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I've read Why are(n't) rechargeable batteries damaged by partial charging? and main source quoted batteryuniversity. I found the article having deficiencies and looking to find more "accurate" and scientifically minded studies on batteries charging / discharging effects / performances (that study disclosed sample size for only one of 6 figures/tables/results, no peer-review, it is not a journal publication).

TL;DR

As for the mentioned article, below are several specific questions I'd like clarifying:

batteryuniversity questions for the article:

  1. for 1st graph they discharge to 3V. What capacity level might it be?
  2. depth of discharge (DoD). Is it probably calculated here (and usually in technical literature) based on original / nominal capacity or remaining capacity?
  3. (point cleared thanks to user_1818839 - was my mis-read)
  4. before table 2 there is a description where "indicated state-of-charge (SoC)" is mentioned, but SoC is nowhere in the following table. What could it mean? IMHO is could mean human error like cut-and-paste, than it is also stated near that phrase that battery is cycled until 70% of capacity is left. What that might be erroneously cut-and-pasted too. Does 70% looks reasonable here?
  5. table 2 there conclusion of mid-range DoD best longevity is not supported for LiPo - for LiPo table gives 20% DoD 9000 as best (jump 3x * drop only 2x from 40%).
  6. table 3. They did not test for sub-freezing. Internet jury is out on that. Google search find numerous claims freezing restores capacity, in that QA here discussion is around protection from freezing: What is the effect on lithium ion batteries from long term storage in sub-freezing temperatures?. Any studies on that one?
  7. table 4. They did not state to what minimal voltage / capacity they discharged. Does it look like that discharge to 0? Cause their remaining capacity column indicate numbers so large for their assessment of decreased remaining capacity that at first glance it looks to me as close to 0. But 0 in many places is said to be much worse that 100% and control boards of devices mostly does not allow it. Does that test adds practical value then? Or from given data you calculate remaining charge much higher than 0?
  8. figure 5 suspiciously does not have long enough NoC axis for us to see when at 4.2V capacity also drops to ~0%. Where to see more complete graph?
  9. figure 6. Finally something to cross-check. They have Note near beginning of article "Tables 2, 3 and 4 indicate general aging trends of common cobalt-based Li-ion batteries on depth-of-discharge, temperature and charge levels, Table 6 further looks at capacity loss when operating within given and discharge bandwidths." IMHO it makes people assume Table 2 and Figure 6 analyze same battery types. Table 2: 100-40 (1000 cycles) and 100-60 (600), whereas on Figure 6 for line 100-50 I see more than 90% retention at 1000 cycles. Clearly Figure 6 gives times less loss compared to table 2 for procedures of non-contradicting (some additional info, e.g. temperature for Fig 6) description. It could indicate my guess above of cut-and-paste error above of 70% for table 2, could it? Any other possible reasons?
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    \$\begingroup\$ LiFePo4 should read LiFePO4, the PO4 being Phosphate, not "Po", informal shorthand for Polymer. There is no such thing as LiPo4, only LiPo (Lithium Polymer) and LiFePO4 (shortened to LFP) (Lithium Iron Phosphate) which are indeed completely different. \$\endgroup\$
    – user16324
    Commented Sep 5, 2021 at 13:12
  • \$\begingroup\$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. \$\endgroup\$
    – Community Bot
    Commented Sep 5, 2021 at 18:36
  • \$\begingroup\$ @user_1818839, thanks a lot! \$\endgroup\$ Commented Sep 6, 2021 at 4:13
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    \$\begingroup\$ "no pair-review" - what's a 'pair-review'? \$\endgroup\$ Commented Sep 6, 2021 at 5:53
  • \$\begingroup\$ @Bruce, my spelling, fixed to peer-review. \$\endgroup\$ Commented Sep 6, 2021 at 10:28

2 Answers 2

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I found the article having deficiencies and looking to find more "accurate" and scientifically minded studies on batteries charging / discharging effects / performances (that study disclosed sample size for only one of 6 figures/tables/results, no peer-review, it is not a journal publication).

Plenty of scientific papers can be found on the Net which investigate battery charge-discharge effects, but most are pure research that is of limited use in predicting the performance of commercial products.

There is no reason to doubt the test data in that article. If you need more accurate data for a particular cell then you should do what they did - test a representative sample. We are engineers not scientists, so we don't need peer review or publication in a journal to validate our data.

The other tables don't show sample size because they are estimates, perhaps aggregated from different sources (they did the research so you don't have to!). In practice the results can vary depending on cell chemistry, construction, impurities etc., so any one particular study (no matter how scientific) doesn't mean much by itself.

for 1st graph they discharge to 3V. What capacity level might it be?

A Lipo cell discharged at 1C typically has less than 1% capacity left at 3.0 V, so this is often taken as the cutoff voltage for capacity measurement. The graph shows the percentage of nominal capacity (in this case 1500 mAh) that was achieved for each of the 11 cells tested.

depth of discharge (DoD). Is it probably calculated here (and usually in technical literature) based on original / nominal capacity or remaining capacity?

DoD is based on the proportion of actual capacity drawn, so '100% DoD' means discharged to 3.0 V. Since you don't know exactly how much capacity the cell has until it is fully discharged any lesser amount will always be a 'guess' based on previous discharges. However if it is discharged under similar conditions (temperature, current, age) the voltage and capacity should track previous discharges closely. Therefore if the cell is fully charged and you take out 50% of its previously determined capacity you can assume the DoD is 50% (or very close to it).

before table 2 there is a description where "indicated state-of-charge (SoC)" is mentioned, but SoC is nowhere in the following table. What could it mean?

This is a slight error in the description. The only figure shown is DoD, which in this case is the opposite of SoC (so the line labeled '10% DoD' is when discharged from 100% to 90% SoC).

it is also stated near that phrase that battery is cycled until 70% of capacity is left... Does 70% looks reasonable here?

70% does sound reasonable, since 80% of nominal capacity is typically considered to be end-of-life. Without a cite we will just have to take their word for it.

table 2 there conclusion of mid-range DoD best longevity is not supported for LiPo - for LiPo table gives 20% DoD 9000 as best (jump 3x * drop only 2x from 40%).

Not sure where you got the 9000 from, but the phrase "note:...Cycling in mid-state-of-charge would have best longevity" refers to cycling around an average of 50% SoC, whereas table 2 only has numbers for cycling from 100%. Cycling around 50% is better because the battery suffers less mechanical stress in this range, and lower calendar aging due to lower oxidation at the lower average voltage.

table 3. They did not test for sub-freezing. Internet jury is out on that.

I never heard of this until now. A Google search returned several anecdotal claims of 'reviving' a 'dead' laptop or phone battery by freezing it, plus dubious advice columns where this morphed into 'restores capacity' without evidence. It's possible that a 'dead' battery might recover enough to be accepted by the device again for various reasons (eg. reduced swelling holding the plates closer together) but a significant restoration of truly lost capacity is extremely unlikely.

The jury is in on accepting evidence-free claims made by people with no technical knowledge or understanding.

table 4. They did not state to what minimal voltage / capacity they discharged.

Table 4 is based on 100% capacity achieved when charged to 4.2 V, implying discharge to 0% (presumably at 3.0 V).

figure 5 suspiciously does not have long enough NoC axis for us to see when at 4.2V capacity also drops to ~0%. Where to see more complete graph?

The purpose of figure 5 is to show the effect of overcharging. The 4.2 V curve is down to ~82% by 400 cycles so is already close to nominal end-of-life, which is probably why the data stops there. It might take thousands of cycles to get to 0% but this is uninteresting.

figure 6. Finally something to cross-check. They have Note near beginning of article "Tables 2, 3 and 4 indicate general aging trends of common cobalt-based Li-ion batteries... IMHO it makes people assume Table 2 and Figure 6 analyze same battery types... It could indicate my guess above of cut-and-paste error above of 70% for table 2, could it? Any other possible reasons?

Most of the tables are estimates, probably taken from many different sources. The apparent anomalies highlight the variations between different battery types and testing regimes that make 'accurate' comparisons difficult.

Manufacturing Li-ion cells is easy enough, but getting the formula 'just right' for best longevity is not. Determining the best cycling regime is also difficult due to the large number of parameters and long testing time required. This article is more about identifying general trends (eg. small DoD around 50% SoC is better than 100% DoD) than providing exact numbers, since these vary depending on the particular product and perhaps even the batch.

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  • \$\begingroup\$ You write: "Not sure where you got the 9000 from" It is from table 2: "20% DoD ~2,000 ~9,000" - so for LiPo it is best per the table, not middle-range as conclusion states, hence was the question. \$\endgroup\$ Commented Sep 10, 2021 at 5:19
  • \$\begingroup\$ You write "~82% by 400 cycles so is already close to nominal end-of-life" End-of-life I suspect is because after 80% linear reduction becomes a sharp drop in capacity, right? The confirmation of which for 4.2V I was looking for by asking for larger X-axis chart. \$\endgroup\$ Commented Sep 10, 2021 at 5:22
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    \$\begingroup\$ A sharp drop is expected some after reaching 80% capacity, but may not occur until well after. Here's a study that tested a UP383562a lipo (used in the Palm Tungsten PDA) recording linear capacity loss down to ~60% at ~900 cycles (graph on page 79/80) Study of Capacity Fade of Lithium-Ion Polymer Battery with Continuous Cycling & Power Performance Modeling of Energy Storage Devices \$\endgroup\$ Commented Sep 10, 2021 at 20:43
  • \$\begingroup\$ "so for LiPo it is best per the table, not middle-range as conclusion states" - No, that is only true for discharging from 100% SoC as shown in the table ("DoD constitutes a full charge followed by a discharge..."). Middle range should be even better (thus the note). \$\endgroup\$ Commented Sep 10, 2021 at 20:49
  • \$\begingroup\$ you write "Middle range should be even better" - you know that from your vast experience, right? I do not, I was reading the study that analysed such things; where have they proved it? Table 2 proved otherwise (for LiPo - one of two they showed in the table), but they still made the statement to the contrary w/out explaining why. Is my logic clear? \$\endgroup\$ Commented Sep 11, 2021 at 2:57
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TL;DR

4.) 30% loss is a common aging factor for quality for many things. Yet 70% is used for reactive loss 1/sqrt(2) = 0.707... because of the exponential asymptote is the half power point.

The 70% of new factor (after burnin) is also used for LED luminaries which are rated at LM70 for 30% lifetime loss for lumen maintenance. and for MTBF of 50kh. The initial burnin can lose a few % due to contaminants burning off depending on vintage and quality. Whereas batteries are modelled by multiple RC's in parallel with rising ESR and declining C (kfarads) resulting in product that is a Figure of Merit FoM for lower product terms in larger sizes with the load RC=T being the decay time from 100% down 71% or up 71% in DoD. Similar yet different. One short ESR*C time constant is the CV charge mode decay term in current, and conversely, decay in voltage after charger is removed.

The critical FoM's for all batteries are; ESR and balanced cell capacity differences. If they are not much less than 1% by repeatable manufacturing processes, then without a battery balancer lifespan is quickly reduced by the quadratic effects of under-over charge in series and rapid aging if the "weakest link".

Ironically this double-electric layer effect is what engineers call memory in all electrolytic caps and all batteries despite being lower with Lithium types so Marketting types called them memory less due to the lower aging effects of float charge.

Yet aging occurs above and below float voltage with heat, from ESR so considering the lifetime Wh of battery cycles, I once proved how you can tradeoff capacity for useful life Wh and improve it by 10x using only 50% of the SoC. But I'm it not sure about where the optimum bias is, e.g. from 100% to 50% but suspect 80% to 30% is better by avoiding the time spent above 4V per cell.

Note:

  • RC means Resistor-Capacitor here in series, not Remote Control. A battery of XXXX mAh can be equated to a capacitor used with about 10% voltage discharge in the 10 kilofarad range.
  • Heat aging is common to all parts from the chemical effect called Arrhenius Law, typically 50% reduction in MTBF for every 10'C rise.
  • The best Balancer usually only ensures series cell voltage balance within 10% of the rated current, but exceeding this is certain cell death not long after from exponential runaway (under/overcharge) with successive cycles and is too much heat. The final result is the battery cannot deliver as much current due to very high ESR, the capacitance loss is great.
  • When a weaker cell discharges faster it can go below the safe voltage while the string voltage is still OK can age quickly. This starts gradually from << 1% differences in voltage yet all share the same current and by the time it is off by 10% capacity the aging rate accelerates much faster as it more likely spends more time hot under or likewise over charged in the danger zone >>4.2 V This problem accelerates even more at high C charge and discharge rates
  • Lithium electrolyte leakage current is minimum in the 60's % or 2/3rd region of %SoC, which is how new batteries are shipped, stored.
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  • \$\begingroup\$ "improve it by 10x using only 50%" compared to what? 0-100% I guess? And 5-95% would result in - do you have data? Is it linear or really 0% is as written many places is very bad and 100% is moderately bad? \$\endgroup\$ Commented Sep 5, 2021 at 7:06
  • \$\begingroup\$ I'm working through your answer to understand all. "ESR and balanced cell capacity differences. If they are not much less than 1% ... under-over charge in series ... rapid aging ... this double-electric layer effect is what engineers call memory". How does it work? - "under-over charge" hints me managing 20-80% of charge would solve it, but for earlier than Li-Ion batteries types "memory" is not solved that way... \$\endgroup\$ Commented Sep 5, 2021 at 7:43
  • \$\begingroup\$ The best Balancer usually only ensures series cell voltage balance within 10% of the rated current but exceeding this is certain cell death not long after from exponential runaway (under/over charge) with successive cycles and is too much heat. So 20~80% only solves the chemical decay that accelerates at low voltage and 3.9~4.2 and worse. NiCads had to be exercised to reduce the ESR in the double charge layers \$\endgroup\$ Commented Sep 5, 2021 at 8:14
  • \$\begingroup\$ "balancer 10%". I'm getting lost. "balanced cell capacity differences .. 1%" Going to your OP: so difference from e.g. 1500mAh to 1520mAh (or 1480) translates to current significantly higher than 4.2 when charging to nominal 80% capacity (~4.05 per article)? How more current 1% capacity difference results in? \$\endgroup\$ Commented Sep 5, 2021 at 8:44
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    \$\begingroup\$ When a weaker cell discharges faster it can go below the safe voltage while the string voltage is still OK can age quickly. This starts gradually from << 1% diferences in voltage yet all share the same current and by the time it is off by 10% capacity the aging rate accelerates much faster as it more likely spends more time hot under or likewise over charged in the danger zone >>4.2 V This problem accelerates even more at high C charge and discharge rates \$\endgroup\$ Commented Sep 5, 2021 at 9:42

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