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WITPRESS

Power Supply,Energy Management

and Catenary Problems

This page intentionally left blank

Power Supply,Energy Management

and Catenary Problems

Editor: Eduardo PiloUniversidad Pontificia Comillas de Madrid, Spain

Published by

WIT PressAshurst Lodge, Ashurst, Southampton, SO40 7AA, UKTel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853E-Mail: [email protected]://www.witpress.com

For USA, Canada and Mexico

WIT Press25 Bridge Street, Billerica, MA 01821, USATel: 978 667 5841; Fax: 978 667 7582E-Mail: [email protected]://www.witpress.com

British Library Cataloguing-in-Publication DataA Catalogue record for this book is availablefrom the British Library

ISBN: 978-1-84564-498-7

Library of Congress Catalog Card Number: 2010920855

The texts of the papers in this volume were setindividually by the authors or under their supervision.

No responsibility is assumed by the Publisher, the Editors and Authors for any injuryand/or damage to persons or property as a matter of products liability, negligence orotherwise, or from any use or operation of any methods, products, instructions orideas contained in the material herein. The Publisher does not necessarily endorsethe ideas held, or views expressed by the Editors or Authors of the material containedin its publications.

WIT Press 2010

Printed in Great Britain by MPG Book Group.

All rights reserved. No part of this publication may be reproduced, stored in aretrieval system, or transmitted in any form or by any means, electronic, mechanical,photocopying, recording, or otherwise, without the prior written permission of thePublisher.

Editor: Eduardo PiloUniversidad Pontificia Comillas de Madrid, Spain

Contents Part A. Energy Management in the Train Operation

Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control T. Albrecht ..................................................................................................... 3 Power management control in DC-electrified railways for the regenerative braking systems of electric trains Y. Okada, T. Koseki & K. Hisatom ............................................................. 13 Impact of train model variables on simulated energy usage and journey time P. Lukaszewicz ............................................................................................ 25 A study of the power capacity of regenerative inverters in a DC electric railway system C. H. Bae, M. S. Han, Y. K. Kim, S. Y. Kwon & H. J. Park ....................... 35 Train operation minimizing energy consumption in DC electric railway with on-board energy storage device K. Matsuda, H. Ko & M. Miyatake.............................................................. 45 Computer-aided design of ATO speed commands according to energy consumption criteria M. Dominguez, A Fernandez, A.P. Cucala & L.P. Cayuela ........................ 55 Charge/discharge control of a train with on-board energy storage devices for energy minimization and consideration of catenary free operation M. Miyatake. K. Matsuda & H. Haga .......................................................... 65 Evaluation of energy saving strategies in heavily used rail networks by implementing an integrated real-time rescheduling system M. Luethi ..................................................................................................... 75

Part B. Power Supply System Analysis, Design and Planning Online temperature monitoring of overhead contact line at the new German high-speed rail line Cologne-Rhine/Main N. Theune, T. Bosselmann, J. Kaise, M. Willsch, H. Hertsch & R. Puschmann .......................................................................................... 87 Electric traction energy metering on German Railways and the impact of European standardisation on the energy billing process in Germany K. Weiland ................................................................................................... 95 Development of feeder messenger catenary with the auxiliary wire K. Nishi, Y. Sato & T. Shimada................................................................. 101 Catenary and autotransformer coupled optimization for 2x25kV systems planning E. Pilo, L. Rouco & A. Fernandez ............................................................. 113 Investigation into the computational techniques of power system modelling for a DC railway A. Finlayson, C. J. Goodman & R. D. White............................................. 123

Optimal design of power supply systems using genetic algorithms J.R. Jimenez Octavio & E. Pilo.................................................................. 135 Application of linear analysis in railway power system stability studies S. Danielsen, T. Toftevang & O.B. Fosso.................................................. 145 Fast estimation of aggregated results of many load flow solutions in electric traction systems L. Abrahamsson & L. Sder ...................................................................... 157 DC protection calculations an innovative approach R. Leach, D. Tregay & M. Berova............................................................. 171 Author index............................................................................................. 187

Preface In recent years, energy consumption has become a crucial concern for every transportation mode. However, it is in electrified railways where energy savings have shown a bigger potential due to (i) regenerative braking, allowing the conversion of kinetic energy into electric power, and (ii) vehicle interconnection, which permits other trains to use regenerated power. In the future, increasing energy efficiency and the emission reductions could lead railways to a significant gain of modal share. Hence, an important effort has been done by the industry, the operators, the research centers and governments to face this challenge. The proceedings of the last editions of COMPRAIL conferences on railways clearly reflect this sustained effort and main achievements of the past years. This book gathers selected research papers published in the Computer in Railways (COMPRAIL) series (IX, X and XI), which have been updated for this edition. Although the book is focused on infrastructure, in many cases it is not possible to analyze separately the train operation and the infrastructures behaviour, particularly when the overall energy efficiency is taken into consideration. The analysis of the impact of regenerative braking is a good example of that, as it depends on all theses aspects: the on-board electronic system and its control, the way the train is driven, the other trains in the area (scheduling), the electrical characteristics of the traction network, the presence of reversible substations (substations with inverters) and energy storage devices, etc. Accordingly, a number of papers describing important issues related to energy management and train operation have also been included. This book is organized in two parts. The first focuses on energy management issues in train operation and spans topics such as train driving, scheduling, regenerative braking and on-board energy storage; the second deals with infrastructure including topics such as catenary design and monitoring, traction power systems analysis, computational issues in simulations and optimization. Readers will find in this volume important papers dealing with a variety of topics of current interest. Finally, I would like to thank the authors for their revision of the papers as well as the team of WIT Press that has worked in the edition of this book. The Editor

Part A Energy Management in the

Train Operation

Reducing power peaks and energy consumptionin rail transit systems by simultaneous trainrunning time control

T. AlbrechtFriedrich List Faculty of Transportation Sciences,Chair of Traffic Control and Process Automation,Dresden University of Technology, Germany

Abstract

Costs for traction energy in electric rail transit systems do not only depend onthe energy actually consumed by the single trains. Other major factors affectingthe energy bill are power peaks, which stand for investment and sometimes foroperating costs and the efficient use of energy regenerated during braking, whichcan contribute to reducing peaks and energy consumption. For constant headwayoperation on a single line, the headway itself and the interval between the depar-ture times of two trains from the two different terminus stations (synchronizationtime) strongly influence energy consumption and power peaks. But these factorsare mostly not fixed in favour of reducing energy costs but determined by trafficdemand and operational restrictions.

This paper examines the possibilities of train running time modification in orderto reduce power peaks and energy consumption for any situation of given headwayand synchronization time. The problem can be described as the search for an opti-mal distribution of a trains running time reserve along its ride. The application ofGenetic Algorithms is proposed.

A case study is carried out for a German DC electric rapid rail system, wheredifferent cost functions are examined. Simulation studies are performed takinginto account stochastically varying station dwell times. It is shown that using trainrunning time modification, improvements in overall energy consumption can beachieved and power peaks can be reduced significantly.Keywords: energy saving train control, coordinated train control, regenerativebraking, genetic algorithm.

Energy Management in the Train Operation 3

1 Introduction

Minimizing energy consumption in electric railways systems is not only a questionof minimizing the trains energy needs for tractioning but also of efficiently usingregenerative energy. This topic is of special importance in DC systems with non-inverting substations. Here, energy billing is mostly realized at substation leveland the efficient use of regenerative energy can directly contribute to reducing theamount of energy to be purchased. But energy costs are not only determined bythe energy itself, power peaks often also influence the energy bill. According to aUITP survey of underground railway system operators [1], more than 80% of theoperators paid a capacity price for the fixed cost of energy supply, which dependson the effective value consumed during a fixed time period, e.g. 15 min.

Since the availability of fast and precise network simulators for modelling theeffects of the power supply system including regenerative braking, someapproaches have been taken to more efficiently using regenerative energy by meansof coordinated train control. Most of them deal with train dwell time control as amethod for improving the usage of regenerative energy. Control methods appliedare fuzzy control [2], search techniques [3] and heuristics [4, 5, 6]. They all havethe goal of providing decision safety, if and how long a train about to be startingshall wait at its station, so that no high power peaks occur during its accelerationand a big part of the energy needed for accelerating the train can be taken fromtrains braking at the same instant. This approach suffers from mainly two points:

1. As long as operating personal is responsible for the clearance of the train,precise timekeeping in the order of seconds can not be guaranteed. Passen-gers arriving during the additional dwell time trying to board the train willnot be denied their wish in most cases for reasons of customer satisfaction,but the optimal departure time passes by.

2. Train travel time reserve used as additional dwell time could also have beenused on earlier stages of the trains ride along the line as running time reservefor longer coasting phases. This effect is independent of the mode of opera-tion of the train (manual or automatic).

To overcome these two obstacles, this paper proposes an approach using train run-ning time control instead of train dwell time control for synchronizing accelerationand braking phases. The differences between the two approaches are illustrated infigure 1.

In the next section, the problem of distributing train running time reserve alonga line is examined and the solution for minimizing a single trains energy con-sumption is briefly presented. For the minimization of system energy consumptionin constant headway operation, the use of Genetic Algorithms (GA) is proposedin section 3. Section 4 examines the potential of the proposed method by meansof a case study for a German DC rapid railway system. The results for multi-traincoordination obtained using Genetic Algorithms are compared to the timetablewith minimal energy consumption for the single train.

4 Power Supply, Energy Management and Catenary Problems

time t

time t

necessarydwell timeat station

additionaldwell timefor optimal

synchronization

additionalrunning timeallows additionalenergy saving

improved usageof regenerativeenergy by delayeddeparture

power P

power P

a) dwell time control

b) running time control

power curveof second train

E

3 Using Genetic Algorithms for train running time control inconstant headway operation

To find an optimal combination of timetables for the two directions in constantheadway operation can not be regarded as multi-stage decision problem, as thedecisions have to be made simultaneously for many trains.

The application of Genetic Algorithms (GA) is proposed here for the solution ofthis problem. This universal solving tool can be used for practically any problemthat can be coded into binary form.

For coding, each unit of running time reserve (e.g. 1 unit = 1 s) makes up onegene. The information the gene contents is the section of the track on which thisparticular unit of running time reserve is to be spent. This coding results in abinominal distribution of the different timetables favouring timetables with equallydistributed running time reserve. This contributes to finding reasonable and notextreme solutions.

The initial population is created randomly except for one individual, whichpresents the timetable with minimal energy consumption for the single train.

The cost function to be minimized can be chosen freely. During simulation stud-ies the minimization of energy consumption and of 15-min-average power for allor selected substations have been used.

The size of the search space N for the particular problem of distributing k unitsof running time reserve among n sections of the line is equal to a combination withrepetitions

N =

(n+ k 1

k

). (1)

For a typical problem like the one presented in the next section the solutioncan be found using only 25 inviduals in one population for 50 generations, thisis extremely fast taking into account the size of the search space N 1014. Thesolution of one such problem takes about 60 - 90 mins using a MATLAB imple-mentation on a 2.4 GHz Standard PC.

4 Case study

A case study has been carried out for one line of the Berlin S-Bahn network. Itconsists of a track of 18 kms length with 14 stations (30 s dwell time at everystation). Power supply is realized by 4 substations situated at kms 0, 8.6, 11.8 and18 [8]. The different sections are electrically coupled. The vehicle used for thesimulations is a BR 481 EMU. Energy-optimal train control between two consec-utive stations is realized using the controller presented in [7]. The quality criteriaare computed using a network simulator based on the solution of the nodal voltageequations, specificities of DC systems are taken into account as proposed in [9].

At first, the influence of the parameters headway and synchronization time areexamined. Then, the results of train running time modification using Genetic Algo-rithms are presented. The obtained distribution of train running time reserve is used


300 600 900 1200 1500160

180

200

220

headway in s

energy consumption in kWh

300 600 900 1200 15000

25

50

75

100

headway in s

regenerative rate in percent

Figure 2: Energy consumption and regenerative rate for different headways.

as timetable to keep in simulations. The same simulation is carried out for a con-troller using Dynamic Programming and the minimization of the energy consumedby a single train as a target function. The both control strategies are compared.

4.1 Variation of headway

To examine the influence of the chosen headway on the energy consumed in thenetwork, a constant headway operation in only one direction of a line was sup-posed. It can be measured, how good the trains travelling in one direction are coor-dinated for themselves. It was assumed, that all trains travel with the timetablecausing minimal energy consumption for the single train. As figure 2 shows, thereare headways, which allow almost perfect reception of regenerated energy by thetrains travelling in only one direction, e.g. at 300 s. Receptivity of the networkdecreases with increasing headway, simply due to the fact of less trains operating.The increase of overall energy consumption is connected with it. The frequenciesvisible in the function plots depend on track geometry and vehicle properties.

4.2 Variation of synchronization time for a given headway

When operating at headways with inherent receptivity, the synchronization timebetween the two directions does hardly influence energy consumption or receptiv-ity of the line. For all other headways, this factor is of major importance. Here, aheadway of 600 s was chosen, being typically operated on the Berlin network dur-ing peak hours. Although this headway is a local minimum of energy consumption,the regenerative rate is far below ideal values.

In figure 3 the results obtained for energy consumption, 15-min-average powerand line receptivity are presented for a range of synchronization times for the givenheadway.


0 50 100 150 200

365

375

385

395

405

synchronization time in s

energy consumption in kWh (sum of all substations)

Minimal energy cons.for single train

Opt. criterion 15minav. power

Opt. criterion energy consumption

0 50 100 150 200

3

3.5

4


15minaverage power in MW (sum of all substations)

Opt. criterion15minav. power

Opt. criterionenergy consumption


0 50 100 150 200

70

80

90

100


regenerative rate in percent

Opt. criterionenergy consumption

Opt. criterion15minav. power


Figure 3: Energy consumption, 15-min-average power and regenerative rates fordifferent synchronization times and a headway of 600 s.

4.3 Variation of train running times for given headway and synchronizationtime

Choosing synchronization time is not only a question of energy consumption, thechoice is also influenced by the number of trains and, e.g. connections to otherlines. For a range of possible synchronization times in a 600 s headway situation,it was examined, what benefits can be achieved using train running time control.The application of Genetic Algorithms as proposed in section 3 was realized herefor two different cost functions. The results are plotted in figure 3.

It can be seen, that the values of energy consumption and 15-min-average powerare much smaller for the timetables optimized for system energy and power thanwith the initial timetable. It must furthermore be recognized, that the values


obtained for the different cost functions do in general not differ too much, but stillsignificantly. For an operator the optimal compromise can be found if its actualcost function is used for optimization.

As an example for a situation with a remarkable potential of train running timemodification, the situation for 180 s synchronization time will be examined closer.In figure 4 the initial timetable (optimized for energy consumption of the singletrain) is compared to a timetable optimized using GA with 15-min-average poweras cost function. The latter timetable leads to energy savings of 4% and a reductionof the sum of 15-min-average power of all substations of 17%.

Part a) shows the different distributions of running time reserve along the sec-tions of the line for both solutions. Whereas in the initial solution running timereserve is almost equally distributed among the sections, this is not the case for thesystem optimized timetable. It can already be seen from the resulting train trajec-tories in part b) of the figure, that there is more overlap of starts and stops in theoptimized timetable compared to the synchronous movement of the trains in themiddle sections with the initial timetable.

In part c) the sum of the demanded power, the power regenerated from brakingand the regenerative power not used in the network but wasted in braking resis-tances are plotted over time. The differences in the plots of these powers, servingfor the calculation of regenerative rates, are clearly visible: In the timetable opti-mized for multiple train operation the power peaks are much smaller and fewerenergy is wasted in the braking resistances. Part d) shows the reduction of theeffective power measured in the single substations by plotting the time-dependentcurves.

4.4 Simulation studies taking into account stochastically varying stationdwell times

All results shown before were computed under the assumption of constant dwelltimes in the stations. Here it will be examined, if and how the optimal timetablescan be realized in practical operation with stochastically varying dwell times. Forevery scenario to be described, 200 simulations were realized with varying dwelltimes at all stations.

At first, it is assumed that, given a certain timetable, the strict keeping of thistimetable is obligatory. The reserve to spend on the next section tres is calculatedwith

tres = scheduled arrival time shortest travel time actual departure time.(2)

When negative tres occur, time-optimal driving is applied. This corresponds toa very simple P-controller.

With an assumed variation of 10 s of station dwell time the calculated amount ofenergy saving and power reduction can also be realized under practical conditions.It can be seen that the absolute value of energy consumption is 6% higher than thetheoretical value (see fig. 5a), which obviously results from the situations, where


2 4 6 8 10 section no.0

20

40

60

sec

2 4 6 8 10 section no.0

20

40

60

sec

0 500 1000 1500 s

20

40

60

km/h

0 500 1000 1500 s

20

40

60

km/h

0 200 400 s

2

4

6

MWdemandedpower

usedregenerated

power

wastedregeneratedpow.

0 200 400 s

2

4

6

MWdemanded power

wastedregenerated

powerusedregeneratedpower

0 200 400 600 800 s

1

1.5

2

MW

SS1 SS2

SS3SS4

0 200 400 600 800 s

1

1.5

2

MW SS4

SS1SS3

SS2

a) Distribution of running time reserve along the sections of the line.

b) Vehicle speed over time in the two directions.

c) Demanded power and regenerated power used and wasted over time.

d) Mean effective power curves for the four substations (SS) over time interval.

Figure 4: Comparison between initial timetable on the left and timetable optimizedfor 15-min-average power (headway 600 s, synchronization time 180 s).


10s 15s 20s 25s390

400

410

420simple controller

Dynamic Programmingcontroller

10s 15s 20s 25s3.2

3.3

3.4

3.5

3.6

single train optimization

multitrain coordination

10s 15s 20s 25s65

70

75

80

85

90

in kWha) Energy consumption

in MW (sum of all subst.)b) 15-min-av. power c) Regenerative rate

in percent

Maximal deviation of station dwell times (equal distribution)Figure 5: Energy consumption, 15-min-average power and regenerative rates for

different variations of dwell time.

only few or none of the running time reserve is left and time-optimal driving hasto be applied in order to keep the timetable.

As mentioned earlier, the results of the optimization with Dynamic Program-ming can easily be used for online control. Compared to the strict timekeepingcontrol, energy consumption is reduced drastically and almost reaches the valueof multi-train optimization. With increasing dwell time variation, the advantage ofthis controller shows up clearly: Energy consumption as well as 15-min-averagepower decrease with this controller whereas with the simple controller and themulti-train optimized timetable the results rise fairly stronger. On the other hand,the regenerative rate remains higher for all examined cases with the multi-trainoptimized timetable.

As the GA optimized timetable fulfils its purpose by optimally coordinatingstarts and stops in the order of seconds, exact timekeeping is the only possibilityto reach this under stochastically varying dwell times. Whereas for smaller varia-tions this can be reached by the simple controller, higher variations call for a moresophisticated controller combining the philosophies of energy saving of the singletrain and coordination of starts and stops. The development of such a controller ispart of future work.

5 Conclusions

The paper presents a new approach to train running time control in order to achieveenergy cost reductions.

Given an optimal combination of headway and synchronization time, it is suf-ficient to apply a controller based on the minimization of a single trains energyusing Dynamic Programming. When these conditions can not be met, the modifi-


cation of train running times can contribute to significantly reducing power peaksand energy consumption and thereby reducing energy costs in rail transit systems.

Acknowledg ments

This paper contains parts of the authors doctoral thesis to be submitted to DresdenUniversity of Technology. It was elaborated within the research project intermobilRegion Dresden, which is funded by the German Federal Government, the Min-istry of Research and Eduction (BMBF) under the project no. 19 B 9907 A 8. Theauthor wishes to thank Prof. H. Strobel for his helpful advice during the researchand the elaboration of this paper. He is also very grateful to Prof. H. Biesenack andProf. A. Stephan for supporting the analysis of the railway power supply system.

References

[1] UITP, Reducing energy consumption in Underground systems - an importantcontribution to protecting the environment. Proc. of the 52nd InternationalCongress, Stuttgart 1997.

[2] Chang, C.S., Phoa, Y.H., Wang, W. & Thia, B.S., Economy/ regularity fuzzy-logic control of DC railway systems using event-driven approach. IEE Proc.-Electr. Power Appl., 143(1), pp. 9-17, 1996.

[3] Firpo, P., & Savio, S., Optimized train running curve for electrical energy sav-ing in autotransformer supplied AC railways. Proc. of the IEE ConferenceElectric Railways in a United Europe, pp. 23-27, 1995.

[4] Gordon, S.P. & Lehrer, D.G., Coordinated train control and energy manage-ment control strategies. Proc. of the 1998 ASME/ IEEE Joint Railroad Confer-ence, pp. 165-176, 1998.

[5] Guo, H.-J., Ohashi, H. & Ishinokura, O., DC electric train traffic schedulingmethod considering energy saving - Combination of train traffic parameters forlarger regenerative power (In Japanese). Transactions IEE Japan, 199-D(11),pp. 1337-1344, 1999.

[6] Sanso`, B. & Girard, P., Instantaneous power peak reduction and train schedul-ing desynchronization in subway systems. Transportation Science, 31(4), pp.312-323, 1997.

[7] Albrecht, T. & Oettich, S., A new integrated approach to dynamic schedulesynchronization and energy saving train control. J. Allan, R.J. Hill, C.A. Breb-bia, G. Sciutto, S. Sone, J. Sakellaris (eds.), Computers in Railways VIII, WITPress, pp. 847-856, 2002.

[8] Biella, W., Die rechnergesteuerte adaptive Fahrkennlinienvorgabe zur Ener-gieoptimierung bei DC-Nahverkehrsbahnen (Diss.) TU Berlin, 1988.

[9] Cai, Y., Irving, M.R. & Case, S.H., Iterative techniques for the solution ofcomplex DC-rail-traction systems including regenerative braking. IEE Proc.-Gener. Transm. Distrib., 142(5), pp. 445-452, 1995.


e

Power management control in DC-electrified railways for the regenerative braking systems of electric trains

Y. Okada1, T. Koseki1 & K. Hisatomi2 1The University of Tokyo, Japan 2Shin-Keisei Electric Railway Co. Ltd., Japan

Abstract

Most electric trains in DC-electrified railways are presently equipped with a regenerative braking system. On braking, the traction controller of a train can convert kinetic energy into electrical energy during deceleration of the train only when other powering trains consume the electrical energy as electrical loads for the regenerating train in the electrical circuit. Therefore, the traction controller of the braking train must reduce the electrical power following squeezing control of regenerative power when the electrical loads are too small in the electrical circuit, because there are, typically, no other devices to absorb the regenerated energy in the electrical circuit. However, actual traction controllers have often reduced regenerative power excessively because they do not recognize the states of the electrical circuit, which include positions of other trains and substations and power consumption/regeneration of other trains in the electrical circuit. In this paper, the authors discuss an improvement of the squeezing control of regenerative power based on information of the electric circuit. The information includes voltage at the pantograph, estimated positions and power consumption/regeneration of other trains etc.

1 Regenerative braking in DC-electrified railway

Fig.1 shows the typical power flow on braking in a DC-electrified circuit. The black solid arrows show the typical power flow in the present system, in which only the powering train consumes the power regenerated from a braking train. Therefore, the braking train must reduce the electrical power following squeezing control of regenerative power when the power consumption of powering trains is too small since there is, typically, no other device to absorb


the regenerated energy in the electrical circuit. However, there are many possible solutions for effective usage of regenerative braking. For example, brake choppers with resistances on board or in the electrical circuit contribute to maintenance reduction of trains. Another method is to install energy storage devices which include flywheels, batteries and double layer capacitors on board or in the electrical circuit, and commutated rectifiers at substations contribute to efficient energy usage. In addition, reduction of voltage regulation at substations and of feeding resistance can contribute to effective regenerative braking. However these methods require additional hardware, which mean additional cost. The other solution, which does not cause excessive cost, is to improve the squeezing control of regenerative power, which can enhances the performance of regenerative braking.

Powerconverter

M otorPow er

converter M otor

Pow ering trainRegenerating train

Energy storage by fly w heels, batteriesand double layer capacitors

Pow er consum ption w ith brake chopperand resistance

Substation

Pow er systemLoads

Im provem ent ofsqueezing control ofregenerative pow er

Reduction ofline resistance

Reduction ofvoltage regulation

Introduction ofcom m utated rectifier

Typical pow er flow in present system

System s for efficient energy usage andm aintenam ce reduction

System s for only m aintenance reduction

Energy storage by fly w heels, batteriesand double layer capacitorsPow er consum ption w ith D C chopperand resistance

Figure 1: Typical power flow on braking.

In this paper, the authors discuss improvement of the squeezing control of regenerative power with information of the electrical circuit and brake choppers with resistances.

2 Problems of squeezing control of regenerative power

On braking, the braking train converts kinetic energy to electrical energy. And other powering trains consume the electrical energy as electrical loads in the electrical circuit. Therefore, when electrical loads are too small in the circuit, the braking trains must reduce regenerative power following the characteristic shown by the solid line in Fig.2 to avoid excessive voltage at the pantograph. This control is called squeezing control of regenerative power.

Computers in Railways IX, J. Allan, C. A. Brebbia, R. J. Hill, G. Sciutto & S. Sone (Editors) 2004 WIT Press, www.witpress.com, ISBN 1-85312-715-9


1650 1750Voltage of pantograph[V]

Motor current 1900

C onventional characteristic

M axim al line voltage

0

Figure 2: Typical characteristic of squeezing control.

However, actual traction controllers often reduce regenerative power excessively [1]. The reasons for the excessive reduction are as follows; 1. traction controllers reduce regenerative power excessively in low-speed

range because they reduce AC motor current directly instead of their DC current,

2. traction controllers reduce motor current at lower voltage than maximal voltage limit of feeding circuit as shown by the solid line in Fig.2 and,

3. actual traction controllers often reduce motor current at lower voltage than the conservative voltage limit shown by the solid line in Fig.2.

In these problems, squeezing DC current of traction controller instead of AC motor current can solve the problem in 1(above). However, a traction controller needs to recognize the state of the electrical circuit in which braking trains exist to solve the problems in 2 and 3. When the traction controller cannot recognize the states of the electrical circuit, it must control regenerative power with statically conservative characteristic shown by the solid line in Fig.2 to avoid excessive voltage at the pantograph, because the voltage at the pantograph rises when a powering train, which exists in the electrical circuit, reduces its power consumption. The faster the reduction of power consumption is, the higher the voltage of the pantograph rises. Therefore, the traction controller must squeeze regenerative power regarding reduction of power consumption of register-controlled trains, which reduce their power consumption faster than any other train, in the electrical circuit. However, the reduction of power consumption of trains controlled by VVVF-inverters, armature choppers or a field chopper is slower than that of resistor-controlled trains. Traction controller squeezes, consequently, regenerative power excessively when powering trains controlled by these methods to reduce their power consumption.

3 Improvement of squeezing control

The improvement of electrical circuits, power management with data communication in an electrical circuit etc. are proposed to improve squeezing control of regenerative power [1], [2], [3]. In this paper, the authors propose squeezing control of regenerative power whose characteristics vary according to states of the electrical circuit. It is necessary to know the behaviour of the


pantograph voltage rising quickly at the stop of the power consumption of powering trains in the same electric circuit for improving the squeezing control of the braking train. For that purpose, the traction controller must have the following information; 1. the position and velocity of the trains, voltage at pantograph, DC current of

traction controller and power regeneration of the regenerating train, 2. running profile of the line on which the regenerating train exists, 3. control method of every train on the line, 4. the time when powering trains in the electrical circuit reduce their power

consumption and 5. distance between the braking train and the powering trains.

In the above, the information in 1 can easily be measured, and the information in 2 and 3 can be stored on board as data of traction controller. However, the information given in 4 and 5 needs to be estimated from the information in 1, 2 and 3. And, the characteristics of squeezing control of regenerative power must be determined, based on the information. One must propose how to estimate the information in 4 and 5 and how to determine the characteristics of squeezing control of regenerative power. The voltage regulation at the pantograph in the case of powering trains with various control methods, reduce their power consumption for determining characteristics of squeezing control of regenerative power in the following part of this paper.

Filtercapacitor

FilterreactorInternal

resistance

Feeder line(variable)

Substation Feeder line(1km ) Braking train

fc

0

Powering train

Squeezing control ofregenerative pow er

Tractioncontroller

l

r

fc

0 : C urrent operation from braking operation

ch

fc

B rake chopper operation

Brakingresistor

ch

r

Figure 3: Electrical circuit for examination.

4 Voltage regulation at the pantograph

4.1 Electrical circuit for examination of voltage regulation

Fig.3 shows the electrical circuit to calculate voltage regulation at the pantograph. The electrical circuit consists of a substation, a powering train and a braking train controlled by VVVF-inverter. The powering train is controlled by


VVVF-inverters, field-current choppers or resistor controllers. Fig.4 shows the equivalent circuits of the powering train and Fig.5 shows characteristics at reduction of power consumption at the powering train. The line voltage at the electrical circuit is limited up to 1900V. The authors will monitor the voltage at a filter capacitor of a braking train instead of that at pantograph.

Filter reactor

Filter capacitor

Tractioncontroller

Tractioncontroller

(b) Field chopper control Resistor control

(a) VVVF-inverter control

a

ll

a

Figure 4: Equivalent circuits of a powering train.

Ia[A]

1600 1600

Tim e[s] Tim e[s]

50

0 2.5 3.5 5

800

50

0 2.5 2.55 2.60 2.65

VVVF-Inverter control cResistorcontrol

5

1600

Tim e[s]

50

0 2.5 3.1 5

bField chopper control

Ia[A] Ia[A]

1.0s 0.6s 50m s

Figure 5: Characteristics at reduction of power consumption.

ECharacteristic ofsqueezing control

I0

I00 >I0 I =I00

I00

motor current. In addition, the distance between the powering and the braking trains is 2 km. Fig.7 shows voltage at the filter capacitor of the braking train. It also shows that the braking train can keep electric braking action by reducing its regenerative power continuously for avoiding excessive pantograph voltage, even if the other train stops its powering in various cases from Emax=1600[V] up to 1850[V]. In addition, Fig.8 demonstrates the relation between the voltage at the filter capacitor and the DC current from the braking train while the powering train reduces its power consumption in the case that Emax is 1850V. And Fig.8 illustrates that the traction controller of the braking train can reduce its regenerative power following the design of its squeezing control.

Figure 7: Voltage at the filter capacitor (VVVF-inverter).

Figure 8: Following characteristic of squeezing control (VVVF-inverter).

4.2.2 Case of powering train controlled by field-current chopper Fig.6 (a) shows operation logic for squeezing control of regenerative power when a powering train controlled by a field-current chopper stops its power consumption. In addition, the distance between the powering and the braking trains is 2 km.


Fig.9 shows voltage at the filter capacitor of the braking train. It also shows that the braking train can keep electric braking action by reducing its regenerative power continuously for avoiding excessive pantograph voltage, even if the other train stops its powering in various cases from Emax=1600[V] up to 1850[V]. In addition, Fig.10 illustrates the relation between voltage at the filter capacitor and the DC current of the traction controller of the braking train while the powering train reduces its power consumption in case that Emax is 1850V. And Fig.10 illustrates that traction controller of the braking train can reduce its regenerative power following the design of its squeezing control.

Figure 9: Voltage at the filter capacitor (Chopper).

Figure 10: Following characteristic of squeezing control (Chopper).

4.2.3 Case of resister-controlled powering train Fig.11 shows operation logic for squeezing control of regenerative power in case the powering train, which is resister-controlled, reduces its power consumption. In addition, the first order delay, whose time constant is 1.0 ms, is used to suppress vibration of I00 and the other first order delay, whose time constant is 30 ms, indicates characteristic of response of current at traction motor. Moreover,


the limiter 1 makes its output zero when its input is negative and the Limiter 2 makes its output zero when its input is positive.

E

I0

I00 I

ddt

Proportional gain0.3 Lim iter 1

Lim iter 2+

+

C haracteristic ofsqueezing control I00 >I0 I =I00

I00

higher Emax, since the influence from the action of the powering train is substantially smaller when the distance between the two trains is longer. The logic indicated by Fig.14 (b) determines the possible Emax to avoid excessive voltage at the filter capacitor of the braking train.

Figure 13: Voltage rise.

STARTEmax=1600[V]

C ircuit sim ulation

M axim al Efc < 1900V(during sim ulation)

Emax = Emax-10

End

Emax = Emax+10

No

Yes

(a) The possible Emax to avoid excessive voltage (b) The logic to determ ine the possible Emax

Figure 14: Possible Emax to avoid excessive voltage.

18500 1860

Ich[A]

Efc[V]

150

Figure 15: V-I characteristic for a chopper-control of a braking resistor.

If the braking train has supplemental braking resistor, whose characteristic for operation is assumed as Fig.15, Emax=1850[V] is possible for all the investigated


train distance, since the braking resistor can effectively absorb the power deviation from the spontaneous action of the powering train. In this case, maximal power consumption of the braking resistor at all the investigated train distance is 220kW, which is approximately 7% of maximal power consumption of typical electric train on powering.

5 Conclusion

In this paper, the authors have proposed squeezing control of regenerative power whose characteristics vary according to states of electrical circuit. They have examined the voltage at the filter capacitor of the braking train when the different three kinds of powering trains stop their power consumption. They have concluded: 1. when a powering train, which is controlled by VVVF inverter or field

chopper, stops its power consumption, braking train can successfully reduce its regenerative power with squeezing control whose Emax is close to maximal voltage limitation,

2. the controller of the braking train must reduce its regenerative power conservatively when a resister-controlled powering train close to the braking train stops its power consumption,

3. longer distance between the powering and the braking trains allows higher Emax, since the influence from the action of the powering train is substantially smaller when the distance between the two trains is longer, and

4. the braking resistor, whose power consumption approximately 7% of the maximal power consumption of typical electric train on powering enables Emax to be 1850[V] for all the investigated train distance.

6 Future work

The authors have studied only the squeezing control of regenerative power on board. However, they must also investigate how to estimate and use the following information to introduce a better squeezing control of regenerative power whose characteristics vary according to the states of electrical circuit; 1. the time when powering trains in electrical circuit stop their power

consumption, and 2. distance between the braking train and the powering train which cuts off its

power consumption.

Acknowledgements

and cooperation in the investigation in this paper. Mr. Hideki Iida at Shin-Keisei Electric Railway Co., Ltd. for their assistance The authors are grateful to Prof. Satoru Sone at Kogakuin University and


References

[1] S. Sone, Re-examination of Feeding Characteristics and Squeezing Control of Regenerative Trains, Joint Technical Meeting Transportation and Electric Railway and Linear drives, TER-02-49/LD-02-64, 2002.

[2] Y. Okada, T. Koseki, Evaluation of maximal reduction of electric energy consumed by DC-fed electric trains, NATIONAL CONVENTION RECORD I.E.E. JAPAN, 5-219, pp307-308, 2003.

[3] Y. Okada, T. Koseki, S. Sone, Energy Management for Regenerative Brakes on a DC Feeding System, STECH03, pp 376-380, 2003.


Impact of train model variables on simulated energy usage and journey time

P. Lukaszewicz Aeronautical and Vehicle Engineering, KTH, Stockholm, Sweden

Abstract Several train model input variables, such as running resistance, line voltage, adhesion, braking release time and braking gain time, are studied. An analysis is performed on how variations in the variables impact relatively on calculated energy usage and running time of trains. The study shows that for the calculation of energy usage the simulations are most sensitive to variations in running resistance, followed by line voltage, adhesion, braking release time and braking gain time. For the running time, the study shows that variation in mechanical rolling resistance and air drag has a relatively small influence provided that the tractive force is big enough. If the line voltage and adhesion, which affect here the tractive force, drop below certain levels the running time increases dramatically. The braking release and gain times have little influence on the running time. The results also show which variables should be paid extra attention to, when constructing a train model. Keywords: train modelling, train data, sensitivity, power consumption, energy usage, running time, simulations, ERTS.

1 Introduction

The correctness of computed results of energy usage and running time of trains in a railway network is dependent upon the chosen train model and input data. Therefore it is of interest to examine quantitatively how much the results can differ from each other if the input data used by the same train model varies and which data should be paid extra attention to.

By means of sensitivity analysis, the impact of the following variables is studied for a SJ Rc4 loco hauled freight train:


- Running resistance, which is the total force acting against the travel direction.

- Adhesion. - Tractive force (due to variation in catenary voltage). - Braking gain time, which is the time it takes to obtain the desired

braking force, from when the driver starts braking. - Braking release time, which is the time it takes to reduce the braking

force to zero, from when the driver stops braking. Section 2 describes the method and models. The results are presented in section 3 and are discussed in section 4.

2 Method and models

This sensitivity analysis on how variation in input data affects the final results on computed energy usage and running time is here performed by means of the Energy and Running Time Simulator, ERTS. ERTS is a simulation program developed by KTH and has verified models and data, versus full-scale measurements, of trains and drivers. The verification shows that the discrepancy between calculated and measured train energy usage is within the measurement error of approx. 2% [1].

The train models are detailed especially with respect to braking and tractive forces, electrical efficiency, running resistance, adhesion and slippage.

The driver models in ERTS are developed from full-scale measurements [2]. Observations were made on how real drivers are handling the trains especially with respect to track profile, signalling and type of train and service. The developed driver models, not included here, can drive a train as an average driver would drive, or drive in an optimised way with respect to energy usage or running time.

The driver model in this study is constant and set to drive the train strictly in accordance with the signalled speed. The acceleration is performed at maximal powering. Braking is performed as late as possible with respect to the braking ability which is set to 1/3 of the maximal braking force of the train. This level of the braking ability is obtained from observations on how the trains are driven in reality. The models are described in [1].

2.1 The train model

The train model represents a loco hauled freight train of mixed consist. The locomotive is of type SJ Rc4 and the tractive force diagram for two

different catenary voltages and powering levels is shown in Figure 1, together with the tractive force limit, F , due to adhesion as it is modelled in ERTS.

The calculated magnitude of the tractive force, Fw, takes into account the powering level, effect of speed, catenary voltage and the tractive force, F , available with respect to adhesion. In this study, no wheel slippage is present.


0 5 10 15 20 25 30 35 400

50

100

150

200

250

Ft

(kN

)

v (m/s)

Limit due to adhesion(ERTS)

Notch 9, 15 kV

Notch 3, 15 kV

Notch 9, 12 kV

Notch 3, 12 kV

Fa

Figure 1: Tractive force diagram. Notch 9 is the maximal powering level.

This means that the train speed is the same as the tangential speed at the peripheral of the wheels of the locomotive. The tractive force at the wheels, is calculated by:

),min( FFF tw = (1)

The total energy usage, of the train is calculated at the pantograph level for two cases; E1, when a tractive force is present and the train is moving, and E2 when the train is coasting, braking or not moving. ( )

21

1)(02

16

)(1

0or0;

0,0;106.3

1),(

)1(

EE

FvtPE

Fvvp

tvaKFE

En

iwii

n

iw

i

iiijiw

tot +=

===

>>++=

=

=

=

(2) where, Etot is total energy usage in kWh, n is the total number of time steps t during a simulation. K is a constant accounting for the rotational masses, a is the acceleration, is the slippage (=0), is the efficiency of the locomotive as a


function of power, p, and speed v, and P0 is originating from the auxilliary power. The total running time is calculated from

= = in itT 1 (s), for v>0 (3)

The freight wagons in the train set have 2 axles/wagon and are of two types; open type Oms and covered type Hbis. Basic data for the test train is shown in Table 1:

Table 1: Nominal and basic data for the test train.

Length, incl. loco 418.5 m Mass, gross incl. loco 1197 t Mass of locomotive SJ Rc4 79 t Axles, trailing 52 Max speed 100 km/h, 27.8 m/s Axle load, average 21.5 t Braking gain time, nominal 15 s Braking release time, nominal 30 s Braking level used 1/3 of max

The reason for choosing this train configuration is because of the existence of measured data [1] on energy usage, running resistance, tractive force, efficiency, braking ability and time lags in the tractive and braking systems.

2.2 Track model

The track model represents a tangent CWR. The length of the track is 88 km. A simulation with nominal input data for the train model results in a running time of 3597 s. The signalled speed restrictions are according to Table 2:

Table 2: Speed restrictions for the track model.

Distance (m) speed (km/h) 0 100

20490 40 21364 100 38152 70 39288 100 44106 70 44566 100 51322 40 52534 100 88000 100


3 Impact of variables on energy usage and running time

3.1 Simulation with nominal input data

Figure 2 shows the speed profile for the train obtained from simulation with nominal input data. Table 3 shows the numerical results. This is the reference case, with which all other results are compared with in this study.

Figure 2: Speed profile from simulation with nominal input data.

Table 3: Results from simulation with nominal input data.

Constant grade () Etot (kWh) T (s) Mean speed (m/s) 0 1723.5 3597 24.47 5 3329.9 3758 23.42

3.2 Running resistance

The nominal running resistance, 0RF , of the train set is obtained from full-scale measurements [1] and is calculated as a function of speed, v, by:

20 4.411.22911961 vvFR ++= (4)

The impact of variation of running resistance on energy usage and running time is shown in Figure 3.


Figure 3: Impact of variation of running resistance on energy usage and running time.

In this case, the impact on running time is small, but big on the energy usage. If the resistance has large errors from input data together with resistance originating from grades, the tractive force of the locomotive might not be sufficient. In this case severe delays will be present.

3.3 Adhesion

The available nominal adhesion is calculated in ERTS by the Curtius-Kniffler formula [3] which has been modified [1] to better suit full-scale test data.

07.50.9( 0.161)

44 3.6v = ++ (5)

The results are shown in Figure 4. If the adhesion is higher than nominal, almost no variation occurs. However, if the adhesion ratio for this case starts decreasing below approx 0.7, the running time starts increasing due to insufficient tractive power limited by the adhesion. Energy usage decreases mainly because of lower average speed which reduces the aerodynamic drag.

3.4 Line voltage

The tractive force of the locomotive SJ Rc4 is affected by the line voltage, see Figure 1. A voltage drop decreases the tractive force from the train speed of 17 m/s and up. The variation of running time and energy usage due to variation of line voltage is shown in Figure 5. The nominal voltage is 15 kV.

3.5 Braking gain time

The variation of braking gain time has for this studied case very small impact on the running time and energy usage, as shown in Figure 6.


Figure 4: Impact of adhesion on energy usage and running time for grade 0 and

5.

Figure 5: Variation of energy usage and running time due to variation of line

voltage.


Figure 6: Variation of running time and energy usage due to variation of braking gain time.

3.6 Braking release time

The variation of braking release time has a slight impact on energy usage. If the braking release time is reduced, compared with the nominal 30 s, a decrease in energy usage is distinguished, Figure 7.

Figure 7: Variation of energy usage and running time due to variation of braking release time.

4 Conclusions

This study shows in a quantitative way the importance of choosing correct input data and their significance. It is therefore important to have up to date models, to collect train data, maintain databases and to have information on how and for which circumstances the data should be used.

Variation of running resistance has little effect on running time, provided the tractive force is sufficient. The energy usage is strongly dependent upon the running resistance.

When the available adhesion, as modelled in ERTS, drops under a certain level the energy usage drops as well. The running time increases significantly.


When the line voltage drops and the tractive force is not sufficient, the energy usage drops as well. The running time increases significantly.

Variation of the braking gain and release times showed little significance in this study.

In this study, only the train model data is studied. An another important factor is the driver behaviour which has a strong impact on energy usage .

References

[1] Lukaszewicz P., Energy Consumption and Running Time for train. KTH Stockholm 2001. TRITA-FKT 2001:25. ISSN1103-470X.

[2] Lukaszewicz P., Driving describing parameters, energy consumption and running time. Computers in Railways VIII. Comprail 2002 Lemnos.

[3] Andersson, E. Berg, M.., Railway systems and vehicles (in Swedish). KTH


A study of the power capacity of regenerative inverters in a DC electric railway system

C. H. Bae, M. S. Han, Y. K. Kim, S. Y. Kwon & H. J. Park Korea Railroad Research Institute, South Korea

Abstract

This paper presents a method of determining power capacity and installation positions of regenerative inverters installed in DC electric railway system. This method uses the regenerative power data obtained from Train Performance Simulation (TPS) and Power Flow Simulation (PFS). The simulation results of TPS and PFS for Seoul subway lines 5 and 6 were applied, and suitable substations where regenerative inverters should be installed and the suitable power capacity to be installed were decided. Keywords: regenerative inverter, electric railway system, train performance simulation, power flow simulation.

1 Introduction

In a DC electric railway system, 22.9kV system voltage is converted into DC 1500V voltage through a 3-phase silicon diode rectifier and supplied to traction energy with railway motor cars. Since the regenerative power generated at the regenerative braking of motor cars cannot be absorbed into the supply grid in the case of diode rectifiers, this power should be used at nearby powering trains or consumed as heat at resistances mounted on the cars. However, if a regenerative inverter is installed in inverse-parallel with the diode rectifier, it can absorb this dump regenerative energy and feed it into an electric high-voltage grid for reuse. Accordingly, the energy can be saved by reusing dump regenerative power wasted away as heat, and the braking and ATO performance of motor cars can be improved through enhancing the regenerative power absorption rate of catenary lines. Despite these advantages, regenerative inverters cannot be installed at all substations for electric railways because the manufacturing and installation cost of regenerative inverters is higher than the benefit from the reuse of regenerative


powers. Thus, they should be installed at sections with a long continuous slope or where regenerative power loss in the resistor bank becomes a problem. In order to determine the appropriate installation positions, number and capacity of the regenerative inverter, it is necessary to calculate the accurate regenerative power generated in a subway line. This paper suggests determination schemes of the capacity and installation positions of regenerative inverters installed in 1500V DC electric railway system. We suggested a method that approximates using parameters related to substations where regenerative inverters are installed, railway lines and operating motor cars, and another that calculates using regenerative power obtained from Train Performance Simulation (TPS) and Power Flow Simulation (PFS) developed by Korea Railroad Research Institute for light rail transit system [1]. We carried out TPS and PFS for Seoul subway lines 5 and 6 and calculated the regenerative power and decided the substations where regenerative inverters should be installed and the suitable power capacity to be installed.

2 Power capacity of the regenerative inverter

Fig. 1 shows a diode rectifier and a regenerative inverter at an electric railway substation. The 12-pulse diode rectifier generates 1500V DC voltage and the IGBT regenerative inverter detects the voltage rise of the catenary line caused by the dump regenerative energy, absorbs the regenerative power, and transmit it to a high-voltage grid for reuse. Since many trains can brake simultaneously in a subway line, the peak power rating of the regenerative inverter needs to be higher than that of industrial inverters. Thus, the regenerative inverter allows the output AC current to limit at a certain level in constant current control mode in general. However, since this current cannot increase infinitely due to the limitations of the overhead line voltage, it is inevitable that the intermittent peak power rating of the regenerative inverters increases as much as possible. In order

Figure 1: DC electric railway substation equipped with a regenerative inverter.


to estimate the correct power capacity of such a regenerative inverter installed at substations for DC electric railways, it is desirable to block the regenerative power loss in the breaking chopper and resistor of all trains on a subway line, make a route for absorbing regenerative energy, and measure this surplus regenerative energy. Although this method can measure the surplus regenerative energy at a substation exactly, it requires regenerative power absorbing equipment, such as a resistor bank, installed at a substation. However, the additional installation of resistor banks at electric railway substations is not easy due to insufficient underground capacity in general. There are other methods, such as approximating based on variables related to the substation, operating line, train condition and regenerative power in other lines and calculating using TPS and PFS. However, because the level of regenerative power varies according to the conditions of the line on which the regenerative inverter is installed, the train condition and the operation condition, it is difficult to determine the accurate capacity through approximation based on these major variables. Accordingly, we need to calculate dump regenerative power in various train operation conditions by conducting TPS and PFS under different conditions of line, train and substation.

3 Approximation method

Fig. 2 shows the layout of a substation for a DC electric railway for calculating the power capacity of a regenerative inverter, and table 1 shows the calculation conditions. A regenerative inverter in charge of a 12km-long regeneration section is installed at substation B, and the number of trains running in the section, n , is obtained by eqn. (1).

hvln

s 60 [trains/hour] (1)

where b means an integer larger than b , distance ( l ), headway ( h ) and commercial speed ( sv ) are represented as units of meters, minutes, and hkm / ,

Figure 2: DC 1500V electric railway power system.


respectively. The total regenerative energy that takes place in a day in section l can be approximated in the following equations. Maximum power consumption per hour, mP , is calculated from the train ton-kilo capacity as follows,

kalwsnPm )1(2 [kW] (2) Here, the coefficient 2 means a double track section, and a is the standard deviation of power variation according to the train diagram. The power capacity of the regenerative inverter can be estimated using a power regeneration rate and a regenerative braking efficiency rate obtained from substations equipped with regenerative inverters at different railway substations. The power regeneration rate, 1 , means the ratio of absorbed regenerative power to the maximum power consumption of substations with a regenerative inverter, mP . The regenerative braking efficiency rate, 2 , means the ratio of absorbed regenerative power to the total regenerative power generated within the section covered by a substation with a regenerative inverter. Here, the total regenerative power includes the regenerative power consumed by nearby accelerating trains and regenerative power loss in the resistor bank. In general, power regeneration rate 1 ranges from 0.23 to 0.20, and regenerative braking efficiency rate 2 from 0.67 to 0.63 [2]. Using these data, the capacity of a regenerative inverter can be calculated as eqn. (3), where W denotes the total regenerative power generated from the section covered by the regenerative inverter. W includes the regenerative power consumed by nearby accelerating trains and power loss in the resistor bank. Accordingly, the capacity of the regenerative inverter should be larger than W considering the operation condition of the line.

2

1

mPW [kW] (3)

Braking force at deceleration rate, , can be obtained as eqn. (4). The braking electric power generated from the regenerative braking performance of a train at speed of v [km/h] is calculated by eqn. (5). ws)r(.Fb 3189 [N] (4)

367vFP bb [kW] (5)

The regenerative peak current, bI , can be calculated as follows.

inv

bb V

PI [kA] (6) On the conditions of table 1, W is obtained as 1480[kW] and bI 3.5[kA]. Thus, the power capacity of the regenerative inverter can be approximated as


1.5MVA, 350% 1 minute. However, this approximated calculation method does not consider the railroad and train operation conditions: grade, curvature, and headway duration. It can be used only to review the total system capacity rather than as a specification to install a regenerative inverter.

Table 1: Calculation conditions.

Item Value Item Value

Number of cars, s 8 (4M4T) Running resistance, r 10kg/ton

Headway, ht 2.5 min Maximum speed, mv 80km/h

Weight, w 48 ton/car Commercial speed, sv 35km/h

Decelerating rate, 0.97 m/s2 Regenerative operation voltage, invV 1650V Train ton-kilo capacity, k 50kW/1000tonkm Power regeneration rate, 1 0.20

Power delivery efficiency, 0.85 Regenerative braking efficiency rate, 2 0.65

4 Power flow simulation method

This section explains how to determine the capacity of a regenerative inverter using TPS and PFS. PFS is performed by changing the power capacity and the installation number of regenerative inverters, and the regenerative power loss of a railway line is calculated. The loss ratio of regenerative power means the ratio of regenerative power consumed as heat on the train to the whole regenerative power generated as shown in eqn. (7). After the optimal position and the number of regenerative inverters are determined, as a way of reducing the calculated loss ratio of regenerative power to the maximum, the root mean square of regenerative power (RMS power) and peak power are calculated. The effective regenerative power per hour calculated by eqn. (8) determines the continuous rating of the regenerative inverter, and is used to determine the peak power rating based on the maximum regenerative power rate and the braking time of motor cars.

1001

reg

inv

PPR (7)

where Preg denotes the 1-hour average value of the regenerative power generated in a subway line and Pinv denotes the 1-hour average output power of regenerative inverters in a subway line. In order to decide the continuous and intermittent peak power capacity of the regenerative inverter, the mean square value of the regenerative power generated in a substation is calculated as eqn. (8).


21

2)(1t

treg

sdttp

TP (8)

Here, P is the root mean square of regenerative power )(tPreg , and Ts sets 1 hour from t1 to t2. The determination method of the suitable installation location and power capacity of the regenerative inverters to be installed is shown in the block diagram in fig. 3, and the details are as follows.

1. Perform PFS for the case that regenerative inverters are installed in all substations on the line. 2. Calculate the mean square of regenerative power of each substation, and rank the substations according to regenerative power. 3. Perform PFS after removing the regenerative inverters from the two substations with the lowest regenerative power. 4. Again calculate the root mean square of regenerative power of each station with a regenerative inverter, and calculate the loss ratio of regenerative power for the whole line. 5. Perform PFS while removing the regenerative inverters one by one from the substations with the lowest regenerative power. 6. Draw the curve of the loss ratio of regenerative power according to the number of regenerative inverters installed in substations, and select the curve that shows the largest reduction in regenerative power loss.

Train Performance Simulation

DC Power Simulation

Decrease Installation Number of Regenerative Inverter

Calculate Loss Rate of Regenerative Power

Calculate Maximum and Root Mean Square

value of Regenerative Power

Decide installation substation

Decide Power Rating of Regenerative Inverter

Figure 3: Flowchart for substation selection.


Figure 4: Flowchart for regenerative inverter capacity.

10 12 14 16 18 20 22 24 26 28 301400

1500

1600

1700

1800

line

volta

ge[V

]

10 12 14 16 18 20 22 24 26 28 30

-4000

-2000

0

2000

4000

6000

8000

com

sum

ed p

ower

[kW

]

Time[min]

Figure 5: Seoul line 6 substation 8 without a regenerative inverter.

Once the position and number of regenerative inverters to be installed are determined, the rated capacity of the regenerative inverter and the peak power capacity are calculated through the procedure in fig. 4. The rated capacity of a regenerative inverter sets the root mean square value of regenerative power obtained from the substations, and the peak power rating is determined by the ratio of the peak regenerative power to the root mean square value of regenerative power. In addition, because the time for the rise of catenary line voltage caused by the dump regenerative power of the subway substations does not exceed 1 minute, the peak power rating is assumed to continue for 1 minute. We performed TPS and PFS using data on trains and lines of Seoul subway lines 5 and 6. Figs. 5 and 6 show the catenary line voltage and the power consumption waveform of substations according to whether a regenerative inverter is installed or not. In fig. 5, the regenerative power generated by the power braking of motor cars is increasing the catenary line voltage instantaneously. Fig. 6 shows that regenerative power is absorbed by the substation and the variation of catenary line voltage is reduced.


Fig. 7 shows absorbed regenerative power according to the number of substations with a regenerative inverter. Fig. 7 (a) shows the case that regenerative inverters are installed in all substations. Regenerative power is different among substations because of the grade differences of line, distance between stations and train operation conditions. Figs. 7(b)(f) show the regenerative power of each substation while removing the regenerative inverters one by one from the substations with the lowest regenerative power. As the number of substations with a regenerative inverter decreases, the regenerative power at nearby substations with a regenerative inverter increases to some degree.

10 12 14 16 18 20 22 24 26 28 301400

1500

1600

1700

1800

line

volta

ge[V

]

10 12 14 16 18 20 22 24 26 28 30

-4000

-2000

0

2000

4000

6000

8000

com

sum

ed p

ower

[kW

]

Time[min]

Figure 6: Seoul line 6 substation 12 with a regenerative inverter.

(a) (b) (c)

(d) (e) (f)

Figure 7: RMS of regenerative power in Seoul line 6.


Figure 8: Loss rate of regenerativepower in Seoul line 5.

Figure 9: Loss rate of regenerative power in Seoul line 6.

Table 2: Power simulation results of Seoul subway lines.

Line Substation RMS of regenerative power[kW] Peak regenerative

power[kW] Ratio [%]

5 Euljiro 4-ga 1449 7102 490 Haengdang 1284 5664 441

Majang 1350 6554 485

6 Eungam 1305 6780 520

Daeheung 1279 6481 507 Samgakji 780 3827 491 Shinnae 941 4833 514

Figs. 8 and 9 show the curve of loss ratio of regenerative power changing according to the number of regenerative inverters in Seoul lines 5 and 6. As a large-capacity regenerative inverter makes it possible to transmit more regenerative power to the supply grid, the loss ratio of regenerative power is reduced, and the curve of regenerative power loss goes down with the increase in the number of regenerative inverters installed. However, the reduction rate of regenerative power loss is not constant. This is because regenerative power is different among substations. As shown in figs. 8 and 9, reduction in the loss ratio of regenerative power decreases gradually with the increase in the number of substations with a regenerative inverter. In the case of Seoul line 6, the reduction in the loss ratio of regenerative power is largest when regenerative inverters are installed at four substations. Because a larger reduction in regenerative power loss is not expected from the installation of more regenerative inverters, it is desirable to install four regenerative inverters. As in fig. 7, the adequate capacity of the regenerative inverters for substations 1 and 5 can be selected as 1.5MVA and 1MVA for substations 6 and 12, respectively. However, it is economically more efficient to install a regenerative inverter only at substation 5 than at both, because substations 5 and 6 are neighboring to each other. We performed PFS for Seoul subway lines 5 and 6, and present the results in table 2. The suitable power capacity of the regenerative inverter is determined by


estimating the rated capacity as larger than the root mean square of regenerative power from each substation and determining the peak power rating using the ratio of peak regenerative power to the rated capacity.

5 Conclusions

This paper presents the methods for determining the installation location and power capacity of regenerative inverters in DC electric railway systems. Using a simple approximated calculation based on the conditions of the substations and train operation and the regeneration rate of other railway lines, the power capacity of the regenerative inverter was calculated. Also, the loss ratio of regenerative power and the root mean square of regenerative power for each substation were obtained using TPS and PFS and the installation location and number of regenerative inverters was decided. Applying TPS and PFS to Seoul subway lines 5 and 6, we obtained the suitable installation location and the power capacity of the regenerative inverters to be installed.

References

[1] S.K. Jung et al., Right Rail transit system development, Korea Railroad Research Institute, 2002.

[2] Electric Railway DC Power Supply System Investigation Committee, Phenomena of Power Supply System Including Regenerative Cars and Future Directions, Technological Report No. 296 of Japanese Institute of Electrical Engineers, 1989


Train operation minimizing energyconsumption in DC electric railway withon-board energy storage device

K. Matsuda, H. Ko & M. MiyatakeSophia University, Japan

Abstract

The optimal train operation which minimizes sum of supplied energy fromsubstations is presented in this paper. In recent years, the energy storage deviceshave enough energy and power density to use in trains as on-board energy storage.The electric double layer capacitor (EDLC) is assumed as an energy storagedevice in our study, because of its high power density. The on-board storagecan assist the acceleration/deceleration of the train and may decrease energyconsumption. Many works on the application of the energy storage devices totrains were reported, however, they did not deal enough with the optimalityof the control of the devices. On the other hand, our previous works were tooptimize acceleration/deceleration commands of the train for minimizing energyconsumption without the energy storage device. Therefore, we intend to optimizeacceleration/deceleration commands together with current commands throughenergy storage devices as our next research target. The proposed method candetermine the optimal acceleration/deceleration and current commands at everysampling point. For this purpose, the optimal control problem of the train operationis formulated mathematically. It is generally difficult to solve the problem becausethe problem is composed of a large-scale non-linear system. However, theSequential Quadratic Programming (SQP) can be applied to solve the problem.Two results with and without on-board energy storage device are compared. Theseoptimized results indicate that the total energy consumption is reduced by at least0.35% by using the EDLC. The relation between internal resistance and energyconsumption is also revealed.Keywords: electric double layer capacitor (EDLC), optimal control, energy savingoperation, SQP method.


1 Introduction

In recent years, the energy storage devices have enough energy and powerdensity to use in trains as on-board energy storage. The devices are for instance,a secondary battery and an Electric Double Layer Capacitor (EDLC). Aboveall, the EDLC has advantages such as maintenance free, long lifetime, rapidcharge/discharge with large current and high efficiency. Therefore, the EDLC is themost suitable to equip trains as an auxiliary power supply. The on-board EDLC isuseful because of the following two reasons. Firstly, it decreases the loss of circuitresistance by compensating voltage drop. Secondly, it enables us to utilize andrecycle regenerative power efficiently and prevent regenerative failure.

Many works on the application of the energy storage devices to trains werereported. However, from an energy-saving point of view, they did not dealenough with the optimality of the control of the devices. On the other hand,our previous works [1, 2] was to optimize notch commands which determine theacceleration/deceleration force in the train without energy storage devices. Weoptimize notch commands together with charge/discharge commands with makinguse of the experience of our previous study. It is significant to investigate theoptimal charge/discharge command minimizing energy consumption in order tomaximize the effect of installing the EDLC.

In this paper, we intend to formulate the optimal control problem of the trainoperation to find notch and charge/discharge commands which minimize amountof consumed energy, propose how to solve it, discuss the optimized results and findknowledge of the optimal operation. The knowledge will be applied to the futurecharge/discharge controllers for EDLCs.

2 Modeling of DC feeding Circuit

We modeled a DC feeding circuit when there is only one train between substations.The model circuit appears in fig. 1. In this figure, Vs and R0 are the supply voltageand the internal resistance at a substation respectively. The values of R1 and R2 arewire resistances. These resistance values are proportional to the distance betweenthe train and substation position. Positions of substations and stations are shownin fig. 2. The constants C and Rc are the capacitance and internal resistance in thecapacitor respectively.

It is necessary to convert voltage by using a chopper because thevoltage difference is high between the pantograph and capacitor. The choppercharacteristic is too complicated to be examined in detail here. Therefore, wesolved the circuit equation on the assumption that the chopper efficiency is 95%.

In addition, the energy consumption in the train is regarded as constant inshort time because acceleration/deceleration commands do not change often. Themotor-inverters of the train are modeled as a current load that helps solving circuitequations simply.


CR1

Chopper

R0 R0

VS VS

Substation1 Substation2

RC

R2

Train

VT

Figure 1: Circuit model with one train between substations.

SS1 ASDS SS2LLa Lb AS:arrival station

DP:departure station

SS:substation

Figure 2: Positions of stations and substations.

3 Formulation of optimal control problem

We formulated the optimal control problem in this section. Here, variables aredefined as follows. Control inputs n and u determine the acceleration/decelerationforce and charge/discharge current through the capacitor, respectively. Theyare defined as table 1. State variables x, v and Vc indicate the train position,speed and capacitor voltage, respectively. Variable VT is the voltage at thepantograph. In fact, it is a state variable if control inputs are determined and thecircuit equation can be solved. However, we defined VT as the auxiliary variablebecause it is difficult to solve circuit equations analytically. Additionally, these allvariables depend on time t. The optimal control problem is described as follows,mathematically.

Table 1: Definition of control inputs n and u.

n or u Operation mode Current through the capacitor-1 maximum deceleration maximum chargenegative deceleration charge0 coast waitpositive acceleration discharge1 maximum acceleration maximum discharge


Minimizing the objective function

J = T0

VsIs(x, VT )dt (1)

Subject to the following equality and inequality constraints

x = v (2)v = f(n, v, VT ) r(v) (3)Vc= Ic(u)/C (4)P T (n, v, VT ) = Ps(x, VT ) + Pc(u, Vc) (5)x (0) = 0 v(0) = 0 Vc(0) = Vc first (6)x (T ) = L v(T ) = 0 Vc(T ) = Vc final (7) 1 n 1 (8) 1 u 1 (9)V T min VT VT max (10)V c min Vc Vc max (11)0 x L (12)v 0 (13)

whereIs sum of load currents supplied by substationsIc current through the capacitorf ,r acceleration/deceleration force and running resistance per kgPT electric power supplied to motor-inverters of the trainPs, Pc power from substations and the capacitorVT min, VT max lower and upper limitations of the voltage at the pantographVc min, Vc max lower and upper limitations of the capacitor voltageVc first, Vc final first and final values of the capacitor voltageL, T distance and running time between the departure and arrival

station.The objective function is sum of supplied energy by two substations given as

eqn. (1). Equality constraints are given as eqns. (2-7). Eqns. (2),(3) are motionequations of the train. The capacitor voltage is given as the eqn. (4). As mentionedabove, we must solve the circuit eqn. (5) because we defined VT as an auxiliaryvariable. Eqns. (6),(7) describe the initial and final conditions of state variables.Inequality constraints of control inputs, state and auxiliary variables are shown ineqns. (8-13). Especially, we did not consider speed limitations in eqn. (13).


We defined functions as below.

PT (n, v, VT ) =

{Mvf(n, v, VT )me (n 0)Mvf(n, v, VT )/ge (n 0)

(14)

P s(x, VT ) =(

Vs VTR0 + R1(x)

+Vs VT

R0 + R2(x)

)(15)

R1(x) = (La + x)r0 R2(x) = (L x + Lb)r0 (16)

P c(u, Vc) =

{VcIc(u)ce (u 0)VcIc(u)/ce (u 0)

(17)

I c(u) = uIc max (18)

Here, me and ge are motor/generator efficiency. Wire resistances R1 and R2 aregiven in eqn. (16) when the position of the departure station is defined as x = 0.The constants La and Lb indicate the distance from the departure and arrival stationto the substation1 and substation2 shown in fig. 1. The constant r0 is the wireresistance per meter. The constant ce is the chopper efficiency. The constant Ic maxis the rated value of the current from the capacitor.

Additionally, maximum acceleration/deceleration characteristics, such as thecontrol input n is 1 or -1, and running resistance are given in fig. 3. thesecharacteristics are influenced by the voltage at the pantograph VT . Especially, weassume that the braking system is the air supplement control. In short, the use ofelectrical and mechanical blended braking system is considered if the regenerativebraking force is not enough for the specific braking force. Moreover, we are notconcerned with the characteristic of the squeezing control because we also assumethe regenerative power can be absorbed at substations.

The absorbed power can be accounted in eqn. (1).

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

Velocity[m/s]

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