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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005 1585
Effective Length of CounterpoiseWire Under Lightning Current
Jinliang He, Senior Member, IEEE, Yanqing Gao, Student Member, IEEE, Rong Zeng, Member, IEEE, Jun Zou,Xidong Liang, Bo Zhang, Jaebok Lee, and Sughun Chang
AbstractIn a high soil resistivity area, counterpoise wires areapplied to decrease the grounding resistance of tower groundingdevices. If the conductor of counterpoisewire is very long, althoughthe power frequency grounding resistance of the tower groundingdevice is decreased, the lightning protection performance of thetransmission line is still not good. The influences of the lengthof grounding electrodes on the lightning transient characteristicwere analyzed. The dynamic and nonlinear effect of soil ionizationaround the grounding electrode was considered in the analysismodel of transient characteristics for the grounding electrodesunder lightning impulse. The counterpoise wire has an effectivelength when lightning passes through it. When the length of a
grounding electrode exceeds the effective length, the groundingconductor will not be utilized effectively. The simulating experi-ments were performed to analyze influences of the length of thecounterpoise wire on the impulse characteristics. The formulae tocalculate the impulse effective lengths of counterpoise wires wereproposed. The model proposed in the paper has been validated bycomparing the numerical results with experimental tests.
Index TermsCounterpoisewire, effective length, grounding de-vice, lightning current, simulating experiment, transient charac-teristic, transmission line.
I. INTRODUCTION
THE performance of grounding devices under high impulsecurrent plays an important role in the safe and reliable op-
eration of power systems. The lightning protection effects of
transmission lines are related to the impulse characteristics of
grounding devices for transmission-line towers.
Reducing the impulse grounding resistance of the grounding
device of a transmission-line tower is a very important measure
to improve the lightning withstand characteristics of transmis-
sion lines.
When a lightning strikes a transmission line, high lightning
current will flow into the grounding device and dissipate into
soil. As already evidenced by many studies, the characteristic
of grounding devices subject to high impulse current is dramat-
ically different from that at low frequency. Because the induc-tive behavior of electrodes can become more and more impor-
tant with respect to its resistive behavior and, in addition, this
Manuscript received July 22, 2003; revised December 11, 2003. Paper no.TPWRD-00387-2003.
J. He, Y. Gao, R. Zeng, J. Zou, and X. Liang, and B. Zhang are withthe Department of Electrical Engineering, Tsinghua University, Beijing100084, China (e-mail: [email protected]; [email protected];[email protected]; [email protected]; [email protected]; [email protected]).
J. Lee and S. Chang are with the Electrical Environment and TransmissionGroup, Korea Electrotechnology Research Institute, Changwon 641600, Korea(e-mail: [email protected]; [email protected]).
Digital Object Identifier 10.1109/TPWRD.2004.838457
large current can generate soil ionization around the electrode,
makes the impulse response typically nonlinear.
The transient characteristic of a grounding electrode depends
upon many electrical and geometrical parameters, which in-
clude the size and the structure of the grounding device, soil pa-
rameters, impulse current parameters, and the feed point. When
the impulse current with high frequency dissipates in the soil,
the distribution of the electric charge in the space varies with
time. And it shows the feature of the time-variable field.
The engineering design of grounding devices in the protec-
tion against lightning is in dire need of scientific guidance. Thescientific design of a grounding device is not only to enhance
the safety of the system but also to reduce the construction cost
to the minimum.
There have been many papers concentrated on the transient
performance of grounding wires from experimental tests and
simulation analysis [1][11]. Pioneering work was conducted
by Sunde in the late 1930s [12], [13].
As mentioned in [14], sometimes the impulse impedance can
be much greater than the power frequency grounding resistance.
In China, in the high soil resistivity area, sometimes long coun-
terpoise wires with conductor lengths of longer than 200 m are
applied to decrease the grounding resistance of tower groundingdevices. Although the power frequency grounding resistances of
those extensive grounding electrodes are reduced, the lightning
protection performance of the transmission line is still not good
because the grounding electrode has effective length.
Several papers had analyzed the effective length of the
grounding electrode [2], [14], [15]. Mazzetti and Vaca [2] an-
alyzed the effective length of the grounding electrode, namely
the fraction of the electrode which is sufficient to dissipate the
larger part of the current, and found the effective length of the
grounding wire to be small in low resistivity soil, but increases
with soil resistivity. Gupta and Thaper [14] found that only the
limited length of the electrode from the point of the feedingof the current is effective in controlling the impulse grounding
impedance; they defined this length as effective length. They
proposed an empirical equation to calculate the effective length
of horizontal grounding wire
(1)
where is the soil resistivity, is the wavehead time. The effec-
tive length is reached when the factor reaches a value
of 0.57, where is the power frequency grounding resistance,
is the wave front time in microseconds, and is the total in-
ductance of grounding electrode. The coefficient is 1.4 for a
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single horizontal electrode fed at one end, 1.55 for a single hori-
zontal electrode fed at the center, and 1.85 for 4-arm star config-
uration fed at the star center, the effective length is for one arm
of center-injection configurations. During their analysis, the soil
ionization phenomenon was not considered. On the other hand,
the influence of the impulse current was not considered too.
The influences of the length of horizontal grounding elec-trodes on the lightning transient characteristic were analyzed by
simulating calculations and experiments in this paper.
II. SIMULATING ANALYSIS OF EXTENDED
GROUNDING ELECTRODES
A. Puncturing of Soil Under Lightning Current
When a high impulse current excites a grounding electrode,
the transient EM field would be generated in the soil around the
grounding electrode
(2)
where is the electric field strength in the soil, is the soil
resistivity and is the current density in the soil.
When the electric field strength surrounding the grounding
conductor exceeds the critical value of soil breakdown elec-
trical field strength , then the soil breakdown around the
conductor will occur. It will make the potential fall around the
grounding conductor smaller. And it will convert the affected
portion of the soil from an insulator to a conductor. The fall of
potential in the area of soil ionization is often omitted for simpli-
fied simulation. That is to say, the resistivity of the area of soil
ionization is approximately considered to be zero. The radius
of the soil ionization zone surrounding the grounding electrode
can be considered to be the equivalent radius of the electrodeduring the transient process.
The transient grounding resistance of a grounding electrode
under impulse current varies with time
(3)
where and are the current and the voltage at the feed
point. The impulse grounding resistance of a grounding elec-
trode is defined as the ratio of the peak value of voltage
developed at the feeding point to the peak value of injected
impulse current [14]
(4)
The defined impulse grounding resistance in (4) does not
have any physical meaning, but if the possible lightning cur-
rent is known, then we can use it to estimate the potential of the
grounding electrode generated by lightning current; this is very
important in lightning protection of the transmission line.
The inductive effect of grounding conductor due to the high
frequency of impulse current would block the current to flow to-
ward the other end of the conductor. This will result in extremely
unequal leakage current distribution along the grounding con-
ductor. The potential distribution along the grounding conductor
is also nonuniform. The ionization degree and equivalent radiusof the ionized soil around every point of the conductor are also
Fig. 1. Shape of the ionized zone around a grounding electrode.
Fig. 2. Modeling of equivalent radii for each segment.
nonuniform. Simulating experiments were proposed to study
the transient performance of grounding devices; the simulation
principle of impulse characteristic of grounding devices was in-
troduced in [16]. During the experiment, photosensitive films
were arranged near the electrode; the tested shape of the ionized
zone around a grounding conductor is illustrated in Fig. 1. The
current density in the point in the soil, where it is much closerto the feed point, is much larger. So, the ionized zone of the soil
around the conductor is not columniform but pyramidal.
B. Analysis Model of Extending Grounding Electrode
With respect to the complexity of the mathematical model,
the used model in this paper is shown in Fig. 2; the conductor
is represented by a set of cylindrical zones to simulate the soil
ionization phenomena as illustrated in Fig. 1. Obviously, this
assumption is reasonable. in Fig. 2 is the equivalent radius of
the th segment, which is time variable when an impulse current
is injected into the grounding electrode; and is the radius of
the metal conductor. is chosen to be large enough that theelectric field at the edge of the ionized zone is below the critical
value given in [17], which is time variable.
A horizontal grounding electrode buried in the soil under
lightning impulse current can be considered as a distributed net-
work as shown in Fig. 3. For a conductor segment, it is com-
posed of series resistance , series inductance , shunt con-
ductance , and shunt capacitance .
The shunt capacitance and shunt conductance in Fig. 3
of the electrode tied to the diameter of the conductor are re-
lated to the equivalent diameters of every conductor segment,
so they are also time-varying. But we should make a point that
the series resistance and series inductance are not affected
by soil ionization. That can be explained as follows. The direc-tions of the current flowing into soil on the boundary between
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Fig. 5. Influence of the length of a ground electrode on the transient potentialat the lightning injecting point.
Fig. 6. Ionized zones along the grounding electrodes with different lengths:(a) very short grounding electrode; (b) short grounding electrode; (c) longgrounding electrode.
maximum potential is obviously high. When the grounding elec-
trode is longer than 20 m, the peak values of maximal transient
potentials are almost the same. The time duration reaching the
maximal transient potential for a long electrode is shorter than
that for a short one. When the length of a grounding electrode
exceeds a certain value, the increment of the grounding elec-
trode length will have little effect on the maximal transient po-
tential and the impulse grounding resistance.
III. IONIZATION ZONE OF EXTENDED GROUNDING ELECTRODE
UNDER LIGHTNING CURRENT
From the simulating analysis, the ionization zones of
grounding electrodes with different lengths can be obtained as
illustrated in Fig. 6. When the length of the grounding electrode
is very short, the ionized zone in soil along the electrode is
almost equal as illustrated in Fig. 6(a); with the increment
of the grounding electrode length, the ionized zone along the
electrode has an obvious pyramidal shape as shown in Fig. 6(b);
when the grounding electrode is very long, the current leaked
by the end of the electrode is limited. And the electric fieldstrength in the soil around the end of the electrode is not strong
Fig. 7. Equivalent radii of the ionized soil zones of an electrode.
Fig. 8. Definition of the effective length of a horizontal grounding electrode.
enough to cause the soil ionization; if it is long enough, there
is not any current reaching the opposite end of the electrode as
shown in Fig. 6(c). That is to say, a grounding electrode has
an impulse effective length. When the length of a grounding
electrode exceeds the impulse effective length, the grounding
conductor will not be utilized effectively.
The equivalent radii of the ionized zones of an electrode in
two terminals and the middle point are shown in Fig. 7, which
change with time. The length of the grounding electrode is 20 m,
and the soil resistivity is 100 , the applied lightning current
is 10 kA, the burial depth of the grounding conductor with radius
of 10 mm is 0.8 m. The ionized zone is very different in different
portions of the electrode.
IV. EFFECTIVE LENGTH OF COUNTERPOISE WIRES
FROM SIMULATING ANALYSIS
Presently, all researchers have realized that a grounding elec-
trode has an effective length under impulse current. In [ 14], it
is defined as the length of the electrode in which the voltage
wave at the terminal end of the electrode has little effect on the
head end. Another definition by some researchers is the length
of a grounding electrode in which the derivative of the impulse
grounding resistance is smaller than a certain value. This defi-
nition is used in our analysis.
We defined the effective length of the grounding electrode
as the length when the decreased value of grounding resistance
with the increment of the length is smaller than a fixed value.
As shown in Fig. 8, we defined
(11)
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Fig. 9. Relation between theeffective lengthand soil resistivity under differenttime duration of the wavefront.
where is the included angle of the tangent through point P and
the horizontal direction. is selected in this paper.
The effective length of the grounding electrode is involved
with the soil resistivity , the front time , the magnitude ,
and the feed point of the injected current. When the feed point isat one end of the grounding electrode, the relation between the
impulse effective length and the soil resistivity for different
front time of impulse current are shown in Fig. 9, where
is 10 kA and the burial depth is 0.8 m.
From Fig. 8, we can observe that the effective length is shorter
for the impulse current with shorter front time. And the effective
length is longer for the soil with higher resistivity. That can be
explained as follows. For the impulse current with the same am-
plitude, the short front time means the big steepness , and
the big steepness means high frequency, which will strengthen
the inductance effect of the grounding conductor. The high resis-
tivity of the soil will block the current flowing into the soil and
force the current moving toward the terminal end of the elec-
trode. So the effective length will be longer for the grounding
electrode buried in soil with higher resistivity.
V. EXPERIMENTAL RESULTS OF EXTENDED
GROUNDING ELECTRODES
The simulation experiments were introduced in [16]. Impulse
experiments using grounding device models were systemati-
cally performed to analyze the influence of different factors
on the impulse characteristics of grounding device models ac-
cording to the simulation principle of impulse characteristics.
During the experiments, soil resistivity was changed in the rangeof 1005103 . Effects of different parameters on impulse
grounding resistance and impulse coefficients of different trans-
mission tower grounding devices were discussed. Formulae to
calculate impulse coefficients and power frequency grounding
resistance of different grounding devices were obtained. The in-
fluence of the length of horizontal grounding electrode on the
impulse resistance in different impulse current was tested and
shown in Fig. 10 and the burial depth is 0.8 m. When the length
of the electrode increases, the impulse grounding resistance de-
creases. When it exceeds a certain value, the impulse grounding
resistance reduces very slowly.
From a lot of experimental results, when the magnitude of
impulse current is fixed at a certain value, the effective lengthof the grounding electrode increases, because the portion of the
Fig. 10. Relationshipbetween theimpulse grounding resistance andthe lengthof the horizontal grounding electrode.
Fig. 11. Influence of the length of the horizontal grounding electrode on theimpulse resistance in different soil resistivity.
Fig. 12. Influence of the impulse current on the effective length of thehorizontal electrode.
impulse current flowing into the soil from the electrode end of
the feed point is reduced and then the effective length increases.
The influence of the length of horizontal grounding electrode
on the impulse grounding resistance in different soil resistivity
was tested and shown in Fig. 11. We can observe that the
grounding resistance easily reaches a saturation state if the soil
resistivity is low.
Under the impulse current with waveshape of 2.6/50 , the
effective length of the grounding electrode is shown in Fig. 12.
With the increase of the impulse current, the effective length
decreases. The influence of the soil resistivity on the effective
length of the horizontal electrode is shown in Fig. 13; with theincrease of soil resistivity, the effective length increases.
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Fig.13. Influence of thesoil resistivity on theeffective length of thehorizontalelectrode.
TABLE ICOMPARISON OF GROUNDING ELECTRODE EFFECTIVE LENGTHS IN DIFFERENT
SOIL RESISTIVITY BETWEEN EXPERIMENTAL AND ANALYZED RESULTS
VI. REGRESSIVE FORMULAS TO CALCULATE EFFECTIVE
LENGTH OF COUNTERPOISE WIRES
The data in Table I, derived from analyzing simulating test
results and numerical ones, are the effective length of the
grounding electrodes buried in the soil with different resistivity,
when the impulse current, with 2.6/50- waveform and 10-kA
amplitude is injected at one end. Comparing the data in Table I,the effective lengths obtained from the simulating calculation
and test are close, but they have differences in comparison
to the results obtained from Guptas formula (1), which is
caused by different definitions of effective length and without
consideration of soil ionization and lightning current in (1).
Synthesizing the results of the impulse effective lengths of
the horizontal grounding electrode from numerical analysis and
simulating test, the formula to estimate the impulse effective
length of grounding electrodes is obtained by the least squares
curve fitting methods, when the feed point is at one end
(12)
where is the front time of applied impulse current in , is
the magnitude of the applied impulse current in kA, and is soil
resistivity in . Formula (12) can be used for the burial depth
of larger than 0.8 m. The influence of conductor radius on the
effective length is not obvious, and we can use (12) to estimate
the effective length of counterpoises with different conductor
radius.
From the practical point of view, the configuration of the
counterpoise should be the center injection type. For 40-kA
lightning current, the effective lengths of end-injection single
electrode, center-injection single horizontal electrode, and
center-injection four-arm star counterpoise are compared inFig. 14, the effective length of center-injection type is for its
Fig. 14 Comparison of the effective lengths of end-injection type andcenter-injection-type counterpoise wires.
one-arm. Similarly, from experimental and analyzed results,
the effective length for one arm of center-injecting single
horizontal electrode was concluded as
(13)
and the effective length for one arm of center-injecting four-arm
star counterpoise wires can be calculated by
(14)
VII. CONCLUSION
When high impulse current excites a grounding electrode,
the large current can generate complicated soil ionization sur-
rounding the grounding conductors, which makes the transientcharacteristic of the grounding electrode typically nonlinear.
The paper presents an effective method for this problem,
which is a numerical calculation approach based on the circuit
model of distributed time-variable parameters. It accurately
takes into account the nonlinear effects of breakdown in the soil
surrounding the ground conductors. This model can be used to
accurately predict the transient characteristic of the grounding
systems excited by impulse currents.
A grounding electrode has an impulse effective length.
When the length of a grounding electrode exceeds the impulse
effective length, the grounding conductor will not be utilized
effectively.The influential factors on the effective length of counterpoise
wire are analyzed. The effective length increases with the soil
resistivity and the wavefront time of impulse current, but de-
creases with the magnitude of lightning current. The formulae
to calculate the impulse effective length of counterpoise wires
are provided in this paper. It will be helpful for the technician to
design and reform ground systems against lightning.
The analyzed results have been validated by comparison with
experimental ones.
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Jinliang He (M02SM02) wasborn in Changsha, China, in 1966. He receivedthe B.Sc. degree in electrical engineering from Wuhan University of Hydraulicand Electrical Engineering, China, in 1988, the M.Sc. degree in electrical engi-neering from Chongqing University, Chongqing China, in 1991, and the Ph.D.degree in electrical engineering from Tsinghua University, Beijing, China, in1994, respectively.
Currently, he is Vice Chief of High Voltage Research Institute at TsinghuaUniversity. He became a Lecturer in the Department of Electrical Engineeringat Tsinghua University in 1994, and an Associate Professor in the same De-partment in 1996. From 1994 to 1997, he was the head of High Voltage Labo-ratory at Tsinghua University. He was also a Visiting Scientist in Korea Elec-
trotechnology Research Institute, involved in research on metal oxide varistorsand high voltage polymeric metal oxide surge arresters from 1997 to 1998. In2001, he was promoted to a Professor at Tsinghua University. His research in-
terests include overvoltages and EMC in power systems and electronic systems,grounding technology, power apparatus, dielectric material, and power distribu-tion automation. He is the author of three books and many technical papers.
Dr. He is a senior member of the China Electrotechnology Society, and amember of the International Compumag Society, the vice chief of China Light-ning Protection Standardization Technology Committee, and members of Elec-tromagnetic Interference Protection Committee and Transmission Line Com-mittee of China Power Electric Society, member of China Surge Arrester Stan-dardization Technology Committee, members of Overvoltage and Insulation
Coordination Standardization Technology Committee in China Electric PowerIndustry.
Yanqing Gao (S02) received the B.Sc. degree from the Department of Elec-trical Engineering, Tsinghua University, Beijing, China, in 1999, where he iscurrentlypursuing thePh.D.degree in theDepartmentof Electrical Engineering,Tsinghua University.
His research fields include overvoltage analysis in power system, groundingtechnology, and electromagnetic compatibility (EMC).
Rong Zeng (M02) was born in Shaanxi, China, in 1971. He received the B.Sc.,M.Eng., and Ph.D. degrees from the Department of Electrical Engineering atTsinghua University, Beijing, China, in 1995, 1997, and 1999, respectively.
From 1999 to 2002, he was a Lecturer in the Department of Electrical En-gineering, Tsinghua University. Currently, he is an Associate Professor in theDepartment of ElectricalEngineeringat Tsinghua University.His research inter-
ests include high voltage technology, grounding technology, power electronics,and distribution system automation.
Jun Zou was born in Wuhan, P. R. China, in 1971. He received the B.S. andM.S. degrees from Zhengzhou University in Zhengzhou, Henan Province, in
1994 and 1997, respectively, and the Ph.D. degree from Tsinghua University,Beijing, China, in July 2001, all in electrical engineering.
His research fields include computational electromagnetics and electromag-
netic compatibility (EMC).
Xidong Liang was born in Jiangyin, China, in 1962. He received the B.Sc.,M.Sc., and Ph.D. degrees in high-voltageengineering from Tsinghua University,Beijing, China, in 1984, 1987, and 1991, respectively.
Currently, he is the Dean of the Department of Electrical Engineering, Ts-inghua University. From 1991 to 1992, he conducted research as a VisitingScholar with the University of Manchester Institute of Science and Technology(UMIST), Manchester,U.K. Then, he wasan AssociateProfessor with TsinghuaUniversity in 1993and a Professor in 1997. Hisinterestsinclude outdoor insula-tion, composite insulators, and organic outdoor insulation materials, and EMC.
Dr. Liang isthe Senior Member of CSEE from 1998 and a Member of CIGRESC33 from 2000.
Bo Zhang was born in Datong, China, in 1976. He received the B.Sc. and
Ph.D. degrees in theoretical electrical engineering from the North China Elec-tric Power University, Baoding, China, in 1998 and 2003, respectively.
He is currently a postdoctoral researcher with the Department of ElectricalEngineering, Tsinghua University,Beijing, China. His research interests includecomputational electromagnetics, grounding technology, and EMC in powersys-tems.
Jaebok Lee was born in Iri, Korea, in 1962. He received the B.Sc., M.Sc., andPh.D. degrees in electrical engineering from Inha University, Inchon, Korea, in1985, 1987, and 1999, respectively.
Currently, he is a Principle Researcher of the electrical environment andtransmission group of the Korea Electrotechnology Research Institute (KERI),Changwon, Korea, where he has been since 1987 as a Researcher of the Power
System Insulation Coordination Lab. He was actively involved in electromag-netic-compatibility (EMC) design of low-voltage power and control systems.His interests include surge protection and electromagnetic compatibility (EMC)in power systems and electronic systems and grounding technology.
Dr. Lee is a member of the Korean Institute of Electrical Engineers (KIEE)and a Korea Chapter member of IEC TC 77A.
Sughun Chang was born in Seoul, Korea, in 1974. He received the B.Sc. andM.Sc. degrees in electrical engineering from Inha University, Inchon, Korea, in1996 and 1999, respectively.
Currently, he is with the Korea Electrotechnology Research Institute (KERI),Changwon, Korea. He was actively involved in electromagnetic-compatibility(EMC) design of low-voltage power and control system. His research interestsinclude surge protection and EMC in power systems and electronic systems andgrounding technology.
Mr. Chang is a member of the Korean Institute of Electrical Engineers(KIEE).