IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING
IEEJ Trans 2009; 4: 771–778
Published online in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/tee.20479
Paper
Energy Saving Speed and Charge/discharge Control of a Railway Vehicle
with On-board Energy Storage by Means of an Optimization Model
Masafumi Miyatake*a , Member
Kunihiko Matsuda*, Non-member
The optimal operation of rail vehicle minimizing total energy consumption is discussed in this paper. In recent years, the
energy storage devices have enough energy and power density to use in trains as on-board energy storage. The on-board
storage can assist the acceleration/deceleration of the train and may decrease energy consumption. Many works on the
application of the energy storage devices to trains were reported, however, they did not deal enough with the optimality
of the control of the devices. The authors pointed out that the charging/discharging command and vehicle speed profile
should be optimized together based on the optimality analysis. The authors have developed the mathematical model based
on a general optimization technique, sequential quadratic programming. The proposed method can determine the optimal
acceleration/deceleration and current commands at every sampling point under fixed conditions of transfer time and distance.
Using the proposed method, simulations were implemented in some cases. The electric double layer capacitor (EDLC) is
assumed as an energy storage device in our study, because of its high power density etc. The trend of optimal solutions such
as values of control inputs and energy consumption is finally discussed.  2009 Institute of Electrical Engineers of Japan.
Published by John Wiley & Sons, Inc.
Keywords: electric railway, rail vehicle, energy storage, electric double layer capacitor (EDLC), energy-saving operation, sequential quadratic
programming (SQP)
Received April 21 2008; Revised October 13 2008
1. Introduction
Electrical regenerative braking has reduced total energy consumption in electric railway systems [1]. However, there are several difficulties in efficient utilization of regenerative energy,
especially under DC power feeding system. One of these difficulties is that the regenerative ability closely depends on catenary voltage at the braking train. The maximum electrical braking
torque is limited if catenary voltage is low. The other difficulty
in utilizing regenerative energy is the need of another accelerating
train or energy storage for absorbing regenerative energy. If the
energy is not absorbed, catenary voltage rises, regenerative failure is occurred, and kinetic energy is disposed with mechanical
friction brake.
One of the ways for absorbing regenerative energy is to use
energy storage. Regenerative energy is stored in the energy storage
and reused in the next acceleration. The energy storage decreases
the loss of circuit resistance by compensating voltage drop. It
also prevents regenerative failure even if the power source cannot
absorb enough energy. Energy-saving effect as well as preventing
regenerative failure is expected.
Energy storage devices have achieved enough energy and power
density to use as on-board power sources of vehicles. There are
many types of energy storage devices such as lead–acid, NiMH
and Li–ion batteries, flywheel energy storage and an electric double layer capacitor (EDLC).
Many research projects on the application of the energy storage
devices to transportation systems have been reported. In railway
applications, a few research papers can be seen in Refs [2–7]. Most
a
Correspondence to: Masafumi Miyatake.
E-mail: miyatake@sophia.ac.jp
∗ Department
of Engineering and Applied Sciences, Sophia University
Kioicho 7-1, Chiyoda-ku, Tokyo 102-8554, Japan
of them discussed reasonable circuit configuration and sizing of
energy storage system, however, very few papers that deal with
optimal charging/discharging control of the energy storage can
be found. The charging/discharging command of energy storage
affects the energy consumption and may influences the optimal
speed profile, the trajectory of a train in the velocity-position state
space. The vehicle speed should be also controlled observing the
state of charge (SOC) of energy storage in order to run the vehicle with small amount of energy. The authors pointed out that
the charge/discharge command and vehicle speed profile should
be optimized together based on the optimality analysis.
It is difficult to discuss the optimal operation because it has
many nonlinear constraints. However, there are a few papers
that deal with the energy-saving vehicle operation with a kind
of optimization. For example, The problem of solving optimal
speed profile was developed in Ref. [8], however, the characteristics of power source cannot be considered. The papers seen in
Refs [9,10] deals with some of practical conditions by using the
dynamic programming (DP), however, it is difficult to apply to
the system with multiple power source, because DP has a serious
disadvantage that the increase of control input dimension causes
explosion of computation time. The optimization of multiple-train
scheduling was realized with DP in Ref. [11], however the conventional—not optimized—speed profile composed of maximum
acceleration, coasting and maximum deceleration was used. Similar technique with DP was used in Ref. [12] for optimization of
hybrid rail vehicles, however, the conventional speed profile was
also used.
To overcome the problem, the new solvable formulation with
gradient method was proposed in Refs [13–15]. It was so flexible
that can be applied to the optimization of not only multiple-train
operation but also the train with energy storage device. However,
the shortcoming of this method is the need of deep mathematical
background. It has not been really applied to the train with energy
 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.
M. MIYATAKE AND K. MATSUDA
storage system, because it is not easy to develop the optimization
program.
The authors have developed the mathematical model characterized by the following items.
Ic
VT
INV.
Chopper
DC link
•
The model is based on a commonly used optimization technique for easy software development.
• It can be applied to the system composed of the main DC
power feeder and auxiliary energy storage.
• It can optimize the notch and charge/discharge commands
simultaneously for minimum energy consumption.
IM
EDLC
VC
Fig. 2. Circuit model of an on-board EDLC train
and Rc are the capacitance and internal resistance in the EDLC
respectively. It is necessary to convert voltage by using a bidirectional chopper because the voltage difference between the DC
link and EDLC is high. The motor-inverters of the train in Fig. 2
were modeled as a current load that helps solving circuit equations
simply.
In this study, the proposed method was assumed to apply to
DC electric railway systems, however, it can be also applied to
road vehicles such as hybrid electric vehicles and fuel cell electric
vehicles with partial modification.
In this paper, the authors intend to formulate the optimal control
problem of the train operation to find notch and charge/discharge
commands which minimize the amount of consumed energy, propose how to solve it, discuss the optimized results and find knowledge of the optimal operation. The knowledge extracted from the
trend of optimization results will be applied to the design and
parameter tuning of future charge/discharge controllers for energy
storage.
3. Formulation of Optimal Control Problem
Advantages: maintenance-free, long lifetime, quick charge/
discharge
3.1. Definition of variables
The optimal control problem is formulated from the circuit model. Variables are defined
as follows: Control inputs n and u determine the acceleration/deceleration force and charging/discharging current, respectively. Table I shows the definition of control inputs. For example,
the definition of control input ‘n’ is illustrated in Fig. 3. State
variables x, v and Vc indicate the train position, speed and EDLC
voltage, respectively. The variable VT is the catenary voltage at the
train. It is treated as an auxiliary state variable to avoid complexity
in solving circuit equations analytically, although it is derived by
solving circuit equations. It is derived by adding circuit equations
in the optimization problem as the constraints.
Disadvantages: lower energy density than that of batteries at
present, wide range of terminal voltage regulation.
Table I. Definition of control inputs n and u
2. Modeling of Energy Storage and DC Feeding
Circuit
The EDLC is assumed in the modeling of energy storage in this
study. It has the following characteristics,
The fact shows the difficulty in using EDLC as a main power
source of high-speed vehicles. However, if it is used with other
main energy sources, the EDLC is expected as one of the most
promising auxiliary devices for transportation systems. The EDLC
supplies large power but small energy, whereas large energy is
supplied by the main power source.
A DC feeding circuit is modeled with one train between substations. The model circuit appears in Fig. 1. In this figure, Vs and R0
are the supply voltage and the internal resistance at a substation
respectively. The values of R1 and R2 are equivalent resistances of
feeder and return circuits. These resistance values are proportional
to the distance between the train and substation. The constants C
R1
R0
Chopper
C
DS
Maximum deceleration
Deceleration
Coasting
Acceleration
Maximum acceleration
Maximum charging
Charging
Standby
Discharging
Maximum discharging
L
AS
Lb
fmax
Vc
VS
−1
(a) Circuit model
La
−1
Negative
0
Positive
1
Maximum
acceleration
Train
SS1
Charging/discharging
command u
Acceleration
force
f
R0
RC
VS
Substation1
Notch command n
R2
VT
IS
Value
0
+1
Substation2
u Control
input
DP:departure station
SS2 AS:arrival station
SS:Substation
fmin Maximum
deceleration
(b) Location of stations and substations
Fig. 1. Modeling of a feeding circuit with one train between
substations
Fig. 3. Definition of control input u
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IEEJ Trans 4: 771–778 (2009)
ENERGY SAVING RAILWAY VEHICLE WITH ON-BOARD ENERGY STORAGE
Q
3.2. Optimal control problem
The optimal control
problem is described as the following mathematical formulation.
Minimizing the objective function
T
J =
Vs Is (x, VT )dt
Initial state
of charge
Final state
of charge
With final
state constraint
(1)
0
Subject to the following equality and inequality constraints
ẋ = v
(2)
v̇ = f (n, v, VT ) − r(v)
(3)
V˙c = −Ic (u)/C
(4)
PT (n, v, VT ) = PS (x, VT ) + PC (u, Vc )
(5)
x(0) = 0, v(0) = 0, Vc (0) = Vc init
(6)
x(T ) = L, v(T ) = 0, Vc (T ) = Vc final
(7)
−1≤n≤1
(8)
−1≤u≤1
(9)
VT
min
≤ VT ≤ VT
Vc
min
≤ Vc ≤ Vc
(12)
(13)
r
PT
max
min , Vc max
Vc init , Vc final
L, T
vmax (x)
Fig. 4. Boundary conditions of EDLC SOC
R1 (x) = (La + x)r0 R2 (x) = (L − x + Lb )r0
Vc Ic (u)ηch
(u ≥ 0)
Pc (u, Vc ) =
Vc Ic (u)/ηch (u ≤ 0)
Ic (u) = uIc
(16)
(17)
(18)
max
Here, ηm and ηg (v) are motor-inverter efficiency in accelerating
and braking respectively. The constant M is the total weight of
the train that includes on-board energy storage. The regenerative
efficiency ηg must be treated as the function of speed v for considering electro-pneumatic blended braking. Equivalent resistances
of feeding system R1 and R2 are given in (16) if the position of
the departing station is defined as (6). The constants La and Lb
indicate the distance from the departure and arrival stations to the
substations 1 and 2 shown in Fig. 2 respectively. The constant
r0 is the equivalent resistances of feeding system per meter. The
constant ηch is the chopper efficiency. The constant Ic max is the
rated value of the EDLC current.
Chopper efficiency is too complicated to be examined in detail
here. Therefore, the chopper efficiency ηch is assumed as the constant value.
(11)
0≤x≤L
Ic
f
Vc
max
Time
(10)
0 ≤ v ≤ vmax (x)
where
Is
Ps , Pc
VT min , VT
max
Without final
state constraint
sum of load currents supplied from substations;
EDLC current;
acceleration/deceleration force influenced
by the voltage VT ;
running resistance per unit weight of the
train;
electric power supplied to motor-inverters
of the train;
power from substations and EDLC;
lower and upper limitation of the catenary
voltage at the train position;
lower and upper limitation of the EDLC
voltage;
first and final values of the EDLC voltage;
distance and running time between the
departure and arrival stations;
speed limitation.
3.3. Discretization of the problem
The continuous
time formulation must be transformed to a discrete time one in
order to apply a mathematical programming to the optimal control problem. Therefore, t is defined as the constant sampling
interval. Control inputs n, u are discretized as (19). Other variables such as VT , x, v, VC etc. are also discretized as (T /t + 1)
dimensional vectors.
n = [n(0), n(t), n(2t), . . . , n(T )]
u = [u(0), u(t), u(2t), . . . , u(T )]
(19)
The discretized objective function is written as (20).
The objective function is sum of supplied energy from two substations given as (1). Equality constraints are given as (2)–(7).
Equations (2) and (3) are motion equations of the train. Gradient
can be considered as including the influence to the running resistance r. If it is considered, r is also the function of x. The EDLC
voltage is given as the (4). Equations (6) and (7) describe the initial
and final conditions of state variables. The constraint (11) gives
the terminal EDLC voltage as well as the initial one as illustrated
in Fig. 4. If the constraint is not given, it is difficult to compare
the solutions under various conditions with energy consumption.
Inequality constraints of control inputs, state and auxiliary variables are shown in (8)–(13).
The functions related with circuit equations as the following
equations.
Mvf (n, v, VT )ηm
(n ≥ 0)
(14)
PT (n, v, VT ) =
Mvf (n, v, VT )/ηg (v) (n ≤ 0)
Vs − VT
Vs − VT
(15)
Ps (x, VT ) =
+
R0 + R1 (x) R0 + R2 (x)
T /t
J = Vs I
s =
Vs (i)Is (i)
(20)
i=0
4. Optimization Method
The optimal control problem is solved by the sequential
quadratic programming (SQP) method in this study. SQP is an
optimization method to solve general nonlinear programming problems. A general optimal control problem with equality and inequality constraints can be derived from the discretized formulation
from (1) to (18) as
Minimize :
J (ω)
Subject to :
gi (ω) = 0 (i = 1, . . . , ng )
(21)
hj (ω) ≤ 0 (j = 1, . . . , nh )
where ω = (n, u, VT , x, v, Vc ) is the vector of variables, J is the
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IEEJ Trans 4: 771–778 (2009)
M. MIYATAKE AND K. MATSUDA
Table II. Specific parameters of feeding circuit and
train operation
Search
direction
ω (k+1)
(k)
α dopt
(k)
dopt
ω (k)
Jqp(ω)
Step (2)
ω (k)
ψ(ω)
Fig. 5. Procedures of SQP method
C
Vc max
Vc min
Vc init
Vc final
Ic max
objective function, g and h are equality and inequality constraints,
ng and nh are the numbers of equality and inequality constraints.
The objective function is rewritten using the second order
approximation around the feasible point ω (k) where k is the number
of search iteration. Similarly, equality and inequality constraints
are also rewritten as the first-order approximation around the feasible point ω (k) in problem (21). The problem is transformed into
a kind of quadratic programming as
Minimize : Jqp
Subject to :
32.3 F
560 V
300 V
560 V
560 V
500 A
weight
power density
energy density
Rc
500 kg
≤ 560 W/kg
2.8 Wh/kg
0.3 (real)
0.03 (ideal)
Table IV. Conditions of simulation in each case
(22)
(i = 1, . . . , ng )
hj (ω (k) ) + ∇hj (ω (k) )d(k) ≤ 0
(j = 1, . . . , nh )
where d(k) = ω − ω (k) , ∇ = ∂∂ω and Bk is positive definite matrix.
In general, the solution d(k)
opt of the approximated problem (22) can
be easily derived by using the interior point method [16,17].
Here, the merit function is defined as:
ng
nh
|gi (ω)| +
max(hj (ω), 0)
(23)
ψ(ω) = J (ω) + µ
i=1
250 × 103 kg
90%
≤90%
95%
∞
M
ηm
ηg
ηch
Vmax (x)
Table III. Specific parameters of the EDLC bank
Step (4)
1
= d(k) Bk d(k) + ∇J (ω (k) )dk
2
gi (ω (k) ) + ∇gi (ω (k) )d(k) = 0
130 s, 1 s
2000 m
0.03 1500 V
0.04 m/m
5000 m
T , t
L
R0
Vs
r0
La , Lb
T [s]
EDLC
Case 1
Case 2
Case 3
130
130
130
Case
Case
Case
Case
130
130
120
120
without
with
with
Rc = 0.03 without
with
without
with
4
5
6
7
VT
max [V]
∞
∞
∞
1650
1650
∞
∞
evaluated as 560 and 2.8 Wh/kg respectively, whose values are
between the values used in the papers [18] and [4]. Paper [18] uses
relatively smaller values, 260 and 0.60 Wh/kg. On the other hand,
paper [4] uses larger values, 6 and 6 Wh/kg.
Maximum acceleration/deceleration characteristics and running
resistance are given in Fig. 6. In the characteristics, electropneumatic blended braking system with the air supplement control
is assumed. Only if the regenerative braking force is not enough
for the specific braking force, air brake works.
In the model used in the examples, the characteristic of the
squeezing control is not included in the analyses for simple implementation that can reduce the number of complicated nonlinear
constraints. It is assumed to use receptive substations with pulse
width modulation (PWM) converters [19] that are now in the initial
state of practical application.
Seven cases are prepared as tabulated in Table IV for evaluation
under various conditions.
The optimization program was developed with Optimization
Toolbox on MATLAB software. By using such convenient toolbox, the program could be implemented with shorter development
period.
i=1
where µ is a large positive constant. Finally, the α in (23) is
searched to minimize ψ(ω (k+1) ) where ω (k+1) = ω (k) + αd(k)
opt .
The optimal point d(k)
opt of the problem (22) is used as the search
direction. The vector ω (k+1) is the new feasible point of the next
iteration.
Consequently, the optimization problem (21) can be solved by
iterating the following procedure.
(1) Give the initial feasible point ω (0) , and set k = 0.
(2) Solve problem (22), and obtain the search direction d(k)
opt as in
Fig. 5.
−6
(3) Stop iteration if the norm ||d(k)
opt || is less than 10 .
(4) Find α minimizing the merit function, and obtain the next
feasible point ω (k+1) as in Fig. 5.
(5) Increase k by 1, and return to the step 2.
5.2. Optimization results
Case 1 is the optimization
5.2.1. Base case analyses
result of the train without the EDLC. Cases 2 and 3 show results
of the sensitive analysis in case of the constant Rc is 0.3 or 0.03 respectively.
Optimization results are shown in Table V and Fig. 7. In Fig.
7, the graphs of control inputs n and u, catenary voltage at train
pantograph, EDLC voltage, train speed and train power at inverter
input are drawn.
Case 1: The optimal control input n without EDLC consists of
the maximum acceleration, reduced acceleration by degrees, coasting and maximum deceleration. The results that are consistent with
the results of previous papers [9,10] indicate the reliability of the
5. Simulations of Optimization and Their Results
Specific parameters are
5.1. Conditions of simulation
tabulated in Tables II and III. In the simulations, a train runs on
a straight line without speed limitations and gradients for simple analyses. The final EDLC voltage is given to equal the initial
one. The small size of EDLC bank is chosen taking the impact
of weight on energy consumption and high cost of EDLC into
account. The maximum output of the EDLC bank at the highest voltage is 560 V × 500 A = 280 kW, while the total power of
the train, that depends on the catenary voltage, is roughly 2 MW.
The maximum power and energy densities of the EDLC bank are
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ENERGY SAVING RAILWAY VEHICLE WITH ON-BOARD ENERGY STORAGE
Table VI. Evaluation of energy consumption
1.2
1300 [V]
1500 [V]
1700 [V]
Acceleration force [N/kg]
1
Total energy
consumption [MJ]
Energy saving
in %
28.02
27.54
—
1.71
0.8
Case 4
Case 5
0.6
Table VII. Evaluation of energy consumption
0.4
0.2
Running resistance
0
0
5
10
15
Velocity [m/s]
20
25
30
Case 6
Case 7
Total energy
consumption [MJ]
Energy saving
in %
37.56
35.43
—
5.67
1.2
Maximum braking force
the EDLC when the train coasts.
Deceleration force [N/kg]
1
It is found from the result that the EDLC is utilized effectively.
The total energy consumption is 26.40 MJ. Compared with case 1,
the total energy consumption is reduced about 4.17%. The result
indicates that energy-saving effect is higher if the internal resistance of the EDLC is reduced by future technical development.
The percentage of saved energy compared with case 1 is evaluated as 0.35 and 4.17% in cases 2 and 3 respectively.
In the voltage graphs in Fig. 7, the voltage recovery by larger
discharge from EDLC in acceleration phase of case 3 is very
slight. That is because the maximum output power of the EDLC is
much smaller than the train power itself. If larger EDLC bank is
installed, more voltage recovery can be realized, however, heavier
train weight may cause larger energy consumption.
0.8
0.6
0.4
Electrical braking force
0.2
0
1300 [V]
1500 [V]
1700 [V]
0
5
10
15
20
Velocity [m/s]
25
30
Fig. 6. (a)Acceleration (b) deceleration characteristics and running resistance
5.2.2. Simulation of weak regenerative condition
In
the simulation, receptive substations are assumed and squeezing
control is omitted. In such conditions, regenerative failure cannot
be simulated properly. However, weaker regenerative condition
can be imitated with limiting the upper catenary voltage VT max .
In cases 4 and 5, VT max is set to 1650 V. The regenerative current is reduced so as to keep the catenary voltage within the upper
limit. The results are shown in Table VI and Fig. 8.
The trend of control input n in cases 4 and 5 is different from
that in base cases in braking. The braking force is reduced in running higher speed by the limitation VT max because such operation
finally increases total regenerative energy. The EDLC voltage Vc
in case 5 is slightly lower than that in case 2 for collecting more
regenerative energy under the limited voltage.
Table V. Evaluation of energy consumption
Case 1
Case 2
Case 3
Total energy
consumption [MJ]
Energy saving
in %
27.55
27.45
26.40
—
0.36
4.17
proposed method.
Case 2: Very little difference of the optimal control input n can
be seen in cases 1 and 2. Regarding the control input u, the higher
the absolute value of power to the train is, the larger the absolute value of current is. Qualitatively, this trend is proper, because
the energy loss by current through the feeder reduced. Despite the
lower limit value of the EDLC voltage Vc min is set to 300 V, the
EDLC stops discharging when the EDLC voltage drops to about
480 V. This result is attributed to the higher internal resistance of
the EDLC. The efficiency of the EDLC itself is reduced according
to the voltage drop of the EDLC. Consequently, the availability of
EDLC for energy-saving operation is low. However, it should be
noted that the availability is not always increased even if a smaller
EDLC bank with fewer cells is used, because the internal resistance is increased by reducing the number of parallel connection
of cells.
Case 3: In this case, there is also little variation in control input
n. However, optimal charging/discharging command includes the
following two significant difference compared with the case 2.
5.2.3. Simulation of shorter running time
The cases
6 and 7 are simulated with reduced margin time by 10 s. Other
condition is the same as cases 1 and 2 respectively. Optimization
results are shown in Table VII and Fig. 9. The trend of control
input n is the same as the results of base cases. On the other hand,
the EDLC voltage Vc , in case 7, drops much lower than that in
case 2. The stored energy in EDLC is more effectively used in
case 7. The trend of Vc in case 7 is similar to that in case 3.
In train coasting, the train collects small current for charging the
EDLC.
Regarding energy consumption in Table VII, the energy-saving
effect by introducing EDLC is 5.67% that is evaluated much higher
than that in cases 1 and 2. The EDLC enables obvious energysaving operation when the train runs with less margin time.
6. Conclusion
(1) The EDLC voltage drops to the lower limitation Vc min when
control input n changes from acceleration to coast at time
50 s.
(2) Substations supply the power with a small current for charging
This paper presents the optimal train operation with EDLC
minimizing energy consumption. SQP can be applied to the formulated optimal control problem with discretization with easier
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M. MIYATAKE AND K. MATSUDA
Speed [m/s]
20
0.5
0
−0.5
−1
0
20
40
Case 2
−0.5
−1
Voltage at pantograph [V]
Case 3
0
0
20
40
60 80 100 120
Time [s]
1800
Train power [W]
Control input u
1
0.5
1600
1400
1200
0
20
40
15
10
5
0
60 80 100 120
Time [s]
Capacitor voltage [V]
Control input n
1
60 80 100 120
Time [s]
0
20
40
500
60 80 100 120
Time [s]
Case 2
400
Case 3
300
5
0
20
40
60 80 100 120
Time [s]
40
60 80 100 120
Time [s]
x 106
0
−5
0
20
Fig. 7. Graphs of optimal control inputs and state variables
20
0.5
Case 2
0
Case 5
−0.5
−1
Case 4
0
20
40
60
Speed [m/s]
Control input n
1
15
10
5
0
80 100 120
0
20
40
Control input u
1
0.5
Case 5
0
Case 2
−0.5
−1
0
20
40
60
80 100 120
500
Case 2
450
Case 5
400
350
300
0
20
40
Train power [W]
Voltage at pantograph [V]
Case 4
Case 5
1600
1500
1400
1300
0
20
40
60
80 100 120
Time [s]
Case 2
1700
80 100 120
550
Time [s]
1800
60
Time [s]
Capacitor voltage [V]
Time [s]
60 80 100 120
Time [s]
4
x 106
2
0
−2
−4
0
20
40
60 80 100 120
Time [s]
Fig. 8. Graphs of optimal control inputs and state variables
discharged if margin time between stations is expected enough.
The EDLC current should be kept low if the consumed
power is low. Regarding the acceleration/deceleration command,
very few differences between with and without EDLC are
observed.
These trends of results may be found with qualitative
investigation or trial and error. However, it is significant that such
study can be investigated quantitatively. The quantitative results
implementation. As a result, it is found that the energy consumption can be reduced by using on-board energy storage device.
Compared with the train without EDLC, the total energy consumption is reduced by 0.36–5.67%. If rectifier substations that
cannot absorb regenerative energy are assumed, the energy-saving
effect will be evaluated much higher.
The optimal EDLC control strategies are also clarified.
For energy-saving operation, the EDLC should not be deeply
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ENERGY SAVING RAILWAY VEHICLE WITH ON-BOARD ENERGY STORAGE
25
Speed [m/s]
Case 6
0.5
0
−0.5
−1
Case 7
0
20
40
60 80
Time [s]
0.5
0
−0.5
−1
Voltage at pantograph [V]
Case 7
0
20
40
60 80
Time [s]
100 120
1800
Train power [W]
Control input u
1
1700
1600
1500
1400
1300
0
20
40
60 80
Time [s]
20
15
10
5
0
100 120
Capacitor voltage [V]
Control input n
1
100 120
0
20
40
60 80
Time [s]
100 120
0
20
40
60 80
Time [s]
100 120
40
60 80
Time [s]
100 120
550
500
450
400
350
300
x 106
4
2
0
−2
−4
0
20
Fig. 9. Graphs of optimal control inputs and state variables
will be used as ideal models for evaluating the design of online
control used in actual rail vehicles.
A further direction of this study will be to optimize the
train operation problem, which has more complicated conditions, for example, rectifier substations, speed limitations and
gradients.
(8) Khmelnitsky E. An optimal control problem of train operation. IEEE
Transactions on Automatic Control 2000; 45(7):1257–1266.
(9) Ko H, Koseki T, Miyatake M. Numerical study on dynamic programming applied to optimization of running profile of a train. IEEJ
Transactions on Industry Applications 2005; 125-D(12):1084–1092.
(in Japanese).
(10) Ko H, Koseki T, Miyatake M. Application of dynamic programming
to optimization of running profile of a train, Computers in Railways
IX, WIT Press; 2004, 103–112.
Acknowledgments
This project has been supported by MEXT.KAKENHI
(19760290).
(11) Albrecht T. Reducing power peaks and energy consumption in rail
transit systems by simultaneous train running time control. Computers
in Railways IX 2004, 885–894.
(12) Ogawa T, Yoshihara H, Wakao S, Kondo K, Kondo M. Design estimation of the hybrid power source railway vehicle based on the multiobjective optimization by the dynamic programming. IEEJ Transactions
on Electrical and Electronic Engineering 2008; 3(1):48–55.
(13) Ko H, Koseki T, Miyatake M. A numerical method for optimal operating problem of a train considering DC power feeding system. IEEJ
Transactions on Industry Applications 2006; 126(8):1104–1112. (in
Japanese).
References
(1) Sone S. Optimisation of regenerative train operation Pt.1 contents
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777
IEEJ Trans 4: 771–778 (2009)
M. MIYATAKE AND K. MATSUDA
Masafumi Miyatake (Member) received the B.S. and M.S.
degrees in electrical engineering from the
University of Tokyo in 1994 and 1996,
respectively. He received the Ph.D degree in
information and communication engineering
from the University of Tokyo in 1999. In
1999, he was a research associate in Tokyo
University of Science. In 2000, he joined
Sophia University. From 2004, he has been
an associate professor in Sophia University. His research interests include energy management control, renewable energy generation and their applications to transportation systems.
Kunihiko Matsuda (Non-member) received the B.S. and M.S.
degrees in electrical and electronics engineering from Sophia University in 2005 and
2007, respectively. He is now working at
Denso Corporation.
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IEEJ Trans 4: 771–778 (2009)