﻿ Peukert's law

# Peukert's law

The Peukert equation (named after Wilhelm Peukert, which she set up in 1897 after tests on lead-acid batteries ) describes the storage capacity of primary or secondary cells (or batteries from them ) as a function of the discharge current, the higher the discharge current (charge per time; Engl. discharge rate ), the less electric energy ( capacity of the cell, Eng. capacity, sometimes their power ) can be removed. This effect is also called the Peukert Effect or English rate -capacity effect.

The Peukert's formula is a phenomenological approximation formula, ie a mathematical fitting of measured values ​​. Physical reasons of the effect, namely, the increasing losses at the internal resistance of the cell and the limited rate of the electrochemical process and the charge transport processes inside the cell will not be described.

In addition to the discharge current influence, in reality many more factors the charge storage capacity of a storage battery, such as temperature, aging effects, the recovery effect, etc.

## Example

A commercially available alkaline battery AA size has a load of 100 mW a capacity of almost 3000 mAh ( the accumulating at the load power is used because of the known battery voltage as a measure of the discharge current of the battery). In triple load of about 300 mW (ie triple discharge ), the capacity is reduced to less than 1800 mAh, ie almost 60 % (see fig. N ). In return, the battery ( lower curve in the second graph ) regenerates after a short time to deliver again almost 10 % of the initial capacity.

For NiMH batteries, the effect is significantly less pronounced ( Peukert number close to 1, see below).

## The equation

The Peukert equation is ( for lead-acid batteries with high currents, ie in the ampere range: see below):

With

• Is the time in hours before the battery is discharged
• ( Peukert's Capacity) is the charge storage capacity in Ah at a discharge current of 1 A.
• Is the actual discharge current in amperes
• Is the dimensionless Peukert number, also called Peukert exponent (see below)
• Is the correction term for the unit ampere
• Is the charge storage capacity in Ah at a discharge current.

In most cases, however, the charge storage capacity is the manufacturer in the data sheet of the accumulator is not specified at a discharge current of 1 A, but the charge storage capacity with a normal or nominal discharge current, which may differ in general from 1 A: . To calculate in this case, the time until the battery is discharged at a discharge current actual, the following general equation is given below:

The scope of the Peukert's formula is limited, since the calculation of both extreme cases the actual behavior of an accumulator is different:

• With decreasing discharge currents the calculated amount of charge increases steadily and exceeds at sufficiently low currents, the stored by charging amount of charge
• Large discharge currents out there is no limit; any desired discharge current can be taken according to the formula, even if only briefly.

### Peukert number

With increasing age, an accumulator, the Peukert number increases generally, ie it is worse.

For an ideal battery, the Peukert number would be equal to 1, ie, the charge storage capacity would be independent of the discharge current:

In this case, would the Peukert equation into the equation

Pass, which describes the relationship between electric charge and electric current in the simplest case.

## Practical implications

For accumulators increases by lower current load (or higher cell capacity under the same load ) in addition to the removable amount of energy and the life, which lowers operating costs.

Primary cells, which are regarded as discharged in applications with high current loads (eg mechanical toys ), can often be reused (eg clocks) for a long time with less stress.

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