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Modeling Indirect Lightning Strikes for Railway Systems With Lumped Components and Nonlinear Effects

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  • Modeling Indirect Lightning Strikes for Railway Systems With Lumped Components and Nonlinear Effects

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untitled IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 53, NO 1, FEBRUARY 2011 249 16 A Shoory, R Moini, H Sadeghi, and V A Rakov, “Analysis of lightning radiated electromagnetic fields in the vicinity of lossy ground,” IEEE Trans Electromagn Compat , vol 47, no 1, pp 131–145, Feb 2005 17 R Moini, B Kordi, G Rafi, and V A Rakov, “A new lightning re turn stroke model based on antenna theory,” J Geophys Res , vol 105, no D24, pp 29693–29702, Dec 2000 18 V Javor, “Approximating deca. IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 53, NO 1, FEBRUARY 2011 [16] A Shoory, R Moini, H Sadeghi, and V A Rakov, “Analysis of lightningradiated electromagnetic fields in the vicinity of lossy ground,” IEEE Trans Electromagn Compat., vol 47, no 1, pp 131–145, Feb 2005 [17] R Moini, B Kordi, G Rafi, and V A Rakov, “A new lightning return stroke model based on antenna theory,” J Geophys Res., vol 105, no D24, pp 29693–29702, Dec 2000 [18] V Javor, “Approximating decaying part of the lightning return stroke channel-base current,” in Proc 3rd Int Symp Lightning Phys Effects, Vienna, Austria, Apr 2008, pp 26 [19] D M Velickovic and S R Aleksic, “A new approximation of pulse phenomena,” (in Serbian), in Proc 2nd Serbian Symp Appl Electrostatics IIEC1986, Nis, Serbia, Nov 1986, pp 6.1–6.9 [20] V Javor and P D Rancic, “Application of one suitable lightning returnstroke current model,” in Proc Eur Int Symp Electromagn Compat Eur 2006, Barcelona, Spain, Sep 2006, pp 941–946 [21] Protection Against Lightning—Part I: General Principles, IEC Standard 62305-1, 2006 [22] F Heidler, W Zischank, Z Flisowski, Ch Bouquegnau, and C Mazzetti, “Parameters of lightning current given in IEC 62305-background, experience and outlook,” presented at the 29th Int Conf Lightning Protection, Uppsala, Sweden, Jun 2008 [23] V Javor, “New functions for IEC 62305 standard lightning currents,” presented at the Int Conf Lightning Protection ICLP, Cagliari, Italy, Sep 2010, pp 1066-1–1066-5 [24] V Javor and P D Rancic, “On the choice of the lightning channel current decay constant in the modified transmission line model with exponential decay,” J Commun., Softw Syst., vol 5, no 4, pp 135–139, Dec 2009 [25] V Javor and P D Rancic, “Electromagnetic field in the vicinity of lightning protection rod at a lossy ground,” IEEE Trans Electromagn Compat., vol 51, no 2, pp 320–330, May 2009 I INTRODUCTION A model with most common devices connected along multiconductor transmission line (MTL) system of Swedish electrified railway systems, i.e., booster transformers (BTs), autotransformers (ATs), and track circuits, for evaluating the voltage and current propagation due to lightning and switching transient sources was developed by the authors [1] As the potential between above ground wires and poles may exceed the insulator impulse withstand voltage levels, flashovers occur and hence needs to be implemented in the model In this paper, for indirect lightning strikes [2], we study the effects of these aforementioned lumped components in conjunction with the nonlinear effects of pole grounding resistances due to soil ionization [3], and line to pole flashovers [4] on the propagating surge voltages along the MTL system II INDUCED VOLTAGES ACROSS LUMPED DEVICES ALONG THE CATENARY TRACK SYSTEM The electromagnetic interference (EMI) source used in the calculations is representative of a subsequent lightning return stroke The lightning is simulated to strike at a 50-m perpendicular distance from the midpoint of the system The lightning channel base-current wave shape, at time t, is expressed by the sum of two functions expressed as (1), with the parameters as stated in Table I [2] With these parameter values, the base-current peak is about 12 kA This current is assumed to propagate upward in the lightning channel in accordance with the modified transmission-line model with linear decay [5], [6] Modeling Indirect Lightning Strikes for Railway Systems With Lumped Components and Nonlinear Effects Z Mazloom, N Theethayi, and R Thottappillil 249 −t I0 (t/τ1 )n exp η + (t/τ1 )n τ2 i (0, t) = With η = exp − Abstract—Induced voltages due to lightning strikes along multiconductor transmission line (MTL) systems terminated with different loads at line ends have been widely studied by solving telegraphers’ equations using the finite-difference time-domain method However, MTL systems with lumped series and shunt-connected devices/components along the lines have not attracted much attention There are methods available for introducing lumped components along MTL systems In this paper, a method previously developed by the authors will be used to determine induced voltages across transformers connected to the catenary wire and track-circuit relay units along the MTL system representative of a Swedish single-track railway system for the case of indirect lightning strikes Nonlinearities like soil ionization and insulator flashovers are also considered It is found that both the nonlinearities and lumped components together dominate the inducedvoltage amplitude and wave shapes across devices/components Index Terms—Crosstalk, power system simulation, transmission-line modeling Manuscript received February 22, 2010; revised May 25, 2010; accepted June 17, 2010 Date of publication December 10, 2010; date of current version February 16, 2011 This work was supported by the Swedish National Rail Administration (Banverket) Z Mazloom is with the Department of Science, Islamic Azad University, Mehriz Branch, Mehriz 89818-56571, Iran (e-mail: Mazloom@ iaumehriz.ac.ir) N Theethayi is with the Mainline and Metros, Bombardier Transportation, Văasteras, SE-722 14, Sweden (e-mail: nelson.theethayi@se.transport bombardier.com) R Thottappillil is with the Division for Electromagnetic Engineering, Royal Institute of Technology, Stockholm, SE-100 44, Sweden (e-mail: Rajeev Thottappillil@ee.kth.se) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TEMC.2010.2072960 (1) τ1 τ2 n τ2 τ1 1/n (2) and I0 as the amplitude of the channel base current, τ and τ as front and decay time constants, respectively, η as the amplitude correction factor, and n as an exponent The field-to-line coupling model adopted in the calculations is the Agrawal et al model [7] In this model, the electromagnetic fields are represented as series- and shunt-connected voltage sources along the lines of the MTL system [2], [7] In the analysis, an MTL system, representative of the catenary track system of a Swedish electrified single-track railway system, as shown in Fig 1, is considered As seen, this 6-km long MTL system consists of five overhead wires, S-rail, I-rail, catenary, return conductor/negative feeder (called as return conductor), and auxiliary wire All lines are terminated to the finitely conducting ground (ground resistivity 1000 Ωm) by their self-characteristic impedance The conductor radii and characteristic impedances are given in Table II Characteristic impedances are calculated for ideal ground, and are only approximate for finitely conducting ground The telegraphers’ equation for the 5-conductor transmission line system above finitely conducting ground is given as follows: B ∂V (x, t) + AI (x, t) + √ ∂x π + Le ∂I (x, t) + ∂t t ς (t − τ ) ∂I (x, t) ∂V (x, t) + Ce = ∂x ∂t 0018-9375/$26.00 © 2010 IEEE t ∂I (x, t − τ ) √ dτ τ ∂ (t − τ ) ∂I (x, τ ) dτ = Exi (x, h, t) ∂τ (3a) (3b) 250 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 53, NO 1, FEBRUARY 2011 TABLE I BASE-CURRENT PARAMETER VALUES Fig Interface scheme between the FDTD method and the circuit solver for solving TL systems that have lumped shunt and series devices at different locations of the MTL systems [1] Fig MTL system representative of a typical railway traction conductor feeding system used for simulations [1] TABLE II CONDUCTOR RADII AND CHARACTERISTIC IMPEDANCES FOR LINE TERMINATIONS IN FIG 1) Case 1: The MTL system without any components, discontinuities, and nonlinearities 2) Case 2: The MTL system corresponding to a BT feeding system with track circuits; a BT unit, I-rail discontinuities, pole grounding resistances, and flashovers 3) Case 3: The MTL system corresponding to an AT feeding system with track circuits; an AT unit, I-rail discontinuities, pole grounding resistances, and flashovers Poles are located at every 60 m along the MTL system in simulation cases and 3, not shown in Fig The voltages across the trackside transformer windings and the relay units, connected across the tracks, are investigated In Fig 2, interconnections and grounding points associated with poles are shown for the case of a BT system At all the poles, the S-rail is shorted to the pole and the overhead wires are connected to the poles by insulators, with impulse withstand voltages as per Table III The resistor Rg is the pole-footing resistance, expressed as follows [3], [4]: Rg (t) = Ig (t) = Fig Insulators, connections, and pole-footing resistance in a single track BT system (adopted from [4]) TABLE III INSULATOR MATERIAL AND WITHSTAND VOLTAGES R0 + IR /Ig E0 2π σg R02 (4a) (4b) In (4), R0 is the pole-footing resistance measured with low current, IR is the lightning current flowing through the footing resistance, and Ig is the current required to produce a soil gradient E0 at which soil breakdown occurs The pole insulator flashovers can be modeled as arcs, as in [4] But due to simplicity, in the calculations made in this paper, the flashover is assumed to form a short-circuit between the pole and the wire as the voltage across the insulator exceeds the insulator withstand voltage The grey waveforms in Figs 4–9 correspond to voltages obtained for the same ports/locations in case In the model, the lumped devices (represented as a circuit model, as shown in Fig 3) along MTL systems are solved, as explained in [1] In Fig 3, the circuit is solved using Kirchhoff’s current laws The voltages and currents along the MTL are solved using the finite-difference timedomain (FDTD) method A BT and AT Port Voltages In (3), V and I are the line voltages and currents, respectively, A and B are constants for taking skin effect into account [8], ς (t) is the transient ground impedance calculated using the expression in [9], and E is the horizontal electric field along the line, including the effects of finitely conducting ground using the Cooray–Rubinstein formula [10] Using the aforementioned MTL system, three cases will be investigated In Fig 4, it is seen that the voltages across the windings along the catenary wire side and return conductor side are having similar magnitudes and are larger compared to corresponding case The oscillatory voltages are due to nonlinearities On the contrary, comparing cases and in Fig 5, it is seen that peak voltages across the AT windings are comparable with nonlinearities included Moreover, the voltages across the AT windings are much higher than the corresponding BT winding cases It is also seen in Fig that the transformer IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 53, NO 1, FEBRUARY 2011 251 Fig Voltages appearing across relay units closer to the middle of the line for cases corresponding to cases (grey) and (black) Fig Voltages appearing across BT windings for cases corresponding to cases (grey) and (black) Fig Voltages appearing across relay units closer to the line ends for cases corresponding to cases (grey) and (black) Fig Voltages appearing across AT windings for cases corresponding to cases (grey) and (black) winding across the negative feeder to the S-rail is suffering the highest induced voltage of more than 35 kV Again, it is seen that the voltage waveforms are oscillatory B Track-Circuit Port Voltages Fig Voltages appearing across relay units closer to the middle of the line for cases corresponding to cases (grey) and (black) The induced voltages across the relay units at the middle of the line are similar for cases and (BT and AT feeding systems, respectively) and show very oscillatory behavior after a short time, as shown in Figs and The peak-induced voltages appearing across the relay units closer to the ends of the system are similar for cases and (BT and AT feeding systems, respectively) and show comparably less oscillatory behavior as per Figs and It is seen that relay unit no in the BT system (see Fig 8, case 2) is suffering the highest voltage peak Otherwise, comparing Figs and with Figs and 9, in general, the peak voltages across the relay units in the middle of the line is doubled compared to the corresponding line end relay units 252 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL 53, NO 1, FEBRUARY 2011 [7] A K Agrawal, H J Price, and S Gurbaxani, “Transient response of a multiconductor transmission line excited by a nonuniform electromagnetic field,” IEEE Trans Electromagn Compat., vol 22, no 2, pp 119–129, May 1980 [8] C R Paul, Analysis of Multiconductor Transmission Lines New York: Wiley, 1994 [9] R Araneo and S Celozzi, “Direct time domain analysis of transmission lines above a lossy ground,” Inst Elect Eng., (IEE) Proc Sci., Meas Technol., vol 148, no 2, pp 73–79, Mar 2001 [10] F Rachidi, C A Nucci, M Ianoz, and M Mazzetti, “Influence of a lossy ground on lightning induced voltages on overhead lines,” IEEE Trans Electromagn Compat., vol 38, no 3, pp 250–264, Aug 1996 The Study On Normalized Site Attenuation With Reflected Rods Di Wu and Gang Zhu Fig Voltages appearing across relay units closer to the line ends for cases corresponding to cases (grey) and (black) III CONCLUSION In this paper, it is shown how nonlinearities associated with polefooting resistance and line to pole insulator flashovers, in conjunctions with lumped series- and shunt-connected devices/components, affect the induced voltages across components along MTL systems of a typical railway system It was seen that the flashover occurs mainly at pole locations up to 300 m away from the MTL system midpoint, closest to the lightning strike location It was also seen that the line insulators subjected to flashovers were mainly of the catenary and return conductors Depending on the relative position of the lumped device/component with respect to the lightning position, for the given lightning source with 12-kA peak current, the peak voltages across the AT windings can be up to 35 kV compared the case of BT windings which is about 15 kV The peak voltage across the relay units can be as high as 60 kV The model (with modifications including more components or extension to double track systems) can be used as a tool for lightning protection studies within railway systems REFERENCES [1] Z Mazloom, N Theethayi, and R Thottappillil, “A method for interfacing lumped-circuit models and transmission-line system models with application to railways,” IEEE Trans Electromagn Compat., vol 51, no 3, pp 833–841, Aug 2009 [2] C A Nucci, F Rachidi, M Ianoz, and C Mazzetti, “Lightning-induced voltages on overhead lines,” IEEE Trans Electromagn Compat., vol 35, no 1, pp 75–86, Feb 1993 [3] Technical Council of the IEEE Power Engineering Society, IEEE Guide for the Application of Insulation Coordination, IEEE Standard 1313.2, 1999 [4] N Theethayi, Y Liu, R Montano, R Thottappillil, M Zitnik, V Cooray, and V Scuka, “Theoretical study on the consequence of a direct lightning strike to electrified railway system in Sweden,” J Electr Power Syst Res., vol 74, pp 267–280, 2005 [5] V Rakov and A A Dulzon, “Calculated electromagnetic fields of lightning return strokes,” Tekhnicheskaya Elektrodinamika, vol 42, no 1, pp 87–89, 1987 [6] R Thottappillil, V A Rakov, and M A Uman, “Distribution of charge along the lightning channel: Relation to remote electric and magnetic fields and to return-stroke models,” J Geophys Res., vol 102, pp 6987–7006, 1997 Abstract—Standard sites are important for antenna calibrations However, many actual sites are not perfect for antenna calibrations due to surrounding reflectors and other measurement uncertainties Earlier studies were either impractical for actual sites or calculating inaccurately This paper develops a new method to compute normalized site attenuation (NSA) with reflectors nearby Based on the conventional NSA, the model with the actual rod-like reflectors is formulated by the wave propagation theory, which is not considered earlier With this new method, the interferences of rods are considered from the shortest reflected path The results of the proposed method show good agreement with the numerical simulation results Index Terms—Antennas, attenuation measurement, electromagnetic compatibility (EMC), moment methods, propagation I INTRODUCTION Antenna factor (AF) is fundamental for computing the incident electric field strength accurately in EMC tests Therefore, antennas need to be calibrated accurately to avoid inaccurate test However, there exists a circular problem in antenna calibrations [1] and site validations [2]: antennas need to be calibrated on a standard site that in turn is validated by the antennas with known AF Thus, the AF contains the uncertainty caused by the site it was calibrated on, but the quality of the site under test can only be known with the uncertainty of the antenna calibration [3] The standard test site is the method to solve this problem [4] A standard test site should be an open, flat, level area that is clear of overhead wires and reflecting structures For assessing an actual site, it is needed to compare the normalized site attenuation (NSA) Manuscript received February 10, 2010; revised July 5, 2010; accepted August 30, 2010 Date of publication October 21, 2010; date of current version February 16, 2011 This work was supported by the Joint Program of the National Natural Science Foundation of China under Grant 60830001, by the Key Project of State Key Laboratory of Rail Traffic and Control under Grant RCS2008ZZ007, and by the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT0949 The authors are with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 100044, China (e-mail: 09111054@bjtu.edu.cn; gzhu@bjtu.edu.cn) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TEMC.2010.2078823 0018-9375/$26.00 © 2010 IEEE ... as 60 kV The model (with modifications including more components or extension to double track systems) can be used as a tool for lightning protection studies within railway systems REFERENCES... system used for simulations [1] TABLE II CONDUCTOR RADII AND CHARACTERISTIC IMPEDANCES FOR LINE TERMINATIONS IN FIG 1) Case 1: The MTL system without any components, discontinuities, and nonlinearities... paper, it is shown how nonlinearities associated with polefooting resistance and line to pole insulator flashovers, in conjunctions with lumped series- and shunt-connected devices /components, affect
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