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Correct way to calculate battery pack capacity?


esaj

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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)?

When you pull peak power, a cell that can't deliver simply drops its voltage and the power is automatically reduced. As long as the drop is not lower than recommanded, no damage or wear will occur. Beside, max currents like 20A is not all, another parameter is how long the cell is capable of sustaining such current. 20A on a monowheel is of course a pulsed current, not a continuous current, so it's not false to claim a cell can deliver that. Not false, but irrelevant.

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I've been looking through the cells available here: (only 18650-cells without built-in protection) http://www.akkula.fi/  and done some comparison on them here:

http://www.dampfakkus.de/akkuvergleich.php?akku1=106&akku2=537&akku3=490&akku4=570&akku5=580&akku6=523&a=5

The lowest curve is the Sony US18650V3, which should be the cell used in the original  FW battery (note: I've done this conclusion only based on the images of the opened battery pack here: http://forum.electricunicycle.org/topic/111-i-plan-to-test/?do=findComment&comment=3368 , http://aijaa.com/lytxx2  I'm not 100% sure if they are original Sony or just some copy!).

dampfakkus didn't have a curves for the LG INR18650-MJ1 3500mAh , but here are some (only the 5A discharge is comparable with above):

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

The LG MJ1 is a LiNiCoAl (NCA) -cell with 10A sustained discharge (so should be the same as the US18650V3), and still looks like the best choice (and not even the most expensive one). Of course it probably does "best" due to being the largest capacity cell, and I don't (yet) know all the other things I should look for than discharge curves and sustained/peak output...

I could probably get those (LG's) at 7,90€ including taxes, or lower a piece (depends on amount ordered, that was the price for a minimum of 10). Of course I'd have to make sure that they sent only matched cells, so the capacity shouldn't vary a lot (I think somewhere was said that the difference shouldn't be more than 2.5% on the same pack). I'm not sure if the person/company building the battery can get them cheaper via B2B-channels (assuming they're even willing to build the packs for me at a reasonable price).

I was earlier a bit worried about the safety of the NCA (it said somewhere in Battery University that they aren't that safe, even though Tesla uses them), but here:  http://batterybro.com/blogs/18650-wholesale-battery-reviews/18880255-battery-chemistry-finally-explained   it is stated that

This chemistry is similar to INR, but without the benefit of manganese. These batteries tend to support lower discharge currents, but make up for it with great capacities and cycle life. They also tend to be more resistant to physical shock, making them good options for e-bikes. Tesla uses them for its awesome electric cars.

So I'm not that worried anymore (if that information is correct ;)).

What else should I take into account when picking cells?

 

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@esaj,
avoid soldering the cells with an iron, cells don't like heat, you risk losing some % capacity or worse, triggering a thermal runaway. Cells are always factory assembled with a point soldering machine. If you can buy cells with connexion tabs, it's better. If you can't avoid the iron, use a powerfull flux for stainless steel to shorten the soldering time.

And expect the discrepancy in capacity between cells to trigger a lot of current balancing by the BMS.

I personnally don't see the benefit of assembling a battery pack oneself (one-shot, too much hassle, risk of underperformance...), but I sure would like to see you do it and give feedbacks

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No, I'm not going to assemble or spot-weld it myself, too high risk since I don't know enough... Probably would either end up with a dead battery pack or burning down the house ;)  Plus the equipment would cost a lot, don't think it's worth it to buy it just for my own use.

Instead, I've asked for a quote for building a pack with BMS if I choose the cells myself (but told them that I'm open to recommendations). That's why I'm concentrating on research about how to pick the "best" cells (in regards to price/capacity/reliability etc). Haven't heard back yet, the person I talked to was interested in the project, and promised to get back on me once he has more time and has done some research of his own.

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I've put the question, about discharge voltage to a couple manufacturers. Tina from King Song was the first to reply, confirming that the user is notified of a low battery at 53v & 48v when fully depleted—this is under load conditions. 

"53V is the controller reminders rider the battery is in low status, for battery, the over discharger voltage is 48V, that is 48/16, 3V per cell" 

In your comments about the lack of capacity in the generic & the GW, why could this difference in discharge voltage cut-off threshold not account for this? 

@esaj, the LG MH1 cells are rated for 10A sustained current & have the best Wh capacity (10Wh) @10A load. IMO a better battery choice than the MJ1s.
http://www.dampfakkus.de/highamps/537-at 10A.png

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@esaj, the LG MH1 cells are rated for 10A sustained current & have the best Wh capacity (10Wh) @10A load. IMO a better battery choice than the MJ1s.
http://www.dampfakkus.de/highamps/537-at 10A.png

​Ok, I had the LG MH1's in the graph with 6 different cells and it clearly lasted the longest time @5A (and had second highest capacity at 3.5V, behind Sanyo NCR18650BL), as both LG INR18650 MH1 (3200mAh) and LG INR18650 MJ1 (3500mAh) are listed in the store I've been looking at. MJ1 has also 10A sustained discharge and gets nearly 11Wh on 10A load. I've understood that both have NCA (LiNiCoAl) chemistry, MJ1 looks just like the bigger capacity version of MH1.

But is there something else that makes MH1 better than MJ1 that I haven't looked into?

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Sorry, I was influenced by what someone had written on the eBike forums, but looking at the stats independently (mainly the mOhm), yes, the MJ1 could be a better battery than the MH1. 
http://endless-sphere.com/forums/viewtopic.php?f=14&t=67317 
http://powercartel.com/2015/02/test-results-for-lg-inr18650-mj1-3500mah-18650-li-ion-battery/

Look at the 1C discharge. Drops from about 3.7-3.6v nominal down to 3.3v. That's around 10% of energy wasted to heat on just 1C. So imagine having a 48v 20AH pack that sags from 48v to 44.1v when hit with a 20 amp load. Pretty pathetic. Now, if you had a 48v 40ah pack, that voltage sag would be cut in half, and you'd be running the bike at 20A still.. it would sag to 46.05v.. that's still pretty bad.. the only way to see a 1 volt drop maximum on 20 amps would be to have a 60AH pack.. get the idea? :lol: 
 

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Look at the 1C discharge. Drops from about 3.7-3.6v nominal down to 3.3v. That's around 10% of energy wasted to heat on just 1C. So imagine having a 48v 20AH pack that sags from 48v to 44.1v when hit with a 20 amp load. Pretty pathetic. Now, if you had a 48v 40ah pack, that voltage sag would be cut in half, and you'd be running the bike at 20A still.. it would sag to 46.05v.. that's still pretty bad.. the only way to see a 1 volt drop maximum on 20 amps would be to have a 60AH pack.. get the idea? :lol: 
 

Hmm, this makes me wonder if I could get more juice by using higher discharge C-rated cells with lower capacities, and they'd probably also be safer...

​At minimum, I'm buying two packs, maybe 3 or 4 depending on price, and put them in parallel in the wheel, replacing the original pack completely, as I don't want to mix used pack with different cells and capacity with the (possible) new ones. So the load should be split to as many separate packs as there are, but still probably they all should have pretty high discharges in case of large peaks or one battery pack failing.

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I've put the question, about discharge voltage to a couple manufacturers. Tina from King Song was the first to reply, confirming that the user is notified of a low battery at 53v & 48v when fully depleted—this is under load conditions. 

"53V is the controller reminders rider the battery is in low status, for battery, the over discharger voltage is 48V, that is 48/16, 3V per cell" 

In your comments about the lack of capacity in the generic & the GW, why could this difference in discharge voltage cut-off threshold not account for this? 

 

​Here is my take on it Jason : our batteries are specified with a nominal voltage of about 3.6-3.7V, meaning that the nameplate Wh capacity corresponds in fact to 80% depth of discharge (DoD), not 100%. Because cycles with 100% DoD will seriously shorten the battery's life, manufacturer don't consider them for rating, which is a good thing, here is what battery-university says about it : http://batteryuniversity.com/learn/article/discharge_methods

Rather than a 100 percent depth of discharge (DoD), manufacturers prefer rating the batteries at 80 percent DoD, meaning that only 80 percent of the available energy is being delivered and 20 percent remains in reserve. A less-than-full discharge increases service life, and manufacturers argue that this is closer to a field representation because batteries are seldom fully discharged before recharge.

I would think that discharging down to Tina's 3V corresponds to 100% DoD, something possible but not advised and not adopted. So on my wheels, I presume that 3.5V/cell corresponds to 80% of DoD, that's when the wheel tilts back (or beep) to stop you from discharging further. That's why at the beginning of a charge cycle, my empty batteries start from 3.5V, and not 3.0V. Not precise, but in the ballpark values, since measurements are taken at the charge plug, not on the cells.

As to Gotway, I had a deeply discharged battery (I could only ride at 5km/h, with a nearly constant and frightening beep because of the imminent cutoff) and I can charge only 300Wh. That can NOT be an honnest 340 Wh battery : on my Firewheel 260Wh battery, I can charge up to 280Wh. Most users don't know because they don't take measures or don't care to complain but we shouldn't let Gotway get away (no pun intended) with it.

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If the Gotway cells are genuinely made by Panasonic, can't you just take the Wh of each cell (as rated by Panasonic) and multiply it by the total amount of cells?

​Could it also be mismatched cells (one or more of the cells in the pack has significantly lower capacity), which to my understanding leads to all the other cells "regressing" to match the lowest cell capacity? From what I've read about battery pack assembly, the cells should be matched so that the real capacity difference between all the cells never exceeds around 2.5% (at the time of building the pack) to prevent this.

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Any speculation is possible.

Mine is that they have sold me a Gotway280Wh for the price of a Gotway340Wh and hoped I wouldn't check and/or wouldn't complain like the majority of users. The underrated value has been confirmed by other users, I'll wait for more.

Gotway has had dubious pratices, like inflating the speeds by 3km/h or not warning anywhere whatsoever in their manual or commercial flyer that the wheel WILL shutdown if too high speed or too low bat (I doubt such dangerous "feature" would have much success in a sale pitch).

So I would presume them culprit before proven innocent.

Yes John, I'll check the cells marking under the shrinkwrap film.

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I think the best way to answer this is to test experimentally, will try to fit in next week... With an inline power-meter, it will provide the voltage at which the first low-battery status is given & the set voltage at which the control-board compels you to get off. There's likely to be variation among which specific cells, but if you read the datasheets of any typical Li-ion, it's usually a 2.5v cut-off.

In my opinion, a cell's voltage at rest is NOT a true representative of the cut-off voltage. 

The chaps at ebikes.ca have created their own universal charger that can do a 80% charge to 4.05v, which they claim will double the lifespan of Li-ion cells. I haven't seen any evidence of the impact of cycle life if depleting down to the lower-end of the spec (<3v), I'm sure it exists, but don't have quantitative information on what this is.   

charge.png

Supporting evidence:

  • With Ninebot, IPS, King Song wheels, even when the battery is fully depleted & you leave it to rest, the status initial reads higher than it is until you try to use it
  • Manufacturer confirms that the cut-off value is 3v 
  • My theory of the return to a partial voltage equilibrium under no-load is confirmed below, not much at .125v, but remember that when serialized in a pack of 16 cells, under load, because of resistance it becomes much more pronounced. 

QMax.thumb.png.3ceeec0627e3f7eeb464d89be

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I think the best way to answer this is to test experimentally, will try to fit in next week... With an inline power-meter, it will provide the voltage at which the first low-battery status is given & the set voltage at which the control-board compels you to get off. There's likely to be variation among which specific cells, but if you read the datasheets of any typical Li-ion, it's usually a 2.5v cut-off.

In my opinion, a cell's voltage at rest is NOT a true representative of the cut-off voltage.

​Oh sure, I was talking about no-load voltages (except on my Gotway, where I can get the voltage while riding thanks to Android app : at 3.1V, you could ride no faster than 5km/h without imminent risk of shutdown, at speed at which my FW or my X3 clone have stopped long ago).

At the low end of state of charge (SoC), the voltage sag is huge even with slight loads and when the load is removed, voltages shoot up so maybe we are talking about the same thing under different conditions (I still highly doubt the 2.5V value though). With LiPo, because the discharge curve is flat and voltage sags rapidly at the end,  it's nearly impossible to know the SoC based on voltage readings. I always set my low voltage alarm on RC LiPos at 3.5V, because we are always told going lower will rapidly kill some cells in the pack and because I know there is not much juice left to be worth risking the undervoltage event. LiIon are a little bit better, but not much, thus our problem in dertermining the end of discharge and/or cut-off voltage.

BTW, I just looked at my trusty IMAX B6 charger, there is an option to discharge LiIon (at 100 mA IIRC) and you can't go lower than 3.0V.

 

The chaps at ebikes.ca have created their own universal charger that can do a 80% charge to 4.05v, which they claim will double the lifespan of Li-ion cells. I haven't seen any evidence of the impact of cycle life if depleting down to the lower-end of the spec (<3v), I'm sure it exists, but don't have quantitative information on what this is.  

Using our common 2A chargers, ​you can easily charge at 80% by stopping when current drops below 1A (see my charge curves for FW and X3 above), that's what I do routinely using the Charge Doctor.

But a charger that systematically stops at 80% is not what can be qualified as "universal". If the pack has a BMS, stopping at 4.05V may not trigger balancing (nearly all BMS use the top-balancing scheme and usually need voltage above 4.1V to trigger). Battery packs need to be fully charged periodically in order to be balanced. That's more and more true at end of life since worn out cells will diverge in capacicty and internal resistance, requiring more frequent balancing.

As to the impact on aging because of undervoltage, it's because of passivation at the electrodes. You have some good videos explaining the phenomenon in LiIon. Of course, I haven't witnessed or experimented it myself but I have no doubt about it because on NiCd or Limh (and probably on LiIon too), it frequently induces voltage inversion, resulting in the killing of the cell.

 

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@hobby16

I heard back from the guy whom I asked about the battery pack building, he said he has found some suitable BMS's with 30-150A max output and over discharge protection triggering around 2.9V. Do you think the 2.9V is low enough voltage to not trigger unnecessarily?

The cells he suggested straight out of the bat were LG 3500mAh (so I guess it's the same MJ1 I was looking at) and Sanyo 3350mAh (So I guess it's the NCR18650BL which I was comparing in the graphs too), he said he'll still take a further look for other options.

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I would say that goes too low voltage.

​Yes, but the wheel main board will stop you from riding at 3.5V per cell, so I'm not worried of actually overdischarging the cells, just that I don't want the protection to cut out if the voltage momentarily goes very low (during acceleration or hill climbing, or due to colder weather), as that has been the problem with the BMS cut outs.

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lol, I wondered when vee would chime in to put to rest our questions about voltage thresholds.

Yes, 2.9V is what I would say the tear and wear zone for a LiIon cell. Of course it's a safe zone against sudden cutoff since the mainboard would deal with the undervoltage warning way before, but it doesn't address the problem of a single defective cell triggering the cutoff for the whole pack. And don't forget the BMS with cutoff mosfets will also cut off if there is a thermal runaway, another sure promise of faceplant ! Yeah, it "features" a temperature detector to protect the battery against high temperatures by... ejecting the bloody rider. It would be funny had it been not so stupid.

We are making a mountain out of a molehill with the BMS overdischarge protection. First, as said before, this protection is already done by the mainboard, except the negligible risk & laughably hypothetical case of a dumb user not powering down his wheel (hell, nothing, even not a paddle, can be fool proof, right ?). Second, the risk a overdischarged battery is very low compared to other risk of malfunction : see eg the quite comprehensive "Lithium-Ion Batteries Hazard and Use Assessment",  page 62.

Is it worth addressing such hypothetical risk with solutions that have huge unintended consequences (like a faceplant) on a monowheel ? I'd say emphatically no.

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Is it worth addressing such hypothetical risk with solutions that have huge unintended consequences (like a faceplant) on a monowheel ? I'd say emphatically no.

​Ok, so it sounds like the protection should be shunted even with such BMS, if I end up ordering a custom-pack... He didn't yet tell me what the assembly + testing + other materials (BMS, shrink wrap, wires...) without cells would cost, so I'll still wait and see before pulling the trigger on ordering. Still, 2-4 independent packs of around 207Wh per pack on nominal voltage (235Wh per pack if calculating on max voltage, like in the Firewheel "779Wh" battery) sounds nice, unless the price shoots through the roof  ;)

Basically, each cell voltage should be monitored, and if any one cell drops below the limit, should come to an alarm.
If you want maximum protection to the battery.

​Yeah, unfortunately it seems that the BMS-circuits don't alarm you, but cut off all power immediately instead. Not nice, especially on high speeds...

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@vee73

How are you doing, vee ? Hope you're recovering fast.

Maybe you know this 8 channel "LiPo checker" (less than $2 on eBay). Really really loud buzzer, even on an RC plane flying far appart ! To miss it on our wheel, you must be stone deaf. :P

The only downside is you can't have it connected permanently, since it drains current on the 2 lowest cells.

P309_6_zps8b4bea6b.jpg

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Yeah. I recovered very well :)
There is no problem.
No pain and no medication. A couple of days to get the staples removed.

Those alarms are familiar to me. I do not want them because they all alarm voltage is set too low.
I would like to self-adjust. In those there is always also badly calibrated.
But they are loud yes :)
But the big helicopter of those is not covered. They need to have 4 pieces that include :)

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