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Instruction manuals and discussions mention battery charge and discharge rates in terms of "1C", "2C" and so on, without giving an indication of what "C" is. I presume it is not a Coulomb. What is readily available for most batteries or battery packs is the capacity in Ah and the nominal voltage, eg 12V 22Ah golf cart battery pack. The "22Ah" implies a discharge rate of 1.1A over 20 hours. Using Peukert's law we can estimate the discharge at different rates, eg the above battery would last 13 hours at 1.5A discharge rate (assuming a Peukert's constant of 1.3). All that is great - what exactly is the "C" and what do people mean when they say "I would not charge it above 3C" ?

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@Kamil 's answer would have been a good one once the units had been correctly stated. –  Russell McMahon Apr 27 at 13:09
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2 Answers 2

First,

'The "22Ah" implies a discharge rate of 1.1A over 20 hours.'

Only if the manufacturer says so. It might as well mean 22A over 1 hour, or any other combination that multiplies to 22Ah.

C is generally the capacity divided by 1 hour, so for your battery it would be 22A. Hence eg. 'charge at 1C' can be stated, independent from the capacity of a battery.

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The notation for C as documented in the standard IEC_61434 is presented by Equation

- C=Capacity[Ah]/1[ℎ]    
  • meaning C is the Current based on ampere-hour rating for total discharge in 1 hour.

Capacity, C is also related to discharge rates according to Peukert's exponential constant,k. Capacity(discharge) = T * I^k for time T and Current I

However in practice, Peukert's constant k is not constant. The "constant", k is a variable which changes with Current ratios, Ambient or more specific cell temperature, as well as Chemistry and charge cycle count due to aging.

For example Lithium Titanate (LTO) has an anode surface area 100 times larger than graphite which results in lower ESR and lower self-heating and which results in a reduction in the internal resistance and increase of the power capabilities of the LTO battery.

"k" increases rapidly below freezing although some are better than others due to lossy self-heating. What it means is the battery capacity can increase a bit with temperature to a limit and is strongly dependent on chemistry and battery temperatures well below and above ambient temperature.) Most batteries appear to die below ~0 °C and age rapidly when sustained use high temp. This is approximated by a "k" increasing rapidly below 0 °C. Aging from Arrhenius "Chemistry" effects also reduces the life cycle count, which is why laptops operated daily on soft material with poor air circulation will fail early in less than a year rather than last several to many years. This is estimated by a rapid rise in k with charge cycles due to temperature rise.

Normally k increases slowly a few % with charge-cycle aging. (e.g. linear up to 6% rise after 1600 cycles then capacity depletes due to anode size and chemistry variations)

Ideally, k=1 means only that the battery chemistry does not change ESR with temperature and therefore the voltage ratio = (loaded Voltage)/(initial lightly loaded voltage) is a strong indicator of State of Charge (SOC) and ESR does not change due to ambient or self-heating or load current. { This is Very Accurate from 10~90% BUT also is very rare }

Large capacity high quality Lithium batteries can indeed vary alot with k=0.99 to 1.28.

Think of k=1 just means temperature compensated, so the thermal effects (NTC and PTC) balance out to give a somewhat constant ESR with temperature. It does not mean the best for efficiency or life cycle rating or cost or capacity /kg.

So don't think k=1 is the best in every other metric, but it would sure make life easy for estimating SOC just based on constant ESR and voltage drop.

Journal reference

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