- Email: [email protected]
Application of charge simulation method for investigation of effects of the trees on lightning protection of structures
ARTICLE IN PRESS
Journal of Electrostatics 66 (2008) 229–233 www.elsevier.com/locate/elstat
Application of charge simulation method for investigation of effects of the trees on lightning protection of structures B. Vahidi, H. Tayebifar, M.J. Alborzi Department of Electrical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15914, Iran Received 27 November 2004; received in revised form 17 September 2007; accepted 3 January 2008 Available online 4 February 2008
Abstract The paper deals with the principles of lightning protection of structures. The principles have been formulated on the base of application of charge simulation method (CSM) in order to investigate the effects of trees on lightning protection of buildings. The simulation results and laboratory test on scale model demonstrate the benefit of this method of computation lightning protection for structures. r 2008 Elsevier B.V. All rights reserved. Keywords: Lightning protection; Charge simulation method; Building; Striking point
1. Introduction Early lightning research focused on the protective effect of lightning rods based on observed lightning strokes [1–3]. At the end of the 19th century this effort resulted in the definition of the protective angle in spite of the divergent observations. Beginning with the 20th century, research work aimed to estimate the protective angle [1,2]. International standards have been developed as fundamental guidance for lightning protection system design and the construction of ever day structures [4–6]. Many researchers worked in the area of lightning protection of structures in order to improve lightning protection methods [1–3,7–9]. In the present paper the leader progression model [10–12] together with the charge simulation method (CSM) [13,14], is used to analyze the effectiveness of nearby trees in reducing the number of lightning stroke to buildings.
This can be done by either analytical or numerical methods. The situation often is so complex that analytical solutions are difficult or impossible, and hence numerical methods are commonly used for engineering applications. The CSM is one of these methods [13,14]. In the simple example of Fig. 1, filled circles and stars show simulation charges and contour points, respectively: 7 X
Pij Qj þ
j¼1 10 X
13 X
Pij Qj ¼ Fi
ði ¼ 1; 2Þ,
j¼11
Pij Qj ¼ Fi
ði ¼ 3Þ,
(1)
j¼1
where Fi is the potential at contour point i and Pij are the potential coefficients. When boundary condition is applied at the junction of two insulators, it must be true that: 0 r1 E n1 ¼ 0 r2 E n2 ,
2. Charge simulation method The calculation of electric fields requires the solution of Laplace’s equations with boundary conditions satisfied. Corresponding author. Fax: +98 21 66406469.
E-mail address: [email protected] (B. Vahidi). 0304-3886/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2008.01.004
(2)
where En1 and En2 are the normal components of electric field at the insulators surfaces. If Fij are field coefficients in the direction, normal to the dielectric boundary at the respective contour points, then 10 X j¼8
Pij Qj
13 X j¼11
Pij Qj ¼ 0
ði ¼ 8; 9; 10Þ,
(3)
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
230
En2
Nomenclature CSM Fi Qj Pij i j e0 er1 er2 En1 D
r1
10 X
charge simulation method potential at contour i jth charge potential coefficient counter number charge number permitivity of the air permitivity of dielectric 1 permitivity of dielectric 2 normal component of electric field to surface of dielectric 1 horizontal distance between building and each tree ! F ij Qj
¼ r2
j¼1
7 X j¼1
F ij Qj þ
13 X
! F ij Qj .
(4)
j¼11
These equations are solved to determine the unknown charges. In order to determine the accuracy of computation some checkpoints must be considered. Computing the potential in these points and comparing it with actual values determine the accuracy of the computation. 3. Model explanation The mathematical explanation of leader progression model phenomena requires an evaluation of the electric field strength, repeated at several times. The calculation of the field is done by means of CSM. The computer simulation can be used to simulate the step-by-step propagation of lightning and the striking process [12]. The method of leader propagation, as explained by Horvath [12], is sufficiently accurate for this paper
Fig. 1. Typical position of charges and contours points in multi dielectric system.
normal component of electric field to surface of dielectric 2 Fij field coefficient Q total charge of a section z vertical distance of middle point of the charge section from the point that field is computed r radial distance from charge section 2l section length X, Y, Z coordination N number of trees H height of trees G ground B building T1–T8 tree
simulation. The simulation starts with the vertical straight section of the leader discharge developed up to a level, which is high enough to nullify the influences of the earth objects [12]. Because an object standing alone on the earth causes a distortion of the field only up to the level of double its height [12], the starting point of the simulations must be above this level. Along the leader channel an equally distributed charge is considered. The charge in the channel produces an electric field, which has its highest intensity near the bottom. Equal steps of leader with a length of 10–20 m represent the propagation. Direction of leader progression is that in, which the potential gradient is a maximum. In this method we ignored leader corona, because by considering the corona, the computation using the CSM is very difficult. Fig. 2 shows phases of propagation of the leader according to this method. The computer simulation proceeds in the following way. The path leader is divided into sections with the length of a step (10–20 m). The charge of each section produces
Fig. 2. Phases of propagation of the leader ((1)–(3) shows stage of propagation of leader according to present paper method. Arrays show the potential gradient on different point on above-mentioned circle).
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
a circle around the top of the objects. If the highest potential gradient exceeds the critical value in a particular direction then a section of the connecting leader has to be
potential expressed by [12] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi z þ l þ r2 þ ðz þ lÞ2 Q qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , ln U¼ 8p0 l z l þ r2 þ ðz lÞ2
(5)
where Q is the total charge of a section, e0 the permitivity of the air, z the vertical distance of middle point of the charge section from the point that field is computed, r the radial distance from charge section and 2l the section length. With application of (5) the potential along the circle (Fig. 2) can be calculated and the maximum of the gradient of potential can be determined. If the maximum is known, the computer creates the next section of the leader channel. The field should then be calculated on the circle (Fig. 2) constructed around the end of the new section, and the cycle begins again. An earthed object modifies the field because on its surface the potential is zero. The influence of the protection tower can be determined with a charge distributed along the axis such that the resulting potential on the surface becomes zero. Under the effect of the object the path of the leader turns away to a small degree only from the vertical [2,3,10,11]. Concerning the striking process, the field at the top of the object is of great importance because the start of a connection leader is dependent on it. On the top of an object there are sharp-pointed structures on which a corona discharge appears but this is not a connecting leader [10,11]. It comes into being only if the potential gradient is high enough over a large distance. Laboratory experiments indicated an average field gradient of 500–600 kV/m in a distance of at least 5–10 m is required to turn the corona discharge into a connecting leader [12]. The computer simulation must also check the potential on
Fig. 3. Simulated configuration.
231
Table 1 Striking point for different leader tip coordination, results for actual dimension (number of trees ¼ 4) H ¼ 8m
N¼4
Starting point of leader (Z ¼ 300 m) X (m)
Y (m)
20 15 5 15 15 15 20 30 40 40
20 15 5 0 5 10 20 30 30 40
D ¼ 5m Striking point
G T1 B B B B T3 T3 G G
Table 2 Striking point for different leader tip coordination, results for actual dimension (number of trees ¼ 8) H ¼ 8m
N¼4
Starting point of leader (Z ¼ 300 m) X (m)
Y (m)
20 15 5 15 15 15 20 30 40 40
20 15 5 0 5 10 20 30 30 40
Fig. 4. Laboratory setup.
D ¼ 5m Striking point
G T1 B B B B T3 T3 G G
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
232
created. The charge on this section has a value at which the potential becomes zero at its top [12]. The upward leader is computed in a step-by-step manner using the same method of downward leader and for higher trees, the upward leader will begin from a higher height. This procedure must be set into the cycle of propagation of the leader so that connecting leader increases stepwise [12]. In this method instead of lightning current, the cloud and lightning-leader voltage are considered.
4. Simulation A computer program is prepared and the abovedescribed computerized method is applied to a configuration shown in Fig. 3 (height of building ¼ 11.85 m, length of building ¼ 18 m and width of building ¼ 10 m). In this simulation, building, trees, ground, air termination conductors, downward and upward leaders are simulated with different kind of charges.
Table 3 Striking point for different leader tip coordination, results for scaled dimension (number of trees ¼ 4) Conditions (all dimensions in m) Building
Length Width Height
0.36 0.2 0.225
Trees Height ¼ 0.24 Tree (X,Y)
T1 ¼ (0,0.1) T3 ¼ (0.36,0.3) T5 ¼ Not used T7 ¼ Not used
T2 ¼ (0.36,0.1) T4 ¼ (0,0.3) T6 ¼ Not used T8 ¼ Not used
Applied voltage
320 kV, 1.2/50 ms
Results
Starting point of leader
Striking point
Comparison of striking point
X
Y
Z
Theoretical simulation
Experimental simulation
0.2 0.1 0.1 0.3 0.3 0.3 0.4
0.2 0.1 0.1 0 0.1 0.2 0.4
0.465 0.465 0.465 0.465 0.465 0.465 0.465
T1 T1 B B B B T3
T1 T1 B B B B T3
Matched Matched Matched Matched Matched Matched Matched
Table 4 Striking point for different leader tip coordination, results for scaled dimension (number of trees ¼ 8) Conditions (all dimensions in m) Building
Length Width Height
0.36 0.2 0.225
Trees Height ¼ 0.24 Tree (X,Y)
T1 ¼ (0,0.1) T3 ¼ (0.36,0.3) T5 ¼ (0.18,0.2) T7 ¼ (0.18,0.4)
T2 ¼ (0.36,0.1) T4 ¼ (0,0.3) T6 ¼ (0.56,0.1) T8 ¼ (0.2,0.1)
Applied voltage
320 kV, 1.2/50 ms
Results
Starting point of leader
Striking point
Comparison of striking point
X
Y
Z
Theoretical simulation
Experimental simulation
0.2 0.1 0.1 0.3 0.3 0.3 0.4
0.2 0.1 0.1 0 0.1 0.2 0.4
0.465 0.465 0.465 0.465 0.465 0.465 0.465
T1 T1 B B B B T3
T1 T1 B B B B T3
Matched Matched Matched Matched Matched Matched Matched
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
5. Simulation results For different X, Y coordination of starting point of leader tip (Z ¼ 300 m) computation has been done and the striking point of leader is found. Results of simulation for four trees and eight trees are shown in Tables 1 and 2.
233
The method presented in this paper can be used to investigate the effect of trees, rods on lightning protection of structures and the proper position of rods or trees can be determined for protection of structures.
References 6. Comparison between laboratory test and simulation In order to compare laboratory tests with computerized simulation results, a scale model for a building was made and the laboratory setup shown in Fig. 4 was prepared in the high-voltage laboratory. Computerized simulation and laboratory test were conducted for the scale model building and the experimental simulation extends beyond a simple point-to-plane geometry. Rather, trees and buildings are simulated in detail. The wave shape and crest voltage of the experimental simulation are discussed mention in Tables 3 and 4. 7. Conclusion In the present paper a method of lightning protection for a building with extensive reference to the effect trees is presented. The model takes into account the main stages of the phenomenon and namely the propagation of the downward leader, the inception and progression of upward leaders from earthed objects and interaction between two leaders. Various physical elements such as leader channel, building, ground, trees, etc. are considered. With the aid of CSM for different numbers of trees and various positions of the starting leader tip, computation was carried out and striking point of lightning is determined. To check the result, we simulate experimentally a scalemodel building not for comparison to with actual building, but for comparison with the theoretical simulation of the same scale-model building. These results are compared in Tables 3 and 4.
[1] R.H. Lee, Protection zones for buildings against lightning strokes using transmission line practice, IEEE Trans. Ind. Appl. 1A-14 (1978) 465–469. [2] F.A.M. Rizk, Modeling of lightning incidence to tall structures; part I: theory, IEEE Trans. Power Delivery 9 (1994) 162–171. [3] F.A.M. Rizk, Modeling of lightning incidence to tall structures; part II: application, IEEE Trans. Power Delivery 9 (1994) 172–193. [4] IEC 61024-1, Protection of structures against lightning; part 1: general principles, 1990. [5] BS6651, Protection of structures against lightning, 1990. [6] NFC 17-102, Lightning protection of structures and open area against lightning using early streamer emission air terminals, 1995. [7] M. Bernardi, L. Dellera, E. Garbagnati, G. Sartorio, Leader progression model of lightning: updating of the model on the basis of recent test results, 23th ICLP, Florence, 1996, pp. 399–407. [8] M.A. Darveniza, A modification to the rolling sphere method for positioning air terminals for the protection air terminals for lightning protection of buildings, 25th ICLP, Rhodes, 2000, pp. 374–379. [9] F. D’ Alessandro, J.R. Gumley, A collection volume method for the placement of air terminals for the protection of structures against lightning, J. Electrostat. 50 (2001) 279–302. [10] L. Dellera, E. Garbagnati, Lightning stroke simulation by means of the leader progression model—part I: description of the model and evaluation of exposure of free standing structures, IEEE Trans. Power Delivery 5 (1990) 2009–2022. [11] L. Dellera, E. Garbagnati, Lightning stroke simulation by means of the leader progression model—part II: exposure and shielding failure evaluation of overhead lines, IEEE Trans. Power Delivery 5 (1990) 2023–2029. [12] T. Horvath, Computation of Lightning Protection, Research Studies Press Ltd, England, 1991, pp. 33–50. [13] N.H. Malik, A review of charge simulation method and its application, IEEE Trans. Electr. Insul. 24 (1989) 3–20. [14] H. Singer, H. Steinbigler, P. Weiss, A charge simulation method for the calculation of high voltage fields, IEEE Trans. PAS 93 (1974) 1660–1668.
Journal of Electrostatics 66 (2008) 229–233 www.elsevier.com/locate/elstat
Application of charge simulation method for investigation of effects of the trees on lightning protection of structures B. Vahidi, H. Tayebifar, M.J. Alborzi Department of Electrical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15914, Iran Received 27 November 2004; received in revised form 17 September 2007; accepted 3 January 2008 Available online 4 February 2008
Abstract The paper deals with the principles of lightning protection of structures. The principles have been formulated on the base of application of charge simulation method (CSM) in order to investigate the effects of trees on lightning protection of buildings. The simulation results and laboratory test on scale model demonstrate the benefit of this method of computation lightning protection for structures. r 2008 Elsevier B.V. All rights reserved. Keywords: Lightning protection; Charge simulation method; Building; Striking point
1. Introduction Early lightning research focused on the protective effect of lightning rods based on observed lightning strokes [1–3]. At the end of the 19th century this effort resulted in the definition of the protective angle in spite of the divergent observations. Beginning with the 20th century, research work aimed to estimate the protective angle [1,2]. International standards have been developed as fundamental guidance for lightning protection system design and the construction of ever day structures [4–6]. Many researchers worked in the area of lightning protection of structures in order to improve lightning protection methods [1–3,7–9]. In the present paper the leader progression model [10–12] together with the charge simulation method (CSM) [13,14], is used to analyze the effectiveness of nearby trees in reducing the number of lightning stroke to buildings.
This can be done by either analytical or numerical methods. The situation often is so complex that analytical solutions are difficult or impossible, and hence numerical methods are commonly used for engineering applications. The CSM is one of these methods [13,14]. In the simple example of Fig. 1, filled circles and stars show simulation charges and contour points, respectively: 7 X
Pij Qj þ
j¼1 10 X
13 X
Pij Qj ¼ Fi
ði ¼ 1; 2Þ,
j¼11
Pij Qj ¼ Fi
ði ¼ 3Þ,
(1)
j¼1
where Fi is the potential at contour point i and Pij are the potential coefficients. When boundary condition is applied at the junction of two insulators, it must be true that: 0 r1 E n1 ¼ 0 r2 E n2 ,
2. Charge simulation method The calculation of electric fields requires the solution of Laplace’s equations with boundary conditions satisfied. Corresponding author. Fax: +98 21 66406469.
E-mail address: [email protected] (B. Vahidi). 0304-3886/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2008.01.004
(2)
where En1 and En2 are the normal components of electric field at the insulators surfaces. If Fij are field coefficients in the direction, normal to the dielectric boundary at the respective contour points, then 10 X j¼8
Pij Qj
13 X j¼11
Pij Qj ¼ 0
ði ¼ 8; 9; 10Þ,
(3)
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
230
En2
Nomenclature CSM Fi Qj Pij i j e0 er1 er2 En1 D
r1
10 X
charge simulation method potential at contour i jth charge potential coefficient counter number charge number permitivity of the air permitivity of dielectric 1 permitivity of dielectric 2 normal component of electric field to surface of dielectric 1 horizontal distance between building and each tree ! F ij Qj
¼ r2
j¼1
7 X j¼1
F ij Qj þ
13 X
! F ij Qj .
(4)
j¼11
These equations are solved to determine the unknown charges. In order to determine the accuracy of computation some checkpoints must be considered. Computing the potential in these points and comparing it with actual values determine the accuracy of the computation. 3. Model explanation The mathematical explanation of leader progression model phenomena requires an evaluation of the electric field strength, repeated at several times. The calculation of the field is done by means of CSM. The computer simulation can be used to simulate the step-by-step propagation of lightning and the striking process [12]. The method of leader propagation, as explained by Horvath [12], is sufficiently accurate for this paper
Fig. 1. Typical position of charges and contours points in multi dielectric system.
normal component of electric field to surface of dielectric 2 Fij field coefficient Q total charge of a section z vertical distance of middle point of the charge section from the point that field is computed r radial distance from charge section 2l section length X, Y, Z coordination N number of trees H height of trees G ground B building T1–T8 tree
simulation. The simulation starts with the vertical straight section of the leader discharge developed up to a level, which is high enough to nullify the influences of the earth objects [12]. Because an object standing alone on the earth causes a distortion of the field only up to the level of double its height [12], the starting point of the simulations must be above this level. Along the leader channel an equally distributed charge is considered. The charge in the channel produces an electric field, which has its highest intensity near the bottom. Equal steps of leader with a length of 10–20 m represent the propagation. Direction of leader progression is that in, which the potential gradient is a maximum. In this method we ignored leader corona, because by considering the corona, the computation using the CSM is very difficult. Fig. 2 shows phases of propagation of the leader according to this method. The computer simulation proceeds in the following way. The path leader is divided into sections with the length of a step (10–20 m). The charge of each section produces
Fig. 2. Phases of propagation of the leader ((1)–(3) shows stage of propagation of leader according to present paper method. Arrays show the potential gradient on different point on above-mentioned circle).
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
a circle around the top of the objects. If the highest potential gradient exceeds the critical value in a particular direction then a section of the connecting leader has to be
potential expressed by [12] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi z þ l þ r2 þ ðz þ lÞ2 Q qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , ln U¼ 8p0 l z l þ r2 þ ðz lÞ2
(5)
where Q is the total charge of a section, e0 the permitivity of the air, z the vertical distance of middle point of the charge section from the point that field is computed, r the radial distance from charge section and 2l the section length. With application of (5) the potential along the circle (Fig. 2) can be calculated and the maximum of the gradient of potential can be determined. If the maximum is known, the computer creates the next section of the leader channel. The field should then be calculated on the circle (Fig. 2) constructed around the end of the new section, and the cycle begins again. An earthed object modifies the field because on its surface the potential is zero. The influence of the protection tower can be determined with a charge distributed along the axis such that the resulting potential on the surface becomes zero. Under the effect of the object the path of the leader turns away to a small degree only from the vertical [2,3,10,11]. Concerning the striking process, the field at the top of the object is of great importance because the start of a connection leader is dependent on it. On the top of an object there are sharp-pointed structures on which a corona discharge appears but this is not a connecting leader [10,11]. It comes into being only if the potential gradient is high enough over a large distance. Laboratory experiments indicated an average field gradient of 500–600 kV/m in a distance of at least 5–10 m is required to turn the corona discharge into a connecting leader [12]. The computer simulation must also check the potential on
Fig. 3. Simulated configuration.
231
Table 1 Striking point for different leader tip coordination, results for actual dimension (number of trees ¼ 4) H ¼ 8m
N¼4
Starting point of leader (Z ¼ 300 m) X (m)
Y (m)
20 15 5 15 15 15 20 30 40 40
20 15 5 0 5 10 20 30 30 40
D ¼ 5m Striking point
G T1 B B B B T3 T3 G G
Table 2 Striking point for different leader tip coordination, results for actual dimension (number of trees ¼ 8) H ¼ 8m
N¼4
Starting point of leader (Z ¼ 300 m) X (m)
Y (m)
20 15 5 15 15 15 20 30 40 40
20 15 5 0 5 10 20 30 30 40
Fig. 4. Laboratory setup.
D ¼ 5m Striking point
G T1 B B B B T3 T3 G G
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
232
created. The charge on this section has a value at which the potential becomes zero at its top [12]. The upward leader is computed in a step-by-step manner using the same method of downward leader and for higher trees, the upward leader will begin from a higher height. This procedure must be set into the cycle of propagation of the leader so that connecting leader increases stepwise [12]. In this method instead of lightning current, the cloud and lightning-leader voltage are considered.
4. Simulation A computer program is prepared and the abovedescribed computerized method is applied to a configuration shown in Fig. 3 (height of building ¼ 11.85 m, length of building ¼ 18 m and width of building ¼ 10 m). In this simulation, building, trees, ground, air termination conductors, downward and upward leaders are simulated with different kind of charges.
Table 3 Striking point for different leader tip coordination, results for scaled dimension (number of trees ¼ 4) Conditions (all dimensions in m) Building
Length Width Height
0.36 0.2 0.225
Trees Height ¼ 0.24 Tree (X,Y)
T1 ¼ (0,0.1) T3 ¼ (0.36,0.3) T5 ¼ Not used T7 ¼ Not used
T2 ¼ (0.36,0.1) T4 ¼ (0,0.3) T6 ¼ Not used T8 ¼ Not used
Applied voltage
320 kV, 1.2/50 ms
Results
Starting point of leader
Striking point
Comparison of striking point
X
Y
Z
Theoretical simulation
Experimental simulation
0.2 0.1 0.1 0.3 0.3 0.3 0.4
0.2 0.1 0.1 0 0.1 0.2 0.4
0.465 0.465 0.465 0.465 0.465 0.465 0.465
T1 T1 B B B B T3
T1 T1 B B B B T3
Matched Matched Matched Matched Matched Matched Matched
Table 4 Striking point for different leader tip coordination, results for scaled dimension (number of trees ¼ 8) Conditions (all dimensions in m) Building
Length Width Height
0.36 0.2 0.225
Trees Height ¼ 0.24 Tree (X,Y)
T1 ¼ (0,0.1) T3 ¼ (0.36,0.3) T5 ¼ (0.18,0.2) T7 ¼ (0.18,0.4)
T2 ¼ (0.36,0.1) T4 ¼ (0,0.3) T6 ¼ (0.56,0.1) T8 ¼ (0.2,0.1)
Applied voltage
320 kV, 1.2/50 ms
Results
Starting point of leader
Striking point
Comparison of striking point
X
Y
Z
Theoretical simulation
Experimental simulation
0.2 0.1 0.1 0.3 0.3 0.3 0.4
0.2 0.1 0.1 0 0.1 0.2 0.4
0.465 0.465 0.465 0.465 0.465 0.465 0.465
T1 T1 B B B B T3
T1 T1 B B B B T3
Matched Matched Matched Matched Matched Matched Matched
ARTICLE IN PRESS B. Vahidi et al. / Journal of Electrostatics 66 (2008) 229–233
5. Simulation results For different X, Y coordination of starting point of leader tip (Z ¼ 300 m) computation has been done and the striking point of leader is found. Results of simulation for four trees and eight trees are shown in Tables 1 and 2.
233
The method presented in this paper can be used to investigate the effect of trees, rods on lightning protection of structures and the proper position of rods or trees can be determined for protection of structures.
References 6. Comparison between laboratory test and simulation In order to compare laboratory tests with computerized simulation results, a scale model for a building was made and the laboratory setup shown in Fig. 4 was prepared in the high-voltage laboratory. Computerized simulation and laboratory test were conducted for the scale model building and the experimental simulation extends beyond a simple point-to-plane geometry. Rather, trees and buildings are simulated in detail. The wave shape and crest voltage of the experimental simulation are discussed mention in Tables 3 and 4. 7. Conclusion In the present paper a method of lightning protection for a building with extensive reference to the effect trees is presented. The model takes into account the main stages of the phenomenon and namely the propagation of the downward leader, the inception and progression of upward leaders from earthed objects and interaction between two leaders. Various physical elements such as leader channel, building, ground, trees, etc. are considered. With the aid of CSM for different numbers of trees and various positions of the starting leader tip, computation was carried out and striking point of lightning is determined. To check the result, we simulate experimentally a scalemodel building not for comparison to with actual building, but for comparison with the theoretical simulation of the same scale-model building. These results are compared in Tables 3 and 4.
[1] R.H. Lee, Protection zones for buildings against lightning strokes using transmission line practice, IEEE Trans. Ind. Appl. 1A-14 (1978) 465–469. [2] F.A.M. Rizk, Modeling of lightning incidence to tall structures; part I: theory, IEEE Trans. Power Delivery 9 (1994) 162–171. [3] F.A.M. Rizk, Modeling of lightning incidence to tall structures; part II: application, IEEE Trans. Power Delivery 9 (1994) 172–193. [4] IEC 61024-1, Protection of structures against lightning; part 1: general principles, 1990. [5] BS6651, Protection of structures against lightning, 1990. [6] NFC 17-102, Lightning protection of structures and open area against lightning using early streamer emission air terminals, 1995. [7] M. Bernardi, L. Dellera, E. Garbagnati, G. Sartorio, Leader progression model of lightning: updating of the model on the basis of recent test results, 23th ICLP, Florence, 1996, pp. 399–407. [8] M.A. Darveniza, A modification to the rolling sphere method for positioning air terminals for the protection air terminals for lightning protection of buildings, 25th ICLP, Rhodes, 2000, pp. 374–379. [9] F. D’ Alessandro, J.R. Gumley, A collection volume method for the placement of air terminals for the protection of structures against lightning, J. Electrostat. 50 (2001) 279–302. [10] L. Dellera, E. Garbagnati, Lightning stroke simulation by means of the leader progression model—part I: description of the model and evaluation of exposure of free standing structures, IEEE Trans. Power Delivery 5 (1990) 2009–2022. [11] L. Dellera, E. Garbagnati, Lightning stroke simulation by means of the leader progression model—part II: exposure and shielding failure evaluation of overhead lines, IEEE Trans. Power Delivery 5 (1990) 2023–2029. [12] T. Horvath, Computation of Lightning Protection, Research Studies Press Ltd, England, 1991, pp. 33–50. [13] N.H. Malik, A review of charge simulation method and its application, IEEE Trans. Electr. Insul. 24 (1989) 3–20. [14] H. Singer, H. Steinbigler, P. Weiss, A charge simulation method for the calculation of high voltage fields, IEEE Trans. PAS 93 (1974) 1660–1668.