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On the attachment of dart lightning leaders to wind turbines
Electric Power Systems Research 151 (2017) 432–439
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On the attachment of dart lightning leaders to wind turbines夽 Mengni Long ∗ , Marley Becerra, Rajeev Thottappillil Department of Electromagnetic Engineering, School of Electrical Engineering of KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 3 November 2016 Received in revised form 28 April 2017 Accepted 12 June 2017 Available online 26 June 2017 Keywords: Dart lightning leaders Lightning attachment Lightning damages Wind turbines
a b s t r a c t Wind turbines are prone to damages due to lightning strikes and the blades are one of the most vulnerable components. Even though the blade tip is usually protected in standard designs, lightning damages several meters away from it have also been observed in some field studies. However, these damages inboard from the tip cannot be explained by the attachment of downward stepped leaders or the initiation of upward lightning alone. In this paper, the attachment of dart leaders in an upward lightning flash is investigated as a mechanism of strikes to inboard sections of the blade and the nacelle of large wind turbines. Dart leaders in an upward lightning flash use the channel previously ionized by the preceding stroke or the continuous current. The analysis is performed with the self-consistent leader inception and propagation model (SLIM). A commercial large wind turbine with 45 m long blades and hub height of 80 m is analysed as a case study. The impact of the prospective return stroke peak current, the rotation angle of the blade and the wind on the location of lightning strikes on this mechanism is analysed. The probability of lightning attachment of dart leaders along the blade for the case study is also calculated. It is shown that this damage mechanism could create a new strike point only when the blade of a wind turbine rotates sufficiently from its initial position (at the inception of the initial upward leader) until the start of the dart leader approach. Thus, dart leader attachment is a mechanism that can explain lightning strikes to the nacelle and to the inboard region several meters away from the blade tip in large wind turbines. However, dart leader attachment cannot explain the lightning strikes observed in the close vicinity of the blade tip (in the region between 1.5 and 6 m from it). © 2017 Elsevier B.V. All rights reserved.
1. Introduction Lightning is a major cause of severe damage and unplanned downtime in wind turbines. Replacement of components damaged by lightning strikes is remarkably expensive due to high costs involved and the long repair time necessary [1]. According to the damage records [2], the blades of the turbine are the components most vulnerable to lightning damage. They have the highest frequency of damage by direct strikes and the highest repair cost due to the structural failure [2,3]. This high probability of lightning strikes is usually explained by the height of wind turbine blades which is much larger than that of the surroundings [4]. As wind turbines increase in height, the frequency of upward initiated lightning is expected to augment [4]. This fact has been supported by several independent field observations indicating that upward lightning is
夽 This work was supported sponsored by the CSC Chinese Scholarship Council and the Swedish strategic research program StandUp for Energy. ∗ Corresponding author. E-mail addresses: [email protected] (M. Long), [email protected] (M. Becerra), [email protected] (R. Thottappillil). http://dx.doi.org/10.1016/j.epsr.2017.06.011 0378-7796/© 2017 Elsevier B.V. All rights reserved.
the main mechanism of damage for tall wind turbines (with tip height above 100 above sea or ground level) [4–8]. Moreover, it has also been recently suggested that the initiation of upward lightning is easier from wind turbines than from static objects due to the rotation of the blades [9]. This means that wind turbines can readily trigger upward lightning under certain meteorological conditions, increasing the expected lightning incidence compared with the surroundings [4,9]. Lightning protection of wind turbines follows the same general principles as standard structures. Thus, lightning receptors along the blade are generally installed and connected to internal downconductors or conductors placed external to or under the blade surface [10]. Both field observations [6,11] and laboratory experiments [12] have shown that the receptors are not the only places where lightning attaches to the blade. The region of the blade away from the tips and towards the blade root is also likely to be struck. For instance, laboratory experiments show lightning attachment points at the middle of the blade, with arcs burning on the blade surface or penetrating into the blade boards [12]. In order to explain the observations in the field, the static conditions for inception of upward connecting leaders from turbine blades under the presence of downward stepped leaders were ana-
M. Long et al. / Electric Power Systems Research 151 (2017) 432–439
lysed in [13,14]. It was found that the blade tip is the most probable lightning strike point under downward lightning. Moreover, it was concluded that the inboard areas further than 3 m from the blade tip are not exposed to direct downward lightning strikes, even for prospective return stroke currents lower than 10 kA. This result disagrees with the field surveys where inboard areas as far as 5 m from the blade tip have been reported to have a small, but still significantnt lightning attachment probability [11]. Recent field studies show that upward lightning is most likely to strike the tip of wind turbine blades [15–17]. Numerical analysis also shows that the so called “self-triggered” and “other-triggered” upward lightning is most likely initiated from the tip receptor in wind turbine blades [18]. Thus, observed lightning damages inboard the blade away of its tip cannot be explained by the initial stage of upward lightning or by the attachment mechanisms generally present in non-moving structures. The rotation of turbine blades has also been recently considered as a possible explanation of lightning inboard damages away from the blade tip [4,9,19]. It has been suggested that a phenomenon called ‘swept stroke’, a common lightning mechanism of damage in aircraft industry, occurs when a lightning strike first attaches to a blade receptor. It takes place when the flash channel is swept along the trailing edge of the blade due to its rotation. Although the displacement of the channel along the trailing edge in wind turbines is not known, damages due to swept strokes in aircraft industry are usually up to about 10 m in length [20]. Since the rotation velocity of turbine blades is lower than the average aircraft speed, it is expected that the lightning channel sweep along a blade can only damage the area in the proximity of the tip receptor (up to few meters from it). Therefore, the ‘swept stroke’ mechanism cannot explain the attachment points observed several meters away from blade tip. An additional lightning mechanism where a subsequent leader discharge attaches to a different blade due to the rotation of the turbine has been also proposed in [4]. This mechanism has been recently suggested as a plausible physical explanation of the lightning damages observed several meters inboard of the blade [21]. Since there has not been any solid assessment in the literature of such a lightning attachment mechanism, this paper intends to quantitatively evaluate its effects on the distribution of strike points in large wind turbines. The analysis is performed with the SelfConsistent Leader Inception and Propagation Model (SLIM) where the attachment of dart leaders is simulated. In this case, upward connecting leaders initiated from receptors on the blade of a wind turbine propagate towards dart leaders occurring prior to subsequent return stroke current pulses in upward lightning flashes. The effect of the prospective return stroke peak current, the wind speed as well as the rotation of blades on the lightning termination is considered in this evaluation.
2. Interception of lightning dart leader from wind turbine blades According to the observation of the operating wind turbines, a significant amount of lightning strikes to the blades of the wind turbines are due to upward lightning [22–24]. Upward leaders generally initiate from the tip of the blade as it reaches its highest point when the background electric field reaches a critical threshold condition [9]. After inception, an upward positive leader ascends and bridges the gap between the wind turbine and the thundercloud establishing an initial continuous current (ICC). The propagation of the upward leader and the continuous current constitute the initial stage of upward lightning which usually lasts several hundreds of milliseconds [25]. One or more lightning dart leader-return stroke sequences can take place after the period of no current at the end of the initial
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Fig. 1. Example of the current measurement of a upward lightning flash initiated from a tall tower on Monte San Salvatore, Switzerland [21].
Fig. 2. Mechanism of attachment of dart leaders to wind turbine blades. (a) Initiation of the upward lightning leader, (b) Interception of the first dart leader, (c) Translation of the remnant channel due to wind.
stage. After the time interval ttotal consisting of the initial continuous current stage tICC and the following no-current interval tNoC (lasting up to several tens of milliseconds), a first lightning dart leader-return stroke sequence can appear (as shown in Fig. 1). It is caused by a dart leader descending along the remnant channel preheated by the initial continuous current (ICC), which is directly above the nacelle. Since the blades of the turbine rotate an angle within this interval ttotal (as shown in Fig. 2), a gap is formed between the remnant channel and the turbine blade. Thus, upward connecting leaders can be incepted not only from the tip but also from receptors inboard the blade. This process is evaluated here as the worst case scenario of lightning attachment to the inner blade receptors by the dart leaders. Observe that the attachment of subsequent dart leaders does not cause a significant change in the lightning strike point since a limited rotation of the blade is expected within the short duration of the interstroke interval. Wind also plays a role in this scenario since the remnant channel is displaced downstream by a distance d depending on the wind speed and the time duration ttotal . Furthermore, intensive turbulence of air flow is produced in the vicinity of the blades, especially the tip of blade [26]. This turbulent flow and the rotation of the blade accelerate the recovery of the temperature and the density of the preheated channel close to the struck blade during the no-current interval. Consequently, it is likely that the air in the remnant channel has recovered to near-atmospheric conditions at the moment of the attachment of a dart leader. Thus, upward connecting leaders initiated by approaching dart leaders are here considered to propagate under near-atmospheric conditions.
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3. Analysis method The lightning attachment process due to dart leaders is analysed here with the Self-consistent Leader Inception and Propagation Method (SLIM) [27–29]. This model simulates the chronological sequence of discharge processes taking place in front of ground objects under the influence of approaching downward lightning discharges. Even though SLIM was originally developed to evaluate the attachment of downward stepped leaders, it has been extended to simulate the interception of dart leaders in [30]. The simulation includes the analysis of four main discharge stages, namely the inception of precursor streamers, the unstable upward leader initiation, the stable upward leader propagation and the connection of both leaders (if the lightning attachment finally completes). This chronological sequence starts at the first streamer inception when the local electric field (due to both the thundercloud and the dart leader) at the surface of the analysed object fulfils the streamer criterion. The first unstable upward leader segment initiates if the charge of any secondary streamer is equal to or larger than a threshold charge Qcrit . Once the unstable upward leader segment initiates, its propagation is evaluated through the charge of the streamer at the tip of the upward leader. When the upward leader starts accelerating continuously, the stable inception condition is reached. Simultaneously, the physical parameters of the leader (potential gradient, channel radius, injected current and propagation velocity) are evaluated based with the thermo-hydrodynamic leader channel model of Gallimberti [31]. The upward connecting leader propagates with energy provided by the streamer zone in front of its tip, where the ionization takes place intensively. One important parameter for the evaluation of connecting leader propagation is the charge per unit length required to thermalize a new leader segment qL. Even though this parameter was first proposed by Gallimberti for rod-plate gap in laboratory condition [31], an analytical expression suitable to dart leader attachment studies has been derived in [30]. Since strong turbulent flow around the blades and the rotation of wind turbines accelerate the recovery of the temperature and density of the gas after the ICC stage, the upward connecting leaders are here assumed to propagate under near-atmospheric conditions. Thus, the critical charge Qcrit for thermalization of the first leader segment is assumed equal to 1 C, such that thermalization of the streamer stem occurs within less than few microseconds [32], necessary for the attachment of dart leaders. The boundary of streamer region 0 , which determines the current density of the transition zone at the root of the streamer and consequently effects qL , is taken as 0.015. Due to the lack of knowledge on the physical properties of upward leaders propagating towards dart leaders, this value has been tuned in [30] based on rocket triggered lightning experiments. The other parameters in the model are the same as in our previous studies of upward leaders propagating under the influence of stepped leader or the thundercloud field [27–29].
4. A case study of dart leader attachment to a large wind turbine In order to analyse the lightning dart leader attachment under the scenario discussed in Section II, a case study is here considered. The analysed case corresponds to the Vestas V90 large wind turbine with 45 m long blades and hub height of 80 m [33]. The assumed location of the lightning blade receptors considered in the analysis is shown in Fig. 3. In the simulation, dart leaders are assumed to descend from the thundercloud charge centre located 4 km above the ground and along the remnant channel preheated by the ICC stage. This channel is first assumed to be located directly above the nacelle of the wind
Fig. 3. Position of the receptors on the analysed blade design.
Fig. 4. 3D plot of the dart leader and the connecting leaders during the lightning attachment. The colour legend indicates time starting at the initiation of dart leader from the thundercloud charge centre.
turbine (d = 0) and a typical dart leader velocity of 1 × 107 m/s is considered. The dart leader is represented by a straight line of charge with density calculated as a function of the height and the prospective return stroke peak current, according to [34]. However, the calculated dart leader charge distribution is multiplied by a constant factor (equal to 0.8) in order to provide better agreement with static electric field measurements [30]. In order to illustrate the inception and propagation of upward connecting leaders under the influence of dart leaders, the prospective return stroke peak current is taken as 12 kA in this section. This value corresponds to the 60% cumulative probability of return stroke peak current in upward lightning [35]. In addition, the time interval ttotal is taken as 260 ms which consists of a period tICC = 210 ms (corresponding to a cumulative probability of the ICC stage duration of 20% [36]) and a typical duration of the no-current period tNoC of 50 ms [25]. Let us consider the propagation of upward connecting leaders of the blade receptors of the analysed large wind turbine from the moment the first dart leader starts. At this instant, the blade from which upward lightning is initiated has rotated 30◦ from its vertical position under the time interval ttotal and a turbine tip velocity of 90 m/s [33]. Fig. 4 shows the simulated 3D image of the connecting leaders initiated from the tip and the 4th receptors and the dart leader as a function of time (given by the colour legend). As the dart leader approaches, an upward connecting leader is first incepted at the tip receptor followed by other leaders gradually incepted from
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Fig. 6. The distribution of lightning terminals of dart leader- return stroke on the blade on different peak current Ip.
Fig. 5. Simulated properties of the successful upward connecting leader from the 4th receptor under a dart leader with prospective return stroke current of 12 kA.
Table 1 The distribution of lightning striking terminals on peak current Ip and rotational angle (without considering the effect of wind). Ip (kA)
inboard receptors. Even though the connecting leader from the tip receptor initiates first and propagates the longest length, there is a significant horizontal gap which cannot be bridged by its streamer zone even when the tips of both leaders are at the same height (of 140 m). Then, the dart leader continues its downward propagation until it finally attaches to the 4th receptor at a height of 124 m above the ground. The electric field shielding effect from the connecting leader initiated at the tip receptor is neglected in this evaluation. Thus, the connecting leader from the 4th receptor is assumed to develop independently. This assumption is justified by the 10 m distance between the 4th receptor and the tip receptor. Fig. 5 shows a simulated streak image, current and velocity of the upward connecting leader from the 4th receptor intercepting the dart leader. The stable inception of the connecting leaders for the 4th inboard receptor is reached when the dart leader reaches a height of 870 m above the ground. The connecting leader propagates a total length of 14 m in the time duration of 76 s. As is shown in the streak image, the height of the streamer front increases and then decreases during the final stage of the attachment since the streamer propagates toward the downward leader tip to bridge the horizontal gap between the two leaders’ tips. The predicted current of connecting leader slowly increases from 0 to 30 A in the first 70 s. Then, it increases rapidly to about 800 A in the last 6 s prior to the return stroke due to the intensified ionization at the streamer front as the dart leader approaches. This also causes the rapid increase of the connecting leader velocity in the final stage of attachment. The velocity of connecting leader increases from 1.0 × 105 m/s to the maximum of 2.1 × 106 m/s closely prior to the return stroke.
ttotal (ms) R1 R2 R3 R4 R5 R6 R nacelle
The rotational angle of the studied blade 30◦
45◦
60◦
262 ≥13 – – 13 > IP ≥ 12 12 > IP ≥ 11 11 > IP ≥ 10 <10
393 ≥22 – 22 > IP ≥ 21 21 > IP ≥ 20 20 > IP ≥ 19 19 > IP ≥ 16 <16
524 ≥31 – 31 > IP ≥ 30 30 > IP ≥ 28 28 > IP ≥ 25 25 > IP ≥ 22 <22
5.1. The prospective return stroke peak current The location of lightning strike point on the blade depends directly on the prospective return stroke peak current Ip as shown in Fig. 6. It is found that the tip receptor is always struck by dart leaders with prospective return stroke peak current larger than a threshold I0 (1) (equal to 13 kA in this case for a rotation angle = 30◦ ). For prospective peak currents lower than this threshold, the lightning dart leader attaches to the inner blade receptors or the nacelle as it is shown in Fig. 6. Interestingly, no strike is predicted for the second and third receptors at any current due to the electrostatic shielding of the tip receptor. As Ip decreases to 12 kA, the lightning strike point shifts to the 4th receptor, 6 m away from the tip of blade A. As the perspective return stroke decreases to 11 kA and 10 kA, the lightning strike point is shifted to the 5th and the last receptor respectively. However, none of the blade receptors is capable of intercepting lightning dart leaders with prospective peak currents equal to or lower than the threshold current I1 (nacelle) of 9 kA. In this case, it is assumed that the dart leader attaches to the receptors on the nacelle.
5. Factors influencing the dart leader attachment to wind turbine blades
5.2. The rotation of the blades
The attachment of lightning dart leaders to receptors of the turbine blades is significantly influenced by the prospective return stroke peak current and the angle of the rotation of the blade of the wind turbine at the start of the dart leader descent. Since wind also affects the dart leader location, its effect on the attachment mechanism is also analysed.
The evaluation is here extended to account for the larger rotational angle of the blades, namely, 45 and 60◦ . These rotation angles are calculated for blade tip velocity of 90 m/s [33] and the time period as listed in Table 1. The cumulative probability of the period ttotal equal to 262, 393 and 524 ms (for the considered angles of 30, 45 and 60◦ ) is 20, 60 and 75 % respectively. As it described above, the period ttotal consists the ICC stage tICC and the no-curent interval
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Table 2 The distribution of lightning striking terminals on peak current and rotational angle (with considering the effect of wind). Ip (kA)
d (m) R1 R2 R3 R4 R5 R6 R nacelle
The rotational angle of the studied blade 30◦
45◦
60◦
4 ≥13 – – – 13 > IP ≥ 12 – <12
6 ≥26 26 > IP ≥ 23 23 > IP ≥ 22 22 > IP ≥ 20 20 > IP ≥ 19 19 > IP ≥ 17 <17
8 ≥32 32 > IP ≥ 31 – 31 > IP ≥ 29 29 > IP ≥ 27 27 > IP ≥ 23 <23
tNoC (the typical value of tNoC is 50 ms). These probabilities are obtained according the statistics of tICC from towers with height ranging from 60 m to 220 m in Sao Paulo [36]. Observe that the values of the period ttotal used here are also comparable with corresponding measurements at Gaisberg Tower [37], with geometric mean value of initial stage duration of 230 ms, and maximum and minimum values of 739 ms and 65 ms respectively. As shown in Table 1, the threshold peak currents I0 (1) and I1 (n) at which dart leaders attach to the inner blade receptors and the nacelle increases with the blade angle. As the blade rotates further away from the dart leader channel, the connecting leader initiated from the blade requires larger energy to bridge the longer gap. This energy comes from the background electric field mainly provided by the approaching dart leader, which positively correlates to the return stroke peak current Ip. According to statistics from Gaisberg Tower [35], the probability of return stroke peak current larger than 13, 22 and 31 kA (the threshold I0 (1) below which dart leaders attach to inner blade receptor in Table 1) is 32%, 5% and 1% in upward lightning. It indicates that the probability of lightning terminal shifting to the inner blade receptors or the nacelle is 68%, 95% and 99%, when the blade rotates with an angle of 30, 45 and 60◦ respectively. On the other hand, the dart leader would attach only to the nacelle for prospective currents below the threshold I1 (nacelle) equal to 10, 16 and 22 kA The probability of this situation is 48%, 81% and 95% for blade angle = 30, 45 and 60◦ respectively. These results indicate that it is most probable for dart leaders to attach to the blade tip and the nacelle, while strikes to inboard receptors are possible but less likely. 5.3. The impact of the wind As the scenario described in section II, dart leader descends along the remnant channel displaced a distance of d due to the wind flow during the period ttotal . Assuming a wind speed of 15 m/s, the simulations are re-evaluated considering the displacement of dart leader channel. As it can be seen in the results shown in Table 2, the incidence of lightning strikes to the wind turbine is weakly influenced by the drift of the dart leader channel due to wind. For this reason, the effect of wind is not considered in the evaluation of the lightning attachment probability presented in the following section. 6. Lightning attachment probability along the blade of wind turbines due to dart leader attachment
• Even though the average number of return strokes following the initial stage of upward lightning is about 4.4 [35], only the first dart leader-return stroke (RS) is considered in this evaluation. Observe that upward leaders propagating following return strokes would probably propagate along the still-hot channel preheated by the previous stroke. Due to the relatively short interstroke period (shorter than the duration of the ICC stage), the remnant channel does not have time to recover to nearatmospheric conditions (here assumed). Thus, the total incidence of lightning strikes to any receptor in a single blade due to upward lightning (including those by attachment of the first dart leader) is expressed as follows:
N Rj =
Nu Nu · (j = 1) + · a · Patt−DL Rj , 3 3
(1)
where Nu is the annual number of upward flashes initiated from the wind turbine. The first term on the right side of (1) represents the number of lightning strikes due to self-triggered or “other triggered” upward leaders in the initial stage while the second term corresponds to the contribution of dart leader attachment. The first term is non-zero only for the first receptor (j = 1) at the blade tip R1 as assumed above. The factor a corresponds to the percentage of upward lightning strikes containing dart leader/return stroke sequences. This parameter is here taken as 0.3 based on statistics of upward lightning from Gaisberg Tower [35]. The term Patt -DL represents the overall probability of dart leader attachment to the j-th studied receptor on the blade or the nacelle. This parameter is calculated as:
60
(j) () 1
I
Patt−DL Rj =
g Ip × f dIp d,
(2)
=−60Ip=I (j) () 0
where the integrals are defined between the lower and upper (j) (j) return stroke peak currents I0 andI1 defining the range at which the dart leader attaches to the studied receptor. This current range is calculated with SLIM for each receptor in the bladeand the nacelle for the analysed wind turbine as shown in Table 2. g Ip is the probability density function of the return stroke peak current Ip in upward lightning. f is the probability density function of the rotation angle (from the vertical axis) during the period ttotal until the dart leader starts its descent. It is worth to note that the integration is performed in the interval between −60 and 60◦ for the angles where the dart leaders can attach to the analysed blade (e.g. blade A). Observe that angles in the range between −60 and 0◦ correspond to dart leaders propagating along the channel produced by upward lightning triggered by the preceding blade (e.g. blade C in Fig. 6). The rotation angles between 0 and 60 correspond to the case when the upward lightning has been triggered by the analysed blade. Eq. (2) can be rewritten in terms of the cumulative distribuof the return stroke peak current in upward lightning tion function G Ip as:
⎛
Patt−DL Rj = ⎝
60
(j)
(j)
G I1 () − G I0 ()
⎞
× f d ⎠ , (3)
=−60
In order to evaluate in detail the distribution of lightning attachment probability along the blades due to dart leaders, calculations are performed based on the following assumptions: • The initial upward leader in upward lightning always initiates from the tip receptor when the blade is in vertical position.
Where the function G(Ip ) is here obtained from the complementary cumulative distribution function reported in [35]. In turn, the probability density function of the blade angle f is obtained from the probability distribution p (tICC ) of the duration of the ICC stage reported in [36] and assuming an average interstroke period tNoC of 50 ms [25]. Considering the duration of the total period ttotal
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Fig.7. The probability of dart leader-return stroke attaching to the individual blade receptor and the receptor of the nacelle in each angle-interval for the analysed case study.
and the blade angular velocity ωblade , the angle density function f is obtained as:
⎧ ◦ ⎨ p + 120 ⁄ωblade − tNoC , if - 60◦ < < 0◦ f () = , ⎩ p ⁄ωblade − tNoC , if0◦ < < 60◦
(4)
The overall probability is here solved numerically using the trapezoidal rule and considering n intervals of the rotation blade angle(n = 12), each interval of the rotation blade angle is 10◦ . The probability of lightning striking to the individual blade receptor and the receptor of the nacelle due to dart leader interception for different angle intervals of the analysed wind turbine is shown in Fig. 7. As it can be seen, the distribution of the attachment point on the turbine is significantly influenced by the rotation angle, which is given by its rotation velocity and the time duration ttotal between the inception of upward leader in the initial stage and the descending of the dart leader. It is found that the tip receptor R1 intercepts most of lightning dart leaders for blade angles in the interval between 10 and 40◦ . As the blade rotates to angles away from this interval, the probability of dart leaders striking the nacelle Rn rapidly increases. This indicates that the effectiveness of dart leaders to attach to any of the blade receptors decreases as the period ttotal increases and the blade is at a larger angle from the vertical position. In-blade receptors (R2-R6) are mainly struck by dart leaders at positive blade angles, with an increasing strike probability as their distance to the tip receptor increases. However, the probability of strikes to all the in-blade receptors is significantly smaller than for the receptors at the blade tip or the nacelle. Overall, the tip receptor of the blade of the analysed turbine intercepts around 18% of the dart leader return strokes; the in-blade receptors intercept 9% of the dart leader return strokes, whereas the nacelle receptor intercepts the remaining 73%. However, the peak current of return stroke attaching to the nacelle receptor is lower than its counterpart attaching to blade receptors. Taking into account the lightning attachment process during both the initial stage and the first dart leader-return stroke sequence in upward lightning flashes, the calculated distribution of lightning striking points along the blade for the analysed case study is shown in Fig. 8. The evaluation suggests that the upward lightning strikes have the highest incidence on the tip receptor, accounting for 81% of all the strikes (mainly due to the upward leaders during the initial stage of the flash). This result is in agreement with field observations reporting that around 70% of the observed lightning damage of wind turbine blades is found on to the first 1.5 m from the tip [11]. However, the evaluation predicts a low probability of lightning strikes to the second and third receptors due to dart leader attachment, in contrast to the field observations where
Fig.8. Predicted distribution of lightning strikes by upward lightning as a function of the distance to the blade tip for the analysed case study.
20% of lightning damage occurring with 1.5–6 m from the blade tip. Thus, it is unlikely that the attachment of dart leaders causes the damages observed within that area of the blade and instead other process (e.g. the swept stroke) is responsible. It is also found that the incidence of dart leaders attaching to receptors located several meters away from the tip accounts for about 2% of all the possible strikes to the blade. Hence, this mechanism can explain the field observations reporting that around 10% of the remaining lightning damage was located in the region further inboard of the blade [11]. On the other hand, a significant probability (16.9%) of strikes to the nacelle due to upward lightning (mainly due to dart leader attachment) is predicted for the analysed wind turbine. Interestingly, lightning strikes to the nacelle of large wind turbines have been also observed in the field study reported in [6]. Unfortunately, it is not possible to compare the predictions in Fig. 8 with the reported registered strike percentages to the nacelle since the measurement system (peak current sensor cards) in [6] detects only upward lightning with current peaks above 5 kA and since their measurements cannot provide accurate statistics of lightning strikes. However, these field observations clearly show that lightning flashes can strike the nacelle of large wind turbines, which can be readily explained by dart leader attachment. This is also confirmed by the relatively low value of the recorded peak currents (lower than 15 kA) [6], which are typical for return strokes in upward lightning. It is worth to highlight that the probabilities and the distribution of attachment points shown in Figs. 7 and 8 apply only for wind farms with similar turbine geometry, tip rotation velocity and lightning conditions as assumed in the analysis in this Section. It can be easily shown that the probability of dart leaders striking areas other than the blade tip decreases as the blade length and rotation velocity of the analysed turbine decreases. In a similar way, dart leader attachment to the nacelle and inboard blade parts is also less likely to occur in wind parks located in areas with a low percentage of upward lightning followed by at least a dart leader-return stroke sequence and/or a short duration of the period ttotal . Interestingly, the most extensive field study up to date [38] has shown no negative lightning strikes hitting the nacelle or inboard blades of wind turbines in Japan. However, the reader should be aware that this field observation does not contradict the lightning damage mechanism discussed here. Observe that the turbines reported in [38] had significantly shorter blades (with an average of about 33 m) and rotate at lower velocity (with an average of 70 m/s) than the turbine design analysed here (with 45 m long blades with tip rotating at 90 m/s). Additional differences can be found when
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carefully analysing the more current oscillograms reported in [38]. It can be shown than of the 674 lightning flashes identified, only about 85 of them include return strokes (about 13% of the total). Observe that this fraction of upward flashes with return stroke sequences (and therefore with dart leaders) in Japan is lower than that reported in Europe at Gaisberg Tower (of about 30%) [35]. Moreover, despite of the limited resolution of these current waveforms in [38], the 50% probability value of the time ttotal can be roughly estimated at about 90 ms. This time is significantly shorter than the corresponding value used here (of 375 ms [36]). In the same way, the maximum ttotal estimated from [38] is less than 450 ms, while it has been reported to be larger than 700 ms in Austria and Brazil [36]. As a consequence of the shorter blade length, slower tip rotation velocity and significantly low ttotal , the rotation angle of the turbines studied in Japan [38] is rather small (less than 15◦ in average). In addition, the probability of occurrence of dart leaders in Japan during upward flashes is lower than the percentage here considered. Therefore, it is unsurprising that no strike to the nacelle or inboard parts of the blade produced by dart leaders have been observed in Japan as reported in [38]. In conclusion, the damage mechanism here discussed is predicted to occur only in cases when the blade of a wind turbine has rotated sufficiently from its initial position (at the inception of the initial upward leader) until the start of the dart leader approach. Thus, the lightning damages to the nacelle or inblade parts of the blade due to dart leader attachment may not occur for all wind turbines. It will take place only for turbines with long blades and turning at high speed and located in sites during upward lightning flashes with long ICC duration prior to the first return stroke. As a consequence, the probability of damages due to dart leader attachment and its attachment distribution for wind parks under conditions different to those evaluated here are expected to be different than those shown in Figs. 7 and 8. In those cases, the assessment of this kind of damage would require the evaluation considering the actual wind turbine model and the local lightning conditions of the wind park site.
7. Discussion The evaluation of lightning attachment of dart leader to wind turbines in this paper considers the scenario that the initial upward leader incepts at the blade when it rotates to the vertical position. This scenario is most probable to take place in the self-initiated upward lightning, since the critical electric field required for the initiation of upward lightning has the lowest threshold when the blade rotates its highest point [18]. In case of other-triggered upward lightning, the inception of upward lightning alternatively depends on the fast electric field change provided by nearby lightning events [23,39]. It is because the rate of the fast electric field change is significantly higher than the speed of the blade rotation. Thus, upward lightning can be initiated from the blade at the arbitrary angle in the half above rotation plane, as long as the fast electric field change reaches the threshold. Consequently, the distribution of angle of blades initiating upward lightning depends on the ratio between the occurrences of self-initiated and other-triggered upward flashes. The field observation indicates that operating wind turbines exhibit an increased tendency to self-initiated upward lightning compared with static structures [23]. A statistic of 169 winter lightning (mostly upward lightning) to operating wind turbines at different locations of Japan shows that 42% of the observed upward lightning is initiated from vertical blades (0◦ ) and it is followed by the blade angle of −30◦ (31%), 30◦ (13%), 60◦ (7%) and −60◦ (7%) [24]. Since considerable amount of upward lightning initiated from the blade is not at the
vertical position, we additionally evaluate lightning attachment of dart leader to wind turbine under these conditions. In this evaluation, we assume that upward lightning is initiated from blade A at the angle of −60, −30, 30 and 60◦ and the peak current of return stroke is also taken as 12 kA. The rotational angle of blades during the ICC and no-current interval is considered in the range of 30 to 60◦ . The evaluation shows that lightning dart leader attaches inboard receptors of blade A in the case that the initial upward leader is incepted from the blade at the angle of 30 and 60◦ . It is well explained by the downward rotation of blade A, resulting that the tip of blade A moves further away from dart leader channel and the inboard receptors are consequently more exposed. Interestingly, lightning dart leader is intercepted by the inboard receptors of the following blade B, if the initial upward leader is incepted from blade A at the angle of −30◦ . The dart leader is beyond lightning attractive zone of the tip receptor of blade A, even when blade A rotates to its vertical position. Different from the above cases, lightning dart leader is predicted to attach to the tip receptor of blade A in the case that upward lightning initiated from the blade at the angle of −60◦ . In this case, the subsequent return stroke strikes to the same point where the upward lightning initiated, unless the blades rotate an angle larger than 60◦ . It is worth to note that this case (upward lightning initiating from the blade at the angle of −60◦ ) accounts for a rather low percentage (7% reported in [24]). Thus, lightning attachment of dart leader after the initial stage of upward lightning still exhibits a high tendency striking to the inboard receptor in the condition that the initial upward leader is incepted from a blade in non-vertical position. Furthermore, the lightning channel connecting to wind turbines is frequently observed in still pictures to be elongated following the trace of blade tip while the blade rotates during the initial continuous current stage [38]. This elongation is also expected to occur during the ICC period by wind, pushing the discharge channel downstream from the turbine (as shown in Fig. 3c). However, the current cut-off at the end of the ICC period indicates the interruption of the conduction path of the lightning channel, which is observed to occur close to the struck object [25]. This indicates that the temperature of the lower section of the channel has decayed sufficiently (reaching values lower than 1500–2000 K [31]), starting the no-current interval tNoC . Unfortunately, there is no information in the literature about the further temperature decay in the lower section of the remnant channel during the period tNoC in upward lightning. However, it is reasonable to assume that the lower section of the remnant channel quickly recovers to nearatmospheric condition due to convective turbulent cooling as well as thermal conduction [30]. Moreover, observe that the fast rotation of the considered turbine will move the blade tip away from the lower section of the remnant channel by more than 5 m during the time tNoC . Therefore, the inception and propagation of upward connecting leaders from wind turbines is expected to occur under atmospheric or near-atmospheric conditions. On the other hand, the initiation and propagation of connecting leaders from individual receptors of a blade in response of a lightning dart leader is considered independent from each other in this paper. Since the connecting leader is always first initiated from the tip receptor, it shields electrostatically the development of other connecting leaders from inboard receptors. Since the physical simulation of competing upward connecting leaders separated only few meters from each other is difficult, this electrostatic coupling between leaders have been neglected. However, this electrostatic shielding will mainly hinder the development of upward leaders from the receptors close to the blade tip (e.g. R2, R3, R4). Since it is predicted that dart leaders have a very low probability to strike these receptors in the analysed case study, this simplification will have no significant effect on the results of the paper.
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8. Conclusion This paper quantitatively evaluates the attachment of lightning dart leaders in upward lightning flashes as a mechanism of lightning strikes to wind turbines, based on numerical simulations with SLIM. The effect of the return stroke peak current, the rotation angle as well as the wind on the probability of strikes to receptors on the blades and the nacelle are investigated. A case study of a large turbine with 45 m blade length and tip rotating at 90 m/s, located in a site with upward lightning properties as those reported for Brazil and Austria, is analysed. Even though it is predicted that most of the upward lightning strikes hit the blades of the analysed turbine, it is shown that the nacelle receptor is likely to be struck by lightning mainly due to the attachment of dart leaders. This result is valid only for turbines with long blades and high tip rotation speed (as in the analysed case study) located in sites with a sufficient fraction of upward lightning with at least one subsequent return stroke and with long ICC duration (with a 50% probability time larger than some hundreds of milliseconds). In those cases, the tip receptor and the inblade receptors is predicted to intercept a lower (but still significant) proportion of dart leaders. However, the more frequent attachment of dart leaders to the nacelle is expected to take place under lower return stroke peak currents than for the blade receptors. Furthermore, it is shown that the probability of attachment point of dart leaders on regions in-board the blade increases with the distance to the tip. For this reason, dart leader attachment in upward lightning cannot cause damages in the area within 1.5–6 m from the blade tip as reported in some field studies. Instead, this mechanism can explain (the less frequent) lightning damages inboard, several meters away from the blade tip in turbines with long blades rotating at high speed. In such cases, it is also shown that receptors on the nacelle of the turbine are exposed to lightning strikes due to attachment of dart leaders, in agreement with field observations of wind parks in Denmark. References [1] T. Naka, et al., Study on lightning protection methods for wind turbine blades, IEEJ Trans. Power Energy 125 (10) (2005) 993–999. [2] H. Braam, et al., Lightning damage of OWECS Part 3: Case Studies, Energy Research Centre of The Netherlands, Petten, 2002. [3] IEC, 61400-24: Wind Turbine Generator Systems — Part 24: Lightning Protection for Wind Turbines, 2010. [4] F. Rachidi, et al., A review of current issues in lightning protection of new-generation wind-turbine blades, IEEE Trans. Ind. Electron. 55 (6) (2008) 2489–2496. [5] G. Diendorfer, On the risk of upward lightning initiated from wind turbines, in: Proceedings of theIEEE 15th International Conference on Environment and Electrical Engineering (EEEIC), Rome, Italy, 2015, pp. 872–876. [6] V. Peesapati, I. Cotton, T. Sorensen, T. Krogh, N. Kokkinos, Lightning protection of wind turbines — a comparison of measured data with required protection levels, IET Renew. Power Generat. 5 (1) (2011) 48–57. [7] J. Montanyà, et al., Global distribution of winter lightning: a threat to wind turbines and aircraft, Nat. Hazards Earth Syst. Sci. 16 (6) (2016) 1465–1472. [8] V. March, et al., Winter lightning activity in specific global regions and implications to wind turbines and tall structures, Proceedings of the 33rd International Conference on Lightning Protection (ICLP) (2016) 1–5. [9] J. Montanyà, O. van der Velde, E.R. Williams, Lightning discharges produced by wind turbines, J. Geophys. Res.: Atmos. 119 (3) (2014) 1455–1462. [10] I. Cotton, N. Jenkins, K. Pandiaraj, Lightning protection for wind turbine blades and bearings, Wind Energy 4 (1) (2001) 23–37. [11] S.F. Madsen, K. Bertelsen, T.H. Krogh, H.V. Erichsen, A.N. Hansen, K.B. Lønbæk, Proposal of new zoning concept considering lightning protection of wind turbine blades, Lightning Res. 4 (2012) 108–117. [12] S. Yokoyama, Lightning protection of wind turbine blades, Electric Power Syst. Res. 94 (2013) 3–9. [13] S.F. Madsen, H.V. Erichsen, Improvements of numerical models to determine lightning attachment points on wind turbines, in: 29th International Conference on Lightning Protection, Uppsala, Sweden, 2008, pp. 9-27- 1-11.
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[14] S.F. Madsen, H.V. Erichsen, Numerical model to determine lightning attachment point distributions on wind turbines according to the revised IEC 61400-24, in: Proceedings of the International Conference on Lightning and Static Electricity, Pittsfield MA, USA, 2009. [15] M. Ishii, NEDO R&D project for measures of lightning protection of wind turbines in Japan, in: Proceedings of the International Symposium on Lightning Protection (XIII SIPDA), Balneário Camboriú, Brazil, 28th September–2nd October, 2015. [16] V. March, Upward lightning observations on a wind turbine and its implications to environmental factor for risk assessment, in: Proceedings of the Asia-Pacific Conf Lightning Protection, Nagoya, Japan, 2015. [17] A. Wada, S. Yokoyama, K. Hachiya, T. Hirose, Observational results of lightning flashes on the Nikaho-Kogen wind farm in winter 2003–2004, in: Proceedings of the XIV International Symposium on High Voltage Engineering, Beijing, China, 2005. [18] M. Long, M. Becerra, R. Thottappillil, On the lightning incidence to wind farms, in: Proceedings of the International Conference on Lightning Protection (ICLP), Estoril, Portugal, 2016. ´ M.S. Savic, ´ S.F. Madsen, I. Badea, Impact of wind turbine blade [19] B.M. Radiˇcevic, rotation on the lightning strike incidence — a theoretical and experimental study using a reduced-size model, Energy 45 (1) (2012) 644–654. [20] A. Larsson, P. Lalande, A. Bondiou-Clergerie, P. Lalande, A. Delannoy, The lightning swept stroke along an aircraft in flight. Part I: thermodynamic and electric properties of lightning arc channels, J. Phys. D: Appl. Phys. 33 (15) (2000) 1866–1875. [21] M. Long, M. Becerra, R. Thottappillil, On the interception of dart lightning leaders from wind turbine blades, in: Proceedings of the International Conference on Lightning Protection (ICLP), Shanghai, China, 2014, pp. 1376–1381. [22] D. Wang, N. Takagi, T. Watanabe, H. Sakurano, M. Hashimoto, Observed characteristics of upward leaders that are initiated from a windmill and its lightning protection tower, Geophys. Res. Lett. 35 (2) (2008), pp. L02803 (1–5). [23] D. Wang, N. Takagi, Characteristics of winter lightning that occurred on a windmill and its lightning protection tower in Japan, IEEJ Trans. Power Energy 132 (6) (2012) 568–572. [24] M. Ishii, M. Saito, D. Natsuno, A. Sugita, Lightning incidence on wind turbines in winter, in: Proceedings of the International Conference on Lightning Protection (ICLP), Shanghai, China, 2014, pp. 1734–1738. [25] V.A. Rakov, M.A. Uman, Lightning: Physics and Effects, Cambridge University Press, 2003. [26] Y.-T. Wu, F. Porté-Agel, Simulation of turbulent flow inside and above wind farms: model validation and layout effects, Boundary-Layer Meteorol. 146 (2) (2013) 181–205. [27] M. Becerra, V. Cooray, A self-consistent upward leader propagation model, J. Phys. D-Appl. Phys. 39 (16) (2006) 3708–3715. [28] M. Becerra, V. Cooray, Time dependent evaluation of the lightning upward connecting leader inception, J. Phys. D: Appl. Phys. 39 (21) (2006) 4695–4702. [29] M. Becerra, V. Cooray, A simplified physical model to determine the lightning upward connecting leader inception, IEEE Trans. Power Deliv. 21 (2) (2006) 897–908. [30] M. Long, M. Becerra, R. Thottappillil, Modeling the attachment of lightning dart and dart-stepped leaders to grounded objects, IEEE Trans. Electromagn. Compat. 59 (1) (2017) 128–136. [31] I. Gallimberti, The mechanism of the long spark formation, J. Phys. Colloques 40 (C7) (1979), pp. C7-193-C7-250. [32] C. Wu, S. Xie, F. Qi, B. Li, J. Wan, J. He, Effect of corona discharges on the inception of positive upward leader-streamer system, Int. J. Modern Phys. B 27 (28) (2013), pp. 1350165 (1–14). [33] Available: http://www.aweo.org/windmodels.html. [34] V. Cooray, V. Rakov, N. Theethayi, The lightning striking distance—revisited, J. Electrost. 65 (5–6) (2007), pp. 296–306, 5//2007. [35] G. Diendorfer, H. Pichler, M. Mair, Some parameters of negative upward-initiated lightning to the Gaisberg Tower, IEEE Trans. Electromagn. Compat. 51 (3) (2009) 443–452. [36] C. Schumann, M.F. Marcelo, A.R. De Paiva, M.A.S. Ferro, T.A. Warner, High-speed observation of upward lightning flashes in Brazil, in: Proceedings of the International Lightning Detection Conference (ILDC), Tucson, Arizona, USA, 2014. [37] M. Miki, et al., Initial stage in lightning initiated from tall objects and in rocket-triggered lightning, J. Geophys. Res.: Atmos. 110 (D2) (2005), pp. D02109 (1–15). [38] NEDO report 20150000000080, Research and Development of NextGeneration Wind Power Generation Technology for Technology Corresponding to Natural Environment etc. for Measures of Lightning Protection (FY2008-FY2012), Annual Report of NEDO, Japan, March 2015 (in Japanese). [39] M. Becerra, M., Long, W. Schulz, R. Thottappillil, On the estimation of the lightning incidence to offshore wind farms, submitted to Electric Power Research Journal.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
On the attachment of dart lightning leaders to wind turbines夽 Mengni Long ∗ , Marley Becerra, Rajeev Thottappillil Department of Electromagnetic Engineering, School of Electrical Engineering of KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 3 November 2016 Received in revised form 28 April 2017 Accepted 12 June 2017 Available online 26 June 2017 Keywords: Dart lightning leaders Lightning attachment Lightning damages Wind turbines
a b s t r a c t Wind turbines are prone to damages due to lightning strikes and the blades are one of the most vulnerable components. Even though the blade tip is usually protected in standard designs, lightning damages several meters away from it have also been observed in some field studies. However, these damages inboard from the tip cannot be explained by the attachment of downward stepped leaders or the initiation of upward lightning alone. In this paper, the attachment of dart leaders in an upward lightning flash is investigated as a mechanism of strikes to inboard sections of the blade and the nacelle of large wind turbines. Dart leaders in an upward lightning flash use the channel previously ionized by the preceding stroke or the continuous current. The analysis is performed with the self-consistent leader inception and propagation model (SLIM). A commercial large wind turbine with 45 m long blades and hub height of 80 m is analysed as a case study. The impact of the prospective return stroke peak current, the rotation angle of the blade and the wind on the location of lightning strikes on this mechanism is analysed. The probability of lightning attachment of dart leaders along the blade for the case study is also calculated. It is shown that this damage mechanism could create a new strike point only when the blade of a wind turbine rotates sufficiently from its initial position (at the inception of the initial upward leader) until the start of the dart leader approach. Thus, dart leader attachment is a mechanism that can explain lightning strikes to the nacelle and to the inboard region several meters away from the blade tip in large wind turbines. However, dart leader attachment cannot explain the lightning strikes observed in the close vicinity of the blade tip (in the region between 1.5 and 6 m from it). © 2017 Elsevier B.V. All rights reserved.
1. Introduction Lightning is a major cause of severe damage and unplanned downtime in wind turbines. Replacement of components damaged by lightning strikes is remarkably expensive due to high costs involved and the long repair time necessary [1]. According to the damage records [2], the blades of the turbine are the components most vulnerable to lightning damage. They have the highest frequency of damage by direct strikes and the highest repair cost due to the structural failure [2,3]. This high probability of lightning strikes is usually explained by the height of wind turbine blades which is much larger than that of the surroundings [4]. As wind turbines increase in height, the frequency of upward initiated lightning is expected to augment [4]. This fact has been supported by several independent field observations indicating that upward lightning is
夽 This work was supported sponsored by the CSC Chinese Scholarship Council and the Swedish strategic research program StandUp for Energy. ∗ Corresponding author. E-mail addresses: [email protected] (M. Long), [email protected] (M. Becerra), [email protected] (R. Thottappillil). http://dx.doi.org/10.1016/j.epsr.2017.06.011 0378-7796/© 2017 Elsevier B.V. All rights reserved.
the main mechanism of damage for tall wind turbines (with tip height above 100 above sea or ground level) [4–8]. Moreover, it has also been recently suggested that the initiation of upward lightning is easier from wind turbines than from static objects due to the rotation of the blades [9]. This means that wind turbines can readily trigger upward lightning under certain meteorological conditions, increasing the expected lightning incidence compared with the surroundings [4,9]. Lightning protection of wind turbines follows the same general principles as standard structures. Thus, lightning receptors along the blade are generally installed and connected to internal downconductors or conductors placed external to or under the blade surface [10]. Both field observations [6,11] and laboratory experiments [12] have shown that the receptors are not the only places where lightning attaches to the blade. The region of the blade away from the tips and towards the blade root is also likely to be struck. For instance, laboratory experiments show lightning attachment points at the middle of the blade, with arcs burning on the blade surface or penetrating into the blade boards [12]. In order to explain the observations in the field, the static conditions for inception of upward connecting leaders from turbine blades under the presence of downward stepped leaders were ana-
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lysed in [13,14]. It was found that the blade tip is the most probable lightning strike point under downward lightning. Moreover, it was concluded that the inboard areas further than 3 m from the blade tip are not exposed to direct downward lightning strikes, even for prospective return stroke currents lower than 10 kA. This result disagrees with the field surveys where inboard areas as far as 5 m from the blade tip have been reported to have a small, but still significantnt lightning attachment probability [11]. Recent field studies show that upward lightning is most likely to strike the tip of wind turbine blades [15–17]. Numerical analysis also shows that the so called “self-triggered” and “other-triggered” upward lightning is most likely initiated from the tip receptor in wind turbine blades [18]. Thus, observed lightning damages inboard the blade away of its tip cannot be explained by the initial stage of upward lightning or by the attachment mechanisms generally present in non-moving structures. The rotation of turbine blades has also been recently considered as a possible explanation of lightning inboard damages away from the blade tip [4,9,19]. It has been suggested that a phenomenon called ‘swept stroke’, a common lightning mechanism of damage in aircraft industry, occurs when a lightning strike first attaches to a blade receptor. It takes place when the flash channel is swept along the trailing edge of the blade due to its rotation. Although the displacement of the channel along the trailing edge in wind turbines is not known, damages due to swept strokes in aircraft industry are usually up to about 10 m in length [20]. Since the rotation velocity of turbine blades is lower than the average aircraft speed, it is expected that the lightning channel sweep along a blade can only damage the area in the proximity of the tip receptor (up to few meters from it). Therefore, the ‘swept stroke’ mechanism cannot explain the attachment points observed several meters away from blade tip. An additional lightning mechanism where a subsequent leader discharge attaches to a different blade due to the rotation of the turbine has been also proposed in [4]. This mechanism has been recently suggested as a plausible physical explanation of the lightning damages observed several meters inboard of the blade [21]. Since there has not been any solid assessment in the literature of such a lightning attachment mechanism, this paper intends to quantitatively evaluate its effects on the distribution of strike points in large wind turbines. The analysis is performed with the SelfConsistent Leader Inception and Propagation Model (SLIM) where the attachment of dart leaders is simulated. In this case, upward connecting leaders initiated from receptors on the blade of a wind turbine propagate towards dart leaders occurring prior to subsequent return stroke current pulses in upward lightning flashes. The effect of the prospective return stroke peak current, the wind speed as well as the rotation of blades on the lightning termination is considered in this evaluation.
2. Interception of lightning dart leader from wind turbine blades According to the observation of the operating wind turbines, a significant amount of lightning strikes to the blades of the wind turbines are due to upward lightning [22–24]. Upward leaders generally initiate from the tip of the blade as it reaches its highest point when the background electric field reaches a critical threshold condition [9]. After inception, an upward positive leader ascends and bridges the gap between the wind turbine and the thundercloud establishing an initial continuous current (ICC). The propagation of the upward leader and the continuous current constitute the initial stage of upward lightning which usually lasts several hundreds of milliseconds [25]. One or more lightning dart leader-return stroke sequences can take place after the period of no current at the end of the initial
433
Fig. 1. Example of the current measurement of a upward lightning flash initiated from a tall tower on Monte San Salvatore, Switzerland [21].
Fig. 2. Mechanism of attachment of dart leaders to wind turbine blades. (a) Initiation of the upward lightning leader, (b) Interception of the first dart leader, (c) Translation of the remnant channel due to wind.
stage. After the time interval ttotal consisting of the initial continuous current stage tICC and the following no-current interval tNoC (lasting up to several tens of milliseconds), a first lightning dart leader-return stroke sequence can appear (as shown in Fig. 1). It is caused by a dart leader descending along the remnant channel preheated by the initial continuous current (ICC), which is directly above the nacelle. Since the blades of the turbine rotate an angle within this interval ttotal (as shown in Fig. 2), a gap is formed between the remnant channel and the turbine blade. Thus, upward connecting leaders can be incepted not only from the tip but also from receptors inboard the blade. This process is evaluated here as the worst case scenario of lightning attachment to the inner blade receptors by the dart leaders. Observe that the attachment of subsequent dart leaders does not cause a significant change in the lightning strike point since a limited rotation of the blade is expected within the short duration of the interstroke interval. Wind also plays a role in this scenario since the remnant channel is displaced downstream by a distance d depending on the wind speed and the time duration ttotal . Furthermore, intensive turbulence of air flow is produced in the vicinity of the blades, especially the tip of blade [26]. This turbulent flow and the rotation of the blade accelerate the recovery of the temperature and the density of the preheated channel close to the struck blade during the no-current interval. Consequently, it is likely that the air in the remnant channel has recovered to near-atmospheric conditions at the moment of the attachment of a dart leader. Thus, upward connecting leaders initiated by approaching dart leaders are here considered to propagate under near-atmospheric conditions.
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3. Analysis method The lightning attachment process due to dart leaders is analysed here with the Self-consistent Leader Inception and Propagation Method (SLIM) [27–29]. This model simulates the chronological sequence of discharge processes taking place in front of ground objects under the influence of approaching downward lightning discharges. Even though SLIM was originally developed to evaluate the attachment of downward stepped leaders, it has been extended to simulate the interception of dart leaders in [30]. The simulation includes the analysis of four main discharge stages, namely the inception of precursor streamers, the unstable upward leader initiation, the stable upward leader propagation and the connection of both leaders (if the lightning attachment finally completes). This chronological sequence starts at the first streamer inception when the local electric field (due to both the thundercloud and the dart leader) at the surface of the analysed object fulfils the streamer criterion. The first unstable upward leader segment initiates if the charge of any secondary streamer is equal to or larger than a threshold charge Qcrit . Once the unstable upward leader segment initiates, its propagation is evaluated through the charge of the streamer at the tip of the upward leader. When the upward leader starts accelerating continuously, the stable inception condition is reached. Simultaneously, the physical parameters of the leader (potential gradient, channel radius, injected current and propagation velocity) are evaluated based with the thermo-hydrodynamic leader channel model of Gallimberti [31]. The upward connecting leader propagates with energy provided by the streamer zone in front of its tip, where the ionization takes place intensively. One important parameter for the evaluation of connecting leader propagation is the charge per unit length required to thermalize a new leader segment qL. Even though this parameter was first proposed by Gallimberti for rod-plate gap in laboratory condition [31], an analytical expression suitable to dart leader attachment studies has been derived in [30]. Since strong turbulent flow around the blades and the rotation of wind turbines accelerate the recovery of the temperature and density of the gas after the ICC stage, the upward connecting leaders are here assumed to propagate under near-atmospheric conditions. Thus, the critical charge Qcrit for thermalization of the first leader segment is assumed equal to 1 C, such that thermalization of the streamer stem occurs within less than few microseconds [32], necessary for the attachment of dart leaders. The boundary of streamer region 0 , which determines the current density of the transition zone at the root of the streamer and consequently effects qL , is taken as 0.015. Due to the lack of knowledge on the physical properties of upward leaders propagating towards dart leaders, this value has been tuned in [30] based on rocket triggered lightning experiments. The other parameters in the model are the same as in our previous studies of upward leaders propagating under the influence of stepped leader or the thundercloud field [27–29].
4. A case study of dart leader attachment to a large wind turbine In order to analyse the lightning dart leader attachment under the scenario discussed in Section II, a case study is here considered. The analysed case corresponds to the Vestas V90 large wind turbine with 45 m long blades and hub height of 80 m [33]. The assumed location of the lightning blade receptors considered in the analysis is shown in Fig. 3. In the simulation, dart leaders are assumed to descend from the thundercloud charge centre located 4 km above the ground and along the remnant channel preheated by the ICC stage. This channel is first assumed to be located directly above the nacelle of the wind
Fig. 3. Position of the receptors on the analysed blade design.
Fig. 4. 3D plot of the dart leader and the connecting leaders during the lightning attachment. The colour legend indicates time starting at the initiation of dart leader from the thundercloud charge centre.
turbine (d = 0) and a typical dart leader velocity of 1 × 107 m/s is considered. The dart leader is represented by a straight line of charge with density calculated as a function of the height and the prospective return stroke peak current, according to [34]. However, the calculated dart leader charge distribution is multiplied by a constant factor (equal to 0.8) in order to provide better agreement with static electric field measurements [30]. In order to illustrate the inception and propagation of upward connecting leaders under the influence of dart leaders, the prospective return stroke peak current is taken as 12 kA in this section. This value corresponds to the 60% cumulative probability of return stroke peak current in upward lightning [35]. In addition, the time interval ttotal is taken as 260 ms which consists of a period tICC = 210 ms (corresponding to a cumulative probability of the ICC stage duration of 20% [36]) and a typical duration of the no-current period tNoC of 50 ms [25]. Let us consider the propagation of upward connecting leaders of the blade receptors of the analysed large wind turbine from the moment the first dart leader starts. At this instant, the blade from which upward lightning is initiated has rotated 30◦ from its vertical position under the time interval ttotal and a turbine tip velocity of 90 m/s [33]. Fig. 4 shows the simulated 3D image of the connecting leaders initiated from the tip and the 4th receptors and the dart leader as a function of time (given by the colour legend). As the dart leader approaches, an upward connecting leader is first incepted at the tip receptor followed by other leaders gradually incepted from
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Fig. 6. The distribution of lightning terminals of dart leader- return stroke on the blade on different peak current Ip.
Fig. 5. Simulated properties of the successful upward connecting leader from the 4th receptor under a dart leader with prospective return stroke current of 12 kA.
Table 1 The distribution of lightning striking terminals on peak current Ip and rotational angle (without considering the effect of wind). Ip (kA)
inboard receptors. Even though the connecting leader from the tip receptor initiates first and propagates the longest length, there is a significant horizontal gap which cannot be bridged by its streamer zone even when the tips of both leaders are at the same height (of 140 m). Then, the dart leader continues its downward propagation until it finally attaches to the 4th receptor at a height of 124 m above the ground. The electric field shielding effect from the connecting leader initiated at the tip receptor is neglected in this evaluation. Thus, the connecting leader from the 4th receptor is assumed to develop independently. This assumption is justified by the 10 m distance between the 4th receptor and the tip receptor. Fig. 5 shows a simulated streak image, current and velocity of the upward connecting leader from the 4th receptor intercepting the dart leader. The stable inception of the connecting leaders for the 4th inboard receptor is reached when the dart leader reaches a height of 870 m above the ground. The connecting leader propagates a total length of 14 m in the time duration of 76 s. As is shown in the streak image, the height of the streamer front increases and then decreases during the final stage of the attachment since the streamer propagates toward the downward leader tip to bridge the horizontal gap between the two leaders’ tips. The predicted current of connecting leader slowly increases from 0 to 30 A in the first 70 s. Then, it increases rapidly to about 800 A in the last 6 s prior to the return stroke due to the intensified ionization at the streamer front as the dart leader approaches. This also causes the rapid increase of the connecting leader velocity in the final stage of attachment. The velocity of connecting leader increases from 1.0 × 105 m/s to the maximum of 2.1 × 106 m/s closely prior to the return stroke.
ttotal (ms) R1 R2 R3 R4 R5 R6 R nacelle
The rotational angle of the studied blade 30◦
45◦
60◦
262 ≥13 – – 13 > IP ≥ 12 12 > IP ≥ 11 11 > IP ≥ 10 <10
393 ≥22 – 22 > IP ≥ 21 21 > IP ≥ 20 20 > IP ≥ 19 19 > IP ≥ 16 <16
524 ≥31 – 31 > IP ≥ 30 30 > IP ≥ 28 28 > IP ≥ 25 25 > IP ≥ 22 <22
5.1. The prospective return stroke peak current The location of lightning strike point on the blade depends directly on the prospective return stroke peak current Ip as shown in Fig. 6. It is found that the tip receptor is always struck by dart leaders with prospective return stroke peak current larger than a threshold I0 (1) (equal to 13 kA in this case for a rotation angle = 30◦ ). For prospective peak currents lower than this threshold, the lightning dart leader attaches to the inner blade receptors or the nacelle as it is shown in Fig. 6. Interestingly, no strike is predicted for the second and third receptors at any current due to the electrostatic shielding of the tip receptor. As Ip decreases to 12 kA, the lightning strike point shifts to the 4th receptor, 6 m away from the tip of blade A. As the perspective return stroke decreases to 11 kA and 10 kA, the lightning strike point is shifted to the 5th and the last receptor respectively. However, none of the blade receptors is capable of intercepting lightning dart leaders with prospective peak currents equal to or lower than the threshold current I1 (nacelle) of 9 kA. In this case, it is assumed that the dart leader attaches to the receptors on the nacelle.
5. Factors influencing the dart leader attachment to wind turbine blades
5.2. The rotation of the blades
The attachment of lightning dart leaders to receptors of the turbine blades is significantly influenced by the prospective return stroke peak current and the angle of the rotation of the blade of the wind turbine at the start of the dart leader descent. Since wind also affects the dart leader location, its effect on the attachment mechanism is also analysed.
The evaluation is here extended to account for the larger rotational angle of the blades, namely, 45 and 60◦ . These rotation angles are calculated for blade tip velocity of 90 m/s [33] and the time period as listed in Table 1. The cumulative probability of the period ttotal equal to 262, 393 and 524 ms (for the considered angles of 30, 45 and 60◦ ) is 20, 60 and 75 % respectively. As it described above, the period ttotal consists the ICC stage tICC and the no-curent interval
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Table 2 The distribution of lightning striking terminals on peak current and rotational angle (with considering the effect of wind). Ip (kA)
d (m) R1 R2 R3 R4 R5 R6 R nacelle
The rotational angle of the studied blade 30◦
45◦
60◦
4 ≥13 – – – 13 > IP ≥ 12 – <12
6 ≥26 26 > IP ≥ 23 23 > IP ≥ 22 22 > IP ≥ 20 20 > IP ≥ 19 19 > IP ≥ 17 <17
8 ≥32 32 > IP ≥ 31 – 31 > IP ≥ 29 29 > IP ≥ 27 27 > IP ≥ 23 <23
tNoC (the typical value of tNoC is 50 ms). These probabilities are obtained according the statistics of tICC from towers with height ranging from 60 m to 220 m in Sao Paulo [36]. Observe that the values of the period ttotal used here are also comparable with corresponding measurements at Gaisberg Tower [37], with geometric mean value of initial stage duration of 230 ms, and maximum and minimum values of 739 ms and 65 ms respectively. As shown in Table 1, the threshold peak currents I0 (1) and I1 (n) at which dart leaders attach to the inner blade receptors and the nacelle increases with the blade angle. As the blade rotates further away from the dart leader channel, the connecting leader initiated from the blade requires larger energy to bridge the longer gap. This energy comes from the background electric field mainly provided by the approaching dart leader, which positively correlates to the return stroke peak current Ip. According to statistics from Gaisberg Tower [35], the probability of return stroke peak current larger than 13, 22 and 31 kA (the threshold I0 (1) below which dart leaders attach to inner blade receptor in Table 1) is 32%, 5% and 1% in upward lightning. It indicates that the probability of lightning terminal shifting to the inner blade receptors or the nacelle is 68%, 95% and 99%, when the blade rotates with an angle of 30, 45 and 60◦ respectively. On the other hand, the dart leader would attach only to the nacelle for prospective currents below the threshold I1 (nacelle) equal to 10, 16 and 22 kA The probability of this situation is 48%, 81% and 95% for blade angle = 30, 45 and 60◦ respectively. These results indicate that it is most probable for dart leaders to attach to the blade tip and the nacelle, while strikes to inboard receptors are possible but less likely. 5.3. The impact of the wind As the scenario described in section II, dart leader descends along the remnant channel displaced a distance of d due to the wind flow during the period ttotal . Assuming a wind speed of 15 m/s, the simulations are re-evaluated considering the displacement of dart leader channel. As it can be seen in the results shown in Table 2, the incidence of lightning strikes to the wind turbine is weakly influenced by the drift of the dart leader channel due to wind. For this reason, the effect of wind is not considered in the evaluation of the lightning attachment probability presented in the following section. 6. Lightning attachment probability along the blade of wind turbines due to dart leader attachment
• Even though the average number of return strokes following the initial stage of upward lightning is about 4.4 [35], only the first dart leader-return stroke (RS) is considered in this evaluation. Observe that upward leaders propagating following return strokes would probably propagate along the still-hot channel preheated by the previous stroke. Due to the relatively short interstroke period (shorter than the duration of the ICC stage), the remnant channel does not have time to recover to nearatmospheric conditions (here assumed). Thus, the total incidence of lightning strikes to any receptor in a single blade due to upward lightning (including those by attachment of the first dart leader) is expressed as follows:
N Rj =
Nu Nu · (j = 1) + · a · Patt−DL Rj , 3 3
(1)
where Nu is the annual number of upward flashes initiated from the wind turbine. The first term on the right side of (1) represents the number of lightning strikes due to self-triggered or “other triggered” upward leaders in the initial stage while the second term corresponds to the contribution of dart leader attachment. The first term is non-zero only for the first receptor (j = 1) at the blade tip R1 as assumed above. The factor a corresponds to the percentage of upward lightning strikes containing dart leader/return stroke sequences. This parameter is here taken as 0.3 based on statistics of upward lightning from Gaisberg Tower [35]. The term Patt -DL represents the overall probability of dart leader attachment to the j-th studied receptor on the blade or the nacelle. This parameter is calculated as:
60
(j) () 1
I
Patt−DL Rj =
g Ip × f dIp d,
(2)
=−60Ip=I (j) () 0
where the integrals are defined between the lower and upper (j) (j) return stroke peak currents I0 andI1 defining the range at which the dart leader attaches to the studied receptor. This current range is calculated with SLIM for each receptor in the bladeand the nacelle for the analysed wind turbine as shown in Table 2. g Ip is the probability density function of the return stroke peak current Ip in upward lightning. f is the probability density function of the rotation angle (from the vertical axis) during the period ttotal until the dart leader starts its descent. It is worth to note that the integration is performed in the interval between −60 and 60◦ for the angles where the dart leaders can attach to the analysed blade (e.g. blade A). Observe that angles in the range between −60 and 0◦ correspond to dart leaders propagating along the channel produced by upward lightning triggered by the preceding blade (e.g. blade C in Fig. 6). The rotation angles between 0 and 60 correspond to the case when the upward lightning has been triggered by the analysed blade. Eq. (2) can be rewritten in terms of the cumulative distribuof the return stroke peak current in upward lightning tion function G Ip as:
⎛
Patt−DL Rj = ⎝
60
(j)
(j)
G I1 () − G I0 ()
⎞
× f d ⎠ , (3)
=−60
In order to evaluate in detail the distribution of lightning attachment probability along the blades due to dart leaders, calculations are performed based on the following assumptions: • The initial upward leader in upward lightning always initiates from the tip receptor when the blade is in vertical position.
Where the function G(Ip ) is here obtained from the complementary cumulative distribution function reported in [35]. In turn, the probability density function of the blade angle f is obtained from the probability distribution p (tICC ) of the duration of the ICC stage reported in [36] and assuming an average interstroke period tNoC of 50 ms [25]. Considering the duration of the total period ttotal
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437
Fig.7. The probability of dart leader-return stroke attaching to the individual blade receptor and the receptor of the nacelle in each angle-interval for the analysed case study.
and the blade angular velocity ωblade , the angle density function f is obtained as:
⎧ ◦ ⎨ p + 120 ⁄ωblade − tNoC , if - 60◦ < < 0◦ f () = , ⎩ p ⁄ωblade − tNoC , if0◦ < < 60◦
(4)
The overall probability is here solved numerically using the trapezoidal rule and considering n intervals of the rotation blade angle(n = 12), each interval of the rotation blade angle is 10◦ . The probability of lightning striking to the individual blade receptor and the receptor of the nacelle due to dart leader interception for different angle intervals of the analysed wind turbine is shown in Fig. 7. As it can be seen, the distribution of the attachment point on the turbine is significantly influenced by the rotation angle, which is given by its rotation velocity and the time duration ttotal between the inception of upward leader in the initial stage and the descending of the dart leader. It is found that the tip receptor R1 intercepts most of lightning dart leaders for blade angles in the interval between 10 and 40◦ . As the blade rotates to angles away from this interval, the probability of dart leaders striking the nacelle Rn rapidly increases. This indicates that the effectiveness of dart leaders to attach to any of the blade receptors decreases as the period ttotal increases and the blade is at a larger angle from the vertical position. In-blade receptors (R2-R6) are mainly struck by dart leaders at positive blade angles, with an increasing strike probability as their distance to the tip receptor increases. However, the probability of strikes to all the in-blade receptors is significantly smaller than for the receptors at the blade tip or the nacelle. Overall, the tip receptor of the blade of the analysed turbine intercepts around 18% of the dart leader return strokes; the in-blade receptors intercept 9% of the dart leader return strokes, whereas the nacelle receptor intercepts the remaining 73%. However, the peak current of return stroke attaching to the nacelle receptor is lower than its counterpart attaching to blade receptors. Taking into account the lightning attachment process during both the initial stage and the first dart leader-return stroke sequence in upward lightning flashes, the calculated distribution of lightning striking points along the blade for the analysed case study is shown in Fig. 8. The evaluation suggests that the upward lightning strikes have the highest incidence on the tip receptor, accounting for 81% of all the strikes (mainly due to the upward leaders during the initial stage of the flash). This result is in agreement with field observations reporting that around 70% of the observed lightning damage of wind turbine blades is found on to the first 1.5 m from the tip [11]. However, the evaluation predicts a low probability of lightning strikes to the second and third receptors due to dart leader attachment, in contrast to the field observations where
Fig.8. Predicted distribution of lightning strikes by upward lightning as a function of the distance to the blade tip for the analysed case study.
20% of lightning damage occurring with 1.5–6 m from the blade tip. Thus, it is unlikely that the attachment of dart leaders causes the damages observed within that area of the blade and instead other process (e.g. the swept stroke) is responsible. It is also found that the incidence of dart leaders attaching to receptors located several meters away from the tip accounts for about 2% of all the possible strikes to the blade. Hence, this mechanism can explain the field observations reporting that around 10% of the remaining lightning damage was located in the region further inboard of the blade [11]. On the other hand, a significant probability (16.9%) of strikes to the nacelle due to upward lightning (mainly due to dart leader attachment) is predicted for the analysed wind turbine. Interestingly, lightning strikes to the nacelle of large wind turbines have been also observed in the field study reported in [6]. Unfortunately, it is not possible to compare the predictions in Fig. 8 with the reported registered strike percentages to the nacelle since the measurement system (peak current sensor cards) in [6] detects only upward lightning with current peaks above 5 kA and since their measurements cannot provide accurate statistics of lightning strikes. However, these field observations clearly show that lightning flashes can strike the nacelle of large wind turbines, which can be readily explained by dart leader attachment. This is also confirmed by the relatively low value of the recorded peak currents (lower than 15 kA) [6], which are typical for return strokes in upward lightning. It is worth to highlight that the probabilities and the distribution of attachment points shown in Figs. 7 and 8 apply only for wind farms with similar turbine geometry, tip rotation velocity and lightning conditions as assumed in the analysis in this Section. It can be easily shown that the probability of dart leaders striking areas other than the blade tip decreases as the blade length and rotation velocity of the analysed turbine decreases. In a similar way, dart leader attachment to the nacelle and inboard blade parts is also less likely to occur in wind parks located in areas with a low percentage of upward lightning followed by at least a dart leader-return stroke sequence and/or a short duration of the period ttotal . Interestingly, the most extensive field study up to date [38] has shown no negative lightning strikes hitting the nacelle or inboard blades of wind turbines in Japan. However, the reader should be aware that this field observation does not contradict the lightning damage mechanism discussed here. Observe that the turbines reported in [38] had significantly shorter blades (with an average of about 33 m) and rotate at lower velocity (with an average of 70 m/s) than the turbine design analysed here (with 45 m long blades with tip rotating at 90 m/s). Additional differences can be found when
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carefully analysing the more current oscillograms reported in [38]. It can be shown than of the 674 lightning flashes identified, only about 85 of them include return strokes (about 13% of the total). Observe that this fraction of upward flashes with return stroke sequences (and therefore with dart leaders) in Japan is lower than that reported in Europe at Gaisberg Tower (of about 30%) [35]. Moreover, despite of the limited resolution of these current waveforms in [38], the 50% probability value of the time ttotal can be roughly estimated at about 90 ms. This time is significantly shorter than the corresponding value used here (of 375 ms [36]). In the same way, the maximum ttotal estimated from [38] is less than 450 ms, while it has been reported to be larger than 700 ms in Austria and Brazil [36]. As a consequence of the shorter blade length, slower tip rotation velocity and significantly low ttotal , the rotation angle of the turbines studied in Japan [38] is rather small (less than 15◦ in average). In addition, the probability of occurrence of dart leaders in Japan during upward flashes is lower than the percentage here considered. Therefore, it is unsurprising that no strike to the nacelle or inboard parts of the blade produced by dart leaders have been observed in Japan as reported in [38]. In conclusion, the damage mechanism here discussed is predicted to occur only in cases when the blade of a wind turbine has rotated sufficiently from its initial position (at the inception of the initial upward leader) until the start of the dart leader approach. Thus, the lightning damages to the nacelle or inblade parts of the blade due to dart leader attachment may not occur for all wind turbines. It will take place only for turbines with long blades and turning at high speed and located in sites during upward lightning flashes with long ICC duration prior to the first return stroke. As a consequence, the probability of damages due to dart leader attachment and its attachment distribution for wind parks under conditions different to those evaluated here are expected to be different than those shown in Figs. 7 and 8. In those cases, the assessment of this kind of damage would require the evaluation considering the actual wind turbine model and the local lightning conditions of the wind park site.
7. Discussion The evaluation of lightning attachment of dart leader to wind turbines in this paper considers the scenario that the initial upward leader incepts at the blade when it rotates to the vertical position. This scenario is most probable to take place in the self-initiated upward lightning, since the critical electric field required for the initiation of upward lightning has the lowest threshold when the blade rotates its highest point [18]. In case of other-triggered upward lightning, the inception of upward lightning alternatively depends on the fast electric field change provided by nearby lightning events [23,39]. It is because the rate of the fast electric field change is significantly higher than the speed of the blade rotation. Thus, upward lightning can be initiated from the blade at the arbitrary angle in the half above rotation plane, as long as the fast electric field change reaches the threshold. Consequently, the distribution of angle of blades initiating upward lightning depends on the ratio between the occurrences of self-initiated and other-triggered upward flashes. The field observation indicates that operating wind turbines exhibit an increased tendency to self-initiated upward lightning compared with static structures [23]. A statistic of 169 winter lightning (mostly upward lightning) to operating wind turbines at different locations of Japan shows that 42% of the observed upward lightning is initiated from vertical blades (0◦ ) and it is followed by the blade angle of −30◦ (31%), 30◦ (13%), 60◦ (7%) and −60◦ (7%) [24]. Since considerable amount of upward lightning initiated from the blade is not at the
vertical position, we additionally evaluate lightning attachment of dart leader to wind turbine under these conditions. In this evaluation, we assume that upward lightning is initiated from blade A at the angle of −60, −30, 30 and 60◦ and the peak current of return stroke is also taken as 12 kA. The rotational angle of blades during the ICC and no-current interval is considered in the range of 30 to 60◦ . The evaluation shows that lightning dart leader attaches inboard receptors of blade A in the case that the initial upward leader is incepted from the blade at the angle of 30 and 60◦ . It is well explained by the downward rotation of blade A, resulting that the tip of blade A moves further away from dart leader channel and the inboard receptors are consequently more exposed. Interestingly, lightning dart leader is intercepted by the inboard receptors of the following blade B, if the initial upward leader is incepted from blade A at the angle of −30◦ . The dart leader is beyond lightning attractive zone of the tip receptor of blade A, even when blade A rotates to its vertical position. Different from the above cases, lightning dart leader is predicted to attach to the tip receptor of blade A in the case that upward lightning initiated from the blade at the angle of −60◦ . In this case, the subsequent return stroke strikes to the same point where the upward lightning initiated, unless the blades rotate an angle larger than 60◦ . It is worth to note that this case (upward lightning initiating from the blade at the angle of −60◦ ) accounts for a rather low percentage (7% reported in [24]). Thus, lightning attachment of dart leader after the initial stage of upward lightning still exhibits a high tendency striking to the inboard receptor in the condition that the initial upward leader is incepted from a blade in non-vertical position. Furthermore, the lightning channel connecting to wind turbines is frequently observed in still pictures to be elongated following the trace of blade tip while the blade rotates during the initial continuous current stage [38]. This elongation is also expected to occur during the ICC period by wind, pushing the discharge channel downstream from the turbine (as shown in Fig. 3c). However, the current cut-off at the end of the ICC period indicates the interruption of the conduction path of the lightning channel, which is observed to occur close to the struck object [25]. This indicates that the temperature of the lower section of the channel has decayed sufficiently (reaching values lower than 1500–2000 K [31]), starting the no-current interval tNoC . Unfortunately, there is no information in the literature about the further temperature decay in the lower section of the remnant channel during the period tNoC in upward lightning. However, it is reasonable to assume that the lower section of the remnant channel quickly recovers to nearatmospheric condition due to convective turbulent cooling as well as thermal conduction [30]. Moreover, observe that the fast rotation of the considered turbine will move the blade tip away from the lower section of the remnant channel by more than 5 m during the time tNoC . Therefore, the inception and propagation of upward connecting leaders from wind turbines is expected to occur under atmospheric or near-atmospheric conditions. On the other hand, the initiation and propagation of connecting leaders from individual receptors of a blade in response of a lightning dart leader is considered independent from each other in this paper. Since the connecting leader is always first initiated from the tip receptor, it shields electrostatically the development of other connecting leaders from inboard receptors. Since the physical simulation of competing upward connecting leaders separated only few meters from each other is difficult, this electrostatic coupling between leaders have been neglected. However, this electrostatic shielding will mainly hinder the development of upward leaders from the receptors close to the blade tip (e.g. R2, R3, R4). Since it is predicted that dart leaders have a very low probability to strike these receptors in the analysed case study, this simplification will have no significant effect on the results of the paper.
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8. Conclusion This paper quantitatively evaluates the attachment of lightning dart leaders in upward lightning flashes as a mechanism of lightning strikes to wind turbines, based on numerical simulations with SLIM. The effect of the return stroke peak current, the rotation angle as well as the wind on the probability of strikes to receptors on the blades and the nacelle are investigated. A case study of a large turbine with 45 m blade length and tip rotating at 90 m/s, located in a site with upward lightning properties as those reported for Brazil and Austria, is analysed. Even though it is predicted that most of the upward lightning strikes hit the blades of the analysed turbine, it is shown that the nacelle receptor is likely to be struck by lightning mainly due to the attachment of dart leaders. This result is valid only for turbines with long blades and high tip rotation speed (as in the analysed case study) located in sites with a sufficient fraction of upward lightning with at least one subsequent return stroke and with long ICC duration (with a 50% probability time larger than some hundreds of milliseconds). In those cases, the tip receptor and the inblade receptors is predicted to intercept a lower (but still significant) proportion of dart leaders. However, the more frequent attachment of dart leaders to the nacelle is expected to take place under lower return stroke peak currents than for the blade receptors. Furthermore, it is shown that the probability of attachment point of dart leaders on regions in-board the blade increases with the distance to the tip. For this reason, dart leader attachment in upward lightning cannot cause damages in the area within 1.5–6 m from the blade tip as reported in some field studies. Instead, this mechanism can explain (the less frequent) lightning damages inboard, several meters away from the blade tip in turbines with long blades rotating at high speed. In such cases, it is also shown that receptors on the nacelle of the turbine are exposed to lightning strikes due to attachment of dart leaders, in agreement with field observations of wind parks in Denmark. References [1] T. Naka, et al., Study on lightning protection methods for wind turbine blades, IEEJ Trans. Power Energy 125 (10) (2005) 993–999. [2] H. Braam, et al., Lightning damage of OWECS Part 3: Case Studies, Energy Research Centre of The Netherlands, Petten, 2002. [3] IEC, 61400-24: Wind Turbine Generator Systems — Part 24: Lightning Protection for Wind Turbines, 2010. [4] F. Rachidi, et al., A review of current issues in lightning protection of new-generation wind-turbine blades, IEEE Trans. Ind. Electron. 55 (6) (2008) 2489–2496. [5] G. Diendorfer, On the risk of upward lightning initiated from wind turbines, in: Proceedings of theIEEE 15th International Conference on Environment and Electrical Engineering (EEEIC), Rome, Italy, 2015, pp. 872–876. [6] V. Peesapati, I. Cotton, T. Sorensen, T. Krogh, N. Kokkinos, Lightning protection of wind turbines — a comparison of measured data with required protection levels, IET Renew. Power Generat. 5 (1) (2011) 48–57. [7] J. Montanyà, et al., Global distribution of winter lightning: a threat to wind turbines and aircraft, Nat. Hazards Earth Syst. Sci. 16 (6) (2016) 1465–1472. [8] V. March, et al., Winter lightning activity in specific global regions and implications to wind turbines and tall structures, Proceedings of the 33rd International Conference on Lightning Protection (ICLP) (2016) 1–5. [9] J. Montanyà, O. van der Velde, E.R. Williams, Lightning discharges produced by wind turbines, J. Geophys. Res.: Atmos. 119 (3) (2014) 1455–1462. [10] I. Cotton, N. Jenkins, K. Pandiaraj, Lightning protection for wind turbine blades and bearings, Wind Energy 4 (1) (2001) 23–37. [11] S.F. Madsen, K. Bertelsen, T.H. Krogh, H.V. Erichsen, A.N. Hansen, K.B. Lønbæk, Proposal of new zoning concept considering lightning protection of wind turbine blades, Lightning Res. 4 (2012) 108–117. [12] S. Yokoyama, Lightning protection of wind turbine blades, Electric Power Syst. Res. 94 (2013) 3–9. [13] S.F. Madsen, H.V. Erichsen, Improvements of numerical models to determine lightning attachment points on wind turbines, in: 29th International Conference on Lightning Protection, Uppsala, Sweden, 2008, pp. 9-27- 1-11.
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