Critical Wind Direction Angles and Edge Module Vulnerability in Fixed Double-Row Photovoltaic (PV) Arrays: Analysis of Extreme Wind Conditions Based on CFD Simulation

Abstract

Fixed double-row photovoltaic (PV) arrays are susceptible to wind-induced damage, while their wind load characteristics remain inadequately investigated. This study employs computational fluid dynamics (CFD) simulations to systematically analyze wind load behavior under varying operational conditions, aiming to identify critical scenarios and structural vulnerabilities. First, the validity of the CFD methodology was verified through direct comparison between wind tunnel pressure measurements of an isolated PV module and corresponding numerical simulations. Subsequently, scaled PV array models were constructed to replicate practical engineering configurations, enabling a systematic evaluation of wind direction effects on mean net wind pressure coefficients and three-component force coefficients. Finally, surface wind pressure distribution patterns were examined for four representative wind angles (0°, 45°, 135°, 180°). Results demonstrate that edge-positioned modules exhibit maximum mean net wind pressure coefficients and three-component force coefficients under oblique wind angles (45° and 135°), which are identified as the most critical operational conditions. In contrast, minimal wind loads were observed at a 90° wind angle, indicating an optimal orientation for array installation. Additionally, significantly higher surface wind pressure coefficients were recorded for edge modules under oblique winds (45°/135°) compared to both interior modules and other wind angles. It was found through the study that under upwind conditions (0–90°), the lower-row components are capable of withstanding greater wind loads, whereas under downwind conditions (90–180°), an increase in the loads exerted on the upper-row components was observed.

1. Introduction

1.1. Research Background

Global climate change has emerged as one of the most formidable challenges to human development, driving unprecedented global political consensus and decisive actions. The escalating threats posed by global warming and environmental degradation have compelled worldwide efforts to reduce reliance on conventional fossil fuels, with renewable energy development becoming a predominant trend in global energy strategies. Solar energy, as a clean, sustainable, and renewable resource, effectively addresses energy scarcity and environmental pollution. Photovoltaic (PV) power generation, recognized as the most efficient means of solar energy utilization [1,2], has become a critical alternative to traditional fossil fuels.

PV systems are primarily categorized into fixed-mounted and tracking-mounted configurations based on installation methods [3,4,5,6]. Studies have demonstrated that tracking systems exhibit superior energy conversion efficiency compared to fixed installations [7,8,9], driving their widespread global adoption [10,11]. However, their structural reliance on rotating beams to support PV modules introduces significant aerodynamic vulnerabilities under wind loads [12,13,14,15]. Notably, China’s solar-rich regions, particularly those in ecologically fragile arid and semi-arid zones such as the Northwest Gobi and North China Plain [16], face heightened wind risks due to flat terrain characteristics. Consequently, fixed-mounted PV arrays remain predominant in high-wind regions, like Southern Xinjiang. These operational realities underscore the imperative to investigate wind pressure distribution patterns and dynamic responses of PV arrays under extreme wind conditions, yielding both theoretical and practical advancements in renewable energy infrastructure resilience [17].

1.2. Literature Review of Relevant Studies

1.2.1. Methodology of Wind Load Characterization of Photovoltaic (PV) Panels

Extensive investigations have been conducted by domestic and international scholars on the wind load characteristics of photovoltaic (PV) panels, with research methodologies broadly categorized into two groups [18]: wind tunnel experiments [19,20,21] and numerical simulations [22,23]. Wind tunnel testing is further subdivided into full-scale measurements [24,25], scaled models [26,27,28,29,30,31], and aeroelastic tests [32,33]. These studies primarily focus on the effects of wind direction angles, panel tilt angles, inter-row spacing, ground clearance, array configurations, and shielding effects on wind load distributions.

Abiola-Ogedengbe et al. [34] quantified surface pressure distributions on PV modules under varying wind direction angles via wind tunnel tests, revealing symmetric pressure patterns along the central axis under frontal winds and asymmetric distributions under oblique flows. Min et al. [35] experimentally analyzed localized pressure distributions in PV arrays and conducted cost–benefit analyses, demonstrating that the first and last rows exhibited peak drag and lift coefficients due to direct wind exposure, while subsequent rows showed 45–86% reductions in these coefficients owing to shielding effects. Li et al. [36] investigated wind loads on rooftop-mounted arrays, identifying the most critical loading conditions at the first and last two rows, with mitigated lift forces in central modules as array spacing increased. A probabilistic assessment model for extreme wind loads was developed by Wang et al. [37] through the integration of meteorological station wind speed measurements and wind tunnel-derived array load coefficients. The methodology employed multivariate joint probability distributions with conditional probability analysis to systematically evaluate critical factors influencing extreme wind loads, including uncertainties in wind load coefficients, structural orientation of host buildings, and directional characteristics of wind speeds, particularly focusing on their combined effects on wind load predictions. Despite wind tunnel testing’s advantages in precision and boundary condition simulation, its high cost and limited flexibility constrain widespread application.

In contrast, numerical simulation methods have gained prominence due to their cost-effectiveness and operational versatility. Chowdhury et al. [29] numerically analyzed ground-mounted PV arrays under atmospheric boundary layer conditions, confirming maximum wind loads on windward rows and peak overturning moments under oblique wind direction angles. Ashish et al. [38] quantified lift and drag coefficients for standalone PV panels, identifying maximum wind loads under frontal winds. Zhang et al. [39] employed CFD simulations to evaluate parametric effects (tilt angle, spacing ratio, wind direction angle, ground clearance) on flexible arrays, proposing region-specific shape coefficients and developing predictive formulae incorporating height and spacing factors. An integrated optimization framework combining computational fluid dynamics (CFD) with genetic algorithms was developed by Khan et al. [40] to minimize aerodynamic lift forces on rooftop photovoltaic (PV) arrays, with optimized configurations achieving a 50% reduction in lift effects. In a separate investigation, Li et al. [41] conducted a systematic investigation via computational fluid dynamics (CFD) simulations into the unsteady aerodynamic characteristics of floating wind turbines subjected to yaw-direction oscillations. Their analysis revealed that during turbine operation, high-frequency oscillations induce negative aerodynamic thrust, a phenomenon attributed to the interaction between tip vortices and flow recirculation near the blade root.

While existing studies have systematically addressed multiple influencing parameters (e.g., tilt angle, ground clearance), fixed-mounted arrays exhibit predetermined geometric constraints through structural framing. Consequently, wind direction angle emerges as the dominant variable governing aerodynamic responses in such configurations, directly modulating the flow separation and reattachment behaviors that dictate pressure field evolution. This critical dependency underscores the necessity for dedicated investigation into wind direction angle effects on fixed double-row PV arrays to inform wind-resistant design optimization.

1.2.2. Wind Load Characteristics of Photovoltaic Panels Under Different Mounting Methods

The installation configuration of photovoltaic (PV) panels significantly influences their wind load characteristics, necessitating dedicated investigations for specific mounting systems. Extensive research has been conducted to systematically evaluate aerodynamic behaviors across various installation types, including fixed-tilt, tracking-mounted, and roof/ground-mounted configurations. Xu et al. [42] combined numerical simulations with wind tunnel testing to assess the effects of inter-row spacing and ground clearance on wind loads for near-ground PV arrays. The findings revealed that inter-row spacing substantially impacts wind load distributions, whereas ground clearance exhibits limited influence. Increased spacing was shown to attenuate shielding effects from windward rows on subsequent modules. Stathopoulos et al. [43] analyzed wind velocity profiles around roof-mounted PV arrays, identifying heightened wind suction forces on leeward modules with minimal roof-height dependency. Fu et al. [44] employed experimental and computational methods to investigate double-row flexible arrays, demonstrating that wind direction angles and panel tilt angles critically govern pressure distributions, with leeward surfaces exhibiting higher overall pressure coefficients than windward surfaces. Chi et al. [45] comparatively analyzed structural responses under parametric variations (tilt angle, wind direction angle, module gaps), establishing positive correlations between tilt angles and structural displacements, contrasted by inverse relationships with module spacing. Notably, structural displacements at 0° and 180° wind direction angles exceeded those at 45° and 135°. Li et al. [46] numerically examined rooftop PV systems across diverse roof geometries and layouts, revealing that maximum wind suction intensities increase with panel tilt angles but decrease with larger array setback distances. Xu et al. [47] conducted CFD simulations of PV modules on two-dimensional slopes, identifying terrain gradient effects that amplify or mitigate wind loads. Steeper slopes (e.g., 30° inclination) were found to reduce wind loads by up to 80% for base-positioned modules compared to flat terrain configurations. The unsteady aerodynamic lift and overturning moment characteristics of cable-supported PV panel arrays were experimentally investigated by Wan et al. [48]. Their analysis revealed deviations from the classical Sears function in two-dimensional aerodynamic admittance functions (AAFs) under zero-tilt conditions, with function values exceeding theoretical predictions in specific transitional regions. For tilted PV panels, significant AAF peaks were observed in high-wavenumber regions, a phenomenon attributed to shear layer instabilities in leading-edge separation zones. In a parallel study, Yao et al. [49] conducted wind tunnel tests to examine wind load characteristics of PV arrays installed on cosine-shaped hills. The effects of slope gradients and ground clearances on aerodynamic behavior were systematically analyzed, revealing that steeper slopes increased positive and negative peak pressures on hilltop panels by 19.0% and 27.5%, respectively. Furthermore, elevated ground clearances for hillside-mounted panels were found to amplify both peak wind pressures and suction forces, with this trend becoming more pronounced under steeper slope conditions. A separate investigation by Wu et al. [50] focused on wind-induced vibration mechanisms and suppression strategies for 35 m-span cable truss-supported PV arrays. Maximum vibrational responses were consistently identified at windward-side modules across all tested wind directions, while mid-array regions exhibited reduced oscillations due to shielding effects. Wake zone amplification was particularly notable under 0° wind conditions where group shielding effects reached maximum intensity. The study additionally demonstrated that increasing initial pre-stress in primary cables provided limited improvements to wind resistance performance.

Despite significant advancements in understanding wind load characteristics across various photovoltaic (PV) array configurations, critical knowledge gaps persist regarding fixed double-row systems—a prevalent, yet understudied, design widely implemented in ecologically vulnerable, high-wind regions such as Southern Xinjiang’s grassroots military installations. The operational context of these arrays, characterized by fragile ecosystems and persistent gale conditions, necessitates a systematic investigation into their aerodynamic behavior. This urgency stems from the configuration’s extensive deployment in environmentally sensitive areas where extreme wind events frequently compromise energy infrastructure resilience.

1.3. Research Gaps and Contributions of This Study

Despite extensive research on the effects of tilt angles, ground clearances, and other parameters on wind loads for photovoltaic (PV) panels, as well as numerous analyses of wind load characteristics for various PV array configurations, critical gaps remain in understanding fixed double-row PV arrays. These standardized-spacing, fixed-mount double-row arrays—such as the 12 × 2 configurations widely used by grassroots units in southern Xinjiang’s high-wind, ecologically fragile border regions—have not been systematically studied for their airflow separation–reattachment patterns, surface pressure reconstruction mechanisms, or overall load distribution under varying wind direction angles. Most existing literature focuses on single modules, tracking arrays, or large-scale power plant setups, leaving insufficient research on wind load evaluation methods for fixed supports with specific row spacing and double-row layouts. Additionally, there are a lack of quantitative insights to guide wind-resistant design, particularly regarding extreme load distributions under complex angles (e.g., 45° and 135° oblique winds), load differences between upper and lower rows, and wind pressure coupling effects between edge and central modules. Current wind load codes, primarily based on general building structures or single-module test data, lack clear provisions for parameters specific to fixed double-row arrays—such as double-row spacing ratios, edge effect amplification factors, and wind angle sensitivity intervals—making it difficult to identify most unfavorable load conditions and optimal layouts.

To address these gaps, this study develops a wind load analysis method for fixed double-row PV arrays through CFD numerical simulations validated against wind tunnel test data. For the first time, it systematically reveals the evolution of mean net pressure coefficients and three-component force coefficients across the full 0–180° wind direction angle range, identifying 45° and 135° oblique winds as the most unfavorable conditions and 90° as the optimal condition. Analysis of surface pressure distributions on 12 × 2 arrays shows that edge modules under oblique winds experience significantly higher loads than central modules, with distinct load disparities between upper and lower rows under forward/reverse wind directions. Using scaled models at real-world engineering scales, the study identifies coupled weak regions at array edges and wind angle-sensitive intervals, proposing a wind direction-optimized layout strategy, prioritizing 90° incoming wind alignment, to enhance structural safety cost-effectively. These findings provide critical parameters and layout strategies for wind-resistant design in high-wind regions and offer experimental data to inform new PV structure provisions in wind load codes. By bridging aerodynamic theory and practical engineering needs, the research advances safety standards for renewable infrastructure in climate-vulnerable environments.

2. Materials and Methods

2.1. Array Modeling and Computational Domain Size

For a fixed photovoltaic (PV) array structure, the wind load it is subjected to is mainly influenced by parameters such as the PV panel tilt angle, mounting height, module spacing, and wind direction angle. This study focuses on a prototype 12 × 2 PV array (panel tilt angle of 30°, spacing of 10 mm, and ground clearance of 100 mm at the lower edge) located at the Southern Xinjiang Comprehensive Solar Energy Utilization Technology Center, as shown in Figure 1. Based on this reference configuration, numerical simulations were performed to investigate the effect of wind direction angle on the aerodynamic coefficients and surface wind pressure distribution characteristics of PV modules at different locations within the array. The analysis aims to elucidate the effect of wind direction on the structural performance of the array, providing insights for optimizing the design and ensuring operational reliability under different wind direction angle conditions.

The photovoltaic (PV) module is composed of photovoltaic glass, encapsulant materials, solar cells, a backsheet, and a frame, exhibiting a typical flat-plate structure. The prototype dimensions of a single module are 2278 mm (L) × 1134 mm (W) × 30 mm (T). In this study, a 1:2 geometrically scaled-down model (1139 mm × 567 mm × 15 mm) was employed for numerical simulations to ensure computational accuracy while effectively managing computational costs. Given that the primary dimensions of the PV module are significantly larger than those of the supporting structure, the numerical simulation model retained only the module body, omitting the influence of columns and brackets. The PV array model consists of two groups of PV modules, PV modules arranged in 2 horizontal rows and 6 columns. The definition of the wind direction angle and the naming convention for each module are illustrated in Figure 2. The north–south aligned rows are labeled R1 and R2, with a row spacing of 2240 mm to avoid mutual shading. The east–west aligned columns are labeled C1 to C12, with a column spacing of 10 mm.

In accordance with the computational domain construction guidelines specified by the Architectural Institute of Japan (AIJ) standard [51], the dimensions of the computational domain in this study were set to 16a (X) × 11b (Y) × 10H (Z). As illustrated in Figure 3. a and b represent the width and length of the PV array, respectively, while H denotes the height of the highest point of the PV array above the ground. This configuration ensures a blockage ratio of less than 0.5%, thereby minimizing the influence of domain boundaries on the flow field and ensuring the accuracy of the numerical simulation results.

2.2. Mesh Division and Solution Condition Setting

The computational domain was configured with a velocity inlet boundary condition for the PV array flow field, while reference pressure was maintained at standard atmospheric pressure within the solver configuration. A pressure–velocity coupling scheme was implemented to enhance numerical convergence during simulation iterations. The mean wind velocity profile was characterized using power–law distribution, expressed as:

$$U\left(z\right)={U_0(z/z_0)}^{\alpha }$$

(1)

where $z_0$ represents the reference height (m), $U_0$ denotes the wind speed at the reference height (m/s), α is the terrain roughness exponent (0.16 for Category B terrain), Z indicates any arbitrary height (m), and $U_z$ corresponds to the wind speed at height (m/s). Additionally, the atmospheric turbulence intensity $I_Z$ was set according to Reference [51], calculated using:

$$I_Z=\left\{\begin{array}{c}0.1{\left({\displaystyle \frac{Z}{Z_G}}\right)}^{-\alpha -0.05}{Z}_b<Z\le Z_G\\ 0.1{\left({\displaystyle \frac{Z_b}{Z_G}}\right)}^{-\alpha -0.05}Z\le Z_b\end{array}\right.$$

(2)

where $Z_G$ represents the maximum height above ground (m) and $Z_b$ denotes the near-surface height (m). To numerically simulate bluff body flows, the RNG k-ε turbulence model was employed in this study. The governing equations for turbulent kinetic energy k and turbulent dissipation rate ε are defined as:

$$k\left(z\right)={1.5\left(U\right(z\left)I\right(z\left)\right)}^2$$

(3)

$$\epsilon ={\displaystyle \frac{c_{\mu }^{0.75}{k}^{1.5}}{0.07F}}$$

(4)

where U represents the incoming flow velocity (m/s), $C_{\mu }$ is a constant with a value of 0.09, and F denotes the characteristic length scale (here taken as the PV panel width). After defining the inlet boundary conditions, these parameters were customized via C-language programming and compiled into user-defined functions (UDFs). The outlet boundary of the PV array flow field was set as a pressure outlet with reference pressure at standard atmospheric conditions. The top and side surfaces of the rectangular computational domain were configured as no-slip walls.

To ensure stabilized atmospheric inflow velocity profiles along the streamwise direction, the ground boundary was assigned a no-slip condition with specified roughness height $k_s$. Following Reference [52], the ground roughness height $k_s$ is calculated as:

$$k_s=E{y}_0/C_s$$

(5)

where $y_0$ represents the roughness length (m), E denotes an empirical constant, and $C_s$ indicates the roughness constant. In this study, $y_0$ was set to 0.03 m [28], E = 9.793, and $C_s$ = 9.477, yielding $k_s$ = 0.031 m through Equation (5). During meshing, the centroid distance $y_p$ between the first and second grid layers near the ground was required to exceed $k_s$, hence $y_p$ = 0.035 m was adopted. The thickness of the first grid layer was configured as 0.035 m with a growth rate of 1.2. A hybrid meshing strategy was implemented: unstructured meshes were applied to conform to geometric contours at wall boundaries, while structured meshes filled the internal flow field.

The poly-hexcore method in ANSYS Fluent 2022R1 was employed to generate hybrid polyhedral–hexahedral core meshes for the PV panel flow domain. Local mesh refinement was subsequently applied near the PV panel models to enhance computational accuracy. Figure 4 illustrates the hybrid mesh configuration and localized refinement effects, with total grid counts ranging between 4.9 and 5.2 million across all simulated cases.

Mesh density critically determines both computational speed and simulation accuracy. To ensure rapid and precise flow field calculations, three mesh configurations (G1, G2, G3) with respective cell counts of 2,420,521, 5,196,478, and 6,790,478 were established. The three-component force coefficients of a representative PV panel (R1C1) were calculated under identical 0° wind direction conditions for all three mesh resolutions. Comparative results are presented in

Table 1. Grid independence verification.

Mesh	Drag Coefficients	Lift Coefficients	Torque Coefficients
G1	0.481	−0.816	−0.051
G2	0.515	−0.892	−0.059
G3	0.523	−0.907	−0.063

.

From a qualitative analysis perspective, both medium-density (G2) and fine (G3) meshes demonstrate superior capability in simulating wind pressure magnitudes and distribution patterns on PV panels compared to the coarse mesh (G1). While the coarse mesh (G1) captures general pressure distribution trends, the medium-density mesh (G2) achieves sufficient accuracy at a lower computational cost. Consequently, the G2 mesh configuration was selected for all subsequent simulations in this investigation.

Table 2. Boundary conditions of the numerical model.

Boundary	Boundary Conditions	Mathematical Implication
Inlet	Speed inlet	U   U(z) = U0(z/z0)0.16
		K   k(z) = 1.5(v(z)I(z))2
		ε   ε = I1.5/l
Outlet	Pressure outlet	k, ε: the same as those at the inlet boundary
Side	Symmetry	$v=0,{\displaystyle \frac{\partial }{\partial z}}$ (u,w,k,ε,ω) = 0
Top	Symmetry	$w=0,{\displaystyle \frac{\partial }{\partial z}}$ (u,v,k,ε,ω) = 0
Model surface	Wall	Standard wall function: KS = 0
Land surface	Wall	Standard wall function: KS = 0

shows the setting of boundary conditions and related parameters. The velocity inlet boundary condition is implemented through a user-defined function (UDF) coded and loaded into Fluent. The UDF consists of three components: the mean wind profile, turbulent kinetic energy, and turbulent dissipation rate. This configuration ensures an accurate representation of the inflow conditions, enabling precise simulation of the wind load characteristics on the PV array.

This study employs three-dimensional steady-state numerical simulations to analyze the average wind loads on photovoltaic (PV) arrays. The simulations were conducted using the Fluent module in ANSYS 2022R1, a commercial software package. The wind speed at the reference point is 12 m/s, at which point the airflow is considered incompressible. The SIMPLEC algorithm is used for velocity–pressure coupling, and the second-order windward scheme is used for discretization of the nonlinear convective terms in the equations of the momentum and turbulence model. The convergence criterion for all physical residuals is set to 1 × 10⁻³ during the computation to ensure the accuracy and reliability of the numerical results.

2.3. Definition of Component Wind Load Parameters

In order to better characterize the wind loads acting on PV modules, dimensionless static three-component force coefficients (drag coefficients C_D, lift coefficients C_L, and moment coefficients C_M), as well as mean wind pressure coefficient, are used in this study to represent the wind load distribution on PV structures, which are calculated by the area-weighted averaging. The static three-dimensional force coefficients are defined, as shown in Figure 5.

Taking the reference dynamic pressure as a reference, the simulation results of the wind pressure of the PV panels are normalized dimensionlessly, and the dimensionless wind pressure coefficients of the upper and lower surfaces of the PV panels can be calculated using the following expression:

$$C_{up}={\displaystyle \frac{P_{up}-P_0}{\frac{1}{2}\rho u^2}}$$

(6)

$$C_{down}={\displaystyle \frac{P_{down}-P_0}{\frac{1}{2}\rho u^2}}$$

(7)

where $C_{up}$ and $C_{down}$ are the wind pressure coefficients on the upper and lower panel surfaces of the PV panels, respectively; $P_{up}$ and $P_{down}$ are the wind pressure coefficients on the upper and lower panel surfaces of the PV panels, respectively; $P_0$ is the incoming atmospheric static pressure; u is the wind speed at the center of the PV panel; and ρ is the atmospheric density (1.225 kg/m³). The wind pressure coefficient of cell i are calculated as follows:

$$C_{pi}={\displaystyle \frac{P_{upi}-P_{downi}}{\frac{1}{2}\rho u^2}}$$

(8)

where $P_{upi}$, $P_{downi}$ are the wind pressures at the center of the upper and lower panel unit i of the PV panel, respectively. The mean net wind pressure coefficient $C_{pm}$ and the three-component force coefficients for PV panels, which include the lift coefficient $C_L$ drag coefficient $C_D$, and moment coefficient $C_M$, are expressed as follows:

$$C_{pm}={\displaystyle \frac{\sum _{i=1}^m{C}_{pi}{A}_i}{WL}}$$

(9)

$$C_L={\displaystyle \frac{F_L}{\frac{1}{2}\rho u^{2}WL}}$$

(10)

$$C_D={\displaystyle \frac{F_D}{\frac{1}{2}\rho u^{2}WL}}$$

(11)

$$C_M={\displaystyle \frac{M}{\frac{1}{2}\rho u^{2}W{L}^2}}$$

(12)

2.4. Computational Validation of Wind Loads on PV Panels

To ensure the reliability of numerical simulation results, rigorous validation procedures were conducted prior to formal experimentation. First, user-defined functions (UDF) were employed to model atmospheric boundary layer conditions at the inlet, with the resulting velocity profile and turbulence intensity distributions shown in Figure 6. Subsequently, wind load simulations were performed on a ground-mounted single photovoltaic panel under these validated boundary layer conditions. The simulated wind pressure coefficients exhibited remarkable consistency with wind tunnel measurements from Reference [34], as demonstrated by the comparative analyses presented in Figure 7 and Figure 8. This systematic validation framework confirms the accuracy of the computational fluid dynamics methodology in replicating complex wind–structure interactions for photovoltaic systems.

As illustrated in the figure, the simulated wind pressure coefficients of photovoltaic panels demonstrate reasonable agreement with wind tunnel measurements, with a maximum discrepancy of 0.15 observed between the two datasets. This minor deviation may be attributed to the deliberate exclusion of photovoltaic panel support structures in the computational model, which were omitted to simplify the atmospheric inflow boundary conditions. The validation results confirm that the numerical simulations yield sufficiently accurate predictions, thereby supporting the reliability of the proposed simulation methodology for aerodynamic analysis of photovoltaic panel arrays under wind loading conditions.

3. Results and Analysis

3.1. Wind Load Characterization of PV Panels

3.1.1. Wind Load Characteristics of Front Row PV Modules

Figure 9 illustrates the variation in the mean wind pressure coefficient for the front-row PV modules with respect to the wind direction angle (α). As shown in the figure, when the wind direction angle α ranges from 0° to 90°, the mean wind pressure coefficients are positive, indicating that the PV modules are subjected to wind pressure. Overall, the mean wind pressure coefficient exhibit a decreasing trend as the wind direction angle increases. However, for the edge modules near the incoming flow (R1C6 and R1C12), the mean wind pressure coefficients initially increase and then decrease, reaching peak values of 1.57 and 1.28, respectively, at a wind direction angle of approximately 45°. When the wind direction angle α ranges from 90° to 180°, the mean wind pressure coefficients become negative, indicating that the PV modules are subjected to wind suction in the opposite direction. The overall mean wind pressure coefficients initially increase and then decrease with increasing wind direction angle, reaching peak values at around 135°. Notably, the mean wind pressure coefficients change more rapidly within the wind direction angle range of 45° to 135°, while the variations are relatively gradual outside this range. This behavior is attributed to the strong correlation between the mean wind pressure coefficient and the projected area of the wind load acting on the PV modules in the windward direction. Within the 45° to 135° range, the projected area changes rapidly, leading to correspondingly rapid changes in the mean wind pressure coefficients.

Figure 10 and Figure 11 illustrate the variation in the mean drag and lift coefficient for the front-row PV modules with respect to the wind direction angle. The results indicate that, when the wind direction angle ranges from 0° to 90°, the drag and lift coefficients of most modules (excluding the edge modules near the incoming flow, R1C6 and R1C12) exhibit two distinct phases of variation. Taking R1C4 as an example, in the 0–60° wind direction angle range, the drag and lift coefficients decrease gradually as the wind direction angle increases; however, when the wind direction angle increases to 60–90°, these coefficients decrease rapidly and approach zero. Specifically, the drag and lift coefficient of R1C4 are 0.58 and −0.99, respectively, at a wind direction angle of 0°, gradually decreasing to 0.50 and −0.87 at 60°, and then dropping sharply to near-zero values at 90°. For the edge modules near the incoming flow (R1C6 and R1C12), the drag and lift coefficients initially increase and then decrease, reaching peak values at a wind direction angle of approximately 45°. For instance, the drag and lift coefficients of R1C6 are 0.32 and −0.55, respectively, at 0°, increasing to 0.64 and −1.11 at 45°, and then decreasing rapidly to near-zero values in the 60–90° range. When the wind direction angle ranges from 90° to 180°, the front-row PV modules transition from the windward side to the leeward side. The drag and lift coefficients generally exhibit an initial increase followed by a decrease, reaching peak values at a wind direction angle of approximately 135°.

Figure 12 illustrates the variation in the mean moment coefficient for the front-row PV modules with respect to the wind direction angle. The results indicate that, when the wind direction angle ranges from 0° to 90°, the moment coefficients of the edge modules near the incoming flow (R1C6 and R1C12) initially increase and then decrease, reaching peak values at a wind direction angle of approximately 45°. This trend suggests that these edge modules are highly sensitive to changes in wind direction. In contrast, the moment coefficients of the modules at other positions decrease gradually as the wind direction angle increases, eventually approaching zero. When the wind direction angle ranges from 90° to 180°, the moment coefficients of all modules exhibit an initial increase followed by a decrease, with peak values occurring at a wind direction angle of approximately 135°.

3.1.2. Wind Load Distribution Characteristics of the Rear Row PV Modules

Figure 13 illustrates the variation in the mean wind pressure coefficient for the rear-row PV modules with respect to the wind direction angle (α). The results indicate that, when the wind direction angle α ranges from 0° to 90°, the mean wind pressure coefficient generally exhibit an initial increase followed by a decrease, reaching peak values at approximately 45°. Notably, the mean wind pressure coefficients of the modules near the incoming flow (R2C6 and R2C12) are significantly higher than those of other modules, reaching values of 1.66 and 1.32, respectively. When the wind direction angle α ranges from 90° to 180°, the rear-row PV modules transition from the leeward side to the windward side, and their mean wind pressure coefficients generally show an increasing trend. It is worth noting that the mean wind pressure coefficients of the modules near the incoming flow (R2C6, R2C12, and R2C11) initially increase and then decrease, reaching extreme values at a wind direction angle of approximately 135°, with values of −1.06, −1.47, and −1.62, respectively. Further analysis reveals that within this wind direction angle range, the mean wind pressure coefficients of the upper-row PV modules are significantly larger than those of the lower-row modules. This phenomenon can be attributed to the fact that the upper-row modules are exposed to the incoming flow earlier, causing strong flow separation on their surfaces. As a result, the wind loads on the modules near the incoming flow are significantly higher than those on the modules farther from the incoming flow.

Figure 14 and Figure 15 illustrate the variation in the mean lift and drag coefficient for the rear-row PV modules with respect to the wind direction angle. The results indicate that, when the wind direction angle ranges from 0° to 90°, the drag and lift coefficients of the PV modules generally exhibit an initial increase followed by a decrease, reaching peak values at a wind direction angle of approximately 45°. When the wind direction angle ranges from 90° to 180°, the drag and lift coefficients of most modules (excluding those near the incoming flow, R2C6, R2C12, and R2C11) display two distinct phases of variation. Taking R2C4 as an example, in the 90–135° wind direction angle range, the drag and lift coefficient increase rapidly as the wind direction angle increases; however, when the wind direction angle increases to 135–180°, these coefficients exhibit a slower growth trend, reaching peak values at 180°. Specifically, the drag and lift coefficients of R2C4 are both 0 at 90°, increasing to 0.42 and −0.73, respectively, at 135°, and then rising gradually to 0.52 and −0.89 at 180°. For the modules near the incoming flow (R2C6, R2C12, and R2C11), the drag and lift coefficients initially increase and then decrease, reaching peak values at a wind direction angle of approximately 135°. For instance, the drag and lift coefficients of R2C12 are both 0 at 90°, increasing to −0.81 and 1.40, respectively, at 135°, and then decreasing gradually to −0.55 and 0.95 in the 135–180° range.

Figure 16 illustrates the variation in the mean moment coefficient for the rear-row PV modules with respect to the wind direction angle. The results indicate that, when the wind direction angle ranges from 0° to 90°, the moment coefficients of the PV modules generally exhibit an initial increase followed by a decrease, reaching peak values at a wind direction angle of approximately 45°. When the wind direction angle ranges from 90° to 180°, the moment coefficients of all modules display an initial increase followed by a decrease, with peak values occurring at a wind direction angle of approximately 135°. Notably, the moment coefficients of the modules near the incoming flow exhibit higher sensitivity to changes in wind direction, with significantly larger variations compared to modules at other positions.

3.2. Wind Pressure Distribution on the Surface of PV Panels

Figure 17 and Figure 18 illustrate the wind pressure distribution characteristics of the PV modules at wind direction angles of α = 0°. The results indicate that, when the front-row PV modules are subjected to a 0° wind direction angle, their upper surfaces experience wind pressure, while their lower surfaces are subjected to wind suction. The wind pressure distribution on the windward side exhibits a distinct band-like pattern with significant gradient changes: the wind pressure gradually decreases from the bottom to the top. This phenomenon can be attributed to the climbing effect of the airflow as it encounters the PV modules. During the climbing process, the airflow velocity decreases gradually due to surface friction and turbulence. Additionally, the flow separation caused by the lower edge of the PV modules further intensifies this trend, resulting in relatively lower wind pressure on the upper parts of the modules. For the rear-row PV modules, the overall wind pressure on their upper surfaces is relatively small, primarily due to the shielding effect of the front-row modules. However, it is noteworthy that the lower corner regions of the rear-row modules exhibit higher wind pressure values. This is because these regions are the first to encounter the incoming flow at this wind direction angle.

Figure 19, Figure 20, Figure 21 and Figure 22 illustrate the wind pressure distribution characteristics of the PV modules at wind direction angles of α = 45° and α = 135°. For the front-row PV modules, at a 45° wind direction angle, localized negative pressure zones appear on the upper surfaces of the modules farther from the incoming flow, while significant negative pressure regions form on the lower surfaces of the modules that first encounter the incoming flow. Simultaneously, the upper surfaces of these modules experience substantial positive pressure. Similarly, at a 135° wind direction angle, the load-bearing surfaces of the PV modules switch: the lower surfaces become the windward side, and the upper surfaces become the leeward side. Under this condition, localized negative pressure zones appear on the lower surfaces of the modules farther from the incoming flow, while significant negative pressure regions form on the upper surfaces of the modules that first encounter the incoming flow. These modules also experience substantial positive pressure, a characteristic particularly evident in the R1C6, R1C12, R2C6, and R2C12 modules, indicating that these positions are subjected to higher wind loads. The mechanism behind this phenomenon can be attributed to the complex flow characteristics of the airflow. Near the incoming flow, the airflow separates upon encountering the PV modules, forming vortices and other complex flow structures, which significantly increase the wind loads on the modules that first encounter the flow. In contrast, the modules farther from the incoming flow are located in regions where the airflow has already separated, resulting in relatively stable flow conditions and lower wind loads. The wind pressure distribution characteristics of the rear-row PV modules are similar to those of the front-row modules, but exhibit different load-bearing behaviors under different wind direction angles. At a 135° wind direction angle, the rear-row modules are primarily subjected to wind suction, while at a 45° wind direction angle, they mainly experience wind pressure.

Figure 23 and Figure 24 illustrate the wind pressure distribution characteristics of the PV modules at a wind direction angle of α = 180°. For the front-row PV modules, the upper regions of their lower surfaces experience significant positive pressure, while the upper regions of their upper surfaces exhibit notable negative pressure. Overall, the wind loads on the front-row PV modules are relatively small, primarily due to the shielding effect of the rear-row modules, which significantly reduces the impact of the airflow on the front-row modules. In contrast, the wind pressure distribution on the rear-row PV modules exhibits characteristics similar to those of the front-row modules’ upper surfaces at a 0° wind direction angle, but with an opposite trend: the wind pressure increases gradually from the bottom to the top. This phenomenon arises because, at a 180° wind direction angle, the upper edges of the rear-row PV modules first encounter the incoming flow, causing the airflow to move from the top downward. This unique flow pattern results in the observed gradient distribution of wind pressure.

The primary wind-loading surface of the photovoltaic (PV) array is the PV panels, whose surrounding airflow can be broadly divided into four regions: the displacement zone (where air shifts before contacting the panel), the separation zone (where flow detaches as it passes over both panel surfaces), the cavity zone (where vortices form on the leeward side), and the wake zone (where downstream turbulent flow arises from energy loss). At wind direction angles of 45° and 135°, the flow separation around the PV panels is depicted in Figure 25, where β represents the panel tilt angle (30° in this study). At 45°, as airflow approaches the array, it first encounters module R1C6, triggering flow separation; the separated flow then moves upward and leftward across the panel surface with diminishing kinetic energy, while the leeward side—untouched by the main flow—forms a cavity zone that generates wind suction on the panel’s back surface. At 135°, the airflow first impacts module R1C12, causing separation and downward flow toward the ground; due to the small gap between the panel’s lower edge and the surface, vortices form in the space between the panel and the ground under this reverse wind condition, resulting in wind pressure on the leeward surface while the windward surface becomes a cavity zone that induces suction on the panel’s front surface.

The comprehensive analysis results indicate that, under wind direction angles of 45° and 135°, the wind pressure coefficients at the edge regions of the PV modules are significantly higher than those at other positions and under other conditions. This suggests that the PV modules in these edge regions are at a higher risk of experiencing extreme wind loads. Therefore, during structural design, it is recommended to reinforce the PV modules and their supporting structures in the edge regions. Measures such as increasing the strength of the supports or adopting more robust connection methods can be implemented. Furthermore, in the design of PV arrays, optimizing the spacing between modules or adding windbreak devices could be considered to mitigate the wind load risks in the edge regions. These measures may effectively enhance the safety and stability of the PV system, ensuring its long-term reliable operation under complex wind conditions.

4. Discussion

4.1. Discussion of Research Results

4.1.1. Critical Working Conditions for Arrays and Discussion of the Most Unfavorable Positions

This study systematically investigates wind load distributions on fixed double-row photovoltaic (PV) arrays across varying wind angles through CFD simulations, providing critical insights for wind-resistant design in high-wind regions such as southern Xinjiang. Jubayer et al. [28] employed the SST k-ω turbulence model to analyze three-component force coefficients of standalone ground-mounted PV modules under different wind directions. Their results revealed maximum lift coefficients during windward surface exposure and peak overturning moments under oblique winds, correlating surface pressure distributions with local vorticity fields. Extending this research, our work identifies 45° and 135° oblique wind angles as critical loading conditions for 30–tilted double-row arrays. Edge modules under these scenarios exhibited maximum pressure coefficients, lift coefficients, and overturning moments, attributed to intensified flow separation and vortex interactions at array peripheries. In contrast, minimal wind loads occurred at 90° wind angle, representing structurally optimal conditions.

Consistent with documented edge effects in single-row arrays [36], edge modules demonstrated significantly higher pressure coefficients than interior modules under both headwind (0–90°) and tailwind (90–180°) conditions. The double-row configuration further amplified load non-uniformity through wake interference mechanisms. These findings provide actionable guidelines for mitigating wind-induced structural risks in ecologically vulnerable deployment areas.

4.1.2. Discussion of Wind Load Variability Between Top-Row and Bottom-Row Photovoltaic Panels

The wind load distribution characteristics of photovoltaic (PV) systems are intrinsically linked to their installation configurations. Fu et al. [41] combined wind tunnel testing and numerical simulations to investigate pressure distribution patterns on double-row flexible PV panels. Their findings revealed that under headwind conditions, central panel regions exhibited significantly higher pressure coefficients than lateral zones, while this trend reversed during tailwind exposure. Crucially, when panel tilt angles exceeded 25°, pronounced pressure coefficient fluctuations were observed, potentially inducing structural fatigue damage. Building on this foundation, our analysis of fixed double-row PV arrays identified distinct inter-tier load disparities: lower-row modules sustained higher average wind pressures under headwinds, whereas upper-row modules dominated during tailwind conditions. This phenomenon arises from flow field interference effects within the array. Initial airflow interacting with front-row modules separates into two characteristic flow regimes: (1) a boundary layer ascending along panel surfaces with velocity gradients, and (2) turbulent vortex zones forming behind modules. This flow restructuring imposes asymmetric wind loads on downstream components.

Specifically, under headwinds, lower-row modules remain preferentially exposed to direct airflow, while upper-row modules become primary impact zones during tailwinds. The resultant pressure differentials create systematic inter-tier load variations, providing critical insights for optimizing structural resilience in multi-row PV array designs.

4.1.3. Discussion on the Effect of Different Structural Rigidity of Support Structures on Wind Load Distribution

The rigidity of photovoltaic (PV) array support structures significantly influences wind load distribution characteristics. However, existing studies have primarily focused on the aeroelastic responses of flexible or tracking systems. For example, Juan et al. [53] developed a semi-empirical framework to predict aeroelastic instability in isolated two-dimensional PV tracking structures. Their research revealed how geometric and mechanical properties affect the critical wind speed at which aeroelastic instability initiates. He et al. [54], through nonlinear rigidity analysis, clarified the complex effects of tilt angles and row spacing on modal responses in flexible systems. These studies collectively demonstrate that low-rigidity systems are highly sensitive to dynamic coupling effects. In contrast, the high structural rigidity of fixed PV arrays exhibits distinctly different load transfer mechanisms. Rigid connections suppress the adaptive deformation capacity of components, making the load distribution more dependent on the geometric constraints of the support topology. Stress concentration in primary load-bearing structures becomes particularly pronounced. In flexible systems, loads are redistributed through component deformation; this mechanism is replaced in rigid systems by a reconstructed energy dissipation path due to their rigidity. This study investigates the wind load characteristics of double-row fixed PV arrays, providing a data foundation for subsequent analyses of structural rigidity in similar fixed support structures. Future research could focus on the wind-induced rigidity effects in double-row PV arrays. Through multi-condition wind tunnel experiments and parameterized numerical simulations, the influence of structural rigidity differences on load distribution in similar fixed arrays can be revealed.

4.2. Limitations and Outlook of This Study

While this study reveals the critical operational conditions of fixed double-row photovoltaic (PV) arrays through systematic numerical simulations and identifies edge regions as the primary weak points for wind-induced damage, providing key design thresholds for optimizing their wind-resistant layouts, further research is still needed in the following areas. First, to validate the accuracy of numerical simulations and provide data support for wind load studies in complex environments, more field measurements and wind tunnel tests could be conducted for the unique climatic conditions in southern Xinjiang, such as strong winds and sandstorms. These efforts would bridge the gap between computational predictions and real-world scenarios dominated by harsh meteorological factors. Second, limited by experimental validation conditions, the verification in this study only compared results for 0° and 180° wind angles. The accuracy of simulations under other wind angles remains unknown. Additionally, the simulations did not account for the influence of support structures. Future research will design wind tunnel control tests using detachable/reconfigurable support devices. By comparing aerodynamic loads with and without these structures, the additional interference contributions under different wind directions can be quantified, clarifying the role of support rigidity in load redistribution. It should also be noted that this analysis was conducted using PV modules with a 30° tilt angle. While the conclusions offer direct references for similar tilt-angle scenarios, they cannot be directly applied to installations with different angles, though the research methodology remains applicable. Future studies could use this methodology to develop simulation models for PV panels with various tilt angles, enhancing the spatiotemporal adaptability of the findings. Furthermore, considering the dynamic interaction between wind loads and the structural strength of PV components, future work should incorporate wind–structure coupling analyses. Such analyses would further evaluate the dynamic response and fatigue performance of PV arrays under extreme wind loads, providing theoretical support for structural reinforcement strategies.

Finally, based on the findings of this study, it is recommended that wind load design guidelines for dual-row photovoltaic arrays be incorporated into relevant industry standards and specifications. In practical engineering applications, photovoltaic array layouts should prioritize alignment with 90° wind incidence angles to mitigate aerodynamic risks. When hazardous wind directions are unavoidable, protective measures such as constructing windbreak walls and reinforcing support structures should be implemented. For edge region photovoltaic modules, enhanced fixation strategies—including increased anchorage points, anti-vibration bolts, and shape memory alloy fasteners—are proposed to improve overall wind resistance. As photovoltaic technology advances and expands into remote regions, continued refinement of wind load characterization will be critical for ensuring the safe and efficient operation of solar power plants. These efforts will not only inform the development of robust engineering standards for photovoltaic infrastructure, but also establish a scientific framework for wind-resistant design of similar lightweight structures in extreme climatic conditions.

5. Conclusions

Numerical simulations were conducted to investigate wind load characteristics of fixed double-row photovoltaic (PV) arrays with a 30° tilt angle under varying wind direction angles. The principal findings are summarized as follows:

(1)

When the wind direction angle is 0°, the mean net pressure coefficients of the front-row PV modules reach the maximum. When the wind direction angle is 180°, the mean net pressure coefficients of the rear-row PV modules reach their maximum. However, for the PV modules at the edges, the mean net pressure coefficients are the largest at wind direction angles around 45° and 135°. In contrast, when the wind direction angle is 90°, the mean net pressure coefficients of the PV modules are the smallest, indicating that this wind direction angle is a favorable condition for the wind resistance of the structure. Therefore, during the installation and layout of the array, this condition can be given priority, and the array should be oriented as much as possible to be consistent with the 90° incoming wind direction to significantly improve the structural safety.

(2)

The variation trends of the drag coefficient and lift coefficient of the PV modules are similar to those of the mean net pressure coefficients. The critical wind direction angles are as follows: 0° and 180° correspond to the maximum lift and drag coefficients of the middle-part PV modules in the front and rear rows, respectively, while around 45° and 135° correspond to the maximum lift and drag coefficients of the PV modules at the edges. Hence, in the array layout design, these oblique wind conditions should be avoided as much as possible.

(3)

Under oblique wind conditions with wind direction angles around 45° and 135°, the PV modules at the four edges of the array are subjected to relatively large overturning moments. Given that large overturning moments may increase the risk of damage to the edge components, it is recommended that special reinforcement measures, such as increasing the number of fixing points or using high-strength connectors, be implemented at these critical parts during the design and installation process to prevent wind-induced damage.

(4)

The maximum values of the wind pressure coefficients of the PV array occur in the PV modules at the four edges under oblique-wind conditions, and the wind pressure they experience is significantly higher than that in other conditions and at other positions of the PV modules. This further confirms that the periphery of the PV module group is the most unfavorable area for wind loads. Additionally, when the wind comes from the front (wind direction angles from 0° to 90°), the lower-row PV modules bear relatively large wind loads; when the wind comes from the reverse direction (wind direction angles from 90° to 180°), the upper-row PV modules are subjected to relatively large wind loads. Therefore, in practical engineering, wind-resistance measures for the corresponding position components should be strengthened based on the characteristics of the local dominant wind direction.