Peukert's law

Peukert's Law, presented by the German scientist W. Peukert in 1897, expresses the capacity of a lead-acid battery in terms of the rate at which it is discharged. As the rate increases, the battery's available capacity decreases.

Peukert's law is as follows:

$C\_p\; =\; I^k\; t\; ,$

where:
*$C\_p\; ,$ is the capacity according to Peukert, at a one-ampere discharge rate, expressed in A·h.
*$I\; ,$ is the discharge current, expressed in A.
*$k\; ,$ is the Peukert constant, dimensionless.
*$t\; ,$ is the time of discharge, expressed in h.

However, more commonly, manufacturers rate the capacity of a battery with reference to a discharge time. Therefore, the following equation should be used:

$t\; =\; H\{left(frac\{C\}\{I\; H\}\; ight)^k\},$

where H is the hour rating that the battery is specified against and C is the rated capacity at that discharge rate. Note that $C\_p\; ,$ no longer appears in this equation.

For an ideal battery, the constant "k" would equal one, in this case the actual capacity would be independent of the current. For a lead-acid battery, the value of "k" is typically between 1.1 and 1.3 however. The Peukert constant varies according to the age of the battery generally increasing with age. Application at low discharge rates must take into account the battery self-drain current.

The Peukert law becomes a key issue in a battery electric vehicle where batteries rated at 20 hour (or even 100 hour) discharges are used at much greater rates of about 1 hour.

References

* W. Peukert, "Über die Abhängigkeit der Kapacität von der Entladestromstärcke bei Bleiakkumulatoren", Elektrotechnische Zeitschrift 20 (1897)
* D. Doerffel, S.A. Sharkh, "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 (2006) 395–400

External links

* [http://www.ee.ncue.edu.tw/note/data/o/21/91.pdf IEEE Paper on Lead batteries]
* [http://www.smartgauge.co.uk/peukert_depth.html A fully detailed explanation of Peukert's effect - By Chris Gibson, designer of battery monitoring equipment]
* [http://www.smartgauge.co.uk/calcs/peukert.xls A Peukert spreadsheet in Microsoft Excel format - Again by Chris Gibson]