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Static Model of a 2x25kV AC Traction System

Conference Paper · December 2015

DOI: 10.1109/PESA.2015.7398917

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 Static Model of a 2x25kV AC Traction System

Mariia Plakhova, Bassam Mohamed and Pablo Arboleya

Department of Electrical Engineering
University of Oviedo
Gijón, Spain
Email: mariiaplakhova@gmail.com, engbassam@gmail.com, arboleyapablo@uniovi.es

Abstract—Transport system, and especially railways as a part of The most common voltage value for the majority of tram and
it, has a highly significant place in the modern world. Railway metro systems is 750V DC. However, there are also some
system has a lot of advantages, comparing to the other type of non-standard values of voltage, e.g. metro-transit systems of
transport, such as: comfort, economy, better control on the travel London and Milan use 630V DC.
time and schedule and less risk factors. Development of high
performance computers, growing complexity of traction drives
and power supplies made possible and, moreover, necessary to In [6], [7] a detailed explanation of all different feeding
model railway systems in order to provide its efficient planning, topologies for AC and DC railways is provided, however a
design and maintenance. This paper introduces a basis of the summary of the basic structure of both, DC and AC, traction
traction system modelling for high speed railway systems. First,
power systems is illustrated on Figure 1.
a brief review of existing traction systems is given. Second, a
2x25kV AC bivoltage network is explained in details. Finally, a
mathematical model of the static AC system has been proposed.
Keywords—Power system, power system modelling, railway system.

.
I. I NTRODUCTION
According to the research, people have known about the
railway system from early 6th century BC [1]. Nevertheless,
it took a long time for the railway system to refine and
get the familiar modern form. Creation of the steam engine
and introduction of the first steam locomotive, based upon it,
showed up the new stage for the transport system. Further
advancement in railway and locomotive technologies caused
the development of the first electrified railways, which was
performed by Siemens in 1879 [2]. Following technical rev-
olution brought out the power supply systems and traction
motors and made them a key parts of the modern electrified
transport systems. DC motors supplied from a low-voltage DC
(1.5kV from the beginning of 20th century and 3kV from
1930s) have been used in the early traction systems due to its
simplicity and ease to control. There are two main directions
in railway systems: low-voltage DC transmission networks for
drives with DC traction motors, and low-frequency (16.7Hz in
Central Europe and 25Hz in the United States) high voltage AC
transmission networks that were updated up to the industrial
values (50 and 60Hz respectively) with the establishment of
high-voltage electrification [3]. Today, the standard range of
voltages is defined by standards EN 50163 [4] and IEC 60850 Fig. 1: Basic Structure of DC and AC Power Systems [6]
[5]. The most common railway systems are following:

• DC high voltage systems: 3kV with the distance

between substations 15-30 km. Over the last 20 years the railway traction systems went trough
• DC medium voltage systems: 1.5kV with the a lot of changes as a result of a significant progress in power
distance between substations 15-30 km. electronics and microprocessor fields. Nevertheless, DC power
• DC low voltage systems: 0.6 - 1.4kV with the supply is still the most common and economic for the public
distance between substations 1-6 km. transportation, whereas AC at industrial frequency is more
• AC single phase systems: 15kV/16.7Hz, useful and efficient for the long-distance lines. Nowadays,
25kV/50Hz. there are no alternatives to the fast travel on the land. Thus, the
• AC three-phase systems: 25kV/50Hz. work on improvement of AC traction systems is substantial.
 Fig. 2: AC railway feeding systems: (a) Direct feed; (b) Direct feed with return conductor; (c) Booster transformer feed; (d)
Booster transformer with return conductor

II. AC T RACTION P OWER S YSTEM Booster transformers (BTs). First BT, rated at about 150
kVA has been used in Japan in 1964 and it could improve the
An electrified line is similar to a typical power transmission characteristics of the feeding circuit. BTs are usually located
and distribution system. Main difference is that trains move along the catenary at distance 3-4 km. The primary and the
and change operation modes constantly, thus varying power secondary windings are connected across a gap of the contact
consumption over a wide range. The number of other factors, wire and across the insulated rail section respectively (Figure
such as train speed, track layouts, traffic demand, and drivers’ 2c). The purpose of a return conductor is the same as in case
behaviour, can also affect power demand [8]. of direct feeding. It is preferable to incorporate a conductor in
parallel with the rails for the return current (see Figure 2d).
AC power-supply systems are widely used in Europe and
allover the world (Great Britain, Spain, Portugal, Italy, Tai- Autotransformer (AT) power feeding. The first AT was
wan, Hong Kong etc.). The development of the commercial presented in Philadelphia in early of XX century [10], after
high-speed railways in 1980s has expanded the use of AC it was installed in Japan in 1972, and starting from 1981 more
power-supply systems, involving larger power flows compare and more countries included ATs in their railway systems,
to DC systems. The most commonly adopted AC traction developing new standards for the AC electrification system.
system (1x25kV or 2x25kV that can be called dual [9] or AT feeding is shown on Figure 3. It combines the advan-
bivoltage at 50Hz) was designed for the lines with high power tage of higher-voltage power transmission with the benefit
requirements. of using standard 25 kV/50 kV equipment. The AT winding
is connected between the catenary and an auxiliary feeder,
In general any railway system can be divided into a number with the rails tied to an intermediate point. The principle of
of electrically isolated sectors. The single phase or three- AT operation is following: the train draws current from the
phase network feeds each sector through the traction sub- two ATs, located nearby, the supply current from each of
stations, which are modified to guarantee the operation in AT depends on the location of the train. Rail currents flow
case of failure. The direct connection of the feed transformer through the AT windings as illustrated in order to maintain
is common in AC railroads. Booster transformers (BTs) and Ampere-turn balance in cores. The AT system operates by
autotransformers (ATs), set into a feeding section, are widely balancing voltage [10]. This is its main advantage over BT
used in AC system to improve transmission efficiency and feeding systems. As for another benefits of the AT system, it
system regulation, decrease rail-to-earth voltage and prevent is easier to maintain, because this topology allows to separate
electromagnetic interference to the telecommunication circuits, a lot of substations.
located nearby.
III. A 2 X 25 K V AC B IVOLTAGE T RACTION S YSTEM
Simple/direct feeding. This is the simplest and the cheapest
Currently, high speed railways are widely implemented and
option of feeding power. It achieves by the direct connection of
used in the whole world. This type of railways demands higher
the traction feed transformer to the catenary and rails of each
values of power, and for this purpose the feeding voltage
substation (Figure 2a). However, there are next disadvantages:
should be also increased. Thru this fact, nowadays, new lines
high feeding impedance with large losses, high rail-to-earth
are often electrified in AC and existing AC lines are converted
voltage (safety issues) and the earth currents as the side-
into bivoltage (e.g. 2x25kV, 50Hz), allowing to get higher
product that can cause interference in the telecommunication
feeding voltage. In this configuration power is transferred using
circuits, that are located nearby. In order to reduce the leakage
high voltage, which then is reduced by autotransformers to
current a return conductor can be added to the system. In this
the suitable for the trains or distribution network level. This
case current is forced to flow rather in a conductor, than in a
configuration has been described in [9], [11], [12], [13].
rail, thus the impedance traction current return path is reduced
(Figure 2b). Figure 3 represents a 2x25kV 50 Hz bivoltage traction system.
 Power Transformer Overhead/Contact Line/Positive Feeder
AT1 AT2 AT3 nance procedures simpler and reduces the level of interference
with the telecommunication systems.
It is also possible to implement bivoltage configuration in DC
traction systems, using DC/DC controlled converters instead
Rail of the ATs.

IV. S TATIC M ATHEMATICAL M ODEL

ATs can break any electrical section fed by one substation
Negative Feeder (one power transformer) into different cells. Cells are usually
assumed to be independent in order to avoid the problem
Fig. 3: AC bivoltage traction system
of unbalanced network and do not complicate the solving
procedure. It allows to make estimation of voltage, current
and load flow faster and easier.
As it is showed on Figure 3 the secondary windings of the Figure 5 illustrates a bivoltage AC system with one cell
power transformers are placed at ESSs and have a central tap and one train in it. The network can be divided into two
connected to the rails (ground), while the poles are connected parts: the high voltage feeding network, which is connected
to the contact/overhead line (or positive feeder) and the neg- to the AC traction network through the primary side of the
ative feeder respectively. From the design and maintenance power transformer, and the AC traction network by itself, that
point of view, it is common to set up the same voltage for the includes the secondary side of the power transformer, ATs and
both, positive and negative feeder. Nevertheless, the positive trains. The source voltage, primary side current and impedance
voltage can be defined by standards, while the negative one are represented by Vsrc , Ip and Zp respectively, while all
can be chosen freely. ATs with a unity turn ratio are usually values, that describe the AC traction network, can be separated
used in this configuration, and this is a specific characteristic into different groups, such as node voltages, line currents
for such schemes. ATs are connected to contact line, rail and (current trough the positive feeder IP F , current trough the
negative feeder at certain intervals, and break the electrical rails IGN D and current through the negative feeder IN F ) and
section fed by one substation into different compartments. line impedances (ZP F , ZGN D and ZN F ), also
These compartments are called cells and in general the length taking into account currents and voltages of the
of each cell can be from 10 km up to 50 km. secondary side of the power transformer and ATs
The Figure 4 shows an example of the current distribution in (I1 , I2 , V1 , V2 , IAT w1 , IAT w2 , VAT w1 , VAT w2 ) together
bivoltage configuration. There are two cells in the scheme, with the characteristics of the train (Vt and It ).
represented in the Figure 4: the first one is between the System will be called static, if it does not consist trains. The
substation and the first AT and the second one is between the mathematical model of the static system is represented by a
first and the second ATs. The most important part to study is system of equations that describes the network. This set of
placed in the second cell, where the train is located. The train equations includes Kirchhoff Voltage and Current Laws (KVL
is consuming a current I = 400A, which consists of two parts: and KCL) for all branches and nodes, power transformer and
the first part is current aI comes from the first AT, while the ATs’ equations. The general form of the equations, which
second part (1 - a)I comes from the second AT. The value of describe the power transformer and ATs’, is given below.
current, supplying by each AT, depends on the factor a, which
defines the location of the train. In this example a = 0.75 Two of the power transformer equations describe the relation
has been assumed, thus the values of current, supplying by between the primary side and each group of the windings on
the first and the second ATs, are 300A and 100A respectively. the secondary side:
The return current flows through the rails to the closest ATs,
then it splits into two, so the current flowing through the rails Np
of the first cell is zero. Also, the current flowing from the Vp = V1 (1)
Np1
second cell to the power transformer through the positive and
negative feeders is 200A, half of the train current. The empty Np
cell (without train) has the feeding and return system of 50kV, Vp = V2 (2)
Np2
so it is possible to increase the transport capacity of the line
together with the distance between the nearby stations. There
are five different loops in this configuration: two in the first where Np is the number of turns of the power transformer
cell (without train) with the current I/2 and three in the second primary winding, while Np1 and Np2 are the number of turns
cell (with train), and two of them have (1 - a)I current and of the power transformer secondary winding first and second
one loop has aI current. Thus, the current distribution of this groups respectively (here and later the winding that connects
scheme can be represented by the current flow in these five the positive feeder and the rails will be considered as the first
loops. winding group, and the winding that connects the rails and the
negative feeder will be the second winding group. This will
The decrease of current though the rails is one of the benefits also work for the ATs windings). From the Figure 5 Vp , V1 and
of the bivoltage configuration. It makes the rails potentials and V2 are the voltage of the primary side of the power transformer
the losses also to be reduced. Among the other advantages, the and voltages of the first and second winding groups of the
bivoltage design for high speed railways makes the mainte- secondary side of the power transformer.
 Power Positive Feeder
Transformer AT1 AT2
25A I/2 = 200A aI = 300A (1 a)I = 100A
200A 100A 100A
400A

200A 300A 100A

25kV 25kV 25kV

400kV

Rails 0A 200A 200A

200A 100A

25kV 25kV 25kV

200A 200A 100A 100A

Negative Feeder
Fig. 4: Current distribution in an AC bivoltage traction system

Ip Zp ZP F IP F IP F ZP F

I1 IAT w1
It

V1 Vt VAT w1
Vp

ZGN D ZGN D
Vsrc

IGN D IGN D

V2 VAT w2

ZN F
I2 IN F IAT w2

Fig. 5: AC bivoltage system with one cell and one train

Power equation of the power transformer will be also included

into the set of equations, which describe the network: N2
VAT w1 = VAT w2 (4)
N1

I p V p = I 1 V1 + I 2 V 2 (3) IAT w1 VAT w1 + IAT w2 VAT w2 = 0 (5)

I1 and I2 are the currents through the power transformer In order to obtain the network, i.e. obtain all currents and
secondary windings. voltages in the system, the next data is required:

Each AT will add two equations to the system (one that • Cell Data that consists all information about all
describes the voltage relation between first and second winding cells: number of cells in the network, length of
groups, and the power equation): each cell, turn ratio of ATs and resistance and
 impedance values for the contact line, rails and [13] V. Zakarukin and A. Krukov, “Methods of joint simulation for external
the negative feeder. power supplies and ac traction systems (written in russian),” Ph.D.
• Train Data that includes all information about dissertation, State Railway University, Irkutsk, 2011.
trains: number of trains, number of cells, in which
each train is located, together with distance and B IOGRAPHIES
active and reactive power values. Active and reac-
tive power of the train can be obtained, knowing Mariia Plakhova received the B.Sc in Industrial
the power consumption of the train and its power Electronics and Automation and the M.Sc in Energy
factor. Management from the National Aviation University
• Value of the source voltage. (Ukraine) in 2012 and 2014. She also received
the M.Sc degree in Sustainable Transportation and
• Number of turns for the primary and secondary Electrical Poweer Systems from the University of
side of the power transformer. Oviedo, Gijon, Spain, in 2015. Her master thesis
was focused on the development of an AC High
Based on the described mathematical model, a power flow speed traction system simulator. Now, she is working
simulator for the traction system can be built. Any developed on modelling and simulation of AC railway traction
and properly working simulator is a tool that can be success- networks.
fully used by any railway company. In order to use this tool
the company should provide necessary information, required Bassam Mohamed received the M.Sc degree from
to solve the system. the University of Oviedo, Gijon, Spain, in 2014. He
is now pursuing his Ph.D studies in the Department
of Electrical Engineering at the University of Oviedo.
V. C ONCLUSIONS His master thesis was focused on implementing
power flow and optimal power solver for transmis-
A rapid increase of the usage of high speed railways requires to sion networks. Now, he is working on modelling and
be able to create a proper models and simulators for the traction simulation of AC and DC micro-grid and railway
systems in order to provide its efficient design, operation and traction networks.
maintenance. For this purpose it is important to understand
the structure and operation principles of the existing traction
systems, and especially a bivoltage configuration due to its
Pablo Arboleya (SM’ 13) Received the M.Eng. and
wide implementation in the current high speed railroads. This Ph.D. (with distinction) degrees from the University
paper has provided a review of the present railways and has of Oviedo, Gijón, Spain, in 2002 and 2005, respec-
established a mathematical model for the bivoltage network. tively, both in electrical engineering. He is Senior
In further works, the proposed model will be used to create a member of the IEEE Power and Energy Society since
2013 and was a recipient of the University of Oviedo
simulator to analyse the power flow in a 2x25kV AC bivoltage Outstanding Ph.D. Thesis Award in 2008. Nowadays,
traction systems. he works as an Associate Professor in the Depart-
ment of Electrical Engineering at the University of
Oviedo (with tenure since 2010).
R EFERENCES
[1] M. Lewis, “Railways in the greek and roman world,”
http://www.sciencenews.gr/docs/diolkos.pdf.
[2] “Siemens history site: In focus,”
http://www.siemens.com/history/en/news/electric railway.htm.
[3] R. Hill, “Electric railway traction. part 1: Electric traction and dc
traction motor drives,” Power Engineering Journal, Feb. 1994.
[4] “Railway application. supply voltages for traction systems,” 2005.
[5] “Railway applications - supply voltages of traction systems. ed.4.0,”
2014.
[6] B. Kiessling, S. A. Puschmann, R., and T. Vega, Lineas de contacto
para ferrocarriles electrificados. Siemens-Aktiengesellschaft, 2008.
[7] B. Kiessling, S. A. Puschmann, R., and E. Schneider, Contact Lines
for Electric Railways; Planning, Design, Implementation, Maintenance.
Siemens-Publicis-Publishing, 2012.
[8] T. Ho, Y. Chi, J. Wang, and K. Leung, “Load flow in electrified railway,”
2nd IEE International Conference in Power Electronics, Machines and
Drives, 2004.
[9] E. Pilo, L. Rouco, and A. Fernandez, “A reduced represen-
tation of 2x25kv electrical systems for high-speed railways,”
IEEE/ASME Joint Rail Conference, 2003.
[10] R. Hill, “Electric railway traction. part 3: Traction power supplies,”
Power Engineering Journal, Dec. 1994.
[11] S. Raygani, A. Tahavorgar, S. Fazel, and B. Moaveny, “Load flow
analysis and future development study for an ac electric railway,”
IET Electrical System in Transportation, 2012.
[12] E. Pilo, Power Supply, Energy Management and Catenary Problems.
WIT Press, 2010.

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