VỀ một GIẢI PHÁP điều KHIỂN QUÁ TRÌNH TRAO đổi NĂNG LƯỢNG hãm của tàu điện ĐƯỜNG sắt đô THỊ VIỆT NAM tiếng anh

1
INTRODUCTION
1, The urgency of the thesis: Electric transportation with outstanding advantages
is the ability to transport large passengers, reduce environmental pollution, reduce
traffic congestion [63,78]. In Vietnam, the planned urban railway network in the near
future has 5 routes deployed in Hanoi city 6 routes in Ho Chi Minh city. However, the
energy required to operate urban railway is up to billions of kWh. Therefore, the goal
of energy saving on train operation is a very urgent issue, with high scientific and
practical significance, but so far, no research group in Vietnam has proposed energy
saving solutions. operate urban electric trains. Therefore, the author selected the topic
with the name: "About a solution to control the energy exchange process of Vietnam
urban railway electrified trains" with the aim of saving energy by a solution for
regenerative braking energy when the train operates in braking mode and in
combination with the optimal theory of determining the optimal train speed profile.
2. Research objectives: Introducing energy saving solutions in electrified train
operation. Thereby, proposing solutions suitable to the characteristics and conditions
of Vietnam's urban railways; and applying these solutions for Cat Linh-Ha Dong urban
railway to assess saving energy.
3. Research objects: Urban electric trains have traction drive system integrated with
supercapacitor energy storage device.
4. Research content: The thesis structure consists of 4 chapters
- Chapter 1: Overview of braking energy recuperation solutions: Synthesizing, analyzing
previously published works, thereby proposing research directions, research objects,
and developing solutions to solve research problems.
- Chapter 2: Implementation of modeling of electric train and supercapacitor energy
storage system.
- Chapter 3: Strategies for optimal control of train operation energy with trains
integrated supercapacitor energy storage system (SCESS).
- Chapter 4: Verification of the correctness of theoretical research through simulation
results on Matlab software with parameters of Cat Linh - Ha Dong urban electric train
line, and an experimental part of Interleaved DC -DC converter in SCESS.

- Finally, some conclusions and further research directions of the thesis are presented
in the conclusions.
5. The novelty of the thesis:
 Proposing SCESS on board integrated with traction motor drive system via
Interleaved bidirectional DC-DC converter and designing supercapacitor control
according to the operation characteristics of a railway vehicle.
 Applying Pontryagin's maximum principle to find optimal transfer points of
operating modes, determine the optimal speed profile of train operation using
supercapacitors on board.


2
CHAPTER 1. OVERVIEW OF SOLUTIONS FOR BRAKING ENERGY
RECUPERATION
1.1 The announced researches on solutions for braking energy recuperation
1.1.1. Domestic research
This is a very new field in Vietnam, so there are very few studies on optimizing the
energy of urban electric train operation [60].
1.1.2. Overseas research
Energy -efficient
operation of electrified
train

Regenerative braking
energy

Energy -efficient
driving

Optimal

speed profile

Eco-driving
tools: ATO,
DAS

Energy
storage
device

Energyoptimised
timetables

Hình 1.7. Strategies for effective management of train operation energy
Studies have shown that there are two groups of solutions with higher energy-saving
percentages: Regenarative recuperation solutions and energy efficient driving solutions
[31].
1.1.2.1. Research on regenrative braking energy recuperation
a) Regenerative braking energy recuperation by energy storage device
The supercapacitor energy storage system (SCESS) is installed onboard, at the traction
substations, or at points along the train track to recover regenerative braking energy
when the train operates in traction mode [9, 12, 21, 25, 44, 45, 46, 53, 58, 66, 68, 69,
72, 73, 75].
b) Reversible substations
Traction substations use active rectifiers for bidirectional energy flow to recuperate
braking energy up to 18% [86], [22].
c) Braking energy recuperation by timetable optimization: This solution does not
require additional investment in infrastructure of the route, with the idea of using
regenerative braking energy from a train operating in the braking mode to switch to
trains operating in accelerating mode.

Typically, Subin Sun (2017) [71] combines the operation of two trains in the same
station, recuperating the regenerative braking energy represented by the power q(t ) in

dv
= u f f (v) + q(t ) / v - ubb(v) - r (v) - g(x )
dx
ì
ï
0 t < tb
ï
ï
With braking mode occuring in interval [tb, tc], q(t ) = íq (t ) tb £ t £ tc
ï
ï
ï
ï
î0 tc

the motion equation: v


3
1.1.2.2. Energy - efficient driving
a) Determining the optimal train journey on the route
- The research team of the University of South Australia including Howlett, Benjamin,
Pudney, Albrecht, Xuan has determined the optimal speed profile through finding the
optimal transfer points with 5 control rules taking into account the actual conditions
on the route. such as the slope, the speed limit, etc., it is possible to find the optimal
time and distance at each train operation mode.
Comment: The research team of the University of South Australia in published studies

does not mention the problem of train running on time.
Hai Nguyen (2018) [2] applied PMP to trains with long-distance diesel locomotives,
found the optimal speed profile corresponding to the lines with different slopes, and in
the objective function also mentioned to the station problem on time.
Comment: In his thesis, Hai Nguyen does not mention the problem of recovering
braking energy.
1.2. Selecting the research direction and the tasks solved of the thesis
Through analysis of published works, there are no works that combine both the
regenerative braking energy recuperation solution by ESS and the optimal speed profile
determination with the on-board ESS while ensuring fixed trip time.
Therefore, the author proposes the selected structure for research.
Braking energy
recuperation

Technology

Energy converter
system
- DC-AC converter
- DC-DC converter

Traction
substation

Control
stratergies
- Control charge/
discharge of supercapacitor
- PMP for train with Onboard SCESS, finding
optimal speed profile.

DC
Link

ESS

VSI

Voltage
source
inverter

IM

Train
Wheel

Fig. 1.14. The selected structure for research
 Technology: Learning about technology of electric train operation in some urban
railway lines in Vietnam; namely, urban railway of Cat Linh - Ha Dong line.
 Energy conversion system on electric trains: focusing on studying Interleaved
DC-DC converter in an effort to ensures energy exchange between
supercapacitor and traction drive system.
 Control strategies: Proposing the control method for Interleave DC-DC converter
ensures the charging-discharging mode of supercapacitors suitable for train


4
running characteristics. Proposing PMP to determine the optimal speed profile
for train operation.

Conclusion of chapter 1
By synthesizing and analyzing a number of domestic and foreign research works on
energy saving solutions, the author has analyzed and selected the research object as an
urban electric train integrated on-board SCESS and proposed independent control
strategies for each train; proposed to control regenerative braking energy recuperation
by managing the charging / discharging mode of supercapacitors; using Pontryagin's
maximum principle to optimize train operation energy with hybrid power systems.
These suggestions will be verified by MATLAB simulation software.
The summary content of Chapter 1 has been published by the author in the work [3].
CHAPTER 2. MODELING ELECTRIC TRAIN AND SUPERCAPACITOR
ENERGY STORAGE SYSTEM
The accuracy and characteristics of the mathematical model is the core factor
determining the quality of the system. So in Chapter 2 centralized modeling system
including:
 Modeling lectric train
 Modeling supercapacitor enregy storage system.
Rday

iday

Overhead contact line

Pantograph

Substation

DC-DC
converter

Etdk

iinv

iC

Rtdk

Usc

i
LL
RL

rbr

ibr

VSI

Csc
IM

IM

Fig. 2.1 Electrical drive configuration equipped with SCESS
2.1. Modeling electric train and SCESS
2.1.1. Modeling electric train
Modeling the train needs to calculate the forces affecting train motion, the traction
motor drive system to make the wheel movement.
2.1.1.1. The forces act on the train

The forces acting on the train include: The main resistance force including wind
resistance (Fwind), rolling friction resistance (Froll); slope resistance (Fgrad).


5
The third rail, 750
VDC
Feeder
Air resistance force
Train

Wheel

Gear

Traction force

IM
Motor
torque

railway

Friction
force
𝛂

Gravity

Fig 2.9 Diagram of forces acting on electric train [1]

Traction / braking force:

Fig. 2.11 Traction force /01 motor

Fig. 2.13 Traction force regression/ 01
motor

Fig. 2.12 Electric braking force/01 motor

Fig. 2.14 Electric braking force regression/
01 motor

Resistance forces:
FTr
Faero
mgsinα

Froll
α

mg

Fig. 2.16 Forces acting on train
a. The main force W0 : The main resistance force (also known as basic resistance force)
includes wind resistance and friction force


6

W0 = Fwind + Froll

(1.1)

 The wind resistance force depends on train speed, size and shape, represented by
the formula [93]:

Fwind =
Where:

  2 1




1
rC d Af v - vwind = rC d Af v - v wind cos(v wind , v )
2
2

{

r

}

2

(1.2)

is the air density; Cd is the air drag coefficient, determined by train shape;

Af is the largest section of the train; v is train speed; vwind is wind speed; b is the sharp
angle created by the direction of the wind velocity with the movement of the train.
 Rolling resistance force Froll
For simplicity, consider rolling frictional force only on hard track and consider
the ideal case that all wheels have the same conditions. At this time, rolling friction
(1.3)
force can be calculated as follows [93]: Froll = fr mg cos a
where fr is rolling resistance coefficient
b. Gradient resistance force F gra d : When the train operates on the slope, the gradient
resistance force is calculated according to the formula [93]: Fgrad = mg sin(a )

(1.4)

where: sin(a) = sin(arctan(ik ))

ik

(‰)is the ratio of slope height to slope, a is the slope of the track.

2.1.1.2 Dynamic equation of the train
The motion equation of the train is often transformed into its own form of impact force
converted into the mass unit of the train as follows:

ì
ï
dt
1
ï
=

ï
ïdx
v
í
ï
dv
ïv
= utr ftr (v ) - ubr fbr (v ) - w 0 (v ) - fgrad (x )
ï
ï
ï
î dx

In the (2.7): utr và ubr are control variables: utr =

(2.7)

Ftr (v )
F (v )
; ubr = br
, and
Ftr max (v )
Fbr max (v )

utr Î [0,1], ubr Î [0,1] ;
The unit main resistance force (also called the unit basic resistance force) is represented
by the David equation: w 0 = a + bv + cv 2
(2.8)
The a,b,c coefficients are supplied by the Manufacturer
2.1.1.3. Motion equation of tractive electrical motor

Tel -TL = J

d wr
;
dt

J = J m + J eq

(2.9)
2

1 m æç Dwh ö÷
ç ÷÷
The inertia torque of the train is calculated [59]: Jeq =
4 N ççè t ÷ø
Load torque when the motor operates in engine mode [59]

(2.10)


7

TL =

Ftr DWh
D Wh
= KmFtr với K m =
2thmor hmech
2thmor hmech

(2.11)

Load torque when the motor operates in generating mode [59]:

Fbr DWh hgen

TL =

2thmech

= KG Fbr với KG =

DWh hgen

(2.12)

2thmech

2.2 Supercapacitor energy storage device modeling
Modeling energy storage device includes supercapacitor modeling and Interleave DCDC converter modeling.
2.2.4 Supercapacitor modeling
Supercapacitors replaced by equivalent electrical circuit model include many parallel
branches [32]. Two RC branches provide two time constants to describe the fast and
slow dynamics.
iL
I

iP
Ci

v sc

R

P

R

Ci0

Ii
R

I
d
R
d

i
i
Ci1

Cd
Vi

Ci C
i0

i
Ci1

(a)
(b)
Fig 2.22. Simple equivalent supercapacitor circuit
As the above analysis, supercapacitor dymamic is considered for a short period of time,
ignore the Rd ,C d branch (with a minute time constant) and the branch containing RP
(characteristic for long-term leakage current in self-discharge) as shown in Figure 2.22b.
See the two capacitors with equivalent capacitance Ci depending on the voltage ui in
relation: C i (u i ) = C i 0 + C i 1 = C i 0 + k v .u i

(2.21)

Given Ci=Csc, ui=usc, Ri=Rsc
The mathematical model of supercapacitor is shown as follows:
ì
ï
du (t )
ï
isc (t ) = Csc (usc ) sc
ï
ï
dt
ï
ï
ï
u
(
t
)
=

R
i
(
t
)
+
usc (0)
sc sc
í sc
ï
ï
usc (0) = Usc,max
ï
ï
ï
p (t ) = usc (t )isc (t )
ï
ï
î SC

(2.22)

2.2.5. Interleaved DC-DC converter modeling
Non-isolated bidirectional DC-DC converter consists of parallel branches (also called
Interleave DC-DC converter) suitable for high-power, high-voltage drives.
2.2.5.1 Power circuit structure of Interleaved DC-DC converter with three
switch branches
Supercapacitor performs the process of energy charging / discharging through the
Interleaved DC-DC converter with three switch branches as shown in Figure 2.24.

8
Rectifier
Electric 
Source

Induction
motor

Inverter

AC

DC

Wheel
Gear

IM

RD

DC

AC

SCESS
Converter
DC

SC

DC

HB1

SBK1

SBK2

SBK3

DBS1

iL
SC

HB3

HB2

DBS2

DBS3

RL1,L1
RL2,L2

UDC-link

CDC

Csc

RL3,L3

esr

RSC

usc
SBS1

SBS3

SBS2
DBK1

DBK2

DBK3

Fig. 2.24. Power circuit structure of Interleaved DC-DC converter
The configuration of Interleaved DC-DC converter includes half-bridges (HBs) in
parallel, as shown in Figure 2.24 with three parallel H-bridge halves: HB1, HB2, HB3.
In order to SCESS charges/discharges according to the train characteristics, the
Interleaved DC-DC converter needs to work in two modes: Boost mode, Buck mode.
2.2.5.2. Modeling bidirectional DC-DC converter with one switch branch
The Interleaved DC-DC converter operates with assumptions: IGBTs are ideal,
converter operates in continuous current mode; conventionally, current positve

direction flowing through the inductance coil regards as charge state of SC, and vice
versa regards as discharge state, the current mode of Interleaved DC-DC converter is
equivalent with the current mode of DC-DC converter with one switch branch as
shown in Figure 2.30a and apply the small - signal averaged method to model
Interleaved DC-DC converter.
The averaged representation of the bi-directional switching power-pole in fig.2.30a is
an ideal transformer shown in fig.2.30b with a turns -ratio 1:d(t), where d(t) represents
the duty-ratio of IGBT.
Boost

Buck

+
D BS

RL,L

S BK

iL

C

RL

UDC-

+

link

S BS
D BK

q = 1 -q

q

Fig.2.30a Average dynamic model of the
switching power-pole with bi-directional
power flow
In fig.2.31, applying the Kirchhoff's fisrt,
describled as follow:

RSC
Csc

usc

-

L

iL

i1 (t )

i2 (t )

-

u2 (t )

d(t):1

+ iinv
uDC -link

+
u1 (t )

ic

-

C

-

Fig. 2.31 Equivalent electrical circuit of
one switch branch bidirectional DC-DC
converter averaged model
second law; the state equation of converter is


9
ì
ï
di (t )
R

1
ï
L = - L i (t ) + 1 d (t )u
ï
(t ) - u (t )
ï
L
DC
link
ï
L
L
L SC
(2.24)
í dt
ï
du
(t ) 1
ï
ï
i (t ) = ic (t ) + i2(t ) = DC -link - d (t )i (t )
ï
L
dt
C
ï
î inv
Detail control design of Interleaved DC-DC converter is shown in chapter 3.
Conclusion chapter 2
The content of Chapter 2 presents the problem of modeling electric train and

supercapacitor energy storage system (SCESS). In train modeling: Analysis of the
forces acting on the train, regression of traction, electric braking force characteristics,
building motion equation of train, motion equation of motor, calculating load torque.
In SCESS modeling, performing supercapacitor and Interleaved DC-DC converter
modeling with 3 switch branches. The content of chapter 2 presented in the work [6]
under the list of published works of the author.
CHAPTER 3. OPTIMAL CONTROL OF ENERGY CONSUMPTION OF
ELECTRIFIED TRAIN INSTALLED SUPERCAPACITOR
In chapter 3, the control structure of train operation energy is proposed with the goal
of saving energy: Designing Interleaved DC-DC converter control enables SCESS to
recuperate regenerative braking energy. Using optimal algorithm determines train
speed profile when train has integrated SCESS.
Traction
substation B

traction
substation A

Traction substation

Voltage source
inverter

Braking resistor

Electric
source

AC
UDC-link

DC

IM
AC

wm,v Tm , v
Wheel

TL

Resistance forces

DC-DC Interleave

DC

Csc

K

usc

FR

Froll
Fgrad

esr

RSC

RU
uDC-link

PSC

RD

SC

u*DC-link

Traction
motor

DC

iL*

DC

iL

RI

Traction motor drive

PWM

POWER MANAGEMENT SYSTEM
( USING OPTIMAL CONTROL THEORY )

Traction, resistance,braking forces

Parameters of train, speed,
distance, running time...

Fig 3.1. The overall control structure of train operation energy


10
3.1. Control DC-DC Interleaved DC-DC converter
*
uDC
-link +

‐

u

iL*

PI

+

1/3

‐

iL1

1

PI

+
_

0

+

CARRIER

‐
iL2

120 deg
phase
delay

+
_

‐
iL3

PI

+
_

CARRIER 3

SBK2
SDK2

CARRIER 2

+
240 deg
phase
delay

PI

SBK1
SDK1

CARRIER 1

DC -link

SBK3
SDK3

Fig. 3.6. Two -loop cascaded control structure for Interleaved DC-DC converter
Designing control law for Interleaved DC-DC converter structure according to average
current mode, with PI controllers both inner-loop and outer-loop.

3.1.1. Design of current - loop controllers
The goal is to design the controllers so that the average current flowing through the
inductance coil iL tracks a certain reference iL* . Designing the inner-loop is in three
steps.
Step 1: Determine the state equation of the bi-directional DC-DC converter in the
average model rewritten as follows:

ìïdi (t )
1
ïï L = - RL i (t ) + 1 d(t )u
(t ) - uSC (t )
L
DC
link
ï dt
L
L
L
í
ïïduDC -link (t )
1
1
= - d (t )iL (t ) + iinv (t )
ïï
dt
C
C
ïî

(3.1)

Step 2: Determine the operating points by giving the left derivative of equation (3.1)
equal to zero and the quantities are in the steady state
ì
ï
-RL
U
1
ï
0=
I Le + U DC -link e D - SC
ï
ï
L
L
L
(3.2)
í
ï
i
1
inv
ï
0=
I D+
ï
ï
C Le
C
ï

î
Solving equation (3.2) finds operating points (I Le,U DC -link e ) corresponding to measured
voltage of supercapacitor U SC and duty-ratio D.
Step 3: Linearize the first equation of equations (3.1)
Since the model (3.1) is nonlinear, it is recommended to design the controllers according
to linearization method around the operating point.
The transfer function between the inductor current and the duty-ratio considered on
the small-signal domain is calculated as follows:

i (s ) U DC -linke / RL
kC
G dd (s ) = L
=
=
d (s )
L
TC s + 1
( s + 1)
RL

(1.5)


11
Where: kC =

U DC -linke
L
; TC =
RL

RL

Beacause the transfer function (3.6) has a first-order, the PI controller may be
effectively used to ensure both zero steady-state error and controlled bandwidth. With
the PI set, the controller is described as follows:

Rdd (s) = k pC (1 +
Gkin _ dd (s ) =

1
TIC s

)=

k pC (1 + TIC s )
TIC s

G dd (s )Rdd (s )
1 + TIC s
=
1 + G dd (s )Rdd (s ) TICTC 2
1
s + TIC (1 +
)s + 1
k pC kC
k pC kC

(3.7)
(1.6)

ì
ï
L
ï
TIC =
ï
ï
RL
k pC ,TIC can be found : ïí
ï
L ⋅ 104
ï
k pC =
ï
ï
2 ⋅U DC -linke
ï
î
3.1.2. Design voltage-loop - control UDC-link
*
Designing the voltage-loop is to control the voltage uDC -link sticking value uDC
with
-link

*
uDC
being constant by the nominal working voltage according to the traction power
-link

standard EN 50163 and IEC 60850. Designing control is the same current loop; the

transfer function between DC-link voltage and inductor current is:

Gda (s ) =
where: kV =

uDC -link (s )
kV
=
iL (s )
TV s + 1

(1.7)

U SC
CU DC -link
;TV = I inve
I inve

Similar to current-loop, designing PI controller for voltage-loop is in the form:
k (1 + TIV s )
1
) = pV
(1.8)
Rda (s) = k pV (1 +
TIV s
TIV s
The closed-loop transfer function becomes:
G da (s )Rda (s )
1 + TIV s
=

Gkin _ da (s ) =
1 + G da (s )Rda (s ) TIVTV 2
1
s + TIV (1 +
)s + 1
k pV kV
k pV kV

k pV ,TIV

ì
ï
CU DC -linke
ï
TIV = ï
ï
I inve
can be found: ïí
ï
CU DC -linke ⋅ 103
ï
k pV = ï
ï
2U SC
ï
ï
î

(1.9)

12
3.1.3. Verifyting the design of the Interleaved DC-DC converter

Through simulation results figures 3.7, 3.8, and 3.9 having validated the design
of the two control loops of charge-discharge modes of supercapacitors according
to the operating characteristics of train. The train's trip time from Cat Linh to
La Thanh station is 68s, when the train operates in accelerating mode from 0 to
28s, the current on supercapacitors is positive, it shows that the supercapacitors
are discharging to support the train in traction mode; from 28 to 48s
supercapacitor current is equal to zero, respectively, the train operates in
coasting mode; from 48 to 68s train operates in the braking mode, the current
on supercapacitors is negative.
SOC%

80
79

78

77

0

10

20

30

40

50

60

68

Time(s)
700

Usc

IL [A]

600
500

400
300
0

10

20

30

40

50

40

50

60

68

Time(s)
1000

isc

500

Time(s)

0

-500
-1000
0

10

20

30

Time(s)

60

68

Fig.3.7. Values of current iL in each Fig.3.8. State of charge, voltage, current
of a SC module in a process of running
branch and total current
train.

Fig 3.9. Charge-discharge of supercapacitor when train integrates SCESS
With different train operation speeds, psc (t ) obtained in charge-discharge mode also
has different values.
3.4. Designing a problem of optimal control of train motion according to
Pontryagin' maximum principle

Using Pontryagin's maximum principle determines optimal speed profile,
thereby determining the saving energy compared to the speed control profile
without control.


13
3.4.1. Optimal control of train operation energy according to PMP
3.4.1.1. Performing motion equations and objective function
In the case of a train using On-board SCESS, the train's equation of motion is shown
again as follows:

ìï dt

ïï = 1
ïdx
v
í
ïï dv
p (v, t )
= utr ftr (v ) - ubr fbr (v ) + sc
- w 0 (v ) - fgrad (x )
ïïv
v
ïî dx

(3.54)

In equation (3.54), psc depends on the speed and trip time. However, in order to design
the optimal control for running energy consumption easily, psc only represents the time
state variable t: psc (t )
With train specifications, and route survey, boundary conditions are defined:

ìï0 £ v(x ) £ V (x )
ïï
ïí0 £ t (x ) £ T
d
ïï
ïï0 £ x £ x f
î

ìv(0) = 0; v(x ) = 0
(3.55) ï
f

ï

í
ïït(0) = 0; t(x f ) = Td
î

(3.56)

Constraints:

ì
ï
0£u £1
ï
tr
ï
ï0 £ u £ 1
í
br
ï
ï
u > 0 or u > 0
Either
ï
ï
tr
br
î

(3.57)

Speed profile comprises of 3 modes: Accelearating  Coasting  Braking
Where: V x - the maximum allowable speed, x f - length of distance

()

(3.58)

v (0) - speed at the beginning, v (x f ) - speed at the end of the route

Td - Duration of the trip is also given by the timetable
Limits of traction and braking force: 0 £ Ftr (v) £ Ftr max (v); 0 £ Fbr (v) £ Fbr max (v)
(3.59)

supercapacitor power per
ìï P (t )
ïï-e sc
ïï
m
0
psc (t ) = íï
ïï
ïï Psc (t )
ïïe
ïî m

unit mass

psc (t ) is

given:

t1 £ t £ t2

(Discharge time)

t2 < t £ t 3

(Coasting time)

t3 < t £ t4

(Charge time)
*

(3.60)

*

Problem set: Find optimal control variables utr , ubr and optimal motion trajectories
*

*

of the train v (x ) , t (x ) , according to the state equation (3.48) to ensure the optimal
standard of train operation energy Ae is minimal with boundary conditions (3.49),
(3.50); constraints (3.51), (3.52); limit control forces (3.53).


14

In case of ensuring the trip time in the station is Td (known in advance), calling the
actual trip time is Ta , we have to add the boundary condition of the objective function:

(Ta -Td ) 0

(3.61)

To ensure the fixed trip time, adding Lagrange multiplier, we have the objective
function to consider regenerative energy recuperation:

x
x
ộ
ộ
ự
p (t ) l ự
1
l
J = ũ ờutr ftr (v ) + ỳ dx + ũ psc dx = ũ ờờutr ftr (v ) + sc + ỳỳ dx min (3.72)
ờ
v ỳỷ
v
v
vỷ
0
0
0
ở
ở
When applying the Lagrange multiplier method, it is necessary to combine the

objective function with the boundary conditions to transfer the problem of
non-binding optimization, then there must be more conditions:
xf

f

f

ảJ
= 0 hay Ta -Td =
ảl

Ta

ũ dt -T

d

=0

(3.73)

0

In equation (3.73), l does not appear explicitly, so it cannot be solved directly
from this equation. Therefore, the algorithm to determine Lagrange multiplier
will be presented in the next section.
3.4.2.2 Speed trajectory optimality of a train based on PMP
The Pontryagin's maximum principle is applied to solve energy efficient operation
problems by finding the optimal transfer points of operating modes from which the

energy optimal operating trajectory of the train is obtained.
Figure 3.11 shows the train running cycle with three modes: Accelerating Coasting
Braking.
vt(km/h)

vh
vb

Accelerating

Braking

Coasting
tc,xc

ta,xa

xh

tb,xb

xb

x (m)

Fig 3.11. Running Characteristic of a train
Combined (3.48) to (3.54) Hamiltonian function is written:

psc (v, t ) l
+ )

v
v
ổ
u f (v ) + psc (v, t ) / v - ubr fbr (v ) - w 0 (v ) - fgrad (x )ữử
1
+p1 + p2 ỗỗỗ tr tr
ữữữ
ỗố
v
v
ữứ
where p1, p2 are adjoint variables.
H = -(utr ftr (v ) +

(3.74)


15
Adjoint variable differential equations are reformed:

dp1
dp (v, t )
ảH
1 dpsc (v, t ) p2 ổỗdpsc (v, t )ửữ 1
ữữ = (1 - p) sc
==
- 2 ỗỗ
ảt
dx
v

dt
v ỗố dt ứữ v
dt

(3.75)

ộ ảf
dp2
p
lự p
ảH
== ờờutr tr - sc2 - 2 ỳỳ + 21
dx
v
v ỷ v
ảv
ở ảv
p
+ 22 ộởờutr ftr (v ) + psc (t ) / v - ubr fbr (v ) - w 0 (v ) - fgrad (x )ựỷỳ
v
p ộ ảf
p
ảf
ảw 0 ựỳ
- 2 ờờutr tr - sc2 - ubr br v ở ảv
v
ảv
ảv ỳỷ

(3.76)

Substitute p =

p2
, so p v = p2
v

ỡ
ù
dp2
ảH
ù
=ù
ù
dx
ảv
ù
ù
ớ
p (t )
ù
utr ftr (v) + sc - ubr fbr (v) - w 0 (v) - fgrad (x )
ù
dv
ù
v
=
ù
ù
v

ù
ợdx
d(p v)
dv
dp dp2
=p
+v
=
dx
dx
dx
dx
dp dp2
dv
v
=
-p
dx
dx
dx

(1.10)

(1.11)
(1.12)

Hamiltonian function is reformulated as:

H = (p - 1)utr ftr + (p - 1)

psc
l p
- pubr fbr - p(w 0 + fgrad ) - + 1
v
v
v

(3.80)

Hamilton function reachs maximum value according to two control variables utr , ubr ,
the components that do not contain utr , ubr can be removed, then only:

H ' = (p - 1)utr ftr - pubr fbr = utr (p - 1)ftr + ubr (-pfbr ) ắắắ
ắ
max
u ,u
tr

br

(3.81)

Two control variables utr , ubr found for the maximum H function will be:

utr

0 Ê p Ê1
p <0
p >1

{
}
max {0, - sgn( f )}
max {0, - sgn( f )}
max 0, - sgn( ftr )

ubr

max {0, - sgn( ftr )}

tr

max {0, - sgn( ftr )}

tr

max {0, - sgn( ftr )}

From the above analysis, five optimal control laws are designed:
Full power (FP): utr = 1, ubr = 0 when p > 1
Partial power (PP): utr ẻ [0,1] , ubr = 0 when p = 1
Coasting (C): utr = 0, ubr = 0 when 0 < p < 1
Full braking (FB): utr = 0, ubr = 1 when p < 0


16
 Partial braking (PB): utr = 0 , ubr Î [0,1] when p = 0.

Substitute Error! Reference source not found., (1.11) in (1.12) finding the
differential equation for p.

(p - 1)
dp (1 - p)
p
p
l p1
¢
¢
(
)
(
)
(
)
=
utr ftr¢(v ) +
p
t
+
u
f
v
+
w
v
(3.83)
sc
dx
v
v3
v br br

v 0
v3 v3
Full power mode: p > 1, ubr = 0, utr = 1, finding accelerating time ta , accelerating
distance x a , multiplier l.
Using equation Error! Reference source not found.

(p - 1)
dp (1 - p)
p
l p
=
ftr¢(v ) +
psc (t ) + w 0¢(v ) - 3 - 31
3
dx
v
v
v
v
v
From (3.48) determining x a , ta :
ì
ï
dx
v2
ï
=
ï
ï
v ⋅ utr ftr (v ) + psc (t ) - v ⋅ w 0 (v ) - fgrad (x ) ⋅ v

ïdv
í
ï
dt
v
ï
=ï
ï
v ⋅ utr ftr (v ) + psc (t ) - v ⋅ w 0 (v ) - fgrad (x ) ⋅ v
ï
îdv

(3.84)

(3.85)

With initial conditions: x(0)=0; t(0)=0
Partial power mode: p = 1, ubr = 0, 0 < utr < 1 , so

dp
= 0, findinf Lagrange
dx

multiplier l .
Using equation (3.83):

1
l p
w 0¢(v ) - 3 - 31 = 0
v

v
v
dp1
= 0, easily, p1 is chosen by 0, so
From (3.75), then
dx
l = v 2w0¢

(3.86)

(3.87)

Therefore,

l = v 2 (b + 2cv )

If

l

(3.88)

is chosen previously, solve (3.88) to find the hold -speed vh

Coasting mode: utr = 0, ubr = 0, 0 < p < 1 , finding braking speed vb, coasting time tc,
coasting distance xc
Coasting speed vb is calculated as following [41,88]

vb =

y(vh )
j ¢(vh )

(3.89)

Where: j = v ⋅ w0 (v), y = v ⋅ w0¢(v)
2

From (3.54) finding xc,tc


17
ì
ï
dx
v
ï
=
ï
ï
-w 0 (v ) - fgrad (x )
ïdv
í
ï
1
dt
ï
=ï
ï
w 0 (v ) + fgrad (x )

ï
îdv
With t (v = vh ) = ta ; x (v = vh ) = x a

(3.90)

Partial braking mode (PB): utr = 0, 0 < ubr < 1, p = 0 finding l
Using equation (3.83)

-

1
l p1
(
)
p
t
- =0
v 3 sc
v3 v3

(3.91)

Therefore,

l = -psc (t ) - p1

(3.92)

Full braking mode (FB): utr = 0, ubr = 1, p < 0, finding braking time tb, braking

distance xb
Using equation (3.84)

dp (p - 1)
p
p
l p
=
psc (t ) + fbr¢(v ) + w 0¢(v ) - 3 - 31
3
dx
v
v
v
v
v

(3.93)

From (3.54) finding tb, xb

ì
ï
dx
v2
ï
=
ï
ï
-v ⋅ ubr fbr (v ) - v ⋅ w 0 (v ) + psc (t ) - v ⋅ fgrad (x )

ïdv
í
ï
1
dt
ï
=
ï
ï
ubr fbr (v ) - w 0 (v ) + psc (t ) / v - fgrad (x )
ï
îdv
with t (v = vb ) = tb , x (v = vb ) = x b .

(3.94)

Conclusion chapter 3
In Chapter 3, designing the control structure of the Interleaved DC-DC converter
ensures the charge-discharge process of supercapacitors, applying the Pontryagin's
maximum principle to find the optimal switch points; from there, finding the optimal
speed profile.
The results of chapter 3 are presented in [1,2,4,5, 6,7,8,9] in the list of published works
of the author.
CHAPTER 4. SIMULATION AND EXPERIMENT RESULTS
The simulation results on MATLAB/Simulink software will be presented in this
chapter to verify the theoretical research results:
 Effectiveness of SCESS in energy recuperation in braking mode;
 Comparison energy efficiency of train operation with /without PMP;
 Experimental results verify the working capability of the Interleaved DC-DC
converter.

18

(m/s)

4.1. Off-line simulation
The simulation results of the control design mentioned in chapters 2 and 3 have two
problems.
4.1.1. Simulation Program of the electric train system installed On-board SCESS
on Cat Linh-Ha Dong line
The simulation results of operation modes of T1 train and T2 train are conducted with
3 scenarios that fully demonstrate train operation situations on the following areas:
Scenario 1: T1 train operates in braking mode t = 48s; T2 train begins operating in
accelerating mode.
Speed profile of T1,T2 (m/s)

20
15
10

train 1
train 2

5
00

20

40

20

40

1000

60

80

100

120

140

160

80

100

120

140

160

DC-link voltage [V]

(V)

800
600
400
200
00

60

Time (s)

Fig. 4.5. Dynamic behavior of DC-link voltage when T1 braking and T2
accelerating
Energy loss of braking resistor of T1 without SCESS(Wh)
150

100

100

75
50
25

50
0
-50

Energy loss of braking resistor of T2 without SCESS(Wh)
125

0

20

40

60

80

100

120

140

160

Energy consumption of line source supplied T1 without SCESS (Wh)
4000
3000
2000
1000
00

20

40

60

80

Time(s)

100

120

140

160

0

0

20

40

60

80

100

120

140

160

Energy consumption of line source supplied T2 without SCESS (Wh)
2500
2000
1500
1000
500
0

0

20

40

60

80

100

120

140

160

Time(s)

Fig.4.6. Energy behaviors of T1 without Fig.4.7. Energy behaviors of T2 without
SCESS, when T1 braking and T2 SCESS, when T1 braking and T2
accelerating
accelerating
Fig.4.5, fig.4.6, fig.4.7 show voltage behavior of DC-link fluctuating from 700 to
900VDC, and energy loss of braking resistors of T1 and T2 is 4,3%.
Scenario 2: Both T1 and T2 operate in accelerating mode.
Fig. 4.8 shows that UDC-link fluctuates in the range of 490 VDC to 900 VDC compared
to the scenario 1. The loss on the braking resistor of T1 and T2 is: 450 (Wh) / 4700
(Wh) = 9.6% shown in Fig. 4.9, Fig.4.10.


19
Speed profile T1,T2 (m/s)

20

train 1

15

train 2

10
5

00

20

40

60

80

100

120

140

160

140

160

DC-link voltage [V]

1400
1200
1000
800
600
400

200
0

0

20

40

60

80

100

120

Time [s]

Fig.4.8. UDC-link behavior when T1 and T2 accelerating
600

Energy loss of braking resistor of T1 without SCESS(Wh)

500
400

450

300

300
150
0
-200
0

200
100

20

40

60

80

100

120

140

0
0

160

20

40

60

80

100

120

140

160

Energy consumption of line source supplied T2 without SCESS (Wh)

Energy consumption of line source supplied T1 without SCESS (Wh)

6000

6000

4500

4500
3000

3000

1500

1500
0
0

Energy loss of braking resistor of T2 without SCESS(Wh)

20

40

60

80

100

Time (s)

120

140

0
0

160

20

40

60

80

100

120

140

160

Time (s)

Fig. 4.9. Energy behavior of T1 when T1 Fig. 4.10. Energy behavior of T2 when T1
and T2 are in accelerating mode
and T2 are in accelerating mode
Scenario 3: T1, T2 operate together in accelerating mode, the tration drive system
integrated SCESS.
Fig.4.11 to Fig.4.13 show that U DC -link fluctuates in the range of 730 VDC to 770VDC,
the loss on the braking resistor 12 (Wh) / 2400 (Wh) = 0.05%. Thus, the regenerative
braking energy part during braking mode was recovered by supercapacitors up to 9.6%.
Speed profile T1,T2 (m/s)

20

train 1

train 2

15
10
5
0

0

20

40

60

80

100

120

140

160

120

140

160

DC-link voltage(V)

900
850
800
750
600
550
500
00

20

40

60

80

100

Time [s]

Fig. 4.11. UDC-link behavior when T1 and T2 accelerate and the train installs
SCESS


20
Energy loss of braking resistor of T2 with SCESS(Wh)

Energy loss of braking resistor of T1 with SCESS(Wh)
15

10

10

5

5

0

0
3000

0

20

40

60

80

100

120

140

160

Energy consumption of supply line supplied T1 with SCESS (Wh)

0

20

40

60

80

100

120

140

160

Energy consumption of supply line supplied T2 with SCESS (Wh)

3000
2000

2000

1000
1000

0
0

0

20

40

60

80

100

120

140

160

Time (s)

0

20

40

60

80

100

120

140

160

Time (s)

Fig. 4.12. Energy behavior of T1 when T1 Fig. 4.13. Energy behavior of T2 when
and T2 are in accelerating mode and T1 and T2 are in accelerating mode and
integrated with SCESS
integrated with SCESS
4.1.2. The optimal speed profile simulation program for train operation on Cat Linh
- Ha Dong line applied PMP with electric train system integrated SCESS on-board.
Cat Linh-Ha Dong urban electric train line has 12 stations (corresponding to 11 areas),
total length is 12.662 km, the train runs from the first station: Cat Linh, to the last
station: new Ha Dong bus station.
a) A survey the train operation energy when the train does not have SCESS
 A survey of energy consumption for running train from Cat Linh-La Thanh

Fig. 4.16. A comparison of optimal

speed profile with original speed
profile with/without PMP

Fig. 4.17. A comparison of
distance versus time

Fig. 4.19. A comparison of energy
consumption levels of train
operation with/without PMP
The survey of energy consumption for the next station is similar to the first station.
Fig.4.18. A comparison of speed versus time
with/without PMP


21

Fig. 4.60. A Comparison of optimal speed profile and original speed profile of 12 stations

Fig. 4.61. A Comparison of Optimal time profile and original time profile of 12 stations

Table 4.3 Results of a comparison of energy consumption with / without energy
optimization strategy PMP
Inter-station
length

Actual
Optimal
Distance Pratical energy trip

Optimal energy
trip
(m)
consumption
time consumption(kWh)
time (s)
(kWh)
(s)

Cat Linh-La
931
19.5
66
18.59
Thanh
La Thanh -Thai
902
10.94
79
9.7
Ha
Thai Ha-Lang
1076
10.5
95
9.8
Lang-VNU
1248
9.9
124

9.5
VNU- Ring road 3
1010
17.4
77
15.4
Ring road 31480
17.4
105
15
Thanh Xuan
Thanh Xuan-Ha
1121
17.6
86
15.7
Đong BS
Ha Đong BS -BV
1324
19.6
98
16.6
Ha Đong
BV Ha Đong -La
1110
17.8
83
15.7
Khe
La Khe-Van Khe

1428
18.2
103
15.7
Van Khe-new Ha
1032
17.4
72
15.5
Dong BS
Total: 12662
176.24
988
157.19
Total consumed energy when PMP is not applied: 176.24 kWh;

68
81
97
126
78
107
87
100
85
105
74
1010

22
Total consumed energy when PMP is applied: 157.19kWh; energy saving: 10.8%; But
the trip time lasts additionally 2 seconds.
b) Conducting a survey of energy consumption when electric trains integrate SCESS,
and ensure the fixed trip time by changing the Lagrange multiplier.
In this problem, consider a station, from Cat Linh - La Thanh station with a distance
of 931m, trip time 68s.
Total consumed energy when PMP is not applied: 19.5kWh.
Total consumed energy when PMP is applied: 18.57kWh (saving 4.6%)
Total consumed energy when applying PMP and having SCESS is 16.53 kWh (saving
15.2%), see Figure 4.66.

.
Fig.4.62. Discharge/charge power of supercapacitor energy storage system

Fig.4.63. A comparison of optimal

speed profile with original speed
profile

Fig. 4.65. A comparison of energy
consumption
levels
of
train
operation with/without PMP

Fig. 4.64. A comparison of speed versus
time

Fig.4.66. A comparison of energy
consumption levels of train operation
with/without PMP and onboard
supercapacitor energy storage system


23
Comment: Depending on modes of train operation, survey of train schedule, number
of passengers, infrastructure of the route ..., which selects appropriate energy saving
solutions.
4.2. Designing experimental model of SCESS
Designing the experimental model of electric train with SCESS is very expensive and
complicated, so the author only designs the Interleaved DC-DC converter with 3 switch
branches in the working modes: Buck (charge) - Boost (discharge) in order to verify
advantages of this converter.

Fig. 4.69. SCESS experimental system

Fig.4.71. PWM with d=0.625

Fig.7.42. Conductance coil currents cảm Fig.7.45. Conductance coil current with
d=0.33
with d=0.625
Conclusion chapter 4
Off-line simulations have demonstrated SCESS's role in saving energy for train
operation by recovering regenerative braking energy, and contributing to voltage
stability on the DC bus, the ability to apply optimal theory in saving energy. Theses
simulations create a premise for the application of solutions to use energy efficiency for
Vietnam urban railway trains in the coming time. The results of chapter 4 are presented
in the project [7,8,9] under the list of published works of the author.

24
CONCLUSIONS AND RECOMMENDATIONS
The thesis is the first research in Vietnam to address the issue of energy saving for
urban electric train operation. In this section, the author summarizes the new
contributions of the thesis as well as points out the next development direction of the
thesis.
Novelty contributions of the thesis
 To propose the use of SCESS on-board integrated with traction motor drive via
bidirectional DC-DC converter and design supercapacitor control according to
train running characteristics
 Applying the Pontryagin's maximum principle finds optimal transfer points of
operating modes, determining the optimal speed profile of trains intergrated
with SCESS on-board.
Recommendations and further research directions Some issues can be researched
further to complete the thesis
 Researching and combining supercapacitor energy storage device with high energy
density storage systems such as batterry, flywheel, ... to expand the capacity of
energy storage suitable for many different control strategies.
 Applying other control methods such as dynamic programing, weighting function
method with the multi-objective problem ... to determine the optimal speed
profile.
 Developing optimal control algorithm regulates many trains running on the route
 Optimal control of energy operation when the train goes on the routes with slope
changes.
 Optimal control of train operation when the speed profile vs time has S-curve
shapes in both acceleration and braking processes.