PhD Thesis - Cranfield University

Chapter 3
Since DoD(t 0)= 0 when the battery is fully charged at t=t 0, the factional depletion model
(FDM) is given by
⎡ t n
i ⎤
DoD(
t)
= ⎢∫
dt⎥
⋅100%
⎢⎣
λ t ⎥
0 ⎦
67
( 3-19)
To predict the workable range of an EV, either the SoC or DoD may be used. With (3.13)
and (3.14), the SoC at time t is,
SoC( t)
= QT
− SoD(
t)
( 3-20)
The accuracy of Q T , which is a function of discharge current, temperature and
environmental related parameters is important in the reliability of the SoC prediction. Since a
predicting error in Q T results in a incorrect SoC estimation, DoD measurement are
sometimes used since it is expressed as a fraction of Q T and can be expressed as,
SoD
DoD =
QT
3.11 Practical Application of Peukert’s Equation
( 3-21)
For practical applications, Peukert’s equation can be expressed using the Peukert Capacity as,
n
C p = I T
( 3-22)
where C p is the Peukert capacity, I is the battery current, n is the Peukert exponent and T is
the discharge time.
Although equation (3-22) may be rearranged to solve for the obtainable discharge time T (in
hours) for different values of discharge current, it should be noted that the Peukert capacity
also varies according to the discharge current. A variation can be made to (3-22) to use the
fixed nominal capacity of the battery and the hour rating at that nominal capacity (data