Power Supply, Energy Management, and Catenary Problems [1 ed.] 1845644980, 9781845644987

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Power Supply, Energy Management and Catenary Problems

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Power Supply, Energy Management and Catenary Problems

Editor: Eduardo Pilo Universidad Pontificia Comillas de Madrid, Spain

Editor: Eduardo Pilo Universidad Pontificia Comillas de Madrid, Spain

Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail: [email protected] http://www.witpress.com For USA, Canada and Mexico WIT Press 25 Bridge Street, Billerica, MA 01821, USA Tel: 978 667 5841; Fax: 978 667 7582 E-Mail: [email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from 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 set individually by the authors or under their supervision. No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. The Publisher does not necessarily endorse the ideas held, or views expressed by the Editors or Authors of the material contained in 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 a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.

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. Söder ...................................................................... 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 infrastructure’s 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

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Part A Energy Management in the Train Operation

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Energy Management in the Train Operation

3

Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control T. Albrecht “Friedrich 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 on the energy actually consumed by the single trains. Other major factors affecting the energy bill are power peaks, which stand for investment and sometimes for operating costs and the efficient use of energy regenerated during braking, which can contribute to reducing peaks and energy consumption. For constant headway operation on a single line, the headway itself and the interval between the departure times of two trains from the two different terminus stations (synchronization time) strongly influence energy consumption and power peaks. But these factors are mostly not fixed in favour of reducing energy costs but determined by traffic demand and operational restrictions. This paper examines the possibilities of train running time modification in order to reduce power peaks and energy consumption for any situation of given headway and synchronization time. The problem can be described as the search for an optimal distribution of a train’s running time reserve along its ride. The application of Genetic Algorithms is proposed. A case study is carried out for a German DC electric rapid rail system, where different cost functions are examined. Simulation studies are performed taking into account stochastically varying station dwell times. It is shown that using train running time modification, improvements in overall energy consumption can be achieved and power peaks can be reduced significantly. Keywords: energy saving train control, coordinated train control, regenerative braking, genetic algorithm.

4 Power Supply, Energy Management and Catenary Problems

1 Introduction Minimizing energy consumption in electric railways systems is not only a question of minimizing the train’s energy needs for tractioning but also of efficiently using regenerative energy. This topic is of special importance in DC systems with noninverting substations. Here, energy billing is mostly realized at substation level and the efficient use of regenerative energy can directly contribute to reducing the amount of energy to be purchased. But energy costs are not only determined by the energy itself, power peaks often also influence the energy bill. According to a UITP survey of underground railway system operators [1], more than 80% of the operators paid a capacity price for the fixed cost of energy supply, which depends on the effective value consumed during a fixed time period, e.g. 15 min. Since the availability of fast and precise network simulators for modelling the effects of the power supply system including regenerative braking, some approaches have been taken to more efficiently using regenerative energy by means of coordinated train control. Most of them deal with train dwell time control as a method for improving the usage of regenerative energy. Control methods applied are fuzzy control [2], search techniques [3] and heuristics [4, 5, 6]. They all have the goal of providing decision safety, if and how long a train about to be starting shall wait at its station, so that no high power peaks occur during its acceleration and a big part of the energy needed for accelerating the train can be taken from trains 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. Passengers arriving during the additional dwell time trying to board the train will not 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 been used on earlier stages of the train’s ride along the line as running time reserve for longer coasting phases. This effect is independent of the mode of operation of the train (manual or automatic). To overcome these two obstacles, this paper proposes an approach using train running time control instead of train dwell time control for synchronizing acceleration and braking phases. The differences between the two approaches are illustrated in figure 1. In the next section, the problem of distributing train running time reserve along a line is examined and the solution for minimizing a single train’s energy consumption is briefly presented. For the minimization of system energy consumption in constant headway operation, the use of Genetic Algorithms (GA) is proposed in section 3. Section 4 examines the potential of the proposed method by means of a case study for a German DC rapid railway system. The results for multi-train coordination obtained using Genetic Algorithms are compared to the timetable with minimal energy consumption for the single train.

Energy Management in the Train Operation

5

a) dwell time control power P

additional dwell time for optimal synchronization

E1I0 →　I =I00 I I00 0, Fw > 0 η ( p, v ) i  3.6 ⋅ 106  i =1 Etot =   = E1 + E2 n   P0(i ) ∆ti ; v = 0 or Fw = 0  E2 =    i =1 (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, ζ is the slippage (=0), η is the efficiency of the locomotive as a

28 Power Supply, Energy Management and Catenary Problems function of power, p, and speed v, and P0 is originating from the auxilliary power. The total running time is calculated from

T = ∑ n =1 ∆ti (s), for v>0 i

(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 Mass, gross incl. loco Mass of locomotive SJ Rc4 Axles, trailing Max speed Axle load, average Braking gain time, nominal Braking release time, nominal Braking level used

418.5 m 1197 t 79 t 52 100 km/h, 27.8 m/s 21.5 t 15 s 30 s 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) 0 20490 21364 38152 39288 44106 44566 51322 52534 88000

speed (km/h) 100 40 100 70 100 70 100 40 100 100

Energy Management in the Train Operation

3

29

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 (‰) 0 5

Etot (kWh) 1723.5 3329.9

T (s) 3597 3758

Mean speed (m/s) 24.47 23.42

3.2 Running resistance The nominal running resistance, FR 0 , of the train set is obtained from full-scale measurements [1] and is calculated as a function of speed, v, by: FR 0 = 11961 + 229.1v + 41.4v 2

(4)

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

30 Power Supply, Energy Management and Catenary Problems

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.

α 0 = 0.9(

7.5 + 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.

Energy Management in the Train Operation

31

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.

32 Power Supply, Energy Management and Catenary Problems

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.

Energy Management in the Train Operation

33

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

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Energy Management in the Train Operation

35

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

36 Power Supply, Energy Management and Catenary Problems 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.

Energy Management in the Train Operation

37

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).

n where b

60  l vs  h

[trains/hour]

(1)

means an integer larger than b , distance ( l ), headway ( h ) and

commercial speed ( vs ) are represented as units of meters, minutes, and km / h ,

Figure 2:

DC 1500V electric railway power system.

38 Power Supply, Energy Management and Catenary Problems 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, Pm , is calculated from the train ton-kilo capacity as follows, Pm  2n  s  w  l  (1  a )  k

[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, Pm . 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. W  Pm 

1 [kW] 2

(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). Fb  9.8  ( 31    r )  s  w [N] Pb 

Fb  v   [kW] 367

(4) (5)

The regenerative peak current, I b , can be calculated as follows. Ib 

Pb [kA] Vinv

(6)

On the conditions of table 1, W is obtained as 1480[kW] and I b 3.5[kA]. Thus, the power capacity of the regenerative inverter can be approximated as

Energy Management in the Train Operation

39

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, t h

2.5 min

Maximum speed, vm

80km/h

Weight, w

48 ton/car

Commercial speed, vs

35km/h

0.97 m/s2

Regenerative operation voltage, Vinv

1650V

Decelerating rate, 

50kW/1000ton․km Power regeneration rate, 1 Regenerative braking Power delivery efficiency,  0.85 efficiency rate, 2 Train ton-kilo capacity, k

4

0.20 0.65

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.

 P  R  1  inv   100 (7)  Preg    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).

40 Power Supply, Energy Management and Catenary Problems P

1 Ts



t2

t1

preg (t ) 2 dt

(8)

Here, P is the root mean square of regenerative power Preg (t ) , 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

Calculate Maximum and Root Mean Square value of Regenerative Power

Calculate Loss Rate of Regenerative Power

Decrease Installation Number of Regenerative Inverter

Decide installation substation

Figure 3:

Decide Power Rating of Regenerative Inverter

Flowchart for substation selection.

Energy Management in the Train Operation

Figure 4:

41

Flowchart for regenerative inverter capacity.

line voltage[V]

1800 1700 1600 1500 1400 10

12

14

16

18

12

14

16

18

20

22

24

26

28

30

20 22 Time[min]

24

26

28

30

comsumed power[kW]

8000 6000 4000 2000 0 -2000 -4000 10

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.

42 Power Supply, Energy Management and Catenary Problems 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.

line voltage[V]

1800 1700 1600 1500 1400 10

12

14

16

18

12

14

16

18

20

22

24

26

28

30

20 22 Time[min]

24

26

28

30

comsumed power[kW]

8000 6000 4000 2000 0 -2000 -4000 10

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.

Energy Management in the Train Operation

Figure 8:

Loss rate of regenerative power in Seoul line 5. Table 2:

Line 5

6

Substation Euljiro 4-ga Haengdang Majang Eungam Daeheung Samgakji Shinnae

Figure 9:

43

Loss rate of regenerative power in Seoul line 6.

Power simulation results of Seoul subway lines. RMS of regenerative power[kW] 1449 1284 1350 1305 1279 780 941

Peak regenerative power[kW] 7102 5664 6554 6780 6481 3827 4833

Ratio [%] 490 441 485 520 507 491 514

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

44 Power Supply, Energy Management and Catenary Problems 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

Energy Management in the Train Operation

45

Train operation minimizing energy consumption in DC electric railway with on-board energy storage device K. Matsuda, H. Ko & M. Miyatake Sophia University, Japan

Abstract The optimal train operation which minimizes sum of supplied energy from substations is presented in this paper. In recent years, the energy storage devices have 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 storage device in our study, because of its high power density. The on-board storage can assist the acceleration/deceleration of the train and may decrease energy consumption. Many works on the application of the energy storage devices to trains were reported, however, they did not deal enough with the optimality of the control of the devices. On the other hand, our previous works were to optimize acceleration/deceleration commands of the train for minimizing energy consumption without the energy storage device. Therefore, we intend to optimize acceleration/deceleration commands together with current commands through energy storage devices as our next research target. The proposed method can determine the optimal acceleration/deceleration and current commands at every sampling point. For this purpose, the optimal control problem of the train operation is formulated mathematically. It is generally difficult to solve the problem because the problem is composed of a large-scale non-linear system. However, the Sequential Quadratic Programming (SQP) can be applied to solve the problem. Two results with and without on-board energy storage device are compared. These optimized results indicate that the total energy consumption is reduced by at least 0.35% by using the EDLC. The relation between internal resistance and energy consumption is also revealed. Keywords: electric double layer capacitor (EDLC), optimal control, energy saving operation, SQP method.

46 Power Supply, Energy Management and Catenary Problems

1 Introduction In recent years, the energy storage devices have enough energy and power density to use in trains as on-board energy storage. The devices are for instance, a secondary battery and an Electric Double Layer Capacitor (EDLC). Above all, the EDLC has advantages such as maintenance free, long lifetime, rapid charge/discharge with large current and high efficiency. Therefore, the EDLC is the most suitable to equip trains as an auxiliary power supply. The on-board EDLC is useful because of the following two reasons. Firstly, it decreases the loss of circuit resistance by compensating voltage drop. Secondly, it enables us to utilize and recycle regenerative power efficiently and prevent regenerative failure. Many works on the application of the energy storage devices to trains were reported. However, from an energy-saving point of view, they did not deal enough 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 the acceleration/deceleration force in the train without energy storage devices. We optimize notch commands together with charge/discharge commands with making use of the experience of our previous study. It is significant to investigate the optimal charge/discharge command minimizing energy consumption in order to maximize the effect of installing the EDLC. In this paper, we intend to formulate the optimal control problem of the train operation to find notch and charge/discharge commands which minimize amount of consumed energy, propose how to solve it, discuss the optimized results and find knowledge of the optimal operation. The knowledge will be applied to the future charge/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 voltage and the internal resistance at a substation respectively. The values of R1 and R2 are wire resistances. These resistance values are proportional to the distance between the train and substation position. Positions of substations and stations are shown in fig. 2. The constants C and Rc are the capacitance and internal resistance in the capacitor respectively. It is necessary to convert voltage by using a chopper because the voltage difference is high between the pantograph and capacitor. The chopper characteristic is too complicated to be examined in detail here. Therefore, we solved the circuit equation on the assumption that the chopper efficiency is 95%. In addition, the energy consumption in the train is regarded as constant in short time because acceleration/deceleration commands do not change often. The motor-inverters of the train are modeled as a current load that helps solving circuit equations simply.

Energy Management in the Train Operation

R1

47

R2

VT

R0

R0 RC

Chopper

C

VS

VS

Train Substation1

Substation2

Figure 1: Circuit model with one train between substations.

SS1

La

DS

L

AS

Lb

DP:departure station SS2

AS:arrival 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 are defined as follows. Control inputs n and u determine the acceleration/deceleration force and charge/discharge current through the capacitor, respectively. They are 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 the pantograph. In fact, it is a state variable if control inputs are determined and the circuit equation can be solved. However, we defined VT as the auxiliary variable because it is difficult to solve circuit equations analytically. Additionally, these all variables 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 negative

maximum deceleration deceleration

maximum charge charge

0

coast

wait

positive 1

acceleration maximum acceleration

discharge maximum discharge

48 Power Supply, Energy Management and Catenary Problems Minimizing the objective function J=




T

Vs Is (x, VT )dt

(1)

0

Subject to the following equality and inequality constraints

where Is

x˙ = v

(2)

v˙ = f (n, v, VT ) − r(v) V˙c = −Ic (u)/C

(3) (4)

P T (n, v, VT ) = Ps (x, VT ) + Pc (u, Vc )

(5)

x (0) = 0 v(0) = 0 Vc (0) = Vc f irst

(6)

x (T ) = L v(T ) = 0 Vc (T ) = Vc f inal

(7)

−1≤n≤1

(8)

−1≤u≤1

(9)

V

T min

V

c min

≤ VT ≤ VT

max

≤ Vc ≤ Vc max

(10) (11)

0 ≤x≤L

(12)

v ≥0

(13)

sum of load currents supplied by substations

Ic f ,r

current through the capacitor acceleration/deceleration force and running resistance per kg

PT Ps , Pc

electric power supplied to motor-inverters of the train power from substations and the capacitor

VT min , VT max Vc min , Vc max

lower and upper limitations of the voltage at the pantograph lower and upper limitations of the capacitor voltage

Vc f irst , Vc f inal L, T

first and final values of the capacitor voltage 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 motion equations of the train. The capacitor voltage is given as the eqn. (4). As mentioned above, we must solve the circuit eqn. (5) because we defined VT as an auxiliary variable. Eqns. (6),(7) describe the initial and final conditions of state variables. Inequality constraints of control inputs, state and auxiliary variables are shown in eqns. (8-13). Especially, we did not consider speed limitations in eqn. (13).

Energy Management in the Train Operation

49

We defined functions as below.

P T (n, v, VT ) = P s (x, VT ) =





M vf (n, v, VT )me

(n ≥ 0)

M vf (n, v, VT )/ge

(n ≤ 0) 

(14)

Vs − VT Vs − VT + R0 + R1 (x) R0 + R2 (x)

(15)

R1 (x) = (La + x)r0 R2 (x) = (L − x + Lb )r0  (u ≥ 0) Vc Ic (u)ce P c (u, Vc ) = Vc Ic (u)/ce (u ≤ 0)

(16) (17)

I c (u) = uIc max

(18)

Here, me and ge are motor/generator efficiency. Wire resistances R1 and R2 are given 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 station to the substation1 and substation2 shown in fig. 1. The constant r0 is the wire resistance per meter. The constant ce is the chopper efficiency. The constant Ic max is the rated value of the current from the capacitor. Additionally, maximum acceleration/deceleration characteristics, such as the control input n is 1 or -1, and running resistance are given in fig. 3. these characteristics are influenced by the voltage at the pantograph VT . Especially, we assume that the braking system is the air supplement control. In short, the use of electrical and mechanical blended braking system is considered if the regenerative braking force is not enough for the specific braking force. Moreover, we are not concerned with the characteristic of the squeezing control because we also assume the regenerative power can be absorbed at substations. The absorbed power can be accounted in eqn. (1).

1.2

1.2 1300[V] 1500[V] 1700[V]

Maximum Braking Force 1 Deceleration Force[N/kg]

Acceleration Force[N/kg]

1

0.8

0.6

0.4

0.2

0.8

0.6

0.4 Electrical Braking Force 0.2

Running Resistance 0 0

5

10

15 Velocity[m/s]

20

25

30

0 0

1300[V] 1500[V] 1700[V] 5

10

15 Velocity[m/s]

20

25

Figure 3: Acceleration/deceleration characteristics and running resistance.

30

50 Power Supply, Energy Management and Catenary Problems

4 Optimization method We show the optimization method for solving the optimal control problem. The optimal control problem is solved by Sequential Quadratic Programming (SQP). SQP is an optimization method to solve a general nonlinear programming problem. A general optimal control problem with equality and inequality constraints can be written as Minimize :

J (ω)

Subject to :

gi (ω) = 0

(i = 1, · · · , ng )

hj (ω) ≤ 0

(j = 1, · · · , nh )

(19)

where ω = (n, u, VT , x, v, Vc )⊤ is the vector of variables, J is the objective function, g and h are equality and inequality constraints, ng and nh are the number of equality and inequality constraints. Next, the objective function is expressed using the second order approximation around the feasible point ω(k) . Similarly, equality and inequality constraints are also expressed as the first order approximation around the feasible point ω (k) in problem (19). The transformed problem is shown as Minimize :

1 ⊤ d Bk dk + ∇J(ω (k) )dk 2 k

Subject to :

gi (ω (k) ) + ∇gi (ω (k) )dk = 0

(i = 1, · · · , ng )

hj (ω (k) ) + ∇hj (ω (k) )dk ≤ 0

(j = 1, · · · , nh )

(20)

where dk = ω − ω (k) , Bk is positive definite matrix. In general, the problem (20) can be solved by the interior point method [3, 4]. The optimization result of the problem (20) is a search direction dk . Here, we define merit function as  ng  nh   ψ(ω) = J(ω) + µ max(hj (ω), 0) (21) |gi (ω)| + i=1

i=1

where µ is a large positive constant. Finally, we have to find α to minimize ψ(ω (k+1) ) where ω (k+1) = ω (k) + αdk . The vector ω (k+1) is the next feasible point. Consequently, The optimization problem (19) can be solved by iterating the following procedure. Step 1) give the initial feasible point ω (0) , and set k = 0 Step 2) solve problem (20), and obtain a search direction dk Step 3) stop iteration if the norm ||dk || is less than 10−6 . Step 4) find α minimizing the merit function, and obtain the next feasible point ω(k+1) Step 5) set k = k + 1, and return step2

Energy Management in the Train Operation

51

5 Optimization result Optimization results are presented in this section. Specific parameters are presented as table 2. Here, the continuous time formulation must be transformed to a discrete time program in order to apply SQP to the optimal control problem. Therefore, ∆t is defined as the sampling interval. In addition, the final capacitor voltage is given to equal the initial one. So, the capacitor does not have to be charged when the train arrives at the station. We show three optimization results when the train run on straight line without speed limitations and gradients. Case 1 is the optimization result of the train without the capacitor. Case 2 and Case 3 show results of the sensitive analysis in case of the constant Rc is 0.3[Ω] or 0.03[Ω] respectively. These three optimization results are shown in table 3. Case 1: The optimization result is shown in fig. 4. The optimal train operation consists of the maximum acceleration, reduced acceleration by degrees, coasting and maximum deceleration. In previous works [1, 2], we obtained the similar optimization result. Therefore, these results indicate the reliability of the proposed method. Case 2: fig. 5(a) shows the optimization result in case that Rc is 0.3[Ω]. The optimal control input n do not differ from one in case 1. Next, we examine charge/discharge characteristics of the capacitor. As supplied power to the train is higher, discharge current is higher. Similarly, this pattern of the charge characteristic is also represented when the train decelerates. Qualitatively, this Table 2: Specific parameters. Operating condition

capacitor parameters

T, ∆t L

130[s],1[s] 2000[m]

C Vc max

32.3[F] 560[V]

R0 Vs

0.03[Ω] 1500[V]

Vc min Vc f irst

300[V] 560[V]

r0 La , Lb

0.04 × 10−3 [Ω/m] 5000[m]

Vc f inal Ic max

560[V] 500[A]

M

250 × 103 [kg]

Rc

0.3[Ω] or 0.03[Ω]

Table 3: Optimization results. Total energy consumption [MJ]

Energy-saving effect[%]

Case 1

27.55

-

Case 2 Case 3

27.45 26.74

0.35% 2.92%

52 Power Supply, Energy Management and Catenary Problems characteristic is proper, because it is the most effective control to compensate the voltage drop at the pantograph and prevent the regenerative failure. In Case 2, despite the lower limit value of the capacitor voltage Vc min set to 300[V], the capacitor stops discharging when the value of the capacitor voltage drops to about 480[V]. This result is attributed to the higher interior resistance of the capacitor. As a result, the efficiency of the capacitor itself is severely down according to the voltage drop of the capacitor. Case 3: The optimization result is shown as fig. 5(b). In this case, there is also little variation in control input n. However, the optimal charge/discharge command includes two significant difference compared to Case 2. Firstly, the capacitor voltage reaches the value of the lower limitation when control input n changes from acceleration to coast at about time 50[s]. Secondly, substations supply the power with a small current for charging the capacitor when the train coasts. It is found from the result that the capacitor is utilized effectively. Finally, the total energy consumption is 26.74[MJ]. Compared with Case 1, the total energy consumption is reduced about 2.92%. The result indicates that energy-saving effect is higher if the interior resistance of the capacitor is lower in the future.

v[m/s]

20

10

0

0

20

40

60

80

100

120

0

20

40

60

80

100

120

0

20

40

60

80

100

120

0

20

40

60 80 time[s]

100

120

n

1

0

-1

1600

T

V [V]

1800

1400 1200

PT[MW]

4 2 0 -2 -4

Figure 4: Optimization result (case 1).

v[m/s]

Energy Management in the Train Operation

20

20

10

10

n

0

u

100

0 1

0

0 0

50

100

-1

1

1

0

0

-1

T

50

1

-1

V [V]

0

0

50

100

-1

1800

1800

1600

1600

1400

1400

Vc[V]

1200

T

50

100

1200

600

600

500

500

400

400

300 P [MW]

0

4 2 0 -2 -4

0

0

50

100

50 100 time[s]

300 4 2 0 -2 -4

0

50

100

0

50

100

0

50

100

0

50

100

0

50

100

0

50 100 time[s]

(a)Case 2 Figure 5: Optimization results.

(b)Case 3

53

54 Power Supply, Energy Management and Catenary Problems

6 Conclusion This paper presents the optimal train operation with EDLC minimizing energy consumption. SQP can be applied to the formulated optimal control problem with discrete-time transformation. As a result, it is found that the energy consumption supplied from substations can be reduced by using on-board energy storage device effectively. Compared with the train without EDLC, the total energy consumption is reduced by 0.35% and 2.92% in Case 1 and Case 2 respectively. It is also clarified that the EDLC should not fully discharge when the internal resistance is high. A further direction of this study will be to optimize the train operation problem which has more complicated running conditions, for example, speed limitations and gradients.

References [1] H. Ko, T. Koseki and M. Miyatake: “Numerical Study on Dynamic Programming Applied to Optimization of Running Profile of a Train”, IEEJ Transactions on Industry Applications, Vol.125-D, No.12, pp. 1084-1092, 2005 (in Japanese). [2] H. Ko, T. Koseki and M. Miyatake, “Application of Dynamic Programming to Optimization of Running Profile of A Train”, Computers in Railways, WIT Press, pp. 103-112, 2004. [3] Imad M. Nejdawi, Kevin A. Clements and Paul W. Davis, “an efficient interior point method for sequential quadratic programming based optimal power flow”, IEEE Trans. on Power Systems, vol.15, NO.4, November 2000, pp. 1179-1183. [4] G. Irisarri, L. M. Kimball, K. A. Clements, A. Bagchi and P. W. Davis, “Economic Dispatch with Network and Ramping Constraints via Interior Point Methods” IEEE Trans. on Power Systems, Vol.13, No.1, February 1998

Energy Management in the Train Operation

55

Computer-aided design of ATO speed commands according to energy consumption criteria M. Domínguez1, A. Fernández1, A. P. Cucala1 & L. P. Cayuela2 1

Instituto de Investigación Tecnológica, Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, Madrid, Spain 2 Dirección de Ingeniería, Metro de Madrid, Spain

Abstract Traffic regulation systems of metro lines equipped with Automatic Train Operation (ATO) use a set of pre-programmed speed commands selecting coasting points and brake deceleration. Different speed commands provides different travel times between stations and the regulation system on-line selects and sends to the train one of these commands. Nowadays, speed commands are designed based on time and comfort criteria. In this paper a new approach of speed commands design, which takes into account not only present operational criteria but also energetic ones, is proposed in order to obtain energy efficient ATO commands. Firstly, the travel time and energy consumption of every command is calculated using a simulator that combines all the possible discrete values of the ATO configuration parameters. A set of systematic rules has been defined to include the consumption, operative and comfort criteria in the selection of the speed commands applying decision theory techniques. A software tool has been implemented for a computer-aided design of the speed commands. This tool includes a thorough simulation module of the train movement (ATO, motor and train dynamics), an automatic generator of every possible command and a graphical assistant for the speed commands selection according to the mentioned rules. The methodology described in this paper has been used to redesign the current ATO commands (4 for each station) of Line 1 of Madrid Underground. The results are presented in this paper. According to the simulation results, about 10% of energy savings are expected to be achieved with these new speed commands. Keywords: energy consumption, speed commands design, train simulation.

56 Power Supply, Energy Management and Catenary Problems

1

Introduction

Metro lines equipped with Automatic Train Operation systems (ATO) use preprogrammed speed commands to control the circulation of trains, providing a set of alternative ATO speed profiles per inter-station. As a result, driving is not influenced by human factors and run-times and energy consumptions are quite stable when signalling systems do not affect the circulation of trains. Traffic regulation systems performance and total energy consumption strongly depend on the off-line design of the ATO speed commands. The ATO speed profile to be executed between two stations is on-line selected by the regulation system according to the required run-time. When a train must be held up, from the user’s point of view a longer run-time is preferred rather than a longer station waiting time. In addition, this regulation strategy involves energy saving because longer run-times are obtained with slower speed profiles. However, these ATO speed profiles are usually designed according to run-time and comfort criteria, but not to energy consumption. There are two main approaches to optimise train driving speed profiles: mathematical optimisation models and computer-aided design based on detailed simulation and direct search techniques. The first approach includes in a mathematical model those restrictions that govern the train movement, such as track geometry, traction equipment, speed restrictions and driving rules. For instance Howlett [1] and Khmelnitsky [2] apply optimal control techniques for determining the optimal switching times in manual driving. The formulation and resolution of these analytical models require very complex techniques as well as important simplifications of the train dynamics or the driving strategy. On the other hand, approaches based on simulation do not require simplifications and enable an accurate calculation of run-times and energy consumption, as Lukaszewicz manual driving modelling [3]. To explore the solution space and select alternative driving, different direct search methods are used, for instance heuristic search for ATO speed commands design [4] or genetic algorithms and fuzzy logic for manual and automatic driving optimisation [5], or genetics for optimisation of coasting points [6, 7]. Wong and Ho [8] compare different search methods for the on-line control of a train using an accurate simulator, determining the coasting points. This work stresses the importance of an accurate train movement modelling for practical applications. The work presented in this paper is focussed on the computer-aided design of the ATO speed commands between two metro stations, to be pre-programmed in the ATO equipment. The variables to optimise will be the configuration data of each particular ATO system, four parameters in the case study of Line 1 of Madrid Underground: coasting, re-motoring and regulation velocities, and braking deceleration rate. The considered ATO system provides only certain discrete values for each parameter, resulting a solution space of 220 alternative speed profiles per inter-station in Madrid Underground , and this fact allows the exhaustive and accurate simulation of the whole feasible ATO speed profiles. Instead of search techniques, decision theory techniques can be directly applied

Energy Management in the Train Operation

57

to select a set of solutions per inter-stations (4 in the case study) including operational and energy consumption criteria. This way, the obtained driving solutions will be fully adjusted to real features and capabilities of the ATO equipment in service. A software tool for computer-aided design of ATO speed profiles has been developed, to support the design procedure defined. Next sections will describe briefly the simulator, the proposed design procedure and the simulation results of its application to Line 1 of Madrid Underground. The obtained solutions are compared with the current driving profiles in service in this line in order to value the expected energy savings.

2

The simulator

The proposed design method is based on the accurate simulation of energy consumption and run-time of all the possible combinations of ATO speed commands for each inter-station. Train velocity, acceleration, traction or brake force and energy consumption are computed at each simulation step. The speed/distance profile between stations is plotted to assist the design process. The simulator is composed of three modules: ATO equipment simulator, train dynamics model and train consumption model. This modular architecture allows the validation of each module separately and an easy adjustment for specific features of a particular ATO equipment. To this end, the simulator input interfaces are designed to enable the definition of track layout, train characteristics, and ATO system configuration. 2.1 ATO equipment simulator This module calculates the type of motion at each simulation step: motoring, coasting or braking. The particular ATO system modelled in the case study (Line 1 of Madrid Underground) supplies a unique traction command (the maximum). In contrast, there are four values for deceleration braking command which can be selected. The regulation speed order is implemented by means of maximum traction and coasting cycles in ramps (or braking and coasting cycles in slopes). This control is also applied when the train reaches the maximum speed of the track. The ATO simulator is configured with the real fixed and variable parameters needed for an accurate simulation. The fixed parameters are: - Safety distance: to be observed when the train has to brake due to a maximum speed reduction. - ATP safety offset: to be observed under the maximum speed - Positive and negative regulation offsets: The regulation speed cycles previously mentioned are applied between the speed limits defined by these offsets. On the other hand, the variable parameters (speed commands to be designed) are: - Braking command: deceleration rate during the braking process.

58 Power Supply, Energy Management and Catenary Problems Regulation speed. The target speed of the train is the minimum between the maximum velocity and the regulation one. - Coasting speed: When reached, traction is turned off up to re-motoring speed. - Re-motoring speed: When reached, traction is turned on up to coasting speed. The ATO simulator model also includes the necessary rules and algorithms to emulate the real operation of the equipment calculating: - Coasting and re-motoring points: where the traction is turned off or turned on. - Starting braking points. The actual ATO braking algorithms are replicated to decide at each simulation step if the train has to brake to observe a speed reduction or a stopping point. -

2.2 Train dynamic model a=

∑ (F − F

g

MI

− Fa )

(1)

This module recalculates train speed and position at each simulation step. They are obtained from the train acceleration a, which is the result of the traction force F minus the rolling and aerodynamic resistance to train movement Fa and track gradient and curvature resistances Fg as shown in eq (1). MI stands for train mass plus the rotational inertial effect. The traction motor curve (maximum force/speed) is given as input data in order to calculate F. Power and grip limitations are taken into account in this curve. The resistance to train movement Fa is modelled as a quadratic function of the velocity with nonnegative parameters depending on each particular train. The track gradient resistance Fg is the resistive force due to gravity, positive for ramps and negative for slopes. While the train is braking, the ATO system regulates the force continuously in order to obtain the braking command reference. The simulator applies precisely this deceleration rate, assuming that the train is able to supply the needed braking force. 2.3 Consumption model The energy consumption E is recalculated according to the time increment ∆t and the current I at each simulation step. The current is obtained from the line current/speed curve. A constant line voltage U is assumed. E = I ·U ·∆t (2) 2.4 Operational and comfort restrictions After simulating every ATO speed profile, a validation model checks the fulfilment of the operational and comfort restrictions specified. In the study case

Energy Management in the Train Operation

59

of Madrid Underground, the current restrictions are the minimum speed along curves (avoiding to wear the track) and the jerk restriction for a comfortable trip.

3

ATO speed commands design and case study

Once inter-station run-times and energy consumption have been simulated for all the possible ATO speed profiles, a set of them are selected to be programmed in the ATO equipment. Decision theory techniques have been used to solve this multicriteria problem finding an appropriate trade-off between costs (energy consumption) and runtimes because the longer the run-time is, the lower the energy consumption is. According to that, the optimal solutions are over the Pareto curve which represents the minimum consumption for each run-time. An example is given in Figure 1. The proposed procedure follows three criteria: domination, sensitivity and uniform distribution of run-times. They have been applied to optimize the speed commands design of the Line 1 of Madrid Underground. The following description of the procedure will be illustrated with this realistic application. The energy consumption and run-times of the current speed profiles and the proposed ones will be compared in order to value the achievable energy saving. In Madrid Underground there are four alternative speed profiles per interstation to be designed, with increasing run-times from the first (flat out, the fastest) to the fourth (slowest). The first speed profile is obtained applying maximum speed and deceleration conditions. 3.1 Domination criterion According to this criterion, optimal solutions are over the Pareto curve which is formed by the solutions with less energy consumption and approximately the same run-time of all the possible ones. Solutions not located on the curve are said to be dominated and are discarded. Possible profiles

Energy Consumption (kWh) Plaza de Castilla (Platform 1)

Current profiles Pareto Curve

12,00

Consumption (kWh)

10,00 8,00 6,00 4,00 2,00 0,00 60,0

65,0

70,0

75,0

80,0

85,0

90,0

95,0

100,0

105,0

Run time (s)

Figure 1:

Current speed profiles dominated by others with less consumption and Pareto curve.

60 Power Supply, Energy Management and Catenary Problems An example of the case study is given in Figure 1 (from Plaza de Castilla station to Valdeacederas station). The marked 4th speed profile currently in service, is dominated by two others over the Pareto curve with almost the same run-time. The proposed solution consumes 28% less energy than the current one (Table 1). Table 1: Profile Current Alternative

28% energy savings with an alternative speed profile. Braking m/s2 0.65 0.7

Coasting km/h 32 35

Motoring km/h 10 20

Time s 75.0 74.4 Saving

Consumption kWh 4.99 3.6 27.89%

3.2 Consumption sensitivity criterion This is the criterion to be applied for the slowest speed profile selection. In the time/consumption graph, the slope of the Pareto curve progressively decreases from the fastest speed profile as the run-time increases. That is to say, solutions near the minimum run-time speed profile have high marginal energetic cost associated per second. These marginal costs go down reaching almost 0 at the end of the curve. The proposed criterion places the slowest speed profile where the Pareto slope becomes almost flat. This strategy guarantees energy savings when trains are held up for traffic regulation purposes. The maximum run-time gap between the fastest and the slowest speed profile is limited in practice by operational requirements, so the slowest profile must be moved and placed before the flat slope of the curve if it is necessary to observe this restriction. Figure 2 shows an example of the case study (from Tetuán to Estrecho stations). The Pareto curve becomes flat for run-times greater than 140 s, and the fastest one takes 70 s. However, the maximum run-time gap defined for Madrid Underground is 20 s. Therefore, the fourth speed profile must take less than 140 s and it is placed 20 s slower than the fastest one, observing the operational requirements. This selection involves that the fourth profile can be 7 s slower than the current one, and this implies 22% of energy savings (Table 2). Possible profiles Current profiles

Energy Consumption (kWh) Tetuán (Platform 1)

Consumption (kWh)

12,00

Alternative 4th profile

10,00 8,00 6,00 4,00 2,00 0,00 68,0

88,0

108,0

128,0

148,0

168,0

188,0

Run time (s)

Figure 2:

Alternative 4th speed profile with less consumption.

Energy Management in the Train Operation

Table 2:

61

An alternative speed profile 7 s slower achieves 21.7% of savings. Braking m/s2 0.65 0.75

Profile Current Alternative

Coasting km/h 42 37

Motoring km/h 10 30

Time s 83.1 90.5 Saving Time

Consumption kWh 5,98 4.68 21.7% 7

3.3 Temporal uniform distribution criterion Once the fastest and the slowest speed profiles have been selected in accordance with the previous criteria, the remaining profiles are designed applying the uniform distribution criterion. The speed commands must be selected in order to obtain a design with a uniform distribution of the run-times over the Pareto curve. This design allows a proper operation of the traffic regulation system.

Consumption (kWh)

Energy Consumption (kWh) Sol (Platform 1)

Possible profiles Current profiles

13,50 13,00 12,50 12,00 11,50 11,00 10,50 10,00 9,50 9,00 72,0

77,0

82,0

87,0

92,0

97,0

102,0

107,0

112,0

117,0

Run time (s)

Figure 3:

Current speed profiles. Energy Consumption (kWh) Sol (Platform 1)

Possible profiles Proposed profiles

Consumption (kWh)

13,50 13,00 12,50 12,00 11,50 11,00 10,50 10,00 9,50 9,00 72,0

77,0

82,0

87,0

92,0

97,0

102,0

107,0

112,0

117,0

Run time (s)

Figure 4:

Proposed speed profiles designed.

In the study case, the uniform distribution criterion is applied to design two profiles (the second and the third) between the two profiles previously selected. Figure 3 shows the current profiles in service between Sol and Tirso de Molina stations. In the proposed design shown in Figure 4, second and third profiles are selected to obtain time differences of 5 s approximately.

62 Power Supply, Energy Management and Catenary Problems 3.4 Redesign of the current ATO speed commands of the Line 1 of Madrid Underground The design procedure has been applied to redesign the ATO speed commands of all the trips between the 26 stations of Line1 of Madrid Underground in order to value the expected energy savings. The discrete possible values of the ATO equipment parameters in service are shown in Table 3. The combination of them supplies 220 possible speed profiles to be simulated between each two stations. The average simulation time for these 220 profiles, for one inter-station, is 4s. Table 3: Braking command Regulation Speed Coasting speed Remotor speed

Table 4:

(m/s2) (km/h) (km/h) (km/h)

Configuration parameters of the ATO in service. 0,8 0,75 0,7 0,65 62 60 57 55 52 50 47 45 42 40 37 35 32 30 27 25 57 55 52 50 47 45 42 40 37 35 32 30 27 25 22 20 30 20 10

Summary table. Average energy savings and run-time increase in the proposed speed profiles in Line 1.

Profile 1 2 3 4

Designed Profiles Consumption kWh 225.4 176.3 147.0 128.3 677.0

Current Profiles Diferences Time Consumption Time Consumption s Km/h % % 1665.5 252.4 0.5 10.7 1794.6 196.5 -0.4 10.3 1915.8 159.1 0.6 7.6 2032.5 145.9 1.4 12.1 7408.5 753.9 0.5 10.2

The simulation results show that 70% of the redesigned speed profiles save more than 10% of energy, while 26% of them save more than 20%. Overall, an average of 10% energy savings is expected increasing the run-times only 0.5% as Table 4 shows. Moreover, not only an energy benefit is obtained, but also speed profiles are time-uniformly distributed.

4

New ATO configuration parameters

Although the new speed profiles for Line 1 have been designed according to the current possibilities of the ATO equipment, the simulator allows researching and justifying further modifications and improvements for future ATO systems. This is another advantage of a computer-aided design based on accurate simulation. In Madrid Underground the ATO system applies a unique set of speed commands for each speed profile between two stations that is executed during the whole trip. A set is composed of a brake deceleration and a pair of coasting and motoring or a regulation speed command. However, being possible to define different sets for a single trip so that they could be on active in particular sections of the trip, more alternative speed profiles would be obtained. In particular, defining the activation of a coasting command set at the end of the trip, just before the final breaking, it is possible to replace braking by coasting. For

Energy Management in the Train Operation

63

instance, the feasible profiles considering the ATO in service in Line 1 between Sol and Tirso de Molina stations are plotted in Figure 3. In Figure 5, new speed profiles are obtained defining different activation sections for the coasting commands sets. The number of solutions below the previous Pareto curve rises notably. In particular, the third profile could be redesigned, saving 17% of energy with the same run-time. These speed profiles are shown in Figure 6. Energy Consumption (kWh) Sol (Platform 1)

Possible profiles Current profiles

C onsum ption (kW h)

14,00 13,00 12,00 11,00 10,00 9,00 8,00 72,0

82,0

92,0

102,0

112,0

122,0

132,0

142,0

152,0

162,0

172,0

Run time (s)

Figure 5:

Simulated speed profiles with a starting point of commands set.

50,0

Alternative speed profile

45,0 40,0

Maximum speed Current speed profile

Speed (km/h)

35,0 30,0 25,0 20,0 15,0 10,0 5,0 0,0 66

Figure 6:

05

,0 66

55

,0 67

05

,0 67

55

,0 68

05

,0 68

55

,0 69

05

,0

,0 ,0 05 55 70 69 Position (m)

70

55

,0 71

05

,0 71

55

,0 72

05

,0 72

55

,0

Comparison between the current speed profile and an alternative one with a starting point of commands set.

5 Conclusions The study shows the importance of a detailed model of the particular ATO system in order to obtain a realistic simulation that allows calculating slight differences between alternative speed profiles. In the case study of Madrid Underground, these differences can be a few seconds. In addition, current ATO equipments provide only a certain range of discrete configuration values. Thus, there is a finite and relatively short number of possible speed profiles that can be exhaustively simulated. Decision theory

64 Power Supply, Energy Management and Catenary Problems techniques can be directly applied to select solutions finding a trade-off between run-times and energy costs. From the redesign of the ATO speed commands of Line 1 of Madrid Underground it is possible to conclude that an improvement of about 10% of energy consumption is expected without degrading run-times. Even 20% of savings are expected with 26% of the redesigned speed profiles. In high frequency metro lines the programmed speed profiles are repeated systematically many times, so the energy savings become a relevant aspect. Finally, the proposed design procedure based on simulation allows the study of new features and configuration parameters to be implemented in future ATO equipments, with the aim of obtaining more energy efficient speed profiles, as it has been shown in the case study.

References [1] P. Howlett, “The Optimal Control of a Train,” Annals of Operations Research, vol. 98, pp. 65, 2000. [2] E. Khmelnitsky, “On an Optimal Control Problem of Train Operation,” IEEE Transactions on Automatic Control, vol. 45, pp. 1257, 2000. [3] P. Lukaszewicz, “Energy Consumption and Running Time for Trains,” in KTH, Department of Vehicle Engineering. Royal Institute of Technology, Stockholm, 2001, pp. 153. [4] F. de Cuadra, A. Fernandez, J. de Juan, and M. A. Herrero, “Energy-saving automatic optimisation of train speed commands using direct search techniques,” in Computers in Railways V - Vol.1 Railway Systems and Management, 1996, pp. 337–346. [5] Y. V. Bocharnikov, A. M. Tobias, C. Roberts, S. Hillmansen, and C. J. Goodman, “Optimal driving strategy for traction energy saving on DC suburban railways,” IET Electric Power Applications, vol. 1, pp. 675, 2007. [6] H. Seong Ho, B. Yun Sub, B. Jong Hyen, A. Tae Ki, L. Su Gil, and P. Hyun Jun, “An optimal automatic train operation (ATO) control using genetic algorithms (GA),” in Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. `Multimedia Technology for Asia-Pacific Information Infrastructure’ (Cat. No.99CH37030), vol.1. [7] C. S. Chang and S. S. Sim, “Optimising train movements through coast control using genetic algorithms,” IEE Proceedings-Electric Power Applications, vol. 144, pp. 65, 1997. [8] K. K. Wong and T. K. Ho, “Coast control for mass rapid transit railways with searching methods,” IEE Proceedings-Electric Power Applications, vol. 151, pp. 365, 2004.

Energy Management in the Train Operation

65

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 Sophia University, Japan

Abstract The optimal operation of rail vehicle with on-board energy storage device minimizing total energy consumption is discussed in this paper. Until now, not enough research deals with the optimal control of the devices. The authors have developed the mathematical model based on a general optimization technique. In our study, the electric double layer capacitor (EDLC) is assumed as an energy storage device, because of its high power density etc. The proposed method can determine the optimal acceleration/deceleration and current commands at every sampling point under fixed conditions of transfer time and distance. The authors have also modified it for applying to catenary free operation. Using the proposed methods, simulations were implemented in some cases. The trend of optimal solutions such as values of control inputs and energy consumption is finally discussed. Keywords: power management, on-board energy storage, optimization, energysaving operation, supercapacitor, catenary free operation.

1 Introduction Electrical regenerative braking has reduced total energy consumption in electric railway systems. However, if the energy is not absorbed by another train, catenary voltage rises and regenerative failure is occurred under DC power feeding system. One of the way for absorbing regenerative energy is to use energy storage. Regenerative energy is stored in the energy storage and reused in the next acceleration. The energy storage decreases the loss of circuit resistance by compensating voltage drop. It also prevents regenerative failure even if substations cannot absorb energy. Energy saving effect as well as preventing regenerative failure is expected.

66 Power Supply, Energy Management and Catenary Problems R1

R2

VT

R0 I

Chopper

RC

VS Substation1 SS1

Train (a) Circuit model

L DS L AS b SS2 5km 2km 5km La

C

♦ Vc

R0 VS Substation2

DP:departure station AS:arrival station SS:substation

(b) Location of stations and substations Figure 1: Modeling of a feeding circuit with one train between substations. Some research projects on the application of the energy storage devices to railway systems have been reported in [1–6]. Most of them discussed reasonable circuit configuration and sizing of energy storage system, however, very few papers that deal with optimal charging/discharging control of the energy storage can be found. The charging/discharging command of energy storage affects the energy consumption and may influences the optimal speed profile, the trajectory of a train in the velocity-position state space. The authors pointed out that the charge/discharge command and vehicle speed profile should be optimized together. There are a few papers that deal with the energy-saving vehicle operation with a kind of optimization in [7–10]. However, they did not consider the control of energy storage. When on-board energy storage is used, catenary free operation technique is sometimes used. Energy management control is significant in this operation because the train have to run with very limited onboard energy. However, no papers can be found that optimize train speed control. The authors have developed the mathematical model composed of DC power feeder and energy storage that was already reported in [11]. In this paper, the authors introduce the simulation results under different condition from [11], add a few discussion to [11]. The authors also modify the model for applying to catenary free operation.

2 Modeling of energy storage and DC feeding circuit The EDLC is assumed in the modeling of energy storage in this study. It has the characteristics of maintenance-free, long lifetime, quick charge/discharge, lower energy density than that of batteries at present, and wide range of terminal voltage regulation. The fact shows the difficulty in using EDLC as a main power source of high speed vehicles. However, if it is used with other main energy sources, the EDLC is expected as one of the most promising auxiliary devices for transportation systems.

67

Energy Management in the Train Operation

Chopper INV. DC link IM

Chopper INV. DC link IM

EDLC

(a) model under catenary

EDLC

(b) model of catenary free operation

Figure 2: Circuit model of an on-board EDLC train. A DC feeding circuit is modeled with one train between substations. The model circuit appears in Figure 2(a). In this figure, Vs and R0 are the supply voltage and the internal resistance at a substation respectively. The values of R1 and R2 are equivalent resistances of feeder and return circuits. These resistance values are proportional to the distance between the train and substation. The constants C and Rc are the capacitance and internal resistance in the capacitor respectively. It is necessary to convert voltage by using a bidirectional chopper because the voltage difference between the DC link and EDLC is high. The motor-inverters of the train were modeled as a current load that helps solving circuit equations simply. If battery is applied instead of EDLC, slight change of the model enables us to deal with the battery system. We have only to change the capacitor in Figure 1 to a voltage source and modify some equations.

3 Formulation of the operation under catenary 3.1 Definition of variables The optimal control problem is formulated from the circuit model. Variables are defined as follows. Control inputs n and u determine the acceleration/deceleration force and charging/dischrging current, respectively. State variables x, v and Vc indicate the train position, speed and capacitor voltage, respectively. The variable VT is the catenary voltage at the train. It is treated as an auxiliary state variable to avoid complexity in solving circuit equations analytically, although it is derived by solving circuit equations. It is derived by adding circuit equations in the optimization problem as the constraints. 3.2 Optimal control problem The optimal control problem is described as the following mathematical formulation. Minimizing the objective function
T J = Vs Is (x, VT )dt 0

(1)

68 Power Supply, Energy Management and Catenary Problems Subject to the following equality and inequality constraints v˙ = nf max (n, v, VT ) − r(v)

x˙ = v,

V˙c = −Ic (u)/C

(3)

PT (n, v, VT ) = PS (x, VT ) + PC (u, Vc )

(4)

x(0) = 0, v(0) = 0, Vc (0) = Vc init

(5)

x(T ) = L, v(T ) = 0, Vc (T ) = Vc f inal

(6)

−1 ≤ (n, u) ≤ 1

(7)

VT Vc

min

≤ VT ≤ VT

min

≤ Vc ≤ Vc

0 ≤ x ≤ L,

(9)

max

v≥0

currents supplied from substations and EDLC current; maximum acceleration/deceleration force;

r PT

running resistance per unit weight of the train; electric power supplied to motor-inverters of the train;

(10)

power from substations and EDLC;

Ps , Pc min , VT max min , Vc max

Vc init , Vc final L, T

(8)

max

where Is , Ic fmax

VT Vc

(2)

lower and upper limitation of the catenary voltage; lower and upper limitation of the capacitor voltage; first and final values of the capacitor voltage; distance and running time between the departure and arrival stations.

The objective function is sum of supplied energy from two substations given as (1). Equality constraints are given as (2)–(6). Equation (2) is a motion equation of the train. Gradient can be considered as including the influence to the running resistance r. The capacitor voltage is given as the (3). Equations (5) and (6) describe the initial and final conditions of state variables. The constraint (9) gives the terminal EDLC voltage as well as the initial one. Inequality constraints of control inputs, state and auxiliary variables are shown in (7)–(10). The functions related with circuit equations are the following equations.  (n ≥ 0) Mv · nf (n, v, VT )ηm PT (n, v, VT ) = Mv · nf (n, v, VT )/ηg (v) (n ≤ 0)   Vs − VT V s − VT Ps (x, VT ) = + R0 + R1 (x) R0 + R2 (x) R1 (x) = (La + x)r0 R2 (x) = (L − x + Lb )r0

(11) (12) (13)

Energy Management in the Train Operation

 Vc Ic (u)ηch Pc (u, Vc ) = Vc Ic (u)/ηch Ic (u) = uIc

(u ≥ 0) (u ≤ 0)

69

(14) (15)

max

Here, ηm and ηg (v) are motor-inverter efficiency in accelerating and braking respectively. The constant M is the total weight of the train including on-board energy storage. The regenerative efficiency ηg must be treated as the function of speed v for considering electro-pneumatic blended braking. The constant ηch is the chopper efficiency assumed as constant and Ic max is the rated value of the EDLC current. The optimal control problem is discretized using sampling time t and solved by the Sequential Quadratic Programming (SQP). SQP is an optimization method to solve general nonlinear programming problems. Please see [11] for the detailed procedure.

4 Consideration of catenary free operation If the train with on-board energy storage runs off the catenary, so called catenary free operation, the mathematical formulation should be modified because the circuit topology is changed to Figure 2(b). The objective function (1) should be changed to (16) because no power is supplied from the catenary.
T J = Vc Ic dt (16) 0

In this study, bidirectional chopper is stopped to avoid switching loss. Then, VT is determined by (17). The equations (11), (14) and (15) should be changed to (18), (19) and (20), respectively. VT = Vc − RC Ic

(17)

Ps = Is = 0

(18)

Pc = Vc Ic

(19)

Ic = PT /VT

(20)

Some other equations such as (8) and (13) must be eliminated for topological change of the circuit. In this operation, the control input u is finally eliminated and only the notch control input n is left. Therefore, the Dynamic Programming (DP) that was already proposed in [8] can be applied to the modified problem. Please refer [8] for details. In the application of DP in this case, the final EDLC voltage Vc final is given to implement backward search from t = T to 0. The initial EDLC voltage Vc init cannot be given together with Vc final because the value is decided by the trajectory of n. When Vc init is initially given instead of Vc final , Vc (T ) should be adjusted so as to satisfy Vc (0) = Vc init .

70 Power Supply, Energy Management and Catenary Problems Table 1: Specific parameters. feeding circuit an d train operation 1[s]

t

0.03[] ηg

R0

1500[V] r0

Vs

0.04 ηm [m/m]

≤ 90 % ηch 90 %

M

95% 250[Ton]

EDLC C Ic

max

32.3[F] Vc

max

560[V] Vc init

500[A]

min

300[V] Vc f inal 560[V] Rc

Vc

560[V] weight 500[kg] 0.3[]

Another problem in using DP is that the EDLC voltage much affect accelerating/decelerating ability. The proposed method in [8] assumes this ability as constant, however, the accelerating/decelerating ability must be calculated in finding the optimal control input at each lattice point in state space.

5 Simulations of optimal operation under catenary 5.1 Condition of simulation Specific parameters are tabulated in Table 1. In the simulations, a train runs on a straight line without speed limitations and gradients for simple analyses. The final capacitor voltage is given to equal the initial one. In the acceleration/deceleration characteristics, electro-pneumatic blended braking system with the air supplement control is assumed. Only if the regenerative braking force is not enough for the specific braking force, air brake works. The detailed value of characteristics is shown in [11]. It is also assumed to use receptive substations that are now in the initial state of practical application for relaxation of constraints. Two cases are prepared as tabulated in Table 2 for evaluation under various conditions. Cases A and B are the optimization of the train without and with the capacitor, respectively. Table 2: Conditions and evaluated energy consumption in each case. T [s] EDLC case A 120 without case B 120 with case 1

130 without

case 2

130 with

minimum total energy energy saving value of Vc [V ] consumption [MJ] in % –

37.56

–

500

35.43

5.67

–

27.55

–

460

27.45

0.35

Cases 1 and 2 were already reported in [11].

Energy Management in the Train Operation

71

Figure 3: Graphs of optimal control inputs and state variables. 5.2 Optimization results Optimization results are shown in Table 2 and Figure 3. In Figure 3, the graphs of control inputs n and u, catenary voltage at train pantograph, capacitor voltage, train speed, and train power at inverter input are drawn. The optimal control input n in both cases consists of the maximum acceleration, reduced acceleration by degrees, coasting and maximum deceleration. The results are consistent with the results of previous paper [8]. Very little difference of the optimal control input n can be seen in cases A and B. Regarding the control input u, the higher the absolute value of power to the train is, the larger the absolute value of current is. Qualitatively, this trend is proper, because the energy loss by current through the feeder reduced. Substations supply the power with a small current for charging the EDLC when the train coasts. Despite the lower limit value of the capacitor voltage Vc min is set to 300[V], the EDLC stops discharging when the EDLC voltage drops to about 460[V]. The efficiency of the capacitor itself is reduced according to the voltage drop of the EDLC. These results can be compared with those of previously reported paper [11]. The only difference between cases A and B and cases 1 and 2 in [11] is the running time T . In [11], T is 130 [s], 10 second longer than this study. The EDLC voltage Vc , in case B, drops much lower than that in case 2. The stored energy in EDLC

72 Power Supply, Energy Management and Catenary Problems Table 3: Specific parameters. general conditions 1[s]

ηm

C

40[F]

Vc

Ic

500[A]

t

70 %

≤ 70 %

ηg

M

30[Ton]

EDLC max

max

Vc init

600[V]

weight 300[kg]

600[V]

Rc

0.1[]

Ts T1

0m

section A

500m

T2

1000m

x

section B

Figure 4: Running condition of tramcar. is more effectively used in case B. Regarding energy consumption in Table 2, the energy-saving effect by introducing EDLC is 5.67%, much improved than that in [11]. From the comparison, it is derived that the shorter the margin time between stations is, the more effectively used the capacity of the EDLC.

6 Simulations of optimal catenary free operation 6.1 Condition of simulation In this study for catenary free operation, a tramcar with EDLC is assumed. Specific parameters are tabulated in Table 3. The tramcar runs 1 km without suppled power from substations as shown in Figure 4. It runs within T1 and T2 at the sections A and B respectively and stops once between sections at x = 500[m] for Ts = 10[s]. In the simulation, the ratio of T1 and T2 is changed while total time T1 + T2 + Ts = T1 + T2 + 10 is fixed at 200[s] in order to find the optimal distribution of margin time for energy-saving operation by sensitivity analysis. 6.2 Optimization results The simulation results are shown in Figure 5. Figure 5 (a) shows a sample of the optimal control input u in section A in case of T1 = 100[s]. Figure 5 (b) is a graph that indicate relation between T1 and energy consumption. In this assumption of simulation, T1 = T2 = 95[s] is the condition of equal division of margin time. From Figure 5 (b), it is observed that the minimum point appears when T1 is 95[s]. However, energy consumption in T1 > 95[s] is larger than that in T1 < 95[s]. The result is mainly caused by that the EDLC voltage at x = 500[m] is lower than that at x = 0[m]. If the tramcar must run faster with

energy consumption [MJ]

Energy Management in the Train Operation

control input n

1 0.5 0 -0.5 -1 0

20

40

60 time [s]

80

(a) A sample of control input.

100

73

40 30 20 10 0 85

90

95

100

105

100

95

90

T1 [s] T2 [s]

(b) Sensitivity analysis in changing T1 .

Figure 5: Simulation results.

lower voltage of the EDLC, larger current flowing from the EDLC increase loss by internal resistance.

7 Conclusion This paper presents the optimal train operation with EDLC minimizing energy consumption. As a result, it is found that the energy-saving effect by using the EDLC is strongly influenced by the margin time of train schedule. On the other hand, regarding the acceleration/deceleration command, very few difference between with and without EDLC is observed. Optimization of train speed profile in catenary free mode is also mentioned in this paper. It indicates that the distribution of margin time in each section can be optimized with the modified optimization model. The model can be used for planning of train schedule. The knowledge extracted from the trend of optimization results will be applied to the design and parameter tuning of future charge/discharge controllers for energy storage.

References [1] M. Ogasa: “Energy Saving and Environmental Measures in Railway Technologies: Example with Hybrid Electric Railway Vehicles” IEEJ Transactions on Electrical and Electronic Engineering, Vol.3, No.1, pp. 15–20, 2008. [2] Y. Taguchi, H. Hata, S. Ohtsuyama, T. Funaki, H. Iijima and M. Ogasa: “Simulation results of Novel Energy Storage Equipment Series-Connected to the Traction Inverter” in Proc. of EPE2007, No. 554, Aalborg, Denmark, 2007. [3] M. Steiner and M. Klohr: “Energy Storage System with UltraCaps on Board

74 Power Supply, Energy Management and Catenary Problems of Railway Vehicles” in Proc. of EPE2007, Aalborg, Denmark, 2007. [4] J. Taufiq: “Power Electronics Technologies for Railway Vehicles” in Proc. of PCC-Nagoya 2007, No. LS5-5-5, Nagoya, Japan, 2007. [5] S. Sone, T. Sato and J. Kouyama:“Proposal and Discussion of High-Speed Regenerative Braking for Realizing Genuine Pure Electric Braking” IEEJ Technical Meeting on Transportation and Electric Railway, No. TER-05-26, pp. 71–74, 2005 (in Japanese). [6] Y. Sekijima, M. Inui, I. Aoyama, Y. Monden: “A trial of Regenerated Energy storage with an Electric Double Layer Capacitor for Rolling Stock” in Proc. of IEEJ JIASC2006, Vol.1, No. 1-OS-5, pp. 125–128, Nagoya, Japan, 2006 (in Japanese). [7] E. Khmelnitsky:“ An Optimal Control Problem of Train Operation” IEEE Trans. on Automatic Control, Vol.45, No.7, pp.1257–1266, 2000. [8] H. Ko, T.Koseki and M. Miyatake: “Application of Dynamic Programming to Optimization of Running Profile of A Train”, Computers in Railways IV, WIT Press, pp. 103–112, 2004. [9] T. Albrecht: “Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control” Computers in Railways IX, pp. 885–894, 2004. [10] M. Miyatake and H. Ko: “Numerical Optimization of Speed Profiles of Inverter Trains Considering DC Feeding Circuit” PCC-Nagoya 2007, No.DS8-3-9, Nagoya, Japan 2007. [11] K. Matsuda, H. Ko, and M. Miyatake: “Train Operation Minimizing Energy Consumption in DC Electric Railway with On-board Energy Storage Device” Computers in Railways X, pp. 767–776, 2006.

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Evaluation of energy saving strategies in heavily used rail networks by implementing an integrated real-time rescheduling system M. Luethi Swiss Federal Institute of Technology ETH, Zurich, Switzerland

Abstract The Swiss Federal Railways in cooperation with the Swiss Federal Institute of Technology ETH has developed an integrated real-time rescheduling system to simultaneously improve rail network capacity and punctuality. The approach combines real-time rescheduling (performed after a delay or incident) with very precise train operation facilitated by providing dynamic schedule information to train drivers. This information enables train drivers to change their driving behaviour and adjust their speed based on the new schedule. This can significantly reduce the number of unnecessary decelerations or stops due to conflicts. Consequently, traffic flow is improved. In addition, also energy consumption is reduced because unintended re-accelerations are minimised. This paper describes results of an analysis performed to calculate the energy savings possible using the integrated real-time rescheduling system. Keywords: rail traffic management; train dispatching; energy optimisation strategies.

1

Introduction

Railway operators have significantly increased passenger and freight service in the last several years. Consequently, railway infrastructure is being used more intensively and the system is becoming less stable. Under these conditions a small initial disturbance can propagate causing substantial knock-on delays throughout the entire network. In order to reduce the impact of these delays, train dispatchers must react quickly and make decisions based on current conditions. Given the complexity of this task, research on real-time rescheduling systems for rail networks has become an important research topic. Good overviews of the

76 Power Supply, Energy Management and Catenary Problems problem and potential solutions are described in D’Ariano [1] and Törnquist and Persson [2]. The focus for real-time rescheduling systems is to minimise knockon delays by detecting and solving train conflicts quickly and thereby optimising usage of rail infrastructure. As real-time rescheduling systems are improved, the information they provide to dispatchers will change from simply detecting conflicts to proposing conflict solutions by re-ordering, re-routing and re-timing of trains based on train predictions and extended algorithms. Another field of active research focuses on the optimal control of train operation (driving), see Albrecht [3], Franke et al. [4] or Howlett and Pudney [5] for more details. In this case, the optimisation objective is to minimise the train’s energy consumption subject to physical (rolling stock and infrastructure) and temporal (timetable) constraints. Today, especially on heavily used railway networks, changing conditions and particularly delays cause trains to stop unnecessarily which wastes energy. Current state-of-the-art for energy optimal driving solutions are only effective for simple systems (e.g. static timetables), extending these systems to heavily utilised and heterogeneous rail systems will require developing dynamically changeable schedules in real time. The Swiss Federal Railways (SBB) in cooperation with the Swiss Federal Institute of Technology (ETH) is implementing a new integrated real-time rescheduling system. The new system combines real-time rescheduling with continual provision of precise and up-to-date information to all affected actors (drivers, guard, infrastructure operators). The new system helps to improve service quality and capacity by reducing unnecessary signal stops. Since it reduces unnecessary stops it could also reduce energy consumption. This paper evaluates the energy savings possible using the integrated real-time rescheduling system with the support of micro-simulation and describes the main influence factors. Section 2 presents a short overview of the integrated real-time rescheduling system’s structure and functionalities. Section 3 reviews results of earlier train energy saving research. Section 4 evaluates the energy savings possible using the integrated real-time rescheduling system and section 5 presents conclusions.

2

Integrated real-time rescheduling system

The main idea behind the SBB’s integrated real-time rescheduling process is to continuously provide all actors with an up-to-date and conflict free schedule for all trains. This schedule would provide detailed information about time, speed and route (with an accuracy of seconds). The new approach combines two elements: - Rescheduling trains in real-time after a disturbance, event, incident or delay; - Controlling trains and infrastructure so that the dynamically calculated trajectories (new schedules) are followed with a predefined accuracy. Figure 1 illustrates the proposed rescheduling system’s structure and data flows.

Energy Management in the Train Operation

Figure 1:

77

Integrated real-time rescheduling structure and data exchange.

One of the main problems in developing a real-time rescheduling system is that it must be both very fast and precise. The system must quickly identify any disturbance, deviation or event. Then it must immediately provide the event information (containing position, speed and state of train and infrastructure) to the traffic management system (and finally the rescheduling algorithm). This information must be as exact as possible to reduce the possibility that the system will make bad predictions and generate sub-optimal schedules. Next, the system must quickly provide the new schedule information to all necessary actors. The rescheduling system uses two ideas to improve its overall accuracy. First, by communicating the new schedule information to train drivers it becomes possible for drivers to very precisely control their trains; this means that the rescheduling algorithm can safely predict when the train will arrive or pass specific points, which greatly increases the accuracy of the entire process. Second, by dividing the rail network into capacity bottleneck areas and links connecting them the process of generating a new schedule is simplified and speeded up [6]. One of the integrated real-time rescheduling system’s most distinctive features is that it immediately communicates a dynamically changeable schedule to all actors including the train driver, guard and passengers. When this real-time schedule information is combined with a supporting assistant system such as a driver-machine-interface (see [7] for an example developed in the Netherlands) or used as input for an Automatic Train Operation (ATO) system, the schedule can be followed very precisely. Therefore, the timetable information or target trajectory, provided by the system to the drivers has an accuracy of seconds. Recent improvements in communications technology have made it possible to quickly and accurately transfer information in both directions between the traffic management system and trains. Thus, train information such as state and position can be made available for the traffic management system almost immediately

78 Power Supply, Energy Management and Catenary Problems and train trajectories can be transmitted to drivers without delay. While the integrated real-time rescheduling system adds a significant level of control to train operations, it relies on the existing signalling and interlocking principles and infrastructure. A more detailed description of the integrated real-time rescheduling system and its benefits is presented in Laube et al. [8], Luethi et al. [9, 10] and Wuest [11].

3

Static energy optimisation

There is wide variation in the amount of energy a train needs to make a given trip. In 1999 and 2000, the SBB completed a set of tests on the line Zurich – Zug – Rotkreuz – Lucerne to identify key factors influencing the amount of energy needed and to assess various strategies for reducing energy demand [12]. These tests were carried out using IC-2000 intercity trains operated with a Re 460 locomotive and 10 wagons. The distance between Lucerne and Zurich is 57 kilometres, runtime is 48 minutes and there is only one significant grade with 13 per mill. The tests showed a large variation in the energy consumption and identified the following main influence factors: - Runtime; - Usage of electrical braking; and - Number of unnecessary signal stops. In addition to these main factors, weather conditions (adhesion) and train load were also found to influence energy consumption. Figure 2 illustrates the influence of runtime on theoretical energy consumption for the track section between Lucerne and Zug. It shows that energy consumption is highest for trips with the minimal runtime (16.6 minutes) and that it decreases significantly with longer runtimes until runtime reaches a certain point (17.25 minutes), and then it continues to decrease although only slightly

Figure 2:

Minimal theoretical energy consumption depending on the runtime.

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In addition to runtime, the train driver influences energy consumption through brake usage and the choice of brake used. The Re 460 locomotive has a powerful electric brake and a pneumatic disc brake where the entire kinetic energy is transferred into heat. Drivers were asked to use mainly the electric brake, but pneumatic brakes must be used when operating on minimal runtime schedules and making signal stops. The test runs showed that brake type has a significant impact on energy consumption. They also showed, using an elaborated optimisation algorithm, that it is possible to achieve energy savings of between 10 and 30% for traffic situations without unnecessary signal stops [4]. Algorithms and consequently train drivers are only able to minimise energy consumption when signals are open and the trains use the pre-planned track. Unexpected speed restrictions (e.g. due to changing a switch position) or closed signals force drivers to use the pneumatic brake thereby increasing energy consumption. The tests showed that energy consumption was approximately 1015% higher for trains having an unnecessary signal stop than for unhindered runs. On track sections with capacity bottlenecks many trains are forced to make one or more unscheduled stops. For example over 50% of all IC-2000 trains from Zurich to Lucerne had to stop at Rotsee in the entrance area to Lucerne station (a major bottleneck) due to delays. To summarise, the driving strategy (especially reducing unnecessary stops) significantly influences energy consumption and therefore offers a large saving potential. However, as the number of trains increases, the number of unnecessary stops due to delays also increases thus increasing energy use. As outlined in the following section, integrated real-time rescheduling can provide drivers with precise and up-to-date schedules that reduce unscheduled stops and thereby reduce energy consumption.

4

Energy optimisation with integrated real-time rescheduling

Railway traffic has grown significantly in the last several years; more trains are being operated often with no additional infrastructure. This situation increases the number of delays caused by train conflicts and also causes knock-on delays to propagate more quickly through the entire network. However, the new integrated real-time rescheduling system makes it possible to effectively implement measures such as re-routing, re-ordering and re-timing of trains thus minimising train conflicts and knock-on delays. As outlined in chapter 2, the integrated real-time rescheduling system continuously provides train drivers with up-to-date driving trajectories enabling them to reduce unnecessary stops. The rescheduling system can use several different strategies and optimisation criteria in developing these new trajectories, including: - Earliest arriving time; - Minimal energy consumption; and - Shortest blocking time. In addition to these criteria, the topology, infrastructure, signalling and operation rules have significant impact on the final trajectory. Albrecht described

80 Power Supply, Energy Management and Catenary Problems the influence of these trajectories that anticipate train driving [13]. As outlined earlier, the precise trajectory strategy can be very effectively used before entering a bottleneck area. For example, the SBB has evaluated the strategy of slowing down and accelerating a train before reaching a capacity critical section so that the train passes through the bottleneck area with the maximum allowable speed. Figure 3 compares traditional train control to this type of dynamic train control using integrated real-time rescheduling. Figure 3 shows that the train with integrated real-time rescheduling arrives earlier in the station and uses less energy. The results show that the time difference can vary between several seconds up to several minutes depending on the train and infrastructure characteristics. The energy evaluation is based on braking and reacceleration – which provide more precise train control – rather than coasting to follow the train trajectory. However coasting could be added to the algorithms to further reduce energy use.

Figure 3:

Comparison of traditional driving behaviour with speed control as part of integrated real-time rescheduling.

The goal of this research was to more precisely evaluate the impact of the integrated real-time rescheduling system (and in particular the point of time the new schedule is transmitted to the train) on energy consumption. The research used the OpenTrack train micro simulation application (see [14] for a description of OpenTrack). The evaluation considered the 18 kilometre track section from

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Rotkreuz to Lucerne. This section includes a single line section starting at Rotsee (near Lucerne) which causes regular conflicts. The research evaluated energy consumption based on when the train received the revised schedule. In all cases it was assumed that the train could enter the critical single line section exactly one minute later than originally scheduled (in other words the signal turned green one-minute later than scheduled). Of course, the earlier a new schedule is generated, the smoother or less deceleration and reacceleration is needed. The closer a train is to the critical point (Rotsee) when it receives the new schedule, the more energy it will use since the target speed (i.e. speed the train should be going to be one minute later) is lower (see Figure 4). This means that train operators must use pneumatic brakes since immediate and strong braking action is needed.

Figure 4:

Possible rescheduling actions depending on the point of time rescheduling is executed resulting in identical arriving times in Lucerne.

Figure 5 illustrates the simulation results. It shows the minimal relative energy consumption depending on the point of time the rescheduling is executed (i.e. the new schedule is received and acted upon by the train driver). Figure 5 shows that for the first 100 seconds after departure from Rotkreuz, the relative energy consumption for all alternatives is minimal and identical. This is due to the fact that the train is accelerating to its target speed. When the rescheduling information is received between 125 and 160 seconds, the relative energy consumption increases, but remains approximately constant. During this period, the reduced target speed varies only marginally and the speed when rescheduling is executed is stable at 125 km/h. When the rescheduling is executed between 160 and 200 seconds after departure from Rotkreuz, the train is in the process of accelerating up to the maximum line speed of 140 km/h and therefore relative energy consumption increases more or less linearly. Finally, when the rescheduling is executed between 200 and 310 seconds, the train must brake and slow down to a lower and lower speed resulting in a maximal relative energy consumption of up to 50%

82 Power Supply, Energy Management and Catenary Problems higher than in the best case (early rescheduling). After 310 seconds, a full stop can not be avoided anymore.

Figure 5:

Influence of rescheduling point of time on relative energy consumption for the section Rotkreuz – Lucerne.

To summarise, the rescheduling point of time is a decisive variable in determining energy consumption. Providing precise train speed control information early enough so that drivers can reduce their need for braking and reacceleration to a minimum reduces energy consumption by up to 50%. The nearer to the critical point where rescheduling information is executed, the more energy will be consumed (since this requires strong braking and reacceleration). However, in all cases where a full stop can be avoided, rescheduling will reduce energy consumption. Delays and blocked routes often occur in heavily used parts of the rail network and in bottlenecks where trains interfere with each other. A significant amount of energy could be saved in these areas by implementing integrated realtime rescheduling. As rail traffic increases, applying integrated real-time rescheduling systems is becoming increasingly necessary, not only to reduce knock-on delays, but also to save energy. To be most effective real-time rescheduling should be combined with energy efficient train control based on elaborated algorithms. Only the combination of both approaches will make it possible to fully achieve potential energy savings.

5

Conclusion

Railway companies are facing huge challenges, on the one hand demand is growing as concerns over sustainability, energy use and climate change become more significant, while on the other hand railways face increasing market pressure to reduce expenditures and capital costs. In short they must increase capacity and service quality at minimum cost.

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Integrated real-time rescheduling systems are being developed to increase infrastructure capacity without making significant investments or causing more delays. An important element of these systems is providing train drivers with upto-date data and new schedules. This enables drivers to precisely control speeds thus minimising unnecessary stops. Unnecessary stops not only reduce network capacity and punctuality, but also increase energy consumption. Therefore, integrated real-time rescheduling systems that eliminate or reduce unnecessary stops can also reduce energy consumption. The research completed for this study showed that on the rail segment from Rotkreuz to Lucerne, energy consumption could be reduced by up to 50% with speed adjustments based on decisions of the integrated real-time rescheduling compared to traditional train control with a full stop and reacceleration. The research also showed that the point of time when rescheduling is executed is very important. Large savings are only achieved when rescheduling is executed early. Real-time rescheduling should be combined with energy efficient train control to minimise energy consumption and achieve the largest possible energy savings.

References [1] D’Ariano, A. Improving Real-Time Train Dispatching: Models, Algorithms and Applications, Trail thesis series, Delft, 2008. [2] Törnquist, J., Persson, J. N-tracked railway traffic rescheduling during disturbances, Transportation Research Part B, 41(3), pp. 342–362, 2007. [3] Albrecht, T. Ein Beitrag zur Nutzbarmachung Genetischer Algorithmen für die optimale Planung und Steuerung eines flexiblen Stadtschnellbetriebes, PhD Thesis, Dresden University of Technology, 2004. [4] Franke, R., Meyer, M., Terwiesch, P. Optimal Control of the Driving of Trains, Automatisierungstechnik, 50(12), pp 606–613, 2002. [5] Howlett, P.G., Pudney, P.J. Energy-efficient train control, Springer, Berlin, 1995. [6] Caimi. G., Burkolter, D., Herrmann, T., Chudak, F., Laumanns, M. Design of a new railway scheduling model for dense services, Proc. of the 2nd International Seminar on Railway Operation Research, Hannover, 2007. [7] Albrecht, T., van Luipen, J., Hansen, I.A., Weeda, A. Bessere Echtzeitinformationen für Triebfahrzeugführer und Fahrdienstleiter, Eisenbahningenieur, 58(6), pp.73–79, 2007. [8] Laube, F., Roos, S., Wuest, R., Luethi, M., Weidmann, U. PULS 90 – Ein systemumfassender Ansatz zur Leistungssteigerung von Eisenbahnnetzen, Eisenbahntechnische Rundschau, 56(3), pp.104–107, 2007 [9] Luethi, M., Laube, F., Medeossi, G. Rescheduling and Train Control: A New Framework for Railroad Traffic Control in Heavily Used Networks, Proc. of the 86th Transportation Research, Washington DC, 2007. [10] Luethi, M., Nash, A., Weidmann, U., Laube, F., Wuest, R. Increasing Railway Capacity and Reliability through Integrated Real-Time

84 Power Supply, Energy Management and Catenary Problems

[11] [12]

[13]

[14]

Rescheduling, Proc. of the 11th World Conference of Transportation Research, Berkeley, 2007. Wuest, R. Dynamic Rescheduling based on Predefined Track Slots, Proc. of the 7th World Congress of Railroad Research, Montreal, 2006. Meyer, M., Roth, M., Schaller, B. Einfluss der Fahrweise und der Betriebssituation auf den Energieverbrauch von Reisezügen, Schweizer Eisenbahn-Revue, 22(8–9), pp 360–365, 2000. Albrecht, T. The influence of anticipating train driving on the dispatching process in railway conflict situations, Proc. of the 2nd International Seminar on Railway Operation Research, Hannover, 2007. Nash, A., Huerlimann, D. Railroad simulation using OpenTrack. Computers in Railways IX, eds. J. Allan, R.J. Hill, C.A. Brebbia, G. Sciutto, S. Sone, WIT Press, pp. 775–784, 2004.

Part B Power Supply System Analysis, Design and Planning

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Online temperature monitoring of overhead contact line at the new German high-speed rail line Cologne-Rhine/Main N. Theune, T. Bosselmann, J. Kaiser, M. Willsch, H. Hertsch & R. Puschmann Siemens AG, Corporate Technology, Germany

Abstract This paper reports on the first fiber-optic temperature measurement of overhead contact line systems at a new ICE3 high speed line of the German Railway. The installation of Fiber Bragg Grating (FBG) sensors, the online acquisition and interrogation of data over a one year period is presented. Keywords: Fiber Bragg Grating, temperature monitoring, overhead contact line, catenary, power management.

1

Introduction

All railway companies try to achieve higher reliability and flexibility in train service. As a consequence the quality of train control processes as well as monitoring equipment for the next generation of high speed railway lines needs to be improved. Next generation of high speed trains will consume more power, because of an increased amount of electrical amenities inside the train and - of course - higher speeds of up to 300 km/h and more. This goal can only be achieved if the overhead contact lines that provide the energy for the trains are protected reliably from thermal overload caused by electrical overcurrents and hotspots at the catenary wire and contact wire. Up to now diagnostic systems for online acquisition of real temperature data do not exist. As a state of the art, conventional Digital Protection Devices (DPDs) in substations inhibit a simple numerical model from which the so-called catenary temperature is estimated with respect to current load and ambient air temperature [5]. If the estimated temperature exceeds a certain limit of e.g. T=70°C the power supply of the overhead contact line is switched off, regardless of the actual temperature on the

88 Power Supply, Energy Management and Catenary Problems overhead contact line. If the actual temperature would be higher, thermal overusage of the overhead contact line system could destrengthen parts of the catenary construction. Furthermore elongation may cause a malfunction of a passing train pantograph or lead to a destruction of the contact wire. If the actual temperature would be lower than the limit, the power supply for the trains would be switched off needlessly. Both cases are connected to cost-intensive down time of the train line. In order to control reliably and adapt to the growing power needs for high speed trains and to use up to date overhead line systems more efficiently an accurate online determination of the overhead contact line and contact wire temperature is essential. The appropriate temperature sensors have to be compact, should be easily integrable in the catenary construction and must be able to measure on high voltages of up to 25 kV. In general conventional temperature monitoring techniques could be applied alternatively, but due to the high voltage level of the overhead line an enormous amount of effort needs to be put into the insulation of these sensors or into provision of independent power supplies etc. [1]. On the other hand FBG sensors offer, because of their vitreous nature, a simple way to measure on high voltages with a minimum of insulation material needed. Multiplexed temperature measurements with the help of FBGs could help to localize hot spots and provide a continuous measurement for the protection of the power line [3]. If the temperature distribution of a complicated network structure could be measured the required material effort of new installations could be optimized which would lead to substantial savings. Furthermore in peak-periods the power supply could be managed intelligently with respect to the actual thermal usage of the catenary. The measuring system, the multiplexed network of sensors and the sensor setup which were implemented on the new high speed rail line between Cologne and Frankfurt will be presented and discussed. In the future this technique can be easily adapted to similar applications of railway transportation systems e.g. long distance railways with overhead contact lines with still higher demands with respect to current load.

2 Theory 2.1 Brief theory of fiber Bragg gratings A change in fiber strain ∆ε and temperature ∆T is connected to a change in center wavelength ∆λ of the Bragg reflex via the two equations ∆λ = (1 − p e ) ⋅ ∆ε , λ (1) ∆λ = [(1 − p e ) ⋅ α + ξ ] ⋅ ∆T , λ whereas p e represents the photoelastic constant, α the linear coefficient of expansion and ξ the thermooptical coefficient of the fiber. Almost in any case where FBGs are part of a composite material both effects, temperature and strain,

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contribute to a center wavelength shift of the Bragg reflex. In case of the catenary temperature sensors the first effect needed to be excluded. This was done through a sensor design that decoupled any stress acting on the sensor housing, e.g. elongating electric wires, from the sensing FBG element. The thermal effect of current load on the overhead contact wires and the estimation of the so called catenary temperature will be discussed in the next section. 2.2 Model for numerical estimation of the catenary temperature Nowadays the DPDs inside transformer substations evaluate the temperature of the catenary with the help of a simple numerical model. The electric current signal I and the ambient air temperature Tamb are processed in an exponential function to compute the catenary temperature Tcat

(

)

 I (t )   , (2) ⋅ Tcat (t ) = Tamb (t ) + T∞ ⋅ 1 − e I   max, ∞  whereas Tamb represents the ambient air temperature, T∞ the maximum excess temperature after t = ∞ , τ the thermal constant of the catenary type, t the time, I the actual current and I max,∞ the maximum current after t = ∞ . In practice, if −t τ

2

the calculated catenary temperature Tcat exceeds 70°C the relay causes a power circuit breaker in the switch yard to switch off the current. The numerical model is uncertain, because various parameters are not accounted for, e.g. wind velocity, wind temperature, incident solar radiation, precipitation etc.

3

Measuring setup

The setup for online measurement of the catenary temperature is based on a polychromator interrogation unit, as in Figure 1:. The polychromator unit consists of a diffraction grating, a CCD array, an ADC card and a PC for online temperature evaluation of the spectral intensity information acquired from the CCD array. As a light source a broadband LED with a center wavelength of λ = 840 nm and a full width at half maximum of ∆λ FWHM = 45 nm was used. As the whole interrogation unit was used in field, e.g. ambient temperatures were ranging from −10°C to +40°C , an Argon calibration lamp was preferred to eliminate the temperature dependent shift in wavelength over CCD-pixel. The Argon spectral peaks between 800 and 850 nm were used as a reference in order to get a calibrated functional dependency between CCD-pixel and wavelength. A 4x1 fiber switch operated continuously between the 4 sensor channels. The whole setup consists of exchangeable card modules and was implemented into a portable 19-inch rack, as in Figure 3:.

90 Power Supply, Energy Management and Catenary Problems

Figure 1:

Polychromator setup with Argon calibration lamp and 4x1 fiber switch.

Figure 2:

Location of FBG temperature sensors on the overhead wires at the injection pylon – 300m apart from the Limburg transformer substation.

4

Application of sensors

Figure 2: shows the locations on the catenary where FBG sensors were installed. The sensors were manufactured in a single ended design that has been used also in other fields of high voltage applications, e.g. power generators [2], as redundancy for this first field demonstration in this delicate application was of major importance. Every single FBG sensor was provided with an individual optical link to the interrogation unit – located in the transformer substation -

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300 m apart from the injection pylon. Two FBG sensors are installed in close

thermal contact to the two injection wires, each of 240 mm 2 cross sectional area. Further two FBG sensors are located at supporting current wires, each of 120 mm 2 cross sectional area. The signals of the four FBG sensors are then transformed into a temperature value. Simultaneously the catenary temperature signal provided by the DPD - also located inside the transformer substation – is calculated. Both data are then submitted - via a GSM link - to a control PC, over 300 km away, to our lab in Erlangen for analysis.

 

Figure 3:

5

Left: Polychromator interrogation unit with online FBG temperature data, Right: DPD with online calculated catenary temperature data

Measurements

In Figure 4: the online catenary temperature data in 12/2002 and 01/2003 acquired from the DPD is shown. In Figure 4:(a) the overall current signal I with values up to 2 kA at an effective voltage of U ≈ 16.5 kV @ 16 2 3Hz can be seen [4]. The measured ambient air temperatures Tamb in (b) range from −10°C to 10°C . The calculated excess temperature ∆T , i.e. the temperature increase that is due to the current load, is shown in (c). In Figure 5: the online FBG sensor temperature data of the sensors 1 to 4 is shown. Overall the temperature data of the four FBG temperature sensors corresponds very well to the calculated data of the DPD. But in detail the differences between the fiber-optical and calculated data can be enormous. This will be shown and discussed in the next section.

92 Power Supply, Energy Management and Catenary Problems

Figure 4:

Figure 5:

6

DPD data between 11/2002 – 01/2003.

Signals of 4 FBG temperature sensors, installed on catenary wires.

Discussion of results

In Figure 6: the difference between FBG sensor #2 and the calculated DPD catenary temperature is plotted. It can be seen that the difference in temperature between the fiber-optical sensor at the catenary and the calculated DPD data can reach up to approx. 8°C . If we zoom into the rectangular dashed part in Figure 6:, then a typical behavior of the FBG catenary sensor can be seen, as in Figure 7:. Here the optical sensor takes into account the incident solar radiation, i.e. due to the solar energy the catenary wire warms up over a period of several hours only interrupted through periods of cloudiness. At that day - after the sunset at around 16.30h - the influence of cold wind dominates and chills the catenary wire.

Power Supply System Analysis, Design and Planning

Figure 6:

Temperature difference between FBG sensor #2 and the DPD temperature data.

Figure 7:

7

93

Zoom into the dashed rectangular part of Figure 6.

Conclusions

For the first time online temperature measurements with FBG temperature sensors on railway overhead lines could be demonstrated. All sensors measured successfully under outdoor conditions over a one year period. As a first experimental result it was found out that the excess temperatures due to current load are small compared to ambient sources of temperature

94 Power Supply, Energy Management and Catenary Problems change. In the future this first result will be analyzed under different seasonal and current load conditions. In the future FBG sensors will be installed on other hotspot locations at the overhead contact line. The measurements indicate that there might be a large cost saving potential for similar future installations. FBG catenary sensors can provide catenary designers with real data acquired over several years and help optimize the construction system with respect to reduction of material expenses and optimization of the power management.

Acknowledgements The authors thank sincerely Mr. Walter Weisel from German Rail Energy for his ongoing support during the whole project. Part of this work was financially supported by the National FAMOS project.

References [1]

[2]

[3]

[4]

[5]

Kießling, F.; Puschmann, R.; Schmieder, A.; Schmidt, P.: “Contact Lines for Electric Railways – Planning, Design, Implementation”. Siemens AG, Publicis Corporate Publishing, Munich, 2001. Theune, N.M.; Müller, M.; Hertsch, H.; Kaiser, J.; Willsch, M.; Krämmer, P.; Bosselmann, T.: “Investigation of Stator Coil and Lead Temperatures on High Voltage inside Large Power Generators via use of Fiber Bragg Gratings”. IEEE Sensors 2002 Conference, Conference Proceedings, Orlando, USA. Bjerkan, L.: “Measurements of overhead transmission line loads with Bragg gratings”. Conference Proceedings, SPIE 3746, OFS-13, Kyongju, Korea, P2-27, 1999. Kohlhaas, J.; Ortstädt, W.; Puschmann, R.; Schmidt, H.: ”Interoperable overhead contact line SICATH1.0 for high-speed line CologneRhine/Main”. Elektrische Bahnen 100 (2002), H. 7, S. 249-257. Digital Overhead Contact-Line Protection 7SA517, Instruction Manual, Edition 08/2001, Siemens AG.

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Electric traction energy metering on German Railways and the impact of European standardisation on the energy billing process in Germany K. Weiland DB Energie GmbH, Germany

Abstract With the onset of liberalisation of energy markets and the formation of DB Energie Inc. as a wholly owned subsidiary of Deutsche Bahn AG (German Railways), proper billing of electric energy to railway-based consumers has become an important issue. Hence, DB Energie had to develop and implement a revenue metering scheme for traction energy consumed by railroad vehicles. The impact of international interoperable traffic has been considered. Keywords: energy meter, metering on-board trains, traction energy, railways.

1

Initial situation

In close co-operation with instrument manufacturers, DB Energie has devised and developed an on-board metering device for electric railway vehicles. The device is derived from a standard, utility grade load profile meter used widely in the power distribution business, but complemented with a GSM-modem and antenna for radio data transmission.

2

National requirements

The meters have to meet German and European calibration standards and regulations, and require approval for use in commercial revenue metering applications. Accordingly, the meters and the adjacent instrument transformers need to be of Class 1 and 0.5, respectively. Both are officially certified for both 16.7 Hz and 50 Hz applications [1, 2, 4].

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3

Technical concept

Though the device has four-quadrant capability, the vehicles’ power factor is not of an immediate interest, because the majority of traction drives employ state of the art power electronics and thus operate at unity power factor. The recorded data of the meter is transmitted by a GSM radio to a central control and data processing station, where the raw data for billing the respective operators will be generated. The meters allow to store either a 5-minute or a 15-minute load profile in its built-in memory. The revenue data are downloaded on a daily basis through a poll request transmitted by the central control station. The data storage and processing scheme allows then for a variety of analysis. One may – for instance – derive a graph of the power and energy consumption for a single train journey

Energy data management

TEMA compact box

Accounting (SAP)

GSM Central control station

Billing system

Load profiles Railway disposition systems

Figure 1:

Additional information, e.g. train number

Information adding system

Consumption data

Structure of the billing system for traction energy.

The energy consumption will be combined with the railroads operative data like planned and actual schedules, train configuration data like weight, number of cars etc. Based on this input, DB Energie will produce individual bills for each train journey on its system. Some customers even use this information for their own management-information-systems as well as for energy saving programs [8]. As shown in the picture above, the optical interface located on the front panel of the meter serves for local downloads. Using this data link, the loco-operators have a means to verify and double check billing data received from DB Energie’s data processing system. The communication interface allows data transmission in compliance with Standards EN 62056-21 [5] or IEC 870-5-2 [6], and the central control station

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will poll the meter. The specification of metering code follows the national standard VDEW – Specifications 2.1 (see picture 3) [7]. The maximum power demand of the meter in the instrument transformer circuit is 50 mVA.

Energy Impulse LED (red) LCD Display

Optical Infrared Interface (i. e. Notebooks)

Energiezähler Antenne

Modem

Figure 2:

Antenna

Energy Meter

GSM Receiver LED (green)

Meter used on board trains.

meter F.F(00000000) 0.0.1(00000000) 0.0.2(00000000) 0.0.3(00000000) 0.0.4(00000000) 0.0.9(00136612) 0.9.1(133743) 0.9.2(000208) 1.8.1(00024.70015*kWh) 2.8.1(00000.02609*kWh)

status information meter: ok absolute meter readings one time per transmission 1/4 h-values incl. events

P.01(991204124050)(00000080)(15)(2)(1.5)(kW)(2.5)(kW)(1121730)(0002001) (0.0012)(0.0000) P.01(991205072451)(00000040)(15)(2)(1.5)(kW)(2.5)(kW)(1121730)(0002001) (0.0000)(0.0000) (0.0005)(0.0000) (0.0011)(0.0000) (0.0011)(0.0000) (0.0010)(0.0000) (0.0010)(0.0000) (0.0038)(0.0000) P.01(991205084821)(00000000)(15)(2)(1.5)(kW)(2.5)(kW)(1121730)(0002418) (0.0041)(0.0000)

GSM-Modem antenna

Figure 3:

4

Compact meter on board trains and load profile codes.

Experiences of DB Energie

As of 2002, electrically propelled vehicles such as locomotives and self propelled trains (MTUs) operating on the German railway infrastructure have

98 Power Supply, Energy Management and Catenary Problems been furnished with this device, allowing DB Energie to meter and analyse the vehicles individual energy consumption profile including regenerative breaking. Since January 2003, billing of electrical traction energy is entirely and exclusively based on metered values. The on board meters have proven their worthiness for this routine in day-to-day business. It turned out, though, that the availability of the radio communication system is an actual bottleneck in this remote metering scheme. Once a vehicle moves into an industrial site with narrow paths, the probability of loss of communications link increases drastically. This may happen, for instance, when a locomotive is moved into a service station or workshop. The following graph depicts the proportion of nonconnected vehicles (missing radio data link) and the duration of this link outage over a month’s period. Quota of non stored metering data in the central database at a month before

10 8

September 03

November 03

Oktober 03

7,31

7,13

6,76 6,02

6

5,24

5,16 4,15 4,15

4,39

4,28

4,28

4,36

4,03 3,54

4

3,21

1 Tag day 8 Tag days 12 Tag days days 15 Tag days 22 Tag

2 0

Figure 4:

5

Proportion of non-connected vehicles and the duration of link outage over a month’s period.

European standardisation process

Within the Europe-wide effort to furnish all electric trains with standardized meters, several manufactures focus on the development of such devices. As a next step, systems for DC traction power are expected to appear in the market soon. In December 2002, CENELEC TC9X called for experts for survey/working group “Metering On Board Trains”. The target of this standardisation group is to facilitate the interoperability of trains and the compatibility of technologies in the various European countries. Under the guidance of Italian Railways (RFI) the requirements stipulated in the different national regulations were collected. Subsequently, in June 2003, the survey group specified the scope and content of the standard to be drafted.

Power Supply System Analysis, Design and Planning

99

The paper describes the process of compiling and balancing the different interests brought up by the participating countries, which in turn are due to different states of implementation of the European Union’s guidelines concerning the liberalisation of European Single Market (ESM) in the field of energy and railway business. Implementing the German energy market rules as agreed upon by utilities and traders, private and foreign railway operators are entitled to be billed on metered electrical energy consumption exclusively. Denmark, Sweden and Germany are frontrunners in this effort, because their respective national regulations already mandate on-board metering. Therefore, the concerned railway infrastructure utilities bear the risk that a future European standard does not match with today’s technology. The process of European standardisation will provide a framework for future on-board meters for trains allowing to employ state-of-the-art metering technology. Also, it follows the known national regulations. Optionally, a meter can be designed as a modular system consisting of a separate modem, a location module, and an antenna. Data transmission should comply with Standard EN 62056-21 [5] or IEC 870-5-2 [6]. The protocols can be adopted to different digital telegrams. This standard permits national system solutions like GSM-R [3] for data transmission, and also the correlation of an individual locomotive (via its meter) with the momentary energy utility when operating in international, cross border traffic or for the identification of different energy grid operators. The present course of standardisation promises an roadmap towards a common meter suitable for almost any train operating on European tracks. Centralised control stations with standard databases store common data formats, and railroad utilities would be able to meet commercial contract requirements for billing energy to any European customer. Though this process of international standardisation, a forum has been established for European railroad operators, for railway infrastructure companies, and not at least for equipment and instrument manufacturers to start a dialogue about their individual needs and expectations. The aim is to eventually harmonise technical and operational standards throughout Europe in order to facilitate a reliable and dependable, cross-border proof revenue metering scheme accepted by all participants. A first major step in this direction has been accomplished by the foundation of CENELEC TC9X. This ongoing standardisation process will eventually set the basis for an effective and precise energy billing scheme within the liberalised TransEuropean railroad community.

References [1] [2] [3]

Kahmann, M., Zayer, P., Handbuch Elektrizitätsmesstechnik, VWEW Energieverlag: Frankfurt, Heidelberg and Berlin, pp. 27-36, 2003. Eichordnung vom 12.08.1988 (BGBI. I pp. 1657 ff.). http://gsm-r.uic.asso.fr/.

100 Power Supply, Energy Management and Catenary Problems [4] [5] [6] [7] [8]

Gesetz über das Mess- und Eichwesen (Eichgesetz), Neufassung vom 23.03.1992, (BGBI. I, pp. 408 ff.). EN 62056-21: Electricity Metering – Data exchange for meter reading, tariff and load control – Part 21: direct local data exchange. IEC 870-5-2 Data Link Transmission Services. Lastenheft Elektronische Energiezähler Version 2.1, VWEW Energieverlag: Frankfurt, Heidelberg and Berlin, 2003. Proceedings of 2nd UIC Railway Energy Efficiency Conference, Paris, 45 February 2004. Energy efficient railways: next steps towards sustainable mobility.

Power Supply System Analysis, Design and Planning

101

Development of feeder messenger catenary with the auxiliary wire K. Nishi, Y. Sato & T. Shimada Railway Technical Research Institute, Japan

Abstract Feeders are a standard installation of DC electrified railways in Japan in order to complement the electric capacity of contact wires. Recently in metropolitan area in Japan, the installed area of the feeder messenger catenary system that has the function of feeder in messenger has been expanded. Then we developed a new feeder messenger catenary system with the auxiliary wire that has the function in which the contact wire is hard to break. For this purpose, we investigated the best structure of this catenary system first and simulated electric performance. Then we performed running tests by using a pantograph installed on the current collection testing equipment of our institute and evaluated the current collecting performance of the new system. From the results of these tests, it has been proved that there are no problems in its current collecting performance up to 150km/h. Keywords: feeder messenger, auxiliary wire, tension shift.

1

Introduction

Now in 1,500V DC electrified railways of metropolitan area in Japan, the installed area of feeder messenger catenary system that has the function of feeder in messenger has been expanded. In this catenary system, the number of parts can be reduced because messenger has the function of feeder [1]. However, it is apprehended the contact wires of this system may be broken like those of conventional catenary system when their residual diameter becomes small [2]. Therefore, we devised a new catenary system that has an auxiliary wire. In the overhead line equipment proposed here, the tension of contact wire shifts to the connected auxiliary wire to prevent it from breaking when its residual diameter has become small. We examined the electrical performance and performed

102 Power Supply, Energy Management and Catenary Problems computer simulation to determine the optimum structure of this system that uses a hard-drawn copper stranded wire PH 590mm2 as the messenger wire, PH 150mm2 as the auxiliary wire and a bronze wire GTM170mm2 as the contact wire. For this overhead contact line structure, we performed running tests by using a pantograph installed on the current collection testing equipment of our institute and evaluated its current collecting performance. Based on the test results, we have confirmed that the contact loss rate is less than 1% up to 150km/h and proved that there are no problems in the quality of current collection. We have also confirmed through measurement that the tension of the contact wire shifts to the auxiliary wire when its residual diameter becomes small. Then, it is proved that the contact wire does not easily break. As a result, we found the possibility of this catenary system to be put into practical use.

2

Structure and feature of the proposed catenary system

The features of this catenary system are described below. An auxiliary wire is installed between the feeder messenger and the contact wire that is connected to the auxiliary wire with ears. Then, tension shifts from the contact wire to the auxiliary wire when the residual diameter of the contact wire becomes small or the contact wire has been softened by arcs and Joule heat. Therefore, the contact wire does not easily break and improves the reliability of this catenary system. This catenary system is classified into the following three types. First we define “composite type” which makes the auxiliary wire contacts the contact wire (Figure 1). a u xilia r y wir e

pu ll-off a r m feeder m essen ger h a n ger 5m

con t a ct wir e

Figure 1:

“Composite type” feeder messenger catenary.

feeder m essen ger ea r 50m m

a u xilia r y wir e

pu ll-off a r m h a n ger 5m

con t a ct wir e

Figure 2:

“Hanger form compound type” feeder messenger catenary.

Power Supply System Analysis, Design and Planning

103

Second we define “compound type” which connects the auxiliary wire with the contact wire by keeping a distance of 50mm in between. We classify the structures of these two compound types into two. One is the structure that connects the auxiliary wire with the messenger by hangers, which we define as the “hanger form compound type (Figure 2)”. The other is the structure that connects the auxiliary wire with dropper, which we define as the “dropper form compound type (Figure 3).” feeder m essen ger

ea r

a u xilia r y wir e

pu ll-off a r m dr opper 5m

50m m

con t a ct wir e

Figure 3:

3

“Dropper form compound type” feeder messenger catenary.

Analysis of the quality of current collection

3.1 Catenary composition By computer simulation, we calculated the contact loss rate in each feeder messenger catenary form in Figures 1~3. Table 1(a) and (b) show the catenary composition for which we performed simulation. We chose two combinations of wires in order that current capacity and voltage drop between substations below the specified value. A PH590mm2 wire is used for the messenger and a PH150mm2 for the auxiliary wire to improve the quality of current collection in a combination and a PH356mm2 wire, which is generally used in Japan, for the messenger wire and the auxiliary wire for to make construction easier in other combination. Moreover, the simulation was performed under different conditions for comparison. Table 1 (a): Simulation condition for catenary composition. 䋨㸇䋩

䋨㸈䋩 2

䋨㸉䋩 2

Composition

PH356mm ×2

PH730mm

Feeder messenger

PH356mm2×2 39.2kN

PH730mm2×1 39.2kN

Tension of feeder messenger

PH590mm2 Composite type PH590mm2 39.2kN PH150mm2 4.9kN

Auxiliary wire Tension of auxiliary wire Tension of contact wire

GTMSn170mm2 14.7kN

GTMSn170mm2 14.7kN

GTMSn170mm2 9.8kN

System height

850mm

850mm

850mm

Interval of dropper Interval of hanger

5m

5m

5m

Contact wire

104 Power Supply, Energy Management and Catenary Problems Table 1 (b): Simulation condition for catenary composition. 䋨㸊䋩

䋨㸋䋩 2

䋨㸌䋩

PH356mm Composite type

PH590mm Compound type

PH356mm2 Compound type

Tension of feeder messenger

PH356mm2 39.2kN

PH590mm2 39.2kN

PH356mm2 39.2kN

Auxiliary wire Tension of auxiliary wire

PH356mm2 4.9kN

PH150mm2 4.9kN

PH356mm2 4.9kN

Contact wire Tension of contact wire

GTMSn170mm2 9.8kN

GTMSn170mm2 9.8kN

GTMSn170mm2 9.8kN

System height

850mm

910mm

910mm

5m

10m 5m

10m 5m

Compositiion Feeder messenger

Interval of dropper Interval of hanger

2

3.2 Simulation results (a) Contact loss rate Figure 4 shows the simulation results of contact loss rate in each catenary composition. The catenary composition whose contact loss rate exceeds the allowable value of 5% in DC electrified railways is only the “composite type” composed of a PH356mm2 messenger under the condition where the maximum speed is 160km/h on narrow-gauge lines in Japan. (b) Contact wire uplift at support Figure 5 shows the simulation results of contact wire uplift at support in each catenary composition. According to the simulation results, the contact wire uplift at support of the compound type is larger than that of other catenary system. However, the values are less than allowable value of 70mm up to 160km/h.

㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪋㪌

㩿㸇䋩 䋨㸉䋩 䋨㸋䋩

㪊㪇

䋨㸈䋩 䋨㸊䋩 䋨㸌䋩

㪈㪌 㪇 㪎㪇

Figure 4:

㪈㪉㪇 㪈㪎㪇 㩷㪪㫇㪼㪼㪻㩷㩿㫂㫄㪆㪿㪀

㪉㪉㪇

Simulation results of contact loss rate.

Power Supply System Analysis, Design and Planning

㪈㪉㪇

㩿㸇㪀 㩿㸉䋩 㩿㸋䋩

㪬㫇㫃㫀㪽㫋㩷㪲㫄㫄㪴

㪏㪇

105

㩿㸈㪀 䋨㸊䋩 䋨㸌䋩

㪋㪇 㪇 㪎㪇

Figure 5:

㪉㪉㪇

Simulation results of contact wire uplift at support.

㪪㫋㫉㪸㫀㫅㩷㩷㪲㬍㪈㪇 㪴

㪈㪉㪇㪇 㪄㪍

㪈㪉㪇 㪈㪎㪇 㪪㫇㪼㪼㪻㩷㩿㫂㫄㪆㪿㪀

㩿㸇䋩 㩿㸉䋩 㩿㸋㪀

㪏㪇㪇

㩿㸈䋩 㩿㸊㪀 㩿㸌䋩

㪋㪇㪇 㪇 㪎㪇

Figure 6:

㪈㪉㪇 㪈㪎㪇 㩷㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪉㪉㪇

Simulation results of contact wire strain at support.

Contact wire strain at support Figure 6 shows the contact wire strain at support in each catenary composition. The value of contact wire strain is less than the allowable value of a 1000×10-6 in all catenary compositions up to 160km/h. From these simulation results, these catenary compositions, except the one that uses PH356mm2 wire for the messenger wire, satisfy the allowable value up to 160km/h to prove that the possibility for practical use is high.

4

Current collecting performance tests

4.1 Outline of test We installed a feeder messenger catenary that provided satisfactory simulation results on the current collection test equipment in our institute and performed current collecting performance tests. Table 2 shows the catenary composition and Table 3 shows the property of pantographs used in this tests. Table 4 shows

106 Power Supply, Energy Management and Catenary Problems the tension distribution of each wire. We ran pantograph at 80 to 150km/h at intervals of 10km/h to perform current collecting performance tests. Table 2:

Catenary compositions.

F eeder m essen ger P H 590m m 2 ×1 Au xilia r y wir e P H 150m m 2 ×1 Con t a ct wir e GTM170m m 2 ×1 Spa n len gt h 50m H a n ger in t er va l 5m Dr opper in t er va l 5m or 10m Syst em h eigh t 960m m

Table 3:

Property of the pantograph used in experiments.

P a n t ogr a ph t ype F or m m 1 [kg]

P S21 Lozen ge 9.3

P S32 Sin gle a r m 9.8

k 1 [N/m ]

35970

10740

m 2 [kg]

3.8

4.2

k 2 [N/m ]

18720

21520

m 3 [kg] c [Ns/m ] P 0 [N]

9.4 58.8

8.7 10 58.8

Aer odyn a m ic u pwa r d for ce [N/(km /h )2 ]

2.0×10 -3

4.7×10 -4

Table 4:

Con dit ion (1) (2) (3)

m1 k1 m2 k2 m3

c

P0

Tension distribution of each wire. Ten sion Ra t io of F eeder Au xilia r y Con t a ct m essen ger wir e wir e yoke 39.2kN 4.9kN 9.8kN 2:1 34.3kN 6.6kN 13.0kN 2:1 34.3kN 4.9kN 14.7kN 3:1

4.2 Test results of the “composite type” 4.2.1 Contact loss rate and uplift under different conditions Figure 7 shows the contact loss rate measured in current collecting tests under different conditions in Table 4. In the case of the pantograph PS21, the contact loss rate was 1% or less up to 150km/h (Figure 7 (a)) to prove the satisfactory quality of current collection. Contact breaks occurred at 140km/h or over under the condition (1), but not under the condition (2) or (3). When the tension distribution of contact wire increases, therefore the contact loss rate decreases. This phenomenon appeared notably in the case

Power Supply System Analysis, Design and Planning

107

where PS32 was used (Figure 7 (b)). There were no problems in the contact wire strain and uplift, since they were much less than the allowable values up to 150km/h. 㪌㪅㪇

㪚㫆㫅㪻㫀㫋㫀㫆㫅㩿㪈㪀 㪚㫆㫅㪻㫀㫋㫀㫆㫅㩿㪉㪀 㪚㫆㫅㪻㫀㫋㫀㫆㫅㩿㪊㪀

㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪌㪅㪇

㪉㪅㪌

㪇㪅㪇 㪎㪇

Figure 7:

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

㪚㫆㫅㪻㫀㫋㫀㫆㫅㩿㪈㪀 㪚㫆㫅㪻㫀㫋㫀㫆㫅㩿㪊㪀

㪉㪅㪌

㪇㪅㪇 㪎㪇

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

(a) Experiment results of contact loss rate (PS21) (b) Experiment results of contact loss rate (PS32).

4.2.2 Contact loss rate when spring hangers were used The current collection performance of pantograph was measured when one or two hangers were used in place of spring hangers from the support in order to make the spring constants of the catenary near the support smaller. Figure 8 shows the contact loss rate when the pantograph PS32 was used. Figure 8 shows that the contact loss rate was almost the same whether normal hangers or spring hangers were used up to 130km/h. 㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪌㪅㪇

㪥㫆㫉㫄㪸㫃㩷㪿㪸㫅㪾㪼㫉 㪪㫇㫉㫀㫅㪾㩷㪿㪸㫅㪾㪼㫉

㪉㪅㪌

㪇㪅㪇 㪎㪇

Figure 8:

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

Experiment results of contact loss rate (PS32).

At 140km/h or over, however, the contact loss rate decreased significantly when spring hangers were used to show that the current collecting performance improved. The contact wire strain was smaller than that in the case where normal hangers were used. There were no problems in the contact wire uplift at support, since it was much smaller than the allowable value though it had became larger.

108 Power Supply, Energy Management and Catenary Problems 4.3 Test results of the “compound type” 4.3.1 Comparison of contact loss rate by suspended type We constructed two structures of the “dropper form” whose dropper intervals were 5m and 10m in our institute and performed current collecting tests for the structures of Figure 9. Figure 10 (a) and (b) shows the results of current collecting performance tests of the “hanger form” and the “dropper form”. The contact loss rate was small with the “dropper form” of 5m dropper intervals in both cases of PS21 and PS32. The contact loss rate of PS21 was 1% or less up to 150km/h, and the current collecting performance was extremely good. In the case of PS32, the contact loss rate was 1% or less up to 130km/h, and nearly 2% from 140km/h to 150km/h, and the results were allowable value.

Ear

P u ll-off a r m F eeder m essen ger Dr opper Au xilia r y wir e 10m

50m m

Con t a ct wir e

(a) Dropper interval with 10m

5m

50m m

(b) Dropper interval with 5m Figure 9:

“Dropper form compound type” feeder messenger catenary.

4.3.2 Comparison of contact loss rate by tension distribution We performed current collecting tests on the “dropper form” whose dropper interval was 5m to ensure the best current collecting performance under the condition of wire tension distributions shown in Table 4. Figure 11 and 12 show the measured contact loss rate and contact wire strain respectively, when the pantograph PS21 was used. The contact loss rate was small when the tension distribution of contact wire was large at the speed up to 130km/h (Figure 11). The contact wire strain also became small when the tension distribution of the contact wire was large (Figure 12). At the speed of 150km/h, the contact wire strain to exceeded the allowable value of 500×10-6 in the case of (1) contact wire tension 9.8kN, but was less than the allowable value in the case of (3) contact wire tension 14.7kN. As mentioned above, the current collection performance was also good to suit high speed

Power Supply System Analysis, Design and Planning

109

operation with the “compound form” when the tension distribution of contact wire was increased. 㪈㪇㪅㪇

㪿㪸㫅㪾㪼㫉㩷㪽㫆㫉㫄 㪻㫉㫆㫇㫇㪼㫉㩷㪽㫆㫉㫄㩷㩿㫀㫅㫋㪼㫉㫍㪸㫃㩷㪈㪇㫄㪀 㪻㫉㫆㫇㫇㪼㫉㩷㪽㫆㫉㫄㩷㩿㫀㫅㫋㪼㫉㫍㪸㫃㩷㪌㫄㪀

㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪌㪅㪇

㪇㪅㪇 㪎㪇

Figure 10:

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

㪿㪸㫅㪾㪼㫉㩷㪽㫆㫉㫄 㪻㫉㫆㫇㫇㪼㫉㩷㪽㫆㫉㫄㩷㩿㪈㪇㫄㪀 㪻㫉㫆㫇㫇㪼㫉㩷㪽㫆㫉㫄㩷㩿㩷㪌㫄㪀

㪌㪅㪇

㪇㪅㪇 㪎㪇

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

(a) Test results of contact loss rate (PS21) (b) Test results of contact loss rate (PS32). 㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪌㪅㪇

㪚㫆㫅㪻㫀㫋㫀㫆㫅㩷㩿㪈㪀 㪚㫆㫅㪻㫀㫋㫀㫆㫅㩷㩿㪊㪀

㪉㪅㪌

㪇㪅㪇 㪎㪇

Figure 11:

㪍

㪚㫆㫅㫋㪸㪺㫋㩷㫃㫆㫊㫊㩷㫉㪸㫋㪼㩷㪲㩼㪴

㪈㪇㪅㪇

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

Test results of contact loss rate (different tension).

㪪㫋㫉㪸㫀㫅㩷㪲㪈㬍㪈㪇㪄㪍㪴

㪎㪌㪇

㪚㫆㫅㪻㫀㫋㫀㫆㫅㩷㩿㪈㪀 㪚㫆㫅㪻㫀㫋㫀㫆㫅㩷㩿㪊㪀

㪉㪌㪇 㪄㪉㪌㪇 㪄㪎㪌㪇 㪎㪇

Figure 12:

5

㪈㪇㪇 㪈㪊㪇 㪪㫇㪼㪼㪻㩷㪲㫂㫄㪆㪿㪴

㪈㪍㪇

Test results of the contact wire strain.

Tension shift test

For the “compound type” that was constructed in our institute, we ground the contact wire flat and measured changes in the tension auxiliary wire and contact

110 Power Supply, Energy Management and Catenary Problems wire. Figure 13 shows the measured tension in the auxiliary wire and the contact wire versus the residual diameter of the contact wire. From these measurement results, we confirmed that the tension shifted from the contact wire to the auxiliary wire with as the wear of the contact wire advanced. Although the limit of the residual diameter of the contact wire was normally 8.5mm, we set the residual diameter at 3.3mm. Furthermore we set it at 1.5mm locally in this experiment. However the contact wire did not break. This proves that this structure is strong against the local wear of the contact wire. 㪈㪌

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅㩷㫉㪼㫊㫌㫃㫋㫊 㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋㩷㫉㪼㫊㫌㫃㫋㫊

㪈㪌

㩷㪫㪼㫅㫊㫀㫆㫅㩷㪲㫂㪥㪴

㪫㪼㫅㫊㫀㫆㫅㩷㪲㫂㪥㪴

㪉㪇

㪈㪇 㪌

㪈㪇 㪌 㪇

㪈㪌

㪈㪈 㪎 㪩㪼㫊㫀㪻㫌㪸㫃㩷㪻㫀㪸㫄㪼㫋㪼㫉㩷㪲㫄㫄㪴

Figure 13:

6

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅㩷㫉㪼㫊㫌㫃㫋㫊 㪜㫏㫇㪼㫉㫀㫄㪼㫅㫋㪸㫃㩷㫉㪼㫊㫌㫊㫋㫊

㪊

㪈㪌

㪈㪉 㪐 㪍 㪩㪼㫊㫀㪻㫌㪸㫃㩷㪻㫀㪸㫄㪼㫋㪼㫉㩷㪲㫄㫄㪴

㪊

(a) The auxiliary wire tension (b) The contact wire tension.

Summary of the tests

We performed simulation, experiments of current collecting performance and tension shift tests of the feeder messenger catenary with the auxiliary wire which was composed of a small number of parts and strong against the wear of the contact wire. The acquired results are shown below. (1) Simulation results show that the quality of current collection satisfied allowable value up to 160km/h with the “compound form” whose messenger was PH590mm2, and the “compound form” whose messenger were PH590mm2 and PH356mm.2 (2) From current collecting performance tests on the “compound form”, we found that the current collecting performance improved when the total tension in the contact wire and the auxiliary wire was increased (19.6kN). (3) From the current collecting performance tests on the “compound form,” it was found that the best current collecting performance was on the “dropper form” whose dropper intervals was 5m or over, and we found that the current collection performance improved when the total tension in the contact wire and auxiliary wire was increased (19.6kN). (4) In the measurements on the “compound form” when contact wire wear advanced, we observed that the tension shifted from the contact wire to the auxiliary wire as contact wire wear advanced.

Power Supply System Analysis, Design and Planning

7

111

Conclusion

Based on this research, we confirmed that there are no problems in the current collecting performance up to the speed of 150km/h with the “composite form” and the “compound form” whose dropper intervals are 5m, on the structure of feeder messenger catenary that uses PH590mm2 as the messenger. We also observed the tension shifts to the auxiliary wire when the wear of the contact wire advanced. We found that this structure was strong against the local wear of the contact wire. These catenary systems are more stable than others to require less maintenance.

References [1]

[2]

A. Iwainaka, A. Suzuki & Y. Shimodaira, Development of single copper feeder messenger wire for overhead contact lines, Computers in Railways VII, pp.703-712, 2000. T. Hamada, A. Suzuki ＆ T. Shimada, Current collecting characteristic of catenary with non-tension contact wires, Computers in Railways VIII, pp.419-428, 2002.

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113

Catenary and autotransformer coupled optimization for 2x25kV systems planning E. Pilo, L. Rouco & A. Fernández Instituto de Investigación Tecnológica, E.T.S. de Ingeniería ICAI, Univ. P. Comillas, Madrid, Spain

Abstract In the design process of a 2x25kV power supply, the location and sizing of autotransformers and the choice of the catenary type are usually two aspects very closely interrelated. As a result, the number of autotransformers can normally be reduced or augmented if the catenary is upgraded or downgraded respectively. In this paper, coupling equations between these two aspects are described in detail. These equations are used to formulate a multi-attribute optimization problem in which the global efficiency of the investment is optimized. In this problem, the considered attributes are: (i) investment cost and (ii) a performance index that is defined in the paper. The optimization procedure gives a reduced set of catenary and autotransformers combinations that maximize efficiency. This optimal reduced set can be used as an input in the design process of power supply. For the solution of this problem, different dominancy criteria are evaluated. Furthermore, sensitivity studies are carried out during the optimization process to help in the search of catenary and autotransformers combinations. As a study case, the proposed optimization procedure has been used to obtain a reduced set of catenaries and autotransformers based in the catenary C-350, which has been used in the Madrid – Barcelona – French border new high-speed line. Keywords: power supply system, high speed railways, multi-attribute optimization, long-term infrastructure planning.

1

Introduction

In the design process of a 2x25kV power supply, the location and sizing of autotransformers and the choice of the catenary type are usually two aspects very

114 Power Supply, Energy Management and Catenary Problems closely interrelated. As a result, the number of autotransformers can normally be reduced or augmented if the catenary is upgraded or downgraded respectively. In this paper these relationships are analyzed and used to formulate a multi-attribute optimization problem in which the global efficiency of the investment is optimized [1]. Section 2 describes the power supply system of AC-electrified railways. In section 3 an equivalent model is used to represent bi-voltage 2x25kV and to analyze the relationships between catenary parameters and autotransformers separation. In section 4 the optimization problem is described. In section 5 the optimization procedure is applied to a real case. Finally, in section 6 the conclusions of this work are presented.

2 The power supply of AC electrified railways 2.1 General structure Figure 1 shows the general structure of power-supply systems of AC electrified railways: Three-phase high-voltage network Traction substation 1

Sector 1-L

Sector 1-R

Figure 1:

Sector 2-L

Traction substation 2

Sector 2-R

Traction substation 3

Sector 3-L

Sector 3-R

Structure of the power supply system.

As shown, the electrical system is divided in electrically-isolated singlephased sectors, which are fed from the three-phase network through a traction substation. These substations are connected between two of the three phases of the high-voltage network. Each of these sectors can use either mono-voltage system (1x25kV) or bi-voltage system (2x25kV). In mono-voltage systems [2], the feeding conductors are set to the specified voltage level (see Figure 2).

Vtransp

Figure 2:

Vfeed POS

Mono-voltage system configuration.

In bi-voltage systems, a higher voltage is set between feeding conductors [3, 4]. This voltage is reduced by using autotransformers distributed along the

Power Supply System Analysis, Design and Planning

115

catenary (see Figure 3). In these systems, the term cell very often refers to the portion of catenary located between two consecutive autotransformers. Typical values for cell lengths are 10-15km.

Vfeed POS

Vtransp

Vfeed NEG

Figure 3:

Bi-voltage system configuration.

As this paper is focused on this system, it is assumed that all the sectors are fed using bi-voltage system. 2.2 Catenary The typical configuration of the catenary of an AC railway line is shown in Figure 4. The catenary contains several physical conductors that can be grouped into three groups: positive, negative and ground wires. In case of multiple tracks, other conductor arrangements are possible. Positive Negative Neutral

Positive feeder Sustainer

Contact wire

Negative Feeder

Return wire

Rail

Longitudinal section

Figure 4:

Transversal section

Typical conductor distribution.

The positive wires are the positive feeder, the sustainer wire and the contact wire. There is usually only one negative wire called negative feeder. The ground wires are the rail, the collector wire and the return wire. The conductors of each group are connected between them at regular intervals (typically 300m). Additionally, ground conductors are frequently connected to earth.

116 Power Supply, Energy Management and Catenary Problems

3

The effect of autotransformers and catenary upgrades

3.1 Base magnitudes In order to improve numerical stability, normally per unit magnitudes are used to carry out all the necessary calculations. Thus, the circuit can be divided into three zones based on their nominal voltage. Figure 5 shows the considered zones: (i) high-voltage zone, (ii) positive zone and (iii) negative zone. Positive zone

High voltage K1:1

Zthevenin

Train 1

Ztr2

Ztr1

Zcat

Zcat

Zcat

Ztr3 Vthevenin

-1:1

K2:-1

-1:1

Negative zone

Figure 5: Zone division for base magnitudes selection. A base power Sbase has to be chosen and is common to all the zones (a typical value is 10MW). Furthermore, base voltages have to be selected for the three zones. If base voltages are exactly the voltages of every zone in a scenario without any kind of load, transformation ratios take values of 1 and –1. Base impedance and base currents can be determined from the base power and voltage of each zone. 3.2 The 1x25kV equivalent model of 2x25kV systems In [5] the behavior of bi-voltage systems is analyzed and a equivalent model is proposed to represent bi-voltage 2x25kV systems as if they were mono-voltage 1x25kV. This is the model used in the presented work. Figure 6 shows the approximated behavior of the circuit with a train consuming a current I , assuming: (i) that voltage drop along a cell in the positive and in the negative side have the same value but different sign and (ii) that, as far as autotransformers can be supposed ideal, it can be assumed that there are current flows only in the autotransformers that are immediately adjacent to the considered train. In this figure Vcell n is the voltage drop along the cell n, I p,trans and I n,trans are respectively the positive and negative currents in the transmission cells, I p,train and I n,train are respectively the positive and negative currents in the cell of the train, L cell is the length of the cell of the train, x is the relative position of the train, expressed as a fraction of L cell .

Power Supply System Analysis, Design and Planning

Ip,trans

Vcell1

AT1

Vcell2

Vcell3

»0

»0

Ip,train

In,train

Vcell4

AT2

Vcell5

I

117

Vcell6 »0

»0

»0

»0

xLcell

I0 VHV

Lcell »0

-Vcell1

»0

-Vcell2

-Vcell4

-Vcell3

Figure 6:

-Vcell6

Downwards cell

Downwards cell

In,train

In,trans Transmission cell

-Vcell5

Transmission Transmission cell cell

Cell of the train

Approximated behavior of bi-voltage system.

Based on these simplifications, the positive phase of the bi-voltage system can be represented as shown in Figure 7. In this model, two different contributions have been identified: (i) the equivalent impedance of the catenary z eqv ,cat that depends only on the configuration of physical conductors and (ii) z gap that is associated to the separation between autotransformers. Zeqv,SS

Zeqv,cat

Positive Zgap

Vthevenin Train

Ground High Voltage Network

Figure 7:

Transformer

Catenary

Mono-voltage equivalent circuit of bi-voltage system.

The parameters of this equivalent circuit are calculated as follows: z eqv ,cat = z eqv ,cat ⋅ Dss ,train

(1)

where the symbol ~ is used to refer per length unit magnitudes and Dss ,train is the distance between the substation and the train The equivalent impedance z eqv ,cat of the catenary can be obtained from the elements of the equivalent conductors impedance matrix [6], where the subindexes p and n represents the positive and negative conductors respectively. z eqv , cat =

z pp ⋅ z nn − z pn ⋅ z np

z pp + z nn + z pn + z np

(2)

The impedance gap z gap associated to the separation of autotransformers can be obtained as follows:

118 Power Supply, Energy Management and Catenary Problems z gap = Lcell x (1 − x )

z 2pp + z pp z np + z pn z pp + z pn z np z pp + z pn + z np + z nn

(3)

The voltage drop associated to the impedance z gap is referred as voltage deviation from the equivalent model of the catenary. As shown in Figure 8, this voltage deviation starts and ends in cell in which is located the train. In other words, at the end of this cell all the voltage deviation is recovered and thus no extra voltage drop has to be added to the trains that are located downwards. Figure 8 summarizes the voltage drops in the sector in a scenario with only one train: 1 VAT1-VAT2 Traction Substation

2 VAT1-Vtrain 3 Zgap·itrain

A.T. 1

Train

XAT1 Xtrain

A.T. 2

XAT2 (km)

VSS dV/dx=Zeq,CAT·Itrain

VCAT 2 1 3 (V)

Figure 8:

Voltage drops in a bi-voltage sector.

It can be seen that the deviation impedance is proportional to the distance between autotransformers. Consequently, as far as the number of autotransformers is increased, the relative weight of the deviation is reduced. 3.3 Influence of catenary type and autotransformers distance on voltages Using the described model, sensitivity of the voltage drops to catenary upgrades or to autotransformer additions can be analyzed. These are two common investment decisions to be taken in the design process of the power supply in bi-voltage 2x25kV electrified railways. Figure 9 shows the effect of upgrading the catenary in the voltage drops along the catenary ∆Vcat . When upgrading the catenary, the most important effect is a reduction of voltage drops all along the sector. Additionally, the voltage drop due the separation autotransformers (corresponding to z gap ) can also be reduced. Figure 10 shows the effect of shortening the distance between consecutive autotransformers, which is typically achieved by adding extra autotransformers to the sector. Unlike the catenary upgrade, the benefits of this enhancement are limited to the cell whose distance has been reduced, due to the local influence of voltage deviations VDESV .

Power Supply System Analysis, Design and Planning

V (in kV)

119

V (in kV)

DVSE

DVSE

DVcat

DVcat

X (in m) SS

Train 1

Figure 9:

X (in m)

Train 2

SS

Train 1

Train 2

Effect of upgrading the catenary.

V

VDESV

VDESV

x SS

Train AT1 AT1

Figure 10:

AT2 AT2

Effect of shortening length of cells.

As it has been described, both catenary upgrades and autotransformer additions can be used to reduce voltage drops.

4

The optimization problem

In the design process of AC-electrified railways, voltage limitations are commonly active, especially when evaluated in degraded situations (substation out of order). Thus, determining the most efficient way of reducing voltage drops is a key factor in the design of the power supply. As it has been described, catenary upgrades and autotransformer additions are often investment decisions that are exchangeable in order to reduce voltage drops, from a technical point of view. Therefore, economical criteria have to be considered to determine the most efficient combination of catenaries and autotransformer distributions. For that reason, a multi-criteria optimization problem has been formulated and solved. The goal of this optimization is to obtain a reduced repository of combinations of catenary types and autotransformer distributions, in which the efficiency of its elements is maximized. This set is to be used as an input in the

120 Power Supply, Energy Management and Catenary Problems design of the power supply system. To determine this repository, the considered attributes are: (i) investment cost and (ii) a efficiency index that is to be defined. In order to evaluate the efficiency of each {catenary,autotransformers} combination the efficiency index ZEQ is defined in eqn. (4). This index corresponds to the total equivalent impedance seen between the substation output and a train located in the further cell of the corresponding sector. In order to simplify the resulting expression, it has been assumed that autotransformers are uniformly distributed.

L   n −1 L + x  + z gap ZEQ = z eq ,cat  n   n

(4)

where n is the number of autotransformers of this sector and L is the length of

L  L  n −1 L + x  + ( z pp − z eq ,cat ) x (1 − x ) ZEQ = z eq ,cat  (5) n  n  n As ZEQ depends on the relative position x of the train in its cell, one of the

this sector. Expanding z gap in eqn. (4) becomes:

following criteria for can be assumed: a. The train is located in the middle of its cell ( x = 0.5 ) b. The train is located where the index ZEQ reaches its maximum. It should be noted that ZEQ incorporates the effect of both catenary type and autotransformers in an equilibrated manner, as it corresponds to their contribution in the total voltage drops. The considered cost function is: Ccat , n = Ccat ⋅ L + C AT ⋅ n (6) where Ccat , n is the cost associated to catenary cat with n autotransformers,

Ccat is the per length unit cost of the catenary cat and C AT is the unitary cost of each autotransformer. To get the optimal repository the following steps have to be accomplished: a) Exploration of the possible catenary/autotransformer configurations. As the sustainers and the contact wires are fixed, the number of combinations is not excessive. Symmetry restrictions can also be used to reduce the search space. b) Eliminate dominated configurations (a configuration is dominated if it is worse in cost and in efficiency than another configuration). Relaxed dominancy criteria can also be applied in order the eliminate configurations (i) a bit cheaper but much lower efficiency or (ii) a bit more efficient but much more expensive. c) Within the resulting repository, chose the final configurations trying to cover uniformly the costs range.

Power Supply System Analysis, Design and Planning

121

5 Study case The proposed optimization procedure has been used to get a repository of catenaries and autotransformers based on the catenary C-350 that has been used in the Madrid – Barcelona – French border new high-speed line. The considered costs are summarized in Table 1. Table 1:

Costs structure of the study case.

Description Autotransformer Fixed cost of catenary

Cost 200 units 29 units/km

Cost per added feeder

0.3 units/km/feeder

LA-110 conductor LA-180 conductor LA-280 conductor LA-380 conductor

0.716 units/km 0.832 units/km 0.95 units/km 0.125 units/km

Observations Cost per autotransformer Includes installation of catenary towers, insulators, contact wires and sustainers Only in configurations with positive or negative feeder To be included only if used To be included only if used To be included only if used To be included only if used

Figure 11 shows the 5 catenary/autotransformers combinations chosen (marked with arrows), that have been evaluated for sector 30km, 40km and 50km long.

Figure 11:

Effect of shortening length of cells.

122 Power Supply, Energy Management and Catenary Problems Each curve represents the effect of adding up to 5 autotransformers to the catenary specified, for the given sector length. As shown in Figure 11, the efficiency gain of upgrading catenary (change to a lower curve of the same family) is normally a more efficient option than adding an extra autotransformer (go to the following point of the same curve). It can also be observed that the efficiency of adding autotransformers decreases very quickly and, thus, none of the chosen configurations uses more than 2 autotransformers.

6 Conclusions Using the mono-voltage equivalent model of bi-voltage systems, the existing relationships between the location of autotransformers and the choice of the catenary have been analyzed. Furthermore, a procedure has been proposed to obtain a reduced repository of combinations of catenary types and number of autotransformers in which efficiency and cost are optimized As a study case, the proposed optimization procedure has been used to obtain a reduced set of catenaries and autotransformers based in the catenary C-350, which has been used in the Madrid – Barcelona – French border new high-speed line. The solution obtained in the study case suggests that upgrading catenary is normally a much more efficient option than adding an extra autotransformer. The reason for that is that the marginal cost of using larger conductors in the catenary can be neglected compared to the marginal cost of adding an autotransformer.

References [1] [2]

[3]

[4]

[5]

[6]

E. Pilo, “Optimización del Diseño de la Electrificación de Trenes de Alta Velocidad,” in IIT, vol. PhD: Univ. Pont. Comillas de Madrid, 2003. J. D. Glover, A. Kusko, and S. M. Peeran, “Train voltage analysis for AC railroad electrification,” IEEE Transactions on Industry Applications, vol. IA-20, pp. 925-934, 1984. R. J. Hill and I. H. Cevik, “On-line simulation of voltage regulation in autotransformer-fed AC electric railroad traction networks,” IEEE Transactions on Vehicular Technology, vol. 42, pp. 365-372, 1993. P. H. Hsi, S. L. Chen, and R. J. Li, “Simulating on-line dynamic voltages of multiple trains under real operating conditions for AC railways, ” IEEE Transactions on Power Systems, vol. 14, pp. 452-459, 1999. E. Pilo, L. Rouco, and A. Fernández, “A reduced representation of 2x25 kV electrical systems for high-speed railways.,” presented at IEEE/ASME Joint Rail Conference, Chicago, 2003. E. Pilo, L. Rouco, A. Fernández, and A. Hernández-Velilla, “A simulation tool for the design of the electrical supply system of high-speed railway lines, ” presented at IEEE PES Summer meeting 2000, Seattle, 2000.

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123

Investigation into the computational techniques of power system modelling for a DC railway A. Finlayson1, C. J. Goodman2 & R. D. White1 1 2

Atkins Rail, UK University of Birmingham, UK

Abstract The use of computer simulation techniques is now a fundamental part of the design process for electrified railways and at the feasibility stage clients will often request detailed calculations to be performed for the basic design. This will establish a level of confidence in both the project and basic design parameters that will justify the capital expenditure further on in the project life-cycle. This paper will address how the total impedance of a railway network may be represented, where the impedances of the traction return circuit and traction power system are either combined together to form one impedance or studied independent of one another. The accuracy of the modelling in this manner, particularly how it affects the accuracy of rail voltage results shall be assessed. It will also examine how much impedance is typically in the rails and what proportion this needs to be before it has an unacceptable effect on the numerical results. To assess this, a range of proportions will be studied, for example 70% of the total impedance to be modelled in the conductor with 30% modelled in the rails, 60%/40%, etc. In this way, a proper scientific assessment of the combined or split calculation methods can be made via simplified case studies. Keywords: DC railway, modelling, simulation, computational techniques, accuracy, numerical method, rail voltage, stray current.

1

Introduction

DC electrified railway systems across the world are growing, both in passenger and freight traffic, as an alternative solution to increasing road congestion. DC electrified railways account for approximately 50% of electrified railway lines throughout the world [1]. This growth may be in the form of new build railway

124 Power Supply, Energy Management and Catenary Problems systems or the upgrade of existing railway systems and is inclusive of metro, tramway, light rail and heavy rail systems. However this growth has to be managed to ensure that the proposals for an improved infrastructure are designed both safely and correctly and that the design delivers value for money. Computer simulation is the tool that many consultants and manufacturers, associated with the rail industry, are using to evaluate proposals and validate final designs prior to the launch of the project and any major capital expenditure. The use of computer simulation techniques is now a fundamental part of the design process for electrified railways and at the tender stage clients will often request detailed calculations to be performed for the basic design [2]. This will establish a level of confidence in both the project and basic design parameters that will justify the capital expenditure further on in the project life-cycle. 1.1 DC railway modelling and simulation Modelling and simulation are the names we use for applying the laws of physics and logic via the processing power of computers to predict the behaviour and performance of railway infrastructure [2]. The various levels of engineering modelling and simulation with respect to the DC railway may be considered as; timetable and operational planning, train performance and signalling, traction equipment and the power supply system. These engineering levels are not considered to be exhaustive but what is important is the power system supply, as this paper is primarily concerned with the modelling of the power system for the DC railway.

2

The DC railway

2.1 Operational functions The DC railway usually has the primary operational function of passenger transportation, whereas the AC railway has the dual operational functions of passenger and freight transportation. However the DC railway may also be used within the mining industry, as well as freight transportation [3], so it may be considered to have dual operational functions also. However, for the purpose of this paper the DC railway shall be considered as predominantly suburban railways often referred to as transit systems. Transit systems may be classified based upon the demand for traction current from the power system. For example, a metropolitan railway (metro) may be considered to be a mass transit system as there will be more trains carrying more passengers with short headways between trains and therefore a large demand for traction current from the power system. Conversely, a tram railway may be considered to be a light rapid transit (LRT) system as there will be less trams and also less demand for traction current from the power system than the mass transit system. Either of these systems may utilise an overhead line or third/fourth rail feeding arrangement. The following DC traction supplies are commonly used [4]:

Power Supply System Analysis, Design and Planning

• • • •

125

3000 V (overhead line) 1500 V (overhead line) 750 V (third rail and overhead line) 630 V (third and fourth rail)

2.2 Components of the DC railway The DC electrified railway comprises of many interacting variables or components. These variables are usually contained within sub-systems such as; civil engineering, permanent way, electrification, signalling, tele-communications, rolling stock, station services and third parties outside the railway environment. Whilst this list is typical (non-exhaustive), all of these variables must be considered both individually and interacting with one another during the design process of a railway system. However, for the purpose of this paper the components that are of most concern are; • Electrification • Rolling stock • Signalling 2.3 Other considerations for modelling In studying the DC railway power system, there are two further technical problems that need to be included in the circuit model of the DC power system. Firstly, there is the variation of rail voltage with respect to the train operational timetable and secondly there is the magnitude of stray current with respect to the train operational timetable. 33kV AC

33kV AC

11kV AC

11kV AC

750VDC

750VDC

750VDC

T1 T2 R2 R1

Figure 1:

The DC railway represented in a single line diagram.

2.4 DC railway operation Figure 1 shows a typical two track DC railway with one feeder station with a primary voltage of 33 kV AC and a secondary voltage of 11 kV AC. The

126 Power Supply, Energy Management and Catenary Problems 11 kV AC is then rectified and an output voltage of 750 V DC is produced which in turn will power the rolling stock on the rail network. The rolling stock will draw traction current from T2 and will return traction current through R2. However not all of the traction return current will return through the running rails and this may be due to the earthing and track bonding arrangements associated with the DC railway.

3

Choosing the model and method

3.1 The basic model There are many methods available to us in solving the power system model of a DC railway. Examples of these may include multi-conductor modelling, finite element analysis or transmission line theory to name but a few. However, given the nature of the DC railway, the power system model may be considered to be dynamic, i.e. the electrical load changes with demand and with multiple electrical loads, i.e. trains. Whilst these parameters may appear complex, the DC railway power system is easier to model than the alternative AC railway. This is because the effects of capacitive and inductive reactance in the equivalent steady state circuits may be ignored due to the general principles of DC circuit theory [5]. Applying this to figure 1 will give rise to the equivalent circuit shown in figure 2, where Zc1, Zc2 and Zc3 represent the impedance of the traction power conductor, whilst Zr1, Zr2 and Zr3 represent the impedance of the traction return conductor.

Zt

Zc2

Train 1

Train 2 I

Return Rail

Zr1

Figure 2:

Zc3 Zt

Zc1

Substation 1

Zt

Traction Power

I Zr2

Substation 2

Train n I Zr3

Electrical circuit for DC railway.

Figure 2 may still not be considered to be the simplest model of the DC railway. The electrical substations may be modelled in their Thévinin equivalent model, a voltage source (Vs) with a source impedance (Zs) and the train may be modelled as an impedance (Zt) that is dependent upon whether the train is motoring, coasting or braking. Figure 3 now shows two cases of the simplified circuit, with the Thévénin equivalent voltage source representing two electrical substations and a single train represented by an impedance somewhere between the two electrical substations. The circuit shown to the left of figure 3 represents the DC railway where the traction power and traction return conductors are split from one

Power Supply System Analysis, Design and Planning

127

another, whilst the circuit to the right shows them combined. The circuit to the right suggests that the DC railway power system model may be solved as a simple DC circuit, using short transmission line theory [6].

Figure 3: Traction Power Conductor

Simplified electrical circuit of a DC railway. Zc1

Zc1 It1

Return Rails

Figure 4:

Traction Power Conductor

Zc2 It1

It2

Zr1u

Zr1d

Zr1u

Zr2d

50% It1

50% It1

50% It1 50% It2

50% It1 50% It2

Return Rails

Developing the combined impedance model.

3.2 Representing the traction return conductor in the combined impedance model Figure 3 is representative of a one track railway. In practice, the DC railway, under consideration for this paper, will usually be a minimum of two tracks, namely up (u) and down (d). Considering figure 4, there are two trains present, one on each track and there are four traction return conductors, or as is more commonly known return paths. These return paths are considered to have identical impedance characteristics and the percentage of traction return current (It1 and It2) in each return path is shown. Considering the configuration shown to the left of figure 4, will give rise to the equivalent impedance of all the return paths combined being expressed as:

Zrn =

Zr1u n

Ω

(1)

where ‘n’ is equal to the total number of traction return conductors in the circuit. However, considering the configuration to the right of figure 4, the equivalent impedance of all the return paths combined will be expressed as:

Zrn =

T * Zr1u n

Ω

(2)

128 Power Supply, Energy Management and Catenary Problems where T is the number of trains present. However, because the number of trains present between electrical substations and on different tracks varies, this will be difficult to program in a computer simulation tool. The equivalent impedance of all the return paths combined may be expressed as an alternative to equation 1 by

Zrn = Zr1u Ω

(3)

This paper will assess which the accuracy of modelling the equivalent return rail impedance as either equations 1 or 3 for a number of tracks, as these are feasible methods that may be used by computer simulation tools. 3.3 The method Figure 3 may be solved via a number of well known network analysis techniques such as mesh or nodal analysis [5]. For simple circuits such as that shown in figure 3 where there is only 1 train present, the solution may be solved by deriving linear equations and solving them as simultaneous equations. If the circuit contains more electrical loads, it is better to solve the circuit via a series of linear equations represented in matrices where the general equation may be given as

[V ] = [Z ]* [I ]

(4)

The computational efficiency of the numerical procedures undertaken by both mesh and nodal analysis may be measured by counting the number of numerical operations (OC) i.e. multiplication, division, addition and subtraction for each equation ‘N’ to be solved, i.e. ‘N’ is equal to the number of nodes in the circuit or the number of loop currents in the circuit, dependent upon the network analysis technique chosen. This may be defined as [10];

OC =

2 N 3 3N 2 7 N + − 3 2 6

(5)

Table 1 shows the difference in operational counts taking into account the simplified models shown in figure 3. Table 1 illustrates that nodal analysis has a much lower OC when 4 or more linear equations are required to be solved. This can be attributed to the fact that in nodal analysis, each node represents an equation and one node has to be set to zero. Table 1: Number of Traction Return Paths 1 2 4 6 8

N 2 4 8 12 16

Summary of OC. Mesh Analysis OC 9 62 428 1354 3096

N 2 3 5 7 9

Nodal Analysis OC 9 28 115 294 527

Power Supply System Analysis, Design and Planning

129

If using mesh analysis, each loop current represents an equation and each and every loop current must be used. This means that for an equivalent circuit that requires 4 or more equations to be solved, mesh analysis will always have one more equation to be solved than nodal analysis, thus meaning that nodal analysis is the more efficient method. 3.4 Injecting train currents If the combined impedance circuit of figure 3 is used to solve the power system then it presents us with a problem as the technical issues cited in section 2.3 are not represented in the model, whereas the rail voltage is represented and calculated directly in the split impedance model. This problem may be overcome by either including these parameters in the model for real time simulation or they can be accounted for in a post processing program, i.e. a separate program that operates on the results from the initial simulation [7]. This may be done by injecting the train currents (It) into a homogenous rail. The ground impedance (Ze) is represented as a lumped parameter that ignores the effect of ground capacitance, because any reactive component represented by the ground will be so small that it can be ignored [4, 8, and 9] and in any case is only relevant for transient conditions, as is shown in figure 5. The current flowing in the earth (Ie) represents the stray current and this may also be studied as part of the post processing program.

Figure 5:

4

Post process injecting train currents model.

Case studies

The theoretical analysis of railway modelling techniques discussed in section 3 may be applied to the practical railway, where numerical analysis can be applied to ascertain the accuracy of modelling between the split impedance method (with the traction return path impedance modelled as per equation 2) and the combined impedance method with the equivalent traction return path impedance modelled as per equations 1 and 3. The network analysis technique chosen was nodal analysis as this calculates the train voltage directly and is considered to be more efficient than mesh analysis, as defined in section 3.4. The following railway types have been identified as case studies; • 1500 V DC Overhead Line Railway (OHL) • 750 V DC 3rd Rail Conductor Railway • 750 V DC Overhead Line Railway

130 Power Supply, Energy Management and Catenary Problems Practical traction return circuits, traction power system and voltage source impedances have been used in the case studies. A range of proportions have been studied, for example 60% of the total impedance to be modelled in the traction conductor (α) with 40% modelled in the rails etc., where the summation of the traction powers system and return circuit impedances is equivalent to the loop impedance ZL. Each case study includes six traction return circuit with up to six trains present, i.e. one on each track. 4.1 Calculating the error The train voltage may be expressed as a percentage of the supply voltage derived by the electrical substation. This may be expressed generally as;

Vt =

Vtrain × 100 Vs1

%

(6)

where Vtrain is the train voltage and Vs1 is the electrical substation voltage. Equation 6 will satisfy both the split and combined impedance analyses. The error in train voltage calculation may be expressed as;

%error = Vtsplit − Vtcombined

%

(7)

where Vtsplit is the result of equation 6 for the split impedance model and Vtcombined is the result for the combined impedance method. A back calculation may be performed using the result of equation 7 to calculate the error in terms of voltage magnitude if required, as shown in equation 8.

V =

%error × Vs1 100

V

(8)

4.2 Summary of results Table 2 shows the percentage error (%) in train voltage calculation, using equation 7.

5

Discussion and conclusion

5.1 Discussion The results in table 2 suggest that either equations 1 and 3 for the equivalent traction return path impedance are satisfied when there is only one train present, as in the case of equation 1 and six trains being present, as in the case of equation 3. This does not definitively define which equivalent rail return impedance should be used. Therefore an intermediate step was introduced by assessing three trains being present. The choice for three trains is purely

Table 2: Summary of case study results. System

Type

Voltage

ZL Ω/m

α%

V DC

Train Current A

Substation Spacing km

Error for 3 Trains and six return paths

Error for 6 Trains and six return paths

Eqn. (1)

Eqn. (3)

Eqn. (1)

Eqn. (3)

Eqn. (1)

Eqn. (3)

% error

% error

% error

% error

% error

% error

1500

OHL

0.0784

60

4000

2

0

1.668

-0.667

1.001

-1.668

0

750

OHL

0.1472

55

1000

1.5

0

2.705

-1.082

1.623

-2.705

0

750

3rd rail

0.0651

37

5000

3

0

17.086

-6.834

10.252

-17.086

0

750

3rd rail

0.0828

50

5000

3

0

17.112

-6.845

10.267

-17.112

0

Power Supply System Analysis, Design and Planning

Error for 1 Train and six return paths

131

132 Power Supply, Energy Management and Catenary Problems academic and is used to define a utilisation factor of the traction return circuits, although in reality the number of trains may vary. This now shows that the error is lower when using equation 1 to derive the equivalent traction return impedance. However, whilst the error is acceptable for the overhead line railways, it is not so for the 3rd rail railway. The impedance is too low in the traction power conductor, allowing a large voltage drop to occur between the train and the electrical substation, mainly due to the high values of current drawn by the trains. Furthermore, the impedance in the traction return circuit is more dominant and the inconsistency in the assumptions of equations 1 and 3 suggest that this impedance must be modelled accurately, i.e. as per equation 2 and the split impedance method. Therefore this type of railway should be modelled as a split impedance railway, such that the train and rail voltages are calculated correctly. Furthermore, it is noticeable that the magnitude of percentage error increases as the number of tracks occupied increases. This must also be considered when deriving the power system model, with respect to split or combined impedance method. 5.2 Conclusion The case studies confirm that the most efficient method for solving the power system model is to combine the traction power and return conductor impedances such that the OC of the circuit is reduced to as low as reasonably possible. This will allow post process simulation of the data obtained from the real time solution and allow effective management of the computing overhead that is always the fundamental driver with computational techniques and the desired accuracy. This statement is true, with the exception of the 3rd rail traction conductor railway, where the most appropriate method would be to model the impedances of the railway separately.

Acknowledgement and disclaimer Information and guidance given in this paper are views held by the authors. The authors would like to thank colleagues within Atkins Rail and the University of Birmingham for their support and advice in writing this paper and for their kind permission in allowing this work to be published as part of the collaborative agreement to develop a DC multi train simulator. The authors, Atkins Rail and the University of Birmingham accept no liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause.

References [1]

Profillidis, VA. (2000). Railway Engineering. 2nd Edition. Aldershot: Ashgate Publishing Ltd. Chapter 13 pp252. ISBN 0 – 7546 – 1279 – 1.

Power Supply System Analysis, Design and Planning

[2]

[3] [4]

[5]

[6]

[7]

[8]

[9]

[10]

133

Goodman, CJ, (2005). Modelling and Simulation. The IEE Second Residential Course on REIS 2005. Wrightsons. Chapter D3. ISBN 0 – 86341 – 511 – 3. BS EN50122-1:1998 Railway applications - Fixed installations Part 1: Protective provisions relating to electrical safety and earthing. Kiessling, F, Puschmann, R, Scmeider, A. (2001). Contact Lines for Electric Railways. 1st Edition. Munich Erlangen: Publicis Coproate Publishing Ltd. Chapter 1 pp33.ISBN 3 – 89578 – 152 – 5. Bird, J. (2004). Electrical Circuit Theory and Technology. Revised 2nd Edition. Newnes. Chapters 30, 31, 33, 44 pp 531 – 559, 575 – 598 and 869 – 900. ISBN 0 – 7506 – 5784 – 7 Stevenson, WD Jr. (1982). Elements of Power System Analysis. 4th Edition. McGraw Hill. Chapters 5, pp 88 – 126. ISBN 0 – 07 – 066584 – 2 Yu, JG, (1992). Computer Analysis of Touch Voltages and Stray Currents for DC Railways. PhD Thesis submitted to the University of Birmingham, UK White, RD, Zhang, Z (2003) Atkins Rail internal report. Predictions of 50Hz induced voltage into lineside cables on 25kV railway. Report Number: BF 5001270/RDW/001. Issue 4.0 August 2003 Case, S, (2005). Earthing, Bonding and Stray Current Mitigation Principles. The IEE Second Residential Course on REIS 2005. Wrightsons. Chapter D4. ISBN 0 – 86341 – 511 – 3. Gerald CF, Wheatley PO. (2004). Applied Numerical Analysis. 7th Edition. Pearson/Addison Wesley. Chapter 2 pp 88 – 100. ISBN 0 – 321 – 1909 – X

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Optimal design of power supply systems using genetic algorithms J. R. Jimenez-Octavio & E. Pilo Instituto de Investigación Tecnológica, E.T.S. de Ingeniería ICAI, Univ. P. Comillas, Madrid, Spain

Abstract This paper presents an optimization model based on genetic algorithms for designing traction power supply systems. The proposed model is suitable both for planning new lines and for expanding the old ones, resulting in a more efficient operation as well as in lower investment costs. The minimization of fixed installation represents the optimization criterion for searching innovative designs that fulfil certain technical constraints: maximum voltage drops and maximum power consumption in the substations. The variables involved in the optimization problem are: number, type and location of railway overhead lines; and number, size and location of traction substations. Finally, the evaluation of possible designs involves simplified electrical modelling of the studied railway stretch. Thus, electrical simulations and calculations have also been adapted for their implementation in the genetic algorithm. A section of the Madrid-Barcelona high-speed line has been considered as a study case in order to analyze the performance of the proposed model. The results reveal the suitability of the new designs obtained with the presented model and its goodness and robustness. Keywords: railway, power supply system, optimization, genetic algorithms.

1

Introduction

The design of the electrification is a complex task that involves different interdisciplinary analysis. Normally, the design process is done iteratively by refining candidate designs based on its estimated performance. In this process simulation tools are crucial to evaluate the performance in many different situations. However, they do not usually include criteria to modify candidate designs in order to obtain the final solution. Thus, the designer has to decide the

136 Power Supply, Energy Management and Catenary Problems best changes to be done to the candidate design in order to fulfil technical constraints and to reduce costs in a reasonable way. As this is not an obvious task, the development of decision-making computer-aided tools based on optimization models can be very useful to ensure efficient uses of investments. In [1] simplified models have been formulated to represent bi-voltage 2x25kV meshed topologies in a simplified way. Based in these models, an optimization procedure has been presented in [2] to select the most efficient centenary and autotransformer combinations. The results of this optimization can be used as an input for the optimization of the power-supply system presented in [3], which formulates a mixed integer programming (MIP) optimization problem. This procedure is suitable for small-medium network sizes (up to 200-250 km), but for bigger problems computation times are too long. In this paper, a genetic algorithm based optimization procedure (GA) is presented and its performance is analyzed. Furthermore, the solutions and computing times are compared to the MIP-based optimization. The optimization is formulated to minimize the total construction cost of the power supply system while fulfilling technical restrictions. The optimization variables include: (i) substations (number, location), (ii) location of neutral zones, (iii) catenary for every sector (starting and ending point, feeding system, conductors), and (iv) the locations of the required autotransformers. The total construction cost includes: (i) substations, (ii) their connection to the highvoltage network, (iii) catenaries and (iv) autotransformers. The second section of this paper describes the electrification of AC power supply systems. The third section presents how the genetic algorithm is formulated in order to perform the optimization. In the fourth section, the performance of the proposed method is evaluated in a section of the new MadridBarcelona high-speed line. Finally, the fifth section summarizes the conclusions of this work.

2

AC power supply

As shown in Figure 1, the railway electrical system is divided in electricallyisolated single-phased sectors, which are fed from the three-phase network through a traction substation [4, 5]. Three-phase high-voltage network Traction substation 1

Sector 1-L

Sector 1-R

Figure 1:

Sector 2-L

Traction substation 2

Sector 2-R

Sector 3-L

Traction substation 3

Sector 3-R

General structure of the power supply system.

Power Supply System Analysis, Design and Planning

137

These substations are connected between two of the three phases of the highvoltage network. It should be noted that topology could be modified in case of failures to guarantee the operation. For instance, if one of the transformers of a substation fails, the other takes on the corresponding sector. Each of these sectors can use either mono-voltage system (such as 1x25kV) or bi-voltage (such as 2x25kV) system. In mono-voltage systems, the feeding conductors are set directly to the specified voltage level (see Figure 2). In bivoltage systems, a higher voltage is set between feeding conductors [6, 7]. This voltage is reduced by using autotransformers distributed along the catenary (see Figure 3). Positive

Train

High-Voltage network

Figure 2:

Mono-voltage system configuration. Positive

Train

Negative

High-Voltage network

Figure 3:

Dual system configuration.

In [1], the behaviour of dual systems is analyzed and a model is presented to represent bi-voltage systems as if they were mono-voltage systems. This representation is used in this paper to characterize mono-voltage and bi-voltage systems in a similar manner.

3

The optimization problem

An optimization problem formulation has been carried out introducing several criteria for improving classic designs. Particularly, total construction costs are minimized and technical criteria are considered as restrictions. This optimization problem has been tackled using a genetic algorithm. While solving the optimization problem, the number of sectors (see Figure 2) is determined and thus the number of substations and neutral zones, as well as their location. Moreover, the catenary type (and number of autotransformers in dual systems) of each subsector is obtained.

138 Power Supply, Energy Management and Catenary Problems The formulation of this problem is organized in five steps. Firstly, the constant parameters are presented. Then, the optimization variables are established. Next, the objective function is defined. The considered restrictions are formulated afterwards and finally, certain parameters and questions related to the genetic algorithm implemented are pointed out. 3.1 Constant parameters The input data used as constant terms are called constant parameters. In the proposed design method, several calculations have to be done prior to the optimization itself. It has been supposed that the cost of installing a traction substation depends mainly on the place where it has been located. After studying the railways to be electrified and the possible connections to the available three-phase networks, the railway has to be partitioned into zones and the best feeding solution has to be identified for each zone. For each zone, the following parameters have to be specified:  



Position where each zone ends. Cost of installing a substation in each zone. Both the cost of the substation and the cost of the line to connect it to the selected three-phase network are included. Maximum power that could be delivered by a substation depending of the zone it was installed. This value has to be established to avoid (i) excessive voltage drop or excessive unbalances in the three-phase network, and (ii) excessive power flow through the transformers of the substation.

To perform this optimization, it has been assumed that a reduced set of catenary types (with associated autotransformers in dual systems) has previously been selected. A multi-criteria optimization can be done to determine this set [2], but actually it is not necessary for the purposes of this paper. For each catenary type, c , the following parameters have to be specified:



  

Impedance per length unit. In dual systems, the equivalent model [1] has to be used to represent them as simple systems. The impedance per length unit (see [1]) due to the autotransformers separation (for simple systems its value is 0). This parameter depends on the catenary line parameters. The cost per length unit of installing each catenary type. The cost of installing each catenary type in a subsector that does not depend on the length of catenary installed. It corresponds to the cost of the autotransformers and thus is 0 for simple systems.

Several operation scenarios are used to evaluate technical constraints. A scenario is a list of trains that are simultaneously consuming electrical power. To

Power Supply System Analysis, Design and Planning

139

define each scenario, sc , the following parameters have to be specified for each train, t :

     

Position of each train in the railway. Power that consumes each train: St . Other parameters to be defined are: Length of the railways to be electrified Maximum acceptable voltage drop Impedance of substations (all the substations are assumed to have the same value). The current I t consumed by each train. It is estimated assuming an average voltage: V

I t  sc, t  

St  sc, t  V

(1)

3.2 Variables The variables are quantities that are changed in order to minimize the total cost of construction and to fulfil with technical constraints. The variables defined in the proposed model are: 

 

Number of traction substations supplying the stretch considered for the optimization. Location of each substation along the stretch. Type of catenary used in each subsector.

3.3 Objective function The total cost of construction of the electrification to be minimized (see Eq. (2)) includes the cost of building the substations, CSub , the cost of the catenaries, CCat , and the cost of the autotransformers, C AT , (if dual systems are used).

C  CSub  CCat  C AT

(2)

3.4 Restrictions The following restrictions have been included in the genetic algorithm formulation as penalty factors added to the fitness function.  

Maximum acceptable voltage drop for the operating conditions. Maximum power that can be delivered by the substations.

140 Power Supply, Energy Management and Catenary Problems From the genetic algorithm point of view, the dynamic behaviour of these restrictions is remarkable. That is, the restrictions are included in a penalty function that: is active in case of not fulfilling each restriction; and proportionally increases with the number of generations. 3.5 Genetic algorithm Over the years, much work has been done in engineering optimization and the current tendency is to deal with real-life applications which are multi-objective by nature. Therefore, a standard genetic algorithm has been applied to the computation of the aforementioned optimization problem, although some specific tools and functions have been tailored too. Thus, its main characteristics can be summarized as follows: 

 

The individuals have been codified in binary code, including each chromosome the optimization variables described in section 3.2. The mechanisms of nature used for this optimization have been: a Roulettebased algorithm for the selection process; and monopoint schemes for crossover and mutation processes, whose parameters of probability are collected in Table 1. The fitness function that leads the genetic algorithm has been built by the objective function, section 3.3, and the penalty functions derived from section 3.4, as follows:

F  CSub  CCat  C AT      d  s

(3)

s  r v

(4)

 d  1     n  1 

where F is the fitness function which depends of the different costs involved in optimization problem and a penalty factor. This penalty function is composed of a static and a dynamic part as can be seen in Eq. (4), where: r is the static penalty,  is the dynamic penalty, n is the number of generations computed and v the degree of violation of each restriction. Table 1 collects the numeric parameters of the genetic algorithm used in the numerical simulation correspond to standard values of randomized operators and another related to penalty functions. Table 1:

Genetic algorithm parameters.

Property Static penalty, r Dynamic penalty  Crossover probability Mutation probability Population size

Value 106 0.2 0.7 0.03 200

Power Supply System Analysis, Design and Planning

4

141

Example

The proposed model has been used to obtain the power supply of a section of the new Madrid – Barcelona high-speed line between the km 306 and km 441.6. Table 2:

Catenary repository to be used.

Catenary

C5

C4

Contact wire

Bz 150mm2

Bz 150mm2

Sustainer wire

Bz 100mm2

Bz 100mm2

Positive feeder

Without feeder

Negative feeder Return wire Number of AT per sector ZCAT (ohm/km) CFIX (units) CCAT (units/km) ZDESV (ohm/km)

LA-110 LA-110 1 0,100530 200 26,136 0,037155

Table 3: From km 306 (Start) 341,5 346 350 377 397 410 413 415

To km 341,5 346 350 377 397 410 413 415 441.6 (End)

Without feeder LA-380 LA-280 1 0,085893 200 28,140 0,036300

C3 Bz 150mm2 Bz 100mm2

C2 Bz 150mm2 Bz 100mm2

C1 Bz 150mm2 Bz 100mm2

LA-110

LA-280

LA-280

LA-280 LA-110 1 0,072287 200 30,900 0,033548

LA-380 LA-280 1 0,066348 200 33,840 0,028995

LA-380 LA-280 2 0,066348 400 33,840 0,014497

Zone partitioning for installing a substation. CZONE 1000 ∞ 1500 ∞ 2500 ∞ 2000 ∞ 2000

PZONE 60 MVA 100 MVA 100 MVA 60 MVA 60 MVA

Description Fed from 220kV network Forbidden due to environmental protection Fed from 220kV network Forbidden due to environmental protection Fed from 400kV network Forbidden due to environmental protection Fed from 220kV network Forbidden due to environmental protection Fed from 220kV network

The scenarios that have been considered in this study case correspond to traffic meshes of trains consuming 24MVA (typically double compositions of 12MVA trains) separated by 24 km. These hypotheses correspond to high-speed trains circulating at 350 km/h, with frequencies of 4 min. Table 2 shows the considered catenary repository. It has been obtained by using the multi-criteria optimization procedure described in [3]. Table 3 shows the cost of installing a substation and the maximum power that could be delivered depending on the location. The results obtained can be discussed in two main aspects: on the one hand the robustness of the genetic algorithm and; on the other hand, the accuracy by comparing with another optimization procedure. Figure 4 shows the fitness function evolution along generations of the genetic algorithm. In different colours are plotted: the optimum evolution, which is reached with only 11 generations; and the first and second quartiles, which can give an idea of the robust behaviour of the algorithm. It seems clear that at the

142 Power Supply, Energy Management and Catenary Problems tenth generation penalized individuals disappear of most of the solutions. Thus, at least the 50% of possible solutions are feasible and their fitness values are exactly the costs of the objective function. Figure 5 shows the location of substations and subsectors; and the types of catenaries (red lines refers to the solution obtained with the genetic algorithm 4

x 10

2

Q2 Q1 Optimum evolution Optimum

1.9

1.8

1.7

Fitness

1.6

1.5

1.4

1.3

1.2

1.1

1

0

2

4

6

Figure 4:

8

10 12 Generation

14

16

18

20

Fitness evolution.

5

Catenary type

4

3

Limit of cost zone Catenary per subsector−GA Substation−GA Neutral zone−GA Catenary per subsector−MIP Substation−MIP Neutral zone−MIP

2

0

Figure 5:

20

40

60 80 Railway stretch [km]

100

120

Location of substations and subsectors and types of catenaries.

Power Supply System Analysis, Design and Planning

143

and blue lines to the MIP-based one (colour refers to the online version)). Marked with circles are pointed out the location of substations along the stretch considered, between the km 306 and km 441.6 of the Madrid-Barcelona high speed line. However, the horizontal axis shows the relative kilometre points, from km 0 to km 135.6, to make clearer the understanding. Moreover, the vertical axis means the type of catenary used in each subsector. As well as in Figure 5, Table 4 collects the numeric catenary assignment that has been obtained with the GA optimization, while Table 5 shows the assignment obtained with the MIP optimization. Table 6 compares the minimum total cost of the electrification obtained with both methods as well their computation time. The proposed genetic algorithm finds similar solutions in terms of total cost in significantly shorter time. Table 4:

Catenary assigned to each sector in the GA model.

From km 306.000 (substation) 323.15 (neutral zone) 340.3 (substation) 367.55 (neutral zone) 394.8 (substation) 417.9 (neutral zone) Table 5:

Model MIP GA

5

Catenary C4 C5 C4 C3 C5 C5

Catenary assigned to each sector in the MIP model.

From km 306.000 (substation) 332.791 (neutral zone) 347.791 (substation) 374.824 (neutral zone) 391.138 (substation) 425.534 (neutral zone) Table 6:

To km 323.15 (neutral zone) 340.3 (substation) 367.55 (neutral zone) 394.8 (substation) 417.9 (neutral zone) 441 (substation)

To km 332.791 (neutral zone) 347.791 (substation) 374.824 (neutral zone) 391.138 (substation) 425.534 (neutral zone) 441.200 (substation)

Catenary C5 C5 C5 C5 C5 C4

Compared results between MIP and GA models. Global Cost 11760 € 11813 €

CPU Time 1:05:42 Pentium-4, 1.7 GHz 0:00:58 Pentium-4, 1.7 GHz

Conclusions

This paper presents a genetic algorithm based procedure whose main goal I to minimize the total cost of construction of the power supply while satisfying technical constraints such as voltage drops or power limitations. For the sake of the evaluation of the performance of the model, a section of the new Madrid – Barcelona high-speed line has been studied with a MIP

144 Power Supply, Energy Management and Catenary Problems optimization together with the proposed genetic algorithm optimization. Both procedures have found quite similar solutions in terms of costs, but the proposed algorithm performs the optimization in a significantly shorter time. As the genetic-algorithm approach has obtained very promising results, future developments will be focused on designing particular evolutionary strategies to enhance the convergence. Additionally, more complex technical restrictions will be considered.

References [1] E. Pilo, L. Rouco, and A. Fernández, "A reduced representation of 2x25 kV electrical systems for high-speed railways." IEEE/ASME Joint Rail Conference, Chicago, 2003. [2] E. Pilo, L. Rouco, and A. Fernández, "Catenary and autotransformer coupled optimization for 2x25kV systems planning" WIT Transactions on the Built Environment, vol. 78, pp. pp.747-756, 2006. [3] E. Pilo, L. Rouco, A. Fernández, "An optimization procedure to determine the topology of ac railways power supply networks" ASME/IEEE Joint Rail Conference & Internal Combustion Engine Spring Technical Conference (JRCICE2007). Pueblo, Colorado, USA, March 13-16, 2007 [4] J. D. Glover, A. Kusko, and S. M. Peeran, "Train voltage analysis for AC railroad electrification" IEEE Transactions on Industry Applications, vol. IA-20, pp. 925-934, 1984. [5] C. Gourdon and C. Herce, "The overhead system of the TGV-Atlantique," presented at International Conference on Main Line Railway Electrification (Conf. Publ. no.312), London, UK, 1989. [6] H. Roussel, "Power supply for the atlantic TGV high-speed line," presented at IEE International Conference on Main Railway Electrification, York, 1989. [7] R. J. Hill and I. H. Cevik, "Parallel computer simulation of autotransformerfed AC traction networks," presented at ASME/IEEE Joint Railways Conference, 1990.

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Application of linear analysis in railway power system stability studies S. Danielsen, T. Toftevaag & O. B. Fosso Department of Electric Power Engineering, Norwegian University of Science and Technology, Trondheim, Norway

Abstract Dynamical phenomena, such as oscillations and instability in railway power systems, have become of growing concern in the experts’ community in recent years. On several occasions, modern advanced electric rail vehicles have been the source for low- frequency power oscillations leading to an unstable power system due to the lack of damping, and as a consequence of operating problems. A method to study these phenomena is needed. Well known linear techniques based on small-signal analysis provide valuable information about the inherent characteristics of even non-linear single-phase power systems. This paper describes how a railway power system and its dynamical railway-related components are modelled in a commercially available power system analysis software and studied by linear analysis such as eigenvalues, participation factors and parameter sensitivities. This is used to gain knowledge about the interaction between the rail vehicles and the electric infrastructure. Linear analysis is found to be a powerful tool in this respect, provided that adequate models of the relevant components can be established in the RMS mode. The results reflect the experienced poor interaction. Keywords: AC railway power supply, traction power system, stability, advanced electric rail vehicle, rotary frequency converter, low-frequency oscillations, eigenvalue analysis.

1

Introduction

The recent development of electric rail vehicles with utilization of power electronics and complex control systems has introduced new phenomena of dynamical interaction between the vehicles and the railway power supply. One

146 Power Supply, Energy Management and Catenary Problems Long distance 60 km Rotary converter

M 3~ 50 Hz system

Advanced electrical rail vehicle

G 1~ 16 ⅔ Hz system

Figure 1:

Sketch of the railway power system to be studied.

such phenomenon is low-frequency power oscillations leading to system instability, typically in the frequency range of 0.1-0.3 times the fundamental frequency. The vehicles may oscillate together internally (Menth and Meyer [1]) or against the electric infrastructure (Danielsen and Toftevaag [2]). There is a need for an integrated method for studying these oscillations. Low-frequency power oscillations are not new to power systems (Kundur [3]). One method to study these inherent qualities of the power system is by utilization of linear analysis. Several specialized power system analysis computer programs include such tools, i.e. Simpow (Fankhauser, et al. [4]). This paper introduces linear analysis to a railway power system study where the system comprises both electric infrastructure and rolling stock as shown in Figure 1. An alternative method is time-domain simulations as used by Eitzmann, et al. [5].

2

Linear analysis theory

A dynamical system may be described by a number of characteristic differential equations, normally based on the physics of the system to be studied. Based on these equations and information about the initial conditions, the state of the system can be determined and the response of a disturbance can be calculated. If the system is non-linear, commonly the system is linearized around an operating point (Δ-values). In that way the mathematical tools that are used for linear systems can be utilized for non-linear systems as well, such as railway power systems. This is formally only valid in vicinity of the linearization point. A common way to describe a linear or linearized system is by a state space model as in eqn. (1) where x is the state vector containing the state variables, i.e. the variables of which the time derivative is to be considered, and u is the  is a vector containing the time vector containing disturbance variables. x derivative of the state variables and y is called the output vector.

x  Ax  Bu

y  Cx  Du

(1)

Matrix A is the state matrix and contains important information about the inherent qualities of the linear/linearized system. The roots of the characteristic eqn. (2), λ, are called the eigenvalues of the system.

det( A   I )  0

(2)

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The number of eigenvalues for a system is equal to the dimension of A and the number of first-order differential equations describing the system. An eigenvalue can be a complex number λ = σ + jω describing a mode of the system where the imaginary part describes the oscillation frequency and real part describes the damping or time decay of the oscillation. A negative real part identifies a stable mode. Complex eigenvalues appear as conjugate pairs, but only the eigenvalue having positive imaginary part is shown in the figures in this paper. The concept of participation factors utilizes information from the state matrix to find a measure for the relative participation of a specific state variable in a specific mode. The factor itself is a phasor where its length reflects the relative degree of participation in the mode compared to the other state variables (Kundur [3]). Linear analysis of large power systems requires a lot of computations, but it is a simple task for a computer with suitable software (Slootweg, et al. [6]).

3 Concept of power system modelling In an AC power system, both voltage and current vary as a sine with the fundamental frequency f1 (such as 16 ⅔ Hz or 50 Hz) plus additional harmonics. The voltage drop Δu(t) given by a current i(t) over an inductive impedance is described eqn. (3).

u  t   R  i  t   L

di  t  dt

(3)

and currents by phasors, i.e. U  U Re  j U Im . The calculated voltage drop over the impedance will then depend on the resistance R and the fundamental angular frequency ω1 = 2πf1 times the inductance L. This common simplification implies that the current is no longer a state variable where its time derivative is considered. In traditional power systems analysis, the impact of this simplification may be neglected in the view of stability (Kundur [3]). For analysis of power systems with power electronic converters such as an advanced electric rail vehicle, this simplification may not be valid any more (Danielsen, et al. [7]). In the present studies the current is therefore kept as a state variable giving the expression for the voltage drop of any series inductive impedance in both single-phase and three-phase networks as in eqn. (4). This includes the synchronous machines’ stator inductances as well. A common simplification for power system analysis is to represent voltages



d  RL  U   Re  dt  U     Im    L 1 

 1 L   I Re    d I R  L   Im  dt 

(4)

Keeping the current as a state variable is often used in studies of power electronic components in instantaneous value mode analysis of three-phase systems modelled in the rotating dq reference frame (Harnefors [8]), but is here

148 Power Supply, Energy Management and Catenary Problems applied to an entire single-phase power system. The phasors are RMS values of the respective voltages and currents, i.e. root mean squared values over one fundamental frequency period, hence harmonic effects are neglected.

4 Rotary converter 4.1 Introduction The rotary converter is the dominant solution of electric power conversion from the three-phase 50 Hz utility grid to the single-phase 16 ⅔ Hz decentralized fed railway power system in Norway and Sweden (Banverket/Jernbaneverket [9]). Such a converter consists of a three-phase synchronous motor (M) mounted on the same shaft as a single-phase synchronous generator (G), see Figure 1. Both motor and generator are equipped with automatic voltage regulators and exciters. 4.2 Electromechanical eigenfrequency A pronounced characteristic of these rotary converters is the poorly damped electromechanical eigenfrequency around 1.6 Hz due to the lack of explicit motor damper windings (Toftevaag and Pálsson [10]). These low frequency oscillations are shown to be related to the basic swing equation (Biesenack [11]). This equation is linearized in eqn. (5) and describes the electromechanical behaviour (which is characteristic for all synchronous machines (Kundur [3])):

2H H Δδ D KE’

d 2  d  D  K E '  1    0 . dt 2 dt

(5)

Inertia constant in MWs/MVA Change in power angle radians Damping constant in pu torque/pu speed Transient synchronizing torque coefficient in pu torque/rad

From the swing equation, an expression (eqn. (6)) for the eigenvalues λ1,2 describing the electromechanical swing mode for a single machine connected to stiff network can be derived (in this case the synchronous motor connected to the 50 Hz network):

1,2  

D  D  K E '  1 .     4H 2H  4H  2

(6)

Eqns. (5) and (6) are valid for the converter in islanded operation, and need some modifications to be valid in interconnected operation when taking the damping and synchronizing torque of the generator into account as well. 4.3 Linear analysis In this paper, a rotary converter in islanded operation is studied. There is no connection to other converters in the railway power system. The converter is

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connected to a typical 66 kV three-phase utility grid having a short-circuit ratio of 250 MVA. The converter is feeding a 3.67 MW resistive load over 60 km overhead contact line with the impedance of (0.19+j0.21) Ω/km. Including the line’s transmission losses this results in a loading close to the converter’s rated load. Both machines are represented by 5th order standard synchronous- machine models which are increased to 7th order models due to eqn. (4). The low-frequency modes found by linearization of the converter at this operation point are shown in Table 1. Classification of the different modes is done by use of participation factors that indicate which state variables that participates mostly in each mode. The most participating state variables in the electromechanical mode are the converter speed and motor power angle. Damping ratio for the electromechanical mode is low but acceptable. Table 1: No. 8, 9 10, 11 13, 14

Low-frequency modes from linear analysis of rotary converter. Eigenvalues

Mode Generator exciter Motor exciter Electromechanical

– 5.00 [1/s] ± j2.90 [Hz] – 4.83 [1/s] ± j3.19 [Hz] – 0.46 [1/s] ± j1.59 [Hz]

Damping ratio 26% 23% 5%

5 Advanced electric rail vehicle 5.1 Introduction Almost all new electric rail vehicles today utilize the advantages of the induction machine as the traction motor (Östlund [12]). The motor speed and torque are controlled by use of a three-phase power electronic pulse-width modulated inverter. The motor inverter takes the required power from the vehicle internal DC-link capacitor as shown in Figure 2. It is the task for the line inverter to modulate the DC-link voltage into an AC voltage at main transformer lowvoltage side in amplitude and phase such that the resulting voltage drop over the transformer leads to the needed current to keep the DC link voltage at reference.

Control system

1~

= 3~

=

3~M Single-phase main transformer

Figure 2:

Line inverter

DClink

Motor inverter

Three-phase asynchronous motor

Sketch of an electric advanced rail vehicle.

150 Power Supply, Energy Management and Catenary Problems All these components are controlled by an advanced computer based control system. As both line and DC link capacitor exchange energy and because the power control cannot be faster than the fundamental frequency, this result in a dynamical continuous feedback system (Menth and Meyer [1]). 5.2 The model A model of such an advanced rail vehicle is made based on literature (Östlund [12] and Steimel [13]) and is given a thorough description by Danielsen, et al. [7] for use in RMS simulations. Such RMS models of rail vehicles are not standard as most simulation studies in the rail vehicle industry are performed in instantaneous-value time-domain simulations. The model comprises two major simplifications; the motor side is replaced by a resistor and the control system is analogous and continuous. Also, the reactive power consumption at current collector is controlled to be zero. The line inverter control consists of the following controllers: Synchronizing controller (phase locked loop, PLL) to track the phase of the line voltage, DC link voltage controller (VC) for active power control and AC current controller (CC). The controllers are implemented in a vehicle-internal rotating reference frame, also known as vector control. 5.3 Linear analysis The rail vehicle is operated at approximately half its rated power (3.67 MW) fed from an ideal voltage source through 60 km of overhead contact line. This means that in this sub-case, there is no rotary converter in the system. The linear analysis identifies two low-frequency modes. Their figures are shown in Table 2. The vehicle seems to be well damped. Eigenvalues no. 12 and 13 will be subject to further studies as it describes the power oscillations. In order to check the sensitivity of the interesting low frequency mode (eigenvalue 12 and 13), Figure 3 shows how the eigenvalue (positive imaginary part only as the pair is a complex conjugate) moves when different parameters for the locomotive are changed. The range of the change is from 0.5 to 2.0 times the original value which is given in brackets in the legend. Arrows show the movement direction of the eigenvalue when the most influencing parameters are increased. The different parameters are explained in appendix. It can be noticed that reducing either the voltage controller integration time (TIVC) or the current controller gain (KPCC) will within the range alone move Table 2:

Low-frequency modes from linear analysis of the vehicle.

No.

Eigenvalues

6, 7

– 12.9[1/s] ± j7.04 [Hz]

12, 13

– 5.67 [1/s] ± j3.31 [Hz]

Mode AC current measurement, AC voltage measurement VC, AC current meas., DC-link voltage, PLL

Damping ratio 28% 26%

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6 MP (2) 5

KISOGI (1) C

Imaginary [Hz]

KUSOGI (0,8)

TIVC

KPVC MP

TIPLL (0,079)

4 KPCC

KPPLL (51)

3

TIVC (0,04)

KISOGI KUSOGI

KPVC (0,9) TICC (0,5)

2

KPCC (1,347) TUDC (0,008) 1

TIDC (0,008) C (0,04)

0 -25

Figure 3:

-20

-15

-10 Real [1/s]

-5

0

5

Root loci for the low-frequency mode when parameters are changed.

the eigenvalue into the right half plane and make the vehicle unstable. The voltage controller gain (KPVC) has also influence on the mode. Changed DC link capacitance (C) will move the eigenvalue in the same way as the inertia constant H for synchronous machines in eqn. (6) as both express energy storages.

6 System interaction 6.1 Unstable system The rotary converter and the rail vehicle are now combined into one system as shown in Figure 1. For the vehicle this leads to two changes even though the operating point is kept (as in section 4.3 and 5.3): First, the voltage source (both amplitude and phase) is no longer constant but will change as the converter oscillates. And second, the total inductance L that the vehicle current controller has to change the line current in has increased due to the converter transformer and the generator stator windings. The latter change may have an impact on the vehicle low-frequency mode. Table 3: No. 16, 17 18, 19 23, 24 25, 26

Low-frequency modes from linear analysis of the railway power system. Eigenvalues

– 4.83 [1/s] ± j3.18 [Hz] – 5.14 [1/s] ± j2.94 [Hz] – 2.19 [1/s] ± j2.18 [Hz] + 0.23 [1/s] ± j1.59 [Hz]

Mode Motor exciter Generator exciter Vehicle DC-link Rotary conv. electromech.

Damping ratio 24% 27% 16% -2%

152 Power Supply, Energy Management and Catenary Problems The low-frequency modes are shown in Table 3. Both damping and frequency of the vehicle DC-link mode is decreased. The real part of the eigenvalue describing the converter’s mode is positive and indicates an unstable system. 6.2 Stability improvement By use of the linear analysis tool, again the influence of the vehicle control parameters on the different modes can be studied. Figure 4 shows the converter’s electromechanical root loci when the parameters for the voltage and current controllers are changed. The arrows show the direction of movement when the parameter value is increased. 1,7

Imaginary [Hz]

TICC

KPCC

1,6

KPVC TIVC KPCC

KPVC

TICC

TIVC

1,5

1,4 0

0,1

0,2

0,3

0,4

0,5

Real [1/s]

Figure 4:

Root loci for the rotary converter mode when vehicle control parameters are changed (0.5 to 2.0 times original value).

It can be observed that all the control variables influence on the damping of the converter’s eigenfrequency. None of them, however, are alone able to stabilize the system within the variation range studied. The sensitivity to the control parameters for the converter’s mode may be compared to the respective sensitivities of the vehicle DC-link mode shown in Figure 3. Increase of TIVC, KPVC and KPCC will increase damping of both modes. These parameters should therefore be focused when improving the stability in this case. Further studies are however needed to see if change of vehicle control parameters only is sufficient to stabilize the system or not. 6.3 Interaction with a poorly damped rotary converter To show how the rotary converter and the vehicle interact in this unstable system, the absolute value of the participation factors for the unstable electromechanical mode +0.23 1/s ± j1.59 Hz are shown in Figure 5. State variables given by in eqn. (4) and the synchronous machines’ exciters are

Power Supply System Analysis, Design and Planning

0,12

0.24

0.48

153

0.24

0,10 0,08 0,06 0,04 0,02

Converter motor

Figure 5:

Converter generator

DC link volt.

AC curr. contr.

AC curr. contr.

AC curr. meas.

DC volt. contr.

AC curr. meas.

DC curr. meas.

PLL

DC volt. meas.

PLL

AC volt. meas.

AC volt. meas.

Speed

Field winding

Power angle

D damper wind

Q damper wind

D stator wind.

Q stator wind.

Speed

Field winding

Power angle

D damper wind

Q damper wind

D stator wind.

Q stator wind.

0,00

Vehicle

Absolute value of participation factors to show how state variables participate in the rotary converter electromechanical mode.

omitted. Participation of the converter speed and motor power angle is easily observable. In the vehicle control system, the AC voltage measurements and the DC-link voltage controller integral part point out as the largest participants.

7 Concluding remarks In this paper linear analysis tools for studying low-frequency power system oscillations have been applied to a railway power system to gain knowledge about the interaction between power supply infrastructure and rolling stock. The linear analysis clearly states the instability and provides information about which parts of the advanced components that participate in the oscillation and which parameters to change for improvement. The vehicle DC-link voltage controller points out to have an important role. It is obvious that good results require adequate models that may be difficult to obtain, at least for the very complex advanced electric rail vehicles. The concept of keeping current as a state variable needs more investigation.

Acknowledgement The work presented in this paper is a part of a PhD study funded by the Norwegian National Rail Administration (Jernbaneverket).

References [1] Menth, S. & Meyer, M., Low frequency power oscillations in electric railway systems, Elektrische Bahnen. 104 (4), pp. 216-221, 2006. [2] Danielsen, S. & Toftevaag, T., Experiences with respect to low frequency instability from operation of advanced electrical rail vehicles in a traction

154 Power Supply, Energy Management and Catenary Problems

[3] [4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

power system with rotary converters. MET2007 8th International Conference "Drives and Supply Systems for Modern Electric Traction". Warsaw, Poland, pp. 51-57, 2007. Kundur, P., Power System Stability and Control, McGraw-Hill California, 1994. Fankhauser, H.R., Aneros, K., Edris, A.A. & Torseng, S., Advanced simulation techniques for the analysis of power system dynamics, Computer Applications in Power, IEEE. 3 (4), pp. 31-36, 1990. Eitzmann, M.A., Paserba, J.J., Undrill, J.M., Amicarella, C., Jones, A.L., Khalafalla, E.B. & Liverant, W., Model development and stability assessment of the Amtrak 25 Hz traction system from New York to Washington DC. Railroad Conference. pp. 21-28, 1997. Slootweg, H., Persson, J., van Voorden, A.M., Paap, G.C. & Kling, W., A Study of the Eigenvalue Analysis Capabilities of Power System Dynamics Simulation Software. 14th Power Systems Computation Conference 2002. Sevilla, Spain, pp. 2002. Danielsen, S., Fosso, O.B., Molinas, M., Suul, J.A. & Toftevaag, T., Simplified models of a single-phase power electronic inverter for railway power system stability analysis – development and evaluation, Accepted for publication in Electric Power System Research September 1st 2009. pp. 2009. Harnefors, L., Modeling of Three-Phase Dynamic Systems Using Complex Transfer Functions and Transfer Matrices, Industrial Electronics, IEEE Transactions on. 54 (4), pp. 2239-2248, 2007. Banverket/Jernbaneverket, Requirements on rolling stock in Norway and Sweden regarding EMC with the electrical infrastructure and coordination with the power supply and other vehicles (BVS 543.19300/JD 590), 2007 Toftevaag, T. & Pálsson, M.T., Low frequency oscillations in the Norwegian electric traction power supply caused by interaction between the supply system and propulsion machinery – analysis and consequences. MET’05 7th International Conference “Modern Electric Traction in Integrated XXI st Century Europe”. Warsaw, Poland, pp. 137-142, 2005. Biesenack, H., Theorie und Betriebsverhalten von Synchron-SynchronUmformern, Doktor Ingenieur thesis, Fakultät für Technik und Naturwissenschaft, Hochschule für Verkehrswesen "Friedrich List", 1972. Östlund, S., Electric Traction (original title in Swedish: Elektrisk Traktion), School of Electrical Engineering, Electrical Machines and Power Electronics, Royal Institute of Technology (KTH), Stockholm, Sweden, 2001. Steimel, A., Electric Traction - Motive Power and Energy Supply, Oldenbourg Industrieverlag, München, 2008.

Appendix MP is voltage dependency of motor load where value 2 is constant impedance characteristic. KUSOGI and KISOGI describe the filtering of line voltage and

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current, respectively. TIPLL and KPPLL are the integration time and gain of the PLL, resp. TIVC and KPVC are the integration time and gain for the DC-link voltage controller, resp. TICC and KPCC are the integration time and gain for the current controller, resp. TUDC and TIDC are the filter time constants for the DC voltage and current measurements, resp. C is the DC-link capacitor in Farad.

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Fast estimation of aggregated results of many load flow solutions in electric traction systems L. Abrahamsson & L. S¨oder Electric Power Systems, Royal Institute of Technology (KTH), Sweden

Abstract Transports on rail are increasing and major railway infrastructure investments are expected. An important part of this infrastructure is the railway power supply system. The future railway power demands are naturally not known for certain. This means investment planning for an uncertain future. The more remote the uncertain future, the greater the amount of scenarios that have to be considered. Large numbers of scenarios make time demanding (some tens of minutes, each) simulations less attractive and simplifications more so. The aim of this paper is to present a fast approximator that uses aggregated traction system information as inputs and outputs. This facilitates studies of many future railway power system loading scenarios, combined with different power system configurations, for investment planning analysis. Since the electrical and mechanical relations governing an electric traction system are quite intricate, an approximator based on neural networks (NN), is applied. This paper presents a design suggestion for a NN estimating power system caused limits on active and reactive power load, i.e., limits on the levels of train traffic. Keywords: railway, neural networks, load flow.

1 Introduction For environmental and economic reasons, in Sweden and the rest of Europe, both personal and goods transports on rail are increasing. Therefore major railway infrastructure investments are expected. An important part of this infrastructure is the railway power supply system. One phase low frequency AC railway power supply systems are normally connected to the normal 50 Hz power system through frequency converters, see Figure 1.

158 Power Supply, Energy Management and Catenary Problems

50 Hz

50 Hz

3 phase

3 phase

Public grid

Converter

Converter 16.7 Hz Previous power system section

Z

1 phase

Railway grid

16.7 Hz

This power system section

Z1

1 phase

Z2

S1

Z3

Next power system section

Z

S2

Figure 1: A section of the railway power supply system, illustrated as an electric circuit. The converters may be merely used as power sources, as in Sweden for example, whereas in other countries the railway administrations produce electricity on their own and sell it on the market when profitable. The catenary (the overhead contact line from which the locomotive extract electric power) has a relatively high impedance, i.e., the railway power grid normally can be considered weak. The weakness can be somewhat reduced by strengthening the catenary system, placing the converter stations closer to each other, or connecting a High Voltage (HV) transmission line in parallel to the catenary system. One important consequence of a weak railway power supply system is that when traffic is dense, fast, and/or the trains are heavy, the voltage will drop. For voltages lower than nominal, the locomotives cannot extract as much tractive force as is normally the case. This means that, depending on the strength of the power system, there is a limit on the intensity of the train traffic, caused by voltage drops in the catenary that reduces the maximal tractive force. Railway power supply systems are changing all the time. When a train moves, the impedances between it and the feeding points changes, because both catenary and HV line impedances are distance dependent. The magnitude of the apparent power demands also change when the trains move. Both the active and reactive power demands of the locomotives may vary with the slopes of the railway, the train weights, the desired train velocity, etc. When considering future possible railway power supply system investments, for each possible expansion alternative, many different situations of railway operation causing different loading on the railway power supply system have to be studied. This is a kind of transmission expansion planning. Similar approaches can be found in the references [1–3]. In the case of the railway, however, the locations of feeding points are up to the railway power grid administrator, and not to the actors on the market as in the case with the public grid. For each possible investment alternative, the power grid calculations have to be performed fast. There are several algorithms available, e.g., TPSS (Train Power System Simulator, called TTS in [4]) and commercial programs such as TracFeed Simulation [5]. These are however not fast enough, though, when several thousands of cases have to be studied. The intention of this paper is to propose a solu-

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tion of how to design an approximator that rapidly estimates the properties of an electric railway power supply system which are considered important in the studies of future expansion alternatives. In other words, to calculate aggregated results from many load flow calculations in a fast way. The two most important consequences of train traffic related to the state of the power system, having the railway operation costs in mind, are: • The power consumption of the grid, preferably divided up by individual converter stations. • The impact of catenary voltages on the minimal traveling times. In this paper, the power system impact on travel time limits is studied, and therefore these are modeled to be the outputs of the approximator. In order to keep the approximator relatively simple, inputs as well as outputs must contain aggregated information. These aggregated figures can, from the power system point of view, be divided into three groups: issues having influence on the power consumed (inputs), issues having influence on the impedances (inputs), and issues related to voltage drops (outputs). For more details, see sections 3.2.1 and 3.2.2. Since the electrical and mechanical relations of an electric traction system are quite intricate, an approximator of the black box kind is a tempting approach. Therefore, Neural Networks (NN), which basically are a kind of nonlinear predictors, were selected as a suitable approximator type. One reason to use aggregated inputs is that NNs with too many inputs and outputs may need a tremendous amount of training cases in order to become reliable and general [6]. The exact details of the approximation can be studied in section 3. In a numerical example, an X km section of a traction power supply system is modeled, see section 3.2. The operation is then simulated and the parameters and the performance of the approximator are then estimated. The notation X signifies that the inter-converter distance is varied. 1.1 Related work Efforts constructing less complicated approximators, based on knowledge, intuition, and experience have been made in [7], an interesting German paper from 1998. That paper presents an obviously very fast and uncomplicated method of approximating impacts of different levels of traffic and different power system setups, on the train speeds. The models in [7] do, however not consider the impacts of: slopes, non-maximal train velocities, train velocity and catenary voltage dependencies of the reactive power consumption (which implicitly is done in the model proposed here, from now on called TPSA (Train Power System Approximator) since the approximator is trained with simulation results based on load flow calculations), different train types at the same railway section, etc.

2 Basic power system modeling 2.1 Converters Traction systems fed through converters, are normally either low frequency onephase AC systems, or DC systems. A section of the low frequency railway power

160 Power Supply, Energy Management and Catenary Problems supply systems used in Northern Europe can be modeled as in Figure 1. Because of the relative weakness of such systems, converters can more or less be considered as power injectors from strong grids. Thereby, converter stations need to be distributed along the railway such that power does not have to be transmitted over too great distances, and such that the converters do not get overloaded. The frequency converter stations in Sweden control their terminal voltages, although not stiffly. The voltage is controlled linearly with respect to reactive power generation. Converter stations can produce reactive power of both positive and negative signs. If no reactive power is generated, the catenary voltage is controlled at a nominal level (16.5 kV). The voltage angles at the converter station terminals are completely determined (although quite nonlinearly) by the voltage levels, and the active and reactive power flows in and out of the terminals of the converter station. In Figure 1, the power system sections are fed from both ends. In reality, however, a railway power system section can also be supplied only from one side. Singly fed sections are not studied in this paper, but can for example occur at catenary ends, or in cases of converter outages. 2.2 Power transmission The impedances Zj , j ∈ {1, 2, 3}, in Figure 1, denote the total impedances as seen by the locomotives. Included in these impedances one can find catenary impedances as well as (if present) impedances originating from the high voltage lines and the transformers connecting them to the catenary. The impedance values do not only depend on the train positions (impedances are normally length dependent), they also depend on the power system configuration. Basically, there are two kinds of catenary technologies used: Booster Transformer (BT) and Auto Transformer (AT). BT is the cheaper one, with higher impedances than AT [8]. There is also an option of strengthening the power system by installing a High Voltage (HV) transmission line in parallel to the catenary. The impedances between the locomotives and the converter stations are naturally smaller, the more densely the transformers connecting catenary and HV line are distributed. 2.3 Locomotives and trains For a train to move forward, a tractive force is needed, depending on its running resistance (mainly air and mechanical resistance), its weight, the locomotive’s efficiency, and track topography, different force levels are needed for acceleration or speed maintenance. Moreover, depending on the train velocity, the catenary voltage levels, and possible additional controls, the tractive force outtakes are bounded. The following is important, especially from the power system dimensioning viewpoint. For sinking catenary voltage levels, for a constant amount of consumed power, the currents tend to increase. Therefore the tractive force is successively reduced by on-locomotive controllers. This control is installed in order to protect the engine from overloading. The connection between tractive force, F , and

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the electric active power consumed, P , is, P = F · v, excluding electrical and mechanical losses in the train, and where v denotes train velocity. Thus, in weaker traction power systems, if the traffic demand is too high, the trains will be forced to travel either more sparsely, more slowly, or a combination of the two, compared to what would be the case if the power system had an unlimited capacity. An important difference between locomotives and other kinds of power consumers is that locomotives to a greater extent accept substantial voltage drops. Thus, even a typical Swedish locomotive will still be in operation, at a reduced level of tractive force, for voltage drops of about 40 %. The electrical and mechanical rules of train movements are described in some detail in [4, 9]. Summarizing the preceding paragraph, trains are movable and heavily varying electric power loads. In the exemplifying circuit of Figure 1, the apparent power consumed by the two trains Si = Pi + j Qi , i ∈ {1, 2} can be found. As indicated in the above, the apparent power is not constant with respect to time and position. For some (older) locomotive types, the reactive power consumption, Qi , depends on catenary voltage levels, Pi , and v, see e.g. [4, 9] for details. For more modern locomotive types, Qi can be controlled freely but such locomotives are, at least in Sweden, normally operated purely resistively [10].

3 The approximator 3.1 Introduction The aim of the approximator (TPSA), is to obtain a fast estimation of whether a certain power system causes limitations in possible train power consumption levels, i.e., in possible train traffic. Since the voltages are almost stiff at the catenary side of the converter station terminals, the railway power supply system can be divided into separate sections by using the converters as section borders. These sections are almost independent of each other. This means that train traffic on one side of a converter station influences the catenary voltage levels on the other side of that particular converter station to a comparatively small extent. The power flows between these power system sections are normally insignificant, but the smaller the impedances, the more noticeable they are. In [11], one modeling simplification is that a train consumes power only from the feeder units right in front of and right behind it. There, ”feeder unit” means either a converter station or a transformer station connecting the catenary to the transmission line. With this assumption, the inputs to TPSA, as well as the outputs from it, only have to describe the traffic and power system states for one section at the time. The power system sectioning assumption is an essential part of the TPSA model presented here. The fact that the TPSS simulations for the creation of the TPSA training set will treat smaller power systems, and thereby further reduce the simulation times, must simply be considered as a bonus. The main benefit considering future usage of TPSA is that it will now become a general module that can be

162 Power Supply, Energy Management and Catenary Problems used for any traction power system section in a greater system. The part of TPSA that determines the maximal on-average velocities can be used as traffic-dependent constraints in a suitable time table program. Such a constraint states the maximal on-average velocity for an additional train, given an already existing traffic. The main difference between the TPSA model presented in this paper, and the so called TTSA in [4] is that inputs and outputs are aggregated differently. In this paper the choices of aggregation are better adjusted for the kind of information that one can expect to be available. In [4], the active power consumption of the railway was also estimated. Since this paper is more detailed, all focus is here set on the impacts of minimal train running times as a function of the strength and the load of the power supply system. 3.2 The model It is common in train time table planning programs to use models containing binary or integer variables for train location. The models vary, but are similar. From now on, assume we have a binary variable, say xi,j,ti ,tj ,r , that takes on the value 1 when there is traffic on that particular railway section in that particular time window with that particular train, and equals 0 when not. The indices designate the following: i is the node (a node in a traffic planning model, i.e., a train stop) from which the train leaves at time ti , j is the node at which the train will arrive at time tj , whereas r is the train index. The facts explained above regarding train timetable planning are crucial for the modeling of TPSA, i.e., the choices of the aggregated inputs and outputs for the TPSA. The inputs and outputs of TPSA must be such that they are possible to aggregate both from TPSS as well as time tabling programs. The points in time when the studied (additional) train starts, ti , and stops, tj , are crucial when aggregating the inputs and outputs. For example they make it possible to know when to start measuring the behavior of the other trains (connected to the same power system section as the studied train during the time interval between ti and tj ). Obviously, all trains are limited by the catenary voltage levels, but TPSA is designed such that each train is studied at a time. Separate TPSA:s for different numbers of trains on the power system sections would make the approximator less general and probably demand a greater set of training data. The choices of important aggregated TPSA inputs and outputs are in the bullet lists of sections 3.2.1 and 3.2.2 described and motivated. The binary variables AT and HV describing the power system technology are not aggregated, and as shown in Figure 2 even not really inputs to the NN, and therefore not found in the bullet list of section 3.2.1. 3.2.1 The aggregation of inputs The TPSA inputs can be classified as either parameters giving rise to the consumption of active and reactive power, or parameters related to the power system impedances. Some inputs may be connected to both consumption and impedance. In this paper, the trains are allowed to stop only at the locations of converter sta-

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163

tions, a fact that reduces the number of input variables. Additionally, the model is restricted to one type of trains traveling in one direction. The TPSA inputs of this paper can be found in the following bullet list, including short motivations. • The distance between i and j , denote it d(i, j ). The distance gives information of the power system impedances. • The average inclination, E(incl), between the power system section-borders i and j . The average inclination gives information of the net potential energy consumed by the trains. The other trains will not experience the same inclinations as the train studied in the time interval between ti and tj does. • The standard deviation of the inclination, D(incl), between the power system section-borders. The average inclination, E(incl), would for example equal zero for both flat ground as well as for a rail section with 20 per mille uphill half the section and 20 per mille downhill the remaining half. The standard deviation is a measure of how much the inclinations fluctuate, which will influence the consumed electric power of the trains. • The traffic of other trains on the studied power system section in the time interval between ti and tj must also be measured, because within that time interval, the power consumed by “other trains” affects the catenary voltages experienced by the “studied” train. The average velocity, E(v), and the average number of trains, E(trains), on the section are calculated. The velocity is used because higher train speeds means greater power consumption. The average velocity is measured only when trains are in service. The number of trains is important because the more trains, the greater need for electricity. The average number of trains is calculated as total train traffic time divided by the length of the time window, tj − ti . 3.2.2 The aggregation of outputs The TPSA output describes the running times influenced by catenary voltage levels for the studied train. • The fastest possible average velocity of the studied (added) train. 3.2.3 Neural network The output of TPSA is the greatest possible average speed for an added train. The inputs of TPSA describe the power system topology and parameters, the topography of the track, and the number of other trains (on the same power system section as the studied train) as well their average speeds. TPSA is essentially a NN that connects the inputs to the outputs. Moreover, some of the TPSA inputs describing the power system are binary, i.e., AT, which equals 1 for AT catenaries and equals 0 for BT catenaries, and HV, which indicates the presence of HV transmission lines when it equals 1. Two binary variables give four possible combinations. For each of the four cases, an individual NN is constructed, see Figure 2. The separation into four different NNs is motivated by the fact that backpropagation [12, 13] networks are not optimal for such classifications [6]. Backpropagation networks are mainly approximators of smooth functions. Thus, the NNs are only trained with inputs and outputs that can

164 Power Supply, Energy Management and Catenary Problems TPSA Neural Network #1 AT

Neural Network #2

Selector TPSA inputs

TPSA outputs

HV Neural Network #3

Remaining inputs

Neural Network #4

Figure 2: For AT and BT catenary types, who can be either connected to or without an HV transmission line, there are four separate possible neural networks. hidden layer

hidden layer

output layer

f

h g

f input

h g

output

f

h g

f

h

Figure 3: A sketch of an arbitrary neural network. The input vector is three elements long, whereas the output vector is four elements long. be regarded as continuous variables, i.e., “remaining inputs” in Figure 2. Two different NN models are proposed, both based on the assumed outputs and inputs presented in sections 3.2.1 and 3.2.2. An example of a multilayered neural network can be found illustrated in Figure 3. In that network, there are three layers, of which two are hidden. Normally, all neurons in one layer have the same type of transfer functions, e.g., f in the first layer in Figure 3. The first model, M1, is a nonlinear NN with two layers. In M1, the hidden layer has tanh transfer functions, 
5  1 out1n = tanh bn1 + (1) ink wk,n k=1

where subscript n denotes neuron number and superscript 1 denotes the first layer. The input vector is, as can be deduced from the bullet list, of length 5 and the output is just a scalar. The second (output) layer has a linear transfer function out2 = b2 +

N 

out1n wn2

(2)

n=1

where superscript 2 denotes the second layer, and N is the number of neurons in 1 , and w 2 are parameters whose values the first layer. The parameters bn1 , b 2 , wk,n n

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165

are determined in the training step. According to the theory, page 78 in [14], and in [13], this kind of network can be used as a general function approximator, given a sufficient amount of neurons in the hidden layer. The second model, M2, assumes a linear dependency

out = b +

5 

ink wk

(3)

k=1

where k is input index, and wk and b are parameters whose values are determined in the training process presented in section 3.2.3.1. The motivation for testing a linear model at all is explained by the planned future use of TPSA as a running time constraint in a train time tabling program. In such a program, time consuming already as it is, a linear model would probably not extend the computation times as much as a nonlinear one would. The accuracies of the two models are compared and evaluated in section 4.2. 3.2.3.1 Training of the Neural Network In both models, i.e., M1 and M2, the aggregated input and output data sets are normalized to lie in the interval [−1, 1] before training and testing the approximators. Training is essentially a method of determining the values of the parameters w and b (in both M1 and M2), such that the mean square of the estimation error of the network output is minimized. Model M1 is trained by the trainbr (Bayesian regularization backpropagation) algorithm (of Matlab’s NN Toolbox) with an error goal of 10−5 . Thus, out2 of equation 2 is the estimation of the maximal train velocity. Model M2 is trained by the trainb (batch learning) algorithm (of Matlab’s NN Toolbox). Thus, out of equation 3 is the estimation of the maximal train velocity.

4 Numerical example 4.1 Problem setup In order to be as clear a possible, in the numerical example presented in this paper, just a few of all possible parameters are presented and used. That makes the problem setup more surveyable. For example, only one kind of trains is studied (similarly as in [4]), only one kind of each respective catenary type is studied, unidirectional traffic is assumed, and the converter stations are all assumed to be equipped with six 10 MVA converters (Q48/Q49) each such that the installed power should not be a limiting factor in the simulations studied. Furthermore, the train stops are also assumed to coincide with the locations of the power system section borders, i.e., the converter stations. The speed limit is set as high as 150 km/h all over the simulated railway sections, i.e., for Rc4 locomotives a limiting constraint only in very steep downhill situations. Moreover, the number of transformers connecting

166 Power Supply, Energy Management and Catenary Problems

1 0.9 0.8 0.7 0.6

v U P

0.5

Q

0.4

incl incl = 0 −θ

D D

0.3 0.2 0.1 0

0

50

100

150

km

Figure 4: An example of the mechanical and electrical states of a train traveling through a section of the railway electric power supply system. the transmission line (when present) to the catenary is set to three in all cases studied in this paper. The model presented in section 3.2 is as simple as it is in order to comply with these model restrictions. All trains also try to go as fast as possible in the TPSS simulations, excluding a lot of real-life cases. In Figure 4, a train from a TPSS simulation is studied. In that simulation, the converter distance was 160 km on an AT system with HV line and the train departure periodicity was 6 minutes. The velocity of the train, v, is scaled down by a factor of 160 km/h. Additionally, the figure presents the consumed active power, PD , reactive power, QD , and the catenary voltage, U , all expressed in p.u., where Sb = 5 MVA and Ub = 16.5 kV. The catenary phase angles of opposite sign, i.e, −θ , seen by the locomotive of the train can also be found in Figure 4, expressed in radians. Finally, the inclinations of the railway track are also plotted in Figure 4, scaled such that 0 on the y-axis means −10 per mille, and 1 means 10 per mille. In the numerical example, 400 different simulations have been done, 100 for each neural network to train. There are four separate NNs, one for BT catenaries, one for AT catenaries, one for BT with transmission line, and finally one for AT with transmission line – as described in Figure 2. These hundred cases consists of ten different inter converter distances (of length: 30, 57, 80, 98, 114, 127, 138, 146, 154, and 160 km) combined with ten different train departure periodicities (of times: 6, 8, 10, 13, 17, 22, 28, 36, 46, and 60 minutes between each train departure). In the numerical example of [4], the measuring of a train’s running time is not started until the railway is filled up with trains according to a certain train departure periodicity. In this study, in order to speed up the calculations, the measuring is started immediately. In order not to have a completely empty railway when starting measuring, in the initialization procedure, TPSS distributes trains along the track almost as in an ideal situation, i.e., trains going at maximally allowed speed all

Power Supply System Analysis, Design and Planning

167

0.11 Training Set Test Set

0.1

Average Mean Square Error

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01

1

2

3

4 5 6 7 Number of neurons in hidden layer

8

9

10

Figure 5: A study of the average mean square errors on the training and testing sets as a function of the amount of hidden neurons.

the time. After the simulation has started, however, of course the trains distributed along the track with predefined initial velocities will follow the same electrical and mechanical laws of nature as the other trains.

4.2 Numerical results The greatest on-average velocity, for an added train, is determined through TPSS simulations with the problem setup presented in section 4.1. Worth pointing out is that all simulations use the same railway profile, e.g., the first 30 km in all simulated cases have the same inclinations. Consequently, the average values and standard deviations of the inclinations will be different for each inter-converter distance. As rule of thumb [6], two thirds of the simulations may be used for training the NN, whereas the remaining third may be used for testing. That is applied also here. The amount of hidden neurons, i.e., N in equation 2 was set to 4. This was not done arbitrarily, but by studying the average (ten different random choices of training and testing sets) mean square approximation errors for one to ten hidden neurons – see Figure 5. In the case studies, the accuracies of one linear NN and one nonlinear NN are compared for both the training and the testing sets. The approximation errors in Table 1 can be found for network M1, and Table 1 for network M2. The NNs are modeled with the design introduced in section 3. The computer time needed for execution of minor NNs like these is negligible.

168 Power Supply, Energy Management and Catenary Problems Table 1: The approximation errors for the four different neural networks. (b) For model M2

(a) For model M1 M1

Training

Set

M2

Training

Set

HV

BT

AT

HV

BT

AT

Yes No

7.22 · 10−3

8.05 · 10−3

1.04 · 10−2

9.05 · 10−3

Yes No

5.67 · 10−2 7.93 · 10−2

6.04 · 10−2 6.24 · 10−2

Testing

Set

Testing

Set

Yes

1.14 · 10−2

2.39 · 10−2

Yes

6.52 · 10−2

8.80 · 10−2

No

3.03 · 10−2

1.14 · 10−2

No

1.05 · 10−1

7.46 · 10−2

5 Conclusion and summary The paper can be concluded with the fact that a first suggestion to a fast method of estimating the fastest possible train speeds, for an additional train, as a function of the railway power supply system and the traffic level of other already added trains. The function uses aggregated parametric values as both inputs and outputs. In the numerical example, an example of the results of TPSS were presented in a graph. That is followed up with a comparison between the two suggested approximator models M1 and M2. As one could expect, the non-linear model performs noticeably better. Some recommendations for further work: • Include different traveling directions in the model • Include trains with different speed limits • Allow train stops at arbitrary locations • Include different train types • The next step of TPSA: estimate the injected active power, and the dividing up between the converter stations.

References [1] Cruz-Rodrgues, R.D. & Latorre-Bayona, G., HIPER: Interactive Tool for Mid-Term Transmission Planning in a Deregulated Environment. Power Engineering Review, IEEE, 20(11), pp. 61–62, 2000. [2] Buygi, M.O., Balzer, G., Shanechi, H.M. & Shahidehpour, M., Market-Based Transmission Expansion Planning. Power Systems, IEEE Transactions on, 19(4), pp. 2060–2067, 2004. [3] Chennapragada, B., Radhakrishna, C. & Vallampati, R., Risk-based approach for Transmission Expansion Planning in Deregulated Environment. Probabilistic Methods Applied to Power Systems, 2006. PMAPS 2006. International Conference on, Stockholm, Sweden, 1–4. [4] Abrahamsson, L. & S¨oder, L., Fast Calculation of the Dimensioning Factors of the Railway Power Supply System. Computational Methods and Experi-

Power Supply System Analysis, Design and Planning

[5] [6] [7]

[8]

[9]

[10] [11]

[12] [13]

[14]

169

mental Measurements, Prague, The Czech Republic, volume XIII, pp. 85–96, 2007. Stern, J., TracFeed Simulation, Reference Manual. Technical Report BBSE951112-BNA, Balfour Beatty Rail, 2006. Communication with Bj¨orn Levin, SICS - Swedish Institute of Computer Science, 2007. Kista, Sweden. v Lingen, J. & Schmidt, P., Railway Electric Energy Supply and Operation of Railways (original title in German). Elektrische Bahnen, 96(1–2), pp. 15–23, 1998. B¨ulund, A., Deutschmann, P. & Lindahl, B., Circuit design of the Swedish railway Banverket in catenary network (original title in German). Elektrische Bahnen, 102(4), pp. 184–194, 2004. Abrahamsson, L. & S¨oder, L., Basic Modeling for Electric Traction Systems under Uncertainty. Universities Power Engineering Conference, 2006. UPEC ’06. Proceedings of the 41st International, Newcastle upon Tyne, UK, volume 1, pp. 252–256, 2006. Communication with A. B¨ulund, Swedish national railway administration (Banverket), 2007. Borlnge, Sweden. Nyman, A., TTS/SIMON Power Log – a simulation tool for evaluating electrical train power supply systems. Computers in Railways VI, Lisbon, Portugal, 1998. Backpropagation. http://en.wikipedia.org/wiki/Backpropagation, 2007. Neural Network Toolbox (Matlab online help). www.mathworks.com/ access/helpdesk/help/toolbox/nnet/backpro4.html. Retrieved on March 9 2007. Gurney, K., An Introduction to Neural Networks. CRC Press, 2003.

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DC protection calculations – an innovative approach R. Leach, D. Tregay & M. Berova Parsons Brinckerhoff Ltd, UK

Abstract As part of a recent major re-signalling scheme for a DC electrified railway, substantial changes were made to the track layout and electrical feeding/switching arrangements. In addition, as part of this scheme, the opportunity was taken to introduce a novel approach to the way negative bonding in the return circuit is configured, made possible by the introduction of axle counters, in place of track circuits, for train detection purposes. As a consequence, the overall impact on electrical impedance was unclear. The need arose to determine firstly whether the existing protection settings for the track feeder circuit breakers remained safe in the light of these changes and secondly whether the settings could be improved, thereby offering the potential to increase services and/or run longer trains. This paper outlines the challenges that needed to be overcome in gathering, processing and validating input data to arrive at a complete, coherent and consistent set of data necessary for determining the maximum fault impedances seen by each of the circuit breakers. The paper goes on to present the development, implementation and application of the methodology for the calculation of the protection settings, including validation of the results. The results from the calculations were surprising and contrary to original expectations. Keywords: calculations, traction, power, DC, protection, relay, settings, spreadsheet, fault, impedance, overcurrent, overhang, tee, data, hand, modelling, schematic, equivalent and circuit.

1

Introduction

As the result of a major re-signalling project in the UK, the permanent way layout and the third rail DC traction power supply infrastructure underwent substantial change, both in terms of the track layout, particularly at switch

172 Power Supply, Energy Management and Catenary Problems and crossing (S&C) locations, and in the plain line sections of the rail network. The installation of new types of running rails and the renewal of the traction return (negative bonding cables) based on a new technique [1] meant that existing circuit impedances needed to be revisited to determine whether existing DC circuit breaker protection settings remained safe, or needed to be modified in the light of the changes. This necessitated carrying out protection setting calculations for 36 electrical sections, some standard plain line and others, involving diverging routes, resulting in complex feeding arrangements.

2

Issues relating to data

The initial approach was to update the existing calculations, relevant to the affected electrical sections, to reflect any changes in the infrastructure. However, when compiling the data, it was found that before proceeding with any analysis there were a number of issues to resolve, namely:  









   

3

Record drawings often up to 20 years out of date or incomplete Recent changes arising from an earlier Traction Power Supply Upgrade project needed to be included Feeder cable lengths not typically included in earlier calculations where impedance values of some such feeders were actually quite significant Variety of protection relay and circuit breaker current tripping device types needed consideration Recent drawings based on metric units whereas original calculations utilised imperial units (miles and feet) thereby warranting conversion Mileages shown on positive (conductor rail) drawings and negative bonding drawings not always in agreement Details of running rail types not readily available, or unknown Different running rail types in parallel within electrical sections Multiple reference points e.g. record drawings based on miles and feet from London, permanent way drawings at switch and crossing based on local datum point, signalling drawings based on separate datum relating to extent of re-signalling project Changes to conductor rail cross-sections, feeder cables and return circuits arising from changes to permanent-way track layouts

Selection of approach

3.1 Previous practice/issues The existing protection setting calculations supplied by the client relating to previous stages of the traction power system development were based on simple hand calculations, which typically excluded cable lengths and tended to assume connection points were adjacent to the Traction Substations (TSS’s) and Track Paralleling Huts (TPH’s). This presented several issues to overcome:

Power Supply System Analysis, Design and Planning











173

Hand calculations cannot readily cope with complex layouts, or multiple changes in conductor rail and running rail types. With hand calculations it is easy to make mistakes and difficult to check the calculations. Often the lengths of junctions are now typically much longer. This meant that physical connection points to conductor rails and feeder/return cables were rarely adjacent, but often a considerable distance from the TSS or TPH resulting in greater cable lengths. Therefore, it became apparent that cable impedances could not be ignored. Significant ‘Overhangs’ or ‘Tee’ feeds arising from extended junctions were omitted from the original calculations. Historically, conductor rails were of smaller cross section, hence impedance was very similar to the feeder cables and actual connection point was not considered particularly critical.

3.2 Typical arrangements Figures 1 - 3 below illustrate the variety of configurations typically found on most schemes of this kind and associated fault paths. Note: A ‘Tee’ feed is particularly difficult to evaluate in terms of providing suitable protection settings. This arises as a fault in the ‘Tee’ or ‘overhang’ results in fault current from the two feeding circuit breakers flowing along the same path, thereby increasing the apparent impedance seen by the circuit breakers. It is therefore necessary to determine whether a fault at the end of the ‘Tee’, or a fault at the remote end of the section represents the higher  

 

Fault S/S 1

Figure 1:

S/S 2

Normal feeding (no ‘Tee’ feed or ‘Overhang’).  

 

   

S/S 1

S/S 2 Fault

Figure 2:

Branch in section forms a ‘Tee’ feed.

174 Power Supply, Energy Management and Catenary Problems  

Fault S/S 1

Figure 3:

S/S 2

‘Overhang’ with positive connections remote from the substation.

impedance, in order to determine the required settings (see Figs. 2 and 3). The risk is that neither circuit breaker may trip under a fault condition. An ‘overhang’ is the extreme form of a ‘Tee’ feed in electrical circuit terms. 3.3 Approach adopted As a consequence of the above, it was decided that hand calculations were not appropriate for this project. Instead, the process was undertaken through use of a calculation spreadsheet (PB-ProCalc) with data inputted via a customised front end template, incorporating the relevant formulae contained within Sections 8.3 & 8.7 of the client’s process document [3]. The calculations were also modified to take account of the client’s specific requirements within the guidance document [4]. The main changes from the client’s process document are clearly defined in his guidance note [4]. The designer is instructed to exclude any allowance for rail joints and bonding resistances. A 7.5% tolerance is to be added to the settings to compensate for impedance relay tolerances. Any cables over 15m in length are to be separately identified and included in the calculations. In order to validate the accuracy of the spreadsheet, a full check of the formulae within the spreadsheet was carried out using an independent Engineer within Parsons Brinckerhoff (PB). In addition, the spreadsheet was tested against one of the worked examples in the clients process document [3] and against the example ‘Tee’ feed calculation results contained in the clients Guidance document [4]. As a further means of verifying the accuracy of the spreadsheet, a second independent set of calculations were undertaken using Network Rail ‘Tee’-feed computer program [5] for all of the electrical sections on the project. The Proposed Approach was documented [6] and submitted to the client, and formal acceptance received prior to implementation. 3.4 Modelling An equivalent circuit was created for each electrical section based on information derived from design drawings and record drawings (see section headed ‘Detailed Process’ below and the Flow Chart in Appendix A for further details).

Power Supply System Analysis, Design and Planning

175

In order to simplify the calculation process, and to arrive at worst case, the following rules were applied:  Benefits of reinforcement cabling for running rails around S&C locations and at single rail track circuited areas were excluded from calculations as worst case, on assumption these could be disconnected during maintenance, etc. and therefore not available for traction return  Running rails were assumed to be 109lb/yd (smallest cross section) throughout as per original, unless confirmed otherwise  Conductor rail also assumed to have the smallest cross section (100lb/yd), unless confirmed otherwise  In order to simplify calculations in multi-track areas, where different types of running rail are in parallel, a particular rail size was selected and the length adjusted in the spreadsheet to provide an equivalent impedance.  Cable lengths to substations and TP Huts were typically scaled from the conductor rail and negative layout drawings as exact cable lengths were not typically available  ‘Tee’ points and ‘Overhangs’ were worked out separately for positive and negative circuits, making the calculations simpler to handle. This produced exactly the same result as if the elements were combined. 3.5 Fault path The preparation of equivalent circuits for the positive side (conductor rails) was relatively straightforward, although determination of actual connection points was in some cases difficult due to imprecise record data for some areas. The situation with regard to the negative return circuits was, however, often quite complex. In some instances it was far from clear which equivalent circuit should be used for the return circuit, in particular relating to multi-track areas with substation return connections at differing points for each track (sometimes hundreds of metres apart) and potentially involving an ‘overhang’ situation. The dilemma was how to determine the position/length of the ‘overhang’ in relation to the equivalent circuit for the remainder of the main line in terms of whether a single point for all the return connections should be assumed, or each track worked out separately. If a single point of connection is assumed, the issue arises of where it should be placed: at the electrical mid-point for instance; at the closest connection point; or at the furthest point from the substation. All of these options then impact on the length of the assumed ‘overhang’, so in the end it was decided that all of these options should be tested and the worst case taken. By way of illustration, figures 4 & 5 below show two possible options for calculating fault path, with a fault occurring just beyond the substation return connections. The diagrams illustrate a 4 track railway on the left converging to a 2 track railway on the right, with distributed return connections, and a ring of cables around the junction linking all of the tracks together. In both cases the assumption has been made that some of the running rails (and associated return

176 Power Supply, Energy Management and Catenary Problems

Next substation

Fault Substation

Figure 4:

Return connections at the left hand end.

Next substation

Fault Substation

Figure 5:

Return rail connections taken at the right hand end.

cabling) are unavailable for traction return (shown dashed), due to maintenance activities for instance. The solid lines are assumed to be part of the fault path and included in the calculations, whereas the dashed lines are excluded. The overhang is shown in red for each of the options.

4

Detailed process

4.1 Process flow The process of carrying out the protection setting calculations are discussed below and presented in the Flow Chart contained in Appendix A. 4.2 Preparation of a single track schematic diagram A single track schematic diagram (Fig 6) of the positive and negative circuits was first prepared and marked up with all the information necessary for the definition of the geometry, circuit elements (sections of rail(s), or cables) and their dimensions and parameters, i.e. circuit references, boundaries, mileage of important points, rail types, cable sizes, points of change of rail type and identification of the circuit elements together with their respective lengths.

Power Supply System Analysis, Design and Planning

Positive Circuit

177

Substation

E356

37M 2305 

STATION

(j)

UP MAIN

(d)

(a)

(b)

bu sb ar

37M 1652

(c) 37M 1795 

(f)

(e) 37M 2023 

(g)

37M 2419 

37M 3225 '

37M 4114 

DOWN MAIN

STATION

(n)

(k)

37M 1689 

37M 2305

37M 3631 

37M 3971 

37M 4012

-v e

Negative (return) Circuit

UP MAIN

Figure 6:

37M 1395 

(l) 37M 1446 

37M 1696 

(m) 37M 2023 

 (p)

37M 2221 

(o) 37M 2387

(q)

37M 3455 

37M 4061 

DOWN MAIN

Extract from a typical track schematic diagram of a traction power supply system (the shades on the negative circuit indicating different rail types).

(+)-ve

(+)-ve

R3POS

L3 POS L1

R3NEG

R1

R2

L2 (-)-ve

VA

R4

R5

VB

L3 NEG L4

L5

Figure 7:

Equivalent circuit.

The schematic diagram was then used to derive the equivalent electrical circuit (Fig 7). The left hand diagram indicated the absence or presence of a ‘Tee’-feed in the positive and/or negative circuits, left-hand or right-hand ‘Tee’ feed, whilst the right hand diagram identified the equivalent circuit components, used as input data to the calculation spreadsheet summarised in Table 1. For the purpose of traceability and clarity the schematic diagram contained a list of all the source drawings and documents from which the data has been extracted, together with any assumptions made. 4.3 Calculation of fault impedances The data from Table 1 is then input into the Calculation Spreadsheet (PBProCalc), the sheet automatically determining if a ‘Tee’ feed exists or otherwise

178 Power Supply, Energy Management and Catenary Problems Table 1: Equiv. Circuit Comp.

L1

L2

L3 POS L3 NEG L5 (Up) L5 (Down)

Ref.

Input data summary table. Type of circuit element (cable/rail)

Total length (feet)

(i)

Cable type ‘z’

75

75

(h)

Conductor rail type 100lb/yd

6163

6163

(g)

Conductor rail type 150lb/yd

889

889

(f)

Conductor rail type 100lb/yd

806

806

(e)

Conductor rail type 150lb/yd

396

396

(d)

Conductor rail type 150lb/yd

228

228

(c)

Cable type ‘z’

100

100

(b)

Conductor rail type 150lb/yd

79

79

(a)

Cable type ‘z’

500

500

282 282

282 282

2 x Running rail type CEN60E1

327

327

2 x Running rail type CEN60E1

7

7

294

294

(j) (n) (m) (l) (m) (l)

Conductor rail type 150lb/yd 2 x Running rail type CEN60E1

2 x Running rail type BS113A 2 x Running rail type CEN60E1

327

327

2 x Running rail type BS113A

250

250

2 x Running rail type 109lb/yd

51

51

4 x Cable type ‘a’

150

150

Type of circuit element (cable/rail)

Length (feet)

Total length (feet)

2 x Running rail type 109lb/yd

6216

6216

2 x Running rail type 109lb/yd

49

49

2 x Running rail type CEN60E1

340

340

L5 (cab)

(k)

Equiv. Circuit Comp.

Ref.

L4 (cab)

(s)

N/A

(r)

(q) L4 (Up) (p)

2 x Running rail type BS113A

41

2 x Running rail type BS113A

176

2 x Running rail type BS113A

1068

217 1068

2 x Running rail type CEN60E1

82

(o)

2 x Running rail type CEN60E1 2 x Running rail type CEN60E1

84 198

364

(r)

2 x Running rail type 109lb/yd 2 x Running rail type CEN60E1

6216 49

6216

(q) L4 (Down)

Length (feet)

(p) (o)

2 x Running rail type CEN60E1

41

2 x Running rail type CEN60E1

340

2 x Running rail type CEN60E1

176

2 x Running rail type BS113A

1068

2 x Running rail type BS113A

82

2 x Running rail type BS113A

84

2 x Running rail type CEN60E1

198

606

1068 166 198

and proceeds to compute the fault impedance seen by each circuit breaker feeding each electrical section (A and B) of the two track railway (in the example given). The result can be seen from Fig 8. 4.4 Derivation of protection settings Impedance relays and Falling Voltage Overcurrent protection were the two types of DC traction feeder protection that existed on the portion of infrastructure involving this project.

Power Supply System Analysis, Design and Planning

179

SECTION LAYOUT (L1, L2, L3POS, L3NEG, L4, L5) 1.563 +VE SECTION LENGTH (B to 'T') - L2 (miles) 0.058 -VE SECTION LENGTH (A to 'T') - L4 (miles) 1.571 -VE SECTION LENGTH (B to 'T') - L5 (miles) 0.119 +VE 'TEE-FEED' LENGTH - L3POS (miles) 0.053 -VE 'TEE-FEED' LENGTH - L3NEG (miles) 0.053 +VE SECTION LENGTH (A to 'T') - L1 (miles)

TEE-FEED CALCULATION 0.0026384 0.0076348 Tee-Feed Calcs Required (Yes/No)? NO 0.0380052 IB/IA at ZTmax SUBSTATION LIGHT LOAD VOLTAGE VLL (V) 790 VA MINIMUM VALUE (V) 285 VB MINIMUM VALUE (V) 285 VA & VB MAXIMUM VALUE [VLL+6%] (V) 837.4 K' MIN 0.3403391 2.9382456 K' MAX 69.71468077 69.714681 IB/IA at K' MIN 2.423407145 2.4234071 IB/IA at K' MAX ----ZA (Ohms) TEE-FEED CIRCUIT R3 [=R3POS+R3NEG] (Ohms) "EQUATION 23" VALUE

ZB (Ohms) ----ZTmax (Ohms) ----RADIAL FEED CALCULATION (remote cb tripped) MAX FAULT IMPEDANCE (A) VIA TEE (Ohms) 0.0804262 MAX FAULT IMPEDANCE (A) VIA MAIN (Ohms) 0.0862535 MAX FAULT IMPEDANCE (B) VIA TEE (Ohms) 0.0111041 MAX FAULT IMPEDANCE (B) VIA MAIN (Ohms) 0.0862535 MAXIMUM FAULT IMPEDANCE CROSS-BONDING ALLOWANCE (Ohms)

IMPEDANCE CB A (Ohms) IMPEDANCE CB B (Ohms)

0 0.0862535 0.0862535

ROUTE SETTING MAX TRACTION LOAD CURRENT IROUTE (A) SUBSTN SOURCE IMPEDANCE MIN (RS Ohms) SUBSTN LIGHT LOAD VOLTAGE MIN [VLL-10%] (V)

ZROUTE (Ohms)

6000 0.012 711 0.1065

'MAXIMUM SAFE' (half-kA from falling voltage curve table) 7 CIRCUIT BREAKER A (kA) 7 CIRCUIT BREAKER B (kA) RECOMMENDED SETTING CIRCUIT BREAKER A (kA) 6.5 6.5 CIRCUIT BREAKER B (kA)

Figure 8:

Extract from the protection setting calculations spreadsheet (PBProCalc) illustrating the calculation of fault impedances and protection settings.

180 Power Supply, Energy Management and Catenary Problems 4.4.1 Impedance relays  For impedance type relays, 7.5% was added to the value derived in the box headed ‘Maximum Fault Impedance’ to determine the actual figure (‘Maximum Safe’) to be used for the settings.  Recommended Settings were then derived manually by rounding up to the next 2.5mΏ, but in any event to be no more than 20% higher than those given for ‘Maximum Safe’ setting to ensure proper discrimination with the circuit breakers feeding the next electrical section.  In order to avoid unnecessarily changing existing settings, where the existing setting is between ‘Maximum Safe’ and 20% above ‘Maximum Safe’, then the recommendation has been to leave the setting unchanged  Additionally a Direct Acting Overcurrent Electromagnetic Trip is set at a higher ’common’ setting to cater for close up faults. 4.4.2 Falling voltage overcurrent protection  In the case of Falling Voltage Overcurrent protection which is principally an electromagnetic device mounted within and forming part of the mechanism of a DC circuit breaker, the settings were derived by converting the manufacturer’s standard protection curves to an impedance table (Fig 9) showing settings (kA) against impedance. The actual ‘Maximum Safe’ setting is determined by taking the impedance value from the calculation spreadsheet i.e. ‘Maximum Fault Impedance’ and then reading off the required setting in kA (rounded down to next kA value on the chart if the impedance is mid way between settings) 4.5 Route setting This is the setting required on a particular electrical section which will allow train services to operate without resulting in ‘nuisance tripping’ and is normally advised by the client. Any settings should normally be above this value. 4.6 Summarising of results The settings required for all of the electrical sections between adjacent substations (or substation and TP Hut) were then summarised on A4 sheets, in order that all the information relevant to those sections was available from one sheet. In all cases ‘Category 1’ safe settings were achieved (based on worst case data and feeding arrangements, hence not requiring any operational restrictions).

5

Further development

Since undertaking the original calculations, further work has taken place to determine whether network modelling would help in determining worst case fault scenarios in complex areas and possibly offer an alternative means of

181

Setting (A)

Power Supply System Analysis, Design and Planning

10000 9500 9000 8500 8000 7500 7000 6500 6000 5500 5000

46

52

58

65.5

73

81

89

98

107

118

129

Impedance (milliΩ)

Figure 9:

Chart of overcurrent settings versus impedance including half (kA) settings (for circuit breaker type RJR530L).

independently checking the spreadsheet results. Proprietary nodal analysis modelling software (B2Spice) was used for this purpose, as it requires little training and allows circuits to be built up easily from standard components. It also allows components to incorporate formulae, such that the operator only has to enter data in terms of along track length (feet, metres, miles, etc), rather than having to work out each component separately. Figure 10 above illustrates a typical circuit built using B2Spice, and has been arranged so that it reflects the schematic diagram in fig 6, with the positive circuit shown at the top and the return circuit (running rails) at the bottom.. Each track has been represented separately (in this case a 2-track railway), as it is quite often the case that each track will have different rail types, hence all changes in rail types, both positive and negative, can be fully incorporated into the model. If required, cross-bonding of running rails at regular intervals can be introduced, although generally omitted in the case illustrated, other than at the tee point. Once built, faults can be introduced where required and voltages at substations ‘A’ and ‘B’ adjusted to determine worst case fault conditions under radial or tee feed conditions.

182 Power Supply, Energy Management and Catenary Problems Tee pos

R2

R1 Conductor Rail

{6163*Conrail100}

{806*Conrail100}

{889*Conrail150}

{75*Cablepos}

889 ft (g)

6163 ft (h)

Cable (i)

806 ft (f)

{79*Conrail150}

{228*Conrail150}

{396*Conrail150}

228 ft (d)

396 ft (e)

{100*Cablepos}

Conductor Rail {500*Cablepos}

79 ft (b)

Cable (a)

Cable (c)

STATION 933.07

-24.30u {282*Conrail150}

282 ft (j+n)

VA

R3 (pos + neg) VB

{282*RunrailRT60}

Substation A

750

750

{49*Runrail109}

{340*RunrailRT60}

{1068*Runrail113}

B

{7*RunrailRT60}

{84*RunrailRT60}

{38*Cableneg } {0*Cableneg } {6216*Runrail109}

{41*Runrail113}

6216 ft (r) Running Rails

{6216*Runrail109}

{176*Runrail113}

606 ft (q) {41*RunrailRT60}

{49*RunrailRT60}

{82*RunrailRT60}

1068 ft (p) {176*RunrailRT60}

{340*RunrailRT60}

{82*Runrail113}

{1068*Runrail113}

{198*RunrailRT60} {327*RunrailRT60}

364 ft (o) {198*RunrailRT60}

{84*Runrail113}

{294*Runrail113}

Cable (k)

301 ft (l)

327 ft (m)

{250*Runrail113} {327*RunrailRT60}

Running Rails

{51*Runrail109}

R5

R4 Tee neg

Figure 10:

Detailed equivalent circuit (using B2Spice) showing elements extracted from the schematic and summary tables.

The models were found to produce identical results to the spreadsheets, hence proving to be a very effective way of checking the PB-ProCalc results. This calibration then, in effect enhances confidence in the PB-ProCalc for use as a reliable tool for this type of application.

6

Discussions and conclusions

It was originally thought that the enhancements and reinforcement to the negative bonding arrangements as described in [1], together with changes to conductor rail size, would logically lower the associated electrical impedances in comparison to the existing infrastructure. Benefits may have been realised in the form of allowing increases in (current based) protection settings, thus permitting higher train currents in section. However, the overall impact was seen to be minimal. This was due to a range of factors which included modifications to the S&C layout and associated detailed electrical feeding arrangements, together with the application of the methodology contained in the client’s process document. This was further supplemented by the corresponding guidance note [4], namely working within the parameters of 7.5% when undertaking the calculations, thus allowing retention of many existing settings. If one was to stay within parameters of 2.5%, as suggested by [3] then definite changes would have been warranted. Consequently, the resultant sensitivity of the calculations to the actual negative bonding reinforcement was seen to be relatively low. Moreover, the majority of settings calculated were noted as being close to existing and therefore not necessitating any changes. Only in a few instances were recommendations made to change settings (actually requiring settings to be reduced). Although no major changes were perceived, this exercise was still seen to be of great benefit in that it provides a solid basis for future applications

Power Supply System Analysis, Design and Planning

183

when ascertaining these types of protection settings. This approach was considered pragmatic and gave a scientific means of calibration between the spreadsheet mathematics and software. Moreover, the method allows for further refinement and development as changes take place in the future. The further development work undertaken has provided additional confidence in the spreadsheet and methods developed, offering an alternative approach for consideration when undertaking calculations in the future.

Acknowledgements The authors would like to thank Network Rail for their permission to publish this paper. The support of Thomas Palfreyman, Head of Electrification, PB Ltd in developing this calculation process and spreadsheet, and in reviewing this paper, is also recognised. Much of this paper has been reproduced from the paper entitled ‘DC protection calculations – an acceptable approach’, authors R. Leach, D. Tregay & M. Berova, first presented at the Eleventh International Conference on ‘Computer System Design and Operations in the Railway and other Transit Systems’ (COMPUTERS IN RAILWAYS XI) and can be found in section 6, page 425, of the book of conference papers (WIT Transactions on the Built Environment, Volume 103), © 2008 and is reproduced with permission of WIT Press, Southampton, UK.

References [1] Development of an Improved Traction Return System, Eur Ing Raymond Leach and Dennis Tregay, paper Railway Engineering – 2007, 9th International Conference, London, UK, 20/21 June 2007. [2] NR/SP/ELP/21051 ‘Calculation of Protection Settings for DC Circuit Breakers’, Issue 2 dated Dec.2005 [3] NR/GN/ELP/27006 ‘Calculation of Protection Settings for DC Track Feeders, Issue 2 dated April 2006 [4] Network Rail Southern Region Power Supply Upgrade Project - Guidance Note A437-00-DC-32031 ‘DC Protection Setting Calculation’, Issue C1.0 dated 11 May 2004 [5] Network Rail Computer Programme “RUN FILE DC3.EXE” [6] Parsons Brinckerhoff (PB) Methodology for Undertaking Protection Setting Calculations associated with re-modelling and negative bonding changes (Issue 1 dated 07/09/06)

184 Power Supply, Energy Management and Catenary Problems

Appendix A: Flow-chart of the protection setting calculation process for the Tee feed case Provide existing records drawings, including: •Comprehensive Track Diagrams •Arrangement of conductor rail, hook switches and jumper cables •Arrangement of track circuits & negative bonding •Others, e.g. Signalling plans

Provide survey drawings showing the existing arrangement of the permanent way, conductor rail and negative bonding

Provide drawings showing the As Built arrangement of the Permanent Way, Conductor rail and Negative Bonding

Provide existing records for protection settings calculations, including type of protective devices and current settings

Provide relevant standards, guidance notes and other instructions

Obtain all necessary input data

Produce a schematic diagram for each electrical section based on the Comprehensive Track Diagram (CTD), including the conductor rail and the negative bonding layout showing points, substations, TPHuts, cable connections, types of conductor and running rails, etc.

Is the electrical section over switches or crossings?

Yes

Analyse the electrical section layout to determine worst case scenario

No

Establish the type of electrical section equivalent diagram Using the existing and As Built drawings populate the schematic diagrams with the coordinates (in Miles and Feet) of important points, including mile posts, points of cable connections, points of change of conductor / running rail type, point tips, etc. A

B

Power Supply System Analysis, Design and Planning

185

B A

Using the information in the schematic diagram populate the Summary table with the types and lengths of the equivalent circuit components. Compare the data describing the equivalent components in the schematic diagram with those in the existing protection settings calculation records Yes

No

Do the data agree?

Establish the reason for discrepancy

Is the discrepancy due to alignment remodelling, different contact rail or negative bonding design or repositioning of the equipment?

No

Yes

Carry out a check & correct error(s)

Independent check of the schematic diagram and input data

Yes Error(s) found?

Running PB DC Protection Setting calculation spreadsheet

Run NR Protection Setting calculation software (Tee-feed)

Protection settings – Results (B)

No

Protection settings – Results (A)

Comparison of protection settings results (A) and (B)

No

Do Results (A) agree with Results (B)?

Yes

Overall independent check

Note: In plain line feeding case latter comparison stage is omitted.

This page intentionally left blank

Power Supply, Energy Management and Catenary Problems

187

Author Index Abrahamsson L. ....................... 157 Albrecht T. ................................... 3 Bae C. H. ................................... 35 Berova M. ................................ 171 Bosselmann T. ........................... 87 Cayuela L. P. ............................. 55 Cucala A. P. ............................... 55

Kwon S. Y. ................................ 35 Leach R.................................... 171 Luethi M. ................................... 75 Lukaszewicz P. .......................... 25 Matsuda K. .......................... 45, 65 Miyatake M. ........................ 45, 65 Nishi K..................................... 101

Danielsen S. ............................. 145 Domínguez M. ........................... 55

Okada Y. .................................... 13

Fernández A. ...................... 55, 113 Finlayson A.............................. 123 Fosso O. B. .............................. 145

Park H. J. ................................... 35 Pilo E. .............................. 113, 135 Puschmann R. ............................ 87

Goodman C. J. ......................... 123

Rouco L. .................................. 113

Haga H. ...................................... 65 Han M. S. ................................... 35 Hertsch H. .................................. 87 Hisatomi K. ................................ 13

Sato Y. ..................................... 101 Shimada T. ............................... 101 Söder L. ................................... 157

Jimenez-Octavio J. R. .............. 135 Kaiser J. ..................................... 87 Kim Y. K. .................................. 35 Ko H. ......................................... 45 Koseki T. ................................... 13

Theune N. .................................. 87 Toftevaag T. ............................ 145 Tregay D. ................................. 171 Weiland K. ................................. 95 White R. D. .............................. 123 Willsch M. ................................. 87

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