UPTEC ES 16002

Examensarbete 30 hpJanuari 2016

Compensating Unbalances in Synchronous Railway Traction Systems with Railway Power Conditioners

Matilda Örnkloo

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Compensating Unbalances in Synchronous RailwayTraction Systems with Railway Power Conditioners

Matilda Örnkloo

The electrified railway presents significant challenges for the electrical grid. This is dueto the characteristics of the constructed railway system. Trains are single-phase loads,fed by two adjacent phases from the grid. Feeding phases will change continuously atevery substation. This load characteristic will lead to unbalances and poor powerquality in the grid. The poor power quality is caused by the unbalance in currents,voltage drops along the line, and induced harmonics from power electronic devicesused in traction.

To decrease the impact of the railway traction system in the public grid, Static VarCompensators (SVCs) and Static Synchronous Compensators (STATCOMs) havebeen implemented. These installations offer voltage control, maintain balance andmitigate harmonics. This thesis investigates other power electronic technologies toimprove the power quality in the grid for the 50 Hz railway traction system.

ISSN: 1650-8300, UPTEC ES 16002Examinator: Petra JönssonÄmnesgranskare: Urban LundinHandledare: Antonios Antonopoulos

Popularvetenskaplig Sammanfattning

I dagens elektrifierade jarnvag ger tagdriften upphov till obalanseri elnatet. Tagen matas fran en kontaktlina ovanfor ralsen. Kontak-tlinan matas i sin tur med strom fran transformatorer kopplade tillett overliggande elnat. Konstruktionen med en matande kontaktlinaleder till en lastkaraktar som medfor obalanser i elnatet.

Nar intensiteten okar pa jarnvagen och allt tyngre laster transporterasblir dessa obalanser storre. Det kan medfora problem for andra kunderi transmissionsnatet som efterfragar el av bra kvalite. En bra elkvaliteinnebar bland annat att den effekt som skickas ut pa natet bestar avratt spanningsniva, har lite overtoner och haller ratt frekvens. Detkonventionella jarnvagssystemet har enfas-transformatorer inkoppladelangs med banstrackningen. Dessa transformatorer tar tva faser frannatet och matar sin sekundara spanning till tagens kontaktlina samten till jord. Fasmatningen andras kontinuerligt for att i storre mandra en jamn effekt fran natet. Tagen ar dock inte en konstant ef-fektforbrukare, utan lasten varierar i och med tagens acceleration. Denhar lastkaraktaren gor det mycket svart att fa ett balanserat nat. Detfinns aven andra problem med dagens konventionella jarnvagssystemmed enfas-transformatorer. Nar banan matas med spanning fran olikafaser kan inte kontaktlinan over tagen vara en kontinuerlig ledare. Vidvarje transformatorstation maste linan styckas upp. Detta ger upphovtill strackor dar tagen kor utan effekttillforsel. Strackningen varierari langd men kan vara upp till 1000 meter langa pa vissa strackor. Vidinstallation av hoghastighetslinjer ar detta inte en onskvard egenskap.

Studier har tidigare gjorts for att studera system som kan forbattraelkvaliten i natet. Tidiga losningar har varit att installera reaktivaeffektkompenserare i natet. Senare har aven aktiv-effektkompenserarestuderats samt direktomvandling fran hogspanningsnatet genom entre-fas till en-fas konfiguration av tva vaxelriktare.

Det har examensarbetet kommer att studera aktiv effektkompenser-ing genom en sa kallad Railway Power Conditioner. Efter en litter-aturstudie valdes en topologi ut och dess analytiska uttryck togs framfor att bestamma dess funktion. Vidare gjordes simuleringar pa denvalda topologin med aktiv effektkompensering samt simuleringar paett konventionellt system for att kunna jamfora prestation. Simu-leringar och berakningar har utforts i PSCAD respektive i MATLAB.Resultatet fran simuleringarna visar tydligt vad som ar problem meddagens elektrifierade jarnvag. Obalansen ar stor och ger upphov tilldalig elkvalite som kan stora andra komponenter i elkraftssystemet.

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Med den aktiva effektkompenseraren kunde daremot elkvaliten i natetforbattras avsevart. Det finns idag redan realiserade system installer-ade av denna typ i Shinkansen, Japan. For att avgora vilken metodsom lampar sig bast for jarnvagen kravs dock ytterligare studier badeinom systemlosningarnas tekniska prestation men aven hur dessa kanmatas ur ett ekonomiskt perspektiv.

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Executive summary

This thesis show how the use of a conventional railway tractionsystem leads to unbalances in the electrical grid. Unbalances have anegative impact on apparatus in the network, leading to lower over-allperformance of the power system. The power quality may even getworse with trains running at higher speeds or trains with a heavierload.

To mitigate this unbalance, power electronic devices can be installed.This study show that railway power conditioners (RPCs) can mitigatethe unbalance in the grid, as they reduce the degree of current unbal-ance significantly.

To determine if the RPC is a competitive solution for the railwaytraction system, further studies must be performed. The system mustbe investigated in terms of harmonics and in what way the harmonicdistortion from both the converters and the traction equipment onthe trains can be reduced. The RPC-system could be compared withother compensation systems, such as with a STATCOM. The compar-ison could include both cost and performance to determine the mostsuitable solution.

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Acknowledgement

I appreciate all the guidance, advice and encouragement that I have gotthroughout this work, from people around me.

Especially I value the patience and assistance from my supervisor, AntoniosAntonopoulos at ABB Corporate Research, Vasteras. With his pedagogicalexplanations he could help me to overcome some mind barriers during thework and without his support I would not have been able to finish this work.

I also appreciate the time my subject reviewer, Urban Lundin at UppsalaUniversity took to answering my questions and for reading my report. I alsowould like to thank my proof reader and opponent Siddy Persson foradditional comments.

At last I would like to thank the Swedish state for the opportunity of freeeducation.

/Matilda Ornkloo, Uppsala

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Contents

1 Introduction 91.1 Scope of the Project . . . . . . . . . . . . . . . . . . . . . . . 91.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 System boundaries . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Conventional System with Single-phase Transformers 132.1 Consequences with unbalances . . . . . . . . . . . . . . . . . . 142.2 Symmetrical Components . . . . . . . . . . . . . . . . . . . . 15

3 Solutions to Mitigate Unbalances with Power Electronic De-vices 163.1 Static Frequency Converter (SFC) . . . . . . . . . . . . . . . . 163.2 Reactive power compensators, (SVC) and

(STATCOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Railway Power Conditioner (RPC) . . . . . . . . . . . . . . . 19

4 Railway Power Conditioner, Design and Function 214.1 Special Design Transformers . . . . . . . . . . . . . . . . . . . 214.2 Generation of Current and Voltage References for an RPC

connected behind a V/V Transformer . . . . . . . . . . . . . . 214.2.1 Control Schematic for the Railway Power Conditioner . 264.2.2 Parameter description and impact of parameter change 31

5 Simulations and Results for a Conventional system and asystem with the RPC implemented 325.1 Conventional System . . . . . . . . . . . . . . . . . . . . . . . 32

5.1.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.1.3 Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.1.4 Case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 Railway Power conditioner . . . . . . . . . . . . . . . . . . . . 405.2.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.3 Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2.4 Case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 Unbalance factor . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 Conclusion and Discussion 48

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7 Future outlooks 49

8 References 50

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1 Introduction

Trains appear as a single-phase loads in the public grid and create unbal-ances. This leads to poor power quality and may disturb other customers inthe grid. When the traffic increases the issue becomes larger and solutionsto improve the power quality are necessary. The poor power quality appearsmainly from unbalances in the current on the grid side. The unbalances occurdue to the train-load characteristic and it has a negative impact on trans-formers, generators and motors in the grid. It will also lower the capacity ofthe transmission lines.

If the railway is placed in remote areas, the grid might be weaker and moresusceptible to voltage drops. Power-electronic device in the traction systemalso increase the harmonic content in the railway. To mitigate these issuesSVCs and STATCOMs have been installed along the railway network. Thisthesis will study alternative power electronic applications to improve thepower quality.

1.1 Scope of the Project

The purpose of this master thesis is to describe the unbalance problem in thesynchronous railway system, study what consequences it has in the electricitynetwork, and investigate systems that can mitigate these problems.

1.2 Background

The electrified railway system is divided into direct current (DC) and al-ternating current (AC) systems. Early electrification before 1950 was doneusing mainly DC systems or low-frequency AC systems. Later systems, de-signed after 1950 are often electrified by AC with an industrial frequency at50 or 60 Hz. This transition of electrification systems is due to the followingadvancement in technology: Before the 50s railway-traction motors could notbe fed by industrial frequencies, but at lower frequencies 16 2/3 Hz or 25 Hz[1]. To change the industry frequency from 50 Hz to a lower frequency thatthe railway can operate with, rotary converters were historically used [1].When modernizing low-frequency railways, nowadays, static converters areinstalled that are based on semiconductor technology. Changing the railwayelectrification system in a region is often associated with large investmentcost. Hence when a system is built and in operation, it will most likely be inoperation during a long time. A system will rather be upgraded than beingfrequently redesigned from the beginning. Various system are, therefore, in

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operation around the world.

DC systems are often fed by a low voltage, typically between 500 to 3500Volts [1]. The comparative low voltage has to do with safety and constraintsregarding technology and economics at the time the DC systems were intro-duced. The safety issue mainly refers to the fact that high-voltage breakerswere difficult and expensive to make at that time. A reasonable way to trans-form the voltage easily between different DC voltage levels was not available.However, with modern technology some of these constraints could be dealtwith [2]. DC systems also require a large current for a given power and asresult the resistive losses will increase. These systems are mainly used inurban areas for subways or trams.

AC systems span a larger voltage range, typically between 15 kV up to 50kV. For low-frequency railways (16 2/3 Hz), 15 kV is used and for industrialfrequency systems (50 or 60 Hz), 25 kV is used. Low-frequency railways canbe found in northern and central Europe since the standard was set whentraction-motor technology for higher frequencies was not mature. In Americathere are some grids operating at 25 Hz, and in Japan where the country hastwo frequency regions, 50 Hz and 60 Hz, most of the trains run at 60 Hz [3].Modern electrification is generally done with industrial frequency at 50 Hz,but still there are several different systems in operation in the world [1]. Theadvantage with an AC system compared to a DC system is that a highervoltage can be used. For the same power the trains can thereby be fed by alower current and the resistive losses are decreased. When higher power isneeded for the trains, the more obvious the advantage with AC systems willbe. With high speed trains, a DC system would require substations on fairlyshort distances. This will not be viable since trains are occasional consumersof power and do not require a constant power supply [1].

For modern railway electrification the most common system is a 25 kV ACsystem at 50 Hz. It does not require a frequency converter and the transform-ers can be lighter due to the higher frequency [1]. However, all AC systemsare still being fed as single-phase loads. In theory it would be better to drawa three-phase current immediately from the grid and have more conductorson the railway. That would reduce the problem of unbalances, but this hasnot been a practical solution in reality. There are only a few three-phaserailway traction systems. More conductors at each railway system wouldalso cost too much since the loads are not a consumer of constant power.

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1.3 Method

This thesis is divided into two main parts. The first part includes a literaturestudy to introduce the reader to the content and provide an overview overthe problem. The second part includes an attempt to find a solution for theproblem.

First investigations have been done on power electronic devices that canmitigate unbalances in the electrical grid produced from the electrified rail-way traction system. Main focus in the thesis has been on the Railway PowerConditioner (RPC). The RPC is a power electronic device that has not beenwidely investigated before. The converter configuration enables active powerto flow between two electrical subsystems, which can be compared to STAT-COMs that mainly work with reactive compensation.

Both a typical railway traction system, in this thesis named Conventionalsystem and a conventional system with an RPC in operation are designedand simulated in this thesis. The purpose with this is to be able to show theperformance of these systems when subjected to the same train-load. Thetwo systems are built in Power Systems Computer Aided Design (PSCAD).PSCAD is a simulation program to build, simulate and model a system ofinterest. PSCAD include both ready-made modules but also allow the userto construct and write code for costume-made modules.

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1.4 Structure

The main structure of the thesis include following four chapters

• Chapter 2 - Conventional SystemThe typical railway traction system used in the railway industry todayis described including its features

• Chapter 3 - Solutions to Mitigate UnbalancesThis chapter describes power electronic solutions for the railway trac-tion system to mitigate the unbalance in the electrical grid

• Chapter 4 - Railway Power ConditionerThe Railway Power Conditioner is described and investigated in termsof an electrical analysis. Information from the investigation is furtheron used for construction and control of the converter configuration inPSCAD

• Chapter 5 - Simulations and ResultsIn this chapter results from the simulations are presented. Simulationshave been done on the conventional system and on a conventional sys-tem with an RPC in operation. This to show their performance whensubjected to a train-load

1.5 System boundaries

This thesis only considers railway systems from a three-phase AC systemto the single-phase train load. The simulations are only done on systemsoperating with a frequency at fixed value of 50 Hz. The grid is assumed tobe a three-phased sinusoidal system with no harmonic distortion and witha fixed voltage amplitude, unless noted otherwise. The only reference toharmonics will be in the rectified-traction-load characteristics and the railwaypower conditioner. Power losses and fault investigations are not carried outwithin the scope of this project.

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2 Conventional System with Single-phase Trans-

formers

In a conventional traction system trains are being fed by two adjacent phasesthrough a single-phase transformer, as can be seen in figure 1. In order toequally load all three phases, the phase connection changes in every substa-tion. With this supply system the currents on the grid side will be unbalancedat every single instant in time, due to the single-phase load characteristic.Furthermore, the railway is required to have neutral zones, marked as NZin the figures, to divide the feeding sections that might vary in amplitude,frequency or phase shift. During these sections the trains will have to rununpowered [4].

The definition of a neutral zone is the distance where the train is not pow-ered. For high-speed and heavy-loaded trains this is a drawback, so thelength and/or the amount of neutral zones should be reduced or avoided ifpossible. In Denmark there has been a detailed study about neutral sectionssince a high-speed railway is planned. For trains running at a speed below200 km/h section insulators have been used and the neutral sections havebeen 8 meters long. For high-speed trains, with speeds above 200 km/h thisconstruction does not fulfill the given standards and other types of neutralsections have to be used, where most of them are over 100 meters long oreven up to 1000 meters long [4] [5].

The conventional system is simple, has a low investment cost, and the existingknowledge is large in this technology. However, when the expectations on therailway increases, regarding denser traffic and heavier loaded trains, certainimprovements or even a complete redesign of the whole system is required [6].

It is no longer viable to have unpowered distances in the railway system.Moreover, the conventional system provides poor power quality in the grid.A modern railway system should preferably be able to maintain the voltagelevels within given limits, mitigate harmonics from the traction equipment,and reduce the negative-sequence currents in the system. The amount ofneutral zones should be reduced or avoided if possible.

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Figure 1: Conventional railway feeding system with single-phase transformersand a conductor divided by neutral zones

2.1 Consequences with unbalances

Under unbalanced situations, negative-sequence current will occur in thegrid. The magnitude of these negative sequence currents depends on thedegree of unbalance. The negative-sequence currents have a negative impacton the grid and apparatuses that operate in the grid. It will decrease thetransmission capability, lower the output power from the transformer, anddisturb rotating machines like motors and generators [7].

Negative-sequence currents in electrical machines such as in a motor or agenerator will decrease their efficiency. The negative-sequence currents willcreate a magnetic flux in the rotor that oppose the direction of rotation of therotor. A relative motion will occur between the magnetic flux and the rotor.This will cause rotor heating problems and may lead to insulation failure andmechanical problems [8]. Heating problems will demand extra cooling, andthe efficiency of the machine will decrease accordingly. The positive sequencecurrent will induce a magnetic flux in the same rotation as the rotor.

The negative-sequence current also affects the transmission lines. It flowsin the transmission lines and does not perform any actual work. It causeadditional power loss, and lower the transmission capability of the line.

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Transformers will also be affected. The negative-sequence current in the gridresults in asymmetrical three-phase currents on the primary side of trans-formers. The rated output of a transformer will be limited by the largestcurrent on the primary side, and thereby the output power will be lower.This leads to additional losses in a transformer and heating of the iron. Thenegative-sequence current may also disturb the relay protection in the grid[7].

The consequences in the grid from negative-sequence currents are severe anddetrimental for most apparatus. The amount of negative-sequence currentshould, therefore, be reduced as much as possible.

2.2 Symmetrical Components

With symmetrical components it is possible to analyze unbalances in a multi-phase system in a simplified manner. The number of phases, n can be dividedin n systems of balanced phasors, called the symmetrical components. Eachset of symmetrical components is equal in length, and adjacent phasors willbe separated by the same angle [9]. However, since most electrical systemsoperate with three phases the following description will be for a three-phasesystem. The main concept with symmetrical components is to transform thephase component to the new set of symmetrical components. The advantageof this method is that the sequence networks are easier to analyze comparedto the three-phase network. Once the sequence networks are found, it is pos-sible to transpose it to the three-phase network again [10]. This method canbe applied for both voltages and currents in the network.

The transformation from phase currents to the sequence currents can beseen further down. IaIb

Ic

=

1 1 11 a2 a1 a a2

I0aI1aI2a

(1)

I0a =1

3(Ia + Ib + Ic) (2)

I1a =1

3(Ia + a2Ib + aIc) (3)

I2a =1

3(Ia + aIb + a2Ic) (4)

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3 Solutions to Mitigate Unbalances with Power

Electronic Devices

To improve stability of the grid, primarily regarding voltage levels, it is possi-ble to have two feeding lines. Even if the grid dynamics may be improved withthis solution it will not solve the problems with negative-sequence currentsor harmonics. Double feeding lines will still require neutral zones to separatethe feeding phases. There are also other solutions for the load-unbalanceproblem. Reactive-power compensators such as the SVC or STATCOMs canbe used. The term static refers to the fact that no rotating part is involved,the devices use static semiconductor-based technology instead. Another in-teresting solution that is less investigated compared to the aforementionedones is to use railway power conditioners (RPCs). In this project focus isto investigate the RPC and its features. Simulations are performed on theconventional system and the same system when the RPC is implemented.Another available technology is static frequency converters (SFCs). SFCsoperate with converters that immediately convert a three-phase input to asingle-phase output and provide an in-line feeding system. This system doesnot require any neutral zones. However, it is considered to be quite expensiveto install, as it requires full-power converters at every substation.

When a train brakes power is dissipated in the catenary. In a conventionalsystem with single-phase transformers this power will flow back up throughthe transformer to the grid. This is often not desirable from the grid own-ers view, as the power fed back to the grid will be an uncontrolled powerflow in time, magnitude and place. Therefore, there are often restrictionsregarding power fed-back and some trains are installed with certain brakesto dissipate the excess power in terms of heat within the locomotive. Withhighly dense traffic railways, such as metro lines, the power can to a largerextent be used by adjacent trains in the system avoid feeding the power backto the network. With a system design with SFCs, it is possible to controlthe power flow feedback to the grid. All three phases can receive power in asymmetrical manner. This is not possible with single-phase transformers [1].

3.1 Static Frequency Converter (SFC)

Recently, full converters are proposed for the 50 Hz railway system, similarlyto the full-converter design in the 3-phase AC 50 Hz to 1-phase AC 16.7Hz systems, as shown in figure 2. The full-converter design consists of athree-phase converter connected to a single-phase converter in back-to-back

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configuration with a common DC-link. Active power, reactive power, andharmonics can be controlled dynamically. This technology does not needneutral zones as the catenary is separated from the feeding grid. This makesthe system flexible and suitable for fast and heavy-loaded trains. Step-upand step-down transformers can be used to obtain the desirable rating onthe converters and for galvanic isolation against the grid [11]. The SFC iscontrolled in a way that the grid sees a symmetrical load, and therefore, thevoltage requirements on the grid can be reduced. This technology can alsoprovide the possibility for regenerating power flow, i.e., braking energy fromthe train can transferred to the grid. It can even improve the power qualityin the grid, but has a higher capital cost compared to other systems [6].

Figure 2: Static Frequency Converter connecting directly to the high powergrid through a coupling transformer

3.2 Reactive power compensators, (SVC) and(STATCOM)

In order to improve the power quality, without tremendously increasing theinitial cost, FACTS devices can be installed in the conventional system. Withthese devices it is possible to use lower grid voltage for the railway thanwithout them, since the unbalances will be reduced. Two common shunt-connected devices used for dynamical balancing is the Static Var Compen-sators (SVC) or the Static Synchronous Compensator (STATCOM). Both

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technologies have been installed in several systems and have improved thepower quality in the grid. In a railway grid, they can offer dynamic voltagecontrol, mitigate harmonics and balance the load between phases. This tech-nology has been installed for this purpose in Japan, England and France [3][12].

These reactive power compensators still require neutral zones, since the feed-ing is done by single-phases transformers as in figure 3. SVCs and STAT-COMs are typically connected to the grid via a coupling transformer to step-down the voltage to a level that does not require a high rating of the com-pensator. The voltage regulation is done by the switching devices and theharmonics can be mitigated by additionally connected filters [12].

The STATCOM can also be connected in a system were the trains are fedby the same combination of phases all along the line. This requires higherratings for the STATCOM, since the unbalances will be larger, as seen fromthe grid. However, one can theoretically avoid having neutral zones with thisconstellation. Section insulators might be needed between adjacent railwaysections. As a result this is not widely used in practice as this technology canresult in undesired power flows between two points in the grid. Through therailway and up through the feeding sections [11]. STATCOMs and SVCs canbe suitable solutions for existing grids, since the infrastructure of the railwaygrid is already in place with single-phase transformers at the feeding points,and the STATCOM/SVC can be used as add-on equipment in the grid toincrease the power quality.

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Figure 3: Conventional system with single-phase transformers, grid con-nected to a STATCOM through a coupling transformer

3.3 Railway Power Conditioner (RPC)

Railway Power Conditioners (RPCs) were introduced by Japanese scholarsin the 90s and has been in commercial operation in Shinkansen since thebeginning of 2000 [13]. Similar devices have also been described in papersin other constellations or with added components that improve their perfor-mance [14]. RPCs do not have a unique definition, but they are often referredto a conditioner placed after a special design transformer, such as a Scott orV/V-transformer, as shown in figure 4. Furthermore the conditioners oftenconsist of two single-phase AC/DC- converters connected back-to-back witha common DC-link. They are placed between the transformer secondarysides.

These devices enable active power flow between two sections of the cate-nary. During an upgrade of Shinkansen in 2002 several RPCs were installedin the railway system to obtain a balanced public grid. Later demonstrationcould show that balance were established between the phases but the RPCcould also compensate for reactive power and keep the voltage levels withingiven requirements [13].

As modern trains also tend to a larger extent use pulse width modulation(PWM) control the need of compensating reactive power is decreased while

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the need of active power transfer still exists [15].

The major advantage with this technology is that total balance can beachieved in the electrical grid. The major disadvantage is that this tech-nology still requires neutral zones.

Figure 4: Railway power conditioner connected to the grid via a step-downtransformer

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4 Railway Power Conditioner, Design and Func-

tion

The main purpose with an RPC is to:

• Transfer active power between two electrical subsystems

• Compensate reactive power on each side of the converters

• Mitigate harmonics

In this thesis no detailed investigation is done to study harmonics. Focushas been on the first two items, transfer active power and reactive powercompensation. The RPC is connected on the secondary side of a tractiontransformer. The traction transformer is often a special designed transformersince the primary side connects to the three-phase grid and the secondaryside consists of two phases and one connection to ground.

4.1 Special Design Transformers

To obtain a more even distribution of loads when designing a railway tractionsystem it is common to use special-design transformers. Special-design trans-formers include impedance-matching transformers or three-phase to two-phase transformers. Common traction transformers are the Scott, the Wood-bridge, the Le Blanc or the V/V transformer. Due to rapid changes in thetrain loads on each side of the transformer output, the system cannot main-tain its balance but still require an additional load compensator [16].

The choice of transformer will also affect the amount of negative-sequencecurrents injected in the grid. The V/V-transformer will inject more negative-sequence current than the Scott or the Woodbridge transformer [17]. How-ever, the V/V transformer has other desirable characteristics, such as a simplestructure, and this is why it is widely used in railway traction systems [17].

4.2 Generation of Current and Voltage References foran RPC connected behind a V/V Transformer

To determine the required output from the converter to keep the systemsymmetrized, the electrical circuit must be analyzed. Figure 5 represents aschematic overview of the system.

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From the three-phase grid a V/V-transformer is connected to the RPC. TheV/V transformer is a transformer with three phases, two windings on theprimary side connected to the grid. On the secondary side there are twophases connected to the load and one phase connected to the ground. Be-tween the phases on the secondary side two converters can be connected inback-to-back configuration. These two feeding phases are named accordingto the voltage across them, the ac-side (ac) and the bc-side (bc).

Figure 5: System overview, V/V transformer with connected RPC. Iac andIbc represent the currents from the V/V transformer output-side and ILac andILbc represent the load currents. Between the two feeding phases the railwaypower conditioner is placed. Two converters in a back-to-back configurationwhere Irefac and Irefbc determine the reference currents from the converters

In the initial system the three-phase voltages on the grid side are assumedto be purely sinusoidal with a phase shift of 120 degrees. The grid-sidevoltages are given in line-to-neutral values and the transformer turns ratiois a constant called K. The transformer is assumed to be ideal. If the inputis symmetrical, then following equations can be written for the referencecurrents. Omega, ω represents the angular speed of the grid.

VA = V1 cos(ωt) → IrefA = I1 cos(ωt) (5)

VB = V1 cos(ωt− 2π/3) → IrefB = I1 cos(ωt− 2π/3) (6)

VC = V1 cos(ωt+ 2π/3) → IrefC = I1 cos(ωt+ 2π/3) (7)

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Assuming that the railway system appears only as an active load at thepoint of common coupling, the voltage and the current can be related by apure resistance, I1 = V1

R. The active power on the primary side of the grid

can be described

P1 =3

2V1I1 (8)

The train load on each of the secondary sides of the transformer can berepresented by one resistive part and one inductive part,

Zac = Rac + jωLac (9)

Zbc = Rbc + jωLbc (10)

The voltages on the secondary side can be described as

Vac(t) = V2 cos(ωt+ ϕ) (11)

Vbc(t) = V2 cos(ωt+ γ) (12)

The variables ϕ and γ represent the phase displacement from the initialangular speed for the system, and occur due to the load characteristic. As-suming that the train loads are PWM-controlled their reactive part can beneglected and the currents can be expressed as

ILac(t) = ILac cos(ωt+ ϕ) (13)

ILbc(t) = ILbc cos(ωt+ γ) (14)

The active power on the secondary side

P2 =V22

(ILac + ILbc) (15)

The active power drawn from the secondary side is assumed to be the same ason the primary side for an ideal transformer. Form (8) and (15) it is possibleto find the current amplitude I1. The ratio between the line-to-neutral andline-to-line voltages and the transformer ratio must be considered at thisstep. Assuming P1 and P2 are equal this yields the current amplitude onprimary side of the transformer, for a symmetrically shared load

I1 =k√

3

3(ILac + ILbc) (16)

The reference input currents for a balanced system are expressed by

23

IrefA =k√

3

3(ILac + ILbc) cos(ωt) (17)

IrefB =k√

3

3(ILac + ILbc) cos(ωt− 2π/3) (18)

IrefC =k√

3

3(ILac + ILbc) cos(ωt+ 2π/3) (19)

The reference currents on the primary side must now be transferred to thesecondary side. Figure 6 describes how the currents flow through the V/Vtransformer. Uppercase letters refer to the primary side of the transformerand lowercase letters refer to the secondary side.

Figure 6: Schematic over current division through the V/V transformer,primary side is noted by uppercase letters and the secondary side is noted bylowercase letters. The transformer has a three-phase input and two output-feeding phases and one connected to ground. Primary voltage is set to 100kV RMS, L-N and the secondary voltage 25 kV RMS.

The current on the primary side can be written as

Ipr.AC = iA (20)

Ipr.BC = iB (21)

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Ipr.AC+ic = −Ipr.BC → iC = −Ipr.BC−Ipr.AC → iC = −iB−iA (22)

These currents must then be transferred to the secondary side of thetransformer

Isec.ac = +iac (23)

Isec.bc = +ibc (24)

Isec.ac = −ic−Isec.bc → ic = −Isec.ac−Isec.bc → ic =1

k(Ipr.AC+Ipr.BC)

(25)

isecC =1

k(iA + iB) (26)

The currents on the secondary side can now be expressed from the primaryside currents

iac = Isec.ac = −1

kIprim.ac = −1

kiA (27)

ibc = Isec.bc = −1

kIprim.bc = −1

kiB (28)

In figure 5 the current schematic is shown and the reference currents fromthe converter can be described with (17), (18), (27) and (28)

irefac = −iac − iLac =1

kiA − iLac (29)

irefbc = −ibc − iLbc =1

kiB − iLbc (30)

Irefac =

√3

3(ILac + ILbc) cos(ωt)− ILac cos(ωt+ ϕ) (31)

Irefbc =

√3

3(ILac + ILbc) cos(ωt− 2π/3)− ILbc cos(ωt+ γ) (32)

When the reference currents are found for the converters, the voltages can becalculated using Kirchhoffs voltage law. Reference voltage for the convertermust be the voltage over the catenary minus the voltage over the inductor,as shown in figure 7.

25

Figure 7: Schematic over voltage division, Vac represent the voltage on thefeeding phase, VL1 is the inductor voltage and V ref

ac refers to the voltagereference from the converter.

V refac = Vac − VL1 → VL1 = jωL1I

refac (33)

V refbc = Vbc − VL2 → VL2 = jωL2I

refbc (34)

The inductance in the coupling reactor will cause a phase shift of 90degrees and the reference voltages on each side will be

V refac = Vac−ωL1(

√3

3(ILac+ILbc) cos(ωt−π/2)−ILac cos(ωt+ϕ−π/2)) (35)

V refbc = Vbc−ωL2(

√3

3(ILac+ILbc) cos(ωt−2π/3−π/2)−ILbc cos(ωt+γ−π/2))

(36)The reference currents and voltages for both converters will be variables

for the control of the RPC.

4.2.1 Control Schematic for the Railway Power Conditioner

The main function with this power conditioner is to allow active power toflow between two electrical subsystems. The power conditioner contains twoconverters connected in back-to-back configuration with a common DC-link,as in figure 8. These converters can operate in both rectification and inversionmode.

26

Figure 8: Two converters in back-to-back configuration, each converter con-sists of four switches two in each leg. The switching devices are Insulated-gateBipolar Transistors (IGBTs). The DC-link capacitor is set to 5 µF.

The controller should use the reference currents and voltages to sym-metrize the currents on the grid side. This control system will use a sinu-soidal pulse width modulation (SPWM) to create gate signals for the IGBTs.The SPWM compares a reference signal to a carrier signal to create the gatepulses. The carrier signal will be a triangular waveform with maximum out-put of 1 and a minimum output of -1. The frequency is initially set to 10kHz for the triangular waveform.

From chapter 4.2, equations for the reference currents and the reference volt-ages can be found. The first attempt to build the controller only consideredthe voltage references. In figure 9 the voltage reference, V ref

ac is normalizedover the DC-voltage. With a simple voltage control, the gate signals can befound immediately after the comparison of the signal and the carrier signalto determine if the switch should be in on-state or off-state. However, in thiscase a simple voltage control was not sufficient and an additional step wasrequired.

27

Figure 9: Voltage control of the converter. The voltage reference is normal-ized over the DC-voltage and further on compared to a carrier signal

The controller based on only the reference voltages created currents thatdid not coincide with the reference currents. A control for the current wasnecessary. In figure 10 the measured current, IMeasured

ac is allowed to deviatefrom the reference current, Irefac by a certain tolerance. In the simulationsthe tolerance is set to 100 A. A smaller tolerance will create a current thatfollows the reference current more accurately, but may cause unnecessarilyhigh switching frequency. A larger tolerance might not be able to createcurrents and voltages that follow the references.

From the left side of the figure, Irefac is compared with an upper limit Iref+toleranceac .

The output from the comparator is 1 if signal A is larger than B, or 0 if sig-nal A is less than B. Further on in the input selector either A or B will belet through depending on the control signal, Ctrl. Signal A is set to 0 andsignal B will either be 0 or 1 according to the voltage control output. Whenthe control signal is 1, signal A will be let through. If the control signal iszero, signal B will be let through. The output from the first input selectorin figure 10 will further on be used in the second input selector.

The second input selector uses a similar operation procedure. The outputwill determine if the device 1 and 2 will be on or off. This is the control func-tion for one leg in one converter. For the second leg in the same converter asimilar procedure will be run as can be seen in figure 11.

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Figure 10: Current control for gate 1 and gate 2. The current reference fromthe converter is let to vary within a band of tolerance. When the currentappears outside this band the switches are forced to turn on or off dependingon if more or less current is required

Figure 12 shows reference current, Irefac plotted along with the measuredcurrent, IMeasured

ac and the band of limitation. The main purpose of the bandis to maintain the current within given limits. For example, if IMeasured

ac isunder the band of limitation the current must be increased. This requireshigher voltage and the switches must operate in a way that result in a highervoltage on the AC-side.

This is the control schematic for one of the converters, a similar conceptwas built for the second converter. The limitation band can be adjusted bychanging the tolerance to obtain desirable accuracy.

29

Figure 11: Current control for gate 3 and gate 4. Similar function as theprevious figure 10

Figure 12: Current limitation of the converter AC-side with a band of toler-ance 0.1 kA. Band of limitation is marked in red, the current reference indark blue and the measured current is marked in light blue.

30

With these control schematic it is possible to control the output from theconverter. In a further step also the DC-link voltage should be controlled tomaintain a constant voltage level.

4.2.2 Parameter description and impact of parameter change

In this study values on the components of the RPC are chosen similarly toother simulated RPCs and some values are chosen after test simulations tofind suitable ones. The main purpose with this thesis is to build a simpleversion of an RPC. In further studies it could be of interest to investigatethe RPC and its components more detailed. This includes investigationsregarding losses in the RPC, switching frequency in the IGBTs and DC-linkcapacitor size.

The switching frequency for the IGBTs in the simulated model is set to10 kHz. High frequency lead to higher losses since each time the switch closesand opens losses occur. However too slow switching leads to slow respondand might give current and voltages that do not follow the reference values.Since this control has an additional current control to maintain the currentwithin the band of limitation the switching frequency will be slightly higherthan 10 kHz.

The DC-link in the RPC includes a smoothening capacitor. This capac-itor shall reduce the ripple on the voltage waveform. The capacitor capaci-tance in this design was set to 5 µH after test simulations. A large capacitorcan reduce the voltage ripple on the waveform but a too large capacitor willlead to high cost. A too small capacitor might lead to a converter designwith poor performance.

In further studies the RPC could be optimized to find more suitable valueson the components in the design.

31

5 Simulations and Results for a Conventional

system and a system with the RPC imple-

mented

The main goal with this chapter is to show how the conventional railwaytraction system and a conventional railway traction system with an RPC inoperation perform under the same loading conditions. These loading condi-tions are divided into four cases.All simulations are done with a three-phase grid voltage of 100 kV RMS andthe voltages are assumed to be purely sinusoidal with a phase shift of 120degrees between the phases. The grid is considered strong if nothing else ismentioned, and the frequency is set to 50 Hz.

The voltage after the traction transformer will be 25 kV RMS, either afterthe conventional system with single-phase transformers or after the systemwith an RPC and a V/V transformer.The inductance of the grid represents the inductive behavior of a transmis-sion line. The transmission lines on the secondary side of the transformer areshort lines (under 80 km), only a resistive and an inductive part is modeledin this simulation. The train load is simulated as a rectified load with oneresistive part and one inductive part. The switching devices are Insulated-Gate Bipolar Transistors (IGBTs) connected with an anti-parallel diode.

Simulations are mainly done with a load of 10 MW. A typical train loadcan vary from a few MW up to 15 MW [1]. However, the train loads areassumed to increase in the future, and also several of them may be runningwithin the same catenary section.

5.1 Conventional System

The first simulations were done on the conventional system with single-phasetransformers. The worst-case scenario occurs when all trains are being fed bythe same two phases all along the catenary. Here, the conventional systemis simulated with a load connected between two phases. The train will drawcurrent from these two phases, while no current will be drawn from thethird phase. The single-phase transformers are assumed to be ideal. Theconventional system was simulated in four cases.

32

5.1.1 Case 1

The first simulation was done with a strong grid i.e a low inductance of 3mH, 0.01 p.u compared to the base-inductance.

Sb = 100 MVA

Vb = 100 kV

Zb = 100 Ω

Zb = Rb = Xb

Xb = jωL

Lb = 0.318 H

Two trains are assumed to draw a constant power of 10 MW each, in eachfeeding section. The train is assumed to be a rectified load with one resistivepart of 62.5 Ω and one inductive part of 10 mH. The load is assumed to beconnected at the feeding point. As expected, the voltages are not affected bythe load since the grid inductance is set to a low value. The voltage wave-forms can be seen in figure 13. However, the current waveforms are affectedseverely by the loading conditions. Current is drawn only from two phasesthrough the transformer, and one phase-current will be zero, as shown infigure 14. The two phase-currents will be separated with 180 degrees, in abalanced situation it should be 120 degrees between all the three currentwaveforms.

33

Figure 13: Grid voltages for the conventional system. Each feeding sectionis loaded with 10 MW

Figure 14: Grid currents for the conventional system. Each feeding sectionis loaded with 10 MW

34

5.1.2 Case 2

In the next simulation the grid inductance remains the same, 3 mH. The loadwill remain the same as previously but the loads are assumed to be placed50 km away from the feeding point. The transmission line is modelled as oneresistor of 5 Ω and one inductance of 70 mH. The voltage and the currentwaveforms are not changing any significantly compared to the previouslycase. The voltage waveforms are still good as shown in figure 15 and thecurrent waveforms in figure 16 are still as bad as before.

Figure 15: Grid voltages for the conventional system. Each feeding sectionis loaded with 10 MW, 50 km from feeding point

35

Figure 16: Grid currents for the conventional system. Each feeding sectionis loaded with 10 MW, 50 km from feeding point

5.1.3 Case 3

In case three one load of 50 MW is placed on the bc-side of the transformeroutput. The distance from the feeding point and the load will be 50 km.The load contains a 12.5 Ω resistor and one inductor of 10 mH. The othersection (the ac-side) is modeled as a section with no train connected to thecatenary. This is done by connecting a resistor of 62500 Ω. Neither in thiscase did the voltage or current waveform change any significantly as can beseen in figure 17 and 18.

36

Figure 17: Grid voltages for the conventional system. One section loadedwith 50 MW and the other section is modeled with no train connected

Figure 18: Grid currents for the conventional system. One section loadedwith 50 MW and the other section is modeled with no train connected

37

5.1.4 Case 4

In the fourth case the bc-section draws a power of 10 MW and the ac-sectioninitially draws a power of 1 MW. The 1 MW load contains of a load of 625Ω and an inductor of 10 mH. After a certain time the train that draw apower of 1 MW will accelerate. The load will hence increase to 50 MWinstantaneously, and to represent that, the resistor is changed to 12.5 Ω.In this case, some disturbances can be observed in the voltage waveforms, asin figure 19 and the current waveforms in figure 20. The rectified load drawsa high current and as can be seen in figure 20 the rectification will distort thecurrent waveforms. This will also be transferred to the voltage waveforms,where some distortion is observable.

Figure 19: Grid voltages for the conventional system. One section is loadedwith 10 MW and the other section is modeled as a train that accelerates ata certain time

38

Figure 20: Grid currents for the conventional system. One section is loadedwith 10 MW and the other section is modeled as a train that accelerates ata certain time

39

5.2 Railway Power conditioner

The same system is now simulated with the addition of a railway power con-ditioner, under the same conditions as the conventional system. The railwaypower conditioner is placed between the two output phases at the secondaryside of a V/V-transformer. Feeding can be done in both directions from thesubstation. The DC-link capacitor of the RPC has a capacitance of 5 mF.Two single-phase transformers are connected between the converter and theload-sides. The converter coupling-inductance on each side of the convertersis set to 4 mH, 10 percentage of the base-inductance. The RPC was alsosimulated in four cases, the same as for the conventional system.

Sb = 50 MVA

Vb = 25 kV

Zb = 12.5 Ω

Zb = Rb = Xb

Xb = jωL

Lb = 0.039 H

5.2.1 Case 1

The first simulation was done with a strong grid, similar as case 1 for theconventional system. Two trains are assumed to draw a constant power of10 MW each, on each feeding section. The train is assumed to be a rectifiedload with one resistive part of 62.5 Ω and one inductive part of 10 mH. Ascan be seen in figure 21, the voltage waveforms have been slightly affected bythe switching actions of the RPC system. However, the current waveformsfor the grid currents have become much better with this system compared tocase 1 for the conventional system, as shown in figure 22.

40

Figure 21: Grid voltages for 10 MW load on both sections

Figure 22: Grid currents for 10 MW load on both sections

41

5.2.2 Case 2

In the next simulation the grid inductance remains the same at 3 mH. Theload will remain the same as previously, but the loads are assumed to beplaced 50 away km from the feeding point. The transmission line is modelledas one resistor of 5 Ω and one inductance of 70 mH. The voltage waveforms,shown in figure 23 will not be significantly affected compared to the previ-ous case for the RPC. The current waveforms in figure 24 will still be wellbalanced, even if the load characteristics is different (contains the 50-km lineimpedance).

Figure 23: Grid voltages for 10 MW load on both sections placed 50 km fromfeeding point

42

Figure 24: Grid currents for 10 MW load on both sections placed 50 km fromfeeding point

5.2.3 Case 3

In case 3, one load of 50 MW is placed in the bc-catenary section, close tothe feeding point. The load on the ac-section is considered to be very small,modeled as a large resistor of 62500 Ω. The voltage waveforms in figure 25are not changed significantly during this load condition compared to previoustwo cases for the RPC. The current waveform is, however, affected by the highload. The rectified load will draw a high current and significant harmonicdistortion can be observed in the current waveforms in figure 26.

43

Figure 25: Grid voltages for the conventional system. One section loadedwith 50 MW and the other section is modeled with no train connected

Figure 26: Grid currents for the conventional system. One section loadedwith 50 MW and the other section is modeled with no train connected

44

5.2.4 Case 4

In the fourth case the bc-side draws a power of 10 MW the ac-side initiallydraws a power of 1 MW. After a certain time the train that drew a power of 1MW will accelerate. The load will hence increase to 50 MW instantaneously.

The voltage waveforms in figure 27 still remained stable. The load stepcan be observed in the current waveforms in figure 28. The current wave-forms before the acceleration were quite good-quality sinusoidal waveforms.After the acceleration the waveforms are also of adequate quality, and thebalance among the three phases is still kept. However, some distortion canbe observed from the high load with rectified characteristics. There is ap-proximately one period until the system reaches the steady state after theacceleration instant.

Figure 27: Grid voltage waveform for train acceleration

45

Figure 28: Grid current waveform for train acceleration

46

5.3 Unbalance factor

From equation (3) and (4) the unbalance factor can be found. Equation (3)will give the positive sequence current for a phase current and equation (4)will give the negative sequence current for a phase. The unbalance factor isdetermined as following:

Kunbalance = |I2a

I1a| (37)

For the first case, the conventional system, described in 5.1.1. Values for thephase currents are found during simulation.

Ia = 0 −175 A

Ib = 3.75 ∗ 103 287 A

Ic = 3.75 ∗ 103 108 A

The unbalance factor, Kunbalance for the conventional system is approximately98 %.

For the equivalent case in 5.2.1, simulated with the RPC in operation, thephase currents will be as following:

Ia = 171 −1.8 A

Ib = 163 237.6 A

Ic = 171 116.8 A

The unbalance factor, Kunbalance for the RPC-system is approximately 0.45%.

47

6 Conclusion and Discussion

This study has shown that railway power conditioners (RPCs) can mitigateunbalances in the grid, as they reduce the degree of current unbalance sig-nificantly. In a conventional system, the unbalance factor can be nearly 100%, when the train is the only load served by the grid. In the system with aV/V-transformer and a connected RPC, the unbalance factor for the sameconditions decreased to about 0.45 %. The RPC could hence fulfill its pur-pose.

The conventional system is simple, cheap and there is a large knowledgebase in this technology, but it creates poor power quality in the grid. Inpractice the feeding from the single-phase transformers will be alternatingbetween the phases in the grid. This is done to equalize the average loadbetween the phases. However, the stochastic behavior of the train load willmake it impossible to have equal loading on all phases with single-phasetransformers. This may disturb other customers in the grid and lower theover-all performance of the power system. The power quality may even getworse with trains running at higher speeds or trains with a heavier load. Toobtain a better power quality, compensation must be implemented either onthe grid-side or at the railway-side.

The RPC can serve as a power compensator on the railway-side to sym-metrize the grid currents. This device contains converters with switchingdevices that will create harmonics. To obtain a better performance morestudies must be carried out to investigate its output harmonics, the lossesand the ratings of an RPC.

48

7 Future outlooks

To determine if this is a competitive solution for the railway traction sys-tem, further studies must be performed. The system must be investigated interms of harmonics and in what way the harmonic distortion from both theconverters and the traction equipment on the trains can be reduced.

The RPC-system could also be compared with other compensation systems,such as the STATCOM. The comparison could include both cost and perfor-mance. In this study only the basic operation of the RPC has been inves-tigated. The behavior of this system could be further analyzed under faultconditions. It is also interesting to understand if the system can providefurther support to the electrical grid, during the time that no train load ispresent.

49

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[2 ] L.Abrahamsson, T.Schutte, S.Ostlund, Use of converters for feeding ofAC railways for all frequencies, Energy for Sustainable Development,vol 16, issue 3, page 368-378, 2012

[3 ] T.Uzuka, Faster than a speeding bullet - An overview of Japanese high-speed rail technology and electrification, IEEE Electrification Maga-zine,vol 1, issue 1, page 11-20, 2013

[4 ] N.Y.Da,i K.W.Lao, M.C.Wong, C.K. Wong, Hybrid power quality con-ditioner for co-phase power supply system in electrified railway, IETPower Electronics, Vol 5, Issue 7, page 1084-1094, 2012

[5 ] Copenhagen Ringsted Team, Preliminary design of neutral section - TheNew Line Copenhagen Ringsted Alignment and Railway Technology,page 1-19, 2012

[6 ] T.Bagnall, F.Silizar, Conference on railway excellence 2014 Adelaide,Power electronics based traction power supply for 50 Hz, 2014

[7 ] Q.Liu, Xr. Li, Xj. Li, B.Lei, D.Chen, Y.Pan, Impact of negative se-quence current of traction load on the grid running state, AdvancedPower System Automation and Protection, International Conference,vol 2 , page 879-883, 2011

[8 ] J.Wang, R. Hamiltion, A review of negative sequence current, ProtectiveRelay Engineers, 63rd Annual Conference, page 1-18, 2012

[9 ] J.J.Grainger, W.D Stevenson, Power System analysis, page 416-420,1994

[10 ] J. Duncan Glover, M.S.Sarma, T.J.Overbye, Power system analysisand design, 5th edtion, page 428-431, 2012

[11 ] C.Zhao, Power supply for 50 Hz railway Systems: System simulationspecification, unpublished ABB, 2014

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[12 ] L.Xiaqing, Z.Li, Research on balance compensation of STATCOM,Beijing Institute, 2nd IEEE conference on industrial electronics andapplications, page 563-568, 2007

[13 ] T.Uzuka, S.Ilkedo, Railway static conditioner field test, Quarterly re-port of RTRI, vol 45, no2, 2004

[14 ] N.Y.Dai, K.W. Lao, M.C.Wong, A hybrid railway power conditioner fortraction power supply system, Applied Power Electronics Conferenceand Exposition, 28th Annual IEEE, page 1326-1331, 2013

[15 ] Z.Shu, S.Xie, K.Lu, Y.Zhao, X.Nan, D.Qiu, F.Zhou, S.Gao, Q.Li, Dig-ital detection, control, and distribution system for co-phase tractionpower supply application, IEEE Transactions on Power Electronics,vol 60, issue 5, page 1831-1839, 2011

[16 ] K.W.Lao, M.C.Wong, N.Y.Dai, C.K Wong, C.S Lam, A systematic ap-proach to hybrid railway power conditioner design with harmonic com-pensation for high-speed railway, IEEE Transactions on Power Elec-tronics, vol 62, issue 2, page 930-942, 2011

[17 ] A.Luo, C.Wu, J.Shen, Z.Shuai, F.Ma, Railway static power condition-ers for high-speed train traction power supply systems using three-phase V/V transformers, IEEE Transactions on Power Electronics, vol26, issue 10, page 2844-2856, 2011

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