A Multi-Objective Simulator for Optimal Power Dimensioning on

Electric Railways using Cloud Computing

Alberto Garc

ıa Fern

andez, Silvina Ca

ıno Lores, F

elix Garc

ıa-Carballeira and Jes

us Carretero

Computer Science and Engineering Department, University Carlos III of Madrid,

Avda. Universidad 30, 28911 Leganes, Madrid, Spain

Keywords:

Railway Simulator, Power Dimensioning, Ontology, Multi-Objective Optimisation, Cloud Computing.

Abstract:

Power dimensioning and energy saving have been traditionally two main issues regarding the deployment of

electric grids. Electric railways are also concerned about these issues, and simulators have been traditionally

used to test such infrastructure deployments. The main goal of this paper is to present the Railway electric

Power Consumption Simulator, a simulation model and tool for the railway energy provisioning problem. This

simulator aims to propose electric railway infrastructure deployments, optimizing the quality of the electric

ﬂow supplied to train, as well as saving as much energy as possible. The paper describes the simulator

structure, as well as the ontology used to translate railway infrastructure elements into an electric circuit.

Because these two objectives are conﬂicting, a multi-objective optimization problem is formulated and solved.

Finally, a standard railway scenario is used to illustrate the capabilities of the tool, trying to ﬁnd the best

electric substation placements in order to optimize such objectives. The evaluation shows how the tool can

handle hundreds of simulated scenarios using Cloud Computing techniques.

1 INTRODUCTION

Power dimensioning and energy saving have been tra-

ditionally two main issues regarding the deployment

of electrical grids. Since their conception in the In-

dustrial Age, power grids are designed and deployed

following a trade-off between supporting high quality

provisioning to the consumers, and saving as much

energy as possible. Railway electric lines, as a par-

ticular case of electric grids, are also concerned about

these issues, trying to supply a steady ﬂow of energy

to the moving trains, but not exceeding the power re-

quired by them.

Within this context, simulators have been the main

tools to design and test railway electric lines. Prior to

its installation, a particular deployment can be tested

on a simulator, modelling the infrastructure and the

train trafﬁc in order to check the behaviour of the

system. Simulators like the ones introduced in (Pilo

et al., 2000; Bobi et al., 2007) are able to analyse per

instant if the power supplied to the trains is enough of

not, if there are voltage drops or over-voltages, etc.

Nevertheless, as computer systems evolve, the

role of simulators must become much more from

merely imitators of the real-world, to expert systems

with the ability of taking decisions and complement

the user knowledge with metrics in order to achieve

the best solutions. In previous works (Garc

ıa et al.,

2014), we stated that modern simulators should be

capable of proposing and evaluating new designs, tak-

ing into account all possible issues that may affect, or

even determine, the ﬁnal validity of a solution. This

search across the problem domain may be driven by

expert’s knowledge implemented within the simula-

tor, in the form of generation or evaluation rules that

may reduce the number of simulations performed, or

give those solutions a score indicating their ﬁtness ac-

cording to speciﬁc criteria.

The research community has been aware of this

need for optimal planning of power distribution sys-

tems as a whole (Pilo et al., 2015). In particular,

many of the relevant works in the ﬁeld are focused

on providing a near-optimal solution in a computa-

tionally efﬁcient manner. To achieve this, different

artiﬁcial intelligence (AI) techniques have served as

a base for the implementation of the aforementioned

decision making process, such as particle swarms

(del Valle et al., 2008), genetic algorithms (Ramirez-

Rosado and Bernal-Agustin, 1998; Carrano et al.,

2005), ant colonies (Gomez et al., 2004), simulated

annealing (Parada et al., 2004), artiﬁcial neural net-

works (Abrahamsson and Soder, 2009), multi-agent

428

Carretero J., Caino S., Garcia-Carballeira F. and Garcia A..

A Multi-Objective Simulator for Optimal Power Dimensioning on Electric Railways using Cloud Computing.

DOI: 10.5220/0005573404280438

In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2015),

pages 428-438

ISBN: 978-989-758-120-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

systems (Nguyen et al., 2011), and evolutionary al-

gorithms (Strbac and Djapic, 1995). These method-

ologies provide a holistic approach in which the sim-

ulator proposes consistent, well-suited solutions to a

particular problem.

Additionally, it may occur that the optimisation

process depends on different conﬂicting criteria, lead-

ing to a Multi-objective Optimization (MOO) prob-

lem. Works like (Augugliaro et al., 2004; Mendoza

et al., 2006; Carrano et al., 2006; Ramirez-Rosado

and Dominguez-Navarro, 2004; Soler et al., 2015) ap-

proach the system’s design from a MOO perspective,

which allows the user to deﬁne several optimisation

metrics such as minimization of power losses, over-

all deployment cost, system failure index, or maxi-

mization of energy savings, etc. This approach has

been also translated to the ﬁeld of railway power

supply systems, especially along with the previously

cited evolutionary techniques. In (Chang et al., 1995;

Chang et al., 1998), a trade-off between failure recov-

ery and load sharing is exposed and tackled as a MOO

problem.

Nowadays, many scientiﬁc areas make use of

the Cloud to overcome scalability issues in simula-

tions, and increase their performance. In particu-

lar, computing frameworks like MapReduce (Dean

and Ghemawat, 2008) have been increasingly used

as building-blocks for distributed large scale simula-

tors in a wide range of areas (Radenski, 2013; De-

craene et al., 2011; Kim et al., 2014). Railway simu-

lators have been also affected by this trend, integrat-

ing MapReduce and Cloud environments to existing

techniques with promising results in large datasets

and scenarios (Liu et al., 2010). Finally, works like

(Deelman et al., 2008) and (Angeli and Masala, 2012)

demonstrate the economic feasibility of migrating sci-

entiﬁc or engineering simulations to the Cloud, even

though making use of Cloud resources entails paying

for such resources to the Cloud services provider.

The main goal of this paper is to present a sim-

ulation model and tool for the railway energy pro-

visioning problem. This simulator aims to propose

electric railway infrastructure deployments, optimiz-

ing the quality of the electric ﬂow supplied to train, as

well as saving as much energy as possible. Because

these two objectives are conﬂicting, a MOO problem

will be formulated and solved. In order to handle the

high number of simulations performed, the simulator

is suited for Cloud Computing. The evaluation will

show how the tool can handle hundreds of simulated

scenarios using Cloud Computing techniques.

From the related works researched by the authors,

only (Abrahamsson and Soder, 2009), (Nguyen et al.,

2011), (Pilo et al., 2015), and (Soler et al., 2015) stay

close to the present work, in terms of usefulness and

capabilities. (Abrahamsson and Soder, 2009) pro-

poses a fast approximator based on neural networks

in order to plan power supply investments. On the

contrary, our approach is independent from underly-

ing AI techniques, so different search strategies can

be implemented just performing a few modiﬁcations.

In (Nguyen et al., 2011), an agent-based smart power

router is implemented, which can ﬂexibly integrate

network areas and optimally manage power ﬂows.

Nevertheless, this approach is outside the railway do-

main, so it does not take into account the particu-

lar railway domain characteristics. (Pilo et al., 2015)

and (Soler et al., 2015) propose both an optimization

problem of the AC railway power system, with mod-

els well-developed and consistent, but such models do

not consider as many details regarding the infrastruc-

ture as our model does. Finally, neither of these pro-

posals are based on Cloud Computing, nor they can

make use of elastic computing infrastructures accord-

ing to simulation sizes and deadlines.

The paper is structured as follows: Section 2 in-

troduces the simulator developed, including its struc-

ture and the ontology used to represent the railway

domain; Section 3 exposes the MOO problem, deﬁn-

ing the search problem, optimization metrics, and ob-

jectives; Section 4 describes the evaluation conducted

and the results obtained; and ﬁnally Section 5 pro-

vides key ideas as conclusions and some insight in

future work.

2 RAILWAY POWER

CONSUMPTION SIMULATOR

The Railway electric Power Consumption Simulator

(RPCS) proposes solutions for the problem of design-

ing and deploying electric infrastructure on railway

lines, trying to optimize the trade-off between power

supplied and energy saving. In this section we will

describe in detail the simulated domain, the ontology

implemented by simulator that represents such do-

main, and the main structure of the application. In the

following section we will analyse in detail the MOO

problem derived from the trade-off between energy

supply quality and energy saving, and its implemen-

tation within the simulator.

In collaboration with ADIF

, the Spanish railway

company, we have developed during the last years

the RPCS with the aim of testing and verifying dif-

ferent scenarios: developing new routes, increasing

train trafﬁc across the tracks, or testing failure situa-

http://www.adif.es

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429

tions where services have to be operated on degraded

mode. Currently the tool considers only direct current

(DC) systems, but its extension to AC systems is now

work in progress. The tool translates railway infras-

tructure elements such as tracks, feeders, electrical

substations and trains into an electric circuit, and then

solves that electric circuit. Along with the tool, we

have proposed the ontology that drives such transla-

tion of real infrastructure elements into elements of an

electric circuit: voltage sources, branches, and con-

sumers (current sources). We ﬁrst describe the tool

and its modules, and then we detail the ontology.

2.1 Application Description

The aim of this simulator is, provided a number of

trains circulating across the lines, to calculate if the

amount of power supplied by the electrical substa-

tions is sufﬁcient to allow that trains to render without

delays, failures, or any other contingency. Starting

from a description of the railway infrastructure (i.e.

tracks, catenaries deployed over the tracks, electric

substations placed along the tracks, as well as addi-

tional elements like feeders and switches), the simu-

lator reads the position of the trains and their instan-

taneous power demand. Then, for each instant of the

simulated period, the electric circuit formed by the

trains and the infrastructure is composed and solved

using Modiﬁed Nodal Analysis (MNA). More details

about MNA can be found on (Jahn et al., ). Useful

mean voltages, voltage drops, and temperatures of the

wires are examples of results provided by the tool.

The structure of the application is shown in Fig. 1.

It is a modular application with consists of a prepara-

tion phase in which all the required input data is read

and fragmented to be executed in a predeﬁned number

of threads. Two classes of input ﬁles are handled:

• A shared infrastructure speciﬁcation ﬁle contain-

ing the initial and ﬁnal time of the simulation, be-

sides a wide range of domain-speciﬁc simulation

parameters such as station and railway speciﬁca-

tions and power supply deﬁnition.

• A set of train movement data ﬁles, structured in

a time-based manner, in which each line contains

the calculation of speed and distance proﬁles for

a particular train at a speciﬁc instant regarding the

infrastructure constraints, and most important, the

instantaneous power demand, with a one second

interval.

Once all data have been read, the ontology mod-

ule translates the infrastructure and train positions

on the current instant into an electric circuit, and

solves that circuit. Tracks, feeders, and catenaries are

branches of the electric circuit, whereas trains act as

consumers, and the converter-rectiﬁer groups are the

voltage sources. The complete transformation pro-

cedure will be described along with the ontology in

Section 2.2. Finally, the simulator executes the algo-

rithm module for each instant to be simulated. With

this module, electric results are calculated on every

instant, using the MNA technique and an iterative pro-

cess. These results will be merged in the main thread

to constitute the ﬁnal output ﬁles. The MNA general

formulation is:











−As · is

ws2



(1)

In this problem, branches are considered resistors,

and there are only independent voltage sources, so the

previous equation can be simpliﬁed as:



G B

C 0











(2)

where G, B, and C are matrices of known val-

ues obtained from the circuit elements (connections,

conductances, etc.), u

and i

are the unknown volt-

ages and and currents, and ﬁnally i and e contain the

sum of the currents through the passive elements, and

the values of the independent voltage sources respec-

tively. Note that, due to the fact that the trains are in

movement, the system is constantly changing, so ev-

ery instant the electric circuit must be composed and

calculated, varying the position of the consumers. As

consequence, the MNA must be performed on every

simulated instant, thus requiring a signiﬁcant amount

of computing power to perform the whole simulation.

Simulated times may vary, from one hour, to one day,

to one week, implying from 3 600 circuits simulated

on short scenarios, to 86 400 on average scenarios, to

604800 on very large scenarios.

The simulator outputs electric data indicative

of the state of the circuit and all its components.

They include, for each simulated instant, voltages

and currents in all trains, voltages and currents in

the converter-rectiﬁer groups, and currents in all

branches. Additional data is post-processed calculat-

ing useful mean voltages on trains and zones of the

circuit. With all these data, several conclusions can

be drawn from the simulation:

• If the power supplied to the trains is enough of

not. Particularly:

– If the power stations are powerful enough.

– If the power stations are placed properly along

the tracks.

– If the train trafﬁc is excessive, given a particular

conﬁguration of the power stations.

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ALGORITHMMODULE

>t

end

ALLOCATE

CONSUMERS

SOLVE

CIRCUIT

ITERATIVE

PROCESS

WRITE

RESULTS(t

)

=t

ini

YES

ONTOLOGYMODULE

DATAMODULE

SCENARIOS

TRAIN

MOVIMENTS

SIMULATION

PARAM.

SIMULATION

RESULTS

TR ANSLATE

TR ACKS

TR ANSLATE

CATENARIES

TR ANSLATE

FEEDERS

TRANSLATE

ELECTR ICAL

SUBSTATIO NS

TRANSLATE

TRAINS

Figure 1: Application structure and its modules.

• If the current through catenaries and feeders are

excessive, overheating the wires. Particularly:

– If there is a design fault in the circuit that pro-

vokes too much current through a wire.

– If the wires deployed are too thin.

Figure 2 illustrates an example of the graphs out-

putted by the simulator. Fig. 2(a) displays possi-

ble voltage drops by plotting the minimum voltage

achieved at each point of the track. Fig. 2(b) rep-

resents the nominal and root mean square power of

a converter-rectiﬁer group along the simulated day.

Fig. 2(c) plots the current that circulates through a

feeder along the simulated day, as well as its root

mean square and the maximum current that this feeder

can accept before overheating. Finally, Fig. 2(d) dis-

plays a diagram of the positions of all trains circulat-

ing over a track during the day.

2.2 Ontology

Along with the tool, an ontology of the railway elec-

tric infrastructure domain has been developed. The

main objective of this ontology is to propose a taxon-

omy for translating real infrastructure elements into

an electric circuit. This electric circuit should reﬂect

the real behaviour of the system (i.e. trains, tracks,

electrical substations) as accurate as possible. There

are several reasons for developing an ontology. The

RPCS is a complete suite which includes not only the

simulation algorithm, but also:

• Project Management: the user can handle differ-

ent projects associated to geographical zones.

• Inventory Management: the user can handle an in-

ventory with materials or common pieces used by

the railway company. Besides, new materials or

pieces with different properties can also be added

by the user.

• CAD Tools. The RPCS includes several

computer-aided design (CAD) tools to display the

project, drawn electric or geographical schemas,

etc.

All these features are easier to develop if there is a

common ontology that homogenizes the problem do-

main. Besides, as multiple railway-related tools are in

development by the authors (Garc

ıa et al., 2014), an

ontology may ease the interaction between these tools

when importing or exporting elements from one to the

other. The entities and their relationships are repre-

sented in Fig. 3 through a semiformal UML model.

We proceed to describe such entities:

• Material. This entity represents a particular con-

ductive material with speciﬁc electric properties

such as resistivity or temperature coefﬁcient. Ma-

terials compose the rails and wires of the system,

thus inﬂuencing the electric behaviour of such

system.

• RailType and WireType. These entities represent

a particular typology of rail or wire, deﬁned by

the material that composes the rail or wire, and its

section. Material and section determine the resis-

tance per kilometre of that type of rail or wires.

Examples of those types are: copper 153 mm

wire, or UIC-54 6934 mm

steel rail.

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(a) Voltage drops (b) Average electrical power

Figure 2: Different graphs outputted by RPCS.

• FeederType. This typology represents a group of

wires. Feeders are usually deployed using several

wires in order to avoid overheating. This entity

represent a particular conﬁguration of wires (e.g.

3 x Cu153, which represents a feeder conﬁgured

with three cables of copper, 153 mm of section

each one).

• CatenaryType. A typology for catenaries, which

consist of supporting wire, contact wire, and op-

tionally, a compliment feeder in order to increase

the aggregated section of the catenary, avoiding

excessive overheating of the supporting and con-

tact wire because of the current.

• RailStretch and CatenaryStretch. These entities

represent a section of the track, from a starting

milemarker to a ﬁnal milermarker, in which a par-

ticular typology of rails or catenary has been de-

ployed. For instance, on a track, from the mile-

marker 20km to the milemarker 25km, the cate-

nary is composed of a supporting wire of Cu 153

, a contact wire of Cu 150 mm

, with no

compliment feeder, whereas in other stretch of the

track, a different typology of rails or catenary may

be deployed.

• Substation, Group, PositiveFeeder, and Negative-

Feeder. These entities represent an electrical sub-

station and its equipment: a main building that

contains one or several converter-rectiﬁer groups

(see entity Group). These groups transform the

power from the main grid into direct current, suit-

able for feeding the system, thus constituting the

voltage sources of the electric circuit. These

sources are connected to the catenaries at some

milemarker through positive feeders (see Positive-

Feeder entity). Finally, in order to close the cir-

cuit, the substation also contains the ground ref-

erence, and the circuit is closed through negative

feeders connected to the rails at some point of the

track (see NegativeFeeder entity).

• Train and TrainPosition. These entities represent

a particular train with its electric characteristics,

and the collection of time/position/power records

that constitute its run along the tracks. Trains de-

mand such registered power at the particular time

and point indicated by such registers.

• Track. This is the main entity that represents a rail

track: two rails (in a common case), and an over-

head catenary. The kind of catenary or rails can

change along the length of the track, as stated be-

fore. Trains run across the track, stopping eventu-

ally on stations or yards at some milemarker. Oth-

erwise connected explicitly by the user, tracks are

considered electrically independent ones from the

others.

• CatenariesConnection and CatenarySwitch.

These entities represent particular connections

and switches which allow the user to customize

the electric circuit, connecting electrically two

tracks, or separating electrically to ends of a

track.

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Material

-electricalResistivity

-specificConductance

-temperatureCoefficient

RailType

-section

-material : Material

WireType

-section

-material : Material

Track

-ID

-name

-initialMileMarker

-finalMileMarker

FeederType

-wires[] : WireType

-isolatedYesNo

CatenaryType

-contactWire : WireType

-catenaryWire : WireType

-complimentFeeder : FeederType

RailStretch

-initialMileMarker

-finalMileMarker

-railType : RailType

-railToGroundConductance

CatenaryStretch

-initialMileMarker

-finalMileMarker

-catenaryType

Substation

-ID

-name

-positiveFeeders[] : PositiveFeeder

-negativeFeeders[] : NegativeFeeder

-groups[] : Group

-connectionMatrix

Group

-ID

-name

-openCircuitVoltage

-power

-internalImpedance

PositiveFeeder

-ID

-track : Track

-connectionMileMarker

-feederType : FeederType

NegativeFeeder

-ID

-track : Track

-connectionMileMarker

-feederType : FeederType

Train

-ID

-name

-timeTable

-auxPower

-totPower

-maxVoltage

-trainPositions[] : TrainPosition

TrainPosition

-train : Train

-instant

-track : Track

-positionMileMarker

-powerDemand

CatenarySwitch

-track : Track

-positionMileMarker

CatenariesConnection

-track1 : Track

-positionMileMarker

-track2 : Track

-positionMileMarker2

-feeder : FeederType

1 N

composed

configured

can

include

0-1 0-1

configured

1 1

houses

positioned at

positioned

1 N

2 1

deployed

configured

Figure 3: Semiformal modeling of the RPCS ontology using UML.

The main algorithm that composes the electric cir-

cuit proceeds as follows: starting from a set of electri-

cally independent tracks, voltage sources (Group) and

ground connections are connected to the track from

the electric substation at some points indicated by the

feeders (PositiveFeeder or NegativeFeeder). Trains

run across the track demanding power at the time and

point marked by their TrainPosition instances, thus

acting as consumers in a circuit. Catenaries constitute

the load branches of the circuit, whereas rails con-

stitute the return branches of the circuit. The differ-

ent typologies of catenaries and rails along the track

are represented through stretchs (see CatenaryStretch

and RailStretch). These stretchs will be translated to

branches of some resistance depending on their con-

ﬁguration, through wire and rail electric properties.

Figure 4 represents how a particular infrastruc-

ture is translated into an electric circuit. In the ﬁg-

ure, three tracks, two electrical substations, and three

trains are translated into an electric circuit, where the

branches are numbered. Each electric substations is

translated into a set of branches and voltage sources

(see branches 0 to 4 and 9 to 11). The positive feeders

are translated into branches from the substation to the

catenaries (5 to 8 and 12 to 13), whereas the negative

ones connect the tracks to the substation (22, 23, and

24). Each catenary and track is considered a single

branch (16, 17, 20, 25, 26, and 27), but the user can

introduce switches in the circuit in order to divide the

same track in several independent branches (18, 19,

and 21). Finally, each train is represented as a branch

and current source, that connects the catenary (load

branch) to the track (return branch).

3 MOO APPROACH TO ENERGY

SAVING ON RAILWAY LINES

In the previous section we have described the RPCS

application, detailing how it can be used in order to

simulate a scenario with several tracks, trains, elec-

tric substations, etc. Nevertheless, as we stated be-

fore, modern simulators should be capable of propos-

ing and evaluating new designs taking into account

possible issues that may affect the ﬁnal validity of a

solution. In order to do so, we have implemented an

enhancement to the RPCS basic structure, turning to-

wards a MOO problem.

In this MOO problem, not one, but many simu-

lations will be executed. Each one of these simula-

tions constitutes a variation of the input data –either

the infrastructure or the trains–, and the results are

evaluated according to a set of optimisation metrics in

order to ﬁnd the optimum initial conﬁguration, with

regard to a speciﬁc optimisation criteria. The way

we vary the input data deﬁnes the problem’s search

space, which constitutes the set of solutions obtained

from the simulations, and the optimisation metrics

and functions deﬁne the goal we pursue in our search.

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Track1

Track2

Electrical

Substation1

Electrical

Substation2

Train1

Train2

Track3

Figure 4: Railway infrastructure and its translation into an electric circuit.

In this particular case, we focus on the trade-off

between energy saving and quality of energy provi-

sioning. The quality of the power supply refers to the

concept of maintaining the system as near to the nom-

inal voltage, U

nom

= 3000V , as possible. As trains cir-

culate along the tracks demanding power, voltage os-

cillations may arise all across the electric circuit, lead-

ing to voltage drops or over-voltages. Note that trains

do not always consume the same amount of power,

and even more, they can return power to the circuit

due to regenerative braking technologies. These situ-

ations should be avoided, maintaining a constant ﬂow

of electric power to the trains. While voltage drops

can be avoided by adding more electric substations

on the tracks, this may lead to over-voltages due to

excessive power. Besides, the more substations to be

placed, the more expensive the deployment is, and the

more aggregated energy is consumed by the electric

substations. This leads to conﬂicting objectives, thus

to a MOO problem: the goal of maintaining a con-

stant power ﬂow, in favour of providing more energy,

against the target beneﬁt of saving energy.

The problem search space to be studied will be

the placement of the electrical substations along the

tracks –i.e. the connection milemarker of the substa-

tion to the track–. By modifying the substations’ loca-

tions, we vary the electric circuit, thus we obtain dif-

ferent measures of instantaneous and mean voltages,

as well as consumed potency. Therefore, substation

placement has a direct impact on the power supply

quality and energy savings.

We aim to ﬁnd the corresponding Pareto fron-

tier of the MOO problem, thus giving the user the

set of optimal solutions and letting him or her chose

the preferred option. We propose a set of restric-

tion rules that must be fulﬁlled by the design in or-

der to be considered as acceptable, and set of optimi-

sation metrics in order to score those accepted solu-

tions. Both sets are obtained analysing the European

regulations (AENOR, 2004), (CENELEC, 2012), and

(CENELEC, 2015)

. A formalisation of the resulting

MOO problem is described next.

3.1 Problem Formalisation

As previously described, there are two objectives that

guide the optimisation process:

• Improve the quality of the power supply.

• Reduce the amount of power consumed by the

groups.

We deﬁne from these goals the following criteria:

• Maximise the mean useful voltage per train, O

• Minimise total amount of energy consumed by the

groups, O

This normative is still under vote by the CENELEC

committee until 15th of July, 2015

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The mean useful voltage, described in European

normative UNE-EN-50388 (CENELEC, 2012), is de-

ﬁned as the mean of all voltages at the pantograph of

each train in the geographic zone, along all simulation

steps. This measure indicates the quality of the power

supply. The lower the mean useful voltage is, the less

energy is transferred from the supply stations to the

trains, on average.

For the formalisation of this problem, let T be the

set of trains in the whole system, and G be the set of

groups in the network. The ﬁrst objective is deﬁned

in Eq. 3, where U

is the mean useful voltage per

train, and U

max

constitutes the maximum permanent

voltage.

max O

− 2800

max

− 2800

∀t ∈ T (3)

The second objective is formulated in Eq. 4,

where E

is the energy consumed per group, in kW/h.

min O

∑

i=1

i 6= g,∀g ∈ G (4)

The problem is subject to the following con-

straints:

• According to the normative (CENELEC, 2012),

the mean useful voltage per train, U

, must never

be lower than 2800V , and it shall not surpass the

maximum permanent voltage, U

max

2800 ≤ U

≤ U

max

(5)

• No sharp voltage drops or over-voltages shall ex-

ist on normal (non failure) operating conditions

(AENOR, 2004). Therefore, instantaneous volt-

ages should be in the range of non-permanent con-

ditions on every instant of the simulation. This

derives Eq. 6a and Eq. 6b.

min

≤ U

max

∀t ∈ T (6a)

min

≤ U

max

∀g ∈ G (6b)

• The mean voltages on trains and the simulated

zone, shall be within the limits of permanent op-

erating conditions, even if voltages fall beyond

that limits for a moment during the simulation

(AENOR, 2004; CENELEC, 2012). This yields

Eq. 7a and Eq. 7b.

min

≤ U

max

∀t ∈ T (7a)

min

≤ U

muz

≤ U

max

(7b)

4 EVALUATION

We selected as benchmark a standard railway scenario

described in the proposed draft of the European nor-

mative prEN-50641 (CENELEC, 2015). This pro-

posal of normative establishes the requirements for

the validation of simulation tools used for the design

of traction power supply systems. Therefore, it is

meaningful to apply such normative to conduct the

optimisations. Key parameters of this test case are

indicated in Tab. 1, and a general overview of the el-

ements of the experiment are shown in Fig. 5.

The search space was generated by conducting the

simulation with a different positioning of several sub-

stations. For each substation E

, the initial and ﬁnal

points of the interval in which they can be placed must

be deﬁned –E

ini

and E

f in

, respectively–, along with

the distance between each planned position for the

generation of the experiment set, ∆

As each substation can be assigned to any of the

points within the former interval, and all of the substa-

tions have to be combined with the others to generate

the experiment set, we would get as many different

experiments as indicated by Eq. 8, where M is the

number of substations to be manipulated. The equa-

tion indicates that, the ﬁner the grain of the planned

experiments, the more simulations have to be exe-

cuted in order to generate the solution space.

N =

∏

k=1



f in

− E

ini

∆



(8)

For this evaluation, we generated a set of 4 000 so-

lutions using the variations of the positions indicated

in Tab. 2, displacing each substation from one kilo-

metre to the next, without overlapping their ranges.

From this set, we sampled for this evaluation only

1000 random experiments, aiming to increase this

number for future works.

Since each experiment is composed of 4 800 sim-

ulation steps –one per simulated instant, correspond-

ing to 1h and 20m of simulated time–, it would be

required to solve 4 800 equation systems per experi-

ment. Considering that the number of experiments to

be simulated grows exponentially, as indicated by Eq.

8, the overall computing resources required to gen-

erate the solution space of the MOO would outscale

those typically available in current desktop comput-

ers.

To palliate this issue, we developed a version of

the power simulator suitable for the Cloud, which was

based on MapReduce. The complete process of adapt-

ing and implementing the Cloud version is described

in (Ca

ıno-Lores et al., 2015), as well as all the evalu-

ation performed in order to assure scalability when

AMulti-ObjectiveSimulatorforOptimalPowerDimensioningonElectricRailwaysusingCloudComputing

435

Table 1: CENELEC test case deﬁnition.

Trains Tracks Electrical substations Circuit branches (mean) Simulated time Input size (MB)

6 2 3 150 1 h 20 min. 4.2

Table 2: Variations of electrical substations placement on MOO optimization.

Electrical substation E1 E2 E3

Milemarkers(km) (initial, ﬁnal, ∆) (0, 20, 1) (20, 40, 1) (40, 50, 1)

Track1

Track 2

Elec trical

Substation1

Elec trical

Substation2

Electrical

Substation3

Train1 Train2 Train3 Train4

Train 5 Train 6

Figure 5: Schema of the main railway elements in the CENELEC test case. Parallel connections between catenaries or tracks

are not shown.

tackling with a high number of experiments. This

platform allowed us to disseminate the experiments

across a large cluster, resulting in an efﬁcient and scal-

able deployment that accelerated the overall solution

space generation process. Besides, Cloud Computing

paradigm brings us several features that can be useful

in the context of MOO:

• Virtual unlimited scalability of hardware re-

sources. The user is not tight on its local infras-

tructure, and more computing power may be allo-

cate on-demand.

• Flexibility according to instantaneous user needs

(through adapting computing resources). The user

may allocate more or less computing power de-

pending on the size of the simulation, and the

deadline for obtaining the results.

The selected cloud infrastructure consisted of a

general purpose m2.4xlarge node as dedicated master

and one hundred m2.xlarge machines as slaves. Table

?? shows the main aspects of the selected instances.

The results we obtained were parsed and evaluated ac-

cording to the metrics deﬁned in Sec. 3. The Pareto-

optimal frontier for the former data is shown in Fig.

6, along with the other solutions that resulted from the

subsequent simulations. The solutions that belong to

the Pareto-optimal frontier highlighted in Fig. 6 are

the ones that meet the optimisation criteria developed

in Sec. 3, yet the preferred solution still has to be cho-

sen by the end user. The ﬁnal selection could balance

the supply quality (O

) and the wasted energy (O

or be directed towards emphasising one of the optimi-

sation objectives. Table ?? gives the substation con-

ﬁguration for the limit solutions in the Pareto-optimal

frontier, the positions are indicated with respect to the

beginning of the rail track.

5 CONCLUSIONS

In this paper, we have presented the RPCS, a simula-

tion model and tool, with the aim of proposing elec-

tric railway infrastructure deployments. The tool in-

tends to provide optimal solutions with regard to the

quality of the electric ﬂow and the energy consumed.

Because these two objectives are conﬂicting, a MOO

problem is formulated and solved. In this MOO prob-

lem, not one, but many simulations will be executed.

Each one of these simulations constitutes a variation

of the electric substation placement, trying to ﬁnd the

best positions according to the optimization objec-

tives.

In order to solve a single scenario, the tool trans-

lates railway infrastructure elements such as tracks,

catenaries, feeders, and electrical substations, as well

as the trains, which act as consumers, into an elec-

tric circuit. Then, for each simulated instant, the tool

solves the circuit using the MNA technique, obtain-

ing the resulting values of train voltages and currents.

Along with the tool, an ontology to translate railway

infrastructure elements into an electric circuit is pro-

posed, as well as the algorithm to perform such trans-

lation.

In order to illustrate the capabilities of the tool, we

perform an evaluation using a standard railway sce-

nario deﬁned in an European normative. The aim is

to ﬁnd the best electric substations’ placement in or-

SIMULTECH2015-5thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand

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8200

8400

8600

8800

9000

9200

9400

0.1 0.2 0.3 0.4 0.5 0.6 0.7

(kW /h)

Solution space and Pareto-optimal frontier

Dominated solutions

Non-dominated solutions

Figure 6: Resulting solution space and Pareto-optimal frontier for the CENELEC experiment set.

der to maximize the two aforementioned objectives.

The number of explored solutions reaches one thou-

sand. Besides, for each simulation, the MNA tech-

nique must be performed on every simulated instant,

leading to 4 800 000 equation systems solved. In order

to tackle this amount of computing power required,

the application is built for Cloud Computing, using

instances allocated on demand to solve all of the sim-

ulations derived from the MOO problem.

As future work, we intend to enhance the MOO

problem focusing on different optimization objec-

tives. Currently, we only vary the electric substation

placement, but other infrastructure elements can be

modiﬁed in order to improve the overall system per-

formance: feeder typologies, electric substation con-

ﬁgurations, etc. Besides, a different MOO problem

can be proposed, focusing on fault-tolerance and sys-

tem resilience, as some other works do on general

electric grids, but particularizing the speciﬁc railway

domain characteristics. Furthermore, a different ap-

proach may be proposed, trying to optimize the train

trafﬁc instead of the infrastructure. Thus, the number,

type or even train drivers signature can be explored in

order to improve system efﬁciency. A main guideline

is to transform the tool into a a complete integrated

IDE, so that the user could set its own search vari-

ables, optimization metrics and restrictions, propos-

ing her/his own MOO problems using the tool. Fi-

nally, through this Cloud implementation, we aim to

develop several heuristics, in order to propose sizes

of the Cloud infrastructure (virtual instances, proces-

sors, memory, etc.) according to each particular MOO

problem’s characteristics (problem domain, restric-

tions, solution space, etc.).

ACKNOWLEDGEMENTS

This work has been partially funded under the grant

TIN2013-41350-P of the Spanish Ministry of Eco-

nomics and Competitiveness, and the COST Action

IC1305 ”Network for Sustainable Ultrascale Comput-

ing Platforms” (NESUS).

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