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I was trying to understand what is the worst case scenario of using a string of 4 lithium ion cells (18650 cells, 3.6V nom) in series to form a battery pack, without balance circuitry, to understand when it is really needed, as long as with single cell monitor. I know that normally it is used a BMS, but I was thinking what are the conditions that are setting the threshold from a safe to unsafe system without a BMS (for over/under voltage and balance correciton). During this process I actually learn a lot, or at least I think that. From what I've understood, there are some sources of unbalancing, like:

  1. SOC unbalance, related to manufacturing imperfections, leading to a great self discharge and thus unbalance; but could be also related to anything else which brings this SOC variation, within cells of same impedance and capacity. This SOC variation seems to be the most famous and most documented.
    • From a pure theoretical point of view, I was thinking that with very light stress on the battery (like few % in DOD), with some safe limits and high quality cells from the same batch, seems to be not a big issue even after many hundred (light) cycles. Because I read also that this unbalance could be magnified with deep DOD and high currents.
  2. Impedance mismatching: this is the most harmful when using balancers. Without balancing, the issue is not that big, if not considering under/over voltage protections during discharge/charge.
  3. Capacity difference (which on its turn lead to a SOC variation): this is the most tough to find open information about that. The only paper/article which addresses the issue directly is the one from Yevgen Barsukov, but also here, is just estimating how much really impacts with respect to the pure SOC mismatches:

    It can be that a cells total chemical capacity, Q MAX , was different to start with. But even if all cells were discharged by an equal amount from a fully charged state, their chemical state of charge will be different. I ndeed, if all 3 cells are discharged by 100 mAh, but cell 3 has different total capacity (eg: 2000 mAh instead of 2200 mAh), the resulting chemical states of charge will be 95.4 and 95%. This in turn will also cause different OCVs. As can be seen, 200 mAh difference in Q MAX causes only 0.4% difference in SOC. Because SOC correlates with voltage, this indicates that capacity imbalance causes less voltage difference than charge unbalance (cause 1).

    • This is not very clear to me, I was thinking that the capacity mismatch, if the battery is lightly used and kept to OCV maximum of 4.0V, it would keep both the strongest and the weaker within safe limits. In other words, I was thinking on this graph below, where a over/under voltage detection is used: enter image description here Now, what I am writing may seems difficult, but I try to be clear. Translating this to a system without BMS and think what happens if I reduce the maximum SOC 100% to a maximum SOC 80% and with, for example, a light DOD of 10%. But ALSO cut the charge ONLY when the STRING gets the maximum float voltage related to a SOC of 80% (so a bit less than 4.2V) while never going lower than 70% SOC during discharge. In this case, is it correct to say that a 20% (100%-80%) of capacity mismatch is allowed? Explaining further, if the cells have the same SOC, when discharged of a given energy taken from the overall pack, the weakest cell will be 20% lower in capacity. On the other way, when charging, we may end up with the original situation, because we are putting back the same amount of charge, cutting the charge at the same amount of float voltage. But if we instead are charging from a middle capacity up to their maximum of 80%, the weakest (of 20% in this example) will reach now the 100% of charge. Thus why I though I can assume with this boundaries a 20% of margin allowed, in these use cases. So, the ideal situation is to prepare the batteries to have 80% SOC and use them from this moment.

The hypothetical graph will then be similar to the one shown, but now with the same amount of energy extracted from each cell, thus not reducing the delivered power (which is 10% only of the battery pack). Basically, let the ups and downs go above 80% and below 70%, but letting me to stay within 0% and 100%. In this case, if the assumption is correct, and according to the answers, the problems relates to how fast unbalance sums up over time and cycles.

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If you don't use any form of balancing cells, then you are likely to end up with a totally unbalanced, and therefore unusable, battery pack.

There are several mechanisms by which SOC may drift apart in a series connected pack, the two most important being leakage, and charge efficiency. The drift will continue, and cannot be rectified as it is in lead or nickel chemistries by controlled overcharging.

If you do not know all the cells are equal voltage, by balanced charging, then you don't know what charge termination voltage to use on the battery so the highest SOC cell stays within 4.2v. Similarly for discharge, the lowest SOC cell must stay above your safe threshhold voltage.

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  • \$\begingroup\$ In your last sentence, you assume that I don't know the voltage. But I would assume to use cells initially balanced between each other at their SOC at 80%. Then I thought to use this margin to allow a given amount of unbalance, since as you said, it will happen. But again, with this light usage, I wonder (but please note: IF my interpretations in the OP are correct) how long could take before going out from balance, more than 20%. The original idea was with cells of the same capacity with a tolerance on capacity, which I exagerated with hypothetical cells of different capacity. \$\endgroup\$ – thexeno Nov 2 '17 at 22:33
  • \$\begingroup\$ Explaining further, cover the margin of over voltage shown in the paper linked in the OP due to capacity difference, in Figure 5, by charging to a less voltage, and thus allow a % in capacity mismatch and avoid overvoltage. This shall avoid the overcharge and further degradation of the cell, with positive reaction in unbalance. \$\endgroup\$ – thexeno Nov 3 '17 at 9:16
  • \$\begingroup\$ You don't know how long these cells will go out of balance, leakage and charge efficiency match are not specified by cell manfacturers. If you know the voltage of individual cells, then you're in a better place than just going off battery voltage. All you lose is capacity, if stop charge when the highest is 4.2, and stop discharge when the lowest is 3.whatever, rather than shagging the cells if they breach those voltage limits. Not worth it IMHO, just balance and use normally. \$\endgroup\$ – Neil_UK Nov 3 '17 at 9:19
  • \$\begingroup\$ Are you aware of a statistics regarding how fast, in average, cells are getting unbalanced given a configuration? I thought that would be well known, since maybe this is related to how active balance circuitry is getting stressed in EVs (which I assume must be very well safety defined, like ASIL D), so is part of some good "rule of thumb", like how many hours an electrolytic cap can safely last. \$\endgroup\$ – thexeno Nov 3 '17 at 9:34
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    \$\begingroup\$ "What is the problem with you?" I was still questioning because the paper of Yevgen provides a quite different feedback on the subject, with some data too, so I was trying to really understand the degree of freedom and trying to not take answers for granted. PS: I was thinking that for the laptops, it could be that the balancing is made internally in the motherboard. \$\endgroup\$ – thexeno Nov 3 '17 at 10:47

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