A Parametric Study of Flexible Support Deflection of Photovoltaic Cells Considering Wind-Induced Load Using Time History Technique

Abstract

In this paper, we mainly consider the parametric analysis of the disturbance of the flexible photovoltaic (PV) support structure under two kinds of wind loads, namely, mean wind load and fluctuating wind load, to reduce the wind-induced damage of the flexible PV support structure and improve its safety and durability. The wind speed time history was simulated by the response spectrum method, and the 15.6 m flexible PV support was analyzed comprehensively. The influence of critical parameters, such as panel inclination angle, wind direction angle, and template gap, on the wind-induced response of the flexible PV support was compared and analyzed under two wind loads. The results showed that the panel inclination angle positively correlated with the structural displacement, while the template gap was negatively correlated with the structural displacement. Furthermore, structural displacements were observed to be higher at 0° and 180° wind direction angles compared to those at 45° and 135° angles. Compared with other horizontal force-bearing structures, the horizontal force-bearing structure of inclined steel columns had more robust safety, construction convenience, and economy. It is worth noting that the fluctuating wind load was much smaller than the mean wind load, but its impact on the flexible PV support structure cannot be ignored.

1. Introduction

In recent years, the escalating global climate change and dwindling fossil fuel resources have propelled the development and utilization of renewable energy to the forefront of contemporary research. Notably, in 2023, China’s exports of “three new items” products, encompassing electric vehicles, lithium batteries, and PV equipment, rose by approximately 30%, demonstrating China’s unwavering commitment to energy transition. Solar energy, as a green, clean, and renewable form of energy, is being widely promoted and applied worldwide. With the continuous progress of technology and the rapid upgrading of the industry, the proportion of solar clean energy in the global energy structure has gradually increased, taking a solid step forward in the energy revolution [1].

As the support system of solar PV structures, PV supports directly impact the stability and power generation efficiency of PV systems. There are many types of PV supports, including fixed PV supports [2,3], flexible PV supports [4], and floating PV supports [5,6,7]. Figure 1 illustrates the applicable scopes of the three PV support structures. Baumgartner [8,9,10] was the first to suggest the flexible PV support, a thin-walled structure [11]. Its advantages include large span, flexible operation, high land space utilization, and high power generation efficiency [12], which have been widely used in complex terrains, such as mountains, fish ponds, crops, and sewage treatment plants [13]. It is also due to the influence of a complex environment, coupled with long-term continuous wind load and vibration, accelerating the corrosion of the steel strand, which affects the service life and safety performance of the flexible PV support structure. Predecessors were proposed using composite materials instead of substrate steel wire materials, using composite materials’ corrosion resistance, long life, light safety, and other advantages to improve the durability of flexible PV support structures [14]. However, the inherent structural features of the flexible PV support, including its low-frequency characteristics and minimal mass, render it highly susceptible to wind loads [15,16]. When exposed to wind loads, the flexible PV support is prone to vibrations and deformations, potentially resulting in structural damage, known as wind-induced response damage [17,18], as illustrated in Figure 2. Therefore, it is essential to study the applicability of composite materials and the influence of wind load on the flexible PV support structure [19].

Most research on wind loads about PV supports is centered on fixed PV support structures. Many scholars have explored the wind load characteristics of fixed PV support structures through experiments and numerical simulations [2,20,21,22]. However, compared with fixed PV supports, the research on wind loads of flexible PV support structures is still relatively lacking [23,24,25]. Therefore, the primary aim of this research is to compare and analyze the disparities in wind-induced responses exhibited by flexible PV support structures under two distinct conditions: considering the fluctuating wind loads and not considering the fluctuating wind loads, to reduce the harm of wind loads to PV flexible support structures, to improve the safety and durability of flexible PV support structures, and to improve the power generation efficiency of flexible PV support structures, thus promoting the use of clean solar energy and enhancing the wind resistance design of the flexible PV support structure.

In this study, the Davenport spectrum advocated in China’s building structure code was adopted as the target wind spectrum, and the response spectrum method [26,27,28] was adopted to simulate the wind speed time history; that is, different wind speed values were obtained through the wind speed spectrum. At the same time, utilizing the ANSYS 2022R2 finite element analysis software, a three-dimensional finite element model of the flexible PV support structure will be established. The model will compare and analyze the wind-induced response characteristics of the flexible PV support structure, considering the fluctuating wind load and the mean wind load, evaluate the force-bearing safety, durability, and wind-induced response of the structure, and further study the influence of factors, such as panel inclination angle, wind direction angle, and template gap, on the flexible PV support structure. The reliability [29,30] of the structure is evaluated, and then the applicability of composite materials on the flexible PV support is discussed. By conducting a comprehensive investigation, this research aims to furnish valuable insights into the wind-resistant design of flexible PV support structures, further propelling the widespread application and development of solar clean energy, enhancing the wind-resistance design of flexible PV support structures, and increasing their power generation efficiency.

2. Methodology

2.1. Model Building and Meshing

2.1.1. Flexible PV Support Model

The flexible PV support structure, serving as an efficient and flexible solar power generation support system, mainly consists of five key components: horizontal force-bearing structure, crossbeam structure, triangular frame structure, cable structure, and PV panel structure. The basic shape and cross-section of the flexible PV support structure are shown in Figure 3 and Figure 4. The synergistic operation of these components guarantees the stability and functionality of the entire structure. Among them, the horizontal force-bearing structure can be divided into three forms: the horizontal force-bearing structures of inclined cables, the horizontal force-bearing structures of inclined steel columns, and the horizontal force-bearing structures of eight-shaped inclined steel columns, as shown in Figure 5. Furthermore,

Table 1. Dimensions of each structural component.

Flexible PV Support		Dimension/(mm)
Horizontal force-bearing structure	Foundation	500 mm × 500 mm × 500 mm (length × width × height)
	Column	200 mm × 200 mm × 2400 mm (length × width × height)
Beam		2400 mm × 200 mm × 200 mm (length × width × height)
Thick tripod		1420 mm × 200 mm × 820 mm (length × width × height)
		1160 mm × 200 mm × 1160 mm (length × width × height)
		820 mm × 200 mm × 1420 mm (length × width × height)
Thin tripod		1430 mm × 1155 mm × 1078 mm × 20 mm (L × M × N × diameter)
		1600 mm × 1400 mm × 908 mm × 20 mm (L × M × N × diameter)
		1623 mm × 1400 mm × 682 mm × 20 mm (L × M × N × diameter)
Template gap		10 mm
		50 mm
		100 mm
Cable		15600 mm × 20 mm (span × diameter)
PV panel		1640 mm × 1000 mm × 48 mm (length × width × height)

and

Table 2. Material characteristics.

Material	Density (kg/m3)	Young’s Modulus (Pa)	Poisson’s Ratio
Concrete	2300	3 × 1010	0.18
Structural steel	7850	2 × 1011	0.3
Aluminium alloy	2770	7.1 × 1010	0.33
PV material	2600	1.1 × 1011	0.225

present the dimensions and material properties of the five crucial components that comprise the flexible PV support structure. In this paper, only a single row of flexible PV supports is studied, and PV arrays are not considered.

2.1.2. Mesh Division

For the mesh division of the flexible PV support structure, if the mesh division is too fine, although the calculation results will be more accurate to a certain extent, it will greatly reduce the computing efficiency of the computer. If the mesh of the model is too rough, it will lead to inaccurate calculation results. Therefore, on the premise of ensuring computational efficiency and accuracy, the method of automatic mesh division was used to divide the mesh, the method of surface size adjustment was used to limit the mesh size to 200 mm, the foundation was fixed with fixed constraints, and the support leg structure of the flexible PV support was fixed on the foundation, as shown in Figure 6.

2.2. Structural Wind Pressure Simulation

2.2.1. Wind Speed Calculation

The wind speed, $V\left(x,y,z,t\right)$, can be represented as the sum of the mean wind speed, $\overline{v}\left(z\right)$, and the fluctuating speed, $v\left(x,y,z,t\right)$, expressed as follows:

$$V\left(x,y,z,t\right)=\overline{v}\left(z\right)+v\left(x,y,z,t\right)$$

(1)

The mean wind speed, $\overline{v}\left(z\right)$, is influenced by variations in ground height. Formula (2) [31] can be utilized to describe the alterations in mean wind speed within the near-ground layer:

$${\displaystyle \frac{\overline{v}\left(z\right)}{{\overline{v}}_{10}}}={\left({\displaystyle \frac{z}{10}}\right)}^{\alpha }$$

(2)

$\overline{v}\left(z\right):$ The mean wind speed at a specific elevation point (m/s).

$Z:$ The height at a specific elevation point (m).

${\overline{v}}_{10}:$ The mean wind speed is at a height of 10 m (m/s). In this simulation, the mean wind speed at 10 m altitude refers to Shenyang, Liaoning Province, China (41.48° N, 123.25° E).

$\alpha :$ In this study, the power-law exponent was assumed to be 0.16.

Fluctuating wind is generated by the natural irregularity of wind, and its intensity changes randomly over time [32]. The classification of wind speed spectra encompasses horizontal, vertical, and transverse gust power spectra. However, further investigation revealed that vertical and transverse gust turbulence exert comparatively minor influences on wind speed. Therefore, their effects can usually be ignored when analyzing the dynamic response of structures. Considering the findings above, this study will primarily concentrate on the horizontal gust power spectrum to meticulously investigate its influence on the wind-induced response of flexible PV support structures. Davenport derived an empirical mathematical expression for the fluctuating wind speed spectrum, drawing upon global vital wind records across various locations and heights. This mathematical expression is as follows:

$$S_v\left(n\right)=4k{\overline{v}}_{10}^2{\displaystyle \frac{x^2}{n{\left(1+x^2\right)}^{4/3}}}$$

(3)

$S_v\left(n\right):$ The power spectrum of fluctuating wind (m²/s).

$k:$ In this paper, the surface roughness coefficient took a value of 0.005.

$n:$ The frequency of fluctuating wind (Hz).

${\overline{v}}_{10}:$ The mean wind speed is at a height of 10 m (m/s). In this simulation, the mean wind speed at 10 m altitude refers to Shenyang, Liaoning Province, China (41.48° N, 123.25° E).

$x:$ The integral scale coefficient of turbulence with the value of $1200n/{\overline{v}}_{10}$.

Employing the algorithm above, a horizontal gust wind velocity was conducted. The simulation encompassed a time interval of 0.1 s, spanning a total duration of 30 s. Specifically, the mean wind speed at a height of 10 m in Shenyang was recorded as 25.3 m/s. Consequently, a time history of the fluctuating wind speed was obtained and presented in Figure 7. Furthermore, Figure 8 depicts the power spectral density curve of the simulated wind speed. Notably, the power spectrum aligned closely with the target auto-power spectrum, indicating the reliability of the simulated time history of fluctuating wind speed.

2.2.2. Wind Pressure Calculation

To examine the impact of wind loads on the structural safety of flexible PV supports and analyze their wind-induced response, this study considered two distinct load scenarios: (1) a mean wind load determined using mean wind speed measurements, and (2) a fluctuating wind load calculated utilizing the fluctuating wind speed data.

Under the influence of the mean wind, the mean wind pressure, $W_1$, was determined to be 252.5 N/m². On the other hand, the fluctuating wind pressure, $W_2$, which results from fluctuating wind speeds, was computed as follows:

$$W_2=0.5\rho v^2\left(x,y,z,t\right)$$

(4)

$W_2:$ The fluctuating wind pressure (N/m²).

$\rho :$ The air density (Kg/m³).

$v\left(x,y,z,t\right):$ The fluctuating wind speed (m/s).

Figure 9 presents the wind pressure under both loading conditions. Figure 9 illustrates that the fluctuating peak wind load can attain a value of 479.6 N/m, significantly surpassing the mean wind load. As a result, the actual response of the flexible PV support structure under severe wind conditions may be underestimated in analysis. Therefore, the safety and wind-induced response of the flexible PV support structure under fluctuating wind load should be considered and compared with its response under mean wind load.

2.3. Simulation

2.3.1. Mean Wind Load

Force-Bearing Safety

From the description in Section 2.2, the ANSYS software was employed to conduct a comprehensive analysis and assessment of the force-bearing safety capabilities of three distinct horizontal force-bearing structures, each possessing a span of 15.6 m and a height of 2.4 m, as depicted in Figure 5. These structures included the horizontal force-bearing structure of inclined cables, the horizontal force-bearing structure of inclined steel columns, and the horizontal force-bearing structure of eight-shaped inclined steel columns. It is important to note that the analysis only focused on the application of the 180° horizontal wind direction, specifying a mean wind load of 252.5 N/m², acting on a PV panel, as shown in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The culmination of this simulation process is presented in Figure 10, offering a comprehensive visualization of the simulation results.

The results above indicate that, when subjected to the mean wind load, the displacement values exhibited by the three types of horizontal force-bearing structures were notably similar. However, a closer examination revealed that the displacement values of the horizontal force-bearing structure of eight-shaped inclined steel columns and the horizontal force-bearing structure of inclined steel columns were comparatively lower. Consequently, these two types of structures, namely, the horizontal force-bearing structure of eight-shaped inclined steel columns and the horizontal force-bearing structure of inclined steel columns, demonstrated a higher degree of safety than the horizontal force-bearing structure of inclined cables.

Fatigue Life Evaluation

According to the damage mechanism of the flexible PV support structure, in the actual project, the cable structure bears fatigue load for a long time and is exposed to wind and rain, humidity, and a polluted air environment at the same time. This results in “stress corrosion”, “fatigue corrosion”, and “metal corrosion”, which makes the structure easy to damage, and ultimately leads to the lack of durability of the flexible PV support structure and then affects the power generation efficiency.

Previous studies focused on the fatigue life of flexible PV supports. To enhance its fatigue life, the traditional methods of hot-dip galvanizing or anti-corrosion coating on the surface of the substrate steel wire were often used to increase the structure’s fatigue life [33,34]. However, due to the flexible PV support structure’s structural particularity, the PV modules should be fixed on the cable structure. Therefore, traditional methods to enhance the structure’s fatigue life are not applicable. In this study, a new process was adopted to improve the fatigue life of the flexible PV support; that is, composite materials with high specific strength/stiffness, excellent weather resistance, and strong designability [35,36,37,38] were used to replace the substrate steel wire material, to improve the fatigue life of the flexible PV support structure.

According to the description in the section on Force-Bearing Safety, the horizontal force-bearing structure of inclined steel columns is more economical, safe, and reliable. Because cable structures are more prone to failure than other structures, this section only analyzes the fatigue life of cable structures in horizontal force-bearing structures of inclined steel columns. It compares the fatigue life of composite materials of cable structures and matrix steel wire of cable structures. The applicability of composite materials in flexible PV supports is proven. The composite materials introduced in this section take the glass-fiber-reinforced resin matrix composite as an example. The S-N curves (Figure 11) of the two materials were substituted into ANSYS finite element software, and the fatigue life of the two materials in the horizontal force-bearing structure of the inclined steel column was obtained using the nominal stress method. It is important to note that the analysis only focused on applying the 180° horizontal wind direction, specifying a mean wind load of 252.5 N/m², acting on a PV panel, as shown in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The final simulation results are shown in Figure 12.

Based on the thorough analysis of the simulation results, it was evident that the fatigue life of the cable structure utilizing substrate steel wire material stood at 1 × 10⁶ cycles. In contrast, the fatigue life of the cable structure employing the glass-fiber-reinforced resin matrix composite material attained a significant figure of 3.08 × 10⁶ cycles. This substantial enhancement represents a 208% increase in fatigue life, demonstrating the profound impact of the composite material in bolstering the durability of the flexible PV support structure under mean wind loading conditions. This is consistent with the findings of Ke et al. [14], while also validating the applicability and effectiveness of composite materials in the construction of flexible PV support structures, thus providing a viable alternative to improve such systems’ long-term performance and reliability.

Wind-Induced Response

In investigating the wind-induced response of flexible PV support structures, the horizontal force-bearing design of inclined steel columns was adopted as the primary analytical model due to its superior safety profile, reliability, economic viability, and ease of construction. The central objective of this analysis was to elucidate the influence of three crucial factors: panel inclination angle, wind direction angle, and template gap, on the wind-induced dynamic response of these flexible PV support structures.

• Panel inclination angle

The panel inclination angle, depicted in Figure 13, represents the angle β, formed between the PV panel and the horizontal plane.

Prior research on the panel inclination angle of PV supports has predominantly concentrated on fixed PV support structures, leaving a need for more studies on flexible PV supports with larger spans and more pliable designs. In this section, we specifically delve into the influence of the panel inclination angle on the dynamic behavior of flexible PV support structures under the effects of mean wind loads. It is important to note that the analysis only focused on applying the 180° horizontal wind direction, specifying a mean wind load of 252.5 N/m², acting on a PV panel, as shown in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. Previous studies on panel inclination angles of PV support structures mainly focused on three representative panel inclination angles of 30°, 45°, and 60° [39,40,41,42]. Therefore, this paper analyzed these three panel inclination angles, and the simulation results are shown in Figure 14.

Based on the results of the simulation above, it was observed that the maximum displacement value reached 85.304 mm when the panel inclination angle was set at 30°. As the panel inclination angle increased to 45°, the maximum displacement value also surged to 132.28 mm, representing a notable 55.07% increase compared to the 30° case. Furthermore, at a panel inclination angle of 60°, the maximum displacement value significantly escalated to 289.56 mm, constituting a substantial 239.44% increase over the 30° inclination angle. These findings indicate that under the influence of mean wind loads, a more minor panel inclination angle results in reduced displacement values for the flexible PV support structure, ultimately minimizing the detrimental effects of wind-induced responses on the flexibility and stability of the PV support system.

• Wind direction angle

The wind direction angle, denoted by α, ranges from 0° to 180° and signifies the angle between the wind direction and the long axis of the PV panel on the horizontal plane, as depicted in Figure 15.

Prior research has established that varying wind direction angles impose diverse wind loads on PV supports, thereby eliciting distinct wind-induced responses. Leveraging past findings, numerous studies have primarily focused on analyzing the wind-induced responses of PV supports at four specific wind direction angles [43,44,45,46]: 0°, 45°, 135°, and 180°. In this paper, we aimed to examine the distinct impacts of mean and fluctuating wind load and subsequently compare the effects of these four wind direction angles on the wind-induced response of flexible PV support structures.

In this section, our analysis is limited to only the effect of the mean wind load, where the applied load of order 252.5 N/m² was loaded onto the PV panel, as shown in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. We have considered four representative wind direction angles: 0°, 45°, 135°, and 180°, and the simulation outcomes are presented in Figure 16 and Figure 17.

Based on the results of the simulation above, we observed distinct variations in the structural displacement with varying wind direction angles under the influence of mean wind load. Specifically, when the wind direction angle was 0°, the maximum displacement of the structure reached 130.4 mm. Conversely, at a wind direction angle of 45°, the maximum displacement decreased to 92.06 mm. Similarly, at a 135° wind direction angle, the maximum displacement was recorded at 91.707 mm. However, when the wind direction angle shifted to 180°, the maximum displacement increased to 132.28 mm. These findings indicate a significant sensitivity of structural displacement to changes in wind direction angles. Notably, the structural displacements at 0° and 180° wind direction angles were substantially higher compared to those observed at 45° and 135° wind direction angles. This is in line with Shademan’s [43] findings that “the wind load on the structure is maximum at two wind direction angles of 0° and 180°”. Therefore, we tried to avoid 0° and 180° wind direction angles.

• Template gap

The template gap refers to the distance between PV panels in a PV system (Figure 18).

Drawing from previous research, there are two contrasting viewpoints regarding the impact of template gaps on the wind-induced response of PV systems. Some scholars assert that the template gap significantly influences the wind-induced response [47,48,49], while others contend that its influence is minimal or nonexistent [50,51,52]. In the present study, we delved into this controversy by analyzing the effects of 10 mm, 50 mm, and 100 mm template gaps on the wind-induced response of flexible PV support structures. To uphold the scientific rigor of our simulations, we maintained a constant span for the flexible PV support structure throughout the experiment. This approach enabled us to precisely evaluate the structural displacement of different template gaps and comprehensively understand their interrelationships.

In this section, our analysis is limited to only the effect of the mean wind load, where the applied load of order 252.5 N/m² was loaded onto the PV panel, as shown in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The simulation outcomes for varying template gaps of 10 mm, 50 mm, and 100 mm are presented in Figure 19.

Based on the simulation results, we observed that under the mean wind load, the structural displacement for a 10 mm template gap was 132.28 mm. Conversely, the displacement for a 50 mm template gap was 99.249 mm, representing a reduction of 24.97% compared to the 10 mm gap. When the template gap was increased to 100 mm, the structural displacement further decreased to 74.065 mm, a substantial reduction of 44.01% compared to the 10 mm gap, accompanied by the occurrence of damage, as illustrated in Figure 19c. These findings indicate a significant negative correlation between the displacement of the flexible PV support structure and the template gap under the mean wind load. This also validated the experimental conclusions of Stenabaug et al. and emphasized the significant influence of the template gap on the wind-induced response of flexible PV supports. Therefore, in practical applications, it is crucial to appropriately regulate the size of the template gap based on specific scenarios to ensure structural safety and minimize the effects of the wind-induced response.

2.3.2. Fluctuating Wind Load

Force-Bearing Safety

From the methodology outlined in the section on Force-Bearing Safety, ANSYS software was employed to conduct a comprehensive analysis and assessment of the force-bearing safety of three horizontal force-bearing structures, each possessing a span of 15.6 m and a height of 2.4 m, as depicted in Figure 5. It is important to note that the analysis only focused on the effect of the 180° horizontal wind direction, and the fluctuating wind load, as shown in Figure 9, was the only load condition considered in this section, which was loaded onto the PV panel. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The culmination of this simulation process is reflected in the results presented in Figure 20 and Figure 21, offering a comprehensive evaluation of the structural response under the specified wind loading conditions.

As depicted in Figure 20 and Figure 21 of the simulation results, the horizontal force-bearing structure of inclined cables exhibited the most significant displacement under the fluctuating wind load. In contrast, the displacement of the horizontal force-bearing structure of inclined steel columns and the horizontal force-bearing structure of eight-shaped inclined steel columns was relatively similar. However, considering the complexity and cost of construction, the horizontal force-bearing structure of inclined steel columns offers a more straightforward construction process and is more cost-effective. Therefore, among the three horizontal force-bearing structures, the horizontal force-bearing structure of inclined steel columns emerged as the optimal choice. This finding aligns with the conclusion drawn under the action of mean wind load. Consequently, regardless of the application of mean wind load or fluctuating wind load, the horizontal force-bearing structure of inclined steel columns represented the best option, balancing economic benefits and stress safety considerations. Additionally, the structural displacement observed under fluctuating wind load was significantly higher than that under mean wind load, further emphasizing the importance of considering fluctuating wind load despite its relatively small magnitude.

Fatigue Life Evaluation

Based on the conclusions drawn in the section on Force-Bearing Safety, the horizontal force-bearing structure of inclined steel columns was the preferred option among the three horizontal force-bearing structures. According to the section on Fatigue Life Evaluation, the nominal stress method and S-N curves (Figure 11) of the substrate steel wire material and the glass-fiber-reinforced resin matrix composite material were substituted into ANSYS finite element software to compare the fatigue life of cable structures in horizontal force-bearing structures of inclined steel columns, aiming to compare the fatigue life of cable structures under fluctuating wind loads. The fatigue life of the cable structure of the base steel wire material and the composite material proved the applicability of the composite material in the flexible PV support structure. The fluctuating wind load shown in Figure 9 was applied to the PV panel of a horizontal force-bearing structure. Only the 180° horizontal wind direction was considered in this section. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The stress time history obtained by the final simulation is shown in Figure 22, and the comparison of fatigue life of the two materials in cable structure under fluctuating wind load is shown in Figure 23.

The feasibility of the glass-fiber-reinforced resin matrix composite material replacing the substrate steel wire material can be proven by Figure 22, and it can be seen from Figure 23 that the fatigue life of the cable structure of the substrate steel wire material was 1 × 10⁶ cycles under the action of fluctuating wind load. In contrast, the fatigue life of cable structures using composite materials, especially the glass-fiber-reinforced resin matrix composite material, reached a significantly higher cycle value of 3.08 × 10⁶. This observation once again highlights the feasibility of composite materials in enhancing the durability of flexible PV support structures under fluctuating wind loads. This finding aligns with the conclusion drawn under the mean wind load, with the improvement values remaining identical. Therefore, regardless of the type of wind load, mean or fluctuating, the utilization of composite material remains feasible to enhance the durability of the flexible PV support structure.

Wind-Induced Response

• Panel inclination angle

Previous research on the panel inclination angle of PV support structures has predominantly concentrated on investigating the mean wind load acting on fixed PV supports [53,54,55], while overlooking the significant influence of fluctuating wind loads. This section aims to delve deeper into the impact of the panel inclination angle on the wind-induced dynamic response of flexible PV support structures subjected to fluctuating wind loads.

According to the conclusion in the section on Force-Bearing Safety, the horizontal force-bearing structure of inclined steel columns was the best choice among the three horizontal force-bearing structures. Consequently, in this section, the ANSYS software was employed to simulate the application of fluctuating wind loads to this horizontal force-bearing structure. Three representative panel inclination angles of 30°, 45°, and 60° were considered for the analysis. It is important to note that the study only focused on the effect of the 180° horizontal wind direction, and the fluctuating wind load, as shown in Figure 9, was the only load condition considered in this section, which was loaded onto the PV panel. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The culmination of these simulations is presented in Figure 24 and Figure 25.

As evident from Figure 24 and Figure 25, under the influence of fluctuating wind loads, the panel inclination angle exhibited a positive correlation with structural displacement. Specifically, an increase in the panel inclination angle led to a corresponding augmentation in structural displacement. Consequently, under such fluctuating wind loads, a reasonable reduction in the panel inclination angle can effectively mitigate the adverse effects of wind-induced responses on flexible PV support structures. Notably, the structural displacement under fluctuating wind loads was significantly higher than that observed under mean wind loads, further validating the significance of considering fluctuating wind loads despite their relatively smaller magnitudes.

• Wind direction angle

Under the details outlined in the section on the Wind Direction Angle, the ANSYS software was utilized to investigate the impact of four typical wind direction angles (0°, 45°, 135°, and 180°) on the wind-induced response of a flexible PV support structure. In this section, the fluctuating wind load was applied to the PV panel, as depicted in Figure 9. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The culmination of these simulations is presented in Figure 26 and Figure 27.

The simulation results revealed that under fluctuating wind loads, the maximum structural displacement was 261.6 mm when the wind direction angle was 0° and 229.2 mm when the angle was 180°. Conversely, at 45° and 135° wind direction angles, the maximum displacements were significantly lower, measuring 134.18 mm and 122.34 mm, respectively. It can be seen that the structural displacement at 0° and 180° wind directions was significantly larger than that at 45° and 135° wind direction angles, and the response of the wind direction angle to structural displacement was significant. This observation aligns with conclusions drawn under mean wind load conditions, yet it is noteworthy that the structural displacement under fluctuating wind loads was substantially higher. This underscores the importance of considering fluctuating wind loads in the analysis and design of PV support structures despite their relatively smaller magnitudes.

• Template gap

Under the methodology outlined in the section on the Template Gap, the ANSYS software was employed to examine the impact of varying template gaps of 10 mm, 50 mm, and 100 mm on the wind-induced response of a flexible PV support structure, while ensuring that the structural span remained constant. In this section, the fluctuating wind load, as shown in Figure 9, was applied to the PV panel, and only the 180° horizontal wind direction was considered. A fixed constraint was used on the foundation, and the leg part of the flexible PV support was also fixed on the foundation. The final simulation results are shown in Figure 28 and Figure 29.

Based on the above simulation results, under fluctuating wind loads, the displacement of the flexible PV support structure exhibited a negative correlation with the template gap; in other words, as the template gap increased, the structural displacement decreased. This finding aligns with the conclusion drawn under mean wind load conditions. However, it is noteworthy that the structural displacement under fluctuating wind loads was significantly higher than that observed under mean wind loads, further reaffirming the importance of considering fluctuating wind loads, despite their relatively small magnitudes, in the analysis and design of PV support structures.

3. Conclusions

In this paper, considering the mean wind load and fluctuating wind load, the force-bearing safety of the thin-walled structure of the flexible PV support was analyzed, and the applicability of the composite material in the flexible PV support structure was proven. Key parameters, including the panel inclination angle, wind direction angle, and template gap, were systematically examined to understand their specific impacts on the wind-induced response of the structure. Furthermore, constructive suggestions were proposed to effectively mitigate the potential harm caused by the wind-induced response of the flexible PV support structure. The primary findings of this study are summarized below:

• Among the three kinds of horizontal force-bearing structures, the horizontal force-bearing structure of inclined steel columns had better safety reliability, construction simplicity, and economic feasibility, and it had more advantages in practical application.
• Increasing the panel inclination angle will lead to growing structural displacements. Considering the correlation between power generation efficiency and panel inclination angle, we suggest that the panel inclination angle should be reduced reasonably in the design to reduce the harm of wind-induced responses and improve the overall power generation efficiency of the PV system.
• The structural displacements at 0° and 180° wind direction angles were significantly greater than those at 45° and 135° wind direction angles. It can be seen that the wind direction angle had a significant influence on the wind-induced response of the flexible PV support structure.
• The decrease in the template gap will lead to a reduction in structural displacement. Therefore, a reasonable increase in the template gap is conducive to reducing the influence of the flexible PV support structure on wind-induced response and further promoting the wind resistance design of the flexible PV support structure.
• It is not difficult to see from Figure 30 that although the fluctuating wind load was far less than the mean wind load in numerical terms, the structural displacement under the fluctuating wind load was significantly larger than that under the mean wind load in the analysis of various factors. Thus, the fluctuating wind load was non-negligible in the flexible PV support structure.

In summary, this study provided a valuable reference for the wind resistance design of flexible PV support through an in-depth analysis of the safety, durability, and wind-induced response of the thin-walled structure of the flexible PV support. In the future, the optimal panel inclination angle of the flexible PV support with less wind damage and higher power generation efficiency should be found, and the same regarding the wind direction angle and template gap. This can be achieved by carefully adjusting the key parameters, strengthening the wind resistance design, improving the safety and durability of the thin-walled structure of the flexible PV support, optimizing its power generation efficiency, and proving the applicability of composite materials in the flexible PV support structure. This, in turn, will promote the broad application of PV power generation technology, providing crucial support for the optimal design and safe long-term use of flexible PV support structures. It is of great significance to promote the development of renewable energy and cope with global climate change. With the continuous development of technology and the rapid development of the industry, flexible PV support structures will demonstrate their unique advantages and application value in many fields.