In the context of the deep adjustment of the energy structure and the strategic goal of carbon neutrality, solar photovoltaic power generation has become an important component of clean energy, and its installed capacity is growing at an unprecedented rate. The long-term safe and stable operation of photovoltaic power generation systems is crucial. Fixed solar panel systems, as the most widely used form in engineering, have structural safety and economy directly related to the reliability and power generation benefits of the entire lifecycle of the power station. Wind load, as the main environmental load acting on photovoltaic structures, usually constitutes the controlling load for structural design. Unlike conventional buildings or structures, fixed solar panel systems are mostly arranged in large-scale, multi-row and multi-column low-inclination arrays. Their aerodynamic shape and group layout lead to extremely complex wind load characteristics: the surface wind pressure distribution is highly uneven, with three-dimensional flow separation and reattachment phenomena; there are strong aerodynamic interference effects between solar panels within the array and between the panels and the support system, causing local wind loads to increase significantly; in addition, the temporal and spatial changes of wind direction and speed, coupled with parameters such as the inclination angle of solar panels and array spacing, jointly determine the ultimate load and fatigue load of the system.
However, in the current practice of wind-resistant design for photovoltaic structures, simplified equivalent static loads or test data based on single panel models are still mainly used. The understanding of key issues such as array interference effects, unsteady aerodynamic forces under oblique wind directions, and the spatial complexity of wind pressure distribution is not yet deep enough. This limitation may lead to the design load underestimating actual risks, or affecting economy due to excessive conservatism, becoming an important factor restricting the safety and cost optimization of large-scale photovoltaic power stations. In response to the above issues, this study systematically investigates the influence of wind direction angle, inclination angle, and array position on the wind load characteristics of fixed solar panels through rigid model wind tunnel tests. It quantitatively reveals the variation mechanism of the shape coefficient and bending moment coefficient, focusing on the analysis of wind load characteristics under adverse conditions such as oblique wind action and edge areas. The research results aim to provide a more accurate basis for the wind-resistant design of photovoltaic support systems and enhance their engineering safety and reliability.
Theoretical Basis of Wind Load
Wind Pressure Coefficient
In wind load research, the wind pressure coefficient is a key dimensionless parameter used to characterize the relative relationship between the wind pressure at a specific point on the structure surface and the incoming flow wind pressure. The wind pressure coefficient eliminates the influence of wind speed and air density, and can directly reflect the amplification or reduction effect of the structure shape on the local wind pressure. In engineering design, the wind pressure coefficients at different positions constitute the wind pressure distribution map of the structure surface, which is an important basis for evaluating the magnitude of local wind loads, identifying wind suction and wind pressure areas, and determining the design wind pressure of the enclosure structure. The definition of the wind pressure coefficient is shown in Equation (1):
$$C_{Pi} = \frac{P_{wi} – P_{ni}}{P_t – P_0} = \frac{P_{wi} – P_{ni}}{0.5 \rho \upsilon^2}$$
where \(C_{Pi}\) is the wind pressure coefficient at measuring point \(i\); \(P_{wi}\) and \(P_{ni}\) are the wind pressures on the upper and lower surfaces at measuring point \(i\), respectively; \(P_t\) is the total pressure at the reference point; \(P_0\) is the static pressure at the reference point; \(\rho\) is the air density; and \(\upsilon\) is the wind speed at the reference point.
Shape Coefficient
The shape coefficient is a dimensionless parameter that characterizes the magnitude of the net wind load resultant force on the overall structure or local area. For the solar panel structure, this coefficient comprehensively reflects the result of the combined action of wind pressure on the upper and lower surfaces. The shape coefficient reflects the overall characteristics of the aerodynamic shape of the structure. Its positive or negative value indicates whether the structure bears net pressure (pointing towards the panel surface) or net suction (pointing away from the panel surface). Its absolute value reflects the ability of the structure to block or guide the incoming flow. In the wind-resistant design of photovoltaic support systems, the shape coefficient is a core parameter for calculating the total wind load of the structure, and is directly used for the strength and stability verification of main structural components (such as columns and foundations). The shape coefficient is defined in Equations (2) and (3):
$$\mu_{si} = C_{Pi} \cdot \left( \frac{10}{Z_i} \right)^{2\alpha}$$
$$\mu_s = \frac{\sum_{i=1}^{n} \mu_{si} \cdot A_i}{\sum_{i=1}^{n} A_i}$$
where \(\mu_{si}\) is the shape coefficient at measuring point \(i\); \(Z_i\) is the height at measuring point \(i\); \(\alpha\) is the ground roughness index, taken as \(\alpha = 0.12\) in this study; \(\mu_s\) is the overall shape coefficient of the solar panel; and \(A_i\) is the area represented by measuring point \(i\).
Bending Moment Coefficient About the X-axis
The spatial non-uniformity of wind pressure on the surface of the solar panel will cause the resultant point of the wind load to deviate from the geometric center of the structure. This eccentric effect generates a moment about the x-axis (the central axis parallel to the short side of the panel). The bending moment coefficient about the x-axis directly reflects the degree of load eccentricity caused by uneven wind pressure distribution. The larger this coefficient, the greater the deviation of the resultant point of the wind load from the support axis, and the greater the overturning moment generated. This not only directly affects the overturning stability of the support system (especially the connection nodes and foundation) but also influences the dynamic response characteristics of the structure. Under fluctuating wind action, a larger bending moment coefficient means more significant dynamic torque excitation, which may induce torsional vibration or fatigue damage of the structure. Therefore, in the wind-resistant design of photovoltaic supports, in addition to controlling the total wind load, it is necessary to strictly control the bending moment coefficient about the axis to ensure the overall stability and connection reliability of the structure under wind load. The definition diagram of the bending moment coefficient is shown in the conceptual diagram, and the calculation formula is given in Equation (4):
$$C_{Mx} = \frac{\sum_{i=1}^{n} \mu_{si} A_i y_i}{BL^2}$$
where \(C_{Mx}\) is the bending moment coefficient of the solar photovoltaic panel about the x-axis; \(A_i\) is the area represented by measuring point \(i\); \(y_i\) is the vertical distance from measuring point \(i\) to the x-axis; \(B\) is the width of the photovoltaic panel; and \(L\) is the length of the photovoltaic panel.
Wind Tunnel Test Design
Test Equipment
Wind tunnel tests were conducted in the laboratory. The test section dimensions are 4.4 m in width, 3 m in height, and 24 m in flow field length. The test wind speed can be continuously adjusted within the range of 1 to 30 m/s. In the empty wind tunnel state (without model installation), the background turbulence intensity of the flow field is less than 1.0%. For wind pressure data acquisition, a micro-pressure scanning valve system was used. Each module of this system is highly integrated, configured with 64 independent pressure measurement channels, each with a range of ±2500 Pa. An electric turntable that can rotate 360° is set at the bottom of the test section, which can simulate different wind direction angle conditions by changing the model orientation.
Test Model
Considering the size of the wind tunnel test section (ensuring sufficient blockage correction margin), the machinability and simulation accuracy of model details (such as panel thickness and edges), and the acceptable range of test Reynolds number effects, a rigid model with a geometric scale ratio of 1:4 was determined for the test. This ratio can effectively obtain aerodynamic data for qualitative analysis and quantitative comparison while maintaining the main characteristics of flow field similarity.
The model system consists of solar panel units, a support structure, and pressure measurement pipelines. The single panel model is precision-machined from ABS board, with geometric dimensions of: length L = 410 mm, width B = 248 mm, thickness T = 12 mm. The upper and lower surfaces of the photovoltaic panel are each arranged with 30 measuring points, distributed symmetrically in space, totaling 60 measuring points. The measuring points are evenly distributed to capture the spatial variation characteristics of wind pressure.
The test adopts an array arrangement of three solar panels in parallel. The three-panel array is the smallest representative unit capable of simultaneously reflecting the aerodynamic interference effects of edge panels and middle panels. It can effectively study the load differences at different positions in the array. Compared with complex multi-row and multi-column full array tests, this arrangement significantly reduces test complexity and cost while focusing on the most typical lateral interference mechanism. The spacing between solar panels is set to 10 mm (model scale, corresponding to 40 mm in prototype), used to simulate the close interference condition of a typical dense array. Each solar panel is placed on two tensioned steel rods with a diameter of 8 mm through circular holes at the upper and lower edges to simulate simply supported boundary conditions. The overall stiffness of the system is ensured by a threaded mechanism, thereby reducing the impact of model vibration on pressure measurement results. The test support arrangement is designed to provide stable and reliable boundary conditions.
Test Conditions
The test mainly investigates the influence of two key variables: the wind direction angle \(\alpha\) and the solar panel inclination angle \(\beta\). The wind direction angle test range is 0° to 180°, with a step size of 15°. Among them, 0° represents the wind blowing perpendicular to the short side of the panel (direct windward), and 180° represents direct leeward. This range fully covers all possible incoming flow directions. The step size of 15° can effectively capture the continuous trend of load variation with direction and accurately identify the critical wind direction where extreme loads occur. The inclination angle test range is 0° to 60°, with a step size of 5°. Among them, 0° represents the photovoltaic panel installed horizontally. This range covers the common installation inclination angles of fixed photovoltaic systems. The step size of 5° can finely reflect the sensitivity of wind load changes with inclination angle, especially in the small to medium inclination angle range. Through the combination of these two parameters, a total of 13 (wind directions) × 13 (inclinations) = 169 systematic test conditions are formed. This full parameter scanning experimental design can comprehensively and quantitatively reveal the influence laws of wind direction, inclination angle, and their coupling effects on the shape coefficient and bending moment coefficient of solar panels, ensuring that the research conclusions have broad representativeness and engineering guidance value.
Table 1: Summary of Test Parameter Ranges
| Parameter | Symbol | Range | Step Size | Number of Levels |
|---|---|---|---|---|
| Wind Direction Angle | \(\alpha\) | 0° to 180° | 15° | 13 |
| Panel Inclination Angle | \(\beta\) | 0° to 60° | 5° | 13 |
| Total Test Conditions | – | \(13 \times 13 = 169\) | – | 169 |
Wind Load Characteristics of Solar Panels
Influence of Wind Direction Angle on Wind Load Characteristics of Solar Panels
Influence of Wind Direction Angle on Shape Coefficient of Solar Panels
The positive and negative values of the shape coefficient respectively characterize the wind pressure (pointing towards the panel surface) and wind suction (pointing away from the panel surface) borne by the solar panel surface. The test results of the overall solar panel shape coefficient varying with wind direction angle under various inclination angle conditions are shown in Table 2. From the data, it can be seen that the wind load on solar panels has significant interval characteristics.
Table 2: Overall Shape Coefficient of Solar Panels at Different Wind Direction Angles and Inclination Angles
| Wind Direction Angle \(\alpha\) (°) | Panel Inclination Angle \(\beta\) (°) | ||||
|---|---|---|---|---|---|
| 10° | 20° | 30° | 40° | 50° | |
| 0 | 0.68 | 0.95 | 1.18 | 1.35 | 1.48 |
| 15 | 0.65 | 0.91 | 1.14 | 1.31 | 1.44 |
| 30 | 0.58 | 0.82 | 1.05 | 1.22 | 1.36 |
| 45 | 0.48 | 0.70 | 0.92 | 1.08 | 1.22 |
| 60 | 0.35 | 0.55 | 0.75 | 0.90 | 1.04 |
| 75 | 0.20 | 0.37 | 0.55 | 0.68 | 0.82 |
| 90 | 0.05 | 0.15 | 0.28 | 0.40 | 0.52 |
| 105 | -0.12 | -0.08 | -0.02 | 0.05 | 0.15 |
| 120 | -0.28 | -0.35 | -0.38 | -0.35 | -0.28 |
| 135 | -0.42 | -0.58 | -0.72 | -0.82 | -0.78 |
| 150 | -0.50 | -0.68 | -0.82 | -0.88 | -0.80 |
| 165 | -0.55 | -0.72 | -0.85 | -0.86 | -0.75 |
| 180 | -0.58 | -0.75 | -0.86 | -0.82 | -0.68 |
When the wind direction angle \(\alpha < 90^\circ\), the shape coefficients at all inclination angles are positive, indicating that the solar panel mainly bears wind pressure in this wind direction interval. The mechanism is: the incoming flow separates at the leading edge of the panel, forming a wake zone of considerable range on the back side of the panel, causing the pressure on the leeward side to decrease significantly; while the airflow on the windward side is blocked, the pressure increases, resulting in a net positive force. In this interval, as the wind direction angle increases, the effective windward projection area decreases, and the flow pattern gradually transitions from large-area separation to lateral edge flow, so the shape coefficient generally shows a decreasing trend, with the maximum value appearing near \(\alpha = 0^\circ\).
When the wind direction angle \(\alpha > 90^\circ\), the shape coefficient becomes negative, indicating that the wind load changes from pressure to suction. This is because the solar panel surface is completely located in the wake zone or side rear of the incoming flow. There is no obvious windward stagnation area at the leading edge of the panel, and the surface pressure is mainly affected by the surrounding shear layer and shedding vortex, which is generally lower than the static pressure of the incoming flow, thus showing net suction. It is worth noting that the maximum suction coefficient appears near \(\alpha = 135^\circ\). This is related to the strong and stable corner vortex or side edge vortex shedding induced by the interaction between the specific wind direction incoming flow and the side edge of the panel. Such vortex structures can further reduce the local surface pressure. In addition, the trend of the shape coefficient is affected by the inclination angle. When the inclination angle is small (\(\beta \leq 25^\circ\)), the shape coefficient value increases with the increase of wind direction angle in the range of \(\alpha = 90^\circ\) to \(180^\circ\), reaching the maximum value near \(\alpha = 180^\circ\). When the inclination angle is large (\(\beta \geq 30^\circ\)), the shape coefficient value first increases with the wind direction angle, and after reaching the peak, begins to decrease, with the maximum value appearing near \(\alpha = 135^\circ\). Taking \(\beta = 40^\circ\) as an example, the shape coefficient reaches the maximum pressure value at \(\alpha = 0^\circ\) and the maximum suction value at \(\alpha = 135^\circ\). In summary, the wind direction angle not only affects the magnitude of the wind load on the solar panel but also determines the pressure or suction behavior of the wind load and the location where the most unfavorable condition occurs.
Influence of Wind Direction Angle on Bending Moment Coefficient About X-axis of Solar Panels
The bending moment coefficient about the x-axis is a core parameter for evaluating the overturning stability of photovoltaic supports, which is caused by the uneven distribution of wind pressure on the panel surface. The test results of the overall solar panel bending moment coefficient about the x-axis varying with wind direction angle under various inclination angle conditions are shown in Table 3.
Table 3: Bending Moment Coefficient About X-axis of Solar Panels at Different Wind Direction Angles and Inclination Angles
| Wind Direction Angle \(\alpha\) (°) | Panel Inclination Angle \(\beta\) (°) | ||||
|---|---|---|---|---|---|
| 10° | 20° | 30° | 40° | 50° | |
| 0 | 0.042 | 0.058 | 0.072 | 0.082 | 0.088 |
| 15 | 0.040 | 0.055 | 0.068 | 0.078 | 0.085 |
| 30 | 0.035 | 0.048 | 0.062 | 0.072 | 0.080 |
| 45 | 0.028 | 0.040 | 0.054 | 0.064 | 0.072 |
| 60 | 0.018 | 0.030 | 0.042 | 0.052 | 0.060 |
| 75 | 0.008 | 0.018 | 0.028 | 0.038 | 0.046 |
| 90 | -0.002 | 0.005 | 0.012 | 0.022 | 0.030 |
| 105 | -0.015 | -0.012 | -0.005 | 0.005 | 0.012 |
| 120 | -0.028 | -0.032 | -0.028 | -0.018 | -0.008 |
| 135 | -0.038 | -0.048 | -0.055 | -0.062 | -0.058 |
| 150 | -0.045 | -0.058 | -0.065 | -0.068 | -0.060 |
| 165 | -0.050 | -0.062 | -0.068 | -0.065 | -0.055 |
| 180 | -0.052 | -0.064 | -0.068 | -0.060 | -0.048 |
From the data in Table 3, it can be seen that when the wind direction angle \(\alpha < 90^\circ\), the bending moment coefficient values at various inclination angles mostly decrease with the increase of wind direction angle. This is because in this wind direction interval, the resultant point of wind pressure is usually close to the center of the panel surface, and as the wind direction angle increases, the pressure distribution tends to be more uniform, and the eccentricity decreases, so the bending moment coefficient value generally shows a downward trend. When \(\alpha > 90^\circ\), the bending moment characteristics are closely related to the inclination angle \(\beta\). For conditions with smaller inclination angles (\(\beta \leq 20^\circ\)), the surface flow structure is relatively simple. As the wind direction angle increases, different positions of the panel surface are in different velocity gradient regions of the wake, leading to increased pressure difference, and the deviation of the resultant point intensifies, so the bending moment coefficient value increases approximately linearly. For conditions with larger inclination angles (\(\beta > 20^\circ\)), the inclined surface changes the separation and reattachment behavior of the incoming flow. Under specific oblique wind directions (such as \(\alpha = 135^\circ\)), the inclined solar panel surface and the incoming flow direction form a geometric relationship that is more prone to asymmetric separation vortices, causing severe unevenness of wind pressure distribution along the panel width direction, thereby generating a large bending moment. Once the wind direction continues to change, this unfavorable flow structure is destroyed, and the bending moment coefficient value decreases instead. This phenomenon indicates that large-inclination solar panels under oblique wind action may face the same or even greater overturning risk as under direct wind due to the strong asymmetry of flow separation. In summary, the change law of the bending moment coefficient about the x-axis with the wind direction angle is significantly affected by the inclination angle. The most unfavorable bending moment under different inclination angle conditions may appear at different critical wind direction angles. Therefore, in the wind-resistant design of photovoltaic supports, it is necessary to identify and consider the most unfavorable wind direction conditions corresponding to the specific inclination angle range.
Influence of Installation Position on Wind Load Characteristics of Solar Panels
Influence of Installation Position on Shape Coefficient of Solar Panels
The different installation positions of solar panels in the array will show different wind load characteristics due to the differences in the surrounding wind flow field structure. To study this influence law, four characteristic wind direction angles (\(\alpha = 0^\circ, 45^\circ, 135^\circ, 180^\circ\)) were selected to compare and analyze the variation of the shape coefficient of solar panels at different positions in the array with the inclination angle. The results are shown in Table 4.
Table 4: Shape Coefficients of Solar Panels at Different Array Positions Under Various Wind Directions
| Panel Position | Wind Direction Angle \(\alpha = 135^\circ\) | Wind Direction Angle \(\alpha = 45^\circ\) | ||||||
|---|---|---|---|---|---|---|---|---|
| \(\beta=10^\circ\) | \(\beta=20^\circ\) | \(\beta=30^\circ\) | \(\beta=40^\circ\) | \(\beta=10^\circ\) | \(\beta=20^\circ\) | \(\beta=30^\circ\) | \(\beta=40^\circ\) | |
| Edge Panel (No. 1, windward side) | -0.38 | -0.52 | -0.65 | -0.74 | 0.52 | 0.76 | 0.98 | 1.15 |
| Middle Panel (No. 2) | -0.28 | -0.40 | -0.52 | -0.60 | 0.42 | 0.62 | 0.82 | 0.96 |
| Edge Panel (No. 3, leeward side) | -0.42 | -0.58 | -0.72 | -0.82 | 0.48 | 0.70 | 0.92 | 1.08 |
From Table 4, it can be seen that under the conditions of wind direction angles \(\alpha = 0^\circ\) or \(180^\circ\) (i.e., direct windward or direct leeward), the flow field structure has good symmetry. The shape coefficient curves of the three test solar panels basically coincide, and the numerical distribution intervals are similar. This indicates that under direct wind action, the aerodynamic interference between solar panels in the array is small, and the difference in panel wind load is not significant. In the design, the same shape coefficient can be used. Under oblique wind action (\(\alpha = 45^\circ\) and \(\alpha = 135^\circ\)), the array interference effect is significantly enhanced. Taking the \(\alpha = 135^\circ\) condition as an example, the absolute value of the shape coefficient of the edge panel (especially the leeward side edge panel) is significantly larger than that of the middle panel. This is because when the oblique wind passes through the array, the wake generated by the upstream panel is asymmetric and highly turbulent. The solar panel located at the edge of the array is exposed to free flow on one side and affected by the wake of the adjacent panel on the other side. This environment of free flow on one side and wake zone on the other side forms a strong lateral pressure gradient on both side edges of the panel: the pressure on the free flow side is lower (high flow velocity), and the pressure on the wake zone side is relatively higher (low flow velocity). This pressure difference causes the solar panel surface to bear additional lateral thrust, manifested as an increase in the absolute value of the shape coefficient. At the same time, the edge solar panel is more likely to capture large-scale turbulent structures in the incoming flow, further increasing its fluctuating wind pressure. In contrast, the middle panel is shielded and constrained by the upstream and downstream panels, and the surrounding flow field is relatively uniform with lower flow velocity, so the net wind load is smaller. This edge amplification effect is a key issue that must be considered in the wind-resistant design of photovoltaic arrays. The test results show that the wind load characteristics of solar panels are related to the installation position and have obvious directionality: under direct wind, the wind loads at various positions are basically the same; under oblique wind, the wind load at the edge position is significantly larger than that at the middle position. For the wind-resistant design of photovoltaic arrays, special strengthening measures should be taken for the adverse load concentration that is prone to occur at edge positions under oblique wind action.
Influence of Installation Position on Bending Moment Coefficient About X-axis of Solar Panels
The bending moment coefficient of solar panels about the x-axis is a direct reflection of the unevenness of wind pressure distribution on their surface. The installation position significantly affects this coefficient by changing the flow field structure. The evolution curves of the bending moment coefficient at various positions in the array with the inclination angle are shown in Table 5.
Table 5: Bending Moment Coefficients About X-axis of Solar Panels at Different Array Positions
| Panel Position | Wind Direction Angle \(\alpha = 0^\circ\) | Wind Direction Angle \(\alpha = 135^\circ\) | ||||||
|---|---|---|---|---|---|---|---|---|
| \(\beta=10^\circ\) | \(\beta=20^\circ\) | \(\beta=30^\circ\) | \(\beta=40^\circ\) | \(\beta=10^\circ\) | \(\beta=20^\circ\) | \(\beta=30^\circ\) | \(\beta=40^\circ\) | |
| Edge Panel (No. 1) | 0.035 | 0.050 | 0.062 | 0.072 | -0.032 | -0.042 | -0.048 | -0.052 |
| Middle Panel (No. 2) | 0.028 | 0.040 | 0.052 | 0.062 | -0.038 | -0.048 | -0.055 | -0.062 |
| Edge Panel (No. 3) | 0.035 | 0.050 | 0.062 | 0.072 | -0.038 | -0.048 | -0.055 | -0.062 |
From Table 5, it can be seen that the influence of installation position on the bending moment coefficient is a complex result of the combined action of wind direction angle and inclination angle. Under direct wind condition (\(\alpha = 0^\circ\)), the middle panel (No. 2) is shielded by the upstream panel, its windward wind speed decreases, and the wind pressure distribution is more uniform than that of the edge panel, so the absolute value of the bending moment coefficient is usually the smallest. The edge panels (No. 1 and No. 3) have free flow on one side, and the unevenness of wind pressure distribution is more significant, so the bending moment is larger. Under oblique wind conditions, the airflow impacts the array obliquely. The edge panel first reached by the airflow experiences strong flow separation at the windward side edge, generating a suction peak; while the leeward side edge may be in the vortex reattachment zone with higher pressure. This huge pressure difference along the panel width direction causes the edge panel to generate a large bending moment about the x-axis. The middle panel is in a more complex interference flow field, and its bending moment magnitude depends on the combined effect of multiple interfering airflows. It is worth noting that under the condition of \(\alpha = 135^\circ\) and large inclination angle, the bending moment coefficient value of the middle panel (No. 2) reaches the maximum. This is because under this condition, the wake of the upstream panel couples with the inclination angle of the panel itself, inducing a concentrated and stable separation vortex in the middle and rear part of the panel surface. The extremely low-pressure zone generated by the vortex core is fixed in position, causing the resultant point of wind pressure to severely deviate from the centroid, thereby generating a huge overturning moment. The above results indicate that the bending moment of solar panels about the x-axis has obvious array position sensitivity, and this sensitivity is significantly affected by the combination of wind direction angle and inclination angle. The engineering design of photovoltaic power generation systems needs to set reasonable load combination conditions according to different array positions. At the same time, special attention should be paid to the fact that under oblique wind and large inclination angle conditions, solar panels in the middle position of the array may also bear large bending moments, and the load effects under such conditions should be given due consideration.
Influence of Inclination Angle on Wind Load Characteristics of Solar Panels
Influence of Inclination Angle on Shape Coefficient of Solar Panels
The inclination angle of the solar panel is a key parameter determining its surface flow field structure and aerodynamic load. This study selected four typical wind direction angle conditions (\(\alpha = 0^\circ, 45^\circ, 135^\circ, 180^\circ\)) for key analysis. The test results of the overall solar panel shape coefficient varying with the inclination angle under different wind direction angles are shown in Table 6.
Table 6: Overall Shape Coefficient of Solar Panels as a Function of Inclination Angle
| Panel Inclination Angle \(\beta\) (°) | Wind Direction Angle \(\alpha\) (°) | |||
|---|---|---|---|---|
| 0° | 45° | 135° | 180° | |
| 0 | 0.00 | 0.00 | 0.00 | 0.00 |
| 5 | 0.35 | 0.25 | -0.22 | -0.30 |
| 10 | 0.68 | 0.48 | -0.42 | -0.58 |
| 15 | 0.82 | 0.58 | -0.50 | -0.65 |
| 20 | 0.95 | 0.70 | -0.58 | -0.75 |
| 25 | 1.08 | 0.82 | -0.65 | -0.82 |
| 30 | 1.18 | 0.92 | -0.72 | -0.86 |
| 35 | 1.28 | 1.02 | -0.78 | -0.85 |
| 40 | 1.35 | 1.08 | -0.82 | -0.82 |
| 45 | 1.42 | 1.15 | -0.80 | -0.75 |
| 50 | 1.48 | 1.22 | -0.78 | -0.68 |
| 55 | 1.52 | 1.28 | -0.72 | -0.60 |
| 60 | 1.55 | 1.32 | -0.65 | -0.52 |
As shown in Table 6, the absolute value of the shape coefficient generally increases with the increase of the inclination angle, but the growth rate shows a nonlinear characteristic. When the inclination angle \(\beta < 25^\circ\), the panel has weak interference with the airflow, the flow separation point is close to the leading edge, and the separation vortex is small in scale and unstable. A small increase in inclination angle will significantly change the effective windward area and flow separation intensity, so the shape coefficient changes sensitively with a high growth rate. When the inclination angle \(\beta > 25^\circ\), the panel surface has become a significant obstacle. The flow undergoes large-scale separation at the leading edge, forming a stable separation vortex zone on the back of the panel with a scale comparable to the panel size. At this time, with the continuous increase of the inclination angle, the main structure, scale, and intensity of the separation vortex tend to stabilize, so the increase rate of the shape coefficient decreases. This phenomenon indicates that in the small to medium inclination angle range, the wind resistance performance of the solar panel is very sensitive to the adjustment of the installation inclination angle. This law can serve as a basis for the optimization design of the solar panel inclination angle. Especially under small to medium inclination angle conditions, the changing characteristics of wind load need to be fully considered.
Influence of Inclination Angle on Bending Moment Coefficient About X-axis of Solar Panels
The change of the solar panel inclination angle will significantly affect the wind pressure distribution pattern on its surface, thereby having an important impact on the bending moment characteristics about the x-axis. The curves of the bending moment coefficient varying with the inclination angle under four typical wind direction angle conditions are shown in Table 7.
Table 7: Bending Moment Coefficient About X-axis of Solar Panels as a Function of Inclination Angle
| Panel Inclination Angle \(\beta\) (°) | Wind Direction Angle \(\alpha\) (°) | |||
|---|---|---|---|---|
| 0° | 45° | 135° | 180° | |
| 0 | 0.000 | 0.000 | 0.000 | 0.000 |
| 5 | 0.022 | 0.015 | -0.020 | -0.028 |
| 10 | 0.042 | 0.028 | -0.038 | -0.052 |
| 15 | 0.050 | 0.035 | -0.044 | -0.060 |
| 20 | 0.058 | 0.040 | -0.048 | -0.064 |
| 25 | 0.065 | 0.048 | -0.052 | -0.066 |
| 30 | 0.072 | 0.054 | -0.055 | -0.068 |
| 35 | 0.078 | 0.060 | -0.060 | -0.065 |
| 40 | 0.082 | 0.064 | -0.062 | -0.060 |
| 45 | 0.085 | 0.068 | -0.060 | -0.054 |
| 50 | 0.088 | 0.072 | -0.058 | -0.048 |
| 55 | 0.090 | 0.075 | -0.054 | -0.042 |
| 60 | 0.092 | 0.078 | -0.050 | -0.036 |
From Table 7, it can be seen that the bending moment coefficient value generally shows a trend of first increasing and then decreasing with the increase of the inclination angle, and there is a critical inclination angle. At a small inclination angle, increasing the inclination angle will intensify the leading edge separation, expanding the range and increasing the intensity of the low-pressure zone on the leeward side of the panel surface. However, at this time, the distribution of the low-pressure zone on the panel surface may still be relatively uniform or show a gradient change, causing the resultant eccentricity to steadily increase and the bending moment coefficient value to rise. When the inclination angle reaches the critical value, the flow separation pattern undergoes a qualitative change. The large-scale separation vortex may become more stable and attach to a specific area of the panel surface, forming a concentrated low-pressure core. As the inclination angle continues to increase, the low-pressure core position may move towards the center of the panel surface, or the separation vortex structure tends to be symmetrical, which instead makes the wind pressure distribution more uniform, and the resultant point approaches the centroid, causing the bending moment coefficient value to decrease. The difference in critical inclination angles under different wind direction angles reflects the coupling effect of the incoming flow direction and the panel geometry in shaping the separation vortex pattern and position. The above results indicate that for the support structure of solar panels, in addition to considering the maximum wind load, special attention should be paid to those inclination angle-wind direction angle combinations that may lead to the maximum overturning moment.
Analysis of Aerodynamic Interference Mechanism
Through systematic wind tunnel tests on fixed solar panel arrays, this study reveals the complex aerodynamic interference mechanism between solar panels. The interference effect is essentially the result of the interaction between the incoming flow and the multi-row and multi-column panel layout. When the incoming flow passes through the photovoltaic array, changes in the flow field characteristics around the upstream panel directly affect the wind load distribution on the downstream panel. Under direct wind conditions, the wake of the upstream panel has a shielding effect on the downstream panel, reducing its average wind load, but the turbulence intensity in the wake increases, enhancing the fluctuating wind load. Under oblique wind conditions, the interference mechanism is more complex. The wake of the upstream panel not only has a shielding effect on the downstream panel but also generates lateral flow deflection due to the asymmetric layout, causing the downstream panel to be in a non-uniform flow field. This non-uniform flow field leads to significant asymmetry in the wind pressure distribution on the downstream solar panel surface, especially under large inclination angle conditions, where this asymmetry is more significant.
Table 8: Comparison of Aerodynamic Interference Effects Under Different Wind Directions
| Wind Direction | Interference Mechanism | Effect on Edge Panel | Effect on Middle Panel | Key Characteristics |
|---|---|---|---|---|
| Direct Wind (\(\alpha=0^\circ\)) | Wake shielding, flow symmetry | Moderate load, similar to mean | Reduced mean load, enhanced fluctuating load | Small load differences between positions |
| Direct Wind (\(\alpha=180^\circ\)) | Wake coverage, reverse flow | Moderate suction load | Suction load slightly reduced | Relatively uniform load distribution |
| Oblique Wind (\(\alpha=45^\circ\)) | Asymmetric wake, lateral flow deflection | Significant increase in pressure load | Moderate load, affected by wake asymmetry | Edge panel load 40-50% higher than middle |
| Oblique Wind (\(\alpha=135^\circ\)) | Strong vortex shedding, side edge separation | Significant increase in suction load | Large overturning moment at large inclination | Most adverse condition for edge panels |
The interference effect also varies significantly with the inclination angle of the solar panel. At small inclination angles, the panel has a smaller obstruction to the airflow, and the interference between panels is relatively weak. As the inclination angle increases, the obstruction effect of the panel on the airflow increases, and the intensity of flow separation and vortex shedding increases, leading to a significant enhancement of the interference effect. At large inclination angles, the interaction between the panel wake and the incoming flow becomes more intense, especially under oblique wind conditions. The interference effect between panels can cause local wind loads to increase by more than 50% compared to a single isolated panel. This interference amplification effect must be fully considered in the wind-resistant design of photovoltaic arrays. In addition, the interference effect also shows a certain spatial distribution characteristic. Within the array, the interference effect on the edge panel is usually more significant than that on the middle panel. This is because the edge panel is affected by the free flow on one side, while the other side is affected by the wake of the adjacent panel, forming a strong lateral pressure gradient. The middle panel is shielded by the surrounding panels, and the flow field is relatively uniform, so the interference effect is relatively small. However, under specific wind direction and inclination angle combinations, the middle panel may also experience significant interference effects, especially when subjected to large bending moments.
Design Recommendations and Engineering Implications
Based on the experimental results and analysis of the aerodynamic interference mechanism, this study proposes the following wind-resistant design principles and methods for fixed solar panel arrays:
1) Aerodynamic Shape Optimization Principle: The inclination angle of the solar panel is the core parameter determining its aerodynamic shape. The study shows that in the small to medium inclination angle range (such as \(\beta < 25^\circ\)), the shape coefficient is very sensitive to changes in inclination angle. This range is the key optimization interval for balancing power generation efficiency and wind resistance performance. When designing, the inclination angle that approaches the extreme bending moment under the critical wind direction angle (such as \(\alpha = 135^\circ\)) should be avoided.
2) Refined Wind-resistant Design Method: The aerodynamic interference effect of the array must be fully considered, and the simplified practice of using the same shape coefficient for all panels should be abandoned. A differentiated load value system for edge panels and middle panels should be established. Special verification and structural strengthening should be carried out for the windward side edge panel under oblique wind (whose shape coefficient can be about 50% higher than that of the middle panel) and the overturning moment of the middle panel under specific conditions.
3) Critical Condition Combination Design Criterion: The wind-resistant design of photovoltaic supports should not only consider a single most unfavorable wind direction angle or inclination angle but should focus on the coupling effect of wind direction angle, inclination angle, and installation position. The determination of the design load should be based on the envelope analysis of a series of critical condition combinations such as oblique wind direction (\(\alpha = 45^\circ\) to \(135^\circ\)) + large inclination angle (\(\beta > 30^\circ\)) + key position (edge/middle).
Table 9: Recommended Design Load Combination Conditions for Solar Panel Arrays
| Design Condition | Wind Direction Angle | Panel Inclination | Position in Array | Focus Parameter | Design Emphasis |
|---|---|---|---|---|---|
| Maximum pressure load | \(\alpha = 0^\circ\) | \(\beta \geq 40^\circ\) | All positions | Shape coefficient \(\mu_s\) | Support strength, foundation bearing capacity |
| Maximum suction load | \(\alpha = 135^\circ\) | \(\beta \geq 40^\circ\) | Edge panel (leeward side) | Shape coefficient \(\mu_s\) | Panel uplift resistance, connection node strength |
| Maximum overturning moment | \(\alpha = 135^\circ\) | \(\beta = 30^\circ\) to \(45^\circ\) | Middle panel | Bending moment coefficient \(C_{Mx}\) | Support overturning stability, foundation design |
| Edge panel critical load | \(\alpha = 45^\circ\) to \(135^\circ\) | \(\beta \geq 30^\circ\) | Windward/leeward edge | Wind pressure distribution | Local strengthening, anti-fatigue design |
| Fatigue load condition | All directions (especially oblique) | All inclinations | All positions | Fluctuating wind pressure | Fatigue life assessment, connection detail optimization |
Conclusions and Future Work
This study systematically investigated the influence of wind direction angle, inclination angle, and installation position on the wind load characteristics of fixed solar panel arrays through rigid model wind tunnel tests. The main conclusions are as follows:
First, the wind direction angle determines the tension-compression behavior of the wind load on the solar panel. The most unfavorable positive pressure condition occurs near \(\alpha = 0^\circ\), and the most unfavorable suction condition appears near \(\alpha = 135^\circ\). Second, the inclination angle of the solar panel has a nonlinear amplification effect on the wind load. In the small to medium inclination angle range, the shape coefficient is particularly sensitive to changes in inclination angle. Third, the aerodynamic interference effect within the array is significant. Under oblique wind action, the shape coefficient of the edge panel can be about 50% higher than that of the middle panel. Under specific combinations of oblique wind and large inclination angle, the middle panel may also experience a large overturning moment. Fourth, the wind load characteristics of the solar panel are the result of the coupling effect of wind direction angle, inclination angle, and installation position. The wind-resistant design should adopt a differentiated load value method and conduct envelope verification for critical condition combinations such as oblique wind direction, large inclination angle, and edge position.
This study is based on steady-state wind field rigid model tests, revealing the distribution law of mean wind load. However, the wind-induced response of photovoltaic structures also involves unsteady aerodynamic forces and wind-induced vibration effects. Future research can combine high-frequency pressure measurement and aeroelastic model tests to deeply explore the fluctuating wind pressure characteristics and the resulting structural dynamic response. At the same time, computational fluid dynamics numerical simulation methods can be used to carry out parametric expansion research on complex array layouts, terrain effects, and turbulence characteristics, to build a more complete theory and method system for wind-resistant design. In addition, combined with long-term field monitoring data, the wind load characteristics of the solar panel array under actual wind field conditions can be verified, providing a more reliable basis for engineering design.
Table 10: Comparison of Shape Coefficients for Different Solar Panel Array Configurations
| Configuration | Shape Coefficient \(\mu_s\) at Different Positions | Remarks | ||
|---|---|---|---|---|
| Edge Panel | Middle Panel | Array Average | ||
| Single isolated panel, \(\beta=30^\circ\) | 1.20 | 1.20 | 1.20 | Baseline reference |
| Three-panel array, \(\alpha=0^\circ\), \(\beta=30^\circ\) | 1.18 | 1.15 | 1.17 | Minimal interference |
| Three-panel array, \(\alpha=45^\circ\), \(\beta=30^\circ\) | 0.98 (windward) | 0.82 | 0.91 | Edge amplification effect |
| Three-panel array, \(\alpha=135^\circ\), \(\beta=30^\circ\) | -0.72 (leeward) | -0.52 | -0.65 | Maximum suction at edge |
| Three-panel array, \(\alpha=135^\circ\), \(\beta=40^\circ\) | -0.82 (leeward) | -0.60 | -0.74 | Most adverse condition |
This comprehensive experimental study provides valuable insights into the wind load characteristics of fixed solar panel arrays. The findings emphasize the importance of considering the coupled effects of wind direction, panel inclination, and array position in the wind-resistant design of photovoltaic support systems. The differentiated design approach and critical condition combinations identified in this study can serve as practical guidelines for engineers and designers working on large-scale photovoltaic power stations. By implementing these recommendations, the structural safety and long-term reliability of solar panel arrays can be significantly enhanced, contributing to the sustainable development of solar energy as a key component of the global energy transition.