PhD Thesis - Cranfield University

Chapter 4
P TR (t)
P T
P TR
0
∆t
105
t f
P TR,pk
Figure 4.3 EV acceleration interval
where P TR,pk is the required tractive power
to reach the desired velocity v f over the
acceleration interval, ∆t
Design and sizing of an energy storage system to meet the propulsion demands for a given
acceleration and steady state velocity profile is obtained from the energy requirement of the
propulsion system. The rate of change of energy is defined by the tractive power and is given
by,
deTR
= PTR
(t)
(4.10)
dt
where e TR is the instantaneous tractive energy. Following this, the energy required by the
propulsion load over an interval is obtained by integration of the instantaneous power
equation as,
e
TR ( t f )
∫ TR = ∫
t=
e
TR
t
f
de P dt
(4.11)
⇒ ∆e
= t
TR
f
P
0
TR
TR
The propulsion system has the capability of harnessing energy through regenerative braking.
Therefore, the propulsion power is fundamentally different form the non-propulsion power
in that the power flow is bi-directional. Figure 4.4 illustrates the total available regenerative
energy that is dissipated at the friction brakes in a fuel cell vehicle without any regeneration
capability. The results of Markel et al. [112] can be used to determine the minimal battery
and ultracapacitor size that would be able to recapture all of the available regenerative