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Evaluation of parameters influencing the lightning performance of communication towers by numerical modeling and experimental tests
Journal of Electrostatics 77 (2015) 35e43
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Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Evaluation of parameters influencing the lightning performance of communication towers by numerical modeling and experimental tests Mostafa Yahyaabadi*, Alireza Sadoughi, Bahram Karimi Dept. of Electrical Engineering, Malekashtar University of Technology, Isfahan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 April 2015 Received in revised form 30 June 2015 Accepted 2 July 2015 Available online xxx
This paper analyzes the effective parameters on lightning performance. The effects of tower height, breakdown electric field threshold, the ground slope of installation place, and the effect of the trees around the tower are investigated. A 3-D numerical analysis model is proposed to determine the number of direct lightning strokes to antennas. The communication tower, lightning rod, downward descending leader and upward leaders are modeled by different shapes of charges. Finally, a small-scale communication tower was built and tested in a high voltage laboratory. The experimental tests were consistent with the simulation results verifying the merits of the proposed method. © 2015 Elsevier B.V. All rights reserved.
Index Terms: Lightning leader Communication tower Lightning rod High voltage test
1. Introduction Lightning rod is basically responsible for the stroke interception, the most important task in a Lightning Protection System (LPS). Since its invention by Benjamin Franklin, lightning rod has found a very wide application [1e3]. The protective angle recommended for lightning rods varied within a wide range. Originally, these protective angles were based on experience, but later with the availability of high-voltage test facilities, these angles were also determined by tests on small-scale physical models [4]. In order to analyze the lightning performance of equipment and structures such as communication towers, several analytical methods have been proposed. At first, the Electro Geometric Model (EGM), based on the principle of striking distance, was found to be satisfactory. The striking distance is defined as the “distance between the object to be struck and the tip of the downward-moving leader at the instant that the upward leader is initiated from the object” [5e7]. Several researchers have developed the EGM. Eriksson [8,9] improved the model named “the Collection Volume Method (CVM)”. The Rolling Sphere Method (RSM) was developed for more complex structures. This method is one of the direct applications of EGM for 3-D geometries.
* Corresponding author. Tel.: þ98 3136933303. E-mail addresses: [email protected] (M. Yahyaabadi), [email protected] (A. Sadoughi), [email protected] (B. Karimi). http://dx.doi.org/10.1016/j.elstat.2015.07.002 0304-3886/© 2015 Elsevier B.V. All rights reserved.
However, in analytical methods, the expression of striking distance does not show any explicit reference to the field intensification at the structure top and the propagation of the upward leaders is not considered [10,11]. Therefore, Dellera et al. [12,13] and Rizk [14,15] proposed the Leader Progression Model (LPM) as a numerical approach to determine the path of the lightning and the final encounter. Recently, the LPM has been employed and developed by some researchers [19e24]. In present work, a model in a three-dimensional environment is proposed which takes the communication tower and antennas as well as air terminal and the step nature of downward lightning leader into account. In addition, the inception and propagation of multiple upward leaders are considered. The electrical fields are computed using the Charge Simulation Method (CSM) [16e18]. The number of direct lightning strokes to the antennas of communication towers is calculated accurately. Here, a new definition called the density of strokes causing shielding failures per year is provided. Accordingly, the risky areas in the leader-tip starting surface are determined. On the other hand, an area with a high density of strokes causing shielding failures expresses greater probability of its lightning encounter to antennas. The lightning performance analysis is performed for different conditions and the results are evaluated. Finally, in order to validate the simulation results, some laboratory tests were utilized on a small-scale communication tower.
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2. Leader progression and final jump The leader progression approach is based on the idea that a similarity exists between lightning phenomenon and discharges in long air gaps [12]. Here, the cloud-to-ground lightning flashes are considered and the presence of downward lightning leader is a principle of calculations. The simulation is started with a vertical straight section of the lightning leader propagated up to a level, which is high enough to nullify the influences of the earthed objects. This level is selected higher than twice the highest object [7]. The downward lightning leader develops gradually and to be assured of the leader progression in long air gaps, the propagation is simulated by steps with a length of 10 m. Its direction is towards the maximum potential gradient. During the descent of a downward lightning leader, the upward leaders are initiated from grounded objects and are propagated towards the downward lightning leader. When an upward leader succeeds to intercept the downward lightning leader, a conducting path between the cloud and the ground is created and the return stroke lightning current is drained [25]. The main characteristics used in this model are the direction of the leaders; charge distribution along the downward and upward leaders; inception criteria of the upward leaders; leaders advance speed; and the final jump criterion [26].
2.1. Direction of leader motion The procedure of calculating the downward and upward leader attachment requires the field calculation in the environment of the study. In each step of lightning leader motion, a hemisphere with a radius of a step length is drawn around the tip of the leader. Therefore, the next jump point of the leader is a point on the hemisphere that the voltage gradient along the line connecting the leader tip to the target point is maximum. The path of downward lightning leader including the tilted channel segments is replaced by vertical and horizontal line charges.
2.2. Inception criteria of the upward leaders
i Utip
lis ¼
¼
Einf $lil
E E Einf li þ x0 $Einf $ln init init e l Einf Einf
! x0
i U0 þ Es $lil Utip
Es Eb
h i i1 i þ Utip lil $ Es lil li1 Utip DQ i ¼ KQ $ li1 s l Dlil ¼
DQ i ql
U0 Es Eb
DQ 0 ¼ 0:5$KQ $l2s $ðEs Eb Þ;
¼ lil þ Dlil ; liþ1 l
(5)
(7)
i where Utip is the leader potential in step i; Einit and Einf are the initial and final values of the leader gradient; and x0 and ql are the constants. If the leader length ðliþ1 Þ increases to a maximum value l ðlmax Þ, equal to 2 m, the stable upward leader will be incepted. The constants of the upward leader model are: Es ¼ 450 kV/m; Einit ¼ 400 kV/m; Es ¼ 450 kV/m; x0 ¼ 0.75 m; KQ ¼ 3.5 1011 C/V; ql ¼ 50 106 C/m. When this condition is fulfilled, an upward leader propagates towards the downward lightning leader tip. In order to determine the direction of each upward leader, according to subsection 2-1, the electric field is calculated at fixed distances from the upward leader tip over various directions at each step. The next step is then directed along the line with the field maximum mean. The points with more likelihood of inception and propagation of upward leaders are the top of the lightning rod, the top of the antenna, and the ground surface bellow the lightning tip (Fig. 1).
2.3. Charge distribution along the leaders In the scientific literature, there are different proposals for the charge distribution along the downward leader such as uniform, linear, and exponential distributions [22,27]. Here, the charge density distribution along the downward leader channel is calculated as follows [33,36],
(1)
(2)
where U0 and Eb are the voltage and field on the fitted line of the background electric field and l0s is the initial length of the streamer. Es and KQ are the constant streamer electric field and a geometrical factor, respectively. If the initial streamer charge ðDQ 0 Þ is more than 1mC, the initial leader length is assumed to be 1 cm, then the streamer length and streamer space charge are calculated for each leader movement step as follows [19]:
(4)
(6)
For a reliable assessment of the lightning path and hence an accurate evaluation of the lightning protection performance, it is very essential to appropriately consider the inception and propagation of the upward leaders. Different criteria have been proposed for calculating the electric field intensity to ensure the stability of the upward leader inception [8,12,28,36]. At this work, the model proposed in Ref. [19] is applied to check the upward leader inception condition. The streamer charge is initially calculated as follows [19]:
l0s ¼
(3)
Fig. 1. More likely points to start upward leaders.
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37
( ) 10z0 z z0 z m1 þ m2 ðz z0 Þ z0 75 rðzÞ ¼ I m0 1 0:3e þ 0:7 1 1 0 þ ; HC z 0 HC HC 1 þ m3 ðz z0 Þ þ m4 ðz z0 Þ2
where r is the downward leader charge density in C/m; and z is the variable height of the point on the leader where charge density is to be calculated; z0 and HC are the height of the downward leader tip and the cloud height in meters, respectively (note that the above equation is valid for z0 > 10m), I is the lightning current in kilo amperes, m0 ¼ 1:476 105 , m1 ¼ 4:857 105 , m2 ¼ 3:9097 106 , m3 ¼ 0:522, m4 ¼ 3:73 103 . In the simulations performed for the real tower dimensions, the height of the lightning leader tip is always higher than 10 m from the ground level and therefore, the use of the above equation for the calculation of electric charge distribution along the lightning leader will be valid. In the simulations performed in small scales, the same equation has been used while ignoring the errors in calculations. The charge per meter length of the equivalent channel in upward leaders is assumed 50 mC/m [12]. 2.4. Velocity of downward and upward leaders The interception point of the downward lightning leader by an ! upward leader depends upon the ratio between the downward and upward leader velocities RV ¼ VVdownward . Even though measureupward ments and estimates of the downward lightning leader velocity are more common in literature, only few measurements of the upward leader velocity have been reported [25,34]. The velocity of upward leaders has been found to be related to the downward lightning leader current, the velocity, and the lateral position of the downward lightning leader as well as by the ambient field. Therefore, the velocity of an upward leader changes from flash to flash [25]. Eriksson [8] and Rizk [28,29] have considered equal velocities for both downward and upward leaders. In the work of Dellera et al. [12,13], the ratio of velocities is initially 4:1, later it is reduced to 1:1. The two values for the velocity ratio and their instant of changeover are rather difficult to comprehend and apply. In this paper, the effect of downward to upward leader velocities ratio has been investigated.
(8)
Therefore, the Shielding Failure Number (SFNi), the number of direct lightning strokes to antenna per year when the leader tip position is in the shaded mesh, can be calculated as:
SFNi ¼ 106 g dx$dy
ZImax PðIÞ$dI Imin
where g ¼ 0:015 Td is the ground flash density in strikes per square kilometers per year. Td is the number of thunderstorm days per year and is considered 40 [35]. P(I) is the probability density function of lightning current exceeding I, that could be calculated by the following approximate formula [7,35],
log10 PðIÞ ¼ 0:05
I 74
(10)
In addition, the results published in CIGRE Electra in 1975 [37] and 1980 [38] present a good data base of lightning currents and their relevant parameters. Fig. 3 shows the cumulative statistical lightning current distributions [37]: Finally, the number of direct lightning strokes to the antenna per year SFNT is:
SFNT ¼
n X
SFNi
(11)
i¼1
2.5. Final jump The critical breakdown gradient in the gap between the downward and upward leader tips is in the order of 500 kV/m. Thus, if at any instant the average voltage gradient determined by the potential difference between the downward leader tip and one of the upward leader tips exceeds the critical breakdown gradient, a final jump takes place [1]. 3. The number of direct lightning strokes to antenna As shown in Fig. 2, the area above the communication tower is divided to create a mesh system with differential length of dx in xdirection and dy in y-direction, (the area width is taken to be a distance from the center so that the leaders outside that distance do not strike the tower). For each position of the leader (shaded mesh), simulation starts for I ¼ 3kA and the striking point of the downward leader is found. Then, the simulation procedure will continue for different lightning currents until the lightning current range (Imax, Imin) is determined so that for a given current out of this range, the lightning would never strike the tower and antenna.
(9)
Fig. 2. Lightning strokes calculation model.
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Fig. 3. The cumulative statistical lightning current distributions: 1. negative first strokes, 2. negative subsequent strokes, 3. positive first strokes.
where n is the total number of meshes in the leader tip starting surface. Fig. 4 illustrates the procedure and steps of computing the SFN. 4. Case study and simulation results As a case study, a 91-m communication tower is considered for analyzing its lightning performance by applying the mentioned numerical model. The tower radius at ground level (Rt) is 5.5 m and the distance between the outer part of the antenna and the center of tower (d) is 2 m. According to Fig. 5, the communication tower is modeled by ring charges that are placed on each other in the direction of the tower height and each antenna is modeled by horizontal line charges. A lightning rod with a length of L is installed at the top and it is supposed to be modeled by vertical line charge segments. Fig. 6 depicts the number of direct lightning strokes to the antenna per year. This value decreases with an increase in the lightning rod height but it is never zero. In other words, most of the lightning leaders, but not all that threaten the antennas would be absorbed by the lightning rod. Thus, in a proper design for increasing the height of a lightning rod, the limitations should be considered and a reasonable value be selected. Fig. 7 represents the density of strokes causing shielding failures for the area above the tower that is calculated in more detail. On the other hand, the colored area with a higher density of lines shows the higher density of strokes causing shielding failures. In this calculation, the lightning rod height is considered 1 m. As shown in this figure, all lightning leaders within 20 m of the radial distance from the tower center are absorbed by the lightning rod. In addition, it is seen that the density of strokes causing the shielding failures is high within the interval of 30e40 m from center. Fig. 8 depicts the influence of lightning rod height on the density of strokes causing the shielding failures. According to this figure, the density of strokes causing shielding failures and also the number of the direct lightning strokes are reduced with an increase in the lightning rod height. 5. Experimental tests Here, in order to validate the simulation results, a small-scale communication tower with a ratio of 1e50 was constructed and
Fig. 4. Procedure for calculating the SFN of communication towers.
tested in the High Voltage Laboratory. In this experimental test, the starting point of the lightning leader is located at various positions (including areas with high density of strokes causing of shielding failures). Then, the strike point of lighting leader is observed. The characteristics of a small-scale communication tower in comparison with the case study are presented in Table 1: The characteristics of impulse generator are as follows: Maximum energy: 180 kJ; and maximum voltage impulse wave: 1.8 MV. A sample of lightning voltage impulse wave is presented in Fig. 9A. The lightning test voltage wave parameters are Vpeak ¼ 887kV ; T1 ¼ 1:13m s; T2 ¼ 44:6m s; b ¼ 11:4% (Fig. 9B, C). The blue curve (in the web version) ðU0 Þ is earlier lightning impulse voltage with high-frequency peak oscillation of frequency f 500kHz and the red curve (in the web version) ðUt Þ is the mean value that is drawn through the oscillating impulse voltage (Fig. 9C). With regard to the fact that the location change of the initiation of downward leader is effective on the breakdown voltage
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39
Fig. 7. The density of strokes causing shielding failures for the area above the communication tower.
Fig. 5. The communication tower and antenna.
Fig. 8. The density of strokes causing shielding failures for different lightning rod heights.
Fig. 6. The number of direct lightning strokes the antenna per year.
and as a result, on the impulse current, the lightning current peak has been changed within 12e24 Kilo-amperes in these tests and the simulations performed for small-scale model. In other words, when the distance of the rod tip, that simulates the downward leader and the equipment is increased, the electric breakdown takes place with more voltage and the generated current increases. In order to model the downward leader, a sharp rod is hung from a crane and the voltage is applied to it, while the rod tip height is about 3.2 m above the ground surface. Fig. 10 shows the two impulse tests performed on the smallscale model of a communication tower. According to Fig. 10.A, for a lateral distance of about 60 cm, an encounter to lightning protection system takes place. Therefore, the protection system has a proper performance in this case. Fig. 10.B depicts an encounter to the antenna for a lateral distance of about 120 cm. Since the exact
location of the encounter in recorded images is vague, the strike point is carefully checked after each encounter. The test is repeated for different lateral distances and the results are presented in Table 2. At least the test is performed three times for each configuration of the leader tip lateral distance and lightning rod height. According to these tests, the voltage and current waves associated with each configuration changed a little, but the strike points was similar. Totally, the experimental tests indicate a good agreement with the simulation results. 6. Effective parameters analysis In this section, the presented model is applied to evaluate the influence of different parameters and conditions on the total
Table 1 The characteristics of small-scale communication tower and the case study.
Case study Small-scale
H (meter)
Rt (meter)
d (m)
L (meter)
91 1.82
5.5 0.11
2 0.04
1e10 0.02e0.2
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M. Yahyaabadi et al. / Journal of Electrostatics 77 (2015) 35e43
number of direct lightning strokes to antenna. The simulation results of numerical model are summarized as follows: 6.1. Influence of upward leaders progression As mentioned before, for a reliable evaluation of the lightning encounter to tall structures, it is very essential to consider the inception and propagation of the upward leaders. Fig. 11 illustrates the influence of neglecting the upward leaders on the number of direct lightning strokes to antenna. By “without upward leader influence”, we mean the initial and propagation of the upward leaders are not taken into consideration from the beginning in simulations. In other words, the downward leader continues its path until the final collision point on the structure is specified. These calculations are done to show the effect of considering the upward leaders in simulations as an effective parameter in calculations. According to this figure, when the influence of upward leaders is not considered, the calculated SFN is lower than the actual value. 6.2. Influence of leaders velocity ratio As already mentioned, the downward and upward leader velocity and propagation time change from flash to flash. Fig. 12 de! picts the influence of the leader velocity ratio
Fig. 9. The lightning voltage impulse wave.
RV ¼ VVdownward upward
on
the number of direct lightning strokes to antenna. In this calculation the downward leader velocity is constant. According to this figure, the number of direct lightning strokes to antenna increases with the increment of the ratio between the downward and upward leader velocities. On the other hand, the lower velocity assumed for the upward leaders increases the number of direct lightning strokes to antenna. 6.3. Influence of communication tower height In this section, the probability of shielding failure for different communication tower dimensions has been calculated. As shown in Fig. 13, the number of direct lightning strokes to antenna increases with the increment of the tower height. In Refs. [30], the concept of effective tower height is introduced when the tower is located on top of a mountain. Therefore, according to the entries provided in this section, the effects of installation of the tower on the mountain can be studied. On the other hand, the installation of the tower on mountain tops makes the effective tower height increase and as a result, the number of direct lightning strokes to antenna increases as well. 6.4. Influence of breakdown electric field threshold By switching impulse tests on long air gaps it was shown that rain and other air conditions can change the breakdown voltage threshold (Eb ), for the same air clearance [28,31,32]. In this subsection, the influence of breakdown electric field threshold on the number of direct lightning strikes to antenna is calculated. The calculation results are shown in Fig. 14. 6.5. Influence of ground slope
Fig. 10. A. Impulse test on the small-scale model of the communication tower (Leader tip lateral distance ¼ 60 cm) B. Impulse test on the small-scale model of the communication tower (Leader tip lateral distance ¼ 120 cm).
The effect of ground slope (Fig. 15) on the number of direct lightning strokes has been considered in this subsection. As it is shown in Fig. 16, the probability of shielding failure has its least value for a flat trace. By increasing the ground slope, the probability of shielding failure will increase.
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Table 2 The simulation and experimental test results. Leader tip lateral distance (cm)
30
60
90
120
Lightning rod height (cm)
12 8 4 12 8 4 12 8 4 12 8 4
Strike point Simulation
Experimental
Rod Rod Rod Rod Rod Rod Rod Rod Antenna Rod Rod Antenna
Rod Rod Rod Rod Rod Rod Rod Rod Antenna Rod Rod Antenna
Fig. 11. The influence of upward leaders on the number of direct lightning strikes to antenna. Fig. 13. The influence of tower height on the number of direct lightning strikes to antenna.
Fig. 12. The influence of the leader velocity ratio on the number of direct lightning strikes to antenna.
Fig. 14. The influence of breakdown electric field threshold on the number of direct lightning strikes to antenna.
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M. Yahyaabadi et al. / Journal of Electrostatics 77 (2015) 35e43
6.6. Influence of near trees In order to consider the effect of trees on the number of direct lightning strikes to antenna, the presented model for trees in our previous work [24] is used. According to Fig. 17, a tree has been considered on each side of the communication tower, and the lateral distance of the trees from the tower center (Dtree) is assumed 25 m. For different heights of trees up to 30 m, the number of direct lightning strikes to antenna has been calculated. According to simulation results, the presence of these trees near the communication tower will not have any considerable affect on the number of direct lightning strokes and the density of strokes causing shielding failures. 7. Conclusion
Fig. 15. The communication tower on a sloppy trace.
There are different parameters affecting the number of direct lightning strokes to antenna on the communication tower. Parameters such as communication tower dimensions, installation place, ambient conditions, and the lightning rod height indicate different influences on the probability of shielding failure. The model presented for the calculation of the number of direct lightning strokes takes these different parameters and conditions into consideration. For this purpose, the downward lightning leader progression and the inception and propagation of multiple upward leaders are considered and the number of direct lightning strokes to antenna is determined accurately. Then, the influence of downward and upward leaders, communication tower height, weather conditions, and ground slope are evaluated. It is preferred to consider all of these parameters accurately to improve lightning shielding zone of the lightning rod. The experimental tests performed show a good agreement with the simulation results. References
Fig. 16. The influence of ground slope on the number of direct lightning strikes to antenna.
Fig. 17. The communication tower with trees near it.
[1] R.H. Golde, Lightning Protection, Edward Arnold Publishing Co, London, Britain, 1973. [2] M.A. Uman, The Art and Science of Lightning Protection, Cambridge University Press, Cambridge, U.K, 2008. [3] F.A.M. Rizk, Modeling of lightning exposure of sharp and blunt rods, IEEE Trans. Power Deliv. 25 (4) (Oct. 2010) 3122e3132. [4] F.A.M. Rizk, Modeling of lightning exposure of buildings and massive structures, IEEE Trans. Power Deliv. 24 (4) (Oct. 2009) 1987e1998. [5] F.S. Young, J.M. Clayton, A.R. Hileman, “Shielding of transmission lines, AIEE Trans. Power Appl. (1963) 132e154. [6] G.W. Brown, E.R. Whitehead, Field and analytical studies of transmission lines shielding: part II, IEEE Trans. Power App. Syst. PAS-88 (3) (Mar. 1969) 617e626. [7] T. Horvath, Computation of Lightning Protection, Research Studies Press, London, U.K., 1991. [8] A.J. Eriksson, The incidence of lightning strikes to power lines, IEEE Trans. Power Deliv. 2 (3) (Jul. 1987) 859e870. [9] A.J. Eriksson, “An improved electrogeometric model for transmission line shielding analysis, IEEE Trans. Power Deliv. 2 (3) (Jul. 1987) 871e886. [10] U. Kumar, P.K. Bokka, J. Padhii, A macroscopic inception criterion for the upward leaders of natural lightning, IEEE Trans. Power Deliv. 20 (2) (Apr. 2005) 904e911. [11] A.M. Mousa, Failure of the collection volume method and attempts of the ese lightning rod industry to resurrect it, J. Light. Res. 4 (Suppl. 2: M9) (2012) 118e128. [12] 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 Deliv. 5 (4) (Nov. 1990) 2009e2022. [13] L. Dellera, E. Garbagnati, Lightning stroke simulation by means of the leader progression model Part II: exposure and shielding failure evaluation of overhead lines with assessment of application graphs, IEEE Trans. Power Deliv. 5 (4) (Nov. 1990) 2023e2029. [14] F.A.M. Rizk, Modeling of lightning incidence to tall structures part I: theory, IEEE Trans. Power Deliv. 9 (1) (Jan. 1994) 162e171. [15] F.A.M. Rizk, Modeling of lightning incidence to tall structures part II: application, IEEE Trans. Power Deliv. 9 (1) (Jan. 1994) 172e193. [16] H. Singer, H. Steinbigler, P. Weiss, A charge simulation method for the calculation of high voltage fields, IEEE Power Appar. Syst. (1974) 1660e1668.
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[27] R.H. Golde, Lightning and tall structures, Proc. Inst. Elect. Eng. 125 (Apr. 1978) 347e351. [28] F.A.M. Rizk, Switching impulse strength of air insulation: leader inception criterion, IEEE Trans. Power Deliv. 4 (4) (Oct. 1989) 2187e2195. [29] F.A.M. Rizk, Modeling of transmission line exposure to direct lightning strokes, IEEE Trans. Power Deliv. 5 (4) (Nov. 1990) 1983e1997. [30] Helin Zhou, Nelson Theethayi, Gerhard Diendorfer, Rajeev Thottappillil, Vladimir A. Rakov, On estimation of the effective height of towers on mountaintops in lightning incidence studies, J. Electrost. (2010) 415e418. [31] M. Nayel, Investigation of lightning rod shielding angle, in: IAS 45th Annual Meeting, Houston, TX USA, Oct. 2010. [32] M. Nayel, Investigation of lightning rod striking distance, in: 7th AsiaePacific International Conference on Lightning, Chengdu, China, Nov. 2011. [33] V. Cooray, V. Rakov, N. Theethayi, The lightning striking distance- revisited, J. Electrostat. 67 (2007) 296e306. [34] S. Yokoyama, K. Miyake, T. Suzuki, S. Kanao, Winter lightning on Japan sea coast edevelopment of measuring system on progressing feature of lightning discharge, IEEE Trans. Power Deliv. 5 (3) (1990) 1418e1425. [35] J. He, Y. Tu, R. Zeng, J.B. Lee, S.H. Chang, Z. Guan, “Numeral analysis model for shielding failure of transmission line under lightning stroke, IEEE Trans. Power Deliv. 20 (2) (Apr 2005) 815e821. [36] V. Cooray, On the attachment of lightning flashes to grounded structures with special attention to the comparison of SLIM with CVM and EGM, J. Electrostat. 71 (2013) 577e581. [37] K. Berger, R.B. Anderson, H. Kroninger, Parameters of lightning flashes, Electra 41 (July 1975) 23e37. [38] R.B. Anderson, A.J. Eriksson, Lightning parameters for engineering applications, Electra 69 (March 1980) 65e102.
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Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Evaluation of parameters influencing the lightning performance of communication towers by numerical modeling and experimental tests Mostafa Yahyaabadi*, Alireza Sadoughi, Bahram Karimi Dept. of Electrical Engineering, Malekashtar University of Technology, Isfahan, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 April 2015 Received in revised form 30 June 2015 Accepted 2 July 2015 Available online xxx
This paper analyzes the effective parameters on lightning performance. The effects of tower height, breakdown electric field threshold, the ground slope of installation place, and the effect of the trees around the tower are investigated. A 3-D numerical analysis model is proposed to determine the number of direct lightning strokes to antennas. The communication tower, lightning rod, downward descending leader and upward leaders are modeled by different shapes of charges. Finally, a small-scale communication tower was built and tested in a high voltage laboratory. The experimental tests were consistent with the simulation results verifying the merits of the proposed method. © 2015 Elsevier B.V. All rights reserved.
Index Terms: Lightning leader Communication tower Lightning rod High voltage test
1. Introduction Lightning rod is basically responsible for the stroke interception, the most important task in a Lightning Protection System (LPS). Since its invention by Benjamin Franklin, lightning rod has found a very wide application [1e3]. The protective angle recommended for lightning rods varied within a wide range. Originally, these protective angles were based on experience, but later with the availability of high-voltage test facilities, these angles were also determined by tests on small-scale physical models [4]. In order to analyze the lightning performance of equipment and structures such as communication towers, several analytical methods have been proposed. At first, the Electro Geometric Model (EGM), based on the principle of striking distance, was found to be satisfactory. The striking distance is defined as the “distance between the object to be struck and the tip of the downward-moving leader at the instant that the upward leader is initiated from the object” [5e7]. Several researchers have developed the EGM. Eriksson [8,9] improved the model named “the Collection Volume Method (CVM)”. The Rolling Sphere Method (RSM) was developed for more complex structures. This method is one of the direct applications of EGM for 3-D geometries.
* Corresponding author. Tel.: þ98 3136933303. E-mail addresses: [email protected] (M. Yahyaabadi), [email protected] (A. Sadoughi), [email protected] (B. Karimi). http://dx.doi.org/10.1016/j.elstat.2015.07.002 0304-3886/© 2015 Elsevier B.V. All rights reserved.
However, in analytical methods, the expression of striking distance does not show any explicit reference to the field intensification at the structure top and the propagation of the upward leaders is not considered [10,11]. Therefore, Dellera et al. [12,13] and Rizk [14,15] proposed the Leader Progression Model (LPM) as a numerical approach to determine the path of the lightning and the final encounter. Recently, the LPM has been employed and developed by some researchers [19e24]. In present work, a model in a three-dimensional environment is proposed which takes the communication tower and antennas as well as air terminal and the step nature of downward lightning leader into account. In addition, the inception and propagation of multiple upward leaders are considered. The electrical fields are computed using the Charge Simulation Method (CSM) [16e18]. The number of direct lightning strokes to the antennas of communication towers is calculated accurately. Here, a new definition called the density of strokes causing shielding failures per year is provided. Accordingly, the risky areas in the leader-tip starting surface are determined. On the other hand, an area with a high density of strokes causing shielding failures expresses greater probability of its lightning encounter to antennas. The lightning performance analysis is performed for different conditions and the results are evaluated. Finally, in order to validate the simulation results, some laboratory tests were utilized on a small-scale communication tower.
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2. Leader progression and final jump The leader progression approach is based on the idea that a similarity exists between lightning phenomenon and discharges in long air gaps [12]. Here, the cloud-to-ground lightning flashes are considered and the presence of downward lightning leader is a principle of calculations. The simulation is started with a vertical straight section of the lightning leader propagated up to a level, which is high enough to nullify the influences of the earthed objects. This level is selected higher than twice the highest object [7]. The downward lightning leader develops gradually and to be assured of the leader progression in long air gaps, the propagation is simulated by steps with a length of 10 m. Its direction is towards the maximum potential gradient. During the descent of a downward lightning leader, the upward leaders are initiated from grounded objects and are propagated towards the downward lightning leader. When an upward leader succeeds to intercept the downward lightning leader, a conducting path between the cloud and the ground is created and the return stroke lightning current is drained [25]. The main characteristics used in this model are the direction of the leaders; charge distribution along the downward and upward leaders; inception criteria of the upward leaders; leaders advance speed; and the final jump criterion [26].
2.1. Direction of leader motion The procedure of calculating the downward and upward leader attachment requires the field calculation in the environment of the study. In each step of lightning leader motion, a hemisphere with a radius of a step length is drawn around the tip of the leader. Therefore, the next jump point of the leader is a point on the hemisphere that the voltage gradient along the line connecting the leader tip to the target point is maximum. The path of downward lightning leader including the tilted channel segments is replaced by vertical and horizontal line charges.
2.2. Inception criteria of the upward leaders
i Utip
lis ¼
¼
Einf $lil
E E Einf li þ x0 $Einf $ln init init e l Einf Einf
! x0
i U0 þ Es $lil Utip
Es Eb
h i i1 i þ Utip lil $ Es lil li1 Utip DQ i ¼ KQ $ li1 s l Dlil ¼
DQ i ql
U0 Es Eb
DQ 0 ¼ 0:5$KQ $l2s $ðEs Eb Þ;
¼ lil þ Dlil ; liþ1 l
(5)
(7)
i where Utip is the leader potential in step i; Einit and Einf are the initial and final values of the leader gradient; and x0 and ql are the constants. If the leader length ðliþ1 Þ increases to a maximum value l ðlmax Þ, equal to 2 m, the stable upward leader will be incepted. The constants of the upward leader model are: Es ¼ 450 kV/m; Einit ¼ 400 kV/m; Es ¼ 450 kV/m; x0 ¼ 0.75 m; KQ ¼ 3.5 1011 C/V; ql ¼ 50 106 C/m. When this condition is fulfilled, an upward leader propagates towards the downward lightning leader tip. In order to determine the direction of each upward leader, according to subsection 2-1, the electric field is calculated at fixed distances from the upward leader tip over various directions at each step. The next step is then directed along the line with the field maximum mean. The points with more likelihood of inception and propagation of upward leaders are the top of the lightning rod, the top of the antenna, and the ground surface bellow the lightning tip (Fig. 1).
2.3. Charge distribution along the leaders In the scientific literature, there are different proposals for the charge distribution along the downward leader such as uniform, linear, and exponential distributions [22,27]. Here, the charge density distribution along the downward leader channel is calculated as follows [33,36],
(1)
(2)
where U0 and Eb are the voltage and field on the fitted line of the background electric field and l0s is the initial length of the streamer. Es and KQ are the constant streamer electric field and a geometrical factor, respectively. If the initial streamer charge ðDQ 0 Þ is more than 1mC, the initial leader length is assumed to be 1 cm, then the streamer length and streamer space charge are calculated for each leader movement step as follows [19]:
(4)
(6)
For a reliable assessment of the lightning path and hence an accurate evaluation of the lightning protection performance, it is very essential to appropriately consider the inception and propagation of the upward leaders. Different criteria have been proposed for calculating the electric field intensity to ensure the stability of the upward leader inception [8,12,28,36]. At this work, the model proposed in Ref. [19] is applied to check the upward leader inception condition. The streamer charge is initially calculated as follows [19]:
l0s ¼
(3)
Fig. 1. More likely points to start upward leaders.
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37
( ) 10z0 z z0 z m1 þ m2 ðz z0 Þ z0 75 rðzÞ ¼ I m0 1 0:3e þ 0:7 1 1 0 þ ; HC z 0 HC HC 1 þ m3 ðz z0 Þ þ m4 ðz z0 Þ2
where r is the downward leader charge density in C/m; and z is the variable height of the point on the leader where charge density is to be calculated; z0 and HC are the height of the downward leader tip and the cloud height in meters, respectively (note that the above equation is valid for z0 > 10m), I is the lightning current in kilo amperes, m0 ¼ 1:476 105 , m1 ¼ 4:857 105 , m2 ¼ 3:9097 106 , m3 ¼ 0:522, m4 ¼ 3:73 103 . In the simulations performed for the real tower dimensions, the height of the lightning leader tip is always higher than 10 m from the ground level and therefore, the use of the above equation for the calculation of electric charge distribution along the lightning leader will be valid. In the simulations performed in small scales, the same equation has been used while ignoring the errors in calculations. The charge per meter length of the equivalent channel in upward leaders is assumed 50 mC/m [12]. 2.4. Velocity of downward and upward leaders The interception point of the downward lightning leader by an ! upward leader depends upon the ratio between the downward and upward leader velocities RV ¼ VVdownward . Even though measureupward ments and estimates of the downward lightning leader velocity are more common in literature, only few measurements of the upward leader velocity have been reported [25,34]. The velocity of upward leaders has been found to be related to the downward lightning leader current, the velocity, and the lateral position of the downward lightning leader as well as by the ambient field. Therefore, the velocity of an upward leader changes from flash to flash [25]. Eriksson [8] and Rizk [28,29] have considered equal velocities for both downward and upward leaders. In the work of Dellera et al. [12,13], the ratio of velocities is initially 4:1, later it is reduced to 1:1. The two values for the velocity ratio and their instant of changeover are rather difficult to comprehend and apply. In this paper, the effect of downward to upward leader velocities ratio has been investigated.
(8)
Therefore, the Shielding Failure Number (SFNi), the number of direct lightning strokes to antenna per year when the leader tip position is in the shaded mesh, can be calculated as:
SFNi ¼ 106 g dx$dy
ZImax PðIÞ$dI Imin
where g ¼ 0:015 Td is the ground flash density in strikes per square kilometers per year. Td is the number of thunderstorm days per year and is considered 40 [35]. P(I) is the probability density function of lightning current exceeding I, that could be calculated by the following approximate formula [7,35],
log10 PðIÞ ¼ 0:05
I 74
(10)
In addition, the results published in CIGRE Electra in 1975 [37] and 1980 [38] present a good data base of lightning currents and their relevant parameters. Fig. 3 shows the cumulative statistical lightning current distributions [37]: Finally, the number of direct lightning strokes to the antenna per year SFNT is:
SFNT ¼
n X
SFNi
(11)
i¼1
2.5. Final jump The critical breakdown gradient in the gap between the downward and upward leader tips is in the order of 500 kV/m. Thus, if at any instant the average voltage gradient determined by the potential difference between the downward leader tip and one of the upward leader tips exceeds the critical breakdown gradient, a final jump takes place [1]. 3. The number of direct lightning strokes to antenna As shown in Fig. 2, the area above the communication tower is divided to create a mesh system with differential length of dx in xdirection and dy in y-direction, (the area width is taken to be a distance from the center so that the leaders outside that distance do not strike the tower). For each position of the leader (shaded mesh), simulation starts for I ¼ 3kA and the striking point of the downward leader is found. Then, the simulation procedure will continue for different lightning currents until the lightning current range (Imax, Imin) is determined so that for a given current out of this range, the lightning would never strike the tower and antenna.
(9)
Fig. 2. Lightning strokes calculation model.
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Fig. 3. The cumulative statistical lightning current distributions: 1. negative first strokes, 2. negative subsequent strokes, 3. positive first strokes.
where n is the total number of meshes in the leader tip starting surface. Fig. 4 illustrates the procedure and steps of computing the SFN. 4. Case study and simulation results As a case study, a 91-m communication tower is considered for analyzing its lightning performance by applying the mentioned numerical model. The tower radius at ground level (Rt) is 5.5 m and the distance between the outer part of the antenna and the center of tower (d) is 2 m. According to Fig. 5, the communication tower is modeled by ring charges that are placed on each other in the direction of the tower height and each antenna is modeled by horizontal line charges. A lightning rod with a length of L is installed at the top and it is supposed to be modeled by vertical line charge segments. Fig. 6 depicts the number of direct lightning strokes to the antenna per year. This value decreases with an increase in the lightning rod height but it is never zero. In other words, most of the lightning leaders, but not all that threaten the antennas would be absorbed by the lightning rod. Thus, in a proper design for increasing the height of a lightning rod, the limitations should be considered and a reasonable value be selected. Fig. 7 represents the density of strokes causing shielding failures for the area above the tower that is calculated in more detail. On the other hand, the colored area with a higher density of lines shows the higher density of strokes causing shielding failures. In this calculation, the lightning rod height is considered 1 m. As shown in this figure, all lightning leaders within 20 m of the radial distance from the tower center are absorbed by the lightning rod. In addition, it is seen that the density of strokes causing the shielding failures is high within the interval of 30e40 m from center. Fig. 8 depicts the influence of lightning rod height on the density of strokes causing the shielding failures. According to this figure, the density of strokes causing shielding failures and also the number of the direct lightning strokes are reduced with an increase in the lightning rod height. 5. Experimental tests Here, in order to validate the simulation results, a small-scale communication tower with a ratio of 1e50 was constructed and
Fig. 4. Procedure for calculating the SFN of communication towers.
tested in the High Voltage Laboratory. In this experimental test, the starting point of the lightning leader is located at various positions (including areas with high density of strokes causing of shielding failures). Then, the strike point of lighting leader is observed. The characteristics of a small-scale communication tower in comparison with the case study are presented in Table 1: The characteristics of impulse generator are as follows: Maximum energy: 180 kJ; and maximum voltage impulse wave: 1.8 MV. A sample of lightning voltage impulse wave is presented in Fig. 9A. The lightning test voltage wave parameters are Vpeak ¼ 887kV ; T1 ¼ 1:13m s; T2 ¼ 44:6m s; b ¼ 11:4% (Fig. 9B, C). The blue curve (in the web version) ðU0 Þ is earlier lightning impulse voltage with high-frequency peak oscillation of frequency f 500kHz and the red curve (in the web version) ðUt Þ is the mean value that is drawn through the oscillating impulse voltage (Fig. 9C). With regard to the fact that the location change of the initiation of downward leader is effective on the breakdown voltage
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39
Fig. 7. The density of strokes causing shielding failures for the area above the communication tower.
Fig. 5. The communication tower and antenna.
Fig. 8. The density of strokes causing shielding failures for different lightning rod heights.
Fig. 6. The number of direct lightning strokes the antenna per year.
and as a result, on the impulse current, the lightning current peak has been changed within 12e24 Kilo-amperes in these tests and the simulations performed for small-scale model. In other words, when the distance of the rod tip, that simulates the downward leader and the equipment is increased, the electric breakdown takes place with more voltage and the generated current increases. In order to model the downward leader, a sharp rod is hung from a crane and the voltage is applied to it, while the rod tip height is about 3.2 m above the ground surface. Fig. 10 shows the two impulse tests performed on the smallscale model of a communication tower. According to Fig. 10.A, for a lateral distance of about 60 cm, an encounter to lightning protection system takes place. Therefore, the protection system has a proper performance in this case. Fig. 10.B depicts an encounter to the antenna for a lateral distance of about 120 cm. Since the exact
location of the encounter in recorded images is vague, the strike point is carefully checked after each encounter. The test is repeated for different lateral distances and the results are presented in Table 2. At least the test is performed three times for each configuration of the leader tip lateral distance and lightning rod height. According to these tests, the voltage and current waves associated with each configuration changed a little, but the strike points was similar. Totally, the experimental tests indicate a good agreement with the simulation results. 6. Effective parameters analysis In this section, the presented model is applied to evaluate the influence of different parameters and conditions on the total
Table 1 The characteristics of small-scale communication tower and the case study.
Case study Small-scale
H (meter)
Rt (meter)
d (m)
L (meter)
91 1.82
5.5 0.11
2 0.04
1e10 0.02e0.2
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number of direct lightning strokes to antenna. The simulation results of numerical model are summarized as follows: 6.1. Influence of upward leaders progression As mentioned before, for a reliable evaluation of the lightning encounter to tall structures, it is very essential to consider the inception and propagation of the upward leaders. Fig. 11 illustrates the influence of neglecting the upward leaders on the number of direct lightning strokes to antenna. By “without upward leader influence”, we mean the initial and propagation of the upward leaders are not taken into consideration from the beginning in simulations. In other words, the downward leader continues its path until the final collision point on the structure is specified. These calculations are done to show the effect of considering the upward leaders in simulations as an effective parameter in calculations. According to this figure, when the influence of upward leaders is not considered, the calculated SFN is lower than the actual value. 6.2. Influence of leaders velocity ratio As already mentioned, the downward and upward leader velocity and propagation time change from flash to flash. Fig. 12 de! picts the influence of the leader velocity ratio
Fig. 9. The lightning voltage impulse wave.
RV ¼ VVdownward upward
on
the number of direct lightning strokes to antenna. In this calculation the downward leader velocity is constant. According to this figure, the number of direct lightning strokes to antenna increases with the increment of the ratio between the downward and upward leader velocities. On the other hand, the lower velocity assumed for the upward leaders increases the number of direct lightning strokes to antenna. 6.3. Influence of communication tower height In this section, the probability of shielding failure for different communication tower dimensions has been calculated. As shown in Fig. 13, the number of direct lightning strokes to antenna increases with the increment of the tower height. In Refs. [30], the concept of effective tower height is introduced when the tower is located on top of a mountain. Therefore, according to the entries provided in this section, the effects of installation of the tower on the mountain can be studied. On the other hand, the installation of the tower on mountain tops makes the effective tower height increase and as a result, the number of direct lightning strokes to antenna increases as well. 6.4. Influence of breakdown electric field threshold By switching impulse tests on long air gaps it was shown that rain and other air conditions can change the breakdown voltage threshold (Eb ), for the same air clearance [28,31,32]. In this subsection, the influence of breakdown electric field threshold on the number of direct lightning strikes to antenna is calculated. The calculation results are shown in Fig. 14. 6.5. Influence of ground slope
Fig. 10. A. Impulse test on the small-scale model of the communication tower (Leader tip lateral distance ¼ 60 cm) B. Impulse test on the small-scale model of the communication tower (Leader tip lateral distance ¼ 120 cm).
The effect of ground slope (Fig. 15) on the number of direct lightning strokes has been considered in this subsection. As it is shown in Fig. 16, the probability of shielding failure has its least value for a flat trace. By increasing the ground slope, the probability of shielding failure will increase.
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Table 2 The simulation and experimental test results. Leader tip lateral distance (cm)
30
60
90
120
Lightning rod height (cm)
12 8 4 12 8 4 12 8 4 12 8 4
Strike point Simulation
Experimental
Rod Rod Rod Rod Rod Rod Rod Rod Antenna Rod Rod Antenna
Rod Rod Rod Rod Rod Rod Rod Rod Antenna Rod Rod Antenna
Fig. 11. The influence of upward leaders on the number of direct lightning strikes to antenna. Fig. 13. The influence of tower height on the number of direct lightning strikes to antenna.
Fig. 12. The influence of the leader velocity ratio on the number of direct lightning strikes to antenna.
Fig. 14. The influence of breakdown electric field threshold on the number of direct lightning strikes to antenna.
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6.6. Influence of near trees In order to consider the effect of trees on the number of direct lightning strikes to antenna, the presented model for trees in our previous work [24] is used. According to Fig. 17, a tree has been considered on each side of the communication tower, and the lateral distance of the trees from the tower center (Dtree) is assumed 25 m. For different heights of trees up to 30 m, the number of direct lightning strikes to antenna has been calculated. According to simulation results, the presence of these trees near the communication tower will not have any considerable affect on the number of direct lightning strokes and the density of strokes causing shielding failures. 7. Conclusion
Fig. 15. The communication tower on a sloppy trace.
There are different parameters affecting the number of direct lightning strokes to antenna on the communication tower. Parameters such as communication tower dimensions, installation place, ambient conditions, and the lightning rod height indicate different influences on the probability of shielding failure. The model presented for the calculation of the number of direct lightning strokes takes these different parameters and conditions into consideration. For this purpose, the downward lightning leader progression and the inception and propagation of multiple upward leaders are considered and the number of direct lightning strokes to antenna is determined accurately. Then, the influence of downward and upward leaders, communication tower height, weather conditions, and ground slope are evaluated. It is preferred to consider all of these parameters accurately to improve lightning shielding zone of the lightning rod. The experimental tests performed show a good agreement with the simulation results. References
Fig. 16. The influence of ground slope on the number of direct lightning strikes to antenna.
Fig. 17. The communication tower with trees near it.
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