30th International Conference on Lightning Protection - ICLP 2010

(Cagliari, Italy - September 13th -17th, 2010)

ANALYSIS OF THE OVERVOLTAGE IN THE POWER

DISTRIBUTION NETWORKS USING TWO MODELS OF THE
GROUNDING RESISTANCE: THE TRADITIONAL MODEL
WITH CONSTANT RESISTANCE AND CONSIDERING A
TRANSIENT RESISTANCE

Thair I. A. H. Mustafa*1, Hugo D. Almaguer*2, Nabi M. Almeida*3, Luiz H.Meyer*4, Marcos Telló**5
*
University of Blumenau -FURB, Department of Electrical and Communications Engineering
Campus II, Rua São Paulo, 3250, Blumenau/SC Zip Code 89030-000 Brazil
1
tim@furb.br
2
hugo@furb.br
3
nabima@gmail.com
4
meyer@furb.br
**
Companhia Estadual de Distribuição de Energia Elétrica, CEEE-D
Rua Joaquim Porto Vilanova, 201, Porto Alegre/RS Zip Code 91410-400 Brazil
5
MarcosT@ceee.com.br

In this work, results of the overvoltage level in the

ABSTRACT
secondary network, when the primary is subjected to the
This work presents an analysis of the overvoltage in the lightning discharges will be presented. Simulations using
distribution network caused by lightning discharges. the ATP, applying the traditional grounding resistance
Numerical simulations using TLM- Transmission Line and transient grounding resistance (obtained from TLM)
Modeling and ATP- Alternative Transients Program are for the transformer and customer were performed.
presented to show and to establish comparisons between two
models for the grounding resistance of the transformer and 2 THE TLM METHOD
customer: the traditional model with constant resistance
and considering a transient resistance. The TLM method is a numerical modeling technique
based on temporal and spatial sampling of
1 INTRODUCTION electromagnetic fields. Unlike other time-domain
The lightning discharges are some of the main causes methods, which are based on the direct discretization of
of disturbances in distribution systems. The study of the Maxwell’s time-dependent equations, the TLM method
voltages transferred to the customers or the overvoltage embodies Huygens’s principle in discretized form [2].
depends on the knowledge of the characteristics of the In a typical TLM simulation, a mesh of transmission
voltages induced in the primary networks and on the high lines represents the propagation space. Electric and
frequency behavior of the transformer. Analysis of the magnetic fields are made equivalent to voltages and
overvoltage requires the utilization of reliable models to currents on the network, respectively. The simulation
represent the elements involved in the phenomenon. In starts by exciting the mesh at specific points by voltage
this work, it was used the transformer model already impulses and follows the propagation of these impulses
validated in [1], subjected to the impulse current with over the mesh as they are scattered by the nodes and
standardized waveform. bounce at boundaries.
The numerical method of TLM [2] can be an attractive In this work the 3D mesh employed is based on the
alternative to be used in the studies of impulsive electric Symmetrical Condensed Node (SCN) [2- 4], shown in
grounding problems. The main focus of the TLM Fig. 1. The node has 12 voltage ports, and six total field
application in this work will be the behavior analysis of quantities (Ex, Ey, Ez, Hx, Hy and Hz) at the center of the
the transient impedance or transient grounding resistance cell are calculated from these voltages.
(TGR) in topologies employed in electric power
distribution networks.

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 in accordance with the transversal grounding rod section
diameter (smallest dimension of the structure).
The technique described in [2], known as matched
(absorbing) boundary condition, was used for the
representation of the absorbing contours. According to
the same, the external contours are implemented with the
use of termination impedances, with a value equal to the
characteristic impedance of the environment (in this case,
air and soil), connected to the extremities of the nodes
positioned at the limits of the TLM network.
The system excitation was made by means of a current
surge injection into the conductor nodes that conform the
grounding rod connected to the descending conductor
(see Fig. 2). The employed lightning current surge model
was the one recommended by the International
Electrotechnical Commission – IEC (IEC 60-1) [6].
The transient grounding resistance (TGR) of the
structure is determined from the TLM simulation in the
time domain. The calculation is obtained for each
Figure.1 The TLM Symmetrical Condensed Node (SCN). iteration by means of the ratio between the voltage (Vn)
and the current (In) at the rod excitation node:
The computational codes with the implementation of
TLM formulations mentioned above were developed by Vn (t )
TGR(t ) = (1)
the authors using FORTRAN 90 language. More details I n (t )
about the TLM formulations, its applications and
computational requirements can be found in [2-4]. The number of iterations in the time dominion must
be sufficient to converge the TGR (the transitory
3 MODEL OF THE GROUNDING TOPOLOGY
component) with the grounding resistance value (steady-
AND DEVELOPMENTS
state).
In Fig. 2, the studied grounding topology is The conductive structures above the soil surface
presented; it is compounded of a steel copperweld rod level (such as the descending conductors of the protection
with a 13 mm diameter and a length of 2.40 m, vertically system) were not considered in the simulation. The
positioned [5]. The parameters of the soil utilized were: ionization effects of the soil, as well as the pellicular ones
relative electric permittivity of the soil (εr): 10 and around the conductor, were not considered either.
variation of the electric soil resistivity (ρ): 300 to 2000 The behavior of the transient grounding resistance
Ω.m.
curve was studied for the described grounding topologies
taking into account, the connecting conductors; the
variation of the electric soil resistivity (ρ, in Ωm); and the
variation of the relative electric permittivity of the soil
(εr).

4 RESULTS FROM THE TLM METHOD

With the aim of verify the results obtained, a study
(see Table 1) was performed to compare of grounding
resistance values in the steady state, obtained from the
TLM simulation with those calculated by known analytic
expressions [7]:

ρ  4L  (2)
R=  ln( ) − 1
2πL  a 
Figure 2. Grounding topology with a vertical copperweld rod;
were L is the rod length, a the radius of the transversal
For the TLM-3D network conformation, the spatial rod section.
length of the cubic SCN nodes edges was ∆l = 13 mm,

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 Table 1: Comparison of grounding resistance results
considering different values of soil electric resistivity.
Ω) from
R (Ω Relative
5 RESULTS FROM THE ATP SIMULATION
Resistivity Ω) from
R (Ω
analytic Variation(%)
Ωm)
(Ω TLM The ATP [8] was used to perform the simulations
expression [7]
for the analysis of the overvoltage on a costumer
300 100,74 125,29 19,59
connected to the secondary of the distribution transformer
400 129,76 167,05 22,32
modeled in [1]. It was simulated the case of direct
500 158,00 208,82 24,33
lightning discharges in the primary of the transformer.
1.000 293,00 417,63 29,84
The basic configuration used in the simulations is
1.500 423,35 626,44 32,42
shown in Fig. 5. This figure shows the transformer and
2.000 550,00 835,26 34,15
the costumer being grounded with a transient grounding
resistance (TGR), obtained using the TLM method.
The Fig.3 shows the transient grounding resistance
curves, obtained through the TLM simulation for the
values of resistivity of the soil between 300 and 2000
Ω.m.

Figure 3. Transient grounding resistance obtained from TLM

simulation.

The Fig.4 present a result of the transient

grounding resistance measured in high frequency [5], for
the one rod topology and considering a soil resistivity of
1500 Ω.m. It can be observed that the curve shape and
trend are very similar to the simulated one. Similar
analysis can be done for the steady-state values.

Figure 5. Modeling that was used for simulation in the ATP.

The Table 2 and Fig. 6 show the results obtained in

this stage of the research: The peak of the overvoltage in
a phase of the costumer submitted to the lightning
discharge that occurred in the primary of the distribution
transformer, considering the constant grounding
resistance (CGR), transient grounding resistance and
different values of the soil electric resistivity.

Figure 4. Transient grounding resistance curve for the one-rod

grounding structure.

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 implement others configurations of the grounding
Table 2: Overvoltage values obtained with ATP simulation. topologies (ex. three vertical and interconnected rods, soil
stratification).

Peak of overvoltage (V) ACKNOWLEDGMENT

Resistivity
Ωm)
(Ω Using Using The authors would like to thank the Companhia Estadual
CGR TGR de Distribuição de Energia Elétrica – CEEE-D in Rio
300 677 709 Grande do Sul State and University of Blumenau - FURB
400 631 700 in Santa Catarina State, Brazil for their financial support
500 588 686
in the researches.
1.000 509 647
1.500 322 624
2.000 261 610
7 REFERENCES

[1] A. G. Kanashiro and A. Piantini, “Surges transferred to

the low-voltage network via transformer – The influence
of the load connected to the secondary” in Proceedings
of GROUND´2002- Internatiional Conference on
Grounding and Earthing & 3rd Brazilian Workshop on
Atmospheric Electricity, Rio de Janeiro, Brazil, Nov.
2002.
[2] C. Christopoulos, The Transmission-Line Modeling
Method- TLM, New York: IEEE Press and Oxford
University Press, 1995.
[3] H. D. Almaguer, “Contribuição ao Método da
Modelagem por Linhas de Transmissão (TLM) e sua
Aplicação aos Estudos em Bioeletromagnetismo”, Thesis
of PhD’s Degree in Electrical Engineering, Federal
University of Santa Catarina, Brazil, 2003.
[4] P. Naylor and R. Ait-Said, “Simple Method for
Figure 6. Comparison of the overvoltage level between two models
Determining 3 – D TLM Nodal Scattering in Nonscalar
of the grounding resistance, considering different values of the Problems”, Electronics Letters, vol. 38, n. 25, pp. 2353 –
resistivity. 2354, December 1992.
[5] H. D. Almaguer and A. Raizer, “TLM Modeling for
6 CONCLUSIONS impulse grounding in electric distribution systems” in
Proceedings of GROUND´2006 and 2rd LPE-
The overvoltage levels obtained from the simulation International Conference on Grounding and Earthing &
using the model with the transient grounding resistance 2rd International Conference on Lightning Physics and
were bigger than the overvoltage values obtained Effects, Maceió, Brazil, Nov. 2006.
applying the traditional grounding resistance. This [6] IEC - International Electrotechnical Commission,
means that the grounding model proposed (using the “Section of IEC 1000 – 4 – 5”, pp. 39, 1995.
TGR) is more conservative than the traditional model. [7] S. F. Visacro, Aterramentos Elétricos. São Paulo: Ed.
Artliber, 2002
The results show that there is a significant difference
[8] M. Kizilcay, M. and L. Prikler, ATP-EMTP Beginners
in the overvoltage levels, with the increase of the soil Guide for EEUG Members, Osnabruck University of
resistivity and modeling the grounding systems with Applied Science, Germany, June 2000.
transient resistance. [9] M. Telló, G. Dias, A. Raizer, H. D. Almaguer, T. I.
It can lead to an under rating of the protection Mustafa and V. Coelho, Aterramento Elétrico Impulsivo
associated to the distribution network, once that em Baixa e Altas Freqüências,, EDIPUCRS, 1a Edition,
overvoltage levels do not are observed when constant 2008.
grounding resistances are considered.
To identify which of the two models that presents the
higher accuracy, the experimental measurements should
be developed to establish comparisons [8,9].
In the next step of this research, new simulations will
be performed with different values of the grounding
resistance in the transformer and customer, also to

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