Wind Loads on a PV Array

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This study determines the wind loads for a photovoltaic (PV) array at a high angle of tilt. The data is useful for the detailed structural design of an offshore PV array.

Abstract

This study experimentally determines the wind loads on a stand-alone solar array (length-to-width ratio of 0.19; 1/10-scale commercial modules). The freestream velocity in a uniform flow is 14.5 ± 0.1 m/s, and the turbulence intensity is 0.3%. The angle of tilt ranges from 10° to 80° and the wind is incident at angle of 0°–180°. Mean surface pressure measurements on the upper and the lower surface of the inclined solar panels are used to calculate the lift coefficient. For the angle of incidence of 0°–60° for the wind, the variation in the lift coefficient with the angle of tilt is U-shaped. The formation of a strong windward corner vortex results in greater lift force on the right half of the inclined plate for the angle of incidence of 30°–45° for the wind.

1. Introduction

The use of solar energy has increased, due to public concerns about climate change and environmental pollution. The total respective capacity for solar photovoltaic (PV) systems was 303 GW and 402 GW in 2016 and 2017 [1]. A PV system consists of inclined panels, which are usually mounted on the rooftops of residential or commercial buildings. Floating PV on reservoirs, ponds, or lakes are another emergent solar energy system [2,3,4,5]. In nearshore areas, a PV system floats in the ocean using a buoyancy system [6].

To harness solar energy, PV panels for roof-top or ground systems are installed at an optimal tilt angle that allows the sunlight to fall perpendicular to the panels’ surface. Wind loads depend on the tilt angle, the angle of incidence of the wind, and the spacing and sheltering of the arrays [7,8,9,10,11]. For an inclined panel with a length-to-width ratio, L/W, of 2 that faces a uniform flow, Chung et al. [12] showed that there is a decrease in the sectional lift coefficient as the angle of tilt increases (α = 15°–25°). Corner vortices are also observed. For an inclined panel (L/W = 0.22) on flat roofs, an increase in α (= 20°–45°) produces greater suction [13]. Cao et al. [14] noted that wind-induced loads on an inclined panel are due primarily to pressure equalization at large angles of tilt and turbulence at small angles of tilt. The effect of the angle of incidence of wind, β, was investigated by Chou et al. [15]. There is greater suction on the upper surface near the windward corner for β = 15°–60°. A study by Shademan and Hangan [16] obtained similar results.

For a PV system, wind loads are significantly reduced by the presence of neighboring upwind arrays (sheltering effect) [17,18]. Therefore, this study only determines wind loads for a stand-alone PV array (nine panels, L/W = 0.19). In addition, the wind loads on the PV panels in a sea environment are not the same as those for PV panels that are located on land. The motion of a pontoon results in the variation in α during a wave cycle. The safety of PV panels in environments that feature large waves is a practical issue for the system design. To ensure that the system functions properly, the effect of α (up to 80°) and β is determined.

2. Experimental Setup

The experiments were performed in a closed-loop wind tunnel at the Architecture and Building Research Institute (Tainan, Taiwan). The wind tunnel has a working cross section of 2.6 m (height) × 4 m (width) × 36.5 m (length) and a contraction ratio of 4.71. To determine the critical wind loads, a 1/10 scale stand-alone array (nine inclined panels, P1–P9; L = 168 mm and W = 900 mm) was constructed, as shown in Figure 1. The origin of the coordinates (x/L = 0 and y/W = 0) is located at the upper left corner of the inclined plate. When the low surface faces the flow, this corresponds to β of 0°. The lift coefficient, C_L, is negative in the upward direction. The model sits 10 mm above the tunnel floor and the blockage ratio is up to 1.4%.

Meteorological data from nearshore buoys in Taiwan (Qigu, Longdong and Hsinchu) were collected [19] to determine the test conditions. The most common values of β for Qigu (23°05″42″ N) were 210°–225° and 315°–360° for the period of 2013–2017. In Longtong (25°05″48″ N) and Hsinchu (24°45″19″ N), the respective values for β were 0° and 30°–45°. The variation in α for PV panels with respect to wind was ±45°. In this study, the value of α was between 10° and 80° (in increments of 10°) and the value of β ranged from 0° to 180° (in increments of 15°). Note that the angle between the PV arrays and the surface of the sea is fixed for an offshore-type PV system. This is not the case for the wind tunnel tests. However, the experimental results of this study can be used for preliminary structural designs of an offshore PV array and to validate the numerical simulation.

For an inclined panel for which L/W = 2, Chung et al. [12] showed that there is a small increase in wind load when there is an increase in the intensity of the freestream turbulence. Therefore, the experiments for this study used a uniform flow. The freestream velocity was 14.5 ± 0.1 m/s, and the turbulence intensity was 0.3%. A Pitot-static tube was positioned at the same height as the front edge of the inclined panels to determine the static, p_∞, and the dynamic pressure, q, for the incoming flow. The Reynolds number, which is based on the length of the inclined panels, was 1.64 × 10⁵. Note that there is Reynolds number independence for an inclined panel [20]. A total of 434 pressure taps were drilled on the upper and lower surfaces of the model. Flexible polyvinyl chloride tubes of 1.1 mm in diameter and 60 cm in length were connected to SCANIVALVE multichannel modules (Model ZOC 33/64Px 64-port; Model RAD3200 pressure transducer, Scanivalve Co., Liberty Lake, WA, USA) to measure the mean surface pressure. The full-scale range of the sensors was ±2490 Pa, and the accuracy was ±0.15% of the full scale. The sampling rate was 250 Hz, and each record had 32,768 data points. The mean pressure coefficient, C_p (= (p − p_∞)/q), and C_L (= $\frac{1}{A}{{\displaystyle \int }}_A∆C_p\cos \left(\alpha \right)dA)$ were calculated. The differential pressure coefficient, ΔC_p (= C_p,up − C_p,low) was determined using the value of C_p for the upper and lower surfaces.

3. Results and Discussion

3.1. Longitudinal Pressure Distributions

Examples of the pressure distribution in the longitudinal direction, C_pl, (α = 20°–80°) for β = 0° at y/W = 0.5 are shown in Figure 2. Negative values for C_pl (or suction) were observed on the upper surface for all test cases. For α = 20° and 40°, the value of C_pl decreased along the longitudinal direction. The location with the lowest C_pl value moved upstream for α = 60° and 80°. The variation in C_pl ranged from 4.6% (α = 20°) to 10.9% (α = 60°). For an inclined panel with L/W = 2, Chou et al. [21] showed that there is a significant change in the value of C_pl for α ≤ 30°. This is due to the formation of intense side-edge vortices. On the lower surface, the value of α had a significant effect on the C_pl distribution. For α = 20° and 40°, the value of C_pl decreased initially, and then the distributions flattened. The values of C_pl for α = 60° and 80° were greater for the first half of the inclined array. This demonstrates that the localized load was most significant near the front edge for greater values of α. The value of C_pl for L/W = 0.19 (an array) was less than that for L/W = 2 (a panel).

The C_pl distributions for β = 30°at y/W = 0.5 are shown in Figure 3. On the upper surface, the distributions were flat for α = 40°, 60°, and 80° but not for α = 20°. The value of C_pl decreased significantly for the second half of the inclined array. On the lower surface, the C_pl distributions were similar to those for β = 0°. The values for C_pl were lower for β = 30°. For β = 45°, Kopp et al. [22] observed the peak system torque at angles for approaching wind that are close to the angle of the diagonal axes of an inclined panel. Figure 4 shows that the variation in C_pl on the upper surface was more significant at lower values of α. The lowest value of C_pl was observed at x/L = 0.5–0.7 for α = 20°, 40°, and 60°. This corresponds to the formation of the windward corner vortex. An increase in the value of β resulted in a decrease in the value of C_pl on the lower surface. For β = 135°, Figure 5 shows that the flow decelerated along the longitudinal direction on the upper surface. An increase in α produced a more positive value for C_pl on the upper surface and a more negative value for C_pl on the lower surface. The sectional lift coefficient increased as α increased; hence, there is a greater downward force.

3.2. Spanwise Pressure Distributions

For x/L = 0.5, the spanwise pressure, C_ps, distributions for β = 0° are shown in Figure 6. On the upper and lower surfaces, there was an inverted U-shape for α = 20°, 40°, and 60°, which corresponds to side-edge vortices. This agrees with the results for an inclined panel for which L/W = 2 [21]. Therefore, the side panels (P1 and P9) experienced greater suction on the upper surface and less lift force on the lower surface. For α = 80°, the distributions were quite flat. The difference in the pressure between the upper (highly separated flow with lower value in C_ps) and lower surfaces (near stagnation region with greater value in C_ps) was greater than that for α = 20°, 40°, and 60°.

For β = 30°, the C_ps distributions are shown in Figure 7. For the left half (P1–P4), the value of C_ps on the upper surface decreased slightly toward the right side and increased as the value of α increased. For the right half, the opposite was true. Expansion and compression were observed for α = 20°, due to the formation of a strong windward corner vortex and a greater lift force on P6–P8. On the lower surface, the value of C_ps increased from the left to the right sides as the value of α increased. The location of the maximum C_ps moved to the right side when α increased.

For β = 45°, Figure 8 shows that the C_ps distributions were similar to those for β = 30°. However, there was a greater pressure gradient on the upper surface. For α = 20°, a larger windward corner vortex was formed, and the location of the lowest value of C_ps moved to the left. For β = 135°, wind blew over the lower surface of the inclined panels. The C_ps distributions on the lower surface showed similar patterns to those on the upper surface for β = 45°, as shown in Figure 9. This shows the downward force increased from the left to the right edges.

3.3. The Lift Coefficient

C_L was calculated by integrating ΔC_p (differential pressure between upper and lower surface). The variation in C_L with α and β is shown in Figure 10. The value of C_L was negative for β ≤ 75°. The lowest value for C_L was observed for α = 30° and β = 45°. This is similar to the results of Chou et al. [21] for an inclined panel, for which L/W = 2. The value of C_L was relatively small for β = 90°, and it was positive for β ≥ 105°, which represents a downward force. The critical wind loads on the inclined panels occurred for lower values of β; hence, the effect of α on C_L is only shown for β = 0°–60° in Figure 11. For an inclined panel, for which L/W = 2, the value of C_L for β ≤ 75° decreased linearly with α (≤30°), following an increase for α = 50°. At high values of α (= 60°–80°), C_L remained approximately constant for α = 30° and 40° [21]. For β of 0°, 30°, 45°, and 60°, for which L/W = 0.19, the variation of C_L with α was U-shaped. The lowest value of C_L for β = 0° and 30° was observed at α = 20°. For β = 45° and 60°, it respectively corresponded to α = 30° and 40°. For high values of α (= 60°–80°), β had a less significant effect on the amplitude of C_L. Therefore, for an inclined array at lower values of α (≤30°) and β (≤45°), there were lower values in C_L, which was critical to the safe design of the system.

Figure 12 shows the effect of β on C_L for α of 0°–80°. For β ≤ 30°, the value of C_L decreased as α increased (≥ 20°). For β = 75°–105°, the value of α had a less significant effect. This agrees with the results of Chou et al. [21]. The value of C_L for β ≥ 120° decreased as α (= 40°–80°) increased, and the opposite was true for α =10°–30°.

The wind load on each inclined panel was of interest. For α = 30°, the variation in C_L with β is shown in Figure 13. For P1 (the left-most panel), the value of C_L increased linearly as β increased. The variation in C_L with β for P2 and P3 was similar to that for P1. However, there was a sudden increase at β = 60°–75°. For P5–P9, the value of C_L decreased initially, following an increase. The lowest value for C_L, which decreased from P5 to P9, was observed for β = 30°–45°. For β ≥ 90°, the variation in C_L for P1–P9 was less significant. This demonstrates that the wind loads on the inclined array were unsymmetrical at lower β (≤60°).

4. Conclusions

Wind loading on inclined solar panels is a key factor in the proper functioning of the system during its lifetime. This study determined the effect of the angle of tilt and the angle of the incidence of the wind on the mean surface pressure, as well as the lift coefficient for an inclined array (L/W = 0.19). There was a significant localized load near the front edge at greater angles of tilt but less than for L/W = 2. For β of 0°–60°, the variation in C_L with the angle of tilt was U-shaped. The formation of a strong windward corner vortex induced a greater lift force on the right half of the inclined plate for β = 30°–45°. Unsymmetrical wind loads on the inclined array at lower angles of incidence for the wind (≤60°) in the spanwise direction induced a greater bending moment. Wind loads on an inclined array at lower angles of tilt and angles of incidence for the wind are a cause for concern in the design of a system.