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The use of shield wires for reducing induced voltages from lightning electromagnetic fields
Electric Power Systems Research 94 (2013) 46–53
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
The use of shield wires for reducing induced voltages from lightning electromagnetic fields Alexandre Piantini a,∗ , Jorge M. Janiszewski b a b
University of São Paulo, Institute of Electrotechnics and Energy (CENDAT – IEE/USP), Av. Prof. Luciano Gualberto, 1289, 05508-010 São Paulo, SP, Brazil University of São Paulo, Polytechnic School (PTC/EPUSP), Av. Prof. Luciano Gualberto, 1289, trav. 3, 158, 05508-010 São Paulo, SP, Brazil
a r t i c l e
i n f o
Article history: Available online 26 May 2012 Keywords: Electromagnetic transients Lightning induced voltages Overvoltage protection Power distribution lines Scale model Shield wire
a b s t r a c t The mechanisms from which lightning overvoltages can be produced on a power line depend on the system voltage. In medium voltage (MV) overhead distribution systems, lightning transients can be originated from either direct or indirect strokes. The main methods that can be adopted to improve the line lightning performance concern the increase of the critical impulse flashover voltage (CFO) of the line structures, the installation of surge arresters, and the use of one or more shield wires. This paper deals with the evaluation of the effectiveness of shield wires in reducing the magnitudes of the surges induced by nearby strokes on MV distribution lines. Such effectiveness depends on the combination of several parameters such as the relative position of the shield wire with respect to the phase conductors, the grounding interval, the ground resistance, the stroke current steepness, and the relative position of the stroke channel with respect to the grounding points. Realistic situations corresponding to typical configurations of a rural distribution line with either an overhead ground wire or a neutral conductor are considered. The analysis is carried out based on both computer simulations and test results obtained from scale model experiments, under controlled conditions. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The main function of a shield wire is to intercept direct lightning strokes that would otherwise hit the phase conductors producing overvoltages higher than the line lightning impulse withstand level. For this purpose, the shield wire must be installed above the phase conductors, and its proper placement is one important task of transmission-line designers. Other functions involve the lowering of the self-surge impedance of an overhead ground wire system and the raising of the mutual surge impedance of an overhead ground wire system to the protected phase conductors [1]. Direct stroke protection with shield wires can be effective on transmission lines, which are characterized by relatively high values of critical impulse flashover voltage (CFO). On the other hand, the direct stroke performance of distribution lines is generally not much affected by the presence of a shield wire. Because of the low lightning impulse withstand capability of the line poles, even if the shield wire is grounded at every structure the ground potential rise caused by the flow of the stroke current through the pole ground impedance causes, in most of the cases, voltage differences between the ground lead and the
∗ Corresponding author. Tel.: +55 11 3091 2580; fax: +55 11 3812 9251. E-mail addresses: [email protected] (A. Piantini), [email protected] (J.M. Janiszewski). 0378-7796/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2012.04.012
phase conductors larger than the line CFO. The greater the value of the ground impedance, the greater these voltage differences and hence the greater the probability of backflashover occurrence [2–4]. Therefore, for the shield wire to be effective against direct strokes it must be not only grounded at every pole but also the ground resistances must be low – less than 10 if the insulator CFO is less than 200 kV [2]. However, due to its coupling with the phase conductors, a shield wire can also be used with the purpose of reducing induced voltages from external electromagnetic fields. This reduction occurs even if it is beneath the phase conductors, so that a grounded neutral has the same effect. Investigations on the effectiveness of shield wires in terms of decreasing the magnitudes of lightning induced voltages on medium voltage overhead distribution lines have been conducted, e.g., in [4–20]. In [5] the shield wire is assumed to be at zero potential at any time, even during the transient. A simple expression is presented in [6] for the calculation of the ratio between the voltages induced on a phase conductor with and without the presence of a shield wire for the case of a perfectly conducting ground. The formula was derived assuming just one connection of the shield wire or neutral conductor to ground and applies only for points situated close to the grounding point, although results with reasonable accuracy are obtained for the case of multiple groundings as long as the distance between adjacent groundings is short (e.g. 30 m [2]). In [7,8] the shield wire is considered to be a conductor belonging to a multi conductor transmission line and grounded
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at both line terminations. In [9] the model presented in [7,8] is extended and generalized in order to evaluate the effect of periodically grounded shield wires on the attenuation of lightning induced voltages. A procedure for the estimation of the annual number of lightning-induced flashovers on distribution lines and the evaluation of the effectiveness of shield wires is proposed in [10]. Measurements of induced voltages by real lightning flashes are presented in [11,12], while in [13–18] the analyses involve scale model experiments. Comparisons between voltages induced by typical first and subsequent downward negative flashes on lines with different configurations are presented in [19,20]. This paper deals with the evaluation of the effectiveness of shield wires in reducing the magnitudes of the surges induced by nearby lightning strokes on MV overhead distribution lines. Such effectiveness depends on the combination of several parameters such as the relative position of the shield wire with respect to the phase conductors, the grounding interval, the ground resistance, the stroke current steepness, and the relative position of the stroke channel with respect to the grounding points. Initially, the basis for the calculations is described for the simplest case, which consists in a shield wire grounded at one point only. Afterwards, realistic situations corresponding to typical configurations of a rural distribution line with either an overhead ground wire or a neutral conductor are considered and simulation and experimental results are compared to confirm the validity of the method. Finally, the effects of various line and lightning parameters on the induced voltages are evaluated through the use of both computer simulations and test results obtained from scale model experiments, under controlled conditions. 2. Methodology Consider an infinite line with a phase conductor and either a neutral or a shield wire connected to ground at a single point x1 . Neglecting the ground lead inductance, the current Ig (x1 , t) which will flow to ground in the event of a nearby lightning strike can be calculated as [6,21]: Ig (x1 , t) =
Ug (x1 , t) Rg + 0.5 Zg
(1)
where Ug (x1 , t) corresponds to the voltage that would be induced at point x1 in the absence of the connection to ground, Zg is the surge impedance of the shield wire, and Rg represents the ground resistance. The induced voltage Up (x2 ,t) at point x2 on the phase conductor is given by: Up (x2 , t) = U p (x2 , t) − 0.5Zm Ig
x1 , t −
|x2 − x1 | c
(2)
where Up (x2 , t) is the voltage that would be induced at point x2 of the phase conductor in the absence of the shield wire grounding and Zm is the mutual impedance between the conductors. As indicated in Eq. (2), due to the electromagnetic coupling between the shield wire and the phase conductor, the induced voltage on the latter will be reduced regardless of the relative position of the wires. For a given lightning current and stroke location, the amount of reduction will depend on the coupling between the conductors, on the value of the ground resistance, and on the distance between the observation and grounding points. The induced voltages on the phase and shield wires in the absence of the connection to ground are calculated by using the Extended Rusck Model (ERM), which is based on Rusck’s theory [6]. The ERM, which is described in [20], has some features that, unlike the original model, allow for taking into account situations of practical interest such as, e.g., a line with a multi-grounded neutral or shield wire and equipment such as transformers and surge arresters
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Fig. 1. Configuration of the line with the shield wire (dimensions referred to the full-scale system).
[4,22]. The incidence of lightning flashes to nearby elevated objects [23,24] and the occurrence of upward leaders [24–26] can also be considered. Lines with various sections of different directions can be considered through the evaluation of the correct propagation time delays for the elementary voltage components that determine the induced voltage at a given point of the line. The effect of an overhead ground wire or of a neutral conductor is considered by calculating the currents that flow to ground at the various grounding points, taking into account the multiple reflections and, then, the voltages associated with these currents that, due to the coupling between the wires, are induced on the phase conductors. In order to validate the model, several tests were performed on a reduced scale system, under controlled conditions, and measured and calculated induced voltages were compared. The system, whose scale factor for length was 1:50, comprised models of the lightning channel, the ground plane, and of two overhead distribution lines. The ground was simulated by aluminum plates interconnected, thus representing a perfectly conducting plane. The length of the lines was 28 m, which is equivalent to 1.4 km on a full-scale basis. The lines were parallel, matched at both terminations, and symmetric with respect to the lightning channel model, which was equidistant from the lines’ ends. The height of the phase conductors (h) was 20 cm, corresponding to 10 m. The distance between the lightning channel model and each line (d) was equivalent to 70 m. One of the lines had just one conductor, while the other had one phase and also a shield wire, placed at height hg , as shown in Fig. 1. Different heights were considered for the shield wire and tests were performed for various combinations of grounding spacing (xg ) and ground resistance values. A detailed description of the system and of its various components can be found in [20,27,28]. Fig. 2 shows comparisons between measured and calculated voltages induced on the line with the shield wire, in different situations. The main characteristics of the stroke current, whose waveform is presented in [25], are: magnitude I = 36 kA, front time tf = 3.1 s, and propagation velocity of 11% of that of light in free space. These values, referred to the full-scale system, can be converted to the values actually recorded in the scale model experiments by applying the scale factors for time (1:50) and for voltage and current (1:30,000). As a matter of fact, as there are no nonlinearities in the system, the choice of the scale factor for voltage
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a
240 Up` Up Upg
Voltage (kV)
180
120
60
0 6
8
10
12
14
Shield wire height (m)
d = 50 m
b
d = 100 m
d = 200 m
160
Up` Up Upg
Voltage(kV)
120
80
40
0 6
8
10
12
14
Shield wire height (m) Fig. 3. Induced voltage peak values at the point closest to the stroke location as function of the shield wire height hg , for two values of the stroke current front time. I = 50 kA; d = 50 m; h = 10 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
and current is arbitrary, since under this condition the induced voltages are directly proportional to the stroke currents. This is not the case when surge arresters are present, for which the scale factor for voltage and current should be determined [20,22,27]. The good agreement observed between measured and calculated results confirms the adequacy of the model for the evaluation of how effective a shield wire or a neutral conductor can be in mitigating lightning induced voltages on overhead power lines [20,29]. Fig. 2. Measured and calculated phase-to-ground induced voltages at the point closest to the stroke location for the line configuration shown in Fig. 1. I = 36 kA; tf = 3.1 s; d = 70 m; h = 10 m. (a) hg = 7 m; xg = 450 m; Rg = 0 ; stroke location in front of a grounding point. (b) hg = 9 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (c) hg = 7 m; xg = 750 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
3. Parametric analysis In this section the effect of the shield wire on the lightning induced voltages is evaluated taking into account the influence of some of the most important parameters involved in the process. The simulations were performed assuming a horizontal line configuration with distance of 0.75 m between adjacent phases. The line was 3 km long, the height of the phase conductors (h) was 10 m,
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Fig. 5. Induced voltages at the point closest to the stroke location for shield wire heights of 7 m and 11 m. I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; xg = 450 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
[31]. Ground was assumed to be perfectly conducting, an assumption which is reasonable when the line is located above a soil with resistivity lower than about 100 m [32], the distance between the line and the stroke location is not larger than some hundreds of meters, and the line length is shorter than a certain critical value (typically 2 km) [33]. The induced voltages were calculated at the point closest to the stroke location. 3.1. Shield wire height
Fig. 4. Ratio between the peak values of the phase-to-shield wire and phase-toground (in the absence of the shield wire) induced voltages at the point closest to the stroke location as function of the shield wire height hg , for two values of the stroke current front time. I = 50 kA; h = 10 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
and the shield wire was considered either directly above or beneath the middle phase. It is worth mentioning that calculations carried out in [30] on lines with lengths varying from 500 m to 5 km over a perfectly conducting ground showed that the lightning induced voltages in the middle of the line – in front of the stroke location – reached the same peak value in all cases except for the shortest line, where the amplitude was about 3% lower. The diameter of all the conductors was 2 cm. Variations of the conductors’ cross sections affect their characteristic impedances, but the influence on the induced voltages is not important for the range of diameters commonly used [21]. Unless otherwise indicated, the stroke current was represented by a triangular waveshape with peak value of 50 kA, front time of 3 s, time to half value of 50 s, and propagation velocity of 30% of that of light in free space. The stroke channel was vertical, 3 km long, without branches, and the current distribution along the channel was calculated according to the Transmission Line model
Fig. 3 presents the peak values of the induced voltages Upg between phase and shield wire as a function of the shield wire height for stroke current front times of 3 s and 6 s and distances of 50 m, 100 m, and 200 m between the line and the lightning strike point. The grounding spacing is 300 m, the ground resistance is 50 , and the stroke location is equidistant between the closer grounding points. For comparison’s sake, Fig. 3 also shows the voltages which would be induced in the absence of the shield wire (Up ) and, for the case of d = 50 m, the phase-to-ground voltage Up . The condition hg = h (10 m) is equivalent to replace the middle phase with the shield wire. It can be observed that when the shield wire is beneath the phase conductors (i.e., hg < 10 m), the induced voltages Upg and Up decrease in amplitude as hg increases, whereas the opposite behavior is observed for hg > 10 m. This can be explained by the fact that the suppressive effect of the shield wire in a specific condition depends both on the current flowing to ground and on the mutual impedance Zm . The current to ground is directly proportional to the voltage induced on the shield wire (Usw ) and decreases as the surge impedance Zg increases. The voltage Usw is directly proportional to the height hg , whereas Zg increases logarithmically. By its turn, Zm decreases as the distance between the phase and shield wire increases. Therefore, for hg < h both Zm and Ig increase with hg , so that the voltage reduction is more significant when the height of the shield wire is close to that of the phase conductors. For hg > h, the current to ground continues to increase with hg , but Zm decreases. As shown in Fig. 3, the influence of Zm prevails, so that when the shield wire is above the phase conductors, the higher it is, the lower its effectiveness will be in reducing the magnitudes of the induced voltages.
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a
240 Up` Up Upg
Voltage (kV)
180
120
60
0 0
100
200
300
400
Ground resistance ( ) d = 50 m
The suppressive effect of the shield wire can be expressed as the ratio of the voltage between the phase conductor and the shield wire (Upg ) and the voltage that would be induced in the phase conductor in the absence of the shield wire (Up ). The ratios relevant to the situations treated in Fig. 3 are presented in Fig. 4 as function of the height hg ; the variation is from 0.50 to 0.85 for the case of stroke current front time of 3 s (Fig. 4a) and from 0.44 to 0.80 for tf = 6 s (Fig. 4b) in the range of heights considered. For tf = 3 s and hg < h, the effect of the shield wire is more pronounced (i.e., the lowest ratio Upg /Up is obtained) for the shortest distance between the line and the lightning strike point (d = 50 m). For hg = 8 m, the maximum ratio is equal to 0.74 (d = 200 m) and the minimum is about 12% lower (0.66, for d = 50 m). For hg > 10 m, the effect is more significant for d = 100 m; the greatest difference among the ratios for hg = 12 m is about 9% (ratios of 0.63 and 0.58 for d = 50 m and d = 100 m, respectively). On the other hand, Fig. 4b shows that for tf = 6 s and hg < h the lowest ratio corresponds to d = 100 m, while
Fig. 7. Measured induced voltages (phase-to-ground, Up) at the point closest to the stroke location for different shield wire heights (adapted from [4]). I = 24.9 kA; tf = 3.5 s; d = 70 m; h = 10 m; xg = 450 m; Rg = 50 ; stroke location in front of a grounding point.
b
d = 200 m
160
Up` Up Upg
120
Voltage (kV)
Fig. 6. Induced voltages at the point closest to the stroke location. I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; hg = 11 m; xg = 450 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
d = 100 m
80
40
0 0
100
200
300
400
Ground Resistance ( ) Fig. 8. Induced voltage peak values at the point closest to the stroke location as function of the ground resistance Rg , for two values of the stroke current front time. I = 50 kA; h = 10 m; hg = 9 m; xg = 300 m; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
for hg > 10 m the effect is more significant for d = 50 m. A comparison between Fig. 4a and b shows that the effect of the shield wire tends to be less dependent on the distance d for stroke currents with longer front times. Fig. 5 compares, for a specific condition (xg = 450 m, Rg = 50 , and stroke location equidistant from the closest grounding points), the voltages Upg between phase and shield wire corresponding to shield wire heights of 7 m and 11 m. The voltage Up is also shown, for reference. For hg = 11 m, Upg has an initial negative peak because, being the shield wire above the phase conductors, the voltage Usw is larger than Up until the time corresponding to the arrival, at the observation point, of the effect of the current at the nearest grounding point. Only then Usw begins to decrease. Due to this delay, the voltages Up and Up are exactly equal up to about 1.52 s, as shown in Fig. 6. Fig. 7 presents phase-to-ground induced voltages obtained from scale model experiments on lines with shield wires at different heights [4]. The comparison illustrates the fact that the larger the current to ground (which increases with hg ) and the greater the
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Fig. 10. Induced voltages at the point closest to the stroke location for ground resistance values of 50 and 400 . I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; hg = 9 m; xg = 600 m; stroke location equidistant from the closest grounding points. (a) Phaseto-shield wire voltages and (b) phase-to-ground voltages.
Fig. 9. Ratio between the peak values of the phase-to-shield wire and phase-toground (in the absence of the shield wire) induced voltages at the point closest to the stroke location as function of the ground resistance Rg , for two values of the stroke current front time. I = 50 kA; h = 10 m; xg = 300 m; hg = 9 m; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
coupling between the shield wire and the phase conductors, the greater the reduction on the voltages’ magnitudes. 3.2. Ground resistance The ground resistance depends both on the soil resistivity and on the configuration of the grounding system, so that different values are obtained for the same soil resistivity if different grounding arrangements are considered. Therefore, although the lightning fields were calculated under the assumption of a perfectly conducting ground, the value of the ground resistance was varied in order to investigate its influence on the effectiveness of the shield wire in the mitigation of lightning induced overvoltages. The effect of the ground resistance on the phase-to-ground and phase-to-shield wire induced voltages is depicted in Fig. 8a for ground spacing of 300 m, shield wire height of 9 m, stroke current front time of 3 s, and distances of 50 m, 100 m, and 200 m between the line and the
lightning strike point. The voltages that would be induced on the line in the absence of the shield wire are also shown. The results corresponding to tf = 6 s are presented in Fig. 8b. The phase-to-ground voltages Up increase with Rg since higher values of the ground resistance correspond to lower currents to ground and, consequently, to lower amplitudes of the voltage component associated with the product Zm Ig (“suppressive component”) which is responsible for the reduction of the induced voltages. On its turn, the shield wire-to-ground voltage Usw is more sensitive to the variation of Rg , since the suppressive component is associated with the product Zg Ig , which is higher than Zm Ig . Thus the increase of Usw with Rg is more significant in comparison with that of Up , and therefore the net result is a decrease of the voltage Upg between phase and shield wire as Rg increases. It can also readily be seen from Fig. 8 that the dependence of the phase-to-shield wire voltage with the ground resistance is more significant than that of the phase-to-ground voltage. The variation of the ratio Upg /Up as function of the ground resistance is presented in Fig. 9 for the situations treated in Fig. 8. The ratio varies from 0.43 to 0.71 for tf = 3 s (Fig. 8a) and from about 0.42 to 0.63 for tf = 6 s (Fig. 8b) in the range considered. For both values of stroke current front time, the ratios corresponding to the distances of 50 m and 100 m are very close and lower than
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the line and the lightning strike point have been considered as well. The analysis led to the following conclusions:
Fig. 11. Measured induced voltages (phase-to-ground, Up) at the point closest to the stroke location for different values of the ground resistance (adapted from [4]). I = 24.9 kA; tf = 3.5 s; d = 70 m; h = 10 m; hg = 9 m; xg = 450 m; stroke location equidistant from two grounding points.
that relevant to d = 200 m. The effect of the shield wire tends to be less dependent on the distance as the stroke current front time increases; the maximum difference between the ratios relevant to the three values of d is about 11% for tf = 3 s and 7% for tf = 6 s. For illustration purposes, a comparison between the induced voltage waveshapes relative to ground resistances of 50 and 400 is presented in Fig. 10, while phase-to-ground induced voltages obtained from scale model experiments for Rg = 0 and Rg = 1000 are shown in Fig. 11. As pointed out in [4], the influence of the ground resistance tends to decrease as the distance between adjacent grounding points increases, the stroke current front time becomes shorter or the distance between the stroke location and the closest grounding point increases. Lightning induced voltages can be remarkably affected by the soil resistivity. In general the voltages tend to increase with the soil resistivity [7,10,32], but in some cases, depending on the stroke location and the observation point, they may have just the opposite behavior. It is relevant to mention that the value of the ground resistance should be kept as low as possible in order to avoid the injection of high magnitude surges into the neutral between the transformer and the power installations in the case, e.g., of direct strikes to the MV line. The flow of the so called “low-voltage side surges” or “secondary side surges” through the low-voltage windings of a single-phase distribution transformer can lead to its failure even if it is protected with a primary arrester [4,21,34–36].
4. Conclusions An evaluation of the effect of a shield wire on the voltages induced on overhead distribution lines by nearby lightning strokes has been carried out through the use of a model whose validity has been demonstrated from comparisons between measured and calculated induced voltages. The effectiveness of a multi-grounded neutral or shield wire in mitigating lightning induced voltages depends on the combination of the values of various line and lightning parameters, and the influences of the shield wire height and the ground resistance have been investigated based on both computer simulations and test results obtained from scale model experiments. Variations of other parameters such as the stroke current front time and the distance between
• the closer the shield wire is to the phase conductors, the greater the reduction on both the phase-to-ground and the phase-toshield wire induced voltages will be. For the same distance, the effect is larger when the shield wire is above the phase conductors; • the effectiveness of the shield wire varies slightly with the distance d between the line and the lightning strike point. In general, the longer the distance, the greater the reduction observed on the phase-to-ground voltage Up with respect to the voltage induced at the same point in the absence of the shield wire (Up ), i.e., the lower the ratio Up /Up . On the other hand, the ratio of the voltages Upg between the phases and the shield wire and Up has the opposite behavior, i.e., the ratio Upg /Up tends to increase to some extent with the distance; • in general, for stroke currents with longer front times the effect of the shield wire tends to be more significant and the ratios Up /Up and Upg /Up tend to be less dependent on the distance d; • the phase-to-ground voltages increase with the ground resistance, while the phase-to-neutral or phase-to-shield wire voltages diminish as the ground resistance increases; • in some conditions, the phase-to-ground induced voltages can be reduced to about 60% of the values that would result without the shield wire (Up ); the phase-to-neutral or phase-to-shield wire voltages can be less than half the magnitude of Up . References [1] IEEE Guide for Improving the Lightning Performance of Transmission Lines, IEEE Std. 1243, 1997. [2] IEEE Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines, IEEE Std. 1410, 2010. [3] Joint CIGRE-CIRED Working Group C4.402, Protection of Medium Voltage and Low Voltage Networks Against Lightning Part 2: Lightning Protection of Medium Voltage Networks, 2010. [4] A. Piantini, Lightning protection of overhead power distribution lines, in: 29th International Conference on Lightning Protection (ICLP), Uppsala, Sweden, 2008, pp. 1–29 (invited lecture-4). [5] P. Chowdhuri, Lightning-induced voltages on multiconductor overhead lines, IEEE Transactions on Power Delivery 5 (2) (1990) 658–667. [6] S. Rusck, Induced Lightning Over-voltages on Power-Transmission Lines With Special Reference to the Over-voltage Protection of Low-voltage Networks, Trans. Royal Institute of Technology, No. 120, 1958. [7] F. Rachidi, C.A. Nucci, M. Ianoz, Transient analysis of multiconductor lines above a lossy ground, IEEE Transactions on Power Delivery 14 (1999) 294–302. [8] F. Rachidi, C.A. Nucci, M. Ianoz, C. Mazzetti, Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields, IEEE Transactions on Power Delivery 12 (1997) 1404–1411. [9] M. Paolone, C.A. Nucci, E. Petrache, F. Rachidi, Mitigation of lightning-induced overvoltages in medium voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters, modeling and experimental validation, IEEE Transactions on Power Delivery 19 (1) (2004) 423–431. [10] A. Borghetti, C.A. Nucci, M. Paolone, An improved procedure for the assessment of overhead line indirect lightning performance and its comparison with the IEEE Std. 1410 method, IEEE Transactions on Power Delivery 22 (1) (2007) 684–692. [11] S. Yokoyama, K. Miyake, H. Mitani, N. Yamazaki, Advanced observations of lightning induced voltage on power distribution lines, IEEE Transactions on Power Delivery, PWRD-1 (1986) 129–139. [12] S. Yokoyama, K. Miyake, H. Mitani, A. Takanishi, Simultaneous measurement of lightning induced voltages with associated stroke currents, IEEE Transactions on Power Apparatus and Systems, PAS-102 (1983) 2420–2429. [13] S. Yokoyama, Designing concept on lightning protection of overhead power distribution line, in: IX International Symposium on Lightning Protection (SIPDA), Foz do Iguac¸u, Brazil, 2007, pp. 647–662. [14] A. Piantini, J.M. Janiszewski, Lightning induced voltages on overhead lines: The effect of ground wires, in: 22nd International Conference on Lightning Protection (ICLP), Budapest, Hungary, 1994, pp. R3b/1–R3b/5. [15] S. Yokoyama, S.K. Yamamoto, H. Kinoshita, Analogue simulation of lightning induced voltages and its application for analysis of overhead-ground-wire effects, IEE Proceedings C 132 (4) (1985) 208–216. [16] S. Yokoyama, Calculation of lightning-induced voltages on overhead multiconductor systems, IEEE Transactions on Power Apparatus and Systems, PAS-103 (1984) 100–108.
A. Piantini, J.M. Janiszewski / Electric Power Systems Research 94 (2013) 46–53 [17] S. Yokoyama, Experimental analysis of earth wires for induced lightning surges, IEE Proceedings C 127 (1) (1980) 33–40. [18] E. Cinieri, A. Fumi, Effetto della presenza di piú conduttori e di funi di guardia sulle sovratensioni atmosferiche indotte nelle linee elettriche, L’ Energie Elettrica 11/12 (1979) 595–601. [19] F.H. Silveira, A. A. De Conti, S. Visacro, Voltages induced in single-phase overhead lines by first and subsequent negative lightning strokes: influence of the periodically grounded neutral conductor and the ground resistivity, IEEE Transactions on Electromagnetic Compatibility 53 (2) (2011) 414–420. [20] A. Piantini, J.M. Janiszewski, Lightning-induced voltages on overhead lines – application of the Extended Rusck Model, IEEE Transactions on Electromagnetic Compatibility 51 (3) (2009) 548–558. [21] A. Piantini, Lightning protection of low-voltage networks, in: V. Cooray (Ed.), Lightning Protection, UK, The Institution of Engineering and Technology, 2010, pp. 553–634. [22] A. Piantini, J.M. Janiszewski, The effectiveness of surge arresters on the mitigation of lightning induced voltages on distribution lines, Journal of Lightning Research 2 (2007) 34–52. [23] A. Piantini, J.M. Janiszewski, Induced voltages on distribution lines due to lightning discharges on nearby metallic structures, IEEE Transactions on Magnetics 34 (5) (1998) 2799–2802. [24] A. Piantini, J.M. Janiszewski, An improved model for lightning induced voltages calculations, in: Proc. IEEE/PES Transmission & Distribution Conference and Exposition, Latin America, São Paulo, Brazil, 2004, pp. 554–559. [25] A. Piantini, J.M. Janiszewski, The Extended Rusck Model for calculating lightning induced voltages on overhead lines, in: VII International Symposium on Lightning Protection (SIPDA), Curitiba, Brazil, 2003, pp. 151–155. [26] A. Piantini, J.M. Janiszewski, The influence of the upward leader on lightning induced voltages, in: 23rd International Conference on Lightning Protection (ICLP), Florence, Italy, 1996, pp. 352–357.
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[27] A. Piantini, J.M. Janiszewski, A. Borghetti, C.A. Nucci, M. Paolone, A scale model for the study of the LEMP response of complex power distribution networks, IEEE Transactions on Power Delivery 22 (2007) 710–720. [28] A. Piantini, J.M. Janiszewski, An experimental study of lightning induced voltages by means of a scale model, in: 21st International Conference on Lightning Protection (ICLP), Berlin, Germany, 1992, pp. 4.08/195–199. [29] A. Piantini, J.M. Janiszewski, The effectiveness of shield wires in reducing induced voltages from lightning electromagnetic fields, in: 7th Asia-Pacific International Conference on Lightning (APL), Chengdu, China, 2011, pp. 666–672. [30] A. Piantini, J.M. Janiszewski, The Extended Rusck Model for calculating lightning induced voltages on overhead lines, in: 7th International Symposium on Lightning Protection (SIPDA), Curitiba, Brazil, 2003, pp. 151–155. [31] M.A. Uman, D.K. McLain, Magnetic field of the lightning return stroke, Journal of Geophysical Research 74 (1969) 6899–6910. [32] C.A. Nucci, Lightning-induced voltages on distribution systems: influence of ground resistivity and system topology, in: VIII International Symposium on Lightning Protection (SIPDA), São Paulo, Brazil, 2005, pp. 761–773. [33] F. Rachidi, C.A. Nucci, M. Ianoz, C. Mazzetti, Influence of a lossy ground on lightning-induced voltages on overhead lines, IEEE Transactions on Electromagnetic Compatibility 38 (3) (1996) 250–264. [34] R.C. Dugan, S.S. Kershaw Jr., S.D. Smith, Protecting distribution transformers from low-side current surges, IEEE Transactions on Power Delivery 5 (4) (1990) 1892–1901. [35] Task force on low-side surge requirements for distribution transformers, secondary (low-side) surges in distribution transformers, IEEE Transactions on Power Delivery 7 (2) (1992) 746–755. [36] R.C. Dugan, S.D. Smith, Low-voltage-side current-surge phenomena in singlephase distribution transformer systems, IEEE Transactions on Power Delivery 3 (2) (1988) 637–647.
Contents lists available at SciVerse ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
The use of shield wires for reducing induced voltages from lightning electromagnetic fields Alexandre Piantini a,∗ , Jorge M. Janiszewski b a b
University of São Paulo, Institute of Electrotechnics and Energy (CENDAT – IEE/USP), Av. Prof. Luciano Gualberto, 1289, 05508-010 São Paulo, SP, Brazil University of São Paulo, Polytechnic School (PTC/EPUSP), Av. Prof. Luciano Gualberto, 1289, trav. 3, 158, 05508-010 São Paulo, SP, Brazil
a r t i c l e
i n f o
Article history: Available online 26 May 2012 Keywords: Electromagnetic transients Lightning induced voltages Overvoltage protection Power distribution lines Scale model Shield wire
a b s t r a c t The mechanisms from which lightning overvoltages can be produced on a power line depend on the system voltage. In medium voltage (MV) overhead distribution systems, lightning transients can be originated from either direct or indirect strokes. The main methods that can be adopted to improve the line lightning performance concern the increase of the critical impulse flashover voltage (CFO) of the line structures, the installation of surge arresters, and the use of one or more shield wires. This paper deals with the evaluation of the effectiveness of shield wires in reducing the magnitudes of the surges induced by nearby strokes on MV distribution lines. Such effectiveness depends on the combination of several parameters such as the relative position of the shield wire with respect to the phase conductors, the grounding interval, the ground resistance, the stroke current steepness, and the relative position of the stroke channel with respect to the grounding points. Realistic situations corresponding to typical configurations of a rural distribution line with either an overhead ground wire or a neutral conductor are considered. The analysis is carried out based on both computer simulations and test results obtained from scale model experiments, under controlled conditions. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The main function of a shield wire is to intercept direct lightning strokes that would otherwise hit the phase conductors producing overvoltages higher than the line lightning impulse withstand level. For this purpose, the shield wire must be installed above the phase conductors, and its proper placement is one important task of transmission-line designers. Other functions involve the lowering of the self-surge impedance of an overhead ground wire system and the raising of the mutual surge impedance of an overhead ground wire system to the protected phase conductors [1]. Direct stroke protection with shield wires can be effective on transmission lines, which are characterized by relatively high values of critical impulse flashover voltage (CFO). On the other hand, the direct stroke performance of distribution lines is generally not much affected by the presence of a shield wire. Because of the low lightning impulse withstand capability of the line poles, even if the shield wire is grounded at every structure the ground potential rise caused by the flow of the stroke current through the pole ground impedance causes, in most of the cases, voltage differences between the ground lead and the
∗ Corresponding author. Tel.: +55 11 3091 2580; fax: +55 11 3812 9251. E-mail addresses: [email protected] (A. Piantini), [email protected] (J.M. Janiszewski). 0378-7796/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2012.04.012
phase conductors larger than the line CFO. The greater the value of the ground impedance, the greater these voltage differences and hence the greater the probability of backflashover occurrence [2–4]. Therefore, for the shield wire to be effective against direct strokes it must be not only grounded at every pole but also the ground resistances must be low – less than 10 if the insulator CFO is less than 200 kV [2]. However, due to its coupling with the phase conductors, a shield wire can also be used with the purpose of reducing induced voltages from external electromagnetic fields. This reduction occurs even if it is beneath the phase conductors, so that a grounded neutral has the same effect. Investigations on the effectiveness of shield wires in terms of decreasing the magnitudes of lightning induced voltages on medium voltage overhead distribution lines have been conducted, e.g., in [4–20]. In [5] the shield wire is assumed to be at zero potential at any time, even during the transient. A simple expression is presented in [6] for the calculation of the ratio between the voltages induced on a phase conductor with and without the presence of a shield wire for the case of a perfectly conducting ground. The formula was derived assuming just one connection of the shield wire or neutral conductor to ground and applies only for points situated close to the grounding point, although results with reasonable accuracy are obtained for the case of multiple groundings as long as the distance between adjacent groundings is short (e.g. 30 m [2]). In [7,8] the shield wire is considered to be a conductor belonging to a multi conductor transmission line and grounded
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at both line terminations. In [9] the model presented in [7,8] is extended and generalized in order to evaluate the effect of periodically grounded shield wires on the attenuation of lightning induced voltages. A procedure for the estimation of the annual number of lightning-induced flashovers on distribution lines and the evaluation of the effectiveness of shield wires is proposed in [10]. Measurements of induced voltages by real lightning flashes are presented in [11,12], while in [13–18] the analyses involve scale model experiments. Comparisons between voltages induced by typical first and subsequent downward negative flashes on lines with different configurations are presented in [19,20]. This paper deals with the evaluation of the effectiveness of shield wires in reducing the magnitudes of the surges induced by nearby lightning strokes on MV overhead distribution lines. Such effectiveness depends on the combination of several parameters such as the relative position of the shield wire with respect to the phase conductors, the grounding interval, the ground resistance, the stroke current steepness, and the relative position of the stroke channel with respect to the grounding points. Initially, the basis for the calculations is described for the simplest case, which consists in a shield wire grounded at one point only. Afterwards, realistic situations corresponding to typical configurations of a rural distribution line with either an overhead ground wire or a neutral conductor are considered and simulation and experimental results are compared to confirm the validity of the method. Finally, the effects of various line and lightning parameters on the induced voltages are evaluated through the use of both computer simulations and test results obtained from scale model experiments, under controlled conditions. 2. Methodology Consider an infinite line with a phase conductor and either a neutral or a shield wire connected to ground at a single point x1 . Neglecting the ground lead inductance, the current Ig (x1 , t) which will flow to ground in the event of a nearby lightning strike can be calculated as [6,21]: Ig (x1 , t) =
Ug (x1 , t) Rg + 0.5 Zg
(1)
where Ug (x1 , t) corresponds to the voltage that would be induced at point x1 in the absence of the connection to ground, Zg is the surge impedance of the shield wire, and Rg represents the ground resistance. The induced voltage Up (x2 ,t) at point x2 on the phase conductor is given by: Up (x2 , t) = U p (x2 , t) − 0.5Zm Ig
x1 , t −
|x2 − x1 | c
(2)
where Up (x2 , t) is the voltage that would be induced at point x2 of the phase conductor in the absence of the shield wire grounding and Zm is the mutual impedance between the conductors. As indicated in Eq. (2), due to the electromagnetic coupling between the shield wire and the phase conductor, the induced voltage on the latter will be reduced regardless of the relative position of the wires. For a given lightning current and stroke location, the amount of reduction will depend on the coupling between the conductors, on the value of the ground resistance, and on the distance between the observation and grounding points. The induced voltages on the phase and shield wires in the absence of the connection to ground are calculated by using the Extended Rusck Model (ERM), which is based on Rusck’s theory [6]. The ERM, which is described in [20], has some features that, unlike the original model, allow for taking into account situations of practical interest such as, e.g., a line with a multi-grounded neutral or shield wire and equipment such as transformers and surge arresters
47
Fig. 1. Configuration of the line with the shield wire (dimensions referred to the full-scale system).
[4,22]. The incidence of lightning flashes to nearby elevated objects [23,24] and the occurrence of upward leaders [24–26] can also be considered. Lines with various sections of different directions can be considered through the evaluation of the correct propagation time delays for the elementary voltage components that determine the induced voltage at a given point of the line. The effect of an overhead ground wire or of a neutral conductor is considered by calculating the currents that flow to ground at the various grounding points, taking into account the multiple reflections and, then, the voltages associated with these currents that, due to the coupling between the wires, are induced on the phase conductors. In order to validate the model, several tests were performed on a reduced scale system, under controlled conditions, and measured and calculated induced voltages were compared. The system, whose scale factor for length was 1:50, comprised models of the lightning channel, the ground plane, and of two overhead distribution lines. The ground was simulated by aluminum plates interconnected, thus representing a perfectly conducting plane. The length of the lines was 28 m, which is equivalent to 1.4 km on a full-scale basis. The lines were parallel, matched at both terminations, and symmetric with respect to the lightning channel model, which was equidistant from the lines’ ends. The height of the phase conductors (h) was 20 cm, corresponding to 10 m. The distance between the lightning channel model and each line (d) was equivalent to 70 m. One of the lines had just one conductor, while the other had one phase and also a shield wire, placed at height hg , as shown in Fig. 1. Different heights were considered for the shield wire and tests were performed for various combinations of grounding spacing (xg ) and ground resistance values. A detailed description of the system and of its various components can be found in [20,27,28]. Fig. 2 shows comparisons between measured and calculated voltages induced on the line with the shield wire, in different situations. The main characteristics of the stroke current, whose waveform is presented in [25], are: magnitude I = 36 kA, front time tf = 3.1 s, and propagation velocity of 11% of that of light in free space. These values, referred to the full-scale system, can be converted to the values actually recorded in the scale model experiments by applying the scale factors for time (1:50) and for voltage and current (1:30,000). As a matter of fact, as there are no nonlinearities in the system, the choice of the scale factor for voltage
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a
240 Up` Up Upg
Voltage (kV)
180
120
60
0 6
8
10
12
14
Shield wire height (m)
d = 50 m
b
d = 100 m
d = 200 m
160
Up` Up Upg
Voltage(kV)
120
80
40
0 6
8
10
12
14
Shield wire height (m) Fig. 3. Induced voltage peak values at the point closest to the stroke location as function of the shield wire height hg , for two values of the stroke current front time. I = 50 kA; d = 50 m; h = 10 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
and current is arbitrary, since under this condition the induced voltages are directly proportional to the stroke currents. This is not the case when surge arresters are present, for which the scale factor for voltage and current should be determined [20,22,27]. The good agreement observed between measured and calculated results confirms the adequacy of the model for the evaluation of how effective a shield wire or a neutral conductor can be in mitigating lightning induced voltages on overhead power lines [20,29]. Fig. 2. Measured and calculated phase-to-ground induced voltages at the point closest to the stroke location for the line configuration shown in Fig. 1. I = 36 kA; tf = 3.1 s; d = 70 m; h = 10 m. (a) hg = 7 m; xg = 450 m; Rg = 0 ; stroke location in front of a grounding point. (b) hg = 9 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (c) hg = 7 m; xg = 750 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
3. Parametric analysis In this section the effect of the shield wire on the lightning induced voltages is evaluated taking into account the influence of some of the most important parameters involved in the process. The simulations were performed assuming a horizontal line configuration with distance of 0.75 m between adjacent phases. The line was 3 km long, the height of the phase conductors (h) was 10 m,
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Fig. 5. Induced voltages at the point closest to the stroke location for shield wire heights of 7 m and 11 m. I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; xg = 450 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
[31]. Ground was assumed to be perfectly conducting, an assumption which is reasonable when the line is located above a soil with resistivity lower than about 100 m [32], the distance between the line and the stroke location is not larger than some hundreds of meters, and the line length is shorter than a certain critical value (typically 2 km) [33]. The induced voltages were calculated at the point closest to the stroke location. 3.1. Shield wire height
Fig. 4. Ratio between the peak values of the phase-to-shield wire and phase-toground (in the absence of the shield wire) induced voltages at the point closest to the stroke location as function of the shield wire height hg , for two values of the stroke current front time. I = 50 kA; h = 10 m; xg = 300 m; Rg = 50 ; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
and the shield wire was considered either directly above or beneath the middle phase. It is worth mentioning that calculations carried out in [30] on lines with lengths varying from 500 m to 5 km over a perfectly conducting ground showed that the lightning induced voltages in the middle of the line – in front of the stroke location – reached the same peak value in all cases except for the shortest line, where the amplitude was about 3% lower. The diameter of all the conductors was 2 cm. Variations of the conductors’ cross sections affect their characteristic impedances, but the influence on the induced voltages is not important for the range of diameters commonly used [21]. Unless otherwise indicated, the stroke current was represented by a triangular waveshape with peak value of 50 kA, front time of 3 s, time to half value of 50 s, and propagation velocity of 30% of that of light in free space. The stroke channel was vertical, 3 km long, without branches, and the current distribution along the channel was calculated according to the Transmission Line model
Fig. 3 presents the peak values of the induced voltages Upg between phase and shield wire as a function of the shield wire height for stroke current front times of 3 s and 6 s and distances of 50 m, 100 m, and 200 m between the line and the lightning strike point. The grounding spacing is 300 m, the ground resistance is 50 , and the stroke location is equidistant between the closer grounding points. For comparison’s sake, Fig. 3 also shows the voltages which would be induced in the absence of the shield wire (Up ) and, for the case of d = 50 m, the phase-to-ground voltage Up . The condition hg = h (10 m) is equivalent to replace the middle phase with the shield wire. It can be observed that when the shield wire is beneath the phase conductors (i.e., hg < 10 m), the induced voltages Upg and Up decrease in amplitude as hg increases, whereas the opposite behavior is observed for hg > 10 m. This can be explained by the fact that the suppressive effect of the shield wire in a specific condition depends both on the current flowing to ground and on the mutual impedance Zm . The current to ground is directly proportional to the voltage induced on the shield wire (Usw ) and decreases as the surge impedance Zg increases. The voltage Usw is directly proportional to the height hg , whereas Zg increases logarithmically. By its turn, Zm decreases as the distance between the phase and shield wire increases. Therefore, for hg < h both Zm and Ig increase with hg , so that the voltage reduction is more significant when the height of the shield wire is close to that of the phase conductors. For hg > h, the current to ground continues to increase with hg , but Zm decreases. As shown in Fig. 3, the influence of Zm prevails, so that when the shield wire is above the phase conductors, the higher it is, the lower its effectiveness will be in reducing the magnitudes of the induced voltages.
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a
240 Up` Up Upg
Voltage (kV)
180
120
60
0 0
100
200
300
400
Ground resistance ( ) d = 50 m
The suppressive effect of the shield wire can be expressed as the ratio of the voltage between the phase conductor and the shield wire (Upg ) and the voltage that would be induced in the phase conductor in the absence of the shield wire (Up ). The ratios relevant to the situations treated in Fig. 3 are presented in Fig. 4 as function of the height hg ; the variation is from 0.50 to 0.85 for the case of stroke current front time of 3 s (Fig. 4a) and from 0.44 to 0.80 for tf = 6 s (Fig. 4b) in the range of heights considered. For tf = 3 s and hg < h, the effect of the shield wire is more pronounced (i.e., the lowest ratio Upg /Up is obtained) for the shortest distance between the line and the lightning strike point (d = 50 m). For hg = 8 m, the maximum ratio is equal to 0.74 (d = 200 m) and the minimum is about 12% lower (0.66, for d = 50 m). For hg > 10 m, the effect is more significant for d = 100 m; the greatest difference among the ratios for hg = 12 m is about 9% (ratios of 0.63 and 0.58 for d = 50 m and d = 100 m, respectively). On the other hand, Fig. 4b shows that for tf = 6 s and hg < h the lowest ratio corresponds to d = 100 m, while
Fig. 7. Measured induced voltages (phase-to-ground, Up) at the point closest to the stroke location for different shield wire heights (adapted from [4]). I = 24.9 kA; tf = 3.5 s; d = 70 m; h = 10 m; xg = 450 m; Rg = 50 ; stroke location in front of a grounding point.
b
d = 200 m
160
Up` Up Upg
120
Voltage (kV)
Fig. 6. Induced voltages at the point closest to the stroke location. I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; hg = 11 m; xg = 450 m; Rg = 50 ; stroke location equidistant from the closest grounding points.
d = 100 m
80
40
0 0
100
200
300
400
Ground Resistance ( ) Fig. 8. Induced voltage peak values at the point closest to the stroke location as function of the ground resistance Rg , for two values of the stroke current front time. I = 50 kA; h = 10 m; hg = 9 m; xg = 300 m; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
for hg > 10 m the effect is more significant for d = 50 m. A comparison between Fig. 4a and b shows that the effect of the shield wire tends to be less dependent on the distance d for stroke currents with longer front times. Fig. 5 compares, for a specific condition (xg = 450 m, Rg = 50 , and stroke location equidistant from the closest grounding points), the voltages Upg between phase and shield wire corresponding to shield wire heights of 7 m and 11 m. The voltage Up is also shown, for reference. For hg = 11 m, Upg has an initial negative peak because, being the shield wire above the phase conductors, the voltage Usw is larger than Up until the time corresponding to the arrival, at the observation point, of the effect of the current at the nearest grounding point. Only then Usw begins to decrease. Due to this delay, the voltages Up and Up are exactly equal up to about 1.52 s, as shown in Fig. 6. Fig. 7 presents phase-to-ground induced voltages obtained from scale model experiments on lines with shield wires at different heights [4]. The comparison illustrates the fact that the larger the current to ground (which increases with hg ) and the greater the
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Fig. 10. Induced voltages at the point closest to the stroke location for ground resistance values of 50 and 400 . I = 50 kA; tf = 3 s; d = 50 m; h = 10 m; hg = 9 m; xg = 600 m; stroke location equidistant from the closest grounding points. (a) Phaseto-shield wire voltages and (b) phase-to-ground voltages.
Fig. 9. Ratio between the peak values of the phase-to-shield wire and phase-toground (in the absence of the shield wire) induced voltages at the point closest to the stroke location as function of the ground resistance Rg , for two values of the stroke current front time. I = 50 kA; h = 10 m; xg = 300 m; hg = 9 m; stroke location equidistant from the closest grounding points. (a) tf = 3 s and (b) tf = 6 s.
coupling between the shield wire and the phase conductors, the greater the reduction on the voltages’ magnitudes. 3.2. Ground resistance The ground resistance depends both on the soil resistivity and on the configuration of the grounding system, so that different values are obtained for the same soil resistivity if different grounding arrangements are considered. Therefore, although the lightning fields were calculated under the assumption of a perfectly conducting ground, the value of the ground resistance was varied in order to investigate its influence on the effectiveness of the shield wire in the mitigation of lightning induced overvoltages. The effect of the ground resistance on the phase-to-ground and phase-to-shield wire induced voltages is depicted in Fig. 8a for ground spacing of 300 m, shield wire height of 9 m, stroke current front time of 3 s, and distances of 50 m, 100 m, and 200 m between the line and the
lightning strike point. The voltages that would be induced on the line in the absence of the shield wire are also shown. The results corresponding to tf = 6 s are presented in Fig. 8b. The phase-to-ground voltages Up increase with Rg since higher values of the ground resistance correspond to lower currents to ground and, consequently, to lower amplitudes of the voltage component associated with the product Zm Ig (“suppressive component”) which is responsible for the reduction of the induced voltages. On its turn, the shield wire-to-ground voltage Usw is more sensitive to the variation of Rg , since the suppressive component is associated with the product Zg Ig , which is higher than Zm Ig . Thus the increase of Usw with Rg is more significant in comparison with that of Up , and therefore the net result is a decrease of the voltage Upg between phase and shield wire as Rg increases. It can also readily be seen from Fig. 8 that the dependence of the phase-to-shield wire voltage with the ground resistance is more significant than that of the phase-to-ground voltage. The variation of the ratio Upg /Up as function of the ground resistance is presented in Fig. 9 for the situations treated in Fig. 8. The ratio varies from 0.43 to 0.71 for tf = 3 s (Fig. 8a) and from about 0.42 to 0.63 for tf = 6 s (Fig. 8b) in the range considered. For both values of stroke current front time, the ratios corresponding to the distances of 50 m and 100 m are very close and lower than
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the line and the lightning strike point have been considered as well. The analysis led to the following conclusions:
Fig. 11. Measured induced voltages (phase-to-ground, Up) at the point closest to the stroke location for different values of the ground resistance (adapted from [4]). I = 24.9 kA; tf = 3.5 s; d = 70 m; h = 10 m; hg = 9 m; xg = 450 m; stroke location equidistant from two grounding points.
that relevant to d = 200 m. The effect of the shield wire tends to be less dependent on the distance as the stroke current front time increases; the maximum difference between the ratios relevant to the three values of d is about 11% for tf = 3 s and 7% for tf = 6 s. For illustration purposes, a comparison between the induced voltage waveshapes relative to ground resistances of 50 and 400 is presented in Fig. 10, while phase-to-ground induced voltages obtained from scale model experiments for Rg = 0 and Rg = 1000 are shown in Fig. 11. As pointed out in [4], the influence of the ground resistance tends to decrease as the distance between adjacent grounding points increases, the stroke current front time becomes shorter or the distance between the stroke location and the closest grounding point increases. Lightning induced voltages can be remarkably affected by the soil resistivity. In general the voltages tend to increase with the soil resistivity [7,10,32], but in some cases, depending on the stroke location and the observation point, they may have just the opposite behavior. It is relevant to mention that the value of the ground resistance should be kept as low as possible in order to avoid the injection of high magnitude surges into the neutral between the transformer and the power installations in the case, e.g., of direct strikes to the MV line. The flow of the so called “low-voltage side surges” or “secondary side surges” through the low-voltage windings of a single-phase distribution transformer can lead to its failure even if it is protected with a primary arrester [4,21,34–36].
4. Conclusions An evaluation of the effect of a shield wire on the voltages induced on overhead distribution lines by nearby lightning strokes has been carried out through the use of a model whose validity has been demonstrated from comparisons between measured and calculated induced voltages. The effectiveness of a multi-grounded neutral or shield wire in mitigating lightning induced voltages depends on the combination of the values of various line and lightning parameters, and the influences of the shield wire height and the ground resistance have been investigated based on both computer simulations and test results obtained from scale model experiments. Variations of other parameters such as the stroke current front time and the distance between
• the closer the shield wire is to the phase conductors, the greater the reduction on both the phase-to-ground and the phase-toshield wire induced voltages will be. For the same distance, the effect is larger when the shield wire is above the phase conductors; • the effectiveness of the shield wire varies slightly with the distance d between the line and the lightning strike point. In general, the longer the distance, the greater the reduction observed on the phase-to-ground voltage Up with respect to the voltage induced at the same point in the absence of the shield wire (Up ), i.e., the lower the ratio Up /Up . On the other hand, the ratio of the voltages Upg between the phases and the shield wire and Up has the opposite behavior, i.e., the ratio Upg /Up tends to increase to some extent with the distance; • in general, for stroke currents with longer front times the effect of the shield wire tends to be more significant and the ratios Up /Up and Upg /Up tend to be less dependent on the distance d; • the phase-to-ground voltages increase with the ground resistance, while the phase-to-neutral or phase-to-shield wire voltages diminish as the ground resistance increases; • in some conditions, the phase-to-ground induced voltages can be reduced to about 60% of the values that would result without the shield wire (Up ); the phase-to-neutral or phase-to-shield wire voltages can be less than half the magnitude of Up . References [1] IEEE Guide for Improving the Lightning Performance of Transmission Lines, IEEE Std. 1243, 1997. [2] IEEE Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines, IEEE Std. 1410, 2010. [3] Joint CIGRE-CIRED Working Group C4.402, Protection of Medium Voltage and Low Voltage Networks Against Lightning Part 2: Lightning Protection of Medium Voltage Networks, 2010. [4] A. Piantini, Lightning protection of overhead power distribution lines, in: 29th International Conference on Lightning Protection (ICLP), Uppsala, Sweden, 2008, pp. 1–29 (invited lecture-4). [5] P. Chowdhuri, Lightning-induced voltages on multiconductor overhead lines, IEEE Transactions on Power Delivery 5 (2) (1990) 658–667. [6] S. Rusck, Induced Lightning Over-voltages on Power-Transmission Lines With Special Reference to the Over-voltage Protection of Low-voltage Networks, Trans. Royal Institute of Technology, No. 120, 1958. [7] F. Rachidi, C.A. Nucci, M. Ianoz, Transient analysis of multiconductor lines above a lossy ground, IEEE Transactions on Power Delivery 14 (1999) 294–302. [8] F. Rachidi, C.A. Nucci, M. Ianoz, C. Mazzetti, Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields, IEEE Transactions on Power Delivery 12 (1997) 1404–1411. [9] M. Paolone, C.A. Nucci, E. Petrache, F. Rachidi, Mitigation of lightning-induced overvoltages in medium voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters, modeling and experimental validation, IEEE Transactions on Power Delivery 19 (1) (2004) 423–431. [10] A. Borghetti, C.A. Nucci, M. Paolone, An improved procedure for the assessment of overhead line indirect lightning performance and its comparison with the IEEE Std. 1410 method, IEEE Transactions on Power Delivery 22 (1) (2007) 684–692. [11] S. Yokoyama, K. Miyake, H. Mitani, N. Yamazaki, Advanced observations of lightning induced voltage on power distribution lines, IEEE Transactions on Power Delivery, PWRD-1 (1986) 129–139. [12] S. Yokoyama, K. Miyake, H. Mitani, A. Takanishi, Simultaneous measurement of lightning induced voltages with associated stroke currents, IEEE Transactions on Power Apparatus and Systems, PAS-102 (1983) 2420–2429. [13] S. Yokoyama, Designing concept on lightning protection of overhead power distribution line, in: IX International Symposium on Lightning Protection (SIPDA), Foz do Iguac¸u, Brazil, 2007, pp. 647–662. [14] A. Piantini, J.M. Janiszewski, Lightning induced voltages on overhead lines: The effect of ground wires, in: 22nd International Conference on Lightning Protection (ICLP), Budapest, Hungary, 1994, pp. R3b/1–R3b/5. [15] S. Yokoyama, S.K. Yamamoto, H. Kinoshita, Analogue simulation of lightning induced voltages and its application for analysis of overhead-ground-wire effects, IEE Proceedings C 132 (4) (1985) 208–216. [16] S. Yokoyama, Calculation of lightning-induced voltages on overhead multiconductor systems, IEEE Transactions on Power Apparatus and Systems, PAS-103 (1984) 100–108.
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