In recent years, wind energy has grown to be a significant source of sustainable energy to reach emission reduction. Wind turbine installation capacity has increased rapidly in order to meet carbon peak and neutrality targets, which have become common sustainability goals around the world. Based on GWEC (Global Wind Energy Council. 2022) reports, the global wind power total installed capacity reached 837 GW by the end of 2021, about 12.4% growth compared to 2020. With the progress of material technology (such as carbon and glass fiber-reinforced polymers), wind turbine blades have experienced an enormous development due to the new material. Therefore, the size of wind turbines has tremendously increased in recent decades. A large percentage of wind turbines are likely to be installed in places with significant lightning activity [SArajcev et al., 2013]. Lightning strikes on wind turbines are strongly influenced by topological factors, wind turbines installed in mountainous areas are riskier to lightning damage than wind turbines installed in coastal regions [McNiff et al., 2002]. Thus, it is expected that wind turbines need to suffer greater lightning strikes (Agoris, 2002; Cotton et al., 2001; Sorensen, 1998).

Lightning is a tremendous nature phenomenon, the number of lightning strikes increases with structure height, posing significant challenges to wind turbines of growing size (Beckers, 2016). The threat posed by lightning strikes has increased, and caused significant damage due to both direct and indirect effects. According to the insurance company report, lightning strikes cause 23.4% of wind turbine failures in the United States (Gcube-insurance, 2012). Damages to the wind turbine occurred to the blades, rotor, and generator. The blades are the key components that convert wind energy to mechanical energy, and it is also one of the wind turbine’s most vulnerable parts. According to a report from the ECN (Energy Research Centre of the Netherlands), the blades have the highest frequency of lightning strikes (approximately 75%), as well as the most extended downtime (about 10 days per lightning incident) (Rademakers et al., 2002). About 118 lightning strike accidents were recorded, the research has shown that 88.1% were attached to the blade tips. (Madsen et al., 2006). Garolera analyzed 304 cases of lightning-striking accidents in the USA and noted that most of the lightning strike is located at the blade tip, with about 90% of incidents located at the last 4 m of the blade (Garolera et al., 2014). Furthermore, 739 lightning incidents were observed during 7 years, but more than 1032 failures were found. That were indicating a single lightning strike can cause multiple component damage (Rademakers et al., 2002). Despite the fact that wind turbine being equipped with lightning protection equipment, lightning strikes have occurred nevertheless. This is because the manufacturers’ design lightning protection devices mainly regard lightning strikes occurring at the place of the maximum electric field strength, for wind turbines that are the tip of blades. Remarkably, the lightning statistics data for wind turbines shows that only about 60% of lightning strikes occur at the blade tip (maximum electric field strength). However, there are still close to half of the lightning strikes occurring outside the vulnerable lightning strike area. The considerable number of existing protection failures indicates this direction is worth further study.

Different researchers have conducted some experiments with the scaled models to investigate the lightning characteristics. Radicevic presented a study with the reduced-size model, and the result shows the rotation of the blades decreases the number of direct lightning strikes. (Radicevic et al., 2012). Wen experimented with a scaled model and switching impulses (250/2500 μs), and the result indicates that the rotation of the blades improves lightning triggering ability (Wen et al., 2016). Furthermore, A comparison between current parameters from stationary and rotating wind turbines was carried out, and it reveals there is no substantial difference between the two operational modes (Yu et al., 2022). From the above study, some ambiguous and even conflicting conclusions have been obtained, and these results are confusing.

The blades of wind turbine generate periodic electric discharges indicating that the effect of rotation plays a critical role [Montanya et al., 2013]. Meanwhile, the lightning development and attachment mechanism considering space charge density distribution were carried out by some researchers. Gu discovered the electric field distortion produced by the space charge and discussed the variation of the streamer during the discharge process [Gu et al., 2020]. To determine the mechanisms of corona and leader initiation for rotating wind turbines, Yu established a three-dimensional drift and diffusion model. The results reveal that as the spinning speed increases, it becomes more sensitive to initiating corona discharge (Yu et al., 2017). Qu proposed a model to investigate the distribution of charged particle migration. It was further discovered that the rotation effect reduces positive ion concentration (Qu et al., 2019). Wang conducted long-gap discharge experiments to determine the difference in lightning triggering ability between rotating and stationary blades. According to the study, rotation increases its capacity to generate lightning strikes [Wang et al., 2017]. However, the space charge distribution is not the only factor that can influence the upward leader initiation when the blades are rotating. These studies have been limited to the shielding effect of space charges generated by thundercloud electric fields. The effect of the change of atmospheric conditions around the blades due to the rotation is neglected. Nevertheless, this factor is strong enough to influence the initiation process of the upward leader. But very few existing studies have paid attention to this point. M. Ramirez carried out a research to investigate the impact of air density on the discharge process [M. Ramirez et al., 1990]. The influence of pressure and humidity on the corona onset performance was studied, and a mathematical model to evaluate the corona onset voltages was proposed (Hu et al., 2011). Yu examined the corona discharge at low atmospheric pressure and discovered that the corona inception voltage drops as atmospheric pressure falls. (Yu et al., 2006). However, the above studies are concentrated on static conditions, and no further research has been proposed for dynamic systems. Therefore, it is necessary to conduct a numerical simulation to analyze the lightning strike characteristics for rotating blades considering the atmospheric conditions. In this paper, a 2D numerical model of air pressure distribution was established. Combining the inception model of upward leaders, the relevant sensitive factors were examined. Furthermore, the vulnerable strike areas of the blade were analyzed. The study will give a theoretical foundation for wind turbine lightning strike performance.

In the second or subsequent streamer bursts, the streamer-leader transform condition is equal to or greater than approximately 1 μC (Gallimberti, 1979; Lalande et al., 2002). Once the requirement is reached, the ionization process provides the energy and current to sustain the thermal transition. At the same time, the upward leader channel expansion generates the electric field to enable the ionization process (Goelian et al., 1997). If this process reaches a dynamic equilibrium, the upward leader–streamer system can develop continuously and steadily.

According to the streamer criterion, free electrons are accelerated under electric field E. The impact ionization of neutral gas particles increases the electrons. A net ionization coefficient α ′ can be defined as: α ′ = α E − η E (1) Where α E and η E are functions of E representing ionization and attachment coefficient, respectively. Defining the distance between α E and η E where they are equal ( α ′ =0) is l . The criterion from the conversion of electron avalanche to streamer is given below: ∫ 0 l α E − η E d l ≥ ln ⁡ ⁡ N s t a b (2) Where, N s t a b is the critical number of positive ions, taken as 55 × 10⁸ γ is the absolute humidity, P w is the partial pressure of water vapor, α w and α d are ionization coefficients in water vapor and dry air, η w and η d are attachment coefficients.

Eq. 1 is only valid for α ′ > 0 . The electronic avalanche process is formed with the number of electrons increasing exponentially. The electric field gets greater ahead of the space charge zone, resulting in more positive space charges enter to the electrode gap to neutralize the positive space charges, as shown in Figure 1. When the stability number of positive ions or electrons at the head of the avalanche exceeds N s t a b , the streamer is assumed to be formed. The average electric field of the streamers E s t r is affected by the air humidity and the relative air density according to (Eriksson et al., 1986) E s t r = 425 δ 1.5 + 4 + 5 δ γ (3) P z = P 0 ⁡ exp ⁡ ⁡ − z / z 0 (4) T = T 0 − 6 H L (5) γ = γ 0 ⁡ exp ⁡ ⁡ − H L / z H (6) Where γ is the absolute humidity, δ is the relative air density given by δ = P / P 0 T 0 / T , in which P is the atmospheric pressure, T is the temperature, P₀ is the standard atmospheric pressure (1013.25 hPa), H_L is the altitude (km), and T₀ is 293 K; E s t r is equal to 52 MV/m under the standard atmospheric condition (P=P₀, T=T₀; γ = 11 g / m 3 ). It is worth noting that it can be considered as a constant value for stationary objects, but it is necessary to make the corrections for a dynamic system.

In order to determine the stable upward leader’s inception, the positive upward-leader inception theory is adopted (Becerra and Cooray, 2006a; Becerra and Cooray, 2006b). The method of approximate geometric based on the background potential distribution was presented. When △Q is greater than 1 μC, it is considered that the unstable upward leader has been generated since the background potential is strong enough to create a second corona charge. Furthermore, if the leader length exceeds the maximum value of 2 m, the steady leader inception criterion is considered satisfied. Otherwise, the development of the upward leader is considered to be terminated.

Charge conservation theory states that the quantity of charge entering the leader should be equal to the number of space charges remaining in the corona zone. The background potential distribution U 1 0 shift to U 2 0 for the reason of space charge existence and expressed as a straight line, the slope is E 1 and the intercept of the vertical axis Is U 0 ′ , as Figure 2 shows. Accordingly, the distribution of background potential can represented as: U 1 0 ≈ E 1 ∙ l + U 0 ′ (7)

According to the approximate geometric method, the second corona charge defines as: ∆ Q 0 ≈ K Q ∙ l s 2 2 ∙ E s t r − E 1 (8) When thermal ionization is completed (temperature above 1500 K), the stem is transited to the leader with increased conductivity and energy as ∆ Q 0 ≥ 1   μ C . The potential for the tip of leader can be computed with: U t i p i = l L i ∙ E ∞ + x 0 ∙ E ∞ ∙ ln E s t r E ∞ − E s t r − E ∞ E ∞ ∙ e − l L i / x 0 (9)

The charge ∆ Q can be calculated as: ∆ Q ≈ K Q E s t r ∙ l L i − l l i − 1 + U t i p i − 1 − U t i p i ∙ l s i − 1 − l L i (10)

The developed distance of the upward leader and the corona can be expressed with: l s i = l s 0 + E s t r ∙ l L i − U t i p i E s t r − E 1 (11) l L i + 1 = l L i + ∆ l L i = l L i + ∆ Q q L (12) When l L reaches 2 m, the stable upward leader requirement is satisfied. Once ∆ l L i < 0 , the development of the upward leader is terminated. The relevant parameters are shown in Table 1. In a previous study, the validity of model was examined by comparing simulated results with optically observed data which shows great agreement. (Yang et al., 2017).

The positive streamer gradient is affected by the atmospheric conditions (air humidity and air pressure), which make significant changes to lightning strike performance. Hence, it can obtain a method to determine the initiation of the upward leader by taking the atmospheric condition as an essential factor from the above correlating formulas. It is important to note that the lightning strike is assumed to be taken place successfully when the inception condition of the upward leader is satisfied in this study. The initial point is considered the subsequent strike point.

The geometry of the wind turbine increases with the installed capacity, and the blade length also increases accordingly, which leads to the blade tip speed becoming higher. As a result, precisely predicting a lightning strike to a wind turbine is critical. The study applies the geometry of a 2 MW wind turbine model with a 95 m hub and 54 m blades, with rotational speeds ranging from 8.1 rpm to 19 rpm according to the wind. The linear velocity of the blade tip is between 45 and 110 m/s. It is faster than wind speed, but much slower than the downward stepped leader (approximately 10⁵–10⁶ m/s). For the sake of a quantitative study, a symmetric wing NACA0012 was used in this research. Different speeds and attack angles were used as variables in this study to discuss the lightning strike characteristics of wind turbines under different conditions.

According to Bernoulli’s theory, the air velocity on the top surface of the airfoil is greater than on the bottom. Hence, the atmospheric pressure on the blade surface is unequal (the pressure on the lower surface is high and the upper surface is low), and it depends on the two factors of velocity and attack angle. To analyze the lightning striking characteristics of the wind turbine, the air pressure distribution around the blade must be obtained. In this paper, a commercial finite element method (FEM) program based on the COMSOL software (Comsol Group, 2014) is used to analyze the pressure distribution. A two-dimensional model is made for the sake of achieving a balance between computational speed and accuracy.

From the above, it is known that the inception of the upward leader is a necessary condition for the object to be struck by lightning. The major factors must be identified to investigate the upward leader development process. Firstly, the effect of the velocity of the blade is considered. Figure 3 shows the simulated result of air pressure distribution for several different velocities of the blade, the attack angle is set to 4°. As can be seen, the difference in air pressure increases while the blade speeds up. Several velocities between 80 m/s to 120 m/s are simulated, respectively. The simulation result shows that the minimum pressure (relative pressure) is close to −1.22 × 10⁴ Pa when the blade speed is at 120 m/s, while the maximum pressure (relative pressure) reaches 8.93 ×10³ Pa. Therefore, the difference of pressure could cause a huge change in the positive streamer gradient, which can lead to a considerable change in lightning strike characteristics according to Eq. (3). Based on the simulation results, the positive streamer gradient varies between 4.43 × 10⁵ V/m and 5.87 × 10⁵ V/m in this case.

This study makes the assumption that the downward stepped leader channel is vertical with branch-free and non-uniform charge density distribution, which can be expressed as a function of the return stroke peak current (Cooray et al., 2007). In this case study, the return stroke peak current is taken as a typical value with 30 kA. As the downward-stepped leader moves toward the ground, an upward leader can be initiated when downward-stepped leader descends to a certain height. There is a decreasing trend with the increasing velocity at minimum pressure area, which equals 742 m at the velocity of 80 m/s, while it is approximately 714 m for the velocity at 120 m/s. However, the maximum pressure area shows the opposite trend. Note that if the effect of air pressure change is not considered, the downward-stepped leader trigger height is a fixed value of 763 m regardless of how fast the blade rotates. From the above results, it can be seen that the region where the air pressure is higher will be more likely to trigger a lightning strike than the lower-pressure region. The trigger height for the two different regions reaches 714 m and 794 m at 120 m/s, respectively. There is about an 11.2% difference between the two regions, as shown in Figure 4.

On the other hand, the attack angle is also regarded as an important factor. A similar method is adopted, the simulation result of pressure distribution for different attack angles is obtained, represented in Figure 5. In this case study, the obtained result is simulated with different attack angles from 0 to 10° at 100 m/s (the airflow separation effect occurs as the angle of attack increases, there are no more discussion for larger attack angles), respectively. The change in the pressure result in a considerable variation of the positive streamer gradient, which varies between 3.19 × 10⁵ V/m and 5.67 × 10⁵ V/m in this case. The trigger height that makes the upward leader successfully initiated was correspondingly changed. The simulation results are depicted in Figure 6. It is shown that the trigger height decreases dramatically with increased attack angle for the low-pressure area (0°–10°). But this trend in the high-pressure area is not significant. The trigger height is 785 m for the high-pressure area, and is reduced to 612 m in the low-pressure area (−28% reduction) for the case of 10°. The difference in trigger height tends to increase gradually with the increase of the attack angle. According to the simulated results, it can be concluded that the probability of lightning strikes in the low-pressure area will be reduced as the attack angle increases for the blade.

According to the statistics, lightning strikes have already become a severe threat to wind turbines that could cause enormous damage. The size of the wind turbine is getting increasingly larger, which faces more potential threats. As a result, it is expected that the wind turbines would be suffered more lightning strikes. In this paper, a 2D computational fluid dynamics model was established to obtain the distribution of the air pressure field around the blade. Aside from that, an upward leader inception model was established as well, and the initiation process of the upward leader on the blade for different velocities and attack angles was calculated. It can be found that there is a severe shortage without considering the changes in air pressure. The related conclusions are given as follows.

1 The difference between the maximum and minimum air pressure values increases as the blade accelerates, which can reach 2.11 × 10⁴ Pa at 120 m/s. The changes result in the positive streamer gradient varying between 4.43 × 10⁵ V/m and 5.87 × 10⁵ V/m, which leads to a considerable difference in the lightning strike characteristics for the wind turbines.

When the downward stepped leader is descending to a certain height, the upward leader will be initiated at the areas where the conditions are satisfied. After the height of the developing stepped leader decreases further, other places will also meet the conditions of the upward leader initiation. Therefore, more than one upward leader could be generated in the process of the downward stepped leader development. In general, the upward leader that initiates in the first place gets more time to develop an extended channel and has a higher probability of eventually connecting with the downward stepped leader to discharge. Nevertheless, according to the observation data, although the upward leader is successfully initiated and developed subsequently, there are still cases where the initiation point fails to become a lightning strike point. However, in this paper, it is still considered that the successful initiation of the upward leader is an important indication of the lightning strike, ignoring the development process after the initiation.