User Guide

Practical Theory: Understanding the Time to Go Algorithm
12-1
12. Understanding the Time to Go Algorithm
The battery Amp-hour (Ah) rating indicates the current (Amps) the battery can deliver over time
(hours). For example, if a battery can deliver 5 Amps for 20 hours, it has a 100Ah rating.
However, because discharge rate, temperature, and age affect battery capacity, Amp-hour rating
can vary. A 100Ah battery that discharges over two hours might deliver only 56Ah. To
compensate for this nonlinearity, you can use Peukert's Equation to estimate the Amp-hours
remaining (or time to go) in a lead-acid battery based on discharge rate. If capacity testing is not
an option, you can get the numbers for the equation from the discharge curves on manufacturers'
data sheets, but the result will be less accurate than that obtained by using values gotten from
actual capacity testing.
Peukert's Equation demonstrates how the Amp-hour capacity of a lead-acid battery varies
according to rate of discharge. Rather than Ah = I x T, the Peukert Equation reads:
C = I
n
t
where constant C = the theoretical capacity of the battery, I = the discharge current in Amps,
t = the time of discharge, and the exponent n = the Peukert number, a constant for the given
battery. The exponent value can vary from greater than 1 to about 2. Values closer to 1 indicate a
well performing battery; higher numbers indicate more capacity diminishes when the battery is
discharged at higher rates.
Calculate the Peukert number by determining the capacity obtained at any two discharge rates:
(log t
2
– log t
1
)
(log I
1
– logI
2
)
where t
1
is the hours of discharge at current I
1
and t
2
is the hours of discharge at current I
2
.
To determine the Peukert number, discharge the same, fully charged battery twice at convenient
discharge rates.
First, discharge the battery below the normal discharge rate. When the battery reaches discharge
level, as determined from manufacturers' spec sheets, note the Ah consumed and the time the
discharge took. Calculate the average Amps by dividing the Ah consumed by the length of time.
For example, if the Ah consumed was 300 and the discharge took 50 hours, the average Amps
equals 6. Use this value for I
1
in the above formula and use the time the discharge took for T
1
.
Charge the battery and repeat the process for a discharge rate higher than normal. Use the
resulting values for I
2
and T
2
in the formula. Calculate the value for n to obtain an exponent
accurate for your normal rate. Use this exponent n in the Peukert Equation to estimate time
remaining during a normal discharge.
Performing two capacity tests to obtain the variables for Peukert's Formula can yield accuracy as
good as 0.5% to 1%.
n =