Experimental Study on Wind Load of Large-Span Flexible Photovoltaic Structure Considering Different Tilt Angles

Abstract

Due to their light weight, low stiffness, and large range of tilt angle changes, flexible-support photovoltaic structures are highly sensitive to wind loads. Therefore, it is necessary to study the wind load characteristics under large tilt angles and determine reasonable design wind loads. This paper investigates the wind load characteristics of large-span flexible-support PV arrays with different tilt angles through wind tunnel pressure measurements. The results indicate that, in terms of mean wind pressure coefficient, 0° and 180° are the most unfavorable wind direction angles. The first row at the edge of the array is the most unfavorable location, and its shape coefficient is recommended to be 1.3 (for wind pressure) or −1.25 (for wind suction), with subsequent rows of PV panels being appropriately reduced based on this value. The tilt angle of the PV panels significantly affects the shading effect, and under large tilt angle conditions, there is an abrupt drop in the mean wind pressure coefficient and fluctuating wind pressure coefficient of the second row facing the wind. Under large tilt angles, the critical wind direction angles for local extreme wind loads are within the ranges of 15–45° and 135–165°, and the most unfavorable locations occur in the corner areas at the edges of the array. Local extreme wind loads should be considered in the design.

1. Introduction

As the key role of renewable energy in achieving carbon neutrality becomes increasingly prominent, over the past few decades, photovoltaic (PV) technology, as an important alternative to fossil energy, has been widely promoted and applied worldwide [1]. However, due to the low stiffness and light mass of PV panels, wind loads have become the main controlling loads. In the post-disaster investigations of damage [2], large-scale wind-induced damage to PV structures was observed. The essence of this is that the extreme wind loads caused by extreme wind climates exceed the design threshold of the structure [3], or that wind-induced fatigue damage leads to a reduction in the load-bearing capacity of critical components [4]. Therefore, it is very necessary to conduct a comprehensive study on the wind-induced effects on PV structures. Initially, PV panels were mainly installed on building roofs to form PV-building integrated systems [5]. Many scholars have conducted wind tunnel tests on roof-mounted PV structures to explore their wind load distribution, interference effects, and impacts on roof design wind loads [6,7,8]. These studies have revealed that the array gap and PV tilt angle are key factors affecting the wind load of roof-mounted PV arrays [9,10,11,12]. Compared with small-scale roof-mounted PV systems, near-ground large-span PV systems, with their broad application prospects and higher energy-harvesting efficiency, have been widely deployed in open areas such as mountains and the Gobi in recent years. The stable operation of PV arrays highly depends on their supporting structures, which are not only directly related to the operational safety of PV power stations, but also significantly impact the construction investment costs. Well-designed PV supporting structures can effectively reduce the costs in the construction and maintenance processes. At present, PV supporting systems are mainly divided into four types: fixed, flexible, floating, and tracking supporting systems. Among them, flexible PV supporting systems are widely used because of their excellent spanning capabilities that enable better adaptation to different terrains. Tracking supporting systems are favored for their ability to significantly increase power generation and efficiency [13]. Therefore, the tracking-type flexible PV supporting system, which combines good terrain adaptability and high power-generation efficiency, has emerged. However, given the sensitivity of PV components to wind loads and the complex wind load distribution caused by the tilt angle adjustment of large-span flexible-supporting systems, it is highly challenging to determine the design wind loads for PV structures with different tilt angles. Therefore, it is of great practical significance to conduct systematic experimental research on the effects of different tilt angles on the wind load on the surface of large-span flexible PV structures.

To accurately determine the wind effects on PV structures, previous studies have conducted in-depth investigations on the design wind loads, wind-induced vibrations, and shading effects of large-span PV structures through means such as wind tunnel tests, field measurements, and computational fluid dynamics (CFD) simulations. The wind tunnel tests on independent PV panels conducted by Abiola-Ogedengbe et al. [14] showed that under typical wind directions, the pressure coefficients on the surface of the structure are symmetrically distributed, and both the panel spacing and tilt angle significantly affect the surface pressure distribution. Debnath et al. [15] systematically studied the design wind pressure coefficients of tracking PV arrays by integrating wind tunnel tests, CFD simulations, and finite element analysis techniques, and found that the edge and corner PV panels will bear extreme wind loads. Regarding the research on wind loads of PV structures under different topographical conditions, Xu et al. [16] used CFD simulations to model PV structures on a two-dimensional hill surface and found that the wind load in the hilltop area can increase by 150–280%, while the wind load in the hill-foot area can be reduced by 80%. It is recommended to focus on the design of PV structures within the range of 0.2 times the hill length from the top. The wind tunnel test results of Yao et al. [17] based on hilly terrain showed that when the slope is 30°, the positive and negative pressure peaks at the hilltop increase by 19% and 27.5%, respectively, and increasing the height of the PV structure above the ground will further amplify the wind load. Given the unique structural form of PV arrays, their shading effect is particularly significant. The study by Xu et al. [18] found that increasing the row spacing can significantly weaken the shading effect on the rear PV panels, with the most noticeable load changes occurring in the second row facing the wind. The wind tunnel test results of Ding et al. [19] also confirmed that large-span flexible PV structures are significantly affected by the shading effect of the front PV panels, and the shading effect should be a key focus in the study of such structures.

In flexible PV structures with low stiffness, fatigue damage caused by wind-induced vibrations and the failure of key components are particularly prominent issues. The aeroelastic tests on a 45 m-span flexible PV support structure conducted by Zhou et al. [20] showed that increasing the tilt angle of the PV panels can significantly reduce the wind-vibration response of the structure and pointed out that the equivalent static wind load values in current codes are relatively conservative. The wind tunnel tests on cable-supported PV structures by Xu et al. [21] showed that the vertical wind-vibration response increases with the tilt angle of the PV panels but decreases with the increase in cable pre-tension, and the gust response factor is in the range of 1.1 to 2.5. The analytical study by Zhu et al. [22] also showed that the tilt angle has a significant effect on the wind-vibration coefficient of flexible PV structures. The aeroelastic tests on a 35 m-span double-cable-supported PV structure by Wu et al. [23] revealed that the 0° wind direction is the most unfavorable wind direction angle, and the critical wind speed decreases with the increase in the tilt angle. The test results by Liu et al. [24] showed that the critical wind speed of the flexible PV structure is only 18.5 m per second. Wu et al. [25] found that by adding connection cables and inclined cables, the critical wind speed of the flexible PV structure can be increased to 45 m per second. In addition, several studies [26,27] have shown that reducing the structural span, increasing the pre-tension of the upper cables, and increasing the damping ratio can all significantly increase the flutter critical wind speed. Li et al. [28] pointed out that turbulence intensity is the key factor in the wind-induced vibration of PV structures and proposed an empirical GRF model that takes into account the effects of incoming turbulence, PV panel tilt angle, and wind speed.

In summary, the wind effects on PV structures are influenced by a combination of factors such as structural form, row spacing, height above ground, and tilt angle. A large number of experimental studies have shown that tilt angle has a significant impact on the design wind load, shading effect, and critical wind speed of PV structures. Field measurement studies [29,30] also support this conclusion, showing that tilt angle and wind direction significantly alter the pressure distribution on the panel surface, with high tilt angles combined with specific wind directions being the most dangerous. Meanwhile, the shading effect weakens as the tilt angle decreases, and the vortex shedding frequency is highly sensitive to tilt angle and wind direction. Based on this, Bao et al. [31] investigated the non-Gaussian characteristics of the measured wind loads on PV structures and found that the non-Gaussian wind pressure peaks are 30–50% higher than those of the traditional Gaussian method. Fu et al. [32] also found that wind direction and tilt angle significantly affect wind pressure distribution, and when the tilt angle is greater than 25°, the wind load fluctuation intensifies, a factor not yet fully considered in current codes. Given this, it is of great engineering application value and theoretical significance to conduct a systematic study on the wind pressure distribution, shading effect, and non-Gaussian characteristics of large-span flexible PV structures (with a large range of inclination angles, from −60° to 60°) under different inclination conditions in order to determine their design wind loads. Based on this, this paper will conduct an in-depth investigation on the wind pressure distribution, shading effect, and non-Gaussian characteristics on the surface of flexible PV structures with a large range of inclination angles to make up for the current deficiency in the design of wind loads for photovoltaic arrays, considering large inclination angle variations. This will provide a theoretical basis for the safe design and code formulation of such structures.

This study conducts a rigid-model wind tunnel pressure test on an 8-row and 2-span flexible-support PV array to explore the effects of wind direction angle and array position on the wind load characteristics of PV panels under different PV tilt angles, and expects that the relevant results can provide a scientific basis for the wind-resistant design of large tilt angle flexible PV structures. The main structure and content of this paper are as follows: Section 2 details the design scheme, implementation process, and related technical details of the rigid-model wind tunnel test. Section 3 systematically analyzes the distribution patterns of mean and fluctuating wind pressure coefficients under different tilt angle conditions and deeply dissects the quantitative impact mechanism of the shading effect on wind pressure coefficients. Section 4 focuses on the non-Gaussian characteristics of wind pressure on the surface of PV structures under different tilt angle conditions and elaborates on their significant impact and intrinsic correlation with extreme wind pressure coefficients. Section 5 comprehensively summarizes the core work achievements of this study and objectively points out the limitations and areas for improvement in the research process.

2. Wind Tunnel Experiments

2.1. Experimental Arrangements

The wind tunnel pressure test for the large-span flexible-support PV array was implemented in an atmospheric boundary layer wind tunnel. The wind tunnel adopts a horizontal-return structure, with a test section of 4.5 m wide × 2.0 m high × 20.0 m long, equipped with a turntable of 3.5 m in diameter. The wind speed range in the central area of the test section can cover 0 to 30 m/s, with a minimum stable wind speed of 2.0 m/s. The main flow field characteristics of the incoming flow in this area meet the following key indicators: velocity inhomogeneity < 1.5%, turbulence intensity inhomogeneity < 1%, axial static pressure gradient ≤ 0.015/m, and mean flow direction angle < 0.5°. The diameter of the turbulent core area is about 1.5 m. The target atmospheric boundary layer flow field simulated in this test corresponds to the Class B terrain defined in the Code for Loads of Building Structures (GB 50009-2012) [33]. The reference height is taken as 0.16 m. To achieve the target wind profile and turbulence characteristics, a combination of wedges, serrated plates, and ground roughness elements was arranged upstream of the wind tunnel test section. Figure 1 shows the measured mean wind speed profile and turbulence intensity profile. The results show that the simulated wind speed profile conforms to the power-law distribution characteristics of Class B terrain, and the turbulence intensity distribution also matches well with the recommended values in the code, meeting the requirements of this test for the incoming flow conditions.

2.2. Pressure Taps Arrangement and Wind Direction Setting

The test subject is a prototype structure of a large-span flexible-support PV array with 8 rows × 2 columns. The prototype single-bay support has a span of 35 m, with two columns of 400 mm in diameter and 4 m in height, and a row spacing of 6 m. Each support carries 28 monocrystalline silicon PV modules (2278 mm × 1134 mm × 50 mm), with a horizontal spacing of 15 mm between modules. The PV modules are supported by four high-strength steel cables located at their lower part. The ends of the cables are anchored to the steel cross-beams at the top of the columns and are prestressed by tensioning devices. The test model was made according to a geometric scale ratio of 1:25. Accordingly, the model's single-bay span is 1400 mm, the total width of the double-column is 2800 mm, the row spacing is 240 mm, and the center height of the PV panel is 160 mm. The model design tilt angle can be adjusted up to a maximum of 60°. Considering the stiffness requirements of the model structure, the space for the internal pre-buried pressure-measuring pipelines in the panel, and the feasibility of model processing, the theoretical thickness of the PV panel model (which should be ≈2 mm according to the scale ratio) was increased to 10 mm. The PV panel model was made of PMMA (acrylic) sheet, and the model cross-beams and columns were precision-machined from stainless steel. On each model bay, wind pressure taps are arranged on both the upper and lower surfaces corresponding to the center position of each PV panel (i.e., the tap positions on the upper and lower surfaces are directly opposite). The overall structural schematic diagram of the model and the detailed tap arrangement are shown in Figure 2.

Based on the selected geometric scale ratio of 1:25, the 15 mm gap between the prototype PV panels corresponds to a theoretical dimension of 0.6 mm in the model. Given that this gap size is too small, without compromising the overall aerodynamic shape of the model, the gaps between each PV panel were not individually simulated during fabrication. Instead, the 28 PV panels on each single model bay were treated as a continuous integral panel. To simulate the prestressing effect of the prototype steel cables and enhance the overall rigidity of the model (to reduce panel vibration during testing), two bright, round steel bars with a diameter of 8 mm were pre-embedded along the length of each integral panel model. The ends of the steel bars were threaded, passed through the reserved holes in the cross-beams at the top of the columns, and then prestressed and tightened with high-strength nuts to create axial tension within the steel bars. The columns were connected to the cross-beams with bolts, a design that allows for the adjustment of the cross-beam angle and thus the precise setting of the PV panel tilt angle (from 0° to 60°). The column bases were securely fixed to the wind tunnel turntable with screws. The pressure-measuring pipelines were led out from the side edge of the panel close to the column (to avoid interference from the windward/leeward side) and routed down along the inside of the column or through the pre-opened grooves, finally converging and connecting to the pressure-scanning valve system beneath the turntable. The structural composition and layout of the overall PV array model are shown in Figure 3.

Given the geometric scale ratio of 1:25 and the wind speed scale ratio of 1:2.5, the time scale ratio can be calculated as 1:10. The test wind speed was 10 m/s, with a reference point height of 0.16 m. The sampling frequency of the high-frequency electronic pressure-scanning valve was 330 Hz, and the sampling time for each condition was 360 s, resulting in a total of 118,800 data points, which corresponds to 60 min of sampling on the prototype structure. This sampling duration complies with the provisions of the Standard for wind tunnel test of buildings and structures (JGJ/T 338-2014) [34] regarding the sampling duration of wind load data on the prototype structure. There was a total of 56 taps on the upper and lower surfaces of a single PV panel in the test, and the total number of taps for the 16 PV panel models was 896. Due to limitations on the number of scanning valves and the length of the pressure-measuring pipelines, four scanning valves (with a total of 256 channels) were used in the test to measure the wind pressure on four PV panel models (a total of 224 taps) in two rows and two columns during a single measurement. The PV array was divided into regions, and four repeated measurements were conducted on the entire array during the test.

Considering the bilateral symmetry of the PV array model, the range of simulated wind direction angles was set from 0° to 180°, with an interval of 15°. Different wind directions were achieved by precisely controlling the rotation angle of the wind tunnel turntable. The tilt angles of the PV panel system were set at 0°, 5°, 15°, 30°, 45°, and 60°, totaling six key tilt angles. The tilt angle is defined as the angle between the plane of the PV panel and the horizontal plane. The tilt angle adjustment was realized by changing the angle of the steel cross-beam at the top of the column, and the structural design ensured the stability and repeatability of the tilt angle setting. The numbering of the PV array models and the schematic diagram of the test wind direction angles are shown in Figure 4.

2.3. Wind Pressure Coefficients

To facilitate the conversion of wind tunnel pressure test model data to the wind loads on the actual structure, the dimensionless wind pressure coefficient $C_p$ is used to describe the test results. The wind pressure coefficient is defined as the ratio of the pressure caused by the incoming wind on the surface of the PV panel to the reference velocity pressure measured at the reference height. The instantaneous wind pressure coefficient at each tap is expressed as follows:

$$C_{pi}\left(t\right)={\displaystyle \frac{P_i\left(t\right)-P_{\infty }}{P_0-P_{\infty }}}$$

(1)

where $C_{pi}\left(t\right)$ represents the time-history of the wind pressure coefficient at tap $i$. $P_i\left(t\right)$ is the time-history of the wind pressure measured at tap $i$. $P_0$ and $P_{\infty }$ represent the average total pressure and average static pressure measured by the pitot tube at the reference height during the test, respectively. When the wind pressure coefficient is positive, the wind-induced force acts perpendicularly to the PV panel and points inward, representing wind pressure. When the wind pressure coefficient is negative, the wind-induced force acts perpendicularly to the PV panel and points outward, representing wind suction. The formulas for calculating the mean and fluctuating wind pressure coefficients are as follows:

$${\overline{C}}_{pi}={\displaystyle \frac{1}{N}}{\sum }_{t=1}^N{C}_{pi}(t)$$

(2)

$${\tilde{C}}_{pi}=\sqrt{{\displaystyle \frac{1}{N-1}}{\sum }_{t=1}^N{\left[C_{pi}\left(t\right)-{\overline{C}}_{pi}\right]}^2}$$

(3)

where $N$ is the total number of times the wind pressure data is collected at taps. The mean wind pressure coefficient reflects the average statistical characteristics of the vortices formed by the incoming wind on the surface of the structure and roughly indicates whether the wind force on the surface is suction or pressure. The fluctuating wind pressure coefficient, on the other hand, represents the fluctuating characteristics of the wind pressure time-history, with its value indicating the degree of dispersion of the wind pressure time-history. From the above equation, the skewness and kurtosis of wind pressure can be calculated as follows:

$$C_{pi,ske}={\displaystyle \frac{1}{N}}{\sum }_{t=1}^N\left[{\left({\displaystyle \frac{C_{pi}(t)-{\overline{C}}_{pi}}{{\tilde{C}}_{pi}}}\right)}^3\right]$$

(4)

$$C_{pi,kur}={\displaystyle \frac{1}{N}}{\sum }_{t=1}^N\left[{\left({\displaystyle \frac{C_{pi}(t)-{\overline{C}}_{pi}}{{\tilde{C}}_{pi}}}\right)}^4\right]$$

(5)

In addition to these, the extreme wind pressure coefficient is also of great importance to the design wind load of the structure. Existing studies and codes have adopted various methods to calculate the extreme values of wind loads. However, due to the non-Gaussian characteristics of wind load time-histories, accurate estimation of the extremes is considered to be difficult. Liu et al. [35] proposed a PHPM model that calculates the extreme wind pressure coefficient of wind pressure time-history by defining new statistical moments without any infeasible region. This model is considered to be an accurate and effective method for estimating the extreme values of wind loads. Therefore, the extreme wind pressure coefficient in this study is calculated using this method, and the detailed calculation process can be found in the literature [35] and will not be repeated here.

In addition to the wind pressure coefficient, the overall shape coefficient is usually used to calculate the design wind load in the actual design. The shape coefficient is defined as follows:

$${\mu }_{si}={C_{pi}\left({\displaystyle \frac{Z_r}{Z_i}}\right)}^{2\mathsf{\alpha }}$$

(6)

$${\mu }_s={\displaystyle \frac{\sum {\mu }_{si}{A}_i}{\sum A_i}}$$

(7)

In the equation, ${\mu }_{si}$ represents the local shape coefficient of ith tap. $\alpha$ is the ground roughness exponent. $Z_i$ is the height of ith tap and $Z_r$ is the reference height. The overall shape coefficient is ${\mu }_s$. And $A_i$ is the corresponding surface area of ith tap. In this experiment, the reference height is the same as the height of the central tap of the photovoltaic panel, so the mean wind pressure coefficient of the tap on the PV panel is also defined as the shape coefficient.

3. Analysis of Low-Order Moment Coefficients

3.1. Mean Wind Pressure Coefficient Analysis

The mean wind pressure coefficient is used to characterize the mathematical expectation of the wind pressure coefficient time-history (a random variable) on the surface of the structure and is a key parameter in analyzing the distribution of wind pressure or suction on the surface due to vortices. Zhou et al. [20] pointed out that for large-span flexible photovoltaic (PV) support structures, 0° and 180° are two characteristic wind direction angles, representing the directions facing and opposing the incoming wind, respectively. Figure 5 shows the distribution of mean wind pressure coefficients on the surface of PV panels at 0° and 180° wind directions under various tilt angles in this study. When the tilt angle of the PV panel is 0°, regardless of whether it is at 0° or 180° wind direction, there is no significant distribution feature of the mean wind pressure coefficient. Both suction and pressure points appear on the surface of the PV panel, and the values are relatively small. As the tilt angle increases, the incoming flow at 0° wind direction forms a significant wind-induced pressure at the windward leading-edge panel (A1 or A2), and the maximum absolute value of the wind pressure coefficient at this location increases with the tilt angle, as clearly shown in Figure 6. It is worth noting that once the PV panel has a tilt angle, the 0° wind direction will produce mean wind pressure on all panels (whether windward or leeward). In contrast, the 180° wind direction causes all PV panels to experience mean wind suction due to the vortices formed by the incoming flow, with the maximum absolute value of the mean wind pressure coefficient appearing at the windward leading-edge panel (H1 or H2), which bears a large wind suction. Comparing the values of wind suction and wind pressure at the windward leading-edge under the same tilt angle at 0° and 180° wind directions, the magnitudes of the two are comparable, and the trends with tilt angle are consistent. This indicates that under typical wind directions, the tilt angle of the PV panel has a significant impact on the magnitude of the wind load on its windward leading-edge and is a key factor in the study of wind load characteristics.

To investigate the wind load characteristics of the large-span flexible-support PV array under different wind direction angles, the PV panel models A1, B1, G1, and H1 in the 1st, 2nd, 7th, and 8th rows of the left-hand side of the array were selected to plot the variation curves of the overall net mean wind pressure coefficient with the wind direction angle, as shown in Figure 7. The tests show that PV panel A1 is not affected by the incoming flow from the front PV panels in the wind direction angle range of 0–90°, but is affected in the range of 105–180°. PV panel H1 is not affected by the incoming flow from the front PV panels in the wind direction angle range of 90–180°, but is affected in the range of 0–75°. The rest of the PV panels are affected by the incoming flow from the front PV panels under all wind direction angle conditions. From the variation curves of the overall net mean wind pressure coefficient of PV panel A1 in the wind direction angle range of 0–90° and that of PV panel H1 in the range of 90–180° in Figure 7a,b, it can be seen that under the conditions not affected by the incoming flow from the front PV panels, the maximum values of the overall area mean wind pressure coefficients of the PV panels at all tilt angles appear at the wind direction angles of 0° or 180°. Further analysis of the variation curves of the overall net mean wind pressure coefficient of PV panel A1 in the wind direction angle range of 90–180°, that of PV panel H1 in the range of 0–90°, and those of PV panels B1 and G1 in Figure 7c,d shows that under the conditions affected by the incoming flow from the front PV panels, the maximum values of the overall area mean wind pressure coefficients of the PV panels at all tilt angles appear at the wind direction angles of 30° or 150°. The results in Figure 7 show that the overall net mean wind pressure coefficients of the PV panels at all tilt angles are close to 0 at the wind direction angle of 90°, at which point the tilt angle has little effect on the overall net fluctuating wind pressure coefficient, and the wind load on the PV panels is relatively small. The maximum values of the overall area mean wind pressure coefficients of the first and last rows of PV panels in the array appear at the wind direction angles of 0° or 180°. The maximum values of the overall net mean wind pressure coefficients of the PV panels in the middle positions appear in the wind direction angle ranges of 15–45° or 135–165°, but their maximum values are all less than those of the first or last row of PV panels. In summary, in the overall wind load design of the flexible-support PV array, the most unfavorable wind direction angles are 0° and 180°, and the most unfavorable locations are in the 1st row at the edge of the array.

As known from the previous studies, the wind direction angles of 0° and 180° are the most unfavorable for the mean wind pressure coefficient of the PV array. Observing Figure 5, it can be found that as the tilt angle gradually increases, there is a sudden decrease in the absolute value of the mean wind pressure coefficient at the second row of the windward leading-edge. Meanwhile, the third to eighth rows of the windward side show a phenomenon of first increasing and then decreasing values. This phenomenon is referred to as the shading interference effect of the windward front PV panels on the rear PV panels’ wind pressure, which is generally represented by the shading coefficient $R_m$ of the PV array. Its definition is given as follows:

$$R_m={\displaystyle \frac{C_{mi}}{C_{m1}}}$$

(8)

where $C_{mi}$ is the mean wind pressure coefficient of the ith row of PV panels, with $i$ ranging from 1 to 8; $C_{m1}$ is the mean wind pressure coefficient of the windward leading-edge PV panel. At tilt angles of 0° and 5°, due to the small tilt angles, the wind load on the PV panels is relatively small, and the shading effect of the front PV panels on the rear ones in the windward direction is not significant. As a result, the change in the area mean wind pressure coefficient with the increase in windward rows is not significant. When the tilt angle is greater than 15°, the wind load on the PV panels increases, and the shading effect of the front PV panels on the rear ones becomes more pronounced. After the 4th row, the area mean wind pressure coefficients of the PV panels at all tilt angles tend to stabilize, with no significant differences in values. This indicates that the tilt angle has little effect on the wind load of the PV panels after the 4th windward row in the array. Under typical wind direction angles, namely 0° and 180°, the variation in the shading coefficient with the position in the array is shown in Figure 8. It can be seen that the larger the tilt angle, the more significant the shading effect on the second row in the windward direction. The tilt angle is a significant factor affecting the shading effect.

In the actual design of flexible-support PV structures, the envelope value of the mean wind pressure coefficient (shape coefficient) under the full range of tilt angles should be taken. Therefore, for a flexible-support PV array with a tilt angle range of 0–60° for the PV panels, in structural design, the overall shape coefficient of the 1st row of PV panels should be taken as 1.3 (wind pressure) or −1.25 (wind suction). When the PV array has more than 5 rows, the overall shape coefficients of the PV panels in the 2nd row and beyond can be appropriately reduced. The 2nd and 3rd rows can be taken as 0.6 (wind pressure) or −0.7 (wind suction), and the rows after the 4th can be taken as 0.5 (wind pressure) or −0.6 (wind suction). To illustrate the reliability of the results of this study, the shape coefficient obtained from a similar case in Zhou et al. [20] was used for comparison. The results are presented in

Table 1. Comparison of shape coefficient and shading coefficient with [20].

	Shape Coefficient		Shading Coefficient
Windward	1st Row	2nd Row
This study	−1.22	−0.27	22.1%
Zhou et al. [20]	−1.16	−0.13	10.8%

. It can be seen from the table that the windward front row shape coefficient value of −1.22 obtained in this paper is very close to the value of −1.16 obtained in Reference [20], which indicates the rationality of the wind suction design value suggested in this paper. However, there is a significant difference in the degree of influence of the wind suction design value for the second row by the shielding effect, that is, the shielding coefficient. These differences can be attributed to the different cases analyzed and the larger range of panel inclination angles in this paper.

3.2. RMS Wind Pressure Coefficient Analysis

The fluctuating wind pressure coefficient characterizes the fluctuation intensity of the wind pressure coefficient time-history. This characteristic is crucial for assessing the wind-induced dynamic response, fatigue, and local high-suction risks of structures and is an indispensable important parameter in wind tunnel tests and wind load codes. To analyze the variation in the fluctuating wind pressure coefficient with the tilt angle of the PV panels, this study first presents the variation in the critical fluctuating wind pressure coefficients of some PV panels under typical wind direction angles, as shown in Figure 9. It can be seen from the figure that the variation trend of the fluctuating wind pressure coefficient of the 2nd to 8th rows in the windward direction is basically consistent regardless of the wind direction angle. The more complex variation in fluctuating characteristics occurs at the windward leading-edge. As the tilt angle increases from 0° to 15°, the fluctuating wind pressure coefficient at the windward leading-edge gradually increases. However, after the tilt angle exceeds 15°, the fluctuating wind pressure coefficient at the windward leading-edge decreases to some extent. It can be observed that when the tilt angle is less than 15°, the critical fluctuating wind pressure coefficient occurs in the first row facing the wind. After the tilt angle is greater than 15°, the critical fluctuating wind pressure coefficient gradually shifts to the second row facing the wind. In summary, when the tilt angle is less than 15°, the fluctuating wind pressure coefficient of the first row facing the wind dominates, and the vortex energy mainly accumulates on the surface of the first row of PV panels, which is prone to random vibration and fatigue phenomena. When the tilt angle is greater than 15°, the vortex energy gradually transfers to the surface of the second row of PV panels facing the wind. Overall, regardless of how the tilt angle of the PV panels and the incoming wind direction change, the value of the fluctuating wind pressure coefficient is always less than 0.5.

As mentioned earlier, under typical wind direction angles, with a tilt angle of 15° as the dividing line, the critical fluctuating wind pressure coefficients appear in the first and second rows facing the wind, respectively. To further analyze the variation in the most unfavorable fluctuating wind pressure coefficient with the wind direction angle, Figure 10 shows the relationship between the most unfavorable fluctuating wind pressure coefficient of the first row (A1, H1) and the second row (B1, G1) of PV panels facing the wind under typical wind direction angles and the wind direction angle. It can be seen from Figure 10 that under all tilt angle conditions, when the wind direction angle is 90°, the overall net fluctuating wind pressure coefficient of all PV panels stabilizes around 0.1, indicating that the tilt angle has a negligible effect on the fluctuating wind load of PV panels at a wind direction angle of 90°. For PV panels A1 and H1, within the range of wind direction angles not affected by the incoming flow (0–90° for A1 and 90–180° for H1), the overall net fluctuating wind pressure coefficient decreases as the wind direction angle approaches 90°. Within the range of wind direction angles affected by the incoming flow, the overall net fluctuating wind pressure coefficient first increases and then decreases as the wind direction angle approaches 90°. Similarly, for B1 in the range of 0–90° and G1 in the range of 90–180°, the overall net fluctuating wind pressure coefficient decreases as the wind direction angle approaches 90°. For B1 in the range of 90–180° and G1 in the range of 0–90°, the overall net fluctuating wind pressure coefficient also first increases and then decreases as the wind direction angle approaches 90°. In summary, the overall net fluctuating wind pressure coefficient of the PV panels at the windward front of the array continues to decrease as the wind direction angle approaches 90°. In contrast, the overall net fluctuating wind pressure coefficient of the PV panels at the rear of the windward side first increases and then decreases as the wind direction angle approaches 90°. When the wind direction angle is at 90°, the overall net fluctuating wind pressure coefficients of the PV panels at different locations within the array tend to be consistent and have smaller values.

To further investigate the impact of the shading effect of the PV array on the net fluctuating wind pressure coefficient of the PV panels, Figure 11 plots the variation in the net fluctuating wind pressure coefficient of the PV panels A1 to H1 in the left-hand column of the array with the array position under wind direction angles of 0° and 180°. When the tilt angle of the PV panels is in the range of 0–15°, the overall net fluctuating wind pressure coefficient of the 1st row facing the wind reaches the maximum value. This coefficient decreases with the increase in the windward row number and tends to stabilize after the 4th row. When the tilt angle is in the range of 30–60°, the overall net fluctuating wind pressure coefficient of the 2nd row facing the wind reaches the maximum value. At this time, the coefficient first increases to the 2nd row and then decreases with the increase in the windward row number, also tending to stabilize after the 4th row. Under small tilt angle conditions, the shading effect of the front PV panels on the rear ones is significant, resulting in a decrease in the net fluctuating wind pressure coefficient of the rear PV panels. Under large tilt angle conditions, the overall net fluctuating wind pressure coefficient of the 2nd row of PV panels even exceeds that of the 1st row, and the shading effect of the front PV panels on the rear ones is significantly weakened compared with the small tilt angle conditions. This result indicates that the variation in the tilt angle of the PV array significantly affects the intensity and distribution of the shading effect, thereby changing the variation law of the net fluctuating wind pressure coefficient of the PV panels along the array position.

4. Analysis of Non-Gaussian Characteristic and Peak Coefficient

4.1. Non-Gaussian Characteristic Analysis

In addition to the mean and fluctuating wind pressure coefficients, this study further analyzed the impact of tilt angle on the non-Gaussian characteristics of the wind pressure coefficient. Higher-order moments, such as skewness and kurtosis, are often used to analyze the non-Gaussian characteristics of random variables. In Davenport’s theory, which approximates structural wind effects as Gaussian-distributed, the skewness is 0 and the kurtosis is 3. However, recent experimental studies have shown that the wind pressure distribution on structural surfaces has non-Gaussian characteristics, with a probability density function that has distinct skewness and heavy-tailed features. This characteristic affects the magnitude of the extreme wind pressure coefficients obtained from the calculation of the wind pressure coefficient time-histories, which in turn affects the determination of the design wind load. Therefore, it is necessary to study the non-Gaussian characteristics of the wind pressure coefficient.

As shown in Figure 12 and Figure 13, the non-Gaussian characteristics of wind pressure coefficients at different positions of the array under different tilt angles vary significantly. Except for the 0° tilt angle, the influence of array position on the non-Gaussian characteristics is not significant under other tilt angles. When the wind direction angle is 0°, the skewness of the wind pressure coefficients for all conditions except the 0° tilt angle is positive, indicating a right-skewed distribution. Currently, the distribution of the wind pressure coefficient time series shows a distinct right-tail extension, which corresponds to the direction of the extreme values of the data. This phenomenon indicates that when the wind direction angle is 0°, the wind load on the surface of the PV panels exhibits significant non-Gaussian characteristics in the direction of extreme values. When the wind direction angle is 180°, however, the situation is different. The skewness of the wind pressure coefficients for most conditions is negative, indicating that the data distribution extends towards the direction of the minimum values. It is worth noting that when the tilt angle is 0°, the pattern of skewness of the wind pressure coefficients for the PV array is more complex and varies with the position of the windward array.

The non-Gaussian process can be classified into softening and hardening processes based on whether the kurtosis of the wind pressure coefficient is greater than 3. In the existing research on structural wind loads, the softening process (i.e., kurtosis > 3) is more common. This study also supports this conclusion. As can be clearly seen from Figure 13, regardless of the wind direction angle, the kurtosis of the wind pressure coefficient varies within the range of 3.5 to 8 under all conditions except for the 0° tilt angle, showing a distinct softening non-Gaussian process. However, when the tilt angle is 0°, the kurtosis of the wind pressure on the surface of the PV array is more extreme, with a maximum value reaching up to 16. These analyses all indicate that under typical wind directions, the wind load on the surface of the PV array exhibits non-Gaussian characteristics. The skewness of the wind load distribution is related to the incoming wind direction. In contrast, the kurtosis is characterized by values greater than 3, i.e., a softening non-Gaussian process.

4.2. Peak Wind Pressure Coefficient Analysis

Because the wind loads experienced by different regions of the PV array vary significantly under different wind direction angles, in practical engineering design, it is necessary to consider not only the overall shape coefficient of the PV panels, but also focus on the distribution of extreme wind loads within the PV array. This will help to propose rational and effective local or overall wind-resistant measures in the design of PV support structures.

Figure 14 reveals the evolution of peak wind pressure on the first row (A1 panel) and the last row (H1 panel) of the array under wind directions ranging from 0° to 90° at a 60° tilt angle. When the upper surface of the first row A1 panel faces the wind, it exhibits a typical distribution pattern with high values at the edges and stable values in the middle at 0° and 90° wind direction angles. The measurement points from 4 to 26 maintain a relatively uniform distribution. Within the oblique wind direction range of 15° to 75°, extreme peak values appear at the rightmost measurement point near the support, while the values at the left edge measurement points decrease gradually as the position on the panel shifts to the right. The central measurement points remain stable. Notably, the left front edge measurement point, No.1, is always at the forefront of the windward side. Its peak value reaches the maximum at a 45° wind direction angle. When the wind direction angle is less than 45°, there is no significant difference in the values of measurement points No.1 to No.4. After exceeding 45°, the values decreased sharply. The values of the central measurement points generally decrease with increasing wind direction angle, and this trend becomes more pronounced after 45°. For the last row H1 panel, its distribution pattern at the boundary wind directions of 0° and 90° is similar to that of the A1 panel. Under oblique wind directions (15° to 75°), the values of the left edge measurement points also decrease significantly as the position on the panel shifts to the right and tend to stabilize in the central region. The response of this panel exhibits strong non-linearity: the values of the left measurement points increase from 0° to 45° and then decrease sharply from 45° to 90° (with a much greater reduction than the previous increase). The core difference lies in the role change in measurement point No.1. This point shifts from the wake region at 0° to the windward state (becoming the forefront around 45°) and measures the highest peak value in the entire domain at a 45° wind direction angle, which is significantly higher than the peak value of the first row A1 panel under any condition.

To comprehend the influence of the PV panel tilt angle on the local peak wind pressure of the array, Figure 15 shows the variation in the maximum net wind pressure coefficient at key measurement points of the first and last rows with the wind direction angle. The study found that the measurement point at the left edge of the first row structure exhibits a stable characteristic under all tilt angle conditions: its peak value remains essentially constant within the wind direction range of 0° to 45° and gradually decreases with increasing wind direction angle after exceeding 45°. Moreover, the peak intensity of this measurement point systematically increases with the increase in the PV panel tilt angle. For the measurement point at the same position in the last row structure, its peak variation shows a significant non-monotonic response. At a 5° tilt angle, the maximum value appears at a 15° wind direction angle. At a 15° tilt angle, the maximum value shifts to a 30° wind direction angle. Within the tilt angle range of 30° to 60°, the peak value stabilizes at a 45° wind direction angle. It is worth noting that the peak intensity measured by the last row measurement point in the main wind direction range of 15° to 75° is always much higher than that of the first row measurement point under the same conditions. Among them, the measurement point in the last row under the condition of a 60° tilt angle, combined with a 45° wind direction angle, observed the highest peak in the entire array. The comprehensive analysis shows that with the increase in the PV panel tilt angle, the most unfavorable wind direction angle for generating local peak wind pressure exhibits a regular shift trend. From a 15° wind direction at low tilt angle to a 45° wind direction at high tilt angle. This evolution pattern causes the most unfavorable wind direction angle under large tilt angle conditions to significantly deviate from the 0° wind direction condition dominated by the overall mean wind pressure, revealing the essential contradiction that considering only the traditional most unfavorable wind direction angle may seriously underestimate the local wind load risk when evaluating large tilt angle PV arrays.

To ensure the influence of the wind direction angle on the wind suction on the underside of the PV array, this study focuses on analyzing the evolution of the minimum net wind pressure coefficient (compared in terms of absolute value) in the wind direction range of 90° to 180° under a 60° tilt angle for key areas. Figure 16 shows the measurement data of the windward front panel H1 and the windward rear panel A1 of the array. When the underside of panel H1 faces the wind, its wind suction distribution exhibits significant spatial inhomogeneity and wind direction angle dependency: under the boundary wind direction angles of 90° and 180°, the minimum value distribution of the measurement points in the main body of the panel (approximately points 2 to 26) remains relatively stable, while the measurement points at both ends of the panel always show stronger wind suction characteristics. Under oblique wind conditions (105° to 165°), a tripartite feature is observed. The two measurement points near the support on the right side of the panel consistently show extremely high suction values. The middle and right measurement points (approximately points 8 to 26) maintain a relatively stable suction level. And the measurement points in the left area (points 1 to 7) show a clear gradient change. Their wind suction intensity systematically decreases as the measurement point position moves to the right. Particularly noteworthy is the left edge measurement point (Tap No.1), which detects a significant concentration of wind suction under each oblique wind direction, with the suction intensity decreasing in a gradient manner as the measurement point position extends to the right. Comprehensive observations indicate that the right side of the panel near the support and the left edge of the panel form a dual high-suction core under oblique wind conditions, with this spatially inhomogeneous distribution characteristic being most pronounced around the wind direction angle of 150°.

To clarify the influence of different wind direction angles on the wind suction on the surface of the PV array, this study, focusing on the 60° tilt angle condition, analyzed the distribution characteristics of wind suction intensity in the key areas of the windward front and rear parts of the array within the wind direction range of 90° to 180°, as shown in Figure 17. It was found that when the lower surface of the structure faces the wind, the windward front area (H1 panel) shows a significant tripartite response under oblique wind conditions. The right side of the panel near the support continuously experiences extremely high suction, the suction in the middle of the panel remains relatively stable, and the suction intensity in the left edge area decreases in a gradient manner as the position shifts to the right. This spatial inhomogeneity is most pronounced at a wind direction angle of 150°, forming dual high-suction cores in the right support area and the left edge area. In contrast, the windward rear area (A1 panel) exhibits a more intense concentration of wind suction. At a wind direction angle of 135°, the maximum wind suction in the entire domain is detected at the leftmost edge of the panel, and this peak value significantly exceeds the extreme values of the windward front area under any condition. At this time, the rate of decrease in suction intensity in the left area as the position shifts to the right reaches the maximum, showing the sensitivity of the rear structure to changes in wind direction. Further comparison of the load characteristics of the array in different wind direction quadrants revealed that the tail area in the array column direction (including the rear part in the range of 0° to 90° and the windward rear part in the range of 90° to 180°) is always a sensitive area for extreme wind loads. This area generates peak wind pressure intensity far exceeding other locations under oblique wind angles (approximately 45° or 135°), with the 45° wind direction producing the maximum wind pressure peak and the 135° wind direction triggering the maximum wind suction peak. This phenomenon reveals the core contradiction in the wind-resistant design of PV arrays: the traditional most unfavorable wind direction angle determined based on overall load (such as 0° or 180°) underestimates the local failure risk of the array tail area under oblique wind conditions. Especially for large tilt angle flexible-support systems, it is necessary to focus on the dual extreme load effects of the 45° and 135° wind directions on the key nodes of the tail structure. In fact, since this study is based on wind tunnel tests of rigid models, it neglects the influence of the aerodynamic effect of photovoltaic panels on the peak wind load to some extent. The influence of fluid–structure interaction effects of flexible structures on structural wind effects depends on complex factors such as wind speed, aerodynamic damping, and stiffness [36,37,38]. Therefore, it is very necessary to conduct aeroelastic tests on photovoltaic structures to study their wind effects.

5. Conclusions

This study systematically revealed the wind load characteristics of an 8-row, 2-span, large-span flexible-support PV array through rigid model wind tunnel tests. The core conclusions are as follows.

The mean wind pressure coefficient (shape coefficient) of the PV array reaches its maximum value at wind direction angles of 0° and 180°, with the first row at the edge being the most unfavorable location. It is recommended that the shape coefficient be taken as 1.3 (for wind pressure) or −1.25 (for wind suction). The local extreme wind pressure is concentrated at oblique wind direction angles (15–45° and 135–165°), especially in the tail area of the array (such as the eighth row). The 45° wind direction triggers the maximum wind pressure value, while the 135° wind direction causes the maximum wind suction extreme value, both of which significantly exceed the edge values under the 0°/180° conditions.

The tilt angle of PV panels has a critical regulatory effect on the load distribution. An tilt angle of 30° is the turning point for the evolution of wind load characteristics. When the tilt angle is less than 30°, the shape coefficient and the fluctuating wind pressure coefficient of the front row structure are both higher than those of the rear row. After exceeding 30°, the fluctuating wind pressure coefficient of the rear row surpasses that of the front row (e.g., the second row > the first row), while the distribution of the shape coefficient tends to stabilize. This transition is directly related to the aerodynamic interference mechanism. Under typical wind directions, the shading effect of the front row on the rear row significantly increases with the increase in the tilt angle.

For the engineering optimization design of multi-row arrays (more than 5 rows), it is recommended that the shape coefficient of the second–third rows be reduced to 0.6 (for wind pressure) or −0.7 (for wind suction), and for the fourth row and beyond, the shape coefficient should be 0.5 (for wind pressure) or −0.6 (for wind suction).

The research findings indicate that the traditional design based on overall mean load underestimates the extreme local wind load risks in the tail area under oblique wind direction angles. This has significant implications for the refined wind-resistant design of structures with large tilt angle flexible-supports. It should be noted that this study is only based on experimental data and still has many limitations. First, this study draws conclusions based on the results of rigid model pressure measurements of photovoltaic structures under multiple tilt angles. In reality, for structures with greater flexibility, the aerodynamic forces influenced by the tilt angle of the photovoltaic panels are also affected by the mutual interaction between structural vibrations and the flow field. Further aeroelastic tests on large tilt angle photovoltaic structures are needed to study the impact of tilt angle on aerodynamic forces. Secondly, due to the limitations of the scaled model, this study has simplified the gaps between the panels. In reality, even small gaps can still have an impact on the wind load. Computational fluid dynamics (CFDs) should be the best tool for parametric studies on the effects of these gaps. Then, this paper only investigates the design wind load of photovoltaic structures, while wind-induced fatigue affecting the wind resistance capacity of key components is also crucial for structural design. In addition, the design wind loads obtained from the wind tunnel test in this paper are only for the specific case (eight rows, two columns, 6 m spacing, etc.), and parametric studies for different numbers of rows and columns are still needed in the future. Finally, this paper only conducted tests based on Terrain Category B and did not investigate how the presence of complex terrain (hills, valleys) or other surrounding obstacles would affect the critical wind direction angle and peak wind load. In fact, the wind speed acceleration effect brought by complex terrain can influence the value of the design wind load, and the special wind field of terrain such as valleys will restrict the incoming wind direction angle. Experimental research can only analyze wind effects from a relatively ideal environment. To better understand the wind effects on large-span flexible PV structures, further field measurements should be conducted to verify the accuracy of the design wind load calculated from the experimental data.