Electric Power Systems Research 159 (2018) 9–16

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Electric Power Systems Research

journal homepage: www.elsevier.com/locate/epsr

Analysis of the effectiveness of shield wires in mitigating

lightning-induced voltages on power distribution lines
Alexandre Piantini
University of São Paulo, Institute of Energy and Environment, Lightning and High Voltage Research Center – CENDAT/USP, Av. Prof. Luciano Gualberto,
1289, 05508-010, São Paulo, Brazil

a r t i c l e i n f o a b s t r a c t

Article history: The use of multi-grounded shield wires constitutes one of the methods that can be applied to improve
Received 27 February 2017 the lightning performance of overhead power distribution lines. Although the effectiveness of this mea-
Received in revised form 27 July 2017 sure against direct strokes is quite limited, the line performance against indirect strokes can be greatly
Accepted 21 August 2017
improved. However, the degree of improvement varies from case to case, as the magnitudes of the
Available online 8 September 2017
induced surges are significantly affected by many lightning and network parameters, as well as by the
soil resistivity. In addition, the presence of a shield wire or a neutral conductor has different effects on
Keywords:
the phase-to-ground and phase-to-shield wire (or phase-to-neutral) voltages. In this paper, an analysis
Electromagnetic transients
Lightning-induced voltages
is presented of the effectiveness of shield wires in reducing the magnitudes of lightning-induced volt-
Overvoltage protection ages on medium-voltage power distribution lines considering various realistic situations. A discussion
Power distribution lines is provided on the influence of the most important parameters on the effectiveness of the shield wire in
Shield wires terms of both phase-to-ground and phase-to-shield wire voltages.
© 2017 Published by Elsevier B.V.

1. Introduction the ground lead and the phase conductors larger than the line CFO.
Therefore, grounding at every pole, low values for the ground resis-
Lightning is one of the most important sources of disturbances tances, and a sufficient CFO between the ground lead and the phase
on overhead power systems and many studies have been under- conductors are required for the shield wire to be effective [2,3].
taken on the effectiveness of the different alternatives that can be On the other hand, due to its coupling with the phase conduc-
applied to mitigate its effects. Regarding power distribution net- tors, a periodically grounded wire reduces the magnitude of surges
works, the main methods to improve their lightning performance induced by nearby strokes and may improve the lightning per-
are the increase of the critical impulse flashover voltage (CFO) of formance of a distribution line. Its effectiveness depends on the
the line structures, the installation of surge arresters, and the use of combination of the values of several parameters as, for example,
shield wires. A grounded conductor – either a shield wire or a neu- the relative position of the shield wire with respect with the phase
tral – reduces the amplitudes of lightning-induced surges because conductors, the grounding spacing, the ground resistance, the soil
of its electromagnetic coupling with the phase conductors [1]. resistivity, the stroke current waveshape, etc [4].
Shield wires are used on transmission and subtransmission lines A number of theoretical and experimental studies, involving dif-
in order to intercept (ideally all) lightning strokes with currents ferent assumptions and conditions, have been conducted on the
larger than the critical current, i.e., the current that produces an effect of a grounded conductor on lightning-induced voltages. Both
overvoltage equal to the critical impulse flashover voltage (CFO). in Refs. [5] and [6] the shield wire is assumed to be at zero potential
They are much less frequently used on distribution lines, although at any time and it is concluded that it reduces the induced voltages
some utilities have been using them with great success [2]. on the phase conductors. The amount of reduction is dependent
The direct stroke performance of a distribution line is usually not on the position of the shield wire in relation to the ungrounded
much affected by a shield wire because of the ground potential rise conductors [5] and the adoption of the shield wires is an effec-
caused by the flow of the stroke current through the pole ground tive means of reducing the yearly line outage rate [6]. In Ref. [7],
impedance, which generally causes voltage differences between assuming just one connection of the shield wire to ground, a sim-
ple expression is derived for the calculation of the ratio between
the voltages induced on a phase conductor with and without the
presence of the shield wire. Although such expression can be used
E-mail address: piantini@iee.usp.br

https://doi.org/10.1016/j.epsr.2017.08.022
0378-7796/© 2017 Published by Elsevier B.V.
10 A. Piantini / Electric Power Systems Research 159 (2018) 9–16

to evaluate the shielding factor of typical distribution lines with

acceptable accuracy, as demonstrated in Ref. [8], its validity is
restricted, in principle, to the case of only one connection to ground.
The case of a multi-grounded shield wire has been treated, e.g.,
in Refs. [1,3,4,9–21]. In the analysis carried out in Ref. [15], using the
model presented in Refs. [13,22–24], the evaluation of the shielding
effect of the ground wire considered only the case of a perfectly con-
ducting ground. Using an improved version of the Extended Rusck
Model (ERM) [25], which allows for the calculation of lightning
transients taking into account the soil electrical characteristics,
the influence of some of the most important parameters on the
lightning-induced voltages on a line with a shield wire was studied
in Ref. [1]. In Ref. [4] the ERM was used to investigate the shield-
ing factors considering some realistic situations. Such analysis is Fig. 1. Measured and calculated induced currents at one of the shield terminations
extended in this paper, which aims at discussing the effectiveness of a 5 m high telecommunications cable by a rocket-triggered lightning.
of a shield wire in reducing the magnitudes of lightning-induced Adapted from Ref. [25].
voltages on medium-voltage power lines and the way the most
important parameters influence the shielding factors in terms of
both phase-to-ground and phase-to-shield wire voltages. currents that, due to the coupling between the wires, are induced on
The methodology adopted for the analysis is presented in Sec- the phase conductors [15]. The ERM has been validated with exper-
tion 2. The obtained results, which include a parametric analysis, imental data obtained using different techniques: rocket-triggered
are discussed in Section 3. The main conclusions are presented in lightning, lightning flashes to instrumented towers, and scale mod-
Section 4. els.
Fig. 1 presents a comparison between measured and calculated
2. Methodology currents induced at one of the shield terminations of a 2600 m
long, 5 m high telecommunications cable by a rocket-triggered
If we consider an infinite line with a phase conductor and a lightning experiment carried out by Paulino et al. [27]. The stroke
shield wire (or a neutral) grounded at a single point x1 , the fol- current magnitude and propagation velocity were about 16 kA and
lowing relationship exists between the current Ig (x1 ,t) which will 130 m/␮s respectively, and the average soil resistivity of the area
flow to ground in the event of a nearby lightning strike and the was 400 m. The stroke location was 350 m from the line and about
voltage Ug (x1 ,t) that would be induced at point x1 in the absence 2520 m from the measuring point. The shield was grounded at both
of the connection to ground [26]: ends and the ground resistances were 40  and 228 . The induced
current was measured at the termination with the higher ground
U g (x1 , t) = (0.5Z g + Rg )Ig (x1 , t) + LdIg (x1 , t)/dt (1) resistance value. Further details of the experiment can be found in
Ref. [27]. A good agreement is found between measured and calcu-
where Zg is the surge impedance of the shield wire, Rg repre- lated results. Possible reasons for the differences are discussed in
sents the ground resistance, and L is the ground lead inductance. Ref. [25], and involve the facts that in the simulations the line was
Although, strictly speaking, the term “ground impedance” is more considered straight and that neither attenuation nor distortion of
appropriate than “ground resistance”, in this paper the ground the waves along it were taken into account, the fact that the soil was
impedance is represented by the d.c. resistance of the shield wire, considered homogeneous, and the uncertainty in the estimation of
i.e., by the ground resistance. This is a reasonable approximation the stroke current propagation velocity.
in the case of grounding systems of small dimensions – which is In Ref. [28] Yokoyama et al. present measurements of lightning
typically the case of power distribution networks –, for which the currents at the top of a 200 m high tower and the corresponding
inductive and capacitive components of the ground impedance can induced voltages on a 820 m long experimental line located 200 m
be neglected in comparison with the resistive component. from the tower. The heights of the shield wire and the conductor
The induced voltage Up (x2 ,t) at point x2 on the phase conductor where the voltage was measured were 10.5 m and 10 m, respec-
is given by [26]: tively, with a horizontal distance of 2.4 m between them. Fig. 2
U p (x2 , t) = U p ’(x2 , t) − 0.5Zm Ig (x1 , t − |x2 − x1 |/c) (2) shows a comparison between measured and calculated induced
voltages relevant to Case (82-06) [28]. In this case the shield
where Up ’(x2 ,t) is the voltage that would be induced at point x2 of wire was connected to ground at only one point, about 300 m
the phase conductor in the absence of the shield wire grounding from the measuring point, and the value of the ground resistance
and Zm is the mutual impedance between the conductors. Eq. (2) was 12 . Possible reasons for the observed deviations between
shows that, due to the electromagnetic coupling between the shield calculated results and measurements performed in the system
wire and the phase conductor, the induced voltage on the latter will described in Ref. [28] involve, among others, slight imprecisions
be reduced regardless of the relative position of the wires. in the representation of the stroke current, the characteristics of
The induced voltages on the line conductors in the absence of the the optical-electrical converter used for the voltage measurements,
connection to ground are calculated using the ERM [25], which can the fact that the simulated return stroke current was assumed to
take into account realistic situations such as, e.g., a multi-conductor propagate along the lightning channel with neither attenuation nor
line with a multi-grounded neutral or shield wire over a finitely distortion, and the assumptions of a constant current propagation
conducting ground. The incidence of lightning flashes to nearby velocity of 30% of that of light in free space and of a lightning chan-
elevated objects and the occurrence of upward leaders can also be nel perpendicular to a perfectly conducting ground plane. Current
considered, as well as the presence of equipment such as trans- reflections at the top and bottom of the tower and the possible
formers and surge arresters [13]. The effect of a multi-grounded occurrence of upward leaders, not considered in the calculations,
conductor is evaluated by calculating the currents that flow to also contribute to the deviations.
ground at the various grounding points taking into account the Another comparison, now involving scale model experiments
multiple reflections and, then, the voltages associated with these performed under controlled conditions, is presented in Fig. 3, where
 A. Piantini / Electric Power Systems Research 159 (2018) 9–16 11

to-shield wire (Up-sw) voltage that is being considered. Therefore,

two shielding factors are required to evaluate the effect of the shield
wire, namely SFg and SFsw. The former is defined as the ratio of the
peak values of Up and the voltage that would be induced on the
phase conductor in the absence of the shield wire (Up’) at the point
of the line closest to the stroke location. The latter is defined in a
similar way, but with the voltage Up replaced with Up-sw. Thus,

SFg = Up/Up’ (3)

SFsw = Up-sw/Up’ (4)

According to the definitions shown in (3) and (4), the lower the
factor, the more significant the voltage reduction in relation to Up’
and, consequently, the higher the effectiveness of the shield wire.
For the case of a shield wire connected to ground at only one
point, the shielding factor SFg is given by Rusck [7] as

SFg = 1 − (hg /h)Zm /(2R g + Z g ) (5)

In Ref. [8] Andreotti et al. show that, in practice, (5) is valid inde-
Fig. 2. Measured and calculated phase-to-ground induced voltages on an experi-
mental line by a lightning flash that struck an instrumented tower 200 m from the pendently of the position of the grounding point. However, besides
line. Phase conductor and shield wire at heights of 10 m and 10.5 m, respectively. the assumption of a single connection to ground, the expression
was developed for the case of a perfectly conducting soil.
Comparisons involving calculations performed with the ERM
and the results obtained from the application of (5) to more realistic
situations will be presented in Section 3.

2.2. Base case

In order to investigate the influences of the most important

parameters on the effect of a shield wire, a base case is considered
and the shielding factors SFg and SFsw corresponding to different
conditions will be calculated and discussed in Section 3.
The basic configuration adopted in the simulations is that con-
sidered in Ref. [4] and illustrated in Fig. 4. The three-phase line
is 3 km long and the height (h) of the phase conductors is 10 m,
with distance of 0.75 m between adjacent phases. The shield wire
is equidistant from the outer phases, at the height (hg ) of 11 m. The
Fig. 3. Measured and calculated phase-to-ground induced voltages on an experi-
diameter of all the conductors is 1 cm, the grounding interval (xg )
mental line (scale model). Phase conductor and shield wire at heights of 10 m and
11 m, respectively. All parameters referred to the full-scale system.
is 300 m, and the inductance of the ground lead is 11 ␮H (1 ␮H/m).
The stroke channel is vertical, 3 km long, without branches, and
the Transmission Line model [31] is assumed for the calculation
all the parameters are referred to the full-scale system by applying of the current distribution along the lightning channel. The stroke
the scale factors corresponding to each quantity. Such factors can be current is represented by a triangular waveshape with peak value
found, e.g., in Refs. [26,29,30]. The line corresponding to the results (I) of 30 kA, front time (tf ) of 2 ␮s, time to half-value of 80 ␮s, and
shown in Fig. 3 was 1.4 km long, matched, and its two conductors, propagation velocity (vf ) of 40% of that of light in free space (c).
phase and shield wire, were placed at the heights of 10 m and 11 m The induced voltages are calculated at the point of the line
and separated horizontally by a distance of 0.75 m. The shield wire closest to the stroke location, which is equidistant from the line
was grounded every 300 m, the value of the ground resistance was terminations. The lightning stroke channel is equidistant from the
50 , and the phase-to-ground voltage was measured in front of a closest shield wire grounding points. The soil resistivity () is
grounding point. The lightning channel model was 70 m from the 1000 m, the relative permittivity is equal to 10, and the distance
line, equidistant from its terminations, and in front of the observa- between the line and the lightning strike point (d) is 50 m.
tion point. The ground plane was perfectly conducting. The stroke For illustration Fig. 5 presents, for the base case and ground
current waveform is shown in Fig. 11 of Ref. [13]. Further details of resistance (Rg ) of 50 , the induced voltage waveforms Up, Up-sw,
the scale model can be found in Refs. [10,29,30]. Other comparisons and Up’, as well as the shield wire-to-ground voltage (Usw). The cor-
with data obtained from the reduced system considering different responding values for the shielding factors SFg and SFsw are 0.817
configurations for the shield wire can be found in Refs. [10,13,15]. and 0.368, respectively, meaning that in the presence of the shield
wire and under the conditions considered, the phase-to-ground and
2.1. Shielding factors phase-to-shield wire voltages reach, respectively, about 82% and
37% of the peak value of the phase-to-ground voltage that would
The effectiveness of the shield wire in reducing induced voltage be induced in the absence of the shield wire.
magnitudes depends on the line configuration, the soil, and param-
eters of the lightning current as well. It can be evaluated through the 3. Results and analysis
shielding factor, which is defined as the ratio of the induced volt-
ages with and without the presence of the shield wire [7]. However, The influences of the most important parameters on the effec-
as shown in Refs. [1,4], the shielding factor has different behaviors tiveness of the shield wire are analyzed in this section in terms
depending on whether it is the phase-to-ground (Up) or the phase- of both shielding factors (SFg and SFsw), which are presented as
12 A. Piantini / Electric Power Systems Research 159 (2018) 9–16

Fig. 4. Basic configuration adopted in the simulations and definition of the voltages Up, Usw, and Up-sw. Base case: line length = 3 km (both terminations matched); d = 50 m;
h = 10 m; hg = 11 m; xg = 300 m; Rg = 50 ;  = 1000 m, induced voltages calculated at the point closest to the stroke location (equidistant from the closest grounding points
and from the line terminations). Only the poles corresponding to the shield wire grounding points are shown in the figure.

Fig. 6. Shielding factors SFg and SFsw as function of the ground resistance for differ-
ent values of the soil resistivity. hg = 11 m; xg = 300 m; tf = 2 ␮s; vf = 0.4 c; d = 50 m.
Fig. 5. Lightning-induced voltages at the point closest to the stroke location. Base
case: I = 30 kA; tf = 2 ␮s; vf = 0.4 c; d = 50 m; h = 10 m; hg = 11 m; xg = 300 m; Rg = 50 ;
 = 1000 m; stroke location equidistant from the closest grounding points.
(1) Phase-to-ground voltage which would be induced in the absence of the shield Fig. 6 presents the shielding factors SFg and SFsw as function of
wire (Up’); (2) phase-to-ground voltage (Up); (3) shield wire-to-ground voltage the ground resistance Rg for hg = 11 m, xg = 300 m, tf = 2 ␮s, d = 50 m,
(Usw); (4) phase-to-shield wire voltage (Up-sw). and soil resistivities of 10 m, 100 m, and 1000 m. For compar-
ison purposes, the curve obtained using Rusck’s formula (5) is also
presented.
functions of the ground resistance. Unless otherwise indicated, the
The shielding factors SFg and SFsw have opposite behaviors with
conditions and the values of all parameters are the same as those
respect to the ground resistance; the former increases and the lat-
adopted for the base case.
ter decreases as Rg increases. This means that the effectiveness of
If surge arresters are not present and corona is disregarded, the
the shield wire in reducing the phase-to-ground voltages is lower
system is linear and the induced voltages are directly proportional
for high values of Rg . On the other hand, the higher the value of
to the lightning current. Therefore, the shielding factors depend
Rg , the higher the effectiveness of the shield wire in reducing the
on the stroke current waveshape and propagation velocity, but not
phase-to-shield wire induced voltage. This can be explained as fol-
on its magnitude. On the other hand, both SFg and SFsw may vary
lows: an increase in the ground resistance leads to an increase in the
along the line and, for the same stroke location, large differences
phase-to-ground voltages Up, since higher values of Rg correspond
may be observed on the shielding factors corresponding to differ-
to lower currents to ground and, consequently, to lower ampli-
ent observation points. In the analysis presented in this section,
tudes of the voltage component responsible for the reduction of
the calculations refer to the closest point to the stroke location, on
the induced voltages [4,15]. On the other hand, as the shield wire-
which the largest overvoltages are induced.
to-ground voltage (Usw) is more sensitive to the variation of Rg , the
increase of this voltage is more significant than the decrease of Up,
3.1. Ground resistance and soil resistivity and therefore the net result is a decrease of the voltage between
phase and shield wire (Up-sw) as Rg increases [4].
The value of the ground resistance depends not only on the soil The effect of the ground resistance tends to be more pronounced
resistivity – which may vary widely – but also on the dimensions, in the case of low-resistivity soils. For  = 1000 m, a variation of
depth, and arrangement of the grounding electrodes. Therefore, Rg in the range of 10  to 450  leads to a variation of about 16%
for the same soil resistivity, different values of the ground resis- (from to 0.792 to 0.917) in SFg; for  = 10 m, the corresponding
tance are obtained in the case of different grounding systems. variation is approximately 33% (from 0,648 to 0.864).
 A. Piantini / Electric Power Systems Research 159 (2018) 9–16 13

Fig. 7. Shielding factors as function of the ground resistance for different distances Fig. 8. Shielding factors as function of the ground resistance for different heights of
between the line and the stroke location.  = 1000 m; hg = 11 m; xg = 300 m; tf = 2 the shield wire.  = 1000 m; xg = 300 m; tf = 2 ␮s; vf = 0.4 c; d = 50 m.
␮s; vf = 0.4 c.

that the variation of SFg is much smaller in comparison with that

The soil resistivity influences the shielding factors in a similar of SFsw. For instance, in the case of Rg = 10 , SFg decreases from
way, i.e., an increase in  leads to an increase in SFg and a decrease 0.792 to 0.681 (about 14%) when d varies from 50 m to 400 m,
in SFsw, but the variations of SFsw with both  and Rg tend to be whereas SFsw increases from 0.399 to 0.615 (about 54%) for the
more significant. For instance, in the case of Rg = 10 , SFg increases same variation of d.
about 22% (from 0.648 to 0.792) when the soil resistivity increases Larger variations of SFsw are observed also with respect to the
in the range 10 m–1000 m, whereas under the same conditions ground resistance. For d = 100 m and Rg in the range 10 –450 ,
the variation (decrease) of SFsw is 36% (from 0.619 to 0.399). The the variation of SFg was from 0.736 to 0.880 (about 16%), whereas
effect of the soil resistivity on SFsw tends to be more pronounced the corresponding variation of SFsw was from 0.492 to 0.246 (50%).
in the case of shorter distances between the line and the stroke
location [4]. 3.3. Shield wire height
In Ref. [19] a simplified expression is derived for the estimation
of the ratio between the peak values of the induced voltages on A shield wire must be installed above the phase conductors in
multi-conductor and single-conductor lines of the same height. In order to reduce the incidence of direct lightning strokes to them.
addition, results relevant to the use of the simplified formula pro- However, a consequence of an increase in the height of the line
posed by Rusck for the evaluation of the shielding effect of ground is that more flashes are attracted to it, thus increasing the risk of
wires are presented for a line with vertical configuration. The val- backflashovers. Therefore, in practice hg is usually not much higher
ues predicted by (5) for that specific case are about 6% lower in than about 11 m or 12 m. On the other hand, a neutral conductor,
comparison with the calculations performed by the authors. Tak- which functions as a shield wire, is usually placed at a height around
ing into account the uncertainties with which different parameters 7 m. In this typical range of hg , for the conditions of the base case,
of the lightning discharge are known, the authors conclude that the the variation of the shielding factor SFg is not so significant. This is
accuracy of the Rusck formula is quite reasonable. illustrated in Fig. 8, which presents the shielding factors as function
Although, according to Ref. [11], the Rusck formula allows for of the ground resistance for shield wire heights of 7 m, 9 m, and
an accurate prediction of the mitigation effect of the shield wire 11 m. The decrease of SFg when hg increases from 7 m to 11 m is, for
only when the number of groundings is large, Fig. 6 shows that, for the case of Rg = 10 , about 13% (from 0.910 to 0.792). The influence
the situations considered, the shielding factor SFg calculated using of the shield wire height on SFg tends to diminish with Rg .
(5) almost coincides with the results corresponding to  = 10 m. A larger influence is observed on SFsw, which, for Rg = 10  and
However, the differences increase with the soil resistivity, so that the same variation of hg , decreases approximately 19% (from 0.494
the use of (5) is not recommended for the case of moderate or poor- to 0.399). Unlike what happens with SFg, the influence of hg on
conducting soils. As the influence of  increases with the reduction SFsw tends to increase with the ground resistance; for instance, in
of the ground resistance, the largest errors are associated with the the case of Rg = 450 , SFsw decreases from 0.286 to 0.203 (about
case of high-resistivity soils and low ground resistance values. 29%) when hg varies from 7 m to 11 m.
Fig. 8 shows also that, unlike the soil resistivity, the ground resis-
3.2. Distance between the line and the lightning strike point tance, and the distance between the line and the stroke location,
the shield wire height affected the shielding factors similarly in the
The induced voltages, especially the phase-to-ground ones (Up cases considered, i.e., a decrease in hg resulted in an increase in
and Up’), are highly dependent on the distance d between the line both SFg and SFsw.
and the stroke location, and thus the shielding factors are also
affected. Such influence tends to increase in importance in the case 3.4. Grounding spacing
of stroke currents with short front times [15].
The effect of the distance on the shielding factors is illustrated The spacing between adjacent groundings is an important
in Fig. 7, where SFg and SFsw are presented as functions of the parameter in the analysis of the effectiveness of a shield wire. The
ground resistance for distances of 50 m, 100 m, and 400 m. SFg tends variations of the shielding factors with the ground resistance are
to be higher for shorter distances, whereas SFsw has the oppo- presented in Fig. 9 for grounding intervals of 100 m, 300 m, 450 m,
site behavior. This means that, the shorter the distance, the lower and 600 m.
the reduction of the phase-to-ground voltages and the greater the Under the conditions considered, SFg is approximately 1.0 for
reduction of the phase-to-shield wire voltages. Fig. 7 shows also spacings longer than about 600 m within the whole range of Rg ,
14 A. Piantini / Electric Power Systems Research 159 (2018) 9–16

its minimum in the first cycle – at about 4.3 ␮s for xg = 600 m –,

long after the peak value of Up, which occurs at about 2.2 ␮s. As
the grounding interval decreases, Up diminishes, but Usw oscillates
with a higher frequency and presents lighter oscillations, so that
its “first minimum” value – caused by the contributions arriving
from the grounding points – may be higher in comparison with the
case of longer spacing. Therefore, the peak value of Up-sw not only
decreases but is reached at a shorter time (at about 2.6 ␮s in the
case of xg = 300 m).
For spacings shorter than a certain “critical” value, the reduction
in the value of Usw becomes more significant than the reduction of
Up and, in addition, due to the multiple reflections its variation in
time tends to be lower in comparison with cases corresponding to
larger spacings. The consequence is that, for intervals shorter than
the “critical” one – which for the conditions of the base case is about
Fig. 9. Shielding factors as function of the ground resistance for different grounding
300 m –, Up-sw tends to increase as xg decreases.
spacings.  = 1000 m; hg = 11 m; tf = 2 ␮s; vf = 0.4 c; d = 50 m. It can also be observed in Fig. 9 that, although up to the critical
grounding interval SFsw decreases as xg decreases, the differences
between the values of SFsw tend to diminish with the ground
since the voltage components originated in the shield wire ground- resistance. For high values of Rg , SFsw presents just the opposite
ings are either relatively low or arrive at the observation point behavior, i.e., it increases as xg decreases. The reason is that the
after the voltage has reached its peak. This is in fact a predictable amplitudes of the oscillations in Usw are much lower in compari-
result, which is in accordance with previous theoretical (e.g., Refs. son with the cases corresponding to low values of Rg and, therefore,
[13,16,26]) and experimental (e.g. Refs. [10,26]) works where dif- Usw does not reach values as low as in those cases. For example, in
ferent line configurations were considered. For shorter spacings, the situation illustrated in Fig. 10b (Rg = 10 ), Usw reaches about
SFg tends to increase with xg , and such variation is more signifi- −20 kV at 4.3 ␮s for xg = 600 m, whereas for Rg = 500  the cor-
cant in the case of low ground resistance values. For example, the responding value is about 161 kV. Therefore, in the case of high
increase of SFg when xg increases from 100 m to 600 m is about 40% values of the ground resistance, the reduction in Usw associated
(from 0.716 to 1.000) in the case of Rg = 10  and 20% (from 0.835 with shorter grounding intervals dominates and Up-sw (and, con-
to 0.999) for Rg = 450 . sequently, SFsw) increases as xg decreases.
The behavior of SFg can be explained by the fact that each
grounding point gives rise to a voltage component that, due to 3.5. Relative position of the lightning channel and grounding
the coupling between the shield wire and the phase conductor, points
overlaps the voltage induced on the latter. As the polarity of such
components is opposite to that of the induced voltage, the latter is The shield wire factors vary according to the relative position of
reduced. Therefore, the greater the grounding density is, the greater the stroke location and the closest grounding point. In Fig. 11 the
will the number of these components be. Thus, the reductions on variations of SFg and SFsw with the ground resistance are compared
the amplitudes of the phase-to-ground induced voltages tend to for the base case and for stroke location in front of a shield wire
be more significant as the grounding spacing becomes shorter. It grounding. As in the previous cases, the observation point is in front
should be noted, however, that the arrival of the reflections from of the lightning channel.
the grounding points must take place before the induced voltage If, keeping the same distance from the line, the stroke channel is
reaches its peak, otherwise no amplitude reduction will occur. moved from a point equidistant from the closest grounding points
On the other hand, the variation of SFsw with the grounding to another one located in front of a shield wire grounding, both
interval is more complex. Depending on the combination of the val- Up and Usw decrease, as the delay of the effect of the groundings
ues of the various parameters, SFsw may decrease as xg decreases becomes shorter. The reduction of Up causes a reduction in SFg.
up to a certain interval and, then, have an opposite behavior, i.e., for However, as Usw undergoes a larger variation in comparison with
intervals shorter than this one, it may increase as xg decreases. This Up, the phase-to-shield wire voltage increases and so does SFsw.
behavior can be readily observed in Fig. 9; for instance, in the case As expected, much larger variations with the ground resistance are
of Rg = 10 , SFsw diminishes from 0.556, for xg = 600 m, to 0.399, observed on both shielding factors when the stroke location is in
for xg = 300 m. The value corresponding to xg = 450 m is 0.501. On front of a shield wire grounding, as in this case the effect of the
the other hand, for the combination considered for the parame- grounding is felt almost instantaneously at the observation point.
ters, SFsw tends to increase with xg in the case of spacings shorter The influence of the relative position of the lightning channel
than about 300 m. For xg = 100 m and the same ground resistance, and grounding points on the shielding factors depends also on the
the corresponding value of SFsw is 0.559 (approximately 40% larger distance between the line and the stroke location. As shown in Ref.
than the value obtained for xg = 300 m). [4], the influence on SFg tends to decrease as lightning moves away
The reason for this somewhat unexpected behavior can be more from the line (i.e., as d increases), whereas in the case of SFsw such
readily understood with the aid of Fig. 10, which presents the influence may increase or decrease with the distance, depending
phase-to-ground (Up), shield wire-to-ground (Usw), and phase-to- on the value of the ground resistance.
shield wire (Up-sw) voltages for Rg = 10  and spacings of 100 m, In general SFsw tends to increase when lightning strikes in front
300 m, and 600 m. In the case of large grounding spacings, the of a grounding point in the case of low ground resistance values.
shield wire-to-ground voltage presents a relative low frequency However, as its variation with Rg is larger in comparison with the
of oscillation (in comparison with the case of short intervals) and case of lightning channel equidistant from the closest grounding
may exhibit a large variation with time, as heavy oscillations are points, the difference between the values corresponding to the dif-
observed in the case of low ground resistance values, as shown in ferent stroke locations decreases with Rg and, for a certain value
Fig. 10b. For xg = 600 m, Usw varies from 336 kV to −20 kV from of Rg – which depends on parameters such as the distance d –,
2.2 ␮s to 4.3 ␮s. The peak value of Up-sw occurs when Usw reaches this behavior inverts. Therefore, in the case of high ground resis-
 A. Piantini / Electric Power Systems Research 159 (2018) 9–16 15

Fig. 10. Lightning-induced voltages Up, Usw, and Up-sw at the point closest to the stroke location for Rg = 10  and grounding spacings of 100 m, 300 m, and 600 m.
(a) Up; (b) Usw; (c) Up-sw.

Fig. 11. Shielding factors as function of the ground resistance for different positions of the stroke location with respect to the grounding points.  = 1000 m; hg = 11 m;
xg = 300 m; tf = 2 ␮s; vf = 0.4 c; d = 50 m; observation point in front of the stroke channel.

tance values, the minimum value of SFsw may take place when the behavior is observed in the case of low resistivity values [1]. The
lightning channel is in front of a shield wire grounding. effect of the propagation velocity is related also to the stroke cur-
rent front time. For stroke currents with steep fronts, which is
usually the case of subsequent strokes, the induced voltage mag-
3.6. Lightning current parameters
nitude tends to increase with vf , whereas for currents with slower
fronts, typical of first strokes, it may present the opposite behavior
The influence of the stroke current wavetail on the shielding
[1].
factors can be disregarded, and thus the parameters of interest are
For the situations considered in the base case, SFg increases with
the front time and propagation velocity.
vf ; for Rg = 10  the variation is about 7% (from 0.764 to 0.819) when
In general the amplitudes of the induced voltages tend to
vf changes from 0.2 c to 0.8 c. The variation is smaller if higher
increase with vf for high-resistivity soils, whereas the opposite
16 A. Piantini / Electric Power Systems Research 159 (2018) 9–16

values of Rg are considered (about 3% for Rg = 450 ). By its turn, [7] S. Rusck, Induced Lightning Over-voltages on Power-transmission Lines with
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