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components according to
⎡
2
⎤
⎦
dt
⎣
α
V
2
β
N
2
γ
C
T
)
V
nom
(
t
)
N
nom
(
t
)
C
nom
(
t
J
=
+
+
+
ΔR .
(6)
0
In (6), the instantaneous fuel consumption is denoted by
V
(
t
)
,the
NOx
and
N
C
PM
emissions by
, respectively. The nominal values
V
nom
,
N
nom
and
C
nom
represent the total fuel consumption and emissions respec-
tively, for a non-hybrid vehicle with the given duty cycle in Fig. 4(b). The
factors
α
,
β
and
γ>
(
t
)
and
(
t
)
are used to weight the three influence factors in the
combined performance index.
Obviously, the operating mode that minimizes the performance index cor-
responds to a purely electrical strategy, in which the complete traction power
is provided by the battery. Therefore, the recovered energy by recuperative
braking has to be suciently large to recharge the battery in the ideal case.
The state of charge at the final destination has to be equal to the state of
charge at the start to provide a fair comparison of hybrid and non-hybrid op-
erating modes. For that reason, the energy storage device will be recharged at
the final destination if there are deviations from the initial value
σ
0
(0) = 100%
using Mode 4. The emissions and fuel consumption while recharging are con-
sidered in the performance index by
ΔR >
.
Constraints mostly concern the physical operating limits, like the max-
imum engine torque, the motor power and the state of charge [2]. Other
constraints are related to the velocity profile and time table, for instance the
latest possible time of arrival at the final destination. There are two alter-
natives to influence the fuel consumption and the emissions. The first is to
vary the duty cycle by keeping the bounds on the velocity and final time. The
second alternative is to change the operating strategy. In this paper, only the
second alternative is considered with a fixed duty cycle.
0
4
Simulation and Optimization Results
The backward simulation structure for a parallel hybrid railway vehicle in
Fig. 1 was implemented in Matlab/ Simulink. For all simulations, the same
duty cycle is used, see Fig. 4(b). The output variables can be chosen as the
specific and absolute values for fuel consumption and
NOx
/
PM
emissions.
To obtain a reference for optimization, a non-hybrid strategy was simulated.
4.1
Heuristic Hybridization Strategy
In this section, a heuristic operating strategy for the parallel hybrid, is con-
sidered see Fig. 4(b). Here, the normalized velocity is depicted over time.
The duty cycle is split into several parts by vertical dash-dotted lines. The
numbers in brackets above the trajectory stand for the preselected operating
