19th IMACS World Congress
San Lorenzo del Escorial (Spain) 26-30.08.2013
EVALUATION OF ELECTRIC TRACTION'S
ENERGY EFFICIENCY BY COMPUTER SIMULATION
Alexandre A. Zarifian 1, Pavel G. Kolpahchyan 1, Vyacheslav Kh. Pshihopov 2,
Mikhail Yu. Medvedev 2, Nikolay V. Grebennikov 1, Vitaliy V. Zak 3
Rostov State Transport University
2 South Federal University
3 All-Russian Research and Development Institute of Electric Locomotive Building
1
Russian Federation
Contents
1. Introduction.
2. Statement of the optimal control problem.
3. Electronic map of the railway.
4. Traction electrosupply system.
5. Electric rolling stock.
6. Control System Design.
7. The complex computer model.
8. Conclusion.
Abstract
The basic problems related to the evaluation of electric traction’s energy efficiency by the means
of computer simulation, are studied. The goal to minimize the train power consumption for rail road section
is formulated. It is shown how were taken into account the plan and profile of rail way, the traction power
supply system, the design of electric locomotive, the composition of train, the driver’s actions (or automatic
control system's operation).
Keywords
Electric traction, energy efficiency, control system, computer simulation.
1. Introduction
Evaluation of the electric traction’s energy efficiency in various driving conditions of railway trains is a very
complicated problem. Indeed, should be taken into account the following essential factors.
First of all, we need to take into consideration the plan and profile of railway section where the train moves.
Interaction "wheel - rail" and, consequently, the resistance to movement, are particularly intense in
mountain areas. Among them is, for example, the section Belorechenskaya (Goriachiy Klyuch) – Tuapse – Adler
of the North-Caucasian railway, which length is about 290 km, built in the early XX century. The length of the
curves is about 50% of the total length, including a significant number of curves of radius less than 350 m. The
gradients ratio can exceed 20‰.
2
Type of traction power supply (DC or AC) is essential. The mentioned mountain section is electrified with DC.
The electric locomotive is a controlled electro-mechanical system, which is the consumer of electricity from
the traction power substation. Constructions of electric locomotives become more complex. Electric locomotives
of previous generation have the contactor-rheostat control of traction motors. They are replacing by new ones
equipped by microprocessor systems of control and diagnostics. In the long term, the locomotives with
asynchronous traction drive (ATD) will operate at the railways. A freight train, in particular, may have
a significant weight and length which should be taken into account in the most detailed manner.
In improving the traction’s energy efficiency, the locomotive control plays the most important role.
Electricity consumption is highly dependent from the driver’s action, especially for electric locomotives with
manual contactor-rheostat control. For modern locomotives, the main role is played here by control algorithms
built into the onboard computer.
This leads to the problem of minimizing the energy consumption, where the optimality criterion is the power
consumption, and the unknown quantities are the control actions that gives him the minimum.
The test trips, realized with the use of traction-power wagon-laboratories, enable us to confirm the adequacy
of the simulation results, to refine the coefficients in empirical formulas and thus create the basis of traction
calculations.
To illustrate the picture of the processes that take place in the traction mode, we begin with an example.
Fig. 1 shows the record of the freight DC locomotive's operating parameters when moving from the
station Tverskaya in the direction to the station Komsomolskaya of the North-Caucasian railway.
Weight of the train is 3829 tons. Recording of parameters was performed by the traction-power
wagon-laboratory.
3
Fig. 1. Operating parameters of the freight DC locomotive
4
The Tverskaya station (1785 km) is located at the height of 118,45 m; next is the climb up to the fracture of
longitudinal profile at the height of 141,33 meters (1781,3 km); the lowest point of low lying ground is
at the height of 140,93 m (1781 km); next fracture is located at the height of 149,35 meters (1779,9 km);
further low lying ground 148,8 m (1779,8 km) and climb to the height of 169,44 m (1777 km).
The driver’s control action is to select the position of the locomotive's controller (LC), which leads
to the change of traction motor's regime, and thus directly affect the energy consumption. As can be seen
from Fig. 1, the work is done in series (C) and group (СП) connections of traction motors (brown line)
The catenary voltage Uкс (red line) abruptly changes when switching the circuit connections, which is realized
by driver at the fractures of longitudinal profile, but does not drop below the minimum values Uксmin = 2700 V.
We note that the instantaneous catenary voltage Uкс differs from the standard value of 3 kV and is formed
by interaction of the traction substation and the consumer (electric locomotive).
Current Iтэд (green line) consumed by one traction motor, varies from 120 to 680 A, which exceeds the current
of "one-hour" regime Iчас = 480 A.
Driving speed V (blue line) does not exceed 40 km/h at rated speed Vр = 46,7 km/h.
The tangential traction force Fк (violet line) is significantly changed at switching the traction motors connection,
which negatively affects the longitudinal dynamics of the train.
The temperature T of traction motors (yellow line) increases from 35 to 115ºC.
Consequently, the basic parameters of the electric locomotive's operation, that determine
its energy consumption, is continuously changing. Operating modes of train's driving are extremely
diverse.
For this reason, to evaluate the electric traction's energy efficiency, is necessary to create the complex computer
model that enables to consider the interaction of those main factors:
- rail way macrogeometry (plan and profile),
- system of traction power supply,
- design of electric locomotive,
- train configuration (electric locomotive and wagons),
- driver's actions (or automatic control system's operation).
The objective of this paper is the successive consideration of the main constituent elements
of the computer model, intended to obtain the preliminary estimates of electric traction's
energy efficiency.
The data obtained during the experimental rail trips will confirm the adequacy of the results.
6
2. Statement of the optimal control problem. We now proceed to the formulation of the minimizing energy
consumption problem for train operation.
First of all, we formulate the constraints.
а) Traffic schedule must be respected, that is, the time from station A to station B is set:
ΔtAB = tB – tA = const.
b) The values of velocity and acceleration during train movement must not exceed the permissible values,
as dictated by the requirements of traffic safety:
V  V ,
a  a .
Under these constraints, the energy consumption ЕАВ when moving from station A to station B should be minimal:
t
(1)
B
E AB   Pdt  min ,
tA
where Р – power consumed by electric locomotive, which is equal (for traction DC network) to the product
of the instantaneous voltage Uкс and the current consumed by electric locomotive Iкс :
P  U кс I кс
This power is limited by the value of construction power,
P  P ,
while the main part of the total consumed power is spent on train traction, and another, smaller part –
on the own needs:
PP P .
тяг
собст
As a result, we come to Lagrange problem (1), where the optimality criterion when train moving
from station A to station B, is the energy consumption – an integral functional of the form
tB
E AB   Pdt ,
tA
with constraints (a), (b), and the unknown quantities are controlling actions that deliver him the minimum value.
If for any reason will unplanned stop en route, the calculation of energo-optimal control variant should be
7
operatively carried out for the rest of the way AB.
3. Electronic map of the railway. As was noted above, the mountain railway sections have the significant
number of tight curves and the steep climbs and descents.
The railway's plan and profile of one of the mountain sections of the North-Caucasian railway is shown
on Fig. 2. Here are the curves of radius 240 m, the slopes reach 21,3‰.
Fig. 2. Plan (top) and profile (bottom) of a mountain railway section
8
The Way and Structure Departement has full information about the longitudinal profile of the railway (lengths
of sections, vertical heights, slopes), about the plan (radii, angles), etc.
Taking into account the actual geometry (size parameters) of rail track, it is necessary to build an electronic map
of the railway section, wherein all the necessary characteristics of a rail track will be expressed as a function
of the current coordinate s. This is done in [1], a similar approach was used in the software package UM-Loco [2].
3.1. The axis of the straight rail road section.
The curvature is constant, k(s) = 0 (Fig. 3),
C ( s)  0
xC ( s )  ( s  s0 )cos 0  x0
yC ( s )  ( s  s0 )sin 0  y0
where , lПР – the length of section.
y
,
,
,
(2)
(3)
(4)
С
Fig. 3. Axis of the straight rail road section
0
(x0, y0)
0
x
[1]. Грицык, В.И. Построение электронной карты пути / В.И. Грицык, А.А. Зарифьян, Д.А. Лысенко //
Вестник РГУПС. – 2007. – №1. – С. 120-128.
[2]. www.umlab.ru
9
3.2. The axis of the entrance track transition curve (Euler spiral – clothoid)
The curvature varies linearly from 0 to ±1/ RK at a distance
(Fig. 4):
lП
k (s) 
d C
s  s0
s  s0


ds
RK l П
Q
 C (s)  
( s  s0 ) 2
 0
2Q
 ( s  s0 ) 4 ( s  s0 ) 8

xC ( s )  x0  ( s  s0 ) 1 

 ...  cos 0 
2
4
40Q
3456Q


3
4
8

( s  s0 )  ( s  s0 )
( s  s0 )


 ...  sin 0 ;
1 
2
4
6Q 
56Q
7040Q

 ( s  s0 ) 4 ( s  s0 ) 8

yC ( s )  y 0  ( s  s0 ) 1 

 ...  sin 0 
2
4
40Q
3456Q



( s  s0 ) 3  ( s  s0 ) 4 ( s  s0 ) 8


 ...  cos 0 .
1 
2
4
6Q 
56Q
7040Q

where s0  s  s0  l
П
, Q = RK lП.
Fig. 4. Axis of the entrance track transition curve
(5)
(6)
(7)
(8)
3.3. The axis of the curve of constant radius RK
The curvature is constant (Fig. 5), k (s)   1
RK
 C (s)  
s  s0
 0
RK
  s  s0


xC ( s )  RK sin  
  0   sin 0   x0
  RK




 s  s0

yC ( s )  RK   cos 
  0   cos 0   y 0
 RK



where
s0  s  s0  lK
Fig. 5. Axis of the curve of constant radius RK (+ left curve, – right curve)
(RK = 500 m, x0 = 100 m, y0 = –100 m, φ0 = π/6 )
(9)
(10)
(11)
3.4. The axis of the exit track transition curve
to 0 at a distance lП,
The curvature varies linearly from ± 1 RK
d C ,
l П  ( s  s0 )
s  ( s0  l П )
k (s) 
П
where Q = RK lП ,
.
ds

0
0
Q

П
l
s0  s Пs0  l
s0  s0  l ,   
2 RK
~
 C (s)   0 
(12)
Q
~
0  0 
lП
2 RK
~
( s  s0 ) 2
2Q
(13)
~
~

~  ( s  s0 ) 4 ( s  s0 ) 8
~
xC ( s )  x0  ( s  s0 ) 1 

 ...  cos 0 
2
4
40Q
3456Q


~ 3
~ 4
~ 8

( s  s0 )  ( s  s0 )
( s  s0 )
~


 ...  sin 0 
1 
2
4
6Q 
56Q
7040Q

4
8


lП
lП
~
 l П  1 


...
  cos 0 
2
4
3456Q
 40Q


3
4
8

lП 
lП
lП
~

 ...  sin 0 ;
1 
2
4
6Q  56Q
7040Q

(14)
~ 4
~

( s  s0 )8
~
~  ( s  s0 )
yC ( s )  y0  ( s  s0 ) 1 

 ... ,sin 0 
2
4
40
Q
3456
Q


~ 3
~ 4
~ 8

( s  s0 )
( s  s0 )
( s  s0 )
~


 ...  cos 0 
1 
2
4
6Q 
56Q
7040Q



l 4
lП 8
~
 lП  1  П 2 
 ...  sin 0 
4
3456Q
 40Q



lП 3 
l 4
lП 8
~
 ...  cos 0 .
1  П 2 
4
6Q  56Q
7040Q

Plan of a track section, constructed by the above formulas, is shown in Fig. 6.
(15)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0
1400
x,м
-100
К ри вая № 1
,м
y
1300
П ереходн ы е
к ри вы е
-200
П рям ы е
-300
Fig. 6. Plan of a track section
К ри вая № 2
,
3.5. Vertical longitudinal profile
Slope
i  tg 
h
l
0
00
Vertical coordinate
zC ( s )  z0  ( s  s0 )sin
sin  tg  
z C ( s )  z 0  ( s  s0 )  
Example of vertical longitudinal profile (Fig. 7).
The proposed method allows to realize the spatial-coordinate positioning of the locomotive in the function of its
position on the rail road, which is determined by the arc coordinate s = s (t), and that is a sufficient basis for the
creation of the electronic rail road map.
9
8
Высота z, м
7
6
5
4
3
2
1
0
200
400
600
800
1000
1200
Координата S в проекции на плоскость Oxy, м
Fig. 7. Vertical longitudinal profile of a track section
1400
4. Traction electrosupply system. The system includes traction substations (TS) and sections
of traction network (contact network and track circuits).
Fig. 8 shows the schemes of the traction power supply system’s components.
The structure of the AC TS model (Fig. 8a) include: EMF of transformer's secondary winding, its active resistance,
inductance of the transformer and of the power supply system (respectively Eтп, Rтп, Lтп).
Also is take into account the presence of cross-device (Rпк, Lпк, Cпк) and longitudinal (Cпрк) compensation of the
adjacent section of traction network (Rкс0, Lкс0, Rр0).
Model DC TP (Fig. 8b) includes: transformer, rectifier and reactor-filtering equipment. Indications:
EА, EВ, EС – EMF of the transformer's secondary windings, Rтp – their active resistance, Lтр – leakage inductance
of the transformer's secondary windings, and given to them inductance of the primary winding and of the power line,
Rр1, Lр1, Rр2, Lр2 – inductances and active resistances of reactors, Сф1 – Сф5, Lф1 - Lф5 – capacitances and
inductances of harmonic rejection filters.
The calculation schemes of the AC and DC traction networks (Fig. 8c) are similar and differ only in the parameters.
The structure of the traction network’s model includes: resistance, inductance and capacitance of the contact system
(Rкс, Lкс, Cкс), the track circuit resistance (Rр), the resistance of current spreading in the ground (Rз).
The distance between the DC traction substations is an average of 15-20 km, AC – up to 50 km.
The processes in the electrical circuit are described by the system differentially-algebraic equations based
on Kirchhoff's laws.
а)
b)
c)
Fig. 8. Calculation schemes of the traction power supply's elements :
AC TS (a); DC TS (b) and traction network's section (c)
5. Electric rolling stock. In the recent times, several types of electric locomotives were operated in mountain
areas of the North-Caucasian railway.
The freight DC electric locomotive VL10 has a classic design.
It has the axial formula 2(Bo-Bo), mechanical traction drive class I,
traction and braking forces are transmitted from the bogie frames to
the frame body through the king pivot nodes. Traction motors are
sequential excitation.
Power control of the electric locomotive VL10 is due to:
1) Stepwise regulation of voltage applied to the traction
motors (TM). For this purpose were applied the three regroupings of
TM (series, series-parallel and parallel).
2) Connection of the additional resistances (rheostats) in the
anchor chain.
3) Changes of the magnetic field flux through the shunting of
the main poles.
These three way of power control (traction force and speed)
are classical (contactor-rheostat manual control).
The new cargo-passenger DC electric locomotive 2ES4K
has the axial formula 2(Bo-Bo) and mechanical traction drive of
I class. The traction and braking forces are transmitted from the
bogie frames to the body frame by means of the inclined traction
rods.
In traction mode, the electric circuit provides the TM’s
operation with sequential and independent excitations. The
speed control of electric locomotive is performed stepwise with
three regroupings of traction motors: series, series-parallel and
parallel connections.
The locomotive is equipped with a microprocessor control
system, which provides manual and automatic traffic control, the
automatic driving modes of train; the diagnostics of electric
equipment and of motion parameters.
The two-system (AC/DC) electric locomotives EP10 and
EP20, equipped with asynchronous traction drive, are designed to
drive the passenger trains. The axial capacity is of 1200 kW, the
axial formula Bo-Bo-Bo. The traction and braking forces are
transmitted from the bogie frames to the body frame by means of
the inclined traction rods.
The EP10 has a mechanical traction drive of class II
(supporting-bogie engine and supporting-axis gearbox), the
maximum speed is 160 km/h.
The EP20 has a mechanical traction drive of class III
(supporting-bogie engine and supporting-bogie gearbox), the
maximum speed is 200 km/h.
The EP10 and EP20 locomotives are equipped with a
microprocessor control system, which provides manual and
automatic traffic control, the automatic driving modes of train;
the diagnostics of electric equipment and of motion parameters.
[3]. Pshikhopov, V.Kh., Medvedev, M.Yu. Robust control of nonlinear dynamic systems. 2010 IEEE
ANDESCON Conference Proceedings, ANDESCON 2010, art. no. 5633481.
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2012. SAE Technical Papers 5.
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pp. 540-545.
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CD-ROM ISBN 3-9522075-1-9.
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[10]. Kalker, J.J. Three-Dimensional Elastic Bodies in Rolling Contact. – Kluwer Academic Publishers.
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дорог / А.Л. Быкадоров, А.В. Жуков // Вестник РГУПС. – 2010. – №4. – С.98-102.
Thank you for your attention!
Merci beaucoup pour votre attention
Contacts: Alexandre A. Zarifian,
professor of Rostov State Transport University
E-mail: zarifian_aa@mail.ru
Tel.: +7 989 6254899
Russian Federation