14th International Conference on Optimization of
Electrical and Electronic Equipment OPTIM 2014
May 22-24, 2014, Brasov, Romania
Algorithm Based on Attractive Radius for Estimating the Lightning Protection Efficiency
Dragos-Lucian Machidon1, Marcel Istrate1, Ioan Viorel Banu1
1
“Gheorghe Asachi” Technical University of Iasi, Romania
Abstract
The present paper presents a new algorithm for determining the lightning protection zones generated by vertical rods protective
systems. While the general knowledge over the lightning’s orientation process towards the ground or other structures has
significantly improved in the last years, when it comes for calculating the lightning protection zones the rolling sphere method is
still the most common method used although it is based on the late 60’s electrogeometrical theory [1].
As a consequence it is imperative to elaborate a new methodology for determining the lightning protection zones on the base of
the leader progression theory’s principles.
The first attempt to establish a methodology for calculating the protection zones using the concept of attractive
radius was conducted by Rizk in 2010 [2]. He proposed several mathematical expressions for calculating the length
of the protected zone for the case of a single rod and the minimum protected height between two and four rods.
However those expressions are insufficient when calculating the dimensions of the protection zone’s generated by
complex lightning protective systems, as the protection zone’s dimensions in different horizontal planes are of great
concern too.
In this paper the authors continue the work conducted by Rizk, succeeding to improve and develop a complete
methodology, as graphical construction rules and mathematical expression for calculating the dimensions of the
protection zones were established for groups of one up to four vertical rods. Extensive discussions were carried on
for all possible situations thus identifying some existing limitations, especially when estimating the inner protected
height between groups of three or four vertical rods. The obtained model was named the attractive radius method.
According to the principles of the leader progression theory one vertical rod will ensure the protection of a certain
grounded structure if the attractive area of the grounded object is entirely included in the attractive area of the
vertical rod, as the following expression is satisfied [2]:
Ra1  Ra 2  x
(1)
where: Ra1 is the attractive radius of the vertical rod, Ra2 is the attractive radius of the object to be protected and x is
the distance between those two structures. The general expression of the attractive radius is [2]:
Ra  A  hb  I c
(2)
where: h is the height of the grounded object; I is the lightning current intensity; A, b and c coefficients proposed by
different researchers.
Starting from (1) and (2) the mathematical expressions for calculating the protection zone’s dimensions were
established, the main parameters to be determined being presented in Fig.1 for the case of two vertical rods.
Inner protected
zone
Outer protected
zones
d0
rx
h
r0
h0
x
x
h
rx
dx
hx
r0
Fig.1. Vertical and horizontal section through the protection zone of two vertical rods having the same height
References
[1] H.R. Armstrong, E.R. Whitehead, “Field Analytical Studies of Transmission Line Shielding”, IEEE Transaction
on Power Apparatus and Systems, vol. PAS 87, Issue 1, pp.270-281, 1968;
[2] F. A.M. Rizk, “Modeling of substation shielding against direct strikes”, IEEE Transactions on Electromagnetic
Compatibility, vol. 52, no. 3, pag. 664-675, August 2010.
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