Lightning protection with the mesh method: Some models for the effectiveness analysis

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Journal of Electrostatics 64 (2006) 283–288 www.elsevier.com/locate/elstat

Lightning protection with the mesh method: Some models for the effectiveness analysis M. Szczerbin´ski Department of Electrical Power Engineering, AGH—University of Science and Technology, al. Mickiewicza 30, PL 30-059 Krakow, Poland Received 16 September 2004; received in revised form 29 April 2005; accepted 7 July 2005 Available online 8 August 2005

Abstract Lightning protection of structures using the Mesh Method is based on long-term experience but does not involve any theoretical background. This paper proposes to prove the effectiveness of the Mesh Method using modified electro-geometrical theory. A roof constructed from insulating or low-conductivity material has been treated as permeable for the ‘rolling sphere’. The analysis confirms the high efficiency of low-suspended or roof mounted horizontal air terminals. In particular, when any conducting elements in the object interior are not closer to the meshwork surface than half the length of the square mesh side, the mean value of the protection unreliability coefficient falls in the range 5
105 to about 107 (depending on the protection level). When conducting elements are placed directly below the roof surface, the protection effectiveness falls considerably. The calculated protection unreliability is strongly influenced by mean lightning parameters. Considerable discrepancy between the data in references makes it impossible to obtain unambiguous, quantitative evaluation of the efficiency of the low-suspended terminals. r 2005 Elsevier B.V. All rights reserved. Keywords: Lightning protection; Meshwork method; Faraday cage; Rolling sphere method

1. Lightning attachment concept A lightning stroke proceeds via a set of sequential events. The so-called step (downward) leader is a predischarge phenomenon which approaches the ground in discrete steps. When the step leader reaches sufficiently close to the ground or grounded objects, a connecting (upward) leader is initiated from the earth or from an object. Contact of the two leaders produces an ionized channel connecting the cloud to the earth and the main lightning flash takes place. The orientation distance (or striking distance) is taken to be that height of the leader tip above the ground at which critical breakdown strength is reached across the final air gap and the connecting leader starts. On the grounds of investigations that date back to 1940s of the 20th century, the dependence between the orientaTel.: +48 12 2692857; fax: +48 12 6345721.

E-mail address: [email protected]. 0304-3886/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2005.07.002

tion distance and the peak value of the lightning current has been found. The relevant analytical expression that forms the basis for the so-called electro-geometrical model of the lightning interception by a ground object has the form [1,2] D ¼ kI c .

(1)

Here D is the orientation distance in meters, I the peak lightning current in kA, k (A m1) and c are parameters estimated by several authors to be in the ranges 3:3oko15:3 and 0:65oco0:85 [1]. From measurements taken by many researchers (over many years in various parts of the world), sufficient data are available to show that the statistical distribution of the peak values of lightning current follows a logarithmic normal distribution. Thus it is possible to determine the distribution function of the orientation distances "  # 1 1 1 1 D 2 ln f ðDÞ ¼ pffiffiffiffiffiffi exp  . (2) 2 cs D50% cs 2p D

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M. Szczerbin´ski / Journal of Electrostatics 64 (2006) 283–288

In the above equation, the meaning of each variable is as follows: D50% is the median value of the orientation distance, s is the standard deviation of the peak value of lightning current and c the parameter from Eq. (1). The angle j between the last step of the downward leader and the vertical is also a random variable. Its probability density function has the form [3,4] 2 cos2 j. (3) p In the following analysis we assume that the leader always moves in the vertical direction (j ¼ 0). The latter is a commonly accepted simplification [5].

f ðjÞ ¼

2. Mesh method lightning protection concept In the latter part of the 18th century, Benjamin Franklin proposed the original concept of lightning protection for buildings. His well-known idea was to position a metallic lightning rod (called an air terminal in modern parlance) above the building to intercept lightning flashes that otherwise would strike the building. The lightning rods were attached to down conductors, and the down conductors were attached to ground rods driven into the soil adjacent to the building. As stated in [6], this method has worked ‘‘statistically’’ well for historical (non-conductive) construction for many years. However, it does not effectively prevent lightning-induced high electric fields that cause damage to modern ‘chip’-based electronic systems inside a protected structure. Nowadays, the most common method used to design the Franklin rods arrangement is the ‘Rolling Sphere’. This is an imaginary sphere (the radius is equal to the assumed orientation distance of the lightning) which is rolled over the rods and building. All contact points of the protected structure are deemed to require additional air terminations. The sphere radius (60, 45, 30, and 20 m) is chosen according standard level protection [7,8]. A radius of 20 m is recommended for protection of extremely large structures or for housing explosive or flammable contents. The main shortcoming of the Rolling Sphere method is that it assigns equal leader initiation ability to all touch points of the structure, irrespective of the electric field intensification created by geometric shape. More than a century after the invention of the Franklin-type of lightning protection, J.C. Maxwell, in 1876, suggested that a lightning rod attracted a greater number of lightning flashes to a building than in the absence of the rod. He thus proposed to apply the principle of the ‘Faraday cage’ concept, in which a ‘meshwork’ of conductors or air terminations is placed at set intervals over a structure [6]. Since that time, both Franklin and Faraday types of lightning protection have

been in use alone or in combination, but the Faraday type has by far become the more prevalent of the two in some European countries. Today, the Faraday lightning protection scheme is called the meshwork method (MM). During the second half of the 20th century, the rapid development of external protection theory focused on the Franklin rod scheme, but the ‘Faraday cage’ (meshwork) method was generally bypassed. In this paper, we analyze the MM in detail. As we shall show, the lightning stroke probability for a structure equipped with meshwork protection is smaller than for that obtained using the Franklin method. Similarly, we will show that this type of protection provides significant shielding for electromagnetic energy in the frequency range of lightning. With decreasing width of the spaces in the mesh, the voltages induced by lightning in a building internal wiring decrease. For many cases, such as situations involving sensitive electronic devices, such induced voltages are of great importance. Finally, we show that strip-conductor air terminals may be easily assembled on extended structures (e.g. flat roofs) and they are visually inconspicuous despite the presence of rods. Although the mesh method has an obvious advantage over other types of lightning protection, exact expressions for the protective effect produced by this type of air termination do not exist. In practice, mesh size is determined by experience rather by well-founded theoretical principles. For example, there is no documented justification and validation for the spacing (i.e. the length of the mesh size) specified in European standard IEC 61024 [7,8] for the stated protection effectiveness (see Table 1). For example, the IEC mesh method for level IV protection specifies a mesh size of 60 m for the protection of a plane horizontal surface. This situation was analyzed by The International Conference of Large High Voltage Electric System (in French: Conseil International des Grands Reseaux Electriques, CIGRE)— document CIGRE TF33.01.03 [9] for mesh conductors. If the latter are placed 1 m above the surface of the roof, the resulting interception efficiency becomes 0.75 which is somewhat below the value of 0.8 specified in the Standard. As noted by M. Darveniza [10].

Table 1 Required ‘rolling sphere’ radius and mesh size according to protection levels [7] Protection level

Protection effectiveness (%)

‘Rolling sphere’ radius D (m)

Mesh square side M (m)

I II III IV

98 95 90 80

20 30 45 60

5 10 15 20

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According to the conventional RSM (Rolling Sphere Method) with a sphere radius of 60 m, an intermediate mesh conductor is required (giving a mesh size of 10 m) [10]. But M. Darveniza also states that There is no documented justification and validation of the spacing specified in IEC 61024 for the stated interception efficiencies [11]. Note that the 1-m distance assumed in Ref. [9] is arbitrary but it builds a bridge between the Franklin idea and Faraday cage conception. (The genuine Faraday cage conception allows strip conductors to be put directly on the protected surface.) According to Horvath [12], the MM has been verified by long experience without any theoretical or experimental research. Its protective effect probably originates from the good electric conductivity of the air termination system against the insulating or poorly conducting materials of the roof to be protected.

Fig. 1. Rolling sphere’ penetration into a structure of thin (i.e. assumed as not disfiguring the electric field) non-conducting material: The ‘rolling sphere’ contacts a conducting grounded element in the interior (a). The ‘rolling sphere’ cannot contact a conducting grounded element in the interior (b).

3. Models for ‘rolling sphere’ penetration through the mesh Let us assume the situation presented in Fig. 1, in which an insulating (or poorly conducting) roof is ‘penetrable’ by a ‘rolling sphere’. For this case, there are two opposing situations: (a) The ‘rolling sphere’ contacts a conducting grounded element inside the structure (Fig. 1a), hence protection using the mesh method is unreliable on the basis of the ‘rolling sphere’ concept. (b) The ‘rolling sphere’ cannot contact a conducting grounded element inside the structure (Fig. 1b), hence protection with the mesh method is reliable on the basis of the same idea. By taking into account the rolling sphere radii and mesh sizes for particular protection levels (see Table 1), one has the opportunity to calculate—using the simple geometrical dependencies shown in Fig. 2—the maximum possible depth of the ‘rolling sphere‘ penetration for four protection levels specified in the Standard [7]. This analysis has been performed previously by the author [13,14]; some of the results are presented in Table 2. Unfortunately, the results show only how deeply but not how often the ‘rolling sphere’ penetrates the roof and does not enable one to calculate either the probability or the expected frequency of failure of the MM lightning protection. Calculations of the protection failure (the main purpose of the paper) concern a cell of the square mesh lying on a flat roof well inside the meshwork such that

Fig. 2. Determining the maximum depth of penetration pmax of the ‘rolling sphere’ for a given mesh size.

Table 2 Maximum depth of ‘rolling sphere’ penetration pmax through the mesh into the structure as illustrated in Fig. 2 Protection level

‘Rolling sphere’ radius D (m)

Maximum penetration depth pmax (cm)

I II III IV

20 30 45 60

16 41 28 83

no side of the cell in question lies on the roof ridge (e.g. see the cell ‘*’ in Fig. 3). As a result, the ‘rolling sphere’ cannot contact the earth, but must contact the roof or lightning wire only. 3.1. Model 1 Let us assume that no grounded, conducting element of the building interior is so close to the roof surface that it disturbs the lightning attachment process by the meshwork. By considering Fig. 4, we can arrive

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Table 3 Coefficient of protection failure kf for M ¼ 20 m

Fig. 3. The asterisk denotes a typical cell of the mesh lying inside the meshwork.

kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

2.27E–9

2.41E–18

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

1.15E–3

5.30E–5

6.17E–6

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

2.11E–2

5.90E–3

2.48E–3

Table 4 Coefficient of protection failure kf for M ¼ 15 m kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

1.26E–11

—

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

3.50E–4

1.10E–5

1.15E–6

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

1.24E–2

3.17E–3

1.33E–3

Fig. 4. Orientation sketch for Model 1.

at the following equations: Z M=2 NM ¼ Ng ðM  2DÞ2 gðDÞ dD 0

Z

M=2

ðM  2DÞ2

¼ Ng 0

"


exp 

1 1 pffiffiffiffiffiffi ps 2p D  #

 1 1 D ln 2 cs D50%

2

dD,

ð4Þ

where NM (year1) is the annual frequency of shielding failure of a mesh, Ng (m2 year1) is the ground flash density of the lightning and M (m) the length of the mesh cell side. The mesh protection failure coefficient kf may be calculated from the following formula: kf ¼

NM . N gM2

(5)

Values of kf for four typical M lengths taken from the Standards [7,8] and nine combinations of the lightning parameters, c, s and D50% are given in Tables 3–6. Values of the parameter kf for average values of c, s and D50% are written in bold; for NM below E–20 (1020) the shielding failure of the mesh is assumed to be impossible and the coefficient kf has not been calculated (denoted by the symbol ‘—’ in Tables 3–6). 3.2. Model 2 The second model considered in this work addresses the frequent situation where a conducting, grounded element exists within the depth ppM=2 below the meshwork surface. Examples include installations of

Table 5 Coefficient of protection failure kf for M ¼ 10 m kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

2.41E–15

—

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

5.20E–5

1.16E–6

8.56E–8

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

5.24E–3

1.18E–3

4.36E–4

networks of conducting pipes for water, gas, central heating, electric wiring, etc.). These conductors become unwanted ‘lightning rods’ competing with the mesh and reducing the protection effectiveness. To generalize this problem, let us assume that a conducting, horizontal, flat surface resides at a depth p below the meshwork. According to the Eq. (4) and the diagram shown in Fig. 5, the annual frequency of shielding failure of the mesh NM should be calculated from the

ARTICLE IN PRESS M. Szczerbin´ski / Journal of Electrostatics 64 (2006) 283–288 Table 6 Coefficient of protection failure kf for M ¼ 5 m D50% ¼ 50 m

kf s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

1.12–6

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

7.52E–4

D50% ¼ 100 m

—

1.14E–7

1.42E–4

287

Table 7 Coefficient of protection failure kf for the case p ¼ 1 m and for M ¼ 20 m D50% ¼ 150 m

—

5.36E–8

4.64E–5

kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

1.10E–2

9.90E–5

1.24E–6

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

4.29E–2

8.61E–3

2.55E–3

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

9.07E–2

3.92E–2

2.18E–2

Table 8 Coefficient of protection failure kf for the case p ¼ 1 m and for M ¼ 15 m

Fig. 5. Orientation sketch for Model 2.

following equation: Z ðM 2 =4þp2 Þ=2p ðM  2DÞ2 gðDÞ dD NM ¼ Ng

kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

3.02E–4

1.53E–7

2.83E–10

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

1.23E–2

1.51E–3

3.26E–4

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

4.70E–2

1.72E–2

8.64E–3

0

Z

ðM 2 =4þp2 Þ=2p

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð2D  pÞpÞ 0 "   # 1 1 1 1 D 2 ln
pffiffiffiffiffiffi exp  dD. 2 cs D50% ps 2p D

¼ Ng

ðM  2

ð6Þ

The calculated values of kf for the case p ¼ 1 m are presented in Tables 7–10.

4. Conclusions The analysis corroborates the high efficiency of the Meshwork Method—a fact taken for granted in Europe but up to now without enough (if any) theoretical background. In particular, when any conducting element in the object interior are not closer to the meshwork surface than half of the mesh length, the mean value of the protection failure coefficient is in the range from about 5
105 (see Table 3) to about 107 (see Table 6), depending on the M value according to the protection level. When conducting elements of the interior are situated close to the roof surface, the protection effectiveness falls. For example, for the

case p ¼ 1 m and M ¼ 20 m, the kf value becomes about 102 (see Table 7), but for M ¼ 5 m, this effect is clearly smaller and the kf value is about 5
107 (see Table 10). The calculated protection unreliability is strongly influenced by the mean lightning parameters s, c, and D50%. Considerable discrepancy between those parameters in the references cited (found by many researchers over many years in various places) makes it impossible to obtain unambiguous quantitative evaluation of efficiency that is valid for all regions of the world. Although this topic is one of the most crucial unsolved problems in lightning protection research, the author cannot show that the analysis matches experimental data. In the process of lightning protection failure assessment, the calculation of unreliability for a specific arrangement requires statistical data compiled for the arrangement itself. Unfortunately, the statistics in the field of lightning research tend to be much more general, being derived from lightning observations performed at different times, places and conditions. More significantly, the statistics refer to lightning damage only, but they omit how often the protection does the job correctly.

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Table 9 Coefficient of protection failure kf for the casep ¼ 1 m and for M ¼ 10 m kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

4.12E–8

2.11E–13

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

1.13E–3

6.40E–5

8.72E–6

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

1.51E–2

4.36E–3

1.89E–3

Table 10 Coefficient of protection failure kf for the case p ¼ 1 m and for M ¼ 5m kf

D50% ¼ 50 m

D50% ¼ 100 m

D50% ¼ 150 m

s ¼ 0:5 c ¼ 0:65 (sc ¼ 0:325)

—

—

—

s ¼ 1:0 c ¼ 0:75 (sc ¼ 0:75)

4.29E–6

6.35E–7

3.73E–9

s ¼ 1:5 c ¼ 0:85 (sc ¼ 1:275)

1.22E–3

2.40E–4

8.37E–5

The lightning protection technique has proven its effectiveness as evidenced by the comparative statistics of lightning damage to protected and unprotected structures without mentioning the lightning terminal arrangement. Hence the effectiveness of the meshwork protection (the percentage of air terminal attachments versus building attachments) is not statistically quantified. Nevertheless, the analysis presented in this paper should prove useful as a means of comparing the effectiveness of the mesh method compared to the typical Franklin method of lightning protection.

Acknowledgements Financial support of Ministry of Scientific Research and Information Technology, Contract No. 10.10.120. 508/05 is acknowledged.

References [1] Z. Flisowski, Trendy rozwojowe ochrony odgromowej budowli (Trends in the lightning protection of structures), Warszawa, PWN, 1986 (in Polish). [2] T. Horvath, Computation of Lightning Protection, LSP Ltd., Romerset, 1991. [3] H.R. Armstrong, E.R. Whitehead, Field and analytical studies of transmission line shielding, IEEE Trans. PAS-87 1 (1968) 270–281. [4] G.W. Brown, E.R. Whitehead, Field and analytical studies of transmission line shielding—Part II, IEEE Trans. PAS-88 5 (1969) 617–626. [5] A.R. Hileman, J.M. Clayton, Insulation Coordination for Power Systems, Marcel Dekker, New York, 1999. [6] R.H. Golde, Lightning, Academic Press, New York, 1977. [7] IEC 61024-1 International standard protection of structures against lightning—Part 1: General principles, 1990. [8] IEC 61024-1-2 International standard protection of structures against lightning, Part 1–2: General principles: Guide B—Design, installation, maintenance and inspection of lightning protection systems, 1993. [9] CIGRE TF33.01.03, Lightning exposure of structures and interception efficiency of air terminals, Report 118, October 1997, CIGRE, Paris. [10] M. Darveniza, A modification to the rolling sphere method for positioning air terminals for lightning protection of buildings, in: Proceedings of the 25th International Conference on Lightning Protection, Rhodes, 2002, pp. 904–908. [11] M. Darveniza, The placement of air terminals to intercept lightning in accordance with standards—revisited, in: Proceedings of the 26th International Conference on Lightning Protection, Cracow, 2002, pp. 803–808. [12] T. Horvath, Standardisation of lightning protection based on the physics or on the tradition?, in: Proceedings of the 26th International Conference on Lightning Protection, Cracow, 2002, pp. 791–796. [13] M. Szczerbinski, A discussion of ‘Faraday cage’ lightning protection and application to real building structures, J. Electrostat. 48 (2000) 145–154. [14] M. Szczerbinski, attachment process models for the meshwork external protection, in: Proceedings of the 25th International Conference on Lightning Protection, Rhodes, 2000, pp. 323–327.