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Battery's capacity IRL in mods
- Thread starter Dreamject
- Start date
For a one-ampere discharge rate, Peukert's law is often stated as
C p = I k t , C_{p}=I^{k}t,}
where:
C p { C_{p}}
is the capacity at a one-ampere discharge rate, which must be expressed in ampere hours,
I { I}
is the actual discharge current (i.e. current drawn from a load) in amperes,
t { t}
is the actual time to discharge the battery, which must be expressed in hours.
k {k}
is the Peukert constant
The capacity at a one-ampere discharge rate is not usually given for practical cells. As such, it can be useful to reformulate the law to a known capacity and discharge rate:
t = H ( C I H ) k t=H\left({\frac {C}{IH})^{k}}
where:
H {H}
is the rated discharge time (in hours),
C { C}
is the rated capacity at that discharge rate (in ampere hours),
I { I}
is the actual discharge current (in amperes),
k { k}
is the Peukert constant (dimensionless),
t { t}
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 20 ( 100 10 ⋅ 20 ) 1.2 {20{({\frac {100}{10\cdot 20}}\)^{1.2}}}
, which is approximately 8.7 hours. It would therefore deliver only 87 ampere-hours rather than 100.
Peukert's law can be written as
I t = C ( C I H ) k − 1 , It=C\({\frac {C}{IH}}t)^{k-1},}
giving I t {\It}
, which is the effective capacity at the discharge rate I I}
.
Peukert's law, taken literally, would imply that the total charge delivered by the battery ( I t
) goes to infinity as the rate of discharge goes to zero. This is of course impossible, since there is a finite amount of the reactants of the electrochemical reaction on which the battery is based.
If the capacity is listed for two discharge rates, the Peukert exponent can be determined algebraically:
Q Q 0 = ( T T 0 ) k − 1 k
Another commonly used form of the Peukert's law is:
Q Q 0 = ( I I 0 ) α
where:
α = k − 1 2 − k
C p = I k t , C_{p}=I^{k}t,}
where:
C p { C_{p}}
I { I}
t { t}
k {k}
The capacity at a one-ampere discharge rate is not usually given for practical cells. As such, it can be useful to reformulate the law to a known capacity and discharge rate:
t = H ( C I H ) k t=H\left({\frac {C}{IH})^{k}}
where:
H {H}
C { C}
I { I}
k { k}
t { t}
Using the above example, if the battery has a Peukert constant of 1.2 and is discharged at a rate of 10 amperes, it would be fully discharged in time 20 ( 100 10 ⋅ 20 ) 1.2 {20{({\frac {100}{10\cdot 20}}\)^{1.2}}}
Peukert's law can be written as
I t = C ( C I H ) k − 1 , It=C\({\frac {C}{IH}}t)^{k-1},}
giving I t {\It}
Peukert's law, taken literally, would imply that the total charge delivered by the battery ( I t
If the capacity is listed for two discharge rates, the Peukert exponent can be determined algebraically:
Q Q 0 = ( T T 0 ) k − 1 k
Another commonly used form of the Peukert's law is:
Q Q 0 = ( I I 0 ) α
where:
α = k − 1 2 − k
Last edited:
Mooch
Member For 4 Years
For a one-ampere discharge rate, Peukert's law is often stated as
C p = I k t , C_{p}=I^{k}t,}
where:
C p { C_{p}}is the capacity at a one-ampere discharge rate, which must be expressed in ampere hours,
I { I}is the actual discharge current (i.e. current drawn from a load) in amperes,
t { t}is the actual time to discharge the battery, which must be expressed in hours.
k {k}is the Peukert constant
The capacity at a one-ampere discharge rate is not usually given for practical cells. As such, it can be useful to reformulate the law to a known capacity and discharge rate:
t = H ( C I H ) k t=H\left({\frac {C}{IH})^{k}}
where:
H {H}is the rated discharge time (in hours),
C { C}is the rated capacity at that discharge rate (in ampere hours),
I { I}is the actual discharge current (in amperes),
k { k}is the Peukert constant (dimensionless),
t { t}is the actual time to discharge the battery (in hours).
Using the above example, if the battery has a Peukert constant of 1.2 and is discharged at a rate of 10 amperes, it would be fully discharged in time 20 ( 100 10 ⋅ 20 ) 1.2 {20{({\frac {100}{10\cdot 20}}\)^{1.2}}}, which is approximately 8.7 hours. It would therefore deliver only 87 ampere-hours rather than 100.
Peukert's law can be written as
I t = C ( C I H ) k − 1 , It=C\({\frac {C}{IH}}t)^{k-1},}
giving I t {\It}, which is the effective capacity at the discharge rate I I}.
Peukert's law, taken literally, would imply that the total charge delivered by the battery ( I t) goes to infinity as the rate of discharge goes to zero. This is of course impossible, since there is a finite amount of the reactants of the electrochemical reaction on which the battery is based.
If the capacity is listed for two discharge rates, the Peukert exponent can be determined algebraically:
Q Q 0 = ( T T 0 ) k − 1 k
Another commonly used form of the Peukert's law is:
Q Q 0 = ( I I 0 ) α
where:
α = k − 1 2 − k
What value of k would you use here?
Using Google Fu to put formulas and their explanations together, doesn't mean that he really understands them. Hell, I have to admit, I don't understand them either!
Anyways, I'm glad to have you (@Mooch) on board at VU!
Mooch
Member For 4 Years
Often it is.
Peukert's Law applies to lead-acid batteries too, not Li-Ion.
But there are some equations that can be used for Li-Ion. Not very accurate, but they are used in some research applications.
Mooch
Member For 4 Years
Do you mean the equations for Li-Ion battery capacity/run time?
I've seen them in several academic research papers but I don't remember which. They're almost useless though for general use as a huge amount of testing and work needs to done to determine the value of the variables before you can even run the equations. That's ok for a research team working with a particular chemistry and cell but for us, using multiple chemistries and cells, it's much easier to just test the battery.