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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

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

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

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 depar-ture 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 opti-mal 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.

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 non-inverting 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. Passen-gers 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 opera-tion of the train (manual or automatic).

To overcome these two obstacles, this paper proposes an approach using train run-ning time control instead of train dwell time control for synchronizing 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 con-sumption is briefly presented. For the minimization of system energy concon-sumption 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.

timet necessary dwell time at station additional running time allows additional energy saving powerP

b) running time control

power curve of second train

Figure 1: Dwell time modification (a) vs. running time modification (b) for improved usage of regenerative energy.

2 Train running time modification using Dynamic

Programming

The problem of distributing train running time reserve along a line may be regarded as multi-stage decision problem, because at each stop it has to be decided, how much reserve to spend on the next section of the ride. For many cost functions, including the single train’s energy consumption, this problem can be solved using Dynamic Programming [7].

Travel time reserve already spent when reaching an intermediate stop presents the current system state, the transition between two succeeding stations (stages of the process) is realized by a train ride with a certain amount of running time reserve. The optimal distribution of running time reserve is computed recursively from the terminus station with all reserve used up to the first station, so an optimal decision is computed for every possible process state. This makes the algorithm suitable for online control.

3 Using Genetic Algorithms for train running time control in

constant headway operation

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

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

For coding, each unit of running time reserve (e.g. 1 unit = 1 s) makes up one gene. The information the gene contents is the section of the track on which this particular unit of running time reserve is to be spent. This coding results in a binominal distribution of the different timetables favouring timetables with equally distributed running time reserve. This contributes to finding reasonable and not extreme solutions.

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

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

The size of the search spaceN for the particular problem of distributing k units

of running time reserve amongn sections of the line is equal to a combination with

repetitions N =
n + k − 1 k  . (1)

For a typical problem like the one presented in the next section the solution can be found using only 25 inviduals in one population for 50 generations, this

is extremely fast taking into account the size of the search spaceN ≈ 1014. The

solution of one such problem takes about 60 - 90 mins using a MATLAB imple-mentation on a 2.4 GHz Standard PC.

4 Case study

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

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

300 600 900 1200 1500 160 180 headway in s 300 600 900 1200 1500 0 25 headway in s

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

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

4.1 Variation of headway

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

4.2 Variation of synchronization time for a given headway

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

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

0 50 100 150 200 365 375 385 395 405 synchronization time in s energy consumption in kWh (sum of all substations)

Minimal energy cons. for single train

Opt. criterion 15−min−av. power Opt. criterion energy consumption 0 50 100 150 200 3 3.5 4 synchronization time in s 15−min−average power in MW (sum of all substations)

Opt. criterion 15−min−av. power

Opt. criterion energy consumption

Minimal energy cons. for single train

0 50 100 150 200 70 80 90 100 synchronization time in s regenerative rate in percent

Opt. criterion energy consumption

Opt. criterion 15−min−av. power

Minimal energy cons. for single train

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

4.3 Variation of train running times for given headway and synchronization time

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

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

of the sum of 15-min-average power of all substations of 17%.

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

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

4.4 Simulation studies taking into account stochastically varying station dwell times

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

At first, it is assumed that, given a certain timetable, the strict keeping of this

timetable is obligatory. The reserve to spend on the next sectiont_resis calculated

with

tres= scheduled arrival time − shortest travel time − actual departure time.

(2)

When negativet_resoccur, time-optimal driving is applied. This corresponds to

a very simple P-controller.

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

2 4 6 8 10 section no. 0 20 40 60 sec 2 4 6 8 10 section no. 0 20 40 60 sec 0 500 1000 1500 s 20 40 60 km/h 0 500 1000 1500 s 20 40 60 km/h 0 200 400 s 2 4 6 MW demanded power used regenerated power wasted regenerated pow. 0 200 400 s 2 4 6 MW demanded power wasted regenerated power used regenerated power 0 200 400 600 800 s 1 1.5 2 MW SS1 SS2 SS3 SS4 0 200 400 600 800 s 1 1.5 2 MW _SS4 SS1 SS3 SS2

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

b) Vehicle speed over time in the two directions.

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

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

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

10s 15s 20s 25s 390 10s 15s 20s 25s 3.2 3.3 multi−train coordination 10s 15s 20s 25s 65 70

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

different variations of dwell time.

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

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

As the GA optimized timetable fulfils its purpose by optimally coordinating starts and stops in the order of seconds, exact timekeeping is the only possibility to reach this under stochastically varying dwell times. Whereas for smaller varia-tions this can be reached by the simple controller, higher variavaria-tions call for a more sophisticated controller combining the philosophies of energy saving of the single train and coordination of starts and stops. The development of such a controller is part of future work.

5 Conclusions

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

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

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

Acknowledg ments

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

References

[1] UITP, Reducing energy consumption in Underground systems - an important

contribution to protecting the environment. Proc. of the 52nd _{International}

Congress, Stuttgart 1997.

[2] Chang, C.S., Phoa, Y.H., Wang, W. & Thia, B.S., Economy/ regularity fuzzy-logic control of DC railway systems using event-driven approach. IEE

Proc.-Electr. Power Appl., 143(1), pp. 9-17, 1996.

[3] Firpo, P., & Savio, S., Optimized train running curve for electrical energy sav-ing in autotransformer supplied AC railways. Proc. of the IEE Conference

Electric Railways in a United Europe, pp. 23-27, 1995.

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

Confer-ence, pp. 165-176, 1998.

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

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

[7] Albrecht, T. & Oettich, S., A new integrated approach to dynamic schedule

synchronization and energy saving train control. J. Allan, R.J. Hill, C.A.

Breb-bia, G. Sciutto, S. Sone, J. Sakellaris (eds.), Computers in Railways VIII, WIT Press, pp. 847-856, 2002.

[8] Biella, W., Die rechnergesteuerte adaptive Fahrkennlinienvorgabe zur

Ener-gieoptimierung bei DC-Nahverkehrsbahnen (Diss.) TU Berlin, 1988.

[9] Cai, Y., Irving, M.R. & Case, S.H., Iterative techniques for the solution of complex DC-rail-traction systems including regenerative braking. IEE

Proc.-Gener. Transm. Distrib., 142(5), pp. 445-452, 1995.

Power management control in DC-electrified

railways for the regenerative braking systems

of electric trains

Y. Okada

, T. Koseki

& K. Hisatomi

1_{The University of Tokyo, Japan}

2_{Shin-Keisei Electric Railway Co. Ltd., Japan}

Abstract

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

1 Regenerative braking in DC-electrified railway

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

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

Energy storage by fly w heels, batteries and double layer capacitors

P ow er consum ption w ith brake chopper and resistance S ubstation P ow er system Loads Im provem ent of squeezing control of regenerative pow er R eduction of line resistance R eduction of voltage regulation Introduction of com m utated rectifier

Typical pow er flow in present system

S ystem s for efficient energy usage and m aintenam ce reduction

S ystem s for only m aintenance reduction

Energy storage by fly w heels, batteries and double layer capacitors

P ow er consum ption w ith D C chopper and resistance

Figure 1: Typical power flow on braking.

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

2 Problems of squeezing control of regenerative power

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

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

Figure 2: Typical characteristic of squeezing control.

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

1. traction controllers reduce regenerative power excessively in low-speed range because they reduce AC motor current directly instead of their DC current,

2. traction controllers reduce motor current at lower voltage than maximal voltage limit of feeding circuit as shown by the solid line in Fig.2 and, 3. actual traction controllers often reduce motor current at lower voltage than

the conservative voltage limit shown by the solid line in Fig.2.

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

3 Improvement of squeezing control

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

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

1. the position and velocity of the trains, voltage at pantograph, DC current of traction controller and power regeneration of the regenerating train, 2. running profile of the line on which the regenerating train exists, 3. control method of every train on the line,

4. the time when powering trains in the electrical circuit reduce their power consumption and

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

In the above, the information in 1 can easily be measured, and the information in 2 and 3 can be stored on board as data of traction controller. However, the information given in 4 and 5 needs to be estimated from the information in 1, 2 and 3. And, the characteristics of squeezing control of regenerative power must be determined, based on the information.

One must propose how to estimate the information in 4 and 5 and how to determine the characteristics of squeezing control of regenerative power. The voltage regulation at the pantograph in the case of powering trains with various control methods, reduce their power consumption for determining characteristics of squeezing control of regenerative power in the following part of this paper.

Filter capacitor Filter reactor Internal resistance Feeder line (variable)

S ubstation Feeder line

(1km ) B raking train Ｅfc Ｉ0 Ｅｓ P ow ering train S queezing control of regenerative pow er Traction controller Ｉl Ｉｓ Ｉr Ｅfc

Ｉ₀ : C urrent operation from braking operation

Ｉch

Ｅfc

B rake chopper operation B raking resistor

Ｉch

Ｉr

Figure 3: Electrical circuit for examination.

4 Voltage regulation at the pantograph

4.1 Electrical circuit for examination of voltage regulation

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

Filter capacitor

Traction controller (b) Field chopper control R esistor control (a) V V V F-inverter control

Ｉ_a

Ｉa

Figure 4: Equivalent circuits of a powering train.

Ia[A ]

1600 1600

Tim e[s] Tim e[s]

50

0 2.5 3.5 5

800

50

0 2.5 2.55 2.60 2.65

（ａ）V V V F-Inverter control （c）R esistor　control

5

1600

Tim e[s] 50

0 2.5 3.1 5

（b）Field chopper control

Ia[A ] Ia[A ]

1.0s 0.6s 50m s

Figure 5: Characteristics at reduction of power consumption.

Eｆｃ C haracteristic of squeezing control I0 I₀₀ >I₀ →　I =I₀₀ I₀₀<I₀ →　I =I₀ I00 I 10V Emax Eｆｃ[V ] I00[A ] -2000 0 1 1+Ts (T=30[m s]) Ir

(a) O peration logic for squeezing control of regenerative pow er (b) C haracteristic of squeezing control Figure 6: Squeezing control for VVVF-inverter and chopper controlled train.

4.2 Voltage regulation at pantograph of the braking train 4.2.1 Case of VVVF-inverter controlled powering train

Fig.6 (a) shows the operation logic of how to reduce the regenerative power when the powering train controlled by VVVF-inverter stops its power consumption. In this logic, the V-I characteristic in Fig.6 (b) is assumed as the “characteristic of squeezing control” in Fig.6 (a). The first order delay, the time constant of which is assumed T=30[ms], represents the response of the traction

motor current. In addition, the distance between the powering and the braking trains is 2 km.

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

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

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

4.2.2 Case of powering train controlled by field-current chopper

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

reduce its regenerative power following the design of its squeezing control.

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

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

4.2.3 Case of resister-controlled powering train

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

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

Eｆｃ I₀ I00 _I d dt P roportional gain 0.3 Lim iter 1 Lim iter 2 + + C haracteristic of squeezing control I00 >I0 →　I =I00 I00<I0 →　I =I0 I_r 1 1+T₁s (T₁=1[m s]) 1 1+T₂s (T₂=30[m s]) I₀₀

Figure 11: Operation logic for squeezing control (2).

Fig.12 shows voltage at the filter capacitor of braking train when the Emax indicated in Fig.6 (b) is 1600V and the distance between the powering and the braking trains is 2km. Fig.12 also illustrates that the filter capacitor of braking train rises drastically because the powering train spontaneously reduces its power consumption in several milliseconds. Therefore, Emax must be less than 1600V so that traction controller can reduce regenerative power conservatively when resister-controlled train, instead of a VVVF-inverter controlled train or a field-chopper controlled one, cuts off its power.

Figure 12: Voltage at the filter capacitor (3).

In addition, Fig.13 shows maximal voltage at the filter capacitor of the braking train when the distance between the powering and the braking trains varies if Emax is 1600V. This figure means that the longer the between the powering and the braking trains is, the lower the maximal voltage at the filter capacitor of the braking train is, since the line resistance proportional to the distance between the two trains restricts the power to be transferred from the braking to the powering train.

Fig.13 also demonstrates that the longer the distance between the powering and the braking trains is, the higher the Emax can be. Fig.14 shows maximal Emax to avoid excessive voltage at the filter capacitor of the braking train. This figure means the longer distance between the powering and the braking trains allows

Figure 13: Voltage rise.

STA R T

E_max=1600[V ]

C ircuit sim ulation

M axim al E_fc < 1900V

(during sim ulation)

E_max = E_max-10

End

E_max = E_max+10

N o Yes

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

Figure 14: Possible Emax to avoid excessive voltage.

1850

0 1860

I_ch[A ]

E_fc[V ] 150

Figure 15: V-I characteristic for a chopper-control of a braking resistor. If the braking train has supplemental braking resistor, whose characteristic for operation is assumed as Fig.15, Emax=1850[V] is possible for all the investigated

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

5 Conclusion

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

1. when a powering train, which is controlled by VVVF inverter or field chopper, stops its power consumption, braking train can successfully reduce its regenerative power with squeezing control whose Emax is close to maximal voltage limitation,

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

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

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

6 Future

work

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

1. the time when powering trains in electrical circuit stop their power consumption, and

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

Acknowledgements

and cooperation in the investigation in this paper.

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

[3] Y. Okada, T. Koseki, S. Sone, Energy Management for Regenerative Brakes on a DC Feeding System, STECH’03, pp 376-380, 2003.

Impact of train model variables on simulated

energy usage and journey time

P. Lukaszewicz

Aeronautical and Vehicle Engineering, KTH, Stockholm, Sweden

Abstract

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

Keywords: train modelling, train data, sensitivity, power consumption, energy usage, running time, simulations, ERTS.

1 Introduction

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

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

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

- Adhesion.

- Tractive force (due to variation in catenary voltage).

- Braking gain time, which is the time it takes to obtain the desired braking force, from when the driver starts braking.

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

Section 2 describes the method and models. The results are presented in section 3 and are discussed in section 4.

2 Method and models

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

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

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

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

2.1 The train model

The train model represents a loco hauled freight train of mixed consist.

The locomotive is of type SJ Rc4 and the tractive force diagram for two different catenary voltages and powering levels is shown in Figure 1, together with the tractive force limit,

F

The calculated magnitude of the tractive force, Fw, takes into account the powering level, effect of speed, catenary voltage and the tractive force,

F

0 5 10 15 20 25 30 35 40 0 50 100 150 Ft ( kN ) v (m/s) (ERTS) Notch 9, 15 kV Notch 3, 15 kV Notch 9, 12 kV Notch 3, 12 kV

Figure 1: Tractive force diagram. Notch 9 is the maximal powering level. This means that the train speed is the same as the tangential speed at the peripheral of the wheels of the locomotive. The tractive force at the wheels, is calculated by:

)

,

min(

F

F

F

=

(

)

∑

∑

∆

t

during a simulation. K is a constant accounting for the rotational masses, a is the acceleration,

ζ

η

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

∑

∆

=

t

T

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

Length, incl. loco 418.5 m

Mass, gross incl. loco 1197 t

Mass of locomotive SJ Rc4 79 t

Axles, trailing 52

Max speed 100 km/h, 27.8 m/s

Axle load, average 21.5 t

Braking gain time, nominal 15 s

Braking release time, nominal 30 s

Braking level used 1/3 of max

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

2.2 Track model

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

Table 2: Speed restrictions for the track model. Distance (m) speed (km/h) 0 100 20490 40 21364 100 38152 70 39288 100 44106 70 44566 100 51322 40 52534 100 88000 100

Figure 2: Speed profile from simulation with nominal input data. Table 3: Results from simulation with nominal input data. Constant grade (‰) Etot (kWh) T (s) Mean speed (m/s)

0 1723.5 3597 24.47

5 3329.9 3758 23.42

3.2 Running resistance

The nominal running resistance, F_R0, of the train set is obtained from full-scale measurements [1] and is calculated as a function of speed, v, by:

2

0 11961 229.1v 41.4v

FR = + + (4)

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

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

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

3.3 Adhesion

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

0 7.5 0.9( 0.161) 44 3.6v α = + + (5)

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

3.4 Line voltage

The tractive force of the locomotive SJ Rc4 is affected by the line voltage, see Figure 1. A voltage drop decreases the tractive force from the train speed of 17 m/s and up.

The variation of running time and energy usage due to variation of line voltage is shown in Figure 5. The nominal voltage is 15 kV.

3.5 Braking gain time

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

Figure 4: Impact of adhesion on energy usage and running time for grade 0 and 5‰.

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

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

3.6 Braking release time

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

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

4 Conclusions

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

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

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

[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.

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

Abstract

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

Keywords: regenerative inverter, electric railway system, train performance simulation, power flow simulation.

1 Introduction

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

powers. Thus, they should be installed at sections with a long continuous slope or where regenerative power loss in the resistor bank becomes a problem. In order to determine the appropriate installation positions, number and capacity of the regenerative inverter, it is necessary to calculate the accurate regenerative power generated in a subway line.

This paper suggests determination schemes of the capacity and installation positions of regenerative inverters installed in 1500V DC electric railway system. We suggested a method that approximates using parameters related to substations where regenerative inverters are installed, railway lines and operating motor cars, and another that calculates using regenerative power obtained from Train Performance Simulation (TPS) and Power Flow Simulation (PFS) developed by Korea Railroad Research Institute for light rail transit system [1]. We carried out TPS and PFS for Seoul subway lines 5 and 6 and calculated the regenerative power and decided the substations where regenerative inverters should be installed and the suitable power capacity to be installed.

2 Power capacity of the regenerative inverter

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

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

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).

h v l n s   60 [trains/hour] (1)

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

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,

k a l w s n Pm2    (1 ) [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  ranges 1

from 0.23 to 0.20, and regenerative braking efficiency rate  from 0.67 to 0.63 2

[2]. Using these data, the capacity of a regenerative inverter can be calculated as eqn. (3), where W denotes the total regenerative power generated from the section covered by the regenerative inverter. W includes the regenerative power consumed by nearby accelerating trains and power loss in the resistor bank. Accordingly, the capacity of the regenerative inverter should be larger than W considering the operation condition of the line.

2 1    P_m W [kW] (3)

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

w s ) r ( . F_b 98 31   [N] (4)     367 v F P_b b [kW] (5)

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

inv b b V P I  [kA] (6)

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

Number of cars, s 8 (4M4T) Running resistance, r 10kg/ton Headway, t_h 2.5 min Maximum speed, v_m 80km/h

Weight,w 48 ton/car Commercial speed, v_s 35km/h Decelerating rate,  0.97 m/s2 Regenerative operation

voltage,V_inv 1650V

Train ton-kilo capacity, k 50kW/1000ton․km Power regeneration rate, 1 0.20

Power delivery efficiency,  0.85 Regenerative braking

efficiency rate, 2 0.65

4 Power flow simulation method

This section explains how to determine the capacity of a regenerative inverter using TPS and PFS. PFS is performed by changing the power capacity and the installation number of regenerative inverters, and the regenerative power loss of a railway line is calculated. The loss ratio of regenerative power means the ratio of regenerative power consumed as heat on the train to the whole regenerative power generated as shown in eqn. (7). After the optimal position and the number of regenerative inverters are determined, as a way of reducing the calculated loss ratio of regenerative power to the maximum, the root mean square of regenerative power (RMS power) and peak power are calculated. The effective regenerative power per hour calculated by eqn. (8) determines the continuous rating of the regenerative inverter, and is used to determine the peak power rating based on the maximum regenerative power rate and the braking time of motor cars. 100 1 _         reg inv P P R (7)

where Preg denotes the 1-hour average value of the regenerative power generated

in a subway line and Pinv denotes the 1-hour average output power of

regenerative inverters in a subway line. In order to decide the continuous and intermittent peak power capacity of the regenerative inverter, the mean square value of the regenerative power generated in a substation is calculated as eqn. (8).



Here, P is the root mean square of regenerative powerP_reg(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

Decrease Installation Number of Regenerative Inverter

Calculate Loss Rate of Regenerative Power

Calculate Maximum and Root Mean Square

value of Regenerative Power

Decide installation substation

Decide Power Rating of Regenerative Inverter

Figure 4: Flowchart for regenerative inverter capacity. 10 12 14 16 18 20 22 24 26 28 30 1400 1500 1600 1700 1800 line v ol ta ge[ V ] 10 12 14 16 18 20 22 24 26 28 30 -4000 -2000 0 2000 4000 6000 8000 co m sum ed p ower[ kW ] Time[min]

Figure 5: Seoul line 6 substation 8 without a regenerative inverter. Once the position and number of regenerative inverters to be installed are determined, the rated capacity of the regenerative inverter and the peak power capacity are calculated through the procedure in fig. 4. The rated capacity of a regenerative inverter sets the root mean square value of regenerative power obtained from the substations, and the peak power rating is determined by the ratio of the peak regenerative power to the root mean square value of regenerative power. In addition, because the time for the rise of catenary line voltage caused by the dump regenerative power of the subway substations does not exceed 1 minute, the peak power rating is assumed to continue for 1 minute. We performed TPS and PFS using data on trains and lines of Seoul subway lines 5 and 6. Figs. 5 and 6 show the catenary line voltage and the power consumption waveform of substations according to whether a regenerative inverter is installed or not. In fig. 5, the regenerative power generated by the power braking of motor cars is increasing the catenary line voltage instantaneously. Fig. 6 shows that regenerative power is absorbed by the substation and the variation of catenary line voltage is reduced.