Determination of railway rolling stock optimal movement modes
Purpose. To develop a methodology for simulating of an electromotive railway rolling stock in terms of power-optimal modes on a track with a given profile and a set motion graph. Methodology. We have used combined genetic algorithm to determine optimum modes of an electromotive railway rolling sto...
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| Опубліковано в: : | Електротехніка і електромеханіка |
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| Дата: | 2017 |
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| Мова: | Англійська |
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Інститут технічних проблем магнетизму НАН України
2017
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| Цитувати: | Determination of railway rolling stock optimal movement modes / O. Petrenko, B. Liubarskiy, V. Pliugin // Електротехніка і електромеханіка. — 2017. — № 6. — С. 27-31. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859798026994843648 |
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| author | Petrenko, O. Liubarskiy, B. Pliugin, V. |
| author_facet | Petrenko, O. Liubarskiy, B. Pliugin, V. |
| citation_txt | Determination of railway rolling stock optimal movement modes / O. Petrenko, B. Liubarskiy, V. Pliugin // Електротехніка і електромеханіка. — 2017. — № 6. — С. 27-31. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Електротехніка і електромеханіка |
| description | Purpose. To develop a methodology for simulating of an electromotive railway rolling stock in terms of power-optimal modes on a
track with a given profile and a set motion graph. Methodology. We have used combined genetic algorithm to determine optimum
modes of an electromotive railway rolling stock motion: a global search is performed by a genetic algorithm with a one-point
crossover and roulette selection. At the final stage of the optimization procedure we have used Nelder-Mead method for the
refinement of the optimum. Results. We have obtained that traction motor on a tramcar, while driving on a fixed site, has an
excessive power of the cooling system. Its using only in the considered area allows to modernize the cooling system in the way of
its power reducing, which in turn provides an opportunity to increase the overall efficiency of the electromotive railway rolling
stock. Originality. For the first time, we have obtained the train motion equation in the program-oriented form. This allows to use
it for determination of electromotive railway rolling stock optimal control laws according to the Hamilton-Jacobi-Bellman
method. Practical value. We have made the computer program to determine optimum modes of an electromotive railway rolling
stock motion. The experimental studies of program results for the track section have confirmed the adequacy of the model, which
allows to solve the traffic modes optimization problem for the tram track sections and increase the overall efficiency of the
electromotive railway rolling stock.
Разработана методика моделирования движения асинхронного тягового двигателя при движении
электроподвижного состава по энергооптимальным режимам на участке пути с заданным профилем и
установленным графиком движения. Определены оптимальные режимы движения электроподвижного состава
на основе метода Гамильтона-Якоби-Беллмана. Определение режимов работы тягового привода предложено
проводить заранее на основании решения задачи условной оптимизации его режимов. Определение оптимальных
режимов работы тягового привода было проведено на основе комбинированных методов условной минимизации
функции. Использование предлагаемой методики позволяет повысить общий КПД электроподвижного состава.
|
| first_indexed | 2025-12-02T14:19:08Z |
| format | Article |
| fulltext |
Електротехнічні комплекси та системи. Силова електроніка
ISSN 2074-272X. Електротехніка і Електромеханіка. 2017. №6 27
© O. Petrenko, B. Liubarskiy, V. Pliugin
UDC 629.429.3:621.313 doi: 10.20998/2074-272X.2017.6.04
O. Petrenko, B. Liubarskiy, V. Pliugin
DETERMINATION OF RAILWAY ROLLING STOCK OPTIMAL MOVEMENT MODES
Purpose. To develop a methodology for simulating of an electromotive railway rolling stock in terms of power-optimal modes on a
track with a given profile and a set motion graph. Methodology. We have used combined genetic algorithm to determine optimum
modes of an electromotive railway rolling stock motion: a global search is performed by a genetic algorithm with a one-point
crossover and roulette selection. At the final stage of the optimization procedure we have used Nelder-Mead method for the
refinement of the optimum. Results. We have obtained that traction motor on a tramcar, while driving on a fixed site, has an
excessive power of the cooling system. Its using only in the considered area allows to modernize the cooling system in the way of
its power reducing, which in turn provides an opportunity to increase the overall efficiency of the electromotive railway rolling
stock. Originality. For the first time, we have obtained the train motion equation in the program-oriented form. This allows to use
it for determination of electromotive railway rolling stock optimal control laws according to the Hamilton-Jacobi-Bellman
method. Practical value. We have made the computer program to determine optimum modes of an electromotive railway rolling
stock motion. The experimental studies of program results for the track section have confirmed the adequacy of the model, which
allows to solve the traffic modes optimization problem for the tram track sections and increase the overall efficiency of the
electromotive railway rolling stock. References 19, figures 3.
Key words: electromotive railway rolling stock, genetic algorithm, cooling system, traction motor, tramcar, control laws,
optimization problem, efficiency.
Разработана методика моделирования движения асинхронного тягового двигателя при движении
электроподвижного состава по энергооптимальным режимам на участке пути с заданным профилем и
установленным графиком движения. Определены оптимальные режимы движения электроподвижного состава
на основе метода Гамильтона-Якоби-Беллмана. Определение режимов работы тягового привода предложено
проводить заранее на основании решения задачи условной оптимизации его режимов. Определение оптимальных
режимов работы тягового привода было проведено на основе комбинированных методов условной минимизации
функции. Использование предлагаемой методики позволяет повысить общий КПД электроподвижного состава.
Библ. 19, рис. 3.
Ключевые слова: электроподвижной состав, генетический алгоритм, система охлаждения, тяговый двигатель, вагон
трамвая, законы управления, проблема оптимизации, коэффициент полезного действия.
Introduction. The processes of energy conversion
in traction electromechanical converters (traction motors)
relate to constant losses in different elements of its
construction. The most of power loss are caused by
physical processes of energy conversion [1-5]. The
temperature of the traction motors design parts increases
with the operating time and may exceed the permissible
design limitations. This is especially true for the windings
insulation temperature, which is limited to the thermal
class of applied insulation [2-5]. To reduce the
temperature on traction motors, cooling systems that
increase the efficiency of the heat transfer of the motor
construction components are used.
However, cooling systems need additional costs for
their efficient work, which in turn reduces the efficiency
of the electric vehicle in general. Thus, the creation of an
efficient cooling system for electromotive vehicles is one
of the most important scientific and technical problems
solved by many leading scientists in the field of railway
transport [1-5].
The following ways are possible to solve this
problem: reduction of losses in the elements of traction
motors design and increase of efficiency of the cooling
system. Optimization of traction motors designing
processes, which is common in most enterprises of
leading electrotechnical manufacturers, allows to create
traction motors optimal by their efficiency [1].
However, the modes of their operation on the
electromotive railway rolling stock (ERRS), which moves
at different speeds and under different load conditions,
significantly reduce its overall efficiency [1, 6-12].
Determination of optimal motion modes by energy
consumption criteria can improve the efficiency of the
cooling system of traction motors [1, 6-12].
The paper considers the solution of this problem for
the most common motors in production now – an
asynchronous traction motors (ATM) on the base of
Hamilton-Jacobi-Bellman method.
The aim of the paper to improve the methodology
of an electromotive railway rolling stock simulation in
terms of power-optimal modes on a track with a given
profile and a set motion graph.
The task of optimizing of the traction drive
modes. The basic states of the simulation method for the
electromotive rolling stock in terms of power-optimum
modes at the track with a given profile and a fixed motion
graph and initial developments were described in papers
[17, 18]. In this paper we present the results of further
authors researches that were begun in previous works.
The determination of the ATM-SVI circuit
efficiency based on the approaches proposed in the works
[1, 13] is carried out, which include the following: to
solve the problem of determining the optimal modes of
the traction drive, four problems of the conditional
optimization of the parameters of the traction drive must
be solved (in acceleration modes Uop = 1, regenerative
braking mode Uop = 5, maintaining mode of a given
movement speed Uop = 2.3).
The efficiency of the traction drive in a certain mode
of its work will be evaluated according to the criterion of
maximum of its efficiency, subject to compliance with the
requirements imposed by the operation modes.
28 ISSN 2074-272X. Електротехніка і Електромеханіка. 2017. №6
Therefore, the task of determining the efficiency of
the traction drive is to find the extremum of the drive
factor function.
The efficiency of the traction drive (Fig. 1) can be
given under the next equation:
0
,
min,
max,
;5
;
0
,
max,
;3
0
,
max,
;2
;
0
,
max,
max,
;1
max
1
max
1
max
1
max
1
1
d
kd
d
op
d
kd
op
d
kd
op
d
kd
d
op
F
vv
FF
F
U
F
vv
FF
U
F
vv
FF
U
F
vv
FF
F
U
(1)
where 1 – efficiency of the asynchronous traction motor
(ATM) circuit – standalone voltage inverter (SVI), Uop –
the operation mode of an electromotive railway rolling
stock (ERRS), Fd – traction or braking force created by
ERRS, kF – limitation for engagement force of wheel-
rail contact, – railway rolling stock speed, max –
constructive movement speed. Uop = 4 – outburst mode is
an idle mode, so it is not considered in determining of
drive efficiency.
For each of these tasks, it is necessary to consider
two modes: the use of single-time or spatial-vector pulse-
width modulation (PWM). The mode of acceleration and
regenerative braking are similar. Apply the method of
vector objective functions proposed in [1, 14]. As a target
function for the acceleration mode, we select a vector
function with the next parameters:
min,
min,1 1
1
d
c F
F
. (2)
The first component is chosen in such way that when
it is minimized, the maximization of the efficiency of the
traction drive can be obtained.
For regenerative braking mode, the vector target
function has the form:
min,
min,1 1
5
d
c F
F
. (3)
For a given speed maintaining mode we select as a
target function:
min1 143 cc FF . (4)
The value of losses, and hence the efficiency of the
drive, can be determined based on the slip of the traction
motor, the motor voltage (phase or line) and the rotation
speed. Because the operating modes are determined for all
motion speeds (ATD rotation speeds), the rotation speed
is a predetermined constant given in solving problem of
finding the optimal traction drive operation mode.
Thus, the target functions to determine the traction
drive optimal operating modes were chosen, which allow
to find the optimal traction drive modes when different
PWM modes are using.
The general formulation of an optimal control in real
time in [13] is described.
Software-oriented model of the ERRS motion. As
an optimization method, a combined genetic algorithm
was chosen: a global search is performed by a genetic
algorithm with a one-point crossover and roulette
selection. At the final stage of the optimization procedure,
the refinement of the optimum by the Nelder-Mead
method is carried out [1, 13-19].
Let us consider the representation of the train motion
equation in the program-oriented form, which will allow
to use it for determination of the optimal control laws
according to the Hamilton-Jacobi-Bellman method.
In this paper, the forces and supports are calculated
as follows:
Acceleration force FA (for one time step)
tstep
tsteptvtv
mFA
)()(
, (5)
where m – train weight, a conjunction;
tstep
tsteptvtv
a
)()(
, (6)
where a – the equivalent constant acceleration, which is
subjected to a train at a speed difference (t) – (t – tstep)
in one time step, due to the assumption that for each time
step the acceleration is constant and the speed is linearly
dependent on the time for each time step.
The main resistance to rolling Frr (for one time step).
Since the velocity is linearly dependent on the time
for each transition (time step), the rolling resistance for
each time step can be calculated according to the average
speed step and is equal to:
2
)()( tsteptvtv
vavg
. (7)
Thus, the main motion resistance for each time step
will be:
2
avgavgrrrr vcvbaF , (8)
where arr, b, c – coefficients which for the tram car T-3
VPA with a full load 30000 kg have the following values:
1500 N, 0 N·c/m, and 1.5 N·c2/m accordingly.
As a result, the force for ERRS moving on tstep:
rksrrAtot FFFFF )1( . (9)
where Fs, Frk – resistance forces from the slopes and
curves determined by the following equations:
1000
i
gmFs , (10)
m
cR
c
F
r
r
rk
1
0
, (11)
where cr0, cr1– constants, determined by [15]; R – radius
of the curve, i – slope, g – gravitational acceleration.
The required energy for movement on tstep,
considering the limitations and the assumption that the
velocity changes linearly over time, using [15] is listed
below.
ISSN 2074-272X. Електротехніка і Електромеханіка. 2017. №6 29
For the time step from the state n–1 to the state n,
from the equation of equally accelerated motion, the
traveled distance can be obtained by equations (13).
100081.9
1000
)1(
2
)()(
1000
)1(
1
02
1
02
1
mk
i
mgm
cR
c
vc
vbaF
tstep
tsteptvtv
i
mg
m
cR
c
vc
vb
aF
sign
E
s
r
r
avg
avgrrA
T
tstept r
r
avg
avg
rrA
sign
(12)
where sk – the coefficient of clutch, which for the tram
is 0.16, avgv – average speed per step.
nnnnn tatvx 2
1
1 ,
21
1 2
1
n
n
nn
nnn t
t
vv
tvx
nnnnnnn tvtvtvx 11 2
1
2
1
(13)
nnnnn
nnnn
tvvxx
tvvx
11
1
2
1
2
1
nnnnn tvvxx 11 2
1
.
where xn, n, an – position of the train, its speed and
acceleration at n step.
For one hour step we have:
tstepvvxx ttstepttsteptt 2
1
, (14)
where xt – final position of the train for one tstep;
xt–tstep – the initial position of the train for one tstep.
Fig. 1. The typical scheme of traction drive
Expression (14) gives the final position of the train
for transfer, when the initial position, the initial and final
velocities are known, as well as the value of the time step.
Thus, the resulting equations (12 – 14) allow to
improve the simulation method of the electromotive
rolling stock in terms of energy optimum modes.
The solution of the traffic modes optimization
problem for the track section from the tram depot
«Saltovske» to the turning circle of 602 district in
Kharkiv and in the reverse direction was carried out. The
results of solving the traction problem with tram traffic in
optimal mode on Fig. 2 are shown. According to the
results of solving the traction problem, the losses in the
elements of the traction motor design on Fig. 3 are shown.
By means of a comparative analysis of
experimentally determined and computing traction
characteristics and efficiency values, the adequacy of the
proposed mathematical model for the drive efficiency
determination of the was established.
The maximum deviation in the calculation of losses
is 7.42 %, which is quite acceptable for the carried-out
calculations.
30 ISSN 2074-272X. Електротехніка і Електромеханіка. 2017. №6
Fig. 2. The solution results of the traction movement task for the tramcar T-3VPA with traction motor AD931 on the track section
from the tram depot «Saltovske» to the turning circle of 602 district in Kharkiv and in the reverse direction:
1 – movement speed (), km/h ; 2 – speed limitation , km/h; 3 – traction force, (Frr) kN; 4 – movement time (t), min, 5 – losses (Е), kWh
Fig. 3. Loses in traction motor: 1 – core loss Р1, W; 2 – rotor loss Р2, W; 3 – copper losses in stator winding at a slot part Р3, W;
4 – copper losses in stator winding at a front part Р4, W; 5 – mechanical losses Р5, W
ISSN 2074-272X. Електротехніка і Електромеханіка. 2017. №6 31
Conclusions.
1. Using the genetic algorithm and the Yakobi-
Hamilton-Belman method the calculated ratios for the
determination of the railway electromotive traction drive
efficiency are obtained. On this base the methodology of
ATM motion simulation during the movement of the
electromotive rolling stock according to the power-
optimal regimes on the track section with the given graph
and the set motion schedule is improved.
2. The adequacy of the obtained equations, which
determine the efficiency both the maximum efficiency
value of the ATM-SVI circuit in different operating
modes under the coupling constraints, and constructive
speed, is confirmed by the results of the experiment on
the section of the tramway from the depot «Saltovske» to
the turning circle of 602 district in Kharkiv. The
maximum deviation in the calculation of losses does not
exceed 7.42 %.
3. According to the results of solved traction problem,
the change in losses in the elements of the traction tram
traction design was first determined.
4. The use of advanced methodology is proposed to be
carried out in advance based on solving the problem of
work modes conditional optimization.
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Received 01.10.2017
O. Petrenko1, Candidate of Technical Sciences, Associate
Professor,
B. Liubarskiy2, Doctor of Technical Sciences, Professor,
V. Pliugin1, Doctor of Technical Sciences, Professor,
1 O.M. Beketov National University of Urban Economy
in Kharkiv,
17, Marshal Bazhanov Str., Kharkiv, 61002, Ukraine,
e-mail: petersanya1972@gmail.com
2 National Technical University «Kharkiv Polytechnic Institute»,
2, Kyrpychova Str., Kharkiv, 61002, Ukraine.
|
| id | nasplib_isofts_kiev_ua-123456789-147607 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2074-272X |
| language | English |
| last_indexed | 2025-12-02T14:19:08Z |
| publishDate | 2017 |
| publisher | Інститут технічних проблем магнетизму НАН України |
| record_format | dspace |
| spelling | Petrenko, O. Liubarskiy, B. Pliugin, V. 2019-02-15T10:40:58Z 2019-02-15T10:40:58Z 2017 Determination of railway rolling stock optimal movement modes / O. Petrenko, B. Liubarskiy, V. Pliugin // Електротехніка і електромеханіка. — 2017. — № 6. — С. 27-31. — Бібліогр.: 19 назв. — англ. 2074-272X DOI: https://doi.org/10.20998/2074-272X.2017.6.04 https://nasplib.isofts.kiev.ua/handle/123456789/147607 629.429.3:621.313 Purpose. To develop a methodology for simulating of an electromotive railway rolling stock in terms of power-optimal modes on a track with a given profile and a set motion graph. Methodology. We have used combined genetic algorithm to determine optimum modes of an electromotive railway rolling stock motion: a global search is performed by a genetic algorithm with a one-point crossover and roulette selection. At the final stage of the optimization procedure we have used Nelder-Mead method for the refinement of the optimum. Results. We have obtained that traction motor on a tramcar, while driving on a fixed site, has an excessive power of the cooling system. Its using only in the considered area allows to modernize the cooling system in the way of its power reducing, which in turn provides an opportunity to increase the overall efficiency of the electromotive railway rolling stock. Originality. For the first time, we have obtained the train motion equation in the program-oriented form. This allows to use it for determination of electromotive railway rolling stock optimal control laws according to the Hamilton-Jacobi-Bellman method. Practical value. We have made the computer program to determine optimum modes of an electromotive railway rolling stock motion. The experimental studies of program results for the track section have confirmed the adequacy of the model, which allows to solve the traffic modes optimization problem for the tram track sections and increase the overall efficiency of the electromotive railway rolling stock. Разработана методика моделирования движения асинхронного тягового двигателя при движении электроподвижного состава по энергооптимальным режимам на участке пути с заданным профилем и установленным графиком движения. Определены оптимальные режимы движения электроподвижного состава на основе метода Гамильтона-Якоби-Беллмана. Определение режимов работы тягового привода предложено проводить заранее на основании решения задачи условной оптимизации его режимов. Определение оптимальных режимов работы тягового привода было проведено на основе комбинированных методов условной минимизации функции. Использование предлагаемой методики позволяет повысить общий КПД электроподвижного состава. en Інститут технічних проблем магнетизму НАН України Електротехніка і електромеханіка Електротехнічні комплекси та системи. Силова електроніка Determination of railway rolling stock optimal movement modes Article published earlier |
| spellingShingle | Determination of railway rolling stock optimal movement modes Petrenko, O. Liubarskiy, B. Pliugin, V. Електротехнічні комплекси та системи. Силова електроніка |
| title | Determination of railway rolling stock optimal movement modes |
| title_full | Determination of railway rolling stock optimal movement modes |
| title_fullStr | Determination of railway rolling stock optimal movement modes |
| title_full_unstemmed | Determination of railway rolling stock optimal movement modes |
| title_short | Determination of railway rolling stock optimal movement modes |
| title_sort | determination of railway rolling stock optimal movement modes |
| topic | Електротехнічні комплекси та системи. Силова електроніка |
| topic_facet | Електротехнічні комплекси та системи. Силова електроніка |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147607 |
| work_keys_str_mv | AT petrenkoo determinationofrailwayrollingstockoptimalmovementmodes AT liubarskiyb determinationofrailwayrollingstockoptimalmovementmodes AT pliuginv determinationofrailwayrollingstockoptimalmovementmodes |