3.5. Effect on capacity of rapid discharging
As discussed in sect. 2.5.3. The capacity of a battery is dependent on the rate of discharge. The faster the rate of discharge, the less Ah capacity will be available.
Back in 1897, a scientist named Peukert discovered that the relationship between the discharge current I and the discharge time T (from fully charged to fully discharged) may be described approximately as follows:
= I n x T
C p
where C p is a constant (the Peukert capacity) and n is the Peukert exponent. The Peukert exponent is always greater than 1. The greater n is, the poorer the battery performs under high rates of discharge.
Peukert’s exponent may be calculated as follows from measurements on a battery or using discharge tables or graphs. If we read (from a discharge table) or measure discharge time T 1 and T 2 for two different discharge currents (I 1 and I 2 ), then:
= I n 1
= I n 2
C p
x T 1
x T 2
and therefore:
n = log( T 2
/ T 1
) / log (I 1
/ I 2
)
As shown in the tables of section 2.5.3, increasing the discharge current from C / 20 to C / 1 (= increasing the discharge current of a 200 Ah battery from 200 / 20 = 10 A to 200 / 1 = 200 A) can reduce effective capacity by as much as 50 % for a mono block gel battery.
A battery monitor should therefore compensate capacity for the rate of discharge. In practice this is quite complicated because the discharge rate of a house battery will vary over time.
3.6. Is capacity “lost” at high rates of discharge?
Section 2.5.3 cites the example of a battery where the rated capacity under a 20-hour discharge was 200 Ah, thus C 20 = 200 Ah. The corresponding discharge current is:
I 20
= C 20
/ 20 = 10 A
Under a discharge current of 200 A the battery was flat in 30 minutes. So although we started with a 200 Ah battery, it was flat after discharging only 100 Ah.
This does not mean that, with a discharge current of 200 A, the 100 Ah capacity difference (C 20 - C 1 = 200 – 100 = 100 Ah) has “disappeared”. What happens is that the chemical process (diffusion, see sect. 2.2.3.) is progressing too slowly, so that the voltage becomes unacceptably low. A battery discharged with 200 A and “flat” in 30 minutes will therefore also be (nearly) fully charged again after recharging 100 Ah, while the same battery which is discharged with I 20 = 10 A and is flat in 20 hours will be nearly fully charged after recharging 200 Ah.
In fact a battery which has been discharged at a very high rate will recover over time and the remaining capacity can be retrieved after the battery has been left at rest for several hours or a day.
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