GROUND2004 International Conference on Grounding and Earthing

&
And 1st International Conference on
Lightning Physics and Effects
1st LPE Belo Horizonte - Brazil November, 2004

LIGHTNING-INDUCED OVERVOLTAGES IN OVERHEAD POWER DISTRIBUTION LINES:

IMPORTANCE OF THE LINE GROUNDING ELECTRODES MODELING

A. Borghetti(1), G. Celli(1) C.A. Nucci(1) M. Paolone(2), F. Pilo(2)

(1) Department of Electrical Engineering, University of Bologna, 40136 Bologna, Italy.
(2) Department of Electrical and Electronical Engineering, University of Cagliari, 09123 Cagliari, Italy

Abstract Models for the calculation of lightning-induced among buried and aerial electrodes by means of such an
voltages on distribution networks, should be able to take approach can be extremely time consuming.
into account the presence of shielding wires and/or neutral
conductors and of their relevant groundings. The paper On the other hand, in the lumped parameters approach
deals with the estimation of the influence of these
[4-6], which is less time consuming, when grounding
groundings with particular reference to the grounding
electrode model on the calculated values of the lightning- systems are of complex geometry, the elements of the
induced voltages. equivalent electrical network may be complex to be
inferred.
Index Terms Lightning-induced overvoltages, line
grounding, shielding wire, EMTP, lightning outages. Although, from a theoretical point of view, some criticisms
have been addressed to the lumped parameters
approach [7], recent works conclude that, in case it be
1 - INTRODUCTION appropriately applied, such an approach which is an
acceptable compromise between computational time and
The availability of a model of LEMP-illuminated lines able accuracy of the results [8] can be adopted.
of treating realistic line configurations is of utmost
importance for the assessment of the lightning/power In this paper we shall investigate the influence of different
quality performance of such systems. The two main grounding system models on the LEMP-response of an
counter measures against lightning induced overvoltages overhead distribution line.
for overhead distribution lines are the use of surge
arresters or the adoption of periodically-grounded A first grounding system model, based on the lumped
shielding wires; this makes the configuration of the parameters representation, will be used. In it, each
system to be simulated certainly complex [1]. In this elementary segment is modeled with an equivalent p
paper we shall deal with the second mitigation method model, where self and mutual inductances and transverse
and we shall focus, in particular, on the influence of the conductance are the parameters of major concern (Fig.
modeling of the line groundings. 1). As discussed in [4], this kind of cell possesses the
best frequency response for the representation of the
elementary section of the buried wire. Therefore, the
2 - COMPLEX LINE GROUNDING MODEL whole grounding electrode is represented through an
equivalent electric circuit formed by a cascade of these p
Analysis of lightning-induced transients in electric power cells. The most important parameters of the model are
systems requires careful modeling of each part of the the following:
system: here the attention is given to the groundings of
the shielding wire. In the technical literature, the r, the longitudinal resistance of the electrode;
evaluation of the current distribution in both aerial and L, M the self and mutual inductance (magnetic
buried electrodes is generally carried out by means of coupling with other electrode segments);
numerical codes based on either circuit models or on field c and g, the capacitance and conductance to
approach. earth;
c and g, the capacitance and conductance
When dealing with fast transients, the frequency range between different electrodes.
covered by the transient of interest is of crucial
importance for the appropriate choice of the model to be The interactions deriving from the coexistence of a
adopted. The significant frequency range of transients number of grounding electrodes can be taken into
due to lightning electromagnetic pulses (LEMP) is 10 kHz account by means of suitable Current Controlled Voltage
10 MHz. Sources (CCVS) introduced between the transversal
conductance and the earth. These CCVS are controlled
In this respect, the field approach represents the most by the current leaked to earth from the electrodes into
rigorous way to take into consideration the which the grounding system has been discretized [4].
electromagnetic phenomena associated with LEMP [2,3].
However, the evaluation of electromagnetic interference

109
 line. Voltages induced by indirect lightning along such a
r L, M
line can be calculated by introducing an ad-hoc
modification of the above-mentioned coupling model
c'/2 c'/2 [1,11].
c/2 c/2
g/2 g/2
g'/2 g'/2 a)
250
IBN6 Simulated
IBN6 Measured
Fig. 1. Elementary cell for lumped parameters models. 200

Induced Current [A]

A second alternative approach, based on a finite element 150

analysis to model parts that compose the earth

100
embedded electrodes, proposed by Meliopoulos et al. [9],
will be used in this paper too. Short elements of buried 50
electrodes are characterized as transmission lines with
distributed inductances, capacitance and leakage 0
resistance to earth (Fig. 2). Each element of the model
can be accurately calculated: the leakage resistance by -50
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05
means of the method of moments, while inductances and
Time [s]
capacitance can be computed from the resistance by
means of Maxwells equations. b)
1400
IG6 Simulated
AIR 1200 IG6 Measured
1000
SOIL 800
Induced Current [A]

Conductivity 600

400

200
Fig. 2. Single conductor buried in uniform soil and representation 0
of a finite element with circuit elements. Adapted from [9].
-200

-400
Both above models have been previously implemented in
the EMTP. A third, simple model, will be also used. It -600
0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05
consists of a lumped resistance corresponding to the low Time [s]
frequency value of the grounding system.
Fig. 3. Comparison between experimental and simulation results
for the 6th return stroke of the lightning flash triggered on August
2, 2003 (current amplitude: 19.6 kA, maximum time derivative:
3 - ESTIMATION OF LIGHTNING-INDUCED 110 kA/s) at the ICLRT: a) induced-current flowing through the
OVERVOLTAGES ON OVERHEAD DISTRIBUTION arrester located at the line pole closest to the stroke location
LINES IN PRESENCE OF SHIELDING WIRE (pole 6), between phase B and neutral conductors, b) induced-
PERIODICAL GROUNDINGS current flowing through the grounding of the same line pole. The
stroke location (rocket launching station) is 15 m from one end of
The models above described have been also included in the line. Adapted from [16].
the LIOV (lightning induced overvoltage) code [6]. The
LIOV code has been developed in the framework of an
international collaboration involving the University of Concerning the representation of the grounding points of
Bologna (Department of Electrical Engineering), the the shielding wire, two possible solutions have been
Swiss Federal Institute of Technology (Power Systems proposed [1,11,17]. The first one, discussed in the
Laboratory), and the University of Rome La Sapienza Appendix [1,11], concerns the modification of the
(Department of Electrical Engineering). The LIOV code is coupling model to take into account the presence of
based on the field-to-transmission line coupling periodical grounding; the second one [11,17], used to
formulation of Agrawal et al. [10], suitably adapted for the obtain the results presented in this paper, consists of
case of an overhead line illuminated by an indirect implementing the complex grounding models described in
lightning electromagnetic field. The equations are Section II above, in the LIOV-EMTP96 code.
numerically solved by a finite difference time domain
(FTDT) approach. More recently, a 2nd order FDTD The LIOV-EMTP code has been successfully tested
integration scheme has been applied [11] in order to against experimental results obtained through EMP
improve the numerical stability of the code. The return simulators [11] and real scale experiments [16]. In
stroke electromagnetic field is calculated by assuming the particular, Fig. 3 presents a comparison between the
MTLE engineering model and using the Cooray- experimental data and the simulation results obtained by
Rubinstein formula for the case of lossy grounds [12-15]. using the LIOV code relevant to the 0.75 km long
experimental line installed at the International Centre for
The LIOV code has been interfaced with EMTP96 in Lightning Research and Testing (ICLRT [20]) of the
order to make it possible to deal with realistic line University of Florida, composed of 4 conductors (3phase
configurations [17,18] and, specifically, with multi- conductors plus neutral periodically grounded) and
conductor overhead line with shielding wires and/or equipped with surge arresters and 500 resistors at the
neutral conductors grounded at same points along the line terminations.

110
The groundings of the neutral conductors, composed by The presence of lossy ground is taken into account in the
cylindrical vertical rods and placed at five different poles grounding electrode models and in the calculation of the
of the line, are modelled adopting a lumped parameter electromagnetic field using the Cooray-Rubinstein
approach whose equivalent circuit is shown in Fig. 4. formula [12-15]. The ground conductivity value is
considered equal to 0.01 S/m.
As it can be seen, the numerical results shown in Fig. 3
obtained using the LIOV code are in good agreement with In order to compare the results of the two considered
the measurements. grounding system models, a 20 m long horizontal
electrode (counterpoise), buried at 0.6 m depth and with
a radius of 0.5 cm, has been considered connected to
every shielding wire grounding. In a first approximation,
the electromagnetic coupling between the LEMP and the
grounding system conductors has been disregarded.
50 RLC-sections

Further works is certainly needed is this respect to better

assess the validity of such an assumption.

For the case of the lumped parameters model of the type

mentioned in Section II, each electrode has been divided
into forty 0.5m long elementary segments, each
represented with the same number of p cells connected
in series.

In the simulations, also a simplified grounding model

Fig. 4. Lumped parameters representation of grounding rods
consisting of a single lumped resistance has been
adopted for the calculations of Fig. 3.
considered. Its value has been estimated with reference
to the already mentioned low frequency value of the
4 - ANALYSIS OF THE LINE GROUNDING
counterpoise resistance equal to 8.5 .
ELECTRODES MODELING ON THE EVALUATION OF
LIGHTNING-INDUCED OVERVOLTAGES
4.2 - SIMULATION RESULTS
4.1 - GEOMETRY ADOPTED FOR THE SIMULATIONS
In this section the effect on lightning-induced voltages of
the type of grounding electrode model is examined.
To better assess the effect of the shielding wire, of the
distance between two consecutive groundings and of the
Fig. 6 and 7 show for the considered lightning current
model adopted for the grounding resistance on the
waveshapes the amplitudes of the induced
amplitude of the induced voltages, we have considered
overvoltages on the shielding wire and on the phase
the line geometry shown in Fig. 5 in which only the
conductor at ten observation points placed along the line
shielding wire and one phase conductor are present.
Top
each 100 m, for the three different grounding models:
view
375 m
Stroke Location
distributed parameter, lumped parameters representation
and single lumped resistance grounding model.
50 m

Overhead line

1 km
For all the grounding model, the mitigation effect of the
Front
view
Phase
conductor
Shielding
Wire
shielding wire depends significantly on the spacing
g 1 cm between two consecutive groundings. As already
observed in [1,11], an effective protection of the phase
Zc Zg
conductor can be achieved only if the spacing between
Zg Zc
two consecutive groundings is of 200 m. For larger values
9m

Zg Zg Zg Zg Zg
of spacing, only the portion of the line in the immediate
vicinity of the grounding points appears to be protected.
Fig. 5. Line geometry adopted to evaluate the effect of the
presence of a shielding wire. Lightning current: peak value 12 kA
maximum time derivatives: 12, 40 and 120 kA/s. Fig. 6 and 7 show that the differences between the
lightning induced voltages calculated using the distributed
Different distances between line groundings are parameter grounding model and the lumped parameters
considered, namely: 1 km (groundings placed at line representation are negligible, for both the shielding wire
terminations), 500 m (groundings placed at line and the phase conductor. This result supports the
terminations and at line center) and 200 m. adequacy of the lumped parameters representation for
the problem of interest, at least as far as the coupling
As shown in Fig. 5, the considered lightning stroke between the grounding elements and LEMP are
location does not face any of the grounding resistances. disregarded. On the contrary, the adoption of the single
lumped resistance grounding model results in induced
In order to investigate the behavior of different grounding voltage values that significantly differ with respect those
model with the frequency of the lightning electromagnetic calculated by using the other two models, for the cases in
field, simulations have been carried out for three different which the distances between line groundings are of 200
lightning current waveshapes, with the same peak value m and the maximum time derivatives of the lightning
of 12 kA and maximum time derivatives of 12, 40 and 120 currents are larger than the typical median value (40
kA/s. kA/s).

111
a) a)
150 120
distributed parameters gm 12 kA/us distributed parameters gm 12 kA/us
Amplitude of induced voltage in the shielding wire

lumped parameters gm 12 kA/us lumped parameters gm 12 kA/us

Amplitude of induced voltage in the phase

lumped resistance gm 12 kA/us lumped resistance gm 12 kA/us
100 distributed parameters gm 40 kA/us 100 distributed parameters gm 40 kA/us
lumped parameters gm 40 kA/us lumped parameters gm 40 kA/us

conductor along the line [kV]

lumped resistance gm 40 kA/us lumped resistance gm 40 kA/us
distributed parameters gm 120 kA/us distributed parameters gm 120 kA/us
along the line [kV]

50 lumped parameters gm 120 kA/us 80 lumped parameters gm 120 kA/us

lumped resistance gm 120 kA/us lumped resistance gm 120 kA/us

0 60

-50 40

-100 20
0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 700 800 900 1000
Distance along the line [m] Distance along the line [m]

b) b)
150 100
distributed parameters gm 12 kA/us distributed parameters gm 12 kA/us
Amplitude of induced voltage in the shielding wire

lumped parameters gm 12 kA/us lumped parameters gm 12 kA/us

Amplitude of induced voltage in the phase

lumped resistance gm 12 kA/us lumped resistance gm 12 kA/us
80
100 distributed parameters gm 40 kA/us distributed parameters gm 40 kA/us
lumped parameters gm 40 kA/us

conductor along the line [kV]

lumped parameters gm 40 kA/us
lumped resistance gm 40 kA/us lumped resistance gm 40 kA/us
distributed parameters gm 120 kA/us
60 distributed parameters gm 120 kA/us
along the line [kV]

50 lumped parameters gm 120 kA/us lumped parameters gm 120 kA/us

lumped resistance gm 120 kA/us lumped resistance gm 120 kA/us
40

0
20

-50 0

-100 -20
0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 500 600 700 800 900 1000
Distance along the line [m] Distance along the line [m]

c) c)
100 100
distributed parameters gm 12 kA/us distributed parameters gm 12 kA/us
Amplitude of induced voltage in the shielding wire

lumped parameters gm 12 kA/us lumped parameters gm 12 kA/us

80
Amplitude of induced voltage in the phase

lumped resistance gm 12 kA/us lumped resistance gm 12 kA/us

80
distributed parameters gm 40 kA/us
60 distributed parameters gm 40 kA/us
lumped parameters gm 40 kA/us
conductor along the line [kV]

lumped parameters gm 40 kA/us

lumped resistance gm 40 kA/us
40 lumped resistance gm 40 kA/us 60 distributed parameters gm 120 kA/us
distributed parameters gm 120 kA/us
along the line [kV]

lumped parameters gm 120 kA/us

20 lumped parameters gm 120 kA/us
lumped resistance gm 120 kA/us
lumped resistance gm 120 kA/us
0 40

-20
20
-40

-60 0

-80
-20
-100
0 100 200 300 400 500 600 700 800 900 1000
0 100 200 300 400 500 600 700 800 900 1000
Distance along the line [m]
Distance along the line [m]

Fig. 6. Amplitude of the induced voltage in the shielding wire Fig. 7. Amplitude of the induced voltage in the phase conductor
along the line for a variable grounding step. Line configuration along the line for a variable grounding step. Line configuration of
of Fig. 5. Stroke location at 375 m from the left line termination. Fig. 5. Stroke location at 375 m from the left line termination.
Lossy ground g=0.01 S/m; a)g=1000 m, b)g=500 m, Lossy ground g=0.01 S/m; a)g=1000 m, b) g=500 m,
c)g=200 m. c) g=200 m.

We can further observe that, both in the shielding wire

and in the phase conductor, the differences among the The representation of the shielding wire grounding as a
voltages calculated by using the three different grounding single lumped resistance is equivalent to the other two
models tend to increase with the increase of the lightning more complex models only for distances between line
current maximum time-derivative. For a current with groundings larger than 200 m and for typical values of the
maximum time-derivative of 120kA/s, the maximum maximum time-derivatives of the lightning currents. For
difference between the voltages on the phase conductor fast rising lightning currents it may be advisable the
calculated using the single lumped resistance model and adoption of a more accurate model.
the other two models is of the order of 50 %.
Coupling between LEMP and grounding elements,
disregarded in this paper, is being investigated in order to
5 CONCLUSIONS assess the adequateness of such an assumption.

Differences between lightning induced voltages

calculated using the considered grounding models exist 6 APPENDIX
only for the case of distances between line groundings of
200 m. These differences are more sensible for large Section III describes the representation of periodical
values of the lightning current maximum time-derivative. shielding wire grounding of a LEMP-illuminated line using

112
 st
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