XXX -X-XXXX -XXXX -XXXXX.00 20XX IEEE Energy Efficient Train Operation using [612582]

XXX -X-XXXX -XXXX -X/XX/$XX.00 ©20XX IEEE Energy Efficient Train Operation using
Simulated Annealing Algorithm and
SIMULINK model

Daniel Cristian CISMARU
University of Craiova
Faculty of ElectricalE ngineering
Craiova, ROMANIA
[anonimizat]
Abstract —This paper presents an energy -efficient train
operation based on the mathematical model of the train
motion. Starting from the mathematical model it is built the
SIMULINK model associated of the train motion. By using the
Simulated Annealing Algorithm it is calculated the min imum
value of the consumed energy for an electric train route
Keywords — modeling; simulation; Simulated Annealing
Algorithm; SIMULINK; energy efficient train operation
I. INTRODUCTION
To calculate and optimize the energy consumption of an
electric vehicle th rough the chosen driving strategy it is
necessary the mathematical model of the vehicle motion that
can be written in the following form [1], [3],[4], [6] :
 
   

dtvF Pdt= Em(x))r(x)+i (v)r ; R = (Mηi
DF= z ; dtv v; x =
Di = Ω ; (F-R)dtξmv =
c de ps t
rrm
1022 1
2
(1)
where M2 is the developed useful torque of the traction
motor , i is the transmission ratio , ηt is the transmission
efficiency , Dr is the wheel diameter , x is the vehicle position ,
v is the vehicle speed , Ωm it is the angular speed of the
traction motor rotor , F it is Ft (motor active force ) in traction regime or – Ff (braking active force ) in braking regime , m is
the mass of the vehicle , r is the specific train resistance , R is
the total train resistance and ξ is the coefficient of increase
the mass of the train that take account to the pre sence and
weight of the rotating parts from the train structure
(ξ=1.06…1.2) .
In the mathematical model (1) was replaced the specific
train resistance r with its components: the main specific train
resistanc e rps, the specific train resistance on level tangent
track ide and the specific train resistance due to curves rc.
By means of this mathematical model can be simulated
the motion of any electric vehicle as compared with the
concrete control modality o f this. According ly they are
obtained the motion diagrams v(t) and x(t), too. The
modification of vehicle mass, of dependences ide(x) or rc(x),
specific to certain vehicle or route, can be easily operated,
obtaining an exact mathematical model, which it re spects all
the motion conditions.
II. SIMULINK MODEL
The SIMULINK model corresponding to the train motion
was built based on the mathematical model of the vehicle
motion (1) (Fig. 1) [6].
An immediately example of the utilization of the
SIMULINK model it i s the motion diagrams drawing, that
illustrate the dynamic aspect of the electric vehicle.
The motion diagrams of the electric train are drawn on

Fig. 1. SIMULINK model of the train motion

the traction and braking characteristics basis and of the
conditions imposed of route.
The traction and brak ing characteristics consort any
presentation, however summarily would be, of a high -speed
train. For example, for the ETR 500 italian high speed train,
they have been represented the traction and braking
characteristics and the train resistance correspond ing to the
different specific features of the route (through the declivities
consideration) (fig.2).
In the b locks „Ft(v)” and “Ff(v)” (Fig. 1) they are
implemented the trac tion and braking characteristics of the
train. The model is based on the train motion model, at which
the main input variable it is supplied of the block „F”, which
it models the train motion regimes (Fig. 3):
– starting regime (acceleration),
– motion at constant speed regime (cruising),
– coasting regime and
– braking regime.
Also, in the "Braking" interpolation block ( Fig.1 ) is
implemented the braking diagram of train, that is useful for
calculating of the braking distance .
By mea ns of this SIMULINK model (Fig. 1) they have
been simu lated four speed diagrams (Fig. 4), all
corre sponding to a distance of 100km. They have been obtained the time of 1500 s (case a), of 1512 s (case b), of
1632 s (case c) and of 1982 (case d).
III. SIMULATED ANNEALING ALGORITHM
The SIMULINK model allows the calculation of energy
consumption for different motion regimes and different route
configurations.
Also, can be obtained the motion diagrams for a distance
of 100 km, a maximum speed of 210 km/h and different
values of the starting position braking (Fig.5 ) [6]. For each of
these cases, it is calculated the value of the consumed energy
and can be determined its minimum value .
Thus, u sing the same model , to an imposed value of
motion time timp = 2500 s (for example b y schedule reasons ),
can be obtained the dependence shown in Fig. 6 [6] , that has a
minimum for the maximum speed v = 160km/h.

Fig. 2. Traction and braking characteristics and four values of train
resistance of ETR 500 italian high speed train resis tance
a) ide=0; b) i de=5; c) i de=10; d) i de=20

Fig. 3. Four regimes of the train motion

Fig. 5. Motion diagrams for maximum speed 58,3 m/s ( 210km/h )
150 160 170 180 190 200 210 220 230 240 25070080090010001100120013001400
Speed (km/h)Energy (kWh)

Fig. 6. Energ y as a function of speed

Fig. 4. Speed diagram for different values of train resistance
a) ide=0; b) ide=5; c) ide=10; d) ide=20

Similarly, with th e Linear Search Algorithm (Fig.7 ) that
it uses the SIMULINK model, can be f ound the minimum
value of the consu med energy for an imposed value domain
of the interstation time (time – timp < err) but using a high
number of steps and a long time simulation.
A more modern and faster solution is the use of the
Simulated Annealing Algorithm with SIMULINK model
(Fig.8) and that has advantages of simplicity and efficiency,
and it is also less affected by initial conditions [8].
To prove that, we can compare the results obtained using
the two algorithms (Table I). It is noticed that in a two -fold
less time, similar results are obtained. This time difference
increases significantly when the search domain expands or
when the interstation time is larger. TABLE I. COMPARISON BETWEEN ALGORITHMS
Algorithm Number
of steps Simulation
time (s) Energy
(kWh) Maximum
speed (km/h)
Linear
Search 2100 292 772,54 160
Simulated
Annealing 1001 147 773,19 162
IV. CONCLUSIONS
The presented SIMULINK model take account of the
particularity of the vehicle and route and it is relatively easy
of implemented and of used.
Related to other energy optimization techniques found in
literature [1],[10] the presented Simulated Annealing
Algorithm with SIMULINK model avoid utilization of
complex mathematical methods or time expensive
initialize T {initial temperature}
initialize L {number of trials per temperature}
initiali ze Tmin {minimum temperature}
initialize timp {imposed interstation time}
initialize err { interstation time error}
i←1 {initialize number of iteration}
generate the initial solution s
while T>Tmin
for k←1 to L
generate new solution s'
ΔE← E(s') -E(s) { calculate with the SIMULINK model the energy consumption for
solutions s and s' and the difference ΔE }
if ((ΔE<0)and(time -timp<err)) then
s← s' {accept s' if ΔE<0 and interstation time t is near t imp}
else
if ((exp( -ΔE/T)>random[0,1]) and(time -timp<err)) then

s← s' {accept s' considering probability and interstation time t is near t imp}
end if
end if
end for
i←i+1
T←T*αi {decrease T, where α is cooling factor with ranging between 0,8 and 0,99}
end while
output s {best solution}

Fig. 8 . Simulated Anneali ng Algorithm initialize vmin, vmax {minimum and maximum value for constant speed v2}
initialize xmin, xmax {minimum and maximum value for coasting start position x2}
initialize timp {imposed interstation time}
initialize err { interstation time error}
initialize E { energy consumption for v min and x min}
for v ct←v min to v max
for x 2←x min to x max
E'(v ct,x2) {calculate with the SIMULINK model the energy consumption}
if ((E'<E )and( time -timp<err )) then
E←E' { find minimum of E}
end if
end for
end for
output E {best solution}

Fig. 7 . Linear Search Algorithm
𝑒−∆𝐸
𝑇

algorithms.
This Simulated Annealing Algorithm with SIMULINK
model can be useful in the establishment of an energy
efficient train control methods, based on the best utilization
of the installed load. The respective methods are
implemented then in the computer control system on the
electric vehicles, contri buting at the circulation safety
increase, at the decrease of consumptions and allowing even
a possibly ATC (Automatic Train Control).
REFERENCES
[1] P.G. Howlett and P.J. Pudney. Energy -efficient Train Control.
Springer –Verlag London Ltd., 1995.
[2] A. S teimel, “Electric Traction. Motion Power and Energy Supply
Basics and Practical Experience”, Oldenbourg Industrieverlag,
München, 2008
[3] D.C. Cismaru, D.A. Nicola, Gh. Manolea, “Locomotive Electrice.
Rame și Trenuri Electrice”, Ed. Sitech, Craiova, 2009.
[4] D.C. Cismaru, D.A. Nicola, Gh. Manolea, M.A. Drighiciu, C.A.
Bulucea, “Mathematical Models of High -Speed Trains Motion”,
WSEAS Transactions on Circuits and S ystems, Issue 2, Volume 7,
February 2008
[5] D.C. Cismaru, D.A. Nicola, Gh. Manolea, M.A. Drighiciu,
“Simulation of Electric Vehicles Movement”, 7th WSEAS/IASME
International Conference on Electric Power Systems, High Voltages, Electric Machines (POWER'07), Ve nice, Italy, November 21 -23,
2007.
[6] D.C. Cismaru, M.A. Drighiciu, D.A. Nicola, "SIMULINK Model for
Study of Energy Efficient Train Control", Proceedings 12th
International Conference on Applied and Theoretical Electricity,
ICATE 2014 Craiova, Romania
[7] K. Kim, S.I. Chien, "Optimal Train Operation for Minimum Energy
Consumption Considering Track Alignment, Speed Limit, and
Schedule Adherence", JOURNAL OF TRANSPORTATION
ENGINEERING ASCE / SEPTEMBER 2011 137(9): 665 -674
[8] T. Xie, S. Wang, X. Zhao, Q. Zhang, "Op timization of Train Energy –
Efficient Operation Using Simulated Annealing Algorithm", K. Li et
al. (Eds.): ICSEE 2013, CCIS 355, pp. 351 –359, Springer -Verlag
Berlin Heidelberg 2013
[9] X. Li, L. Li, Z. Gao, T. Tang, S. Su, “Train Energy -Efficient
Operation with Stochastic Resistance Coefficient” , International
Journal of Innovative Computing, Information and Contro l, Volume
9, Number 8, August 2013.
[10] X. Vu, “Analysis of necessary conditions for the optimal control of a
train”, Thesis of Doctor of Mathematics, University of South
Australia, July 2006.
[11] M. Larranaga, “Optimization Techniques Applied to Railway
Systems”, Master Thesis, Universidad del Pais Vasco, September
2012.
[12] L.Felixova, “Mathematical Methods of Optimal Control Theory and
their Applications”, Ma ster Thesis, Brno University Of Technology,
Brno 2011.