Wind load characteristics of photovoltaic panel arrays mounted on flat roof

2.1.1. Test model

The geometric scale ratio of wind tunnel test model is 1:25. A building with size L_p × B_p × H_p = 20 m × 20 m × 10 m and flat roof is adopted in this study, and the scaled model size is L_m × B_m × H_m  = 800 mm × 800 mm × 400 mm.

PV panel arrays are arranged symmetrically along the center line of the building, and each row includes 16 panels. The full size of a single panel is 1 m × 1.5 m. The model of the panel used in the experiment is named as module, and the module size is 40 mm × 60 mm. Every four module form a panel unit, mounted on one single bracket. Two types of modules are adopted in the experiment, one is the dummy module without pressure taps, and the other is the measuring module with pressure taps. Two types of measuring tap arrangement are applied for each panel, as shown in figure 1. The panels located at the first and last row is arranged with 6 measuring taps on each upper and lower surface, a total of 12 measuring taps, so each module unit has 48 measuring taps. All the other Panels are arranged with 4 measuring taps on each upper and lower surface, a total of 8 measuring taps, each unit has 32 measuring taps. Figure 1 labels a total of 8 units from M1 to M8 for the study of wind load characteristics.

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2.1.2. Experimental configurations

The test was conducted in the atmospheric boundary layer wind tunnel of Hunan University. The test section of wind tunnel is 30 m long, and the cross section is 3 m × 2.5 m. The mean wind speed profile with power law exponent of 0.15 is adopted to simulate the open terrain. The mean wind speed and turbulence intensity profiles are shown in figure 2, and spectra of the streamwise velocity fluctuation was shown in figure 3. The wind speed at 40 cm high above the floor (roof height) is used as the reference wind speed, which is 10 m s⁻¹. The velocity scale is 1/3. That means the mean wind speed at the roof height in full scale is 30 m s⁻¹. The time scale in this experiment becomes 1/8.33. The definition of wind direction angle is shown in figure 1, and test is performed with 10° interval.

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The multi-channel synchronous pressure measurement system was used to measure the wind pressure of taps. The sampling frequency was 330 Hz, 10 samples are collected for each measuring case. Each sample is 90 s, corresponding to 10 min in full scale.

Pressure coefficients of the upper and lower surface of the PV panel model are given by equations (1) and (2):

$$\begin{eqnarray}&&{C}_{pu}(i,t)=\displaystyle \frac{{p}_{u}(i,t)-{p}_{0}}{0.5\rho {u}_{h}^{2}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{C}_{p{\rm{l}}}(i,t)=\displaystyle \frac{{p}_{l}(i,t)-{p}_{0}}{0.5\rho {u}_{h}^{2}}\end{eqnarray} \tag{ 2 }$$

where C_pu (i ,t), C_pl (i ,t) are the time history of pressure coefficients of the upper and lower surface measuring tap i; p_u (i,t), p_l (i,t) are the time history of wind pressure acting on the measuring tap i of upper and lower surface; p₀ is wind tunnel static pressure; ρ is air density, ρ = 1.225 kg m⁻³; u_h is the mean wind speed at the building height, which is 10 m s⁻¹.

The net pressure coefficient at the measuring point i of the model is:

$$\begin{eqnarray}&&{C}_{pn}(i,t)={C}_{pu}(i,t)-{C}_{pl}(i,t)\end{eqnarray} \tag{ 3 }$$

C_pn (i,t) is time history of net wind pressure coefficient at the measuring point i. The positive net pressure acts downward on a module or a panel.

The force coefficient of the panel unit, C_fp (t), can then be obtained as follows:

$$\begin{eqnarray}&&{C}_{fp}(t)=\displaystyle \sum _{i=1}^{{\rm{n}}}\left[{C}_{pn}(i,t)\times {A}_{i}\right]/\displaystyle \sum _{i=1}^{{\rm{n}}}{A}_{i}\end{eqnarray} \tag{ 4 }$$

where A_i is tributary area of the measuring point i, n is the number of measuring points on the panel unit. The mean force coefficient C_{fp_mean} of panel unit can be obtained by averaging the time series of C_fp (t). For extreme force coefficient, the Cook-Mayne method is adopted, and the extreme value quantile of 80% is used accordingly for the 50 years return period design. Maximum and minimum force coefficients of the panel unit are expressed as C_{fp_min}, C_{fp_max}.

Figure 4 shows the contours of the mean pressure coefficient distribution of the panel array at 0° and 180° for Case 1. When wind direction is 0°, the mean pressure coefficients on the upper and lower surfaces of the row L1 and L2 are both negative. These results indicate that the pressure equalization phenomenon might be induced for the two sides of some panels. Pressure equalization is a phenomenon that occurs in multi-layer systems because openings in various layers allow the external wind pressures to be transmitted to interior layers, reducing the net loads across these layers (Bienkiewicz and Endo, 2009). And the absolute value of pressure coefficients of the upper surface is larger than that of the lower surface. The net pressure coefficients distributed on these two rows are negative, that means these two rows of panels are subjected to suction. Both upper and lower surface pressure coefficients of the last four rows of panels (L3-L6) become positive, and the values are relatively close to zero. Thus, the net pressure coefficient for L3-L6 is also close to null. The last four-rows No. Back located rows L3-L6 are obviously sheltered by the front-located panels. Pressure equalization of windward row panels is more significant than that of leeward row panels.

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When wind direction angle is 180°, the lower surface of the panel is facing the attacking wind. It is clear that the mean pressure coefficients of the upper and lower surfaces of row No. L6 and L5 near windward leading edge of the roof are all negative. These results also indicate the pressure equalization phenomenon. As the absolute mean pressure coefficients at the upper surface are smaller than that on the lower surface, the net pressure coefficients are positive. That means the mean wind loads on L6 and L5 rows of the panel are along the downward direction, is overpressure. The negative pressure coefficients on the upper surface of row L1-L4, far from the front edge of windward, are greater than those on the lower surface. The net mean pressure coefficients of those panels are then negative, showing the effect of lifting up.

Combining the results of wind direction angles of 0° and 180°, the mean wind load characteristics of the front two rows and the last two rows in the array are more critical. Therefore, the force coefficients acting on the four rows of panels are studied in the following.

Considering the symmetry, wind force acting on panel units M1-M8 as shown in figure 1, are checked. Figure 5(a) shows the variation of C_{fp_mean} , C_{fp_max}, C_{fp_min} of panel units M1-M4 with wind direction. It can be seen from figure 5(a) that the C_{fp_mean} of panel units M1-M4 show similar varying trend with wind direction, except for the wind direction from −60° to 60°. The most unfavorable values of C_{fp_max} for M1 ̃ M4 appear in the range of 290°−350. Such results indicate that when wind comes along the oblique direction from the back side, the maximum overpressure can reach the peak value. This may be induced by the conical vortex generated from the leading corner of building. The most unfavorable extreme wind pressure values of M1 and M3 panels are relatively large. That means the panel near the building edge may receive larger downward wind load than those located inner region. The C_{fp_min} of M1 ̃ M4 vary in the range of 0.0~−1.80. The most unfavorable wind direction angle occurs in the range of 200°~220°. That means when wind comes from this direction, the panels will experience the largest suction force along the upward direction. Among the four panels, most unfavorable extreme wind suction is the M2 and M3 panels. The most unfavorable values of C_{fp_max} and C_{fp_min} for each panel unit are shown in figure 5(b). It can be checked the suction for panels tends to be greater than pressing force in terms of absolute values. That means the vortex induced at the leading edge of building may be the main reason of such results.

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Figure 6 shows how the C_{fp_mean} , C_{fp_max}, C_{fp_min} of panel units M5-M8 vary with wind direction angle, and the corresponding most unfavorable values on the panel units. C_{fp_mean} of M5-M8 also changes with wind direction similarly. Most unfavorable C_{fp_max} of M5 ̃ M8 between 180°−190°, and the largest values are close to 1.2. The difference of most unfavorable C_{fp_max} is quite small. Such results suggest that the maximum wind load for the panel is not sensitive to the location. C_{fp_min} of M5 ̃ M8 are also within the range of 0~−1.80, and the most unfavorable wind direction angle range are about 220°~270°. Among the four panel units, the panels with the larger most unfavorable extreme wind suction are M5 and M7. That means the vortex induced by the edge near M5 and M7 is still the major reason for inducing such high suction. And if the panels are close to the edge, they may endure higher peak suction.

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According to the above research results, panels units which are located close to the roof edge may endure stronger wind load. Thus, the parametric influence analysis of wind load characteristics of panel units in the following paper is carried out for M1, M3, M5 and M7.

Three Cases are selected to study the effect of array spacing on force coefficients for panel units with different array spacing under the tilt angle 20°. Figure 7 shows C_{fp_max}, and C_{fp_min} of the M3 and M5 changing with wind direction. It can be seen that C_{fp_max} of panel units shows quite weak dependence on the array spacing. However, C_{fp_min} of panels with different spacing show relative larger discrepancies. The largest value of M3 in Case with largest array spacing (d=89.5 mm) is almost −2.0, and the largest value of M3 in Case with smallest array spacing (d=40.9 mm) is about −1.3. Such results suggest that array spacing is not a critical parameter for the positive peak force coefficients, but it plays an important role for the negative peak force coefficients. C_{fp_max} varies in the range of 0.3 ̃ 0.8, and most unfavorable maximum force coefficient of M3 appears in wind direction range of 300 ̃ 350°, while most unfavorable maximum force coefficient of M5 appears in wind direction range of 150°~200°. C_{fp_min} varies in the range of 0~−1.90, most unfavorable minimum force coefficient of M3 appears in wind direction range of 200°~220°, while most unfavorable minimum force coefficient of M5 appears in wind direction range of 220°~260°. The above results indicate that when the target panel unit is located near the leading edge of incident wind, they tend to be more vulnerable for wind load.

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Figure 8 shows the variation of C_{fp_max}, C_{fp_min} of M3, M5 changing with array spacing. C_{fp_max} of panel units M3 and M5 are basically unchanged with the decrease of array spacing. Such results suggest that the maximum force coefficient of the panel is not sensitive to the array spacing. There is the same tilt angle lead to same pressure equalization is responsible for this phenomenon.

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The absolute value of C_{fp_min} on M5 panel unit first increases and then decreases with the decrease of array spacing, while absolute value of C_{fp_min} on M3 panel decreases with the decrease of array spacing. Generally, largest lift force of panel unit M3 in the first row is larger than that of M5 in the last row. This is because when wind attacks from the back of panel, M5 is basically located inside the separation bubble, while M3 suffers the reattaching flow which has a greater wind speed and turbulence leading to higher lift force. The aerodynamics of this are similar to flow over repeated hills (or dunes), which depend on the hill slope and the spacing between hills (since it takes some time, i.e., distance, for the turbulence in the separated shear layers and reattached boundary layers to come into equilibrium). Here, the spacing is relatively short, so the turbulence continues to increase over many rows, middle located M3 unit got greater wind speed and greater turbulence. The aerodynamics of these lead to the unfavorable C_{fp_min} of M3.

Tilt angles of 10°, 20°, 30° and 40° are selected to study effects on force coefficients of panel units. Figure 9 shows the C_{fp_max}, and C_{fp_min} of typical panel units M1 and M3 changing with wind direction. It can be seen from figure 9 that C_{fp_max} and C_{fp_min} of panel units shows quite strong dependence on tilt angle. C_{fp_max} varies in the range of 0.1 ̃ 1.4 for tilt case 40°. Most unfavorable C_{fp_max} for M1 and M3 appearing in the range of 300–330°. This may due to the increase of projected area with the increase of tilt angle. C_{fp_min} varies in the range of 0~−0.80 for tilt case 10°, most unfavorable minimum force coefficients of M1 and M3 appear about 0° wind angle. For the smaller tilt angle, the weakened flow separation leads to these lower wind loads. These results indicate that pressure equalization can also be induced for small tilt angle cases. C_{fp_min} varies in the range of 0~−1.60 for tilt case 20°~40°, most unfavorable minimum force coefficients of M1 and M3 appear in the range of 190°~220°. These results indicate that there is significant local flow separation for higher tilt angle cases.

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Figure 10 shows the most unfavorable C_{fp_max}, C_{fp_min} of panel units M1, M3 varying with tilt angle. The trends of force coefficients for the two panels follow the same pattern for both minima and maxima. The larger the inclination angel of the panel unit, the larger C_{fp_max} it may endure.

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For minimum force coefficient C_{fp_min}, the extreme suction of panel M1 and M3 for 10 to 20° tilt angle changes greatly. In the tilt range of 20°~40°, C_{fp_min} almost keeps constant for both M1 and M3. These results indicate that for tilt angle greater than 20° the dependence of extreme lift force on the tilt angle of panel becomes quite weak.

Parapet wall of 1 h, 1.4 h, 2 h and 2.7 h (h is defined in figure 1) were set on the flat roof model of PV panel tilt angle 20° case. Figure 11 shows C_{fp_max} and C_{fp_min} of panels M3 and M5 changing with wind direction angle under different parapet heights.

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It can be seen that C_{fp_max} and C_{fp_min} of panel units show quite strong dependence on the parapet height. The largest C_{fp_max} of M5 for Case without parapet is almost 1.2, and it reduces to 0.8 for the cases with parapet. The minimum C_{fp_min} of M5 for Case without parapet is almost −2.0, and reduces to −0.8 for the cases with parapet. Such results suggest that parapet height is a critical parameter for both suction and pressing force.

C_{fp_max} of M3 for with parapet cases varies in the range of 0.1 ̃ 0.8, and most unfavorable maximum force coefficient appears in wind direction about 90°, while most unfavorable maximum force coefficient of M5 appears in wind direction about 250°. C_{fp_min} of M3 varies in the range of 0~−1.60, most unfavorable minimum force coefficient appears in wind direction about 110° for higher parapet cases, while most unfavorable minimum force coefficient of M5 appears in wind direction about 250° for lower parapet cases. The above results indicate that the parapet has more significant effects on wind loads for the end row panel than the middle row panel.

Figure 12 shows the most unfavorable C_{fp_max}, C_{fp_min} of panel units M3, M5 changing with parapet height. C_{fp_max} of the M3 and M5 decrease with the increase of parapet height. The changing amplitude of C_{fp_max} for M5 is larger than M3, which means that C_{fp_max} of the M5 unit is more sensitive to parapet height; C_{fp_max} of most unfavorable panel has a small change within the range parapet height of 2 h to 2.7 h. Such results suggest that parapet height of 2 h is the critical height for C_{fp_max..} Absolute value of C_{fp_min} on M3 and M5 decreases with the increase of parapet height within the range of 0 h~2 h. The changing amplitude of C_{fp_max} for M5 is greater than M3, which means that C_{fp_min} of M5 is more sensitive to parapet height. C_{fp_min} decreases with the increase of parapet height within the range of 0 h~2 h, and C_{fp_min} of parapet height of 2.7 h is slightly greater than that of 2 h. Such results suggest that C_{fp_max} and C_{fp_min} can be significantly reduced by settling a parapet with height 2 h.

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The position of panel unit has a significant influence on wind load characteristics. Figure 13 shows the most unfavorable peak force coefficients for panels about 6 m² under typical test case with tilt angle of 20° at different

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locations, as well as the wind direction that lead to these values. It can be seen from figure 13 that worst C_{fp_max} generally appears on the rear L5 and L6 row of the roof, and the unfavorable wind direction is the direction of incoming flow impinging on the upper surface. These results indicate that there is pressure equalization for rear row panels.

The largest C_{fp_min} of the panels mostly occurs at the oblique wind direction of 200°−240°. When the roof corner is facing wind flow, the conical vortex is generated at the building edge will increase wind suction of panels. These results indicate that the conical vortex is the mechanism for worst C_{fp_min} of the panels.

Different manufacturers may use different bracket systems, and number of panels supported by the bracket system is different. Thus, design force coefficients of different areas and sizes need to be given to facilitate the design of bracket system. In this section, force coefficient is specially studied for case with tilt angle 20° and array spacing 60.3 mm with full-scale area size of 0.75m², 1.5m², 3m², 6m², and 12m². Most unfavorable force coefficients for panel units with different area size in each row are shown in figure 14, where D is the distance from the front edge of the roof.

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It can be seen from figure 14 that force coefficient decreases significantly as area increases. For most unfavorable positive maximum force coefficient of panels, the difference for different rows is small, and the most unfavorable position appears in L6, because wind impinges on the lower surface. For small area size panel, most unfavorable negative minimum force coefficient of each row differs significantly, but when the area size is larger than 3m², most unfavorable negative minimum force coefficients of different row are almost equal. It is indicated that extreme force coefficients for different location can be replaced by one uniform value with considering different area size.

Figure 15 shows design recommended value of most unfavorable positive maximum force coefficient C_{fk_max} and negative minimum force coefficient C_{fk_min} for panel units of different area size. These values are referenced to the dynamic velocity pressure at the roof height based on the 10 min speed.

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