# Wind loads on heliostats and photovoltaic trackers of various aspect ratios

Abstract: For the layout of solar trackers the wind loads on the structure have to be known. They can be calculated by using wind load coefficients given in literature. But so far these values are only valid for aspect ratios of the panel (width to height) of about 1.0. Therefore the wind load coefficients for heliostats of aspect ratios between 0.5 and 3.0 were determined to close this gap. As solar trackers are exposed to the turbulent atmospheric boundary layer the turbulence of the approaching flow has to be modeled. As a reliable method at reasonable cost wind tunnel measurements were chosen. Solar trackers of 30 m2 panel size were investigated at a model scale of 1:20. Wind direction and elevation angle of the panel were varied to investigate especially the constellations at which the highest wind loads are expected (critical load cases). By spires and roughness elements a wind profile and a turbulence intensity of the modeled wind according to typical sites for solar trackers were achieved. The loads were measured by a high frequency force balance placed underneath the models. Additionally measurements of the pressure distribution on a panel with aspect ratio of 1.2 were performed to better understand the effects that lead to the peak values of the wind load coefficients. A significant impact of the aspect ratio was measured. For the critical load cases the aspect ratio dependencies of the accordant peak wind load components were determined. By these the peak wind loads on solar trackers of varies aspect ratios can be calculated. Regarding the single solar tracker components the main results are: Higher aspect ratios are advantageous for the dimensioning of the foundation, the pylon and the elevation drive but disadvantageous for the azimuth drive.

## Summary (4 min read)

### 1 Introduction

- As photovoltaic (PV) and solar thermal power plants are getting more and more important for the world wide energy supply heliostats of central receiver power plants and PV trackers are build in rising quantities.
- At the determination of the aspect ratio two contrary aims have to be taken into account:.
- For a cost effective design of solar trackers therefore the impact of their aspect ratio concerning wind loads has to be known.
- By their report the wind load coefficients for the main wind load components are available.

### 2.1 Selection of method

- Theoretically, the wind loads could be determined at real scale heliostat models exposed to atmospheric wind.
- Thus only simulation approaches at which at least the largest turbulence structures are captured are suitable (especially LES, Large Eddy simulation or DES, Detached Eddy Simulation) (Spalart, 2000).
- For some cases it is possible to determine the peak loads by just multiplying the loads gained at attacking wind of no turbulence (measured or calculated) with the square of the gust factor R accordant to the turbulence intensity of the site (for a typical solar site turbulence intensity of 18% R=1.6) (Peterka and Derickson, 1992, pp. 5ff).
- The second is the case for example for MHy at upright mirror orientation and frontal wind attack.
- Also in this case CFD or wind tunnel measurements at attacking wind of no or low turbulence in combination with the gust factor approach would not lead to realistic results for the peak values.

### 2.2 Specifications

- The mirror area (A=30m²) and the distance of the mirror plane to the ground at upright orientation (H-1/2h=0.4m) was the same for all aspect ratios.
- This means that the elevation axis height H decreases with the aspect ratio.
- Therefore H is explicitly given in the accordant formulas (table 2).
- Nevertheless for ratios of ground distance to mirror area (H-1/2h)/A much different to the value of this study the results might not be valid.
- The wind load components differ with the elevation of the panel α and of the wind direction β.

### 3.1 Similarity

- In order to obtain realistic wind loads by means of wind tunnel tests the most significant modelling laws have to be accounted for.
- For the determination in wind tunnels the micrometeorological fluctuations must be modeled according to the length scale.
- The similarity of the approaching flow depends crucially on the upstream surface characteristics.
- If the range of the frequencies of the actuating force would be in the range of the resonance frequency of the balance resonance raise would appear which would lead to too high measuring results.
- With the force balance it is possible to determine the forces and moments at the pylon feet.

### 3.3 Pressure measurements

- In addition to the measurements with the force balance pressure measurements were performed for a heliostat with the most common aspect ratio of 1.2 and with formed back structure .
- The corresponding model was constructed using sophisticated three-dimensional printing technologies.
- The mean and the fluctuating wind pressure on front and back side of the panel could be directly measured as a function of wind direction and elevation angle.
- The measurements were performed simultaneously on front and back side and throughout the entire surface area of the panel in order to be able to determine the differential pressure directly.
- For facet “A” the positions of the measuring points are given in table 1.

### 5.1 General

- The values of Peterka and Derickson (1992) for ra = 1 are mostly considerably higher than measured by the authors.
- If a heliostat model as described in (Peterka et al., 1986, p. 15) was used part of the reason would be the wide gaps between the three vertical facets.
- The aspect ratio dependencies used in (16) and (17) and given in table 2 represent fitting curves of the measured data .

### 5.2 Fx – horizontal force perpendicular to elevation axis

- For free standing plates on ground, the wind force coefficient decreases with the aspect ratio for aspect ratios < 5 (Sakamoto and Arie, 1983; Letchford and Holmes, 1994).
- For slightly lifted plates this effect is little reduced .
- In accordance (but more pronounced) a reduction of Fx for increasing aspect ratio was measured .
- The effects causing the decrease of Fx with the aspect ratio at load case 1 are also valid in a reduced manner (because of the smaller area of attack of the projection of the panel in wind direction) for load case 2 .
- Fy – horizontal force along elevation axis.

### 5.4 Fz – vertical force

- The absolute values of Fz at load case 2 decrease slightly with the aspect ratio .
- The reason might be that for bigger width b the gusts of maximal wind speed cover a smaller portion of the mirror plane.
- Therefore the mean values of Fz are very low .
- The peak values are caused by temporarily sideward wind attack which causes high pressure values at the frontal edge .
- The high differences to (Peterka and Derickson, 1992) particularly at this case are not clear.

### 5.5 Mx - moment at pylon feet about x axis

- For wind moments this leads to an almost constant aspect ratio dependency – also for at load case 5 .
- Therefore they are missing in the diagram .
- For a linear pressure distribution and different aspect ratios the lever arm of the resulting force is proportional to h whereas the value of the force itself remains the same because the mirror area is not varied.
- For load case 4 the pressure distribution which leads to the peak value of MHy is different to load case 2 .
- Presumably it is caused by a turbulence structure which just hits the mirror plane there.

### 5.7 My - moment at pylon feet about y axis

- (18) For the peak values formula (18) leads to too high results because the peak values of Fx and MHy do not appear at the same point in time since they are caused by different flow conditions.
- Therefore the modification of the formula of the load coefficient for My is the same as for Fx .
- The peak values of My at load case 4 are caused by similar pressure distributions (not shown here) as the ones of the peak values of MHy .

### 5.8 Mz - moment about azimuth axis

- As Peterka and Derickson (1992, p. 5, (5)) assume a squared mirror plane they could take for Mz the same correlation as for MHy for uniformity reasons.
- But for varied aspect ratio a dependency on the width b instead of the height h of the mirror plane would be expected which is confirmed by the measurements, see figure 22.
- The reason for the proportional increase of the absolute values of Mz with b is the approximately linear pressure distribution (not shown here) on the whole mirror plane along b comparable to MHy with h at load case 2 (see 5.6).

### 5.9 Comparison of aspect ratio dependencies without impact of wind profile

- In table 2 the quasi aspect ratio dependencies of Peterka and Derickson (1992, p. 10) and the aspect ratio dependencies representing fitting curves to the values of the peak load measurements (see 5.1) of this study are assorted.
- But at load case 4 the cross bar is exposed directly to the wind and is of higher impact on the wind loads than for the other load cases.
- Therefore the wind moment would be constant for varied aspect ratio.
- In fact the aspect ratio dependencies are less pronounced as it would be the case if the relevant pressure distributions would be linear which would lead to aspect ratio dependencies similar to the ones implicitly given by Peterka and Derickson (1992), see figures 16, 19 and 21.
- The accordant characteristic lever arms of Peterka and Derickson (1992) in table 2 h and H decrease with the aspect ratio.

### 6 Conclusions

- The wind load components vary partly significantly with the aspect ratio of the panel.
- Therefore the aspect ratio must be considered at the layout of the components of solar trackers.
- The main components are the foundation, the pylon, the panel, the elevation and the azimuth drive.
- For stow position with wind direction along with the panel height h (load case 5) only a small reduction with the aspect ratio was measured.
- The elevation drive is loaded by the hinge moment MHy.

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