Observation and Simulation of Lightning Strikes in an Offshore Wind Turbine Cluster

Abstract

Based on the detection data of the Guangdong-Hong Kong-Macau lightning location system from 2013 to 2022, this paper analyzes the characteristics of lightning strikes in an offshore wind turbine cluster (WTC) in Guangdong. This is the first time to quantify the lightning strikes difference between the inner and outer wind turbines (WTs) and discuss the impact mechanisms of WTCs on the characteristics of lightning strikes by the simulation results of electric potential distribution. The observation results show that the stroke density, cloud-to-ground (CG) flash density, and average peak current within the affected area increase by 10.1%, 11%, and 5.1%, respectively, but the lightning multiplicity changes little. The inner and outer WTs show different characteristics of lightning strikes. The stroke density, lightning multiplicity, and average peak current in the area of outer WTs increase by 21%, 4.1%, and 6.8%, respectively, while in the area of inner WTs decrease by 20.2%, 19%, and 3.9%, respectively. The CG flash density in the area of outer WTs increases by 16.1% but changes little in the area of inner WTs. The simulation results show there is a significant difference in the electric potential distribution between the inner and outer WTs: the distortion effect of the outer WTs on spatial electric potential is stronger than that of the inner WTs at a greater height, but the difference is not obvious at a lower height. Such a difference in electric potential distribution leads to different characteristics of lightning strikes between the inner and outer WTs.

Introduction

In recent years, energy issues have become increasingly prominent. As a sustainable energy, wind power has received increasing attention and has been vigorously developed. Wind turbines (WTs) are the core components of wind power generation. As grounded protrusions, the characteristic reactions of WTs to lightning strikes are similar to those of ordinary tall buildings. Generally, tall buildings affect surrounding cloud-to-ground (CG) lightning activities and attract more lightning events (Hussein et al., 2007; Kingfield et al., 2017; C. Zhang et al., 2016). When the effective height of structural exceeds 100 m, both upward and downward lightning may occur (Diendorfer et al., 2011; Rakov, 2013; Soula et al., 2021). WTs have unique structures, and their lightning strike characteristics are more complex. In particular, the rotating blades of WTs are more vulnerable to lightning strikes than stationary tall buildings (Montanyà et al., 2014; D. Wang & Takagi, 2012; D. Wang et al., 2008; Y. Wang et al., 2019). Wilson et al. (2013) observed that the average striking distance of a 125 m WT is 276 m, which is equivalent to a 231 m tall building nearby.

Most WTs in wind farms are arrayed in “clusters.” Most current studies regard wind turbine clusters (WTCs) as a whole to study the characteristics of lightning strikes in WTCs. The WTC had an attractive effect on lightning activities in the impact area (Birkl et al., 2016; H. Chen et al., 2021; Soula et al., 2019), and the peak current of the strokes can also increase (Birkl et al., 2016; H. Chen et al., 2021). For example, Soula et al. (2019) analyzed the lightning distribution of wind farms in southwest France and found that the number and proportion of strokes of CG lightning near wind farms significantly increased after the installation of WTs. Birkl et al. (2016) found that the CG lightning frequency increased by 64% after the installation of onshore WTs, and the peak current moved to a higher value.

WTs are always distributed in linear or planar form, and WTs with planar (cluster) distributions usually cover a large area. The “cluster” effect of a linear distribution is not obvious, but WTCs with a planar distribution may show differences in the characteristics and distribution of lightning strikes inside and outside the WTCs. A few case studies have shown that the interactions among WTs in a WTC can affect the lightning strike characteristics in the coverage area of the WTC. For example, H. Chen et al. (2021) used lightning location data to study the stroke distribution before and after the installation of an offshore wind farm in eastern China and found that the flash density inside the wind farm was lower than the average flash density. WTs at the edge of a wind farm can shield the inner WTs, and this shielding effect is not obvious in mountain wind farms due to topographic relief. Candela Garolera et al. (2015) recorded the simultaneous discharge of multiple WTs using a camera. A large positive CG flash struck the ground near the wind farm, causing multiple WTs to trigger upward lightning at the same time. They found that the affected WTs were outside the wind farm. However, this limited research is insufficient to analyze the lightning strike characteristics in the inner and outer regions of a WTC, which is not enough to determine the differential characteristics of lightning strikes in the inner and outer regions of a WTC. More CG lightning data for WTCs are needed to conduct in-depth research. At the same time, there is a lack of a theoretical explanation, and the general theoretical explanation mostly depends on simulations of the spatial electric field.

Current simulations have done much work on single WTs, including research on the impact of blade angle on the probability of lightning strikes, calculation of striking distance, etc (Li et al., 2015; Yang et al., 2017). Simulations of WTCs have mostly focused on the influence of different blade angles and the distance between WTs on the shielding effect. For example, L. Zhang et al. (2017) used an improved electrical geometric model to study the lightning protection distance of WTCs. Liu et al. (2020) discussed the influence of the blade angle on the shielding effect by using a finite element physical field. However, these simulations were only simple simulations of 2–3 WTs, and the concept of “clusters” cannot be well reflected. At the same time, the shielding of the area of outer WTs in a WTC with planar distribution to the inner area cannot be explained.

In summary, although there is a relatively unified understanding of the characteristics of overall WTCs, the understanding of the differential distribution of lightning strokes in the coverage area of a WTC remains insufficient, and an explanation of the differential mechanism is still needed. Therefore, this paper analyzes the differential distribution of lightning strokes in the coverage area of a WTC based on the positioning and waveform observation data of an offshore WTC in Guangdong Province, China. Furthermore, this paper also reveals the causes of differential distribution through a simulation of the spatial electric potential distribution. This research can not only improve the theoretical understanding of lightning strikes of WTCs and enrich the understanding of lightning strikes on WTCs but also have important application value for improving the lightning protection of WTCs.

Data and Methodology

The wind farm selected in this study is located on the sea near Zhuhai Triangle Island (113.69°E–113.74°E 22.10°N–22.16°N). There are 34 3-MW WTs in the wind farm. The WTs are distributed in cluster, with intervals of 710–860 m and heights of 146 m. The wind farm was installed and placed into operation in 2018. For the above wind farm, this paper analyzes the characteristics and distribution of lightning strikes on the offshore WTC during TB (the period before the installation of the WTC) and TA (the period after the installation of the WTC) based on the lightning location data of the Guangdong-Hong Kong-Macao lightning location system (GHMLLS) from 2013 to 2017 (TB) and 2019 to 2022.10.1 (TA). In addition to the characteristic differences in lightning strikes between the area of the WTs at the outer and inner sides of the WTC, the characteristics of lightning strikes in the WTC are theoretically explained through a three-dimensional electric potential distribution simulation of the WTC, and the positioning data quality is tested based on the waveform data of the Low-frequency electric field detection array (LFEDA).

Lightning Location Data

The lightning location data used in this paper are derived from the GHMLLS jointly built by the meteorological departments of Guangdong Province, Hong Kong, and Macao. The location, time, polarity, and intensity of lightning strokes can be recorded by combining the time-of-arrival and magnetic direction finding location methods. The lightning location system has been in operation since 2005. In 2012, on the basis of the original 6 IMPACT sensors, 11 substations using LS-700X series sensors were added. In 2018, all the original IMPACT sensors were replaced by LS-700X series sensors, and 2 substations were added, which led to the improvement in detection efficiency to a certain extent. The LS-700X series sensors can detect CG lightning and intracloud (IC) lightning at the same time, greatly improving the detection ability of the system. To date, the lightning location system in Guangdong, Hong Kong, and Macao has a total of 19 substations (L. Chen et al., 2020; Y. Zhang, Lyu, et al., 2021). The distribution of the GHMLLS and the WTCs is shown in Figure 1. The WTCs are located in the network, ensuring high positioning efficiency and accuracy.

Figure 1. (a) Distribution of GHMLLS substations and the location of the WTC. (b) A zoom shows the WTC.

The GHMLLS has high detection efficiency and positioning accuracy, which has been verified by artificially triggered lightning experiments. Experiments have shown that the detection efficiency of the GHMLLS for lightning flashes and strokes was 96% and 88%, respectively, and the geometric average value of the positioning error was 193 m (Y. Zhang et al., 2022). Considering that the GHMLLS can detect IC lightning and CG lightning at the same time (L. Chen et al., 2020; Y. Zhang, Lyu, et al., 2021), the IC lightning and CG lightning markers of the GHMLLS system were used to select the CG lightning records. Then, quality control of the CG lightning records was carried out. This study referred to methods similar to those of other scholars to eliminate positive lightning stroke records of 0–10 kA from the data set (Cummins & Murphy, 2009; C. Zhang et al., 2016; Zheng et al., 2016). Also, we compared the fast electric field waveform obtained synchronously by LFEDA, and the data set after deleting the positive lightning stroke between 0 and 10 kA is more consistent with the real situation. The detailed information on LFEDA can refer to the paper (Shi et al., 2017; Y. Zhang, Wang, et al., 2021).

Analysis Method

The difference in lightning strikes between the WTC affected area and the reference area before and after the installation of WTC is analyzed, and the impact of WTC on lightning characteristics and distribution is studied. The reference area is also used to calculate the change of local lightning stroke caused by the interannual climate change and location system update.

Referring to Birkl et al. (2016), as shown in Figure 2a, the impact area of each WT is within each circle with a certain radius, which means the lightning strikes in the area are attracted by the WTs. According to the observation results of Wilson et al. (2013), the radius of the impact area of a single WT is determined, which is 2.2 times the WT height.

Figure 2. (a) The impact area of a WT, (b) the impact area of WTC (A1), the impact sub-area of the WTs (A1–A10), the reference area (A4–A10), and the OA and IA (the blue area is the OA and the red area is the IA).

The calculated influence radius D of each WT is determined to be 320 m. The value is larger than the location error of GHMLLS, which can ensure the reliability of the result. In order to verify the rationality of the affected area, we analyze the change in the average stroke density with the radius of WTs. As shown in Figure 2b, radius values range from D to 10D, with intervals of D. Mark A1 (blue and red circular area) in the range D around WTs, A2 in the range D to 2D around WTs, and so on.

The influences of WTs at the inner and outer sides of the WTC on lightning strikes are different. To study this difference, we divide the coverage area of the WTC into the outer area of the WTC and the inner area of the WTC. As shown in Figure 2b, the blue circles are the OA (outer area), and the red circles are the IA (inner area).

A CG lightning flash can contain multiple strokes. The information of CG flashes is obtained from the information of strokes. Clustering the strokes into CG flashes is first. Referring to H. Chen et al. (2021), The criteria for clustering strokes into CG lightning flashes are as follows: (a) the time interval between strokes shall be less than 500 ms; (b) the distances of strokes are within 10 km. Take the average location of the strokes within a CG lightning that are close to each other as the location of the CG lightning.

The detection efficiency of GHMLLS is different during TB and TA periods due to being upgraded in 2018. It is necessary to normalize the analyzed data and the normalization coefficient ρ is defined as $$\rho =\frac{{F}_{A}}{{F}_{B}}$$, where $${F}_{B}$$ is the arithmetic average value of lightning parameter (such as stroke density, average peak current, and so on) in the reference area during TB period and $${F}_{A}$$ is the arithmetic average value of lightning parameter in the reference area during TA period.

To avoid the impact caused by the WTC, the reference area is defined as A4–A10 area. The CR (change rate) of lightning stroke characteristics before and after installation of the WTC can be defined as $$\mathrm{C}\mathrm{R}=\frac{L\left({T}_{A}\right)-L\left({T}_{B}\right)\times \rho }{L\left({T}_{B}\right)\times \rho }\times 100\%$$, where L is the lightning parameter within the influence range of the WTC. In the following analysis, all the lightning location data are normalized to avoid the influence of the upgrading of the location station network and the annual change in lightning activities.

Results The Impact Area of the WTs

Figure 3 shows the average stroke density and its change rate in each sub-area (A1–A7) during TB and TA periods. During TB and TA periods, the average value of the stroke density in the whole area was 14.6 and 16.9 year⁻¹ km⁻², respectively. The changes during TB and TA periods were caused by the upgrading of the location station network and the annual change in lightning activities. The change rate of the average stroke density in A1 area during TA period was approximately 10% higher than that during TB period. It can be seen that the stroke densities in A2 and A3 areas decrease by about 17.4% and 12.9% respectively. However, in A4–A10 area, the change in the average stroke density is relatively small, which indicates that the WTs can attract more lightning strokes in A1 area and affect the lightning strokes in A2 and A3 areas. It also proves the reliability of the reference area we set in Section 2.

Figure 3. The average stroke density and the corresponding change rate in each sub-area during TB and TA periods (year−1 km−2).

The Characteristics of Lightning Strikes in the Whole WTC

Table 1 shows the average density of strokes and CG flashes in the whole affected area, the areas of outer and inner sides WTs, as well as the reference area during TB and TA periods. Within the influence range of the whole WTC, the average stroke density, and the average CG flash density were 16.2 and 21.4 year⁻¹ km⁻², 9.6 and 10.8 year⁻¹ km⁻², respectively, during TB and TA periods. Compared with that during TB period, the average stroke density within the affected area of the WTC during TA period increased by approximately 10.1%, and the average CG flash density increased by approximately 11.0%. During TA period, the average stroke and CG flash density increased, which was consistent with the observation results of some scholars (Birkl et al., 2016; H. Chen et al., 2021; Soula et al., 2019).

Table 1 Average Density of Stroke and CG Flash During TB and TA Periods

Event	Period	Whole WTC	OA	IA	Reference area
Stroke density	TB	16.2	16.2	16.3	14.7
	TA	21.4	23.6	15.6	17.7
	Change rate	10.1%	21.0%	−20.2%	/
CG flash density	TB	9.6	9.6	9.8	10.9
	TA	10.8	11.2	9.7	11.0
	Change rate	11.0%	16.1%	−1.7%	/

Note. The data in all Tables are the original data $$(L\left({T}_{B}\right)$$ and $$L\left({T}_{A}\right))$$.

Lightning multiplicity defined as the number of strokes contained in a lightning flash is shown in Table 2. It can be seen that the lightning multiplicity within the influence range of the whole WTC was almost unchanged during TA period, which was smaller than the research results of H. Chen et al. (2021). This can be caused by the distribution difference of WTC; the WTC is a linear distribution in the paper (H. Chen et al., 2021).

Table 2 Lightning Multiplicity and Change Rate in the WTC During TB and TA Periods

Period	Whole WTC	OA	IA	Reference area
TB	1.7	1.7	1.7	1.4
TA	2.0	2.1	1.6	1.6
Chang rate	−1%	4.1%	−19.0%	/

Table 3 shows the statistical results of positive and negative stroke events during TB and TA periods. The proportion of negative strokes for the whole WTC was 97.1% and 97.1% during TB and TA periods, respectively. The proportion of negative strokes increased by approximately −0.2% during TA period. This change is not significant.

Table 3 Statistical Results of Positive and Negative Stroke Events in the WTC

Event	Period	Whole WTC	OA	IA	Reference area
Negative strokes	TB	857	630	227	4,896
	TA	850	690	160	4,440
	Change rate	9.3%	20.7%	−22.3%	/
Positive strokes	TB	26	19	8	345
	TA	25	17	7	260
	Change rate	18.7%	10.5%	8.0%	/
Proportion of negative strokes	TB	97.1%	97.1%	96.6%	94.9%
	TA	97.1%	97.6%	95.8%	95.4%
	Change rate	−0.2%	0.2%	−1.2%	/

Considering that there are few positive strokes in the study area, the dispersion of the statistical method of density distribution is too high, so the follow-up research only focuses on the negative strokes. During TB period, the average and median peak current of the whole WTC area was −19.1 and −14.7 kA, respectively. In contrast, during TA period, the average and median peak current within the influence range of the whole WTC was −16.5 and −11.3 kA, respectively. After the installation of the WTC, the average and median peak current of negative strokes within the influence range of the WTC increased by 5.1% and 1.1%.

Differences in Lightning Strikes Between the OA and IA

In Section 3.1, we analyze the change in lightning strikes within the influence range of the whole WTC during TA period. The characteristics of lightning strikes in the whole WTC are basically consistent with the previous observation results. However, the shielding effect of the outer side WTs on the inner side WTs in a planar-distributed WTC may bring about differences between the OA and IA. Considering this situation, we analyze the differences in lightning strikes in the OA and IA at the planar distributed WTC in this section.

As shown in Table 1, in the OA, the average stroke density and CG flash density were 16.2 and 9.6 year⁻¹ km⁻², respectively, during TB period. They were 23.6 and 11.2 year⁻¹ km⁻², respectively, during TA period. The average stroke density increases by 21.0%, and the average CG flash density increases by 16.1%. In the IA, the average stroke density and CG flash density were 16.3 and 9.8 year⁻¹ km⁻², respectively, during TB period and 15.6 and 9.7 year⁻¹ km⁻², respectively, during TA period. In the IA, the average stroke density decreases by 20.2%, and the average CG flash density decreases by 1.7%. The average stroke and CG flash density in the OA increase, while the average stroke and CG flash density in the IA decrease.

To study the difference in stroke distribution between the OA and the IA during TA period, this paper analyzes the stroke position within the influence range of the whole WTC. As shown in Figure 4, during TB period, the distribution of strokes within the influence range of the WTC was dispersed throughout the influence range of the WTC. The average stroke density of the OA mentioned above was 16.2 year⁻¹ km⁻², and the average stroke density of the IA was 16.3 year⁻¹ km⁻². There was little difference in the stroke density between the OA and the IA during TB period. In contrast, high-value areas of strokes were only distributed at the OA during TA period. The average stroke density in the OA was 23.6 year⁻¹ km⁻² and that in the IA was 15.6 year⁻¹ km⁻² during TA period. The average stroke density in the OA is greater. The difference between the OA and IA may be caused by the shielding effect of the outer side WTs on the inner side WTs.

Figure 4. The distribution of strokes within the influence range of the WTC during TB (a) and TA (b) periods (the stroke density unit in the figure is year−1 km−2), and the resolution is 100 × 100 m (Black triangles refer to the outer side WTs, and red triangles refer to the inner side WTs).

Figure 5. Location distribution of negative strokes (the stroke density unit in the figure is year−1 km−2). Strong strokes (a) and weak strokes (b) during TB period, strong strokes (c) and weak strokes (d) during TA period (black triangles refer to the outer side WTs, red triangles refer to the inner side WTs, the resolution is 100 × 100 m).

Lightning multiplicity can be seen in Table 2. The lightning multiplicity in the OA increases by 4.1% from 1.7 during TB period to 2.1 during TA period. However, the lightning multiplicity in the IA decreases from 1.7 during TB period to 1.6 during TA period, a decrease of approximately 19.0%. The lightning multiplicity in the OA and IA were equivalent during TB period, while the lightning multiplicity in the OA was greater during TA period. The lightning multiplicity in the IA is obviously reduced.

According to the statistical results in Table 3, the proportion of negative strokes in the OA was 97.1%, slightly less than 96.6% in the IA during TB period. During TA period, the proportions of negative strokes in the OA and IA were 97.6% and 95.8%. Although the changes in the proportion of negative strokes in the OA and IA are little, the amount of negative strokes in the OA increases by 20.7%, and that in the IA decreases by 22.3%.

As shown in Table 4, during TB period, the average peak current and median peak current in the OA were approximately −19.1 and −14.6 kA respectively, while the average peak current and median peak current in the IA were approximately −19 and −15.1 kA respectively. The average peak current and median peak current in the IA are similar to that in the OA. However, during TA period, the average peak current and median peak current in the OA were approximately −16.8 and −11 kA respectively, and the average peak current and median peak current in the IA were approximately −15 and −9.6 kA respectively. The average peak current and median peak current in the IA during TA period were all smaller than that in the OA, which were different from that during TB period. The average peak current and median peak current of negative strokes show different characteristics in different areas of the WTC, which increase by approximately 6.8% and 5.2% respectively in the OA while these in the IA decrease by approximately 3.9% and 19.5% respectively.

Table 4 Average and Median Peak Current of Negative Strokes in Different Areas of the WTC During TB and TA Periods

Event	Period	Whole WTC	OA	IA	Reference area
Average peak current (kA)	TB	−19.1	−19.1	−19	−19
	TA	−16.5	−16.8	−15	−15.6
	Change rate	5.1%	6.8%	−3.9%	/
Median peak current (kA)	TB	−14.7	−14.6	−15.1	−14.4
	TA	−11.3	−11.7	−9.6	−11
	Change rate	1.1%	5.2%	−19.5%	/

Considering the difference in peak current of negative strokes between the OA and IA, this study divides the peak current into strong strokes (the peak current greater than 40 kA) and weak strokes (stroke peak current less than 15 kA) for further analysis. Table 5 shows the densities and changes of different peak current of negative strokes in the OA and IA during TB and TA periods. The average density of strong negative strokes increases by approximately 28.0% in the OA but decreases by approximately 42.6% in the IA. The average density of weak negative stroke increases by approximately 15.7% in the OA and decreases by approximately 17% in the IA.

Table 5 Average Density of Negative Strokes With Different Peak Currents in the Area of the Outer and Inner Side WTs During TB and TA Periods

	OA		IA		Reference area
Period	Strong peak current	Weak peak current	Strong peak current	Weak peak current	Strong peak current	Weak peak current
TB	1.5	8.1	1.2	7.8	1.4	8.3
TA	1.6	13.6	0.6	9.4	1.1	12.0
Change rate	28.0%	15.7%	−42.6%	−17%	/	/

We further analyze the position distribution of strong and weak strokes. As shown in Figures 6a and 6b, it can be seen that the high-value areas were distributed in the whole WTC during TB period no matter the strong or weak stroke current. In Figures 6c and 6d, it can be seen that the high-value areas were all concentrated at the OA, and there was basically no high-value area inside during TA period. We could see that the reduction of weak stroke density is smaller than that of strong stroke density in the IA during TA period from Table 5. The increase of weak stroke density is smaller than that of strong stroke density in the OA during TA period. Different from the strong strokes, it can be seen from Figure 5 that the weak strokes are distributed in a small high-value area in the IA, which may indicate the shielding effect of the outer side WTs on the inner side WTs in the case of strong strokes is more obvious than that of weak strokes.

Figure 6. The electric potential distribution on four horizontal cross-sections of the simulation area. (a) 300 m height, (b) 450 m height, (c) 600 m height, (d) 750 m height (blue dots represent outer side WTs, red dots represent inner side WTs).

Simulation

To study the mechanism of the distribution of lightning strikes in the WTC in Section 3 and the reasons for the difference in lightning strikes between the OA and IA, the three-dimensional space electric potential distribution of the WTC is simulated.

The simulation area selected for this study is 10,000 × 10,000 × 1,500 m, with a grid point resolution of 10 × 10 m. It is assumed that the spatial background electric field within 1,500 m above the ground increases linearly with increasing height and that the electric field increases 0.06 kV/m for every 1 m increase in height (Biagi et al., 2011). The ground background electric field is set as −2 kV/m, and the upper boundary electric field is set to −92 kV/m. The position of each WT in the WTC is arranged according to the actual situation. The height of each WT model is 150 m, and the blade length is 40 m. The angle of each WT model blade is the same. The WTs and the ground meet the Dirichlet boundary conditions, set as 0 V, and the air boundary meets the Newmann boundary conditions. The spatial electric potential in the simulation region meets the Poisson equation, and the overrelaxation iterative algorithm in MATLAB is used to solve the spatial electric potential distribution. The potential iteration formula is as follows: [Image Omitted. See PDF]where ω (Li et al., 2015) is the optimal value of the relaxation factor: $$\omega =\frac{2}{1+\sqrt{1-{\left[\frac{\mathrm{cos}\left(\frac{\pi }{x}\right)+\mathrm{cos}\left(\frac{\pi }{y}\right)+\mathrm{cos}\left(\frac{\pi }{z}\right)}{3}\right]}^{2}}}$$, where x, y, and z are the number of meshes in three directions of the 3D simulation space.

Taking into consideration the effective height of WTs, the results of electric potential distribution simulation showing that the lowest height is 300 m above ground were given. Figure 6 shows the results of the electric potential distribution simulation at heights of 300, 450, 600, and 750 m above the ground. Although the distortion effect of WTs on spatial electric potential at the OA and IA is relatively strong, the differences in the electric potential distribution between the OA and IA are not obvious at a relatively low height. However, at an increased height, the electric potential line directly above the OA is dense while that is sparse above the IA, which indicates that the distortion effect of the outer side WTs on spatial electric potential is stronger than that of the inner side WTs. The trend becomes more obvious with increasing height.

Discussion Lightning Strike Regularity of the Whole WTC

During TA period, it can be seen that the average stroke density within the influence range of the WTC increased by 10.1%, which was similar to the previous lightning strike events attracted by tall buildings. From the simulation results of the three-dimensional spatial electric potential distribution in Section 4, the electric potential line above the WTC is much denser than that far from the impact area of the WTC, regardless of the height, which leads to the WTC attracting more CG lightning flashes. The amount of negative strokes increases by 9.3%. From the simulation results, the existence of the WTC leads to the overall enhancement of the electric field. On the one hand, the attraction action on CG lightning flashes has been improved. Downward strokes have become more frequent. On the other hand, it may lead to an increase in upward lightning events. It was reported that most upward lightning discharges are negative. For example, Diendorfer et al. (2011) reported that 94% of the upward lightning observed on the GBT from 2000 to 2009 was negative.

During TA period, the lightning multiplicity within the whole WTC showed almost no change. It may be because this is the comprehensive effect of the two regions of the OA and IA. The lightning multiplicity in the OA increases, while the lightning multiplicity in the IA decreases. If only the outer side WTs is considered, the lightning multiplicity in the OA would increase by 5.5% during TA period. In addition, the WTC is located at sea level. This causes WTs to have a low effective height compared with the WTs reported by H. Chen et al. (2021). The change in lightning multiplicity may not be obvious at a relatively low height.

The average peak current and median peak current of negative strokes within the influence range of the WTC increase, which is also revealed in the lightning strikes of tall buildings. For example, C. Zhang et al. (2016) found that the lightning intensity within 1 km around the Canton Tower was much larger than that in other nearby areas; Diendorfer and Schulz et al. (1998) found that the average peak current of lightning near the GBT tower was 20% stronger than that far from the tower. For lightning flashes on WTs and tall buildings, the stroke current wave will be reflected by the bottom of the buildings or the WTs and superimposed on the original current. The electric field and magnetic field generated by the stroke will be enhanced. The location system generally reverses the peak current through the electromagnetic field, so the peak current intensity given will be increased accordingly. For example, Romero et al. (2011) compared the measured data of the stroke on the Säntis Tower with the lightning peak current detected by EUCLID and found that the peak current detected by EUCLID was on average larger than the measured peak current.

The Difference in Lightning Strikes Between the OA and IA

As mentioned in the previous analysis, the high-value areas of negative stroke are distributed in the OA. The outer side WTs reflect the shielding effect on the inner side WTs. According to the simulation results of the spatial electric potential distribution in Section 4, the distortion effect of the outer side WTs is obviously stronger than that of the inner side WTs at a higher height. The downward negative leaders of negative CG lightning flashes tend to develop toward places with a large potential gradient, that is, places with a strong electric field (Coleman et al., 2003; Tan et al., 2006; Xu et al., 2021). Therefore, the development paths of negative leaders more easily pass above the OA. As a result, there is a greater probability that it will be connected with the upward leaders originating from the outer side WTs. This explains why the average stroke density in the OA increased while that in the IA decreased during the TA period.

The shielding effects of the outer side WTs to the inner side WTs lead to the reduction of the strokes connected with the inner side WTs during TA period. Therefore, the decrease in lightning multiplicity in the IA during TA period may be caused by the decrease in the negative CG lightning flashes.

We also find that the distributions of negative strokes with different intensities at the outer and inner side WTs were different. This may be related to the distribution of the spatial electric potential at different heights above the WTC. In terms of downward lightning flashes, we know that the striking distance is related to the stroke intensity (Cooray et al., 2007; Love, 1973; Visacro et al., 2017). In terms of strong strokes, their striking distance is large. They can be connected with the upward leaders originating from WTs at a higher height. According to the electric potential distribution simulation (Figure 6), the difference in the electric potential between the OA and IA at a higher height is obvious. Strong strokes are more likely to be attracted by the outer side WTs with stronger electric potential gradient. Therefore, the increase in the average density of strong strokes in the OA is more obvious.

In contrast, weak strokes have short striking distances (Vogt, 2011), so the downward leaders need to develop downward to a relatively low height. According to the simulation of electric potential distribution above the WTC (Figure 6), there is little difference in the electric potential distribution between the OA and IA at relatively low heights. Therefore, the difference between the probability of the weak stroke connecting the outer and inner side WTs in the WTC is small. Besides, there are some upward lightning discharges in WTCs (Becerra et al., 2018; G. Diendorfer et al., 2011). The shielding effect may be weak on upward lightning (X. Wang et al., 2021), and because the stroke peak currents of upward lightning are usually weak, these may result in a smaller change in the average density of weak strokes than that of strong strokes in the IA.

Conclusions

This paper analyzes the lightning strikes of an offshore wind farm. The characteristics of lightning strikes between the OA and IA are different. We simulate the distribution of spatial electric potential at different heights above the WTC. In addition, we explain the characteristics of lightning strikes in the WTC and the differences between the OA and IA. The following conclusions are drawn in this paper:

1. During TA period, the average stroke density within the impact area of the WTC increased by 10.1%, the average CG flash density increased by 11%, the lightning multiplicity was almost unchanged at 2.0, the proportion of negative strokes changed little, and the average peak current and median peak current of negative strokes increased by 5.1% and 1.1%.

2. There are differences in lightning strike regularity between the OA and IA. During TA period, the average stroke density in the OA increased by 21%, the average stroke density decreased by 20.2% in the IA, and the average CG flash density increased by 16.1% in the OA and decreased by 1.7% in the IA. The lightning multiplicity in the OA was 2.1, with an increase of approximately 4.1%, while the lightning multiplicity in the IA decreased by 19%. Although the change in the proportions of negative strokes in the OA and IA was little, the amount of negative strokes in the OA increased by 20.7%, and that in the IA decreased by 22.3%.

3. In terms of peak current, the average peak current and median peak current of the negative stroke increased by 6.8% and 5.2% in the OA but decreased by 3.9% and 19.5% in the IA. The average density of strong negative strokes increased by 28% in the OA and decreased by 42.6% in the IA. The average density of weak negative strokes increased by 15.7% in the OA and decreased by 17% in the IA.

4. The three-dimensional electric potential distribution simulation results of the WTC show that in the lower height, the difference between the electric potential distribution of the outer and inner side WTs is small. However, the electric potential line above the OA is denser than that above the IA at a relatively high height. Such a spatial electric potential distribution can explain the characteristic of lightning strike distribution found in this study.

It should be noted that the CG lightning location data used in this paper cannot distinguish whether the CG lightning flashes are upward lightning events or downward lightning events. There are not only downward lightning flashes but also a lot of upward discharges in the WTC. In the future, it will be necessary to analyze the upward discharges in the WTC in detail in combination with data such as the waveform of the electric field.

Acknowledgments

This research was funded by the National Key Research and Development Program of China (2017YFC1501501, 2019YFC1510103), the National Natural Science Foundation of China (41775009, 42175090, and 41905004), S&T Development Fund of CAMS (2023KJ050), and the Basic Research Fund of Chinese Academy of Meteorological Sciences (Grant 2021Z011).

Data Availability Statement

The data used in this paper can be obtained from Zenodo at the following Zou et al. (2023), https://doi.org/10.5281/zenodo.7759118 or from the corresponding author ([email protected]).