Distribution of traction return current

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005 2119

Distribution of the Traction Return Current in ATElectric Railway Systems

Andrea Mariscotti, Member, IEEE, Paolo Pozzobon, Member, IEEE, and Maurizio Vanti

Abstract—The problem of determination of the accurate distri-bution of the return current in AT (autotransformer) electric trac-tion systems (supplied at 2 25 kV) for High Speed Railways isconsidered. The path of the traction return current flowing fromthe rolling stock axles back to the supply (i.e., substation) is com-posed of the traction rails and additional earth potential conduc-tors. The overhead supply conductors in contact with the trainpantograph are connected to a symmetrical circuit (the feeder)with the purpose of current balancing. This arrangement and itsinfluence on current to earth are considered: the return currentdivides among rails (as signalling disturbing current) and earth,depending on the value of the electric parameters of the systemand the earth and on the circuit arrangement and on the relativeposition of system devices. The amplitude (as a percentage of thetotal return current) of the disturbing current may be high enoughto cause interference to signalling. This work investigates the be-havior of the return current in AT electric railway systems, on thebasis of a reference system for the variation of the most importantelectrical parameters.

Index Terms—Guideway transportation power systems, powerdistribution interference, power system harmonics.

I. INTRODUCTION

THE increasing complexity of railway systems requires thestudy and the adoption of simulation-based techniques in

order to evaluate the electrical compatibility of the whole elec-trical system with respect to the normative standards and oper-ator’s regulations. New and old locomotives and signalling sys-tems are in operation on the same line and it is essential to ensurecompatibility under normal operation and failure conditions, thatis to say to evaluate the interference mechanism, where the lo-comotive is the source of the disturbance (and new locomotivesequipped with electronic static converters have pushed the spec-trum of disturbances at higher frequency), the signalling circuitis the victim (new signalling systems operate in a wide frequencyrange at power frequency and audiofrequency up to some tens ofkHz) and the line and track are the mean of propagation. This as-pects are covered by the European Standard prEN 50 238 [1], inorder to ensure the cross-acceptance of rolling stock on existingtraction lines in Europe (and abroad). The standard itself indi-cates the need for accurate modeling of the test cases prepared toproof the electromagnetic compatibility (EMC) between rollingstock and signalling. In general, also external electromagnetic in-terference (EMI) is of concern, toward both other railways andtheir own signalling systems and metallic and concrete struc-tures (like bridges, tunnels, pipes, etc.).

Manuscript received April 29, 2004; revised July 20, 2004. Paper no.TPWRD-00211-2004.

The authors are with Dipartimento Ingegneria Elettrica, Università di Genova,Genova 16145, Italy.

Digital Object Identifier 10.1109/TPWRD.2005.848721

Fig. 1. Track circuits diagram: double rail with insulating joints andimpedance bonds.

EMC between different railway systems is a very importantproblem for the realization of new High Speed (HS) lines andtheir integration with old railway systems close to passengerstations, in particular if the old railway system is supplied withdc voltage and equipped with power frequency (50 Hz) trackcircuits and the new HS railway system is supplied with a2 25-kV 50-Hz system.

Crossings and parallelism with existing metallic or concretestructures are of concern for the construction of a new railwayline [2]. Electrolytic corrosion caused by stray currents is adirect consequence of the amount of current flowing outsidethe system to the earth, which is influenced by a series ofsystem parameters [3] (the most important are rail-to-earthconductance, earthed return conductors-to-earth conductance,earth resistivity).

A synthetic description of signalling track circuits (TCs) maybe found in [3], where the basic features useful for the presentanalysis are outlined. TCs consist of a loop circuit composedof a transmitter, which applies a differential voltage to the rails,the rails themselves and the receiver, which picks up the voltageacross the rails at the other end of the loop. Rails are shunted bythe low resistance axles of rolling stock within the track circuitsection and the amplitude of the voltage at the receiver inputterminals drops below a given threshold. Track circuits may besingle rail circuits or double rail circuits (like those installed onAT systems and analyzed in this paper); the latter is shown inFig. 1.

Double rail track circuits with impedance bonds use insu-lating rail joints (IRJ’s) on both rails and the return current(which is a common mode current) flows back through theimpedance bond (see Fig. 1).

In 2 25-kV electric railway traction systems the tractionreturn current flows from the rolling stock axles back to thesupply (i.e., Electric Supply Substation (ESS) or AutoTrans-former (AT)) through the rails (and the impedance bonds nor-mally placed every 1500 m) and the return conductors at earthpotential (two conductors, one overhead conductor (“overhead

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2120 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

r.c.”) and one buried (or simply laid down in a conduit) con-ductor, that we call here “ground r.c.”). The return current di-vides among the rails (the difference of the current in the rails ofthe same track, i.e., the net differential current, produces the dis-turbing current through the signalling conductors), the rcs andthe earth itself, depending on the value of the electric parame-ters of the system, on the circuit arrangement and on the relativeposition of the supply, the rolling stock and signalling devices.Some railway operators adopt extreme reasoning for the calcu-lation of the disturbing current: the return current is assumed toflow entirely in the return rails (no current leaks to the earth) andin the case of broken rail joint, the total return current becomesdisturbing current; this in turn imposes severe limits onto thespectrum components of locomotive return current, as it will beshown in the following.

The interference mechanism may be described as follows: thereturn current flowing through the axles divides among therails currents and the return conductors currents for track 1 and2 and the earth current for left and right sections respectively.The amplitude of the rail currents flowing into the left and rightsections depends highly on the respective circuit arrangement.The electrical parameters which mostly influence the amount ofearth current are earth resistivity, return conductor-to-earth con-ductance and rail-to-earth conductance. Moreover, rail-to-earthconductance is an important parameter in all railway tractionsystems, since it determines the amount of rail current injectedby the signalling transmitter, which leaves the track circuit forthe earth before entering the receiver circuit, and hence deter-mines the required transmitter power and the receiver sensi-tivity. For very high values the shunting effect of rolling stockaxles cannot be detected any longer; this poses an upper limit onthe rail-to-earth conductance which is typically around 1 S/kmwith the standard value at about 0.2 S/km. Measurements per-formed on the new Italian HS line give very low rail-to-earthconductance values, around 0.02–0.05 S/km, but, in authors’opinion, they will grow toward the typical 0.2 S/km due to mois-ture, ageing and dirt.

The influence of geometrical parameters variation (e.g.,height and horizontal displacement of the overhead conductors,horizontal distance between two adjacent tracks, etc.) wasanalyzed in [4] within the allowed ranges for each parameterand it was found negligible, with the overall variation of theelectrical per-unit-length parameters of the traction line limitedto a few percent.

II. 2 25-kV SYSTEM DESCRIPTION

The electric traction system is characterized by a set of‘transfer functions’ (as required in [1]), relating the interferencesignal at the train detection system equipment to the emissiongenerated by the rolling stock; they define how the tractionreturn current of rolling stock (that is locomotive and morein general traction vehicles) is translated into the interferencevoltage/current at the terminals of the train detection equip-ment, e.g., at the track circuit receiver. An additional transferfunction is considered to define the amount of current whichflows to earth and may interfere with external structures; the railpotential (as required by EN 50122-2 [2]) is neglected, since itmay be defined only with an external reference structure. The

TABLE IMODEL ELECTRICAL PARAMETERS VALUES AT DC

transfer function depends on several parameters: frequency,geometrical arrangement of the conductors (catenary, feeder,rails, earth conductors), earthing arrangement (cross bonds,return current in one or both rails, earthing of masts), distancebetween vehicle and train detection equipment, feeding ar-rangement (location of the substation), leakage to earth of therails, earth conductivity.

In this work the standard AT system configuration is con-sidered, which is quite general and common to all AT systemsfor several countries; this includes ATs, so that the line sectionunder study is terminated onto the AT impedance and not oneither a short or open circuit (like in [3]). All the traction linesections are modeled with MTL equations. There are IRJ’swith impedance bonds every 1500 m; the central terminal ofthe impedance bonds is connected with the return conductors(the overhead and the ground earth conductors); additionalequipotential bonding between the return conductors is placedat 750 m, in the middle of two IRJ’s. The section starts with asubstation transformer and ends with an AT, placed after 12 km(not the 15 km used in [4]) like in a real AT system.

The longitudinal discontinuities have been set as follows: thelength of the modeled track section is 12 km (the chainage isfrom km 0.000 to km 12.000); the location of the substation iskm 0.000; the location of the IRJ’s with impedance bonds andequipotential bonding is every 1.5 km starting from km 0.000;additional equipotential bonding only between return conduc-tors of both tracks is located every other 0.750 km; vehicle lo-cation where interference is generated is km 5.999 (close to animpedance bond). The analysis has been performed also for adifferent location of the vehicle (chainage 5.625 km), at a dis-tance of 375 m from the impedance bonds, but it was found thatthere is no noticeable difference in the results, except for thevariables of the first section toward the nearest impedance bond.

Signalling transmitter and receiver are connected across theimpedance bonds, so that rail current and rail-to-rail voltage arecomputed as signalling variables. Additionally, return conduc-tors currents are computed to estimate the influence of equipo-tential bonding on the percentage of return current flowing out-side to the earth.

System components are modeled as follows:

• signalling receiver and transmitter are modeled simply asthe terminals across the impedance bonds;

• the disturbing vehicle is modeled as a sinusoidal currentgenerator of 1-A rms current at the injection point (IP);

• ESS and AT are modeled with a double secondary windingtransformer for the connection to the traction line, while

MARISCOTTI et al.: DISTRIBUTION OF THE TRACTION RETURN CURRENT IN AT ELECTRIC RAILWAY SYSTEMS 2121

Fig. 2. Typical cross section of AT double track systems.

the equivalent circuit of the power-supply line or an opencircuit is connected to the primary side.

The analysis is performed (like for dc and 16.7 Hz systemsconsidered in [3]) using a Multiconductor Transmission Line(MTL) model [5] of the traction line. This model is an evolutionof that presented and validated in [6], [7], with further validationfor AT railway systems (at 2 25-kV ac), performed with themeasurement results obtained on the Italian HS line.

R (resistance) and L (inductance) matrices are computed onthe basis of Carson’s equations [8], [9], taking into consider-ation also the variation of parameters with frequency (such asrail resistance because of skin effect [10]). C (capacitance) ma-trix is determined with the method of images [8], by assumingsoil and ballast as perfect ground. A detailed analysis of the in-fluence of the dielectric constant of soil is under development;preliminary experimental data confirm that the variation of ca-pacitance terms between overhead conductors and rails is below10%, while large variations may be expected for the rail-to-earthand rail-to-rail capacitance terms. The matrix G (conductance)is determined with the results obtained during the measurementcampaign on the 2 25-kV Italian High Speed line and usingreference average values [11]. Conductance between overheadconductors may be assumed 0; the most important parameteris the rail-to-earth (and the rail-to-rail conductance as a conse-quence) and its effect will be analyzed in the following sections.

The values of the electrical parameters used in the modelare reported in Table I, [4], [6]–[8]. For the earth resistivity (auniform ground with constant resistivity is assumed), rail-to-earth conductance and return conductor-to-earth conductancethe lower and upper limit used in the sensitivity analysis (as itwill be explained later on in this section) are also indicated.

The cross section with geometrical parameters of standard ATrailway system line is shown in Fig. 2.

A longitudinal sketch of the considered railway system isshown in Fig. 3, where only a few impedance bonds and equi-potential bonding points are shown.

The analysis is performed at the nominal values of the elec-trical and geometrical parameters and the following variables ofthe return circuit are computed (per 1 Arms of injected currentat all frequencies):

voltage between rails of track 1 or 2per 1 A rms of injected vehicle currentversus frequency at defined locations;

Fig. 3. Longitudinal section of the considered railway system.

TABLE IICODING OF CURVES AT MEASURING POSITIONS WITH NOMINAL PARAMETERS

current in the four rails (internal andexternal for each track) per 1 A rms of in-jected vehicle current versus frequencyat defined locations;current in the four return conductors (“o”for overhead and “g” for ground) per 1 Arms of injected vehicle current versusfrequency at defined locations;stray current to earth leaving the systemat defined locations.

Moreover, a sensitivity analysis is performed for those param-eters which are highly variable or scarcely known; the analysisconsists of the calculation of the above described variables forthe following variations of electrical parameters: rail conduc-tance to earth (often referred to as “leakage to earth”)nominal value, nominal value (0.2 S/km), and nominalvalue; return conductor conductance to earth nominalvalue and nominal value (20 S/km); earth resistivitynominal value, nominal value (100 ohm m), and nominalvalue.

2122 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Fig. 4. Rail current, track 1 (I ) (nominal parameters).

It must be underlined that the case of rail-to-earth conduc-tance increased by an order of magnitude above its nominalvalue are reported for the sake of completeness, but it is notbelieved that it may represent real operating conditions of thetraction system. Such a high value is not compatible with thecorrect operation of the track circuits, since for long track cir-cuits the total resistance from rail to earth is comparable to theaxles resistance of rolling stock (shunting the rails for the detec-tion of occupied track section).

Concerning parameter, it is believed that the two inves-tigated values cover a meaningful interval of attainable values,taking into account aging and oxidation.

The measuring positions are placed in the middle of someIRJs and equipotential bonding points with chainage alongthe track 0.375, 2.625, 4.125, 4.875, 5.625, 6.375, 7.125, 7.875,9.375, and 11.625 km , for which the distance from the IP (ne-glecting the 1-m displacement of the train with respect to trackmiddle) may be defined as: , , , ,

, 0.375, 1.125, 1.875, 3.375, and 5.625 km. The distancespans a wide range of values, where the most common and ap-

propriate ranges are from the lowest one (375 m) up to 3.375 kmfor both supply frequency and audio frequency track circuits.

The examined frequency range is 5 Hz–20 kHz, which is theoperating range of the major part of track circuits; other types oftrain detection equipment (e.g., magnetic loops, axle counters,etc.) are not considered in this work.

III. RESULTS

The output variables are the currents through the rails andthrough the ground and overhead return conductors (r.c.), therail-to-rail voltage and the differential rail current as defined

in the previous section. The differential rail variables are im-portant to evaluate the possible interference to track circuit re-ceivers. The calculated values are shown for some meaningfulmeasuring positions: near the return current IP (the vehicle) at

m, in the middle of the traction line at m,m, m and close to substation and autotransformer

m. The curves are coded as described in Table II.While in [3], calculations were performed for two different

traction line terminations (open and short circuit), here the lineis terminated on the standard AT. Since the short circuit powerrating of AT and ESS is of the same order of magnitude, the twomay be exchanged with little influence on the results.

Results for nominal parameters are shown in Figs. 4 through9. Track 1 and track 2 variables (i.e., rail current, overhead r.c.current and ground r.c. current) show similar behavior, so onlytrack 1 variables are shown.

It is worth noting that, while major resonances (upwardpeaks) occur at the same frequency for all system variables,anti-resonances frequency (downward peaks) depends also onmeasuring position, as described in [11], [12].

Locomotive return current on track 1 flows mainly throughthe rail at measuring positions closer to the IP (at pos. mand m) until it reaches the nearest impedance bond.

With reference to Fig. 4, rail current is larger at the IP (cor-responding to the m and -m positions) and reachesits minimum at the other end (corresponding to the m,

m, and -m positions) at ESS or AT; this meansthat the return current leaves progressively the rails for the re-turn conductors and the earth itself.

The difference between Figs. 4 and 5 is that for track 1 (andfor track 2) the curves of rail current for positions closer to IP are

MARISCOTTI et al.: DISTRIBUTION OF THE TRACTION RETURN CURRENT IN AT ELECTRIC RAILWAY SYSTEMS 2123

Fig. 5. Rail current, track 2 (I ) (nominal parameters).

Fig. 6. Ground r.c. current, track 1 (I ) (nominal parameters).

separated from each other, because of the unsymmetry producedby the presence of the vehicle on track 1.

All curves show resonance peaks at 2.8, 8.4, 12.4, and17.9 kHz, where the current may be as high as 4–5 Arms.It must be remembered that currents are plotted as amplitudevalues and in this case the phase information is vital for acorrect interpretation: currents in the rails and in the returnconductors of the same (left or right) section of either track areopposite in phase and these conductors form loops.

Differential rail currents are computed for both tracks, withno noticeable difference between the two, so only results fortrack 1 are shown in Fig. 8.

For frequencies away from system resonance the differentialrail current is %– % of the traction return current for allpositions, thanks to the high degree of symmetry of the supplysystem and the low impedance of the return conductors.

The differential rail voltage (which is not shown) exhibitsa peak at about 8400 Hz (with amplitude, computed for 1 Ainjected current, comparable to receiver input voltage level),

Fig. 7. Overhead r.c. current, track 1 (I ) (nominal parameters).

Fig. 8. Rail differential current, track 1 (I � I ) (nominal parameters).

TABLE IIICURVES CODING AT MEASURING POSITIONS AND FOR SENSITIVITY ANALYSIS

which could represent a serious threat to signalling circuits. Itmust be underlined indeed that the used frequency ranges aretypically 3–7 kHz and 9–17 kHz, so respectively below andabove this critical frequency. Yet, different loading (transformercharacteristics or train input impedance) or geometrical prop-erties of the railway system could move this resonance towardeither of the two ranges.

2124 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Fig. 9. Rail current, track 1 (I ) (g = 0:02; 0:2;2 mS/m).

Fig. 10. Overhead r.c. current, track 1 (I ) (g = 0:02;0:2;2 mS/m).

In the following, only track 1 r.c. currents are shown, sincecomplete calculations show that track 2 r.c. currents are veryclose and differ only around resonances at high frequency. Sen-sitivity analysis follows. Curves are coded as in Table III.

In Figs. 9 through 11 the results for the variation of the rail-to-earth conductance are again shown only for track 1.

The effect of the larger values of rail-to-earth conductance(see Fig. 9) is, for the lowest frequency interval, to decrease

the total input impedance of the circuit composed of the railsthemselves and the earth in parallel seen at the IP and at thetwo ends of traction line (ESS and AT). So the absorbed currentincreases for -m and -m positions, while the current

MARISCOTTI et al.: DISTRIBUTION OF THE TRACTION RETURN CURRENT IN AT ELECTRIC RAILWAY SYSTEMS 2125

Fig. 11. Ground r.c. current, track 1 (I ) (g = 0:02; 0:2;2 mS/m).

Fig. 12. Rail current, track 1 (I ) (g = 2; 20 mS/m).

through the rail decreases at m position placed in themiddle of the left section (and right section for symmetry) forincreased leakage to earth. At higher frequency the effect ofis remarkable for the position closer to the IP, less and less forincreasing distance from the IP.

Furthermore (see Fig. 9) influences the current distribu-tion of return conductors in contact with the earth (rails andground r.c.) with a negligible effect on the overhead r.c.

In Figs. 12 through 14 calculations are made for two differentvalues of the conductance-to-earth of the ground r.c. , pur-posely in contact with the earth; this parameter may decreasewith ageing and oxidation. Again the results are shown only fortrack 1. Attention is concentrated at the low frequency portion ofthe considered frequency range, where there is a weak depen-dence of the rail current only for the nearest section; at larger

Fig. 13. Overhead r.c. current, track 1 (I ) (g = 2; 20 mS/m).

distance from the IP system currents are again balanced thanksto equipotential bonding and AT/ESS action. At high frequencythere is no noticeable difference among the curves.

For all rails and return conductors currents are larger at anyposition for the lower value; the reason is the lower per-centage of return current flowing directly through the earth. Thecomputation of the stray current to earth (leaving the railwaysystem) gives the curves shown in Figs. 15 and 16.

At high frequency the amount of current leaving the railwaysystem is independent on . On the contrary, below 1 kHz(see Fig. 16) stray current is larger for the intermediate posi-tion between IP and substation and there is a 50% decrease foran order of magnitude decrease of . At the supply frequency(50 Hz), which corresponds to the largest component of the trac-tion return current, only 5 to 30% of the total return current flows

2126 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Fig. 14. Ground r.c. current, track 1 (I ) (g = 2; 20 mS/m).

Fig. 15. Stray current to earth (I ) (g = 2; 20 mS/m).

Fig. 16. Stray current to earth (I ) (g = 2; 20 mS/m) (zoom).

through the earth in the direction of the ESS, depending on themeasuring position; at the two extreme positions the stray cur-rent is double if is increased by a factor of 10.

Fig. 17. Stray current to earth (I ) versus the distance from IP.

Fig. 18. Rail current, track 1 (I ) (� = 10;100;1000 m).

In Fig. 17 is plotted vs. distance from the IP for somefrequency values between 5 Hz and 20 kHz.

Low-frequency curves (5, 50, and 1000 Hz) have similar be-havior, with a minimum close to the IP, an increase up to abouthalfway between the IP and the AT or ESS and then a slow de-crease to the AT or ESS.

Sensitivity analysis results for the earth resistivity param-eter (varied of an order of magnitude above and below the av-erage typical value of 100 m) are shown in Fig. 18 only for therail current of track 1.

In this case, the results show that there is no appreciable in-fluence on the rail current (and ground and overhead r.c. as well)current, due to the peculiar (typical of 2 25-kV railway sys-tems) arrangement and connection of return conductors, whichare a very low impedance path and are bonded together every750 m.

IV. CONCLUSION

The distribution of the return current was computed for thestandard configuration of a double track 2 25-kV ac electric

MARISCOTTI et al.: DISTRIBUTION OF THE TRACTION RETURN CURRENT IN AT ELECTRIC RAILWAY SYSTEMS 2127

railway system with one ESS on one end, an AT on the otherend and a source of return current in the middle. The rail-to-rail voltage was also computed at several measurement posi-tions along the track. Track circuits may be connected at allimpedance bonds along the track, one each 1500 m. The analysisis completed with the investigation of the influence of the mostimportant electrical parameters: the earth resistivity, the rail-to-earth conductance (often referred to as the “leakage to earth”)and the conductance to earth of the ground return conductor.

The conclusions of this analysis may be summarized as:

• only a small portion of the return current flows through therails and the net current circulating in the track circuit iseven smaller; it was shown that it is limited to a few percentof the injected return current with the exception of systemresonance;

• system resonance may occur inside the frequency band inuse by audiofrequency track circuits;

• the increase of the rail-to-earth conductance decreasesthe total impedance seen at the IP and, hence, increasesslightly the absorbed current;

• the amount of current leaving the system (stray current)is proportional to the conductance-to-earth of the groundreturn conductor only for the low-frequency range, that ofinterest for stray current analysis;

• the earth resistivity does not influence the distribution ofthe return current among return conductors due to the par-ticular circuit arrangement and the action of equipotentialbonding.

Results were complemented by the analysis of end-fed con-figurations, with AT out of service (this configuration is called“1 25”). In this case the system is no more symmetric andthe return current flows almost entirely in the direction of theESS, while the residual currents in the other section becomes un-balanced and the differential rail current is in percentage muchlarger. For configurations where the ESS is out of service (withby-pass switches close in front of it) and the section is fed fromadjacent ESS’s, then the effect is simply that of a longer linesection, with the equipotential bonding and feeder connectionpreserved.

The presented results consist of a series of transfer functionsbetween the locomotive return current (which is the source, setto constant 1 A rms over the entire frequency range) and thereturn circuit variables (voltage and current). So, each transferfunction must be multiplied by the real (either measured or cal-culated) spectrum of the locomotive return current to obtain thevoltage/current spectrum at any position along the line and inparticular at signalling receiver input terminals. These resultsare very useful to calculate also the amount of current leavingthe return circuit to the earth, which represents the “stray cur-rents” phenomenon.

These results are intended also as a guideline for track cir-cuits designer and system engineers to predict possible criticalconfigurations and the noise level at the receiver terminals.The transfer function curves have been calculated for standardvalues of several system parameters: an accurate evaluationimplies the use of exact parameter values and the introduc-tion of the real circuits of the receiver and the transmitter,

together with any tuning circuit used for electrical separationof track circuit sections. If the susceptibility of the receiveris also known, it was demonstrated [14] that this method canindicate if Right Side Failure (a track indicated as “occupied”but “free”; no safety critical) and Wrong Side Failure (a trackindicated as “free” but “occupied”; safety critical) events couldpossibly occur. Accurate and general treatment of the subject isvery difficult, since it requires the characterization of receiversusceptibility also for transients.

REFERENCES

[1] Railway Applications — Compatibility Between Rolling Stock and TrainDetection Systems, 2000–04. CENELEC Std. prEN 50 238.

[2] Railway Applications—Fixed Installations—Part 2: Protective Provi-sions Against The Effects of Stray Currents Caused by D.C. TractionSystems, 1998–05. CENELEC Std. EN 501222-2.

[3] A. Mariscotti, “Distribution of the traction return current in AC and dcelectric railway systems,” IEEE Trans. Power Del., vol. 18, no. 4, pp.1422–1432, Oct. 2003.

[4] G. D’Addio, M. Fracchia, A. Mariscotti, and P. Pozzobon, “Sensitivityanalysis of railway line impedance to variations of electrical and geo-metrical parameters,” in Proc. World Congr. Railway Research, Tokyo,Japan, Oct. 19–23, 1999, pp. 262–268.

[5] C. R. Paul, Analysis of Multiconductor Transmission Lines. New York:Wiley, 1994.

[6] S. Brillante, G. D’Addio, P. Ferrari, A. Mariscotti, and P. Pozzobon,“Validation of the analytical model of an electric railway traction line,”in Proc. Int. Conf. Metrology, Jerusalem, Israel, May 16–18, 2002, pp.355–360.

[7] S. Brillante, G. D’Addio, P. Ferrari, A. Mariscotti, and P. Pozzobon,“Measurement techniques for validating the calculation methods ofelectric railway traction line parameters,” in Proc. Int. Conf. Metrology,Jerusalem, Israel, May 16–18, 2002, pp. 154–161.

[8] Directives Concerning the Protection of Telecommunication LinesAgainst Harmful Effects from Electric Power and Electrified Rail-WayLines, 1989. CCITT (International Telegraph and Telephone Consul-tative Committee, Volume III (ISBN 92-61-04 041-1) and IV (ISBN92-61-04 031-4).

[9] J. R. Carson, “Wave propagation in overhead wires with ground return,”Bell Syst. Tech. J., vol. 5, pp. 539–554, Oct. 1926.

[10] A. Mariscotti and P. Pozzobon, “Resistance and internal inductance oftraction rails: A survey,” IEEE Trans. Veh. Technol., vol. 49, no. 2, pp.294–299, Apr. 2000.

[11] A. Mariscotti and P. Pozzobon, “Determination of the electrical param-eters of railway traction lines: Calculation, measurement, and referencedata,” IEEE Trans. Power Del., vol. 19, no. 4, pp. 1538–1546, Oct. 2004.

[12] J. Holtz and H. J. Klein, “The propagation of harmonic currents gen-erated by inverter fed locomotives in the distributed overhead supplysystems,” IEEE Trans. Power Electron., vol. 4, no. 2, pp. 168–174, Apr.1989.

[13] A. Mariscotti and P. Pozzobon, “Synthesis of line impedance expres-sions for railway traction systems,” IEEE Trans. Veh. Technol., vol. 52,no. 2, pp. 420–430, Mar. 2003.

[14] G. D’Addio, P. Ferrari, A. Mariscotti, and P. Pozzobon, “Integrated mod-eling of audiofrequency track circuits,” in EMC York 99, IEE pub. no.464, York, U.K., Jul. 12–13, 1999, pp. 101–106.

Andrea Mariscotti (M’95) was born in Genova, Italy, in 1968. He received theelectronics engineering degree (Hons.) in 1991 and the Ph.D. degree (Hons.) inelectrical engineering in 1997 from the University of Genova, Genova, Italy.

Currently, he is a Research Fellow, working in national and international re-search programs. He was involved in post-Ph.D. activities at the University ofGenova, Genova, Italy, from 1998 to 2000. His research interests (internal andexternal) include electromagnetic compatibility (EMC) applied to electric drivesand transport systems along with modeling and measurement of the electromag-netic interference (EMI) in power systems.

Dr. Mariscotti is a Member of the IEEE Instrumentation and MeasurementSociety and IEEE Circuits and Systems Society.

2128 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Paolo Pozzobon (M’92) was born in Genova, Italy, in 1959. He received thedegree in electrical engineering from the University of Genova, Genova, Italy,in 1986, and the Ph.D. degree in electrical engineering from the University ofPisa in 1990.

Currently, he is Assistant Professor with the Electrical Engineering Depart-ment at the University of Genova, Genova, Italy, where he has been since 1992.He is a Lecturer in power electronics, electrical drives, electric industrial appli-cations, and electrified transport systems and is currently conducting researchin several national and international programs. In 1991–1992, he received thePost Ph.D. Grant from the University of Padova, Padova, Italy, and conductedresearch work on frequency-domain analysis. In 1996, he was one of the pro-moters of the Transport Research Centre, Genova, Italy. His main research in-terests include electric traction, power electronics, and electromagnetic systemcompatibility in rail traction. He is a Member of the IEEE Vehicular TechnologySociety and Electromagnetic Compatibility Society.

Maurizio Vanti was born in Chiavari, Italy, in 1977. He received the electricalengineering degree in 2002 from the University of Genova, Genova, Italy, wherehe is currently pursuing the Ph.D. degree in electrical engineering.

His main research interests include electromagnetic compatibility applied totransport systems, with an emphasis on time-domain and frequency-domainmodeling of power systems.