Electric load estimation techniques for high-speed railway (HSR) traction power systems

1260 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 5, SEPTEMBER 2001

Electric Load Estimation Techniques for High-SpeedRailway (HSR) Traction Power Systems

Pao-Hsiang Hsi, Member, IEEE,and Shi-Lin Chen, Senior Member, IEEE

Abstract—As modern [e.g., high-speed railway (HSR)] tractionpower systems (TPS) become more and more comparable in sizeto grid capacity, dynamic load estimation (DLE) has become notjust an important tool for TPS planning, but also an indispensabletool for utility companies to evaluate traction system’saccurateun-balance impact on the grid. Without a good DLE algorithm, unbal-ance impact can easily be underestimated and causes power systeminstabilities. A good DLE must be carried out with a power en-gineering perspective while incorporating real railway operatingprinciples and practices. However, due to the lack of well-docu-mented literature on this subject and the interdisciplinary natureof DLE, it usually presents a difficult task for the system planner.As such, this paper presents an accurate DLE algorithm capableof achieving these goals, while providing a complete coverage ofall the principles and parameters used during the derivation. Themethodology developed here is applicable to HSR TPS and to con-ventional railways as well with minor modifications. Unbalance im-pact evaluation of the new Taiwan HSR is presented in the last partof the paper, while further application of the proposed DLE algo-rithm is also proposed.

Index Terms—High-speed railway, load estimation, tractionpower systems, unbalance load.

I. INTRODUCTION

T AIWAN will start building its first high-speed railway(HSR) system in the middle of 1998. During the early

planning stage of this project, Taiwan Power Company(TPC—Taiwan’s only electricity supplier) raised great con-cern about the unbalance effect that HSRs large and manysingle-phase loads (45 units of 14MW trainsets moving at 300k/h) may have on Taiwan’s power grid. To accurately evaluatethe grid impact as well as to assess the dynamic behavior ofHSR traction power system (TPS), the HSR Engineering Bureauof the Ministry of Transportation, Taiwan, awarded a researchcontract to NTHU to perform a detailed study on HSR dynamicload estimation (DLE) and Taiwan HSRs unbalance impact.

DLE plays a very important role in the successful operationof HSR. A good DLE can ensure that the traction power systemis properly designed and that utility grid is adequately strongto withstand the big unbalance impact that HSR impose on thegrid. This importance is more emphasized in modern days asTPS become more and more comparable in size to grid capacityand its unbalance impact is big enough to cause generator shut-down (and, therefore, system instability).

To achieve good DLE, the HSR system must be analyzedfrom a power engineering perspective while incorporating realrailway operating principles and practices. However, little liter-

Manuscript received April 10, 1998; revised August 22, 2001.The authors are with the Electrical Engineering Department, National

Tsing-Hua University, Hsin-Chu 300, Taiwan.Publisher Item Identifier S 0018-9545(01)08800-4.

ature had been published on this subject while the interdiscipli-nary nature of DLE and the many undocumented practices makeDLE a quite difficult task. As such, this paper aims to present analgorithm capable of achieving good DLE. Pseudocodes are in-cluded to demonstrate the implementation details, while all theparameters and formula used to derive them are clearly definedand provided in this paper.

II. TRAFFIC SIMULATION

Unlike load forecasting for distribution systems whose maintask is probabilistic evaluation of load amount, individual loadsin HSR systems can usually be estimated quite accurately bytheir speed and, as such, the main task of DLE is the determina-tion of on-line train speeds and positions.

Train motion can be best described by Lomonossoff’s Equa-tion [1]

(1)

wheremass of the trainset;dynamic mass of the trainset (typically5% 10% the value of ) representing therotationary energy stored in the rotating parts ofthe trainset;speed;traction or braking effort output;

“ ” running resistance coefficients of thetrainsets;gravity;slope at current position;curvature at current position converted to equiv-alent slope according to the following [2].

(2)

in whichwheel-rail adhesion coefficient (Normal range: 0.10.3);track gauge(m);axial length(m);radius of curvature (m).

All of the abovementioned parameters can be easily found onsystem specifications or manufacturer’s datasheet except for therunning resistance (RR) coefficients“ .” Various formulashave been developed for the calculation of these coefficients (ifthey are not available from manufacturer’s datasheet), but the

0018–9545/01$10.00 © 2001 IEEE

HSI AND CHEN: ELECTRIC LOAD ESTIMATION TECHNIQUES FOR HSR TRACTION POWER SYSTEMS 1261

Fig. 1. Digital driving mode.

most popular one is the Modified Davis Formula proposed byCommittee 16 of the AREA [3]

(3)

whererunning resistance (in Newtons/metric ton);weight per axle (metric ton);speed (k/h);number of axles ( total car weight onrails);air resistance coefficient with values in the range of0.07 0.16.

The RR of the whole trainset is derived by adding up the RRof each car, including the locomotive(s). For modern trainsets,it has been recognized that (3) tends to overstate resistance andas such an adjustment factor of 0.80.85 is usually applied toderived the RR [3].

Driving Mode: Besides knowing the dynamic equation de-scribing the train motion, to do DLE, we must also determinehow the trains will be driven with the given timetable and systemspecifications. Although the driving mode depends heavily onthe signaling system design, a common assumption of “digitaldriving mode,” which represents maximum usage of the line ca-pacity by the specified trainset is usually made for DLE pur-poses [4].

In “digital driving mode,” it is assumed that there is nospeed limit along the journey except those dictated by trainsetcapacity. The trains will always output its maximum trac-tive/braking effort during acceleration/deceleration whilemaintaining a constant cruising speed (Vtop) in between thesetwo regions (see Fig. 1).

Referring to Fig. 1, if the acceleration curve and decelerationcurve can be described by and , respectively( , ), then the whole trainrunning profile is determined once the cruising speedis found. The in Fig. 1 can be solved mathematicallyby finding the which satisfies ,

, and

(4)

where “ ” and “ ” are the distance and journey time be-tween the two stations, respectively.

The and for each train station can be foundby simulating (1) in the vicinity region of each train station and

curve fitting. They are usually about the same for each stationas the slopes in the train station areas are usually kept small toattain better acceleration and deceleration characteristics.

Grade Deceleration Mismatch:Many DLE programs useFigs. 1 and (4) as the running profile of trains. Though thetraffic pattern in Fig. 1 can be considered as the basic trafficpattern for any train running between its two stops (or a “hop”),that profile is only feasible when the power requirement doesnot exceed train specifications (Pmax) at any time in Regions Iand II. The power requirement of trains in the acceleration andcruising period is described by the following ):

(5)

whererunning resistance at speed;gravity force at current position“s,”;acceleration;mass plus dynamic mass of thetrainset.

If at any time during the journey, deceleration willoccur and this will make (4)s approach and the traffic profile inFig. 1 unrealistic.

Fig. 2 shows the proposed DLE algorithm. The algorithm isexecuted independently for each hop to simulate the instanta-neous speed, position, and power requirement of train for thathop. Aggregate load profile at the substation can be derived bysumming up the power requirement of all trains residing in thedesignated supply section(s) at a given time.During the acceler-ation period (Region I), power requirement is seldom a problemas both and are small while the speed multi-plication is also low. However, during the cruising period (Re-gion II), power requirement can easily exceed for gradesgreater than 22.5% due to the high speed multiplication in (5).When , deceleration will occur and causes mismatchbetween the distance traveled andDist. A simple checking cri-teria for a “deceleration-free” hop is that [from (5)]

(6)

at all times, where is the average speed of the hopmultiplied by an adjustment factor

to reflect the fact that cruising speed must tocompensate for the low speed in Regions I and III.

(7)

Timetable Buffer’s Effect:Besides the grade decelerationmismatch problem mentioned above,the DLE result basedon (4)s approach will usually underestimate the real load aswell. This is because if the minimum time required to drivefrom station A to station B by the specified trainset ish, anextra 0.1 0.15 h will always be allocated in the timetableto allow some flexibility for the driver. Train drivers almostalways keep this 1015% extra buffer time for the latter part ofthe journey as a “reserve time” [4]by cruising at a higherthan that calculated by (4). As a result of this practice, power


Fig. 2. Proposed DLE algorithm (pseudocode included).

requirement in more than 80% of the journey time (Region II)is usually underestimated.

To account for the timetable buffer effect and the distancemismatch due to deceleration in the big slope region, a modifiedDLE traffic simulation engine must be proposed. This is thetopic of the next section.

III. PROPOSEDDLE ALGORITHM

Pseudo code is included in Fig. 2 to point out important pro-gramming details and for easy reference to the reader. Detailsof Fig. 2 is explained in the following subsections.

Fig. 3. Original Vtop scheme.

Fig. 4. Modified Vtop scheme.

Variable Initialization (a): As mentioned previously, Fig. 2is carried out on a “hop-by-hop” basis due to the independentnature of each hop. In Block (a), and (the journey dis-tance and time) of the current hop is inputted to the algorithmwhile the position and time of the train are initialized tothe departure position and time.

Determine (b): Consider a trainrunning at a constantspeedfrom one station to another. To complete km inh, this train must maintain a speed of (k/h).Now, since there must be an acceleration and a deceleration pe-riod, a deficit of (see Fig. 3) will exist between thedistance traveled and if the train uses as the cruisingspeed . Thus, the found by (4) in the previous sec-tion can be approximated by

(8)

As explained before, the found by solving (4) representstheminimumcruising speed necessary to complete km in

h. To incorporate the timetable buffer effect and to compen-sate for the grade deceleration mismatch, some allowance mustbe added to that . To achieve this, we propose to set (seeFig. 4)

(9)

which contains an additional term than (8).The reasons are as follows.

For all trains, the acceleration time from 0 to speedis always longer than the braking time required because

works as an additive braking effort in (1) during brakingand more bogies can output braking effort than can output trac-tion efforts. Thus,if we allocate hours for braking, then therewould be an extra hours’ time buffer in the brakingperiod which can be used to compensate the grade decelera-tion mismatch.With this braking time allocation, the effectivecruising period is now reduced to hours (see Fig. 4)


which must be accompanied by an upward adjustment of thecruising speed by approximately andthis in turn compensate for the timetable buffer effect automat-ically!

Other choice of size the time buffer is also possible but thechoice of represents a very reasonable one as it is alwaysa good and conservative practice to reserve a same amount oftime for braking as that for acceleration, even though the trainneed less.

With (9), we can now determine directly without itera-tion. The , , , and in Fig. 4 can be determineddirectly with the and mentioned in Section II.

Acceleration Period (c –d):After the has been deter-mined by (9), we can start building train running profile bysimulating (1). The resolution used in Fig. 2 is “one second.”Other resolutions can also be used but the numerical integrationmethod should be changed to the trapezoidal rule while possibleovershoot of at Block (d) due to low resolution should alsobe well taken care of.

The “ ” sign used in the “ ” equation of Block(c) is to account for trains running in opposite directions in astandard double track configuration.It is also important to notethat the slope at a same position will be of opposite signs fortrains running in opposite directions.

Cruising Period (e–j): Blocks (e) through (j) in Fig. 2 rep-resent the effective cruising period of the hop. Instantaneouspower requirement is first determined by Block (e) to checkwhether deceleration will occur at current position due to bigslopes. If , deceleration will occur and an “accel-eration flag” would be set. The train will always try to accel-erate itself back to the speed with its full spare capacity( ) whenever the flag is set and until

is reached again resetting the flag.The cruising period ends (Block j) when either the allocated

braking period is reached ( ) orthe Remaining Distance ( ) equals theminimum braking dis-tance( ) required for speed. The loop will exit onthe condition “ ” most of the time if major decelerationhad occurred during the journey. However, if few or only smalldeceleration had occurred, the loop is likely to exit on the con-dition “ ” as had been upward adjusted tocompensate for the timetable buffer effect.The additional checkon will ensure that appropriate braking distance is alwaysreserved.

Braking Period (k–n): As mentioned previously, the brakingperiod consists of a braking time buffer ( in Fig. 4) forcompensating deceleration mismatch and the actual braking pe-riod ( or , which is equivalent to minimum brakingtime) for braking. In Block (k), the capability of the brakingtime buffer to compensate for the deceleration mismatch is firstchecked with the criteria

(10)

where ( ) the distance mismatch. If (10) is satis-fied, the braking time buffer is enough to compensate the decel-eration mismatch. Thus, the train will first cruise at speed

Fig. 5. Test drive simulation.

Fig. 6. TPS structure for Taiwan’s HSR system

for an additional ( )/ seconds to ex-haust the distance mismatch and then start full braking until it is1 km from its destination. The last 1 km will be completed by thetrain at a speed of ( ) where is the remaining timeof the journey and this would make the traffic pattern very sim-ilar to the real ones [5]. On the other hand, if (10) is not satisfied,

will be further adjusted upward by ( )/ k/hso that a feasible traffic profile can be found within two itera-tions.

Fig. 5 shows a test drive in Taiwan’s HSR system from Taipeito Kaohsiung based on the proposed algorithm.As can be seen,major deceleration had occurred at several places with gradientin the range of 2 4% which is accompanied by full accelerationwhen spare capacity becomes available again. Note that mostmodern trains allow to exceed for a short period oftime during the acceleration period to increase line capacity andas such is not “clamped” to during acceleration regionin Fig. 5.

IV. SUMMING UP INDIVIDUAL LOAD

Before summing up the individual loads found in Fig. 2 forsubstation (S/S) load estimation, we must first determine whatkind of TPS configuration is being used. Fig. 6 shows a typicalstructure of an HSR electrical network [6]. As can be seen, thecatenary wire (CW) is separated into many supply sections byphase breaks and each substation powers two supply sections.The two supply sections of any S/S can either be of the samephase or different phases.

Once the TPS structure is determined, we can then sum upall the loads residing in the same one or same pair of supply


Fig. 7. Taiwan HSR S/S #4s dynamic load profile, time in absolute minutes(1� configuration,solid line= 15-min averaged values).

TABLE ITAIWAN’S HSR DLE RESULT (DOUBLE PHASE)

section(s) during a given period of time to derive theorS/S load profile.Here we must note that individual train powershould be divided by its converter efficiency and that an extra

(about 10% of ) must be added to each train toaccount for the auxiliary loads like the lighting and air condi-tioning.

Fig. 7 shows the dynamic load profile of S/S#4 of Taiwan’sHSR system. As can be seen, the instantaneous load profile(dotted line) is characterized by many short-term peaks and assuch its time-averaged value (e.g., 15-min average, solid line)is usually used for S/S planning and transformer rating. Table Ishows the peak value of the instantaneous, 10-min average, and15-min average of S/S#4s load profile. One thing worth men-tioning is that the peaks of supply Sections VII and VIII (seeFig. 6) does not occur at the same time and as such the peak in-stantaneous load for S/S#4 is smaller than the sum of the peaksin supply Sections VII and VIII.

V. SHORTCUT DLE ALGORITHM

The DLE algorithm presented above can simulate precise andinstantaneous conditions of the whole HSR system which is es-sential for system planning and interworking with other sup-porting programs (e.g., on-line train voltage calculation [7]).

Fig. 8. Comparison of 15-min average DLE results.

However, sometimesonly the approximate and time-averagedresponse of the TPS is required. For example, during the earlyplanning stage of HSR, system planner have to generate a pre-liminary DLE with only a limited and provisional set of systemparameters. As such, this section presents a shortcut DLE algo-rithm which canquickly evaluate HSR S/S load profile with aminimum set of parameters.

The idea is quite straightforward. For any hop, the accelera-tion and deceleration time are short (less than 20%) comparedto the cruising time and are mostly less than 5 min each. Now,if we only look at the 15-min average power consumption ofeach train, we can assume that the train isrunning at a constantspeed( ) from beginning to end and consumes con-stant power of the magnitude

(11)

wheredetermined by (9) with a set of andof any typical train;the mass of train;the adjustment factor, which equals 0.5 for dynamicbraking and 0.4 for regenerative braking.

The last term in (11) represents the kinetic energy (0.5)required to accelerate the train from 0 k/h to k/h and sinceabout 20% of this energy is recoverable through regenerativebraking [4], is adjusted from 0.5 to 0.4 if regenerative brakingis used. Again, the power consumption of each train should bedivided by the converter efficiency and add an extra forauxiliary loads.

A minimum set of system parameter is required for thisshortcut DLE algorithm and, as such, it is a very handy toolduring the early HSR planning stage.Also, its high calculationspeed makes it ideal for timetable sensitivity analysis, whichcan quickly evaluate the approximate effect of timetablechanges on S/S load profile.Fig. 8 shows the comparison ofthe 15-min average DLE derived by both the precise DLE andthe shortcut DLE for Taiwan’s HSR S/S # 5. As can be seen,DLE result derived by the shortcut formula is of good referencevalue.

VI. UNBALANCE EVALUATION FOR TAIWAN’S HSR

In this section, we shall apply the DLE algorithm developedabove and use Taiwan’s new HSR as an example to evaluate


Fig. 9. Typical grid HSR connection.

TABLE IIUNBALANCE FACTOR (%) FOR TAIWAN’S HSR

HSRs unbalance impact on the utility grid. Fig. 9 shows thetypical connection between the utility grid and TPS where the

and are the two supply sections of any S/S as shown inFig. 6

To evaluate the unbalance factor of the HSR loads, two ad-ditional parameters must be determined first, i.e., the short cir-cuit capacity (SCC) at the point of common coupling (PCC) andthe type of transformer connection used. Table II shows the un-balance factor for the seven substations in Taiwan’s HSR withvarious transformer connections. These factors have been calcu-lated based on the following formula [8]: (approximate formulais used for space consideration while Scott, Le Blanc, and mod-ified Woodbridge share the same formula [8])

(12)

(13)

(14)

where, , unbalance factor of single phase, V–V,

and Scott connections, respectively;aggregate traction load at the S/S for thesingle phase configuration;

, , the and phase loads in Fig. 9, re-spectively;three-phase SCC at the PCC;

.Please note that although most trains are driven at a powerfactor of 1.0, the reactance in the CW and rail will reduce thepower factor seen by the S/S to around 0.85–0.95. As such, theDLE result in Table I must be further divided by this powerfactor to become the and used in (12)–(14).

As can be seen in Table II, S/S with low SCC at the PCC re-quires the use of expensive transformers to meet the unbalancerequirement (e.g., Scott/Le Blanc/Woodbridge transformers hasto be used for S/S#5) while those with SCC4000 MVA can

TABLE IIITRACTIVE EFFORTOUTPUT CURVE

TABLE IVBRAKING EFFORTOUTPUT CURVE

Fig. 10. RPSA signal flowchart.

employ a cheaper solution like the configuration and V–Vconnection.Please note that Table II assumes a converter ef-ficiency of 0.9. If the efficiency is lower, e.g., 0.8, then the un-balance factor for S/S#5 would become 1.07% which furtherrequires the use of auxiliary equipment like the static VAR com-pensator (SVC) to meet the unbalance requirement. The reader


should also be careful when interpreting these 15-min averageunbalance results for instantaneous conditions.

VII. I NTERWORKINGWITH SUPPORTINGPROGRAMS

Besides being an indispensable grid-impact evaluation tool,the DLE algorithm proposed here can also interwork with othersupporting algorithm to perform in-depth system-wide TPSanalysis. Fig. A-1 shows the signal flowchart for the railwaypower-system state analyzer (RPSA) package developed byNTHU [10]. There are two main simulation engines in thepackage: DLE engine first predicts the on-line train positionsand power consumption of each train and this data is fed to thetrain voltage analysis program (TVAP) circuit analysis engine[7] for TPS state analysis. Since train voltages represents thestate variables of the system, once these voltages are known,the complete state of the TPS is known, and power factor,transmission losses, etc. can be calculated.RPSA is capable ofsimulating the on-line state of the whole HSR system as if itwere under real operating conditions and is a valuable tool forboth the TPS designers and system operators.

VIII. C ONCLUSION

This paper demonstrates the detailed procedures and princi-ples to perform accurate HSR DLE and their grid unbalance im-pact evaluation. As shown by the case study on Taiwan’s newHSR system, HSR can impose problematic unbalance impacton the utility grid and as such its load profile must be carefullystudied with the proposed accurate DLE algorithm to ensure thesafe operation of HSR systems and power grid.

APPENDIX

1) Parameters used in the simulation:

1) Mass and RR CoefficientsM 617 000 kg, DM 68 000 kg, a 4021.5, b 67.72,

c 0.751.2) Timetable

A timetable with 24 dispatches southbound and 24 dis-patch northbound in 2-h period is used, headwaymin.

3) Train Specifications:9.6 MW, 1.1 MW;

converter Efficiency 0.9;(For other efficiencies, divide Table I and IIs result by

Eff/0.9 where Eff is the new efficiency.)

2) RPSA Description [10]:

ACKNOWLEDGMENT

The authors would like to thank Taiwan HSR EngineeringBureau for sponsoring this research and providing necessary as-sistance during the research process.

REFERENCES

[1] R. J. Hill, “Electric railway traction tutorial, Part 1: Electric traction andDC traction motor drives,”Power Eng. J., vol. 8, no. 1, pp. 47–56, Feb.1994.

[2] M. Y. Huang, Modern Railway Engineering. Taiwan: Wen-Sheng,1993, p. 338.

[3] W. W. Hay,Railroad Engineering: Wiley, 1982, pp. 78–79.[4] P. H. Hsi and S. L. Chen, “Design and operating experience of high speed

railways—Visiting report to SNCF, DB, EDF, and DEConsult,” NTHU,1996.

[5] B. D. Heard, “Automatic train protection and the operational railway,” inRailway Engineering, Systems, and Safety—Selected Papers From Rail-tech 96. Suffolk, U.K.: Mechanical Engineering, 1996, pp. 65–72.

[6] HSR Engineering Bureau,Application for Private Participation in theConstruction and Operation of the Taiwan North–South High Speed RailProject, Republic of China: Ministry of Transportation, 1997.

[7] P. H. Hsi and S. L. Chen, “Simulating on-line dynamic voltages of mul-tiple trains under real operating conditions,”IEEE Trans. Power Syst.,vol. 14, pp. 452–459, May 1999.

[8] B. K. Chen and B. S. Guo, “Three phase models of specially connectedtransformers,”IEEE Trans. Power Delivery, vol. 11, pp. 323–330, Jan.1996.

[9] C. H. Yu and S. L. Chen, “Impact of short-circuit capacity on harmonicand voltage fluctuation limitations,” Masters thesis, Nat. Tsing-HuaUniv. (NTHU), Hsin-Chu, Taiwan, 1997.

[10] P. H. Hsi, Design Principles and Specifications of RailwayPower-System State Analyzer (RPSA). Hsin-Chu, Taiwan: Nat.Tsing-Hua Univ. (NTHU), 1998.

Pao-Hsiang Hsi(M’95) received the M.S. degree in electrical engineering fromVirginia Polytechnic Institute and State University, Blacksburg, in 1992. He iscurrently working toward the Ph.D. degree in the Electrical Engineering Depart-ment, National Tsing-Hua University.

He has been a Certified Professional Engineer in power system and communi-cation system engineering in 1989 and 1993, respectively. His current researchinterests include integrating power/communication networks, design and anal-ysis of HSR systems, and distribution automation.

Shi-Lin Chen (M’83–SM’98) received the B.S. degree in electrical engineeringfrom the National Cheng Kung University, Taiwan, and the M.S. and Ph.D. de-grees, both in power engineering, from London University, U.K., in 1973, 1977,and 1981, respectively.

In 1981, he joined the faculty of the Electrical Engineering Department, Na-tional Tsing-Hua University, where he is now a Full Professor. From 1989 to1992, he served as the Manager of Power System Laboratory, Taipower Re-search Institute on a government transfer contract. His current research interestsinclude power system planning, distribution automation, and high-speed railwayengineering.

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Electric load estimation techniques for high-speed railway (HSR) traction power systems