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450
400
AW3
350
300
250
200
150
100
50
0
0
10
20
30
40
50
60
70
80
90
Speed (Km/h)
Fig. 1.
Traintractioncurve
Accordingly, the total resistance acceleration(
a
ω
) is determined by
a
ω
=
a
ω
0
+
a
ω
i
+
a
ω
r
+
a
ω
s
.
(5)
At time t, the motion of a train can be described by
M
train
(1 +
γ
)
a
t
=
F
traction
−F
resistance
.
(6)
where
M
train
is train mass;
γ
is coecient of rotating mass;
F
traction
,
F
resistance
= tractive effort and resistance at time t respectively.
The consumed engine power
P
t
for for speed
V
t
at time t can be formulated
as
P
t
=
F
traction
V
t
η
.
(7)
where
η
= power eciency.
e
t
is the power consumed per interval
Δt
,whichcan
be derived as
e
t
=
P
t
Δt.
(8)
Accordingly, the total consumed energy(E) for a train movement between two
stations is the sum of energy used in all time steps:
N
e
t
.
E
=
(9)
t
=1
where N = total number of times steps needed to travel from one station to
another.
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