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.
Trang 1[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 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
return-stroke 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,
experi-ence 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.
Modeling Indirect Lightning Strikes for Railway Systems
With Lumped Components and Nonlinear Effects
Z Mazloom, N Theethayi, and R Thottappillil
Abstract—Induced voltages due to lightning strikes along
multiconduc-tor transmission line (MTL) systems terminated with different loads at
line ends have been widely studied by solving telegraphers’ equations
us-ing 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
previ-ously 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
rail-way 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
induced-voltage 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
Uni-versity, Mehriz Branch, Mehriz 89818-56571, Iran (e-mail: Mazloom@
iaumehriz.ac.ir).
N Theethayi is with the Mainline and Metros, Bombardier
Transporta-tion, V¨aster˚as, 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
I INTRODUCTION
A model with most common devices connected along multicon-ductor 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 au-thors [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 aforemen-tioned 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 INDUCEDVOLTAGESACROSSLUMPEDDEVICESALONG THE
CATENARYTRACKSYSTEM The electromagnetic interference (EMI) source used in the calcu-lations 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]
i (0, t) = I0
η
(t/τ1)n
1 + (t/τ1)n exp
−t
τ2
With
η = exp −τ
1
τ2
n τ 2
τ1
1 / n
(2)
and I0as the amplitude of the channel base current, τ1 and τ2as 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 ter-minated to the finitely conducting ground (ground resistivity 1000 Ωm)
by their self-characteristic impedance The conductor radii and char-acteristic impedances are given in Table II Charchar-acteristic 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:
∂V (x, t)
∂x + AI (x, t) +
B
√ π
t
0
1
√ τ
∂I (x, t − τ )
∂ (t − τ ) dτ
+ L e
∂I (x, t)
∂t +
t
0
ς (t − τ ) ∂I (x, τ )
∂τ dτ = E
i
x (x, h, t) (3a)
∂I (x, t)
∂x + C e
∂V (x, t)
0018-9375/$26.00 © 2010 IEEE
Trang 2TABLE I
B ASE -C URRENT P ARAMETER V ALUES
Fig 1 MTL system representative of a typical railway traction conductor
feeding system used for simulations [1].
TABLE II
C ONDUCTOR R ADII AND C HARACTERISTIC I MPEDANCES FOR L INE
T ERMINATIONS IN F IG 1
Fig 2 Insulators, connections, and pole-footing resistance in a single track
BT system (adopted from [4]).
TABLE III
I NSULATOR M ATERIAL AND W ITHSTAND V OLTAGES
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
investi-gated
Fig 3 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].
1) Case 1: The MTL system without any components,
discontinu-ities, and nonlinearities
2) Case 2: The MTL system corresponding to a BT feeding
sys-tem 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
sys-tem 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 2 and 3, not shown in Fig 1 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 R gis the pole-footing resistance, expressed as follows [3], [4]:
R g (t) = R0
1 + I R /I g
(4a)
I g (t) = 1
2π
E0
In (4), R0 is the pole-footing resistance measured with low current,
I R is the lightning current flowing through the footing resistance, and
I g 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 1
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 time-domain (FDTD) method
A BT and AT Port Voltages
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 1 The os-cillatory voltages are due to nonlinearities On the contrary, comparing cases 1 and 3 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 correspond-ing BT windcorrespond-ing cases It is also seen in Fig 5 that the transformer
Trang 3Fig 4 Voltages appearing across BT windings for cases corresponding to
cases 1 (grey) and 2 (black).
Fig 5 Voltages appearing across AT windings for cases corresponding to
cases 1 (grey) and 3 (black).
Fig 6 Voltages appearing across relay units closer to the middle of the line
for cases corresponding to cases 1 (grey) and 2 (black).
Fig 7 Voltages appearing across relay units closer to the middle of the line for cases corresponding to cases 1 (grey) and 3 (black).
Fig 8 Voltages appearing across relay units closer to the line ends for cases corresponding to cases 1 (grey) and 2 (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
The induced voltages across the relay units at the middle of the line are similar for cases 2 and 3 (BT and AT feeding systems, respectively) and show very oscillatory behavior after a short time, as shown in Figs 6 and 7 The peak-induced voltages appearing across the relay units closer to the ends of the system are similar for cases 2 and 3 (BT and AT feeding systems, respectively) and show comparably less oscillatory behavior as per Figs 8 and 9 It is seen that relay unit no 5 in the BT system (see Fig 8, case 2) is suffering the highest voltage peak Otherwise, comparing Figs 6 and 7 with Figs 8 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
Trang 4Fig 9 Voltages appearing across relay units closer to the line ends for cases
corresponding to cases 1 (grey) and 3 (black).
III CONCLUSION
In this paper, it is shown how nonlinearities associated with
pole-footing 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
typi-cal 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
sub-jected 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
appli-cation 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
light-ning 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.
[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
Abstract—Standard sites are important for antenna calibrations
How-ever, many actual sites are not perfect for antenna calibrations due to sur-rounding reflectors and other measurement uncertainties Earlier studies were either impractical for actual sites or calculating inaccurately This pa-per 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 pro-posed 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 elec-tric 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 valida-tions [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 ver-sion 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