METRO SIMULATION AND OPTIMIZATION

A. Guasch(a), D. Huguet(b), J. Montero(c) , ), J. Figueras(c)

(a)LogiSim, Universitat Politècnica de Catalunya (b)Siemens, Mobility Division

(c)LogiSim, Universitat Politècnica de Catalunya (d)LogiSim, Universitat Politècnica de Catalunya

(a)toni.guasch@upc.edu, (b) david.huguet@siemens.com, (c)monty@fub.upc.edu, (c)jaume.figueras@upc.edu ABSTRACT Manless Train Operation (MTO) control systems are being introduced in metro lines around de world. In this paper we present an MTO metro simulation system developed for the analysis of metro logistic operations and an optimization model for obtaining Optimal Daily Circulation Plans (ODCP) which reduces the energy consumption by improving the synchronization between accelerating and breaking metros, with energy regenerative breaking systems, within electrical substation areas. The target system for this research project is the line L9 of Barcelona metro network.

Keywords: metro simulation; metro optimization; manless train operations; regenerative breaking

1. INTRODUCTION With smaller inter-station distances, metro operation is essentially of start/stop nature. Due to frequent acceleration and breaking requirements, energy demand is very high. The quantity of energy consumed by trains is influenced by a wide range of factors, which can be grouped as (i) Design of network, (ii) Design of trains & (iii) Service planning operation (Nielsen 2005, Joshi 2008). Hence, optimization of overall system design in order to control consumption of electricity becomes essential.

Traction accounts for about 60-80% of total energy consumption in a Metro system. In order to reduce Metro consumption, modern trains incorporate regenerative braking systems. Metro railways worldwide have reported an average of about 20% saving in traction energy on account of regeneration. It also helps to reduce heat load inside tunnel and thus reduce air conditioning load if available.

The first part of this paper focuses on the optimization of the service operations in order to maximize the energy recovered by the regenerative braking systems in a metro network. Figure 1 shows that, in theory, up to a 40% of the train input energy can be recovered by the braking system. However, in practice, this depends on the overall design of the system. The paper focuses in the situation where the regenerated energy can only be reused by trains moving in the same substation area. If the regenerative energy is not needed in the area, it is dissipated by the electrical

network. In these cases is important the synchronization between accelerations and breakings within a substation area. Thus, the energy flows from the breaking train to the acceleration train. The target optimization problem presented here is obtaining an ODCP that maximizes the number of synchronized operations taking into account the service operational restrictions.

Energy input90% for traccion10% auxiliary needs

Regenerative brake40% of input energy

100% 40%

Figure 1: Regenerative brake energy balance

The capacity of a traditional metro system for

following ODCM is quite limited due to human intervention in the system. Therefore, the results of this project are only effective in Driveless or Manless metro systems (Figure 2).

Unlike conventional or driverless metro systems, a manless system consists of fully automated trains, without any driver or attendant on board the vehicles. Over the past decades, several manless systems were designed and put into operation around the world, offering a high quality of service and generating increased revenue.

driverdriverdriverATP driverdriverdriverATP

driverdriverautomaticATP + ATO driverdriverautomaticATP + ATO

On-boardassistant

automaticautomaticDTO (Driverless) On-boardassistant

automaticautomaticDTO (Driverless)

automaticautomaticautomaticMTO (Manless) automaticautomaticautomaticMTO (Manless)

INCIDENTSDOORSSTART/STOP INCIDENTSDOORSSTART/STOP

Figure 2: Metro systems

The second part of this paper is devoted to

description of a metro simulator which is being developed to analyze manless train operations:

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 210

• Evaluation of ODCM • Analysis of specific operations, for example,

shuttle metros for mass social events. • Analysis of degraded mode operations. The

degraded mode is active when normal operations cannot continue due to incidents, failures or accidents.

2. DESCRIPTION OF THE TARGET SYSTEM Next figure shows the L9 Barcelona metro line. With its 46,6 km will be the first MTO line in Spain and, up to know, the largest MTO line in Europe, It has 51 stations equipped with automatic doors which prevent fatal accidents at the stations.

Figure 3: Barcelona Metro L9

A Daily Circulation Plan (DCP) is composed of a

set of Line Services (LS). A LS specifies a set of consecutive station stops and the absolute starting time after each stop. Automatic Train Supervision (ATS) defines the movement time between stations in order to accomplish the LS. The movement can be chosen from a limited set of predefined times named:

• Slow time • Normal time • Rapid time • Fast time

There is a difference of 5 seconds between each

time level. LS are predefined using Normal Times, however, in case of a train disturbance; the Automatic Train Control (ATC) system can switch to a faster time to recover lost time. If the train is unable to recover the LS switching to a faster time, an order is issued from the ATS to all metros in order to resynchronize with the delayed one. The ability to follow specified LS is critical for minimizing energy consumption by synchronizing accelerating and breaking trains within the same electrical substation area. The MTO technology used in the L9 line guarantees that this will be true most of the time.

Since the L9 line is still under civil construction, the electrical network configuration is not known yet. Therefore, the electrical network substations shown in next figure composed by 6 electrical substations is only an assumption.

Substation 1

Substation 2

Substation 3

Substation 4

Substation 6

Substation 5

Figure 4: L9 electrical substations

The operational strategies have not been devised

yet. We have assumed that there are three different metro lines shown in next figure. Line L9A that goes from northwest to southeast and vice versa; line L9B that goes from southwest to northeast and vice versa and; L9C that moves in the central section that covers central Barcelona.

Figure 5: L9 lines

The above assumed configuration can be upgraded

as soon as real configuration becomes available. 3. OPTIMIZATION MODEL A first optimization model was developed using a discrete time model with a period of one second. The first results were unsuccessful due to the lack of convergence of the CONOPT solver.

The second approach is an event oriented model that uses data obtained from the simulation or real data if available. The data needed for every direct move between two stations is: minimum stop time at starting station; acceleration time (ta), running time (tr) and breaking time (td). The simplified model equations are:

nitdtt

nitrtt

nitatt

nitstt

iririr

iririr

iririr

iririr

,1;rr

,1;rr

,1;rr

,1;rr

d,,1,

r,,1,

a,,1,

s,,1,

==∀+===∀+===∀+===∀+=

−

−

−

−

(1)

Where ts is the stop variable constrained by the

minimum stop time and the desired maximum stop time. r is the set of events and rs, ra, rr and rd are the subset of the end of stop time, end of accelerating time, end of run time and end of breaking time respectively. i indexes the consecutives lines services. In the first model configuration the optimization goal is to obtain

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 211

the set of stop times that maximizes the synchronization between acceleration and breaking periods.

The main problem constraints are:

[ ] nits

nitptptt

nitptptt

ir

irir

irir

,1;rr 10,20

,1;rr

,1;rr

s,

s,1,

s,1,

==∀∈==∀∆−≤−==∀∆+≤−

−

−

(2)

The first two constraints limit the time period

between two consecutive metros to tp seconds plus/minus ∆tp seconds. For example, if the time period is 180 second we can constraint the time between metros to the [144,216] seconds interval. The third constraint states that the stop time at any station must be in the [10,20] seconds interval. The ability of the optimizer to obtain a good solution depends on the relaxation of the constraints. On the contrary, if we relax the constraints the level of service will be poorer.

Since the capacity of the solver is limited and the time it takes to obtain a solution is quite high (1 hour aprox.), we have limited the model time to approximately 2 and a half hours.

A set of constraints have been added to the model to obtain Partial Circulation Plans (PCP) or Optimal Partial Circulation Plans (OPCP) of an approximate duration of 30 minutes that have the quality that the position of the metros at the beginning of the period is equal to the position of the metros at the end of the period. Thus, if a metro is in the Camp Nou station at the beginning of the period, the same or another metro will be at this position at the end of the period. If a PCP or OPCP satisfies this constraints a larger PCP or OPCP can be obtained be replicating the plan as many times as needed.

The size of the optimization model is between 30.000,0 and 45.000,0 equations depending on the working configuration.

4. OPTIMIZATION RESULTS Next figure shows an OPCP. Metros going to the suburbs have a time period of 8 minutes. In the central sector, the period between metros is 2 minutes. Thus, L9A, L9B and L9C metros merging in the central sector are separated by the period of 2 minutes plus or minus the tolerance accepted in the constraint equations.

Table 1 shows a comparative of the results

obtained in this case. The columns are, from left to right,

1. In the first two rows we consider that the

movement time between stations is constant. In the next rows we want to see the impact of having a variable time between stations which is constrained by the ∆tr value specified in the first column. In this case, the modified equations are,

[ ]trtrtr

nitrtrtt

ir

iriririr

∆∆−∈∆==∀∆++= −

,

,1;rr

,

r,,,1, (3)

This is a simplified equation since the time variation with respect to the Normal Time is only attributed to the running time. The capability of playing with the running times easiest the task of synchronizing accelerating and breaking metros.

time

L9C

L9A

L9B

8 min

8 min 2 min

Central sector

event position Figure 6: OPCP

2. The second, third and fourth columns show the

specified time period for each metro line. The three following columns show ∆tp period tolerance with respect to the specified time period.

3. Next column shows the total breaking time (tbt). tbt Is the accumulated breaking time for all metros during one hour approximately.

4. Column number 9 shows the total non synchronized breaking time. The optimization function objective is the minimization of this value.

Table 1: Comparative results (seconds)

∆∆ ∆∆tr

tp (

Cen

tral

sec

tor

)

tp (

L9A

)

tp (

L9B

)

∆∆ ∆∆tp

(L

9C)

∆∆ ∆∆tp

(C

entr

al s

ecto

r)

∆∆ ∆∆tp

(L

9B)

tbt

nsb

t

Imp

rove

men

t

% im

pro

vmen

t

120 480 480 20 60 60 32160 122360 120 480 480 20 60 60 32099 10005 2231 6.9

2.5 120 480 480 20 60 60 32139 7228 5008 15.55 120 480 480 20 60 60 32180 5855 6381 19.8

7.5 120 480 480 20 60 60 32159 5304 6932 21.5

180 480 360 27 180 54 28940 126700 180 480 360 27 180 54 28639 10364 2306 8

2.5 180 480 360 27 180 54 28619 8898 3772 13.15 180 480 360 27 180 54 28600 8370 4300 15

7.5 180 480 360 27 180 54 28580 8759 3911 13.6

5. Column number 10 shows the improvement in synchronization as a result of the optimization.

6. The last column shows the percentage reduction of the total non synchronized breaking time with respect to the total breaking time.

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 212

The first block of results has a central sector time period of 2 minutes while the second block as a central sector period of 3 minutes and the L9B time period has been reduced to 6 minutes instead of 8 minutes in the first block.

The first experiment of each block shows the results without optimization. The only requirement of the solution is satisfying the equations and the constraints. The second experiment of each block increases the synchronization by optimizing the stop times at each metro station by minimizing the non synchronized breaking time. Approximately an additional 36 breaking minutes are synchronized with accelerating metros in one hour period. This is a between 6.9% and 8% improvement.

The three following experiments of each block suppose that the running times can be adjusted with a limit of +/-2.5, +/-5 and +/-7.5 seconds between each station. In the last experiment of the first block 115 breaking minutes are synchronized with accelerating metros in one hour period. This is a between 21.56% improvement.

The results of the last experiment of the second block should be improved since the solution obtained for the solver is not good enough. The main difficulty for obtaining a quasi optimal solution is that the cost function is non convex. We have performed a sensitivity analysis giving the solver different initial values for the same model. In general, the solver performs reasonably will in all cases. Next figure shows the value of the cost function given different starting points in the stop times at metro stations direction west and east.

Ts(r,i) east

Ts(r,i) west

10 2010

20

7.34

6.49

6.697.51

6.9

Cost function

Figure 7: Sensitivity analysis

Significant synchronization improvements are

obtained when the movement times between metro stations can be adjusted within a certain time interval. Unfortunately, L9 ATC only allows four different times: slow, normal, rapid and fast. Since the fast mode is left for delay correction, we only can use three different times instead of a continuous interval. We plan, not done yet, to use the simulator to measure the final improvement after discretization of the continuous interval into three possible values.

We also plan to try the CPLEX solver to solve the problem. This will allow coping with slow, normal and rapid discrete movement times directly. However, we are afraid of the capability of the solver to handle the non convex cost function.

5. SIMULATION A manless metro simulator has been developed in the project for the evaluation of the metro logistic operations and for validation of the previous optimization results.

The basic continuous equations used to model the metro dynamics are,

2vCvBAR

amRT

⋅+⋅+=

⋅=− (4)

Where T is the traction effort shown in figure 8 and R is the resistance that the train has on its movement. The coefficients A, B and C depend on the mechanical resistance, aerodynamic drag and grade resistance. Using these equations, the metro acceleration in traction mode is,

[ ])(1 2vCvBATm

a ⋅+⋅+−= (5)

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00

Speed [km/h]

Tra

ctio

n E

ffo

rt [

daN

]

U>1200 [V]

U=1000 [V]

U=800 [V]

Resistencia

Resistance

Figure 8: Traction effort

Barcelona L9 metro network uses the moving block control system. Under a moving block system, computers calculate a 'safe zone' around each moving train that no other train is allowed to enter. The system depends on knowledge of the precise location and speed and direction of each train, which is determined by a combination of several sensors: active and passive markers along the track and trainborne tachometers and speedometers. With a moving block, lineside signals are unnecessary, and instructions are passed directly to the trains. This has the advantage of increasing track capacity by allowing trains to run closer together while maintaining the required safety margins.

Figure 9 shows the dynamics of two metros moving very close. As metro1 accelerates, the distance (x1-x2) between both metros increases. When metro1 stops at the first station and metro2 moving behind

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 213

accelerates, the distance is reduced. Since metro2 does not stop at the any station, it catches metro1 at the second station. At that point the distance between metros is the length of the metro1 plus a security margin. Metro2 starts moving as soon as metro1 starts but the security distance has to increase to avoid crashing in case of sudden stop of metro1.

0

10

20

30

40

50

60

70

1 101 201 301 401

The securitydistanceincreases withthe speed

The security distance at the station is the train length plus a margin

V1 [km/h]

V2 [km/h]

(x1-x2) [dam]

Figure 9: Moving block dynamics

6. SIMULATION RESULTS Up to know, the simulator has been used, • to obtain the date needed for the optimization • to check that the OPCP generated by the optimizer

can be followed by the simulated metro network. Though the simulator is already operative, further

work is needed along the next months in order to add further experimentation capabilities,

• The first new set of experiments will measure the

synchronization time taking into account that the movement time between stations has three discrete candidates.

• The second experiment set will analyzed and propose working strategies in degraded mode. For example, a probable case is the blocking of a metro in a station. An alternative operational mode has to be proposed to avoid paralyzing the metro network. One possibility shown in next figure is to let metros in both directions to share the same track. A second possibility is to use the first arriving metro as a shuttle using the single track zone in exclusivity.

tren CBTC

tren CBTC

tren CBTC

shuttle

one track

Figure 10: Single track operation in degraded mode

• The third experiment set will propose new operational strategies to cope with specific needs such us crowded events. Two specific events will attract our attention. The mobility needs at the exit

of the Camp Nou soccer stadium and the mobility needs of the Barcelona Fair. The Camp Nou soccer stadium has a capacity of 98 thousand people. Soccer games are usually played on Saturday or Sunday evening. Since L9 will have spare capacity in this time zone, we will try to insert shuttle trains that have the first stop at the soccer stadium and the next stops will be at specific metro stations. For example, stations with the possibility of changing lines. The needs for the Barcelona Fair are more related to having direct metros to the airport at specific times.

7. CONCLUSIONS A metro optimization model and methodology has been developed with the goal of increasing the synchronization between acceleration and breaking metros in manless metro networks with energy regenerative breaking. Further work is needed to estimate the potential saving in electrical terms. However, we think that event small savings will payoff in midterm since the execution of optimal circulation plans does not require any investment by the metro operators.

A metro simulator has been developed with the objective of validating the optimal circulation plans and designing operational procedures for handling degraded mode or special scenarios.

ACKNOWLEDGMENTS This work is being funded by the Departament d’Innovació Universitat i Empresa (Generalitat de Catalunya, Spain) and the Ministerio de Industria, Turismo y Comercio (Spain).

We wish to thank the master students Joan Antoni Navarro and Alvaro Sanchez-Muro for their contribution to the project. REFERENCES Joshi S.S, Pande OH, Kumar A., 2008. Regenerative

Breaking in metrol Rolling stock. International Seminar on Emerging Technologies & Strategies for Energy Management in Railways. New Delhi, 2008.

Nielsen J. B., van Essen H.P., den Boer L.C., 2005.

Tracks for saving energy. Energy saving options for NS Reizigers. Delft, CE, July 2005

AUTHORS BIOGRAPHY Born in 1958, Dr. Antoni Guasch is a research engineer focusing on modelling, simulation and optimization of dynamic systems, especially continuous and discrete-event simulation of industrial processes. He received his Ph.D. from the UPC in 1987. After a postdoctoral period at the State University of California (USA), he

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 214

becomes a Professor of the UPC (www.upc.edu ). He is now Professor in the department of "Ingeniería de Sistemas, Automática e Informática Industrial" in the UPC. Since 1990, Prof Guasch has lead 35 industrial projects related with modelling, simulation and optimization of nuclear, textile, transportation, car manufacturing and steel industrial processes. Prof. Guasch has also been the Scientific Co-ordinator and researcher in 7 scientific projects. He has also been involved in the organization of local and international simulation conferences. For example, he was the Conference Chairman of the European Simulation Multiconference that was held in Barcelona in 1994. Prof. Guasch has recently published a modelling and simulation book that is being used for teaching in many Spanish universities. Prof. Guasch currently research projected sponsored by Siemens is related to the development of power management optimization algorithms for the Barcelona new L9 subway network. L9 will be the first metro line without driver of Spain and one of the largest (45 km) and modern automatic line without driver of the World. Prof. Guasch is also contributing to the development of toopath (www.toopath.com), a web server system for the free tracking of mobile devices. Born in 1975, Dr. David Huguet works in Mobility division of SIEMENS as a Project Research Manager. Dr. Huguet's work is focus on simulation and modelling of metro and tramway for optimizing their kinematic profile and for reducing the traction energy. He is actually professor of the Mechanical Department of the Polytechnic University of Catalonia, where he received his Ph.D. in 2005 for his work on Fluid Mechanics. Actually Dr. Huguet is involved in SIMUL9 and TRAM projects in collaboration with the UPC researchers. Jordi Montero, born in 1968, had his degree in Computer Science in 1998, has been PAS of UPC since 2000. His research interest includes discrete simulation system and he has working in several projects for different enterprises -Aena, Agbar, Almirall Prodesfarma, Damm, Indra, Siemens,...- and sectors: clinical trail, airport, transports, manufacturing, pharmaceutical. Jaume Figueras, born in 1974, had his degree in Computer Science in 1998. His research is in Automatic Control and Computer Simulation an Optimization. He has designed and developed CORAL, an optimal control system for sewer networks, applied at Barcelona (Spain); PLIO, an optimal control system and planner for drinking water production and distribution, applied at Santiago de Chile (Chile) and Murcia (Spain). Nowadays He participates in different industrial projects, like the power consumption optimization of tramway lines in Barcelona with TRAM and SIEMENS and the development of tooPath (http://www.toopath.com) a free web tracking system of mobile devices. He is also the local representative of

OSM (http://www.openstreetmap.org) in Catalonia and participates in different FOSS projects.

Proceedings of the European Modeling and Simulation Symposium, EMSS 2009Vol I - ISBN 978-84-692-5414-1 215