Peukert's law

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Peukert's law, presented by the German scientist Wilhelm PeukertGerman Wikipedia in 1897, expresses approximately the change in capacity of rechargeable lead-acid batteries at different rates of discharge. As the rate increases, the battery's available capacity decreases, approximately according to Peukert's law.

A 2006 critical study concluded that Peukert's equation could not be used to predict the state of charge of a battery accurately unless it is discharged at a constant current and constant temperature.[1] A 50Ah lithium-ion battery tested was found to give about the same capacity at 5A and 50A; this was attributed to possible Peukert loss in capacity being countered by the increase in capacity due to the 30◦C temperature rise due to self-heating, with the conclusion that the Peukert equation is not applicable.

Manufacturers specify the capacity of a battery at a specified discharge rate. For example, a battery might be rated at 100 A·h when discharged at a rate that will fully discharge the battery in 20 hours (at 5 amperes for this example). If discharged at a faster rate the delivered capacity is less. Peukert's law describes a power relationship between the discharge current (normalized to some base rated current) and delivered capacity (normalized to the rated capacity) over some specified range of discharge currents. If Peukert's constant , the exponent, were equal to unity, the delivered capacity would be independent of the current. For a real battery the exponent is greater than unity, and capacity decreases as discharge rate increases. For a lead–acid battery is typically between 1.1 and 1.3. For different lead-acid rechargeable battery technologies it generally ranges from 1.05 to 1.15 for VRSLAB AGM batteries, from 1.1 to 1.25 for gel, and from 1.2 to 1.6 for flooded batteries.[2] The Peukert constant varies with the age of the battery, generally increasing (getting worse) with age. Application at low discharge rates must take into account the battery self-discharge current. At very high currents, practical batteries will give less capacity than predicted with a fixed exponent. The equation does not take into account the effect of temperature on battery capacity.

Formula[edit]

For a one-ampere discharge rate, Peukert's law is often stated as

where:

is the capacity at a one-ampere discharge rate, which must be expressed in ampere-hours,
is the actual discharge current (i.e. current drawn from a load) in amperes,
is the actual time to discharge the battery, which must be expressed in hours.
is the Peukert constant (dimensionless),

The capacity at a one-ampere discharge rate is not usually given for practical cells.[citation needed] As such, it can be useful to reformulate the law to a known capacity and discharge rate:

where:

is the rated discharge time (in hours),
is the rated capacity at that discharge rate (in ampere-hours),
is the actual discharge current (in amperes),
is the Peukert constant (dimensionless),
is the actual time to discharge the battery (in hours).

Using the above example, if the battery has a Peukert constant of 1.2 and is discharged at a rate of 10 amperes, it would be fully discharged in time , which is approximately 8.7 hours. It would therefore deliver only 87 ampere-hours rather than 100.

Peukert's law can be written as

giving , which is the effective capacity at the discharge rate .

If the capacity is listed for two discharge rates, the Peukert exponent can be determined algebraically:

Another commonly used form of the Peukert's law is:

where:

Several representative examples of different α and corresponding k are tabulated below:

α k comments
0 1 ideal battery – capacity independent of current
0.1 1.09 VRSLAB AGM batteries
0.2 1.17 VRSLAB AGM batteries
0.25 1.2 Gelled
0.3 1.23 Gelled
0.33 1.25 flooded Lead-acid battery
0.5 1.33 diffusion control, Cottrell-Warburg
0.75 1.43 Example
0.8 1.44 flooded Lead-acid battery
0.9 1.47 Example
1 1.5 Example

Peukert's law becomes a key issue in a battery electric vehicle, where batteries rated, for example, at a 20-hour discharge time are used at a much shorter discharge time of about 1 hour. At high load currents the internal resistance of a real battery dissipates significant power, reducing the power (watts) available to the load in addition to the Peukert reduction, delivering less capacity than the simple power law equation predicts.

References[edit]

  • W. Peukert, Über die Abhängigkeit der Kapazität von der Entladestromstärke bei Bleiakkumulatoren, Elektrotechnische Zeitschrift 20 (1897)
  1. ^ Doerffel, Dennis; Sharkh, Suleiman Abu (2006). "A critical review of using the Peukert equation for determining the remaining capacity of lead-acid and lithium-ion batteries". Journal of Power Sources. 155 (2): 395–400. doi:10.1016/j.jpowsour.2005.04.030. ISSN 0378-7753.  (subscription required)
  2. ^ http://www.bdbatteries.com/peukert.php Peukert constant vs. battery type

External links[edit]