 3.0v possibly, but 3.5v doesn't make any sense. 

​Maybe what you are dealing with is a particular LiIon cell reference, but on our wheels, according to my data, the cells are near empty at 3.5V, hence the quite conservative voltage warning thresholds by the mainboard (which is a good point).

Here are the two charging profiles logged by Charge Doctor from empty wheels (by empty, I  mean I can't ride them anymore because of the tilt-back) :

  1. Generic X3 clone : the voltage at beginning of charge is 60V => 3.75V per cell
  2. Firewheel 260Wh : voltage at beginning of charge = 58V => 3.6V per cell

charge_X3.jpg

charge_FW_20150412_annoted.jpg

Those are no-load voltages measured at the charging plug by Charge Doctor so loaded voltages at the cells are a little bit lower, hence my estimate of 3.5V. I really don't see how it can go down to 2.5V. If I have the occasion to read voltage right at the cells level, I'll think about what you say and check, but my data say 3.5V, not 2.5V.

BTW, with Gotway, I can check the battery-empty voltage too thanks to the bluetooth app. It was 51V (3.2V per cell), a value a talked about earlier and that I found really too low.

 

 

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Wow, that's really interesting, thanks for sharing graphs! You're right that data shows 58v, this is the charge cycle? It should't really make any different though.  
Here's an idea: maybe a depleted cell returns closer to the equilibrium of the nominal ~3.6v, but if there is any load, say .2A then the drops off precipitously below 3v. I have to get my in-line power-meter connected up & test...  

In my mind the 4.2v (top) to the 3.5-3.6v shown here doesn't compute with everything else I've read.  

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Just had a thought: when your FW is out of juice & you turn on the power switch, does the voltage sag according to the Charge-Doctor tool? Maybe the couple W of an unloaded Wheel will induce the voltage-drop result. 

 

No for first and no for second. There is a slight voltage sag when the wheel is on, I don't remember the exact value but it's less than 1V total.

It can't be much anyway because the internal resistance of the battery is in the vicinity of milli-ohms to sustain peak powers of 350W or more.

I am sure the 2.5V value is for LiFePo, not for our LiIon batteries.

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