Carlos Bernardo
^{1}
Ricardo A. Marques Lameirinhas
^{1,2}^{,}*
^{}
Catarina P. Correia V. Bernardo
^{1,2}
João Paulo N. Torres
^{2,3}

Author Information

Instituto Superior Tecnico, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal

Instituto de Telecomunicações, Avenida Rovisco Pais, 1, Torre Norte-10, 1049-001 Lisboa, Portugal

Academia Militar/CINAMIL, Rua Gomes Freire 203, 1169-203 Lisboa, Portugal

*

Authors to whom correspondence should be addressed.

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Received: 25 November 2023 Accepted: 12 February 2024 Published: 20 February 2024

© 2024 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
Solar energy, as a clean source of energy, plays a relevant role in this much desired (r)evolution. When talking about photovoltaics, despite the multiple studies on parameters that affect the panels operation, concrete knowledge on this matter is still in an incipient stage and precise data remains dispersed, given the mutability of outer factors beyond technology-related properties, hence the difficulties associated with exploration. Wind is one of them. Wind loads can affect the temperature of photovoltaics, whose efficiency is reduced when higher temperatures are reached. The viability of wind as natural cooling mechanism for solar plants and its influence on their electrical energy production is studied in this research work. Some appropriate results were achieved: depending on the module temperature prediction model used and on the photovoltaic technology in question, solar panels are foreseen to be up to approximately 3% more productive for average wind speeds and up to almost 7% more productive for higher speeds. Taking into consideration that wind speed values were collected in the close vicinity of the modules, these results can be proven to be even higher. That being said, this article contributes with accurate insights about wind influence on electrical energy production of solar plants.

Keywords:
Optoelectronics; Photovoltaics; Renewable energies; Solar energy; Wind influence

```latex
I_D=I_S (e^{\frac{U_D}{n U_T}}-1)
```

```latex
I_{cell}=I_{PV}-I_D
```

```latex
I_{cell}=I_{PV}-I_S(e^{\frac{U_D}{n U_T}}-1)
```

```latex
I_{PV}=(C0+C1 \frac{ΔT}{G_{ref}})⋅G
```

```latex
P=U⋅I=U_D (I_{PV}-I_S (e^\frac{U_D}{n U_T}-1))
```

```latex
P∼U_D(I_{PV}-I_S (e^{\frac{U_D}{n U_T}}))
```

```latex
\frac{\text{d}P}{\text{d}U_D} =0⟺I_{PV}-I_S(e^{\frac{U_D}{n U_T}})(1+\frac{U_D}{n U_T })=0
```

```latex
I_{SC}=\frac{G}{G_{ref}}I_{SC_{ref}}
```

```latex
V_{OC}=nU_T \text{ln}(\frac{I_{SC}}{I_S} +1)
```

```latex
T_m=0.943⋅T_a+0.028⋅G-1.528⋅W_{speed}+4.3
```

```latex
T_c=T_{a,NOCT}+\frac{G}{G_{NOCT}} (T_{NOCT}-T_{a,NOCT})
```

```latex
T_c=T_a+\frac{G}{G_{NOCT}} (T_{NOCT}-T_{a,NOCT} )⋅\frac{h_{w,NOCT}}{h_w}⋅[1-\frac{η_STC}{τ⋅α} (1-β_{STC} T_{STC})]
```

```latexT_{c}=\frac{U_{PV}T_{a}+G\cdot\left(\tau\cdot\alpha-\eta_{STC}(1-\beta_{STC}T_{STC})\right)}{U_{PV}+\beta_{STC}\eta_{STC}G}```

```latex
T_c=T_a+G⋅e^{-3.473-0.0594W_{speed}}
```

The methodologies used are explained throughout this section. They refer to by what means the thematic introduced before was developed. Between all the new era softwares and available information, a major concern relies on how to gather trusted sources and achieve tangible and authentic results by simulation methods and calculations. Accordingly, following the equations that represent the operation of solar cells, it is imperative to estimate how wind and its mutable characteristics affect them and how it is revealed on the overall performance of the system. With the previously mentioned in mind, the equations already explained serve as a foundation to all of the remaining work.
As this paper is focused on the effect of wind (velocity and shadowing) on energy generation of solar plants – by studying the changes in temperature of solar cells according to the technologies and designs used –, the temperature values of the different modules had to be known. Having said that, the tools that allowed the acquisition of those values were the cell temperature prediction models mentioned previously, whose names are displayed in bold – Standard Approach, Skoplaki 1, Skoplaki 2, Koehl, Mattei 1, Mattei 2, Kurtz and Tamizhmani. As pointed out before, the reference model is the Standard Approach. Although the NOCT formula implies a wind speed of 1m/s, it does not take accurate wind data into account – despite wind’s known volatility – and, notwithstanding its flaws, it is an industry standard method for calculating cells’ temperature. Therefore, it becomes mandatory to cement fundamental notions when forecasting the power variation due to wind loads by consequent cell temperature fluctuations in solar plants. With this, temperature and resultant power deviations between all the models suggested were analysed in order to understand how different PV technologies behave upon different prediction models and different wind speeds.
This work was applied to all the modules present in the geometry detailed afterwards so as to investigate the effect of wind shadowing between PV arrays.
In order to perform complex engineering computations, a model of each of the intended PV geometries had to be created by scratch. For this task, a Computer-Aided Design (CAD) software is needed and the chosen softwares were FreeCAD and Fusion 360. The first one was used to create the solar PV geometries and the later mentioned ensured the design of the wind tunnels. When it comes to Computational Fluid Dynamics (CFD), which is “a science that, with the help of digital computers, produces quantitative predictions of fluid flow phenomena based on the conservation laws (conservation of mass, momentum, and energy) governing fluid motion” [24], the software that allowed its concretion was Autodesk CFD – a CFD simulation software that engineers can use to predict how liquids and gases will perform when applied to some CAD geometry.
Once acquired the wind speed values by means of CFD, Microsoft Excel was the designated software to compute the calculations of the temperature (and associated peak power variation) for every single module, according to each (1) model, (2) solar cell technology and (3) wind speed value.
As this investigation intends to propose a general perspective on how wind affects the performance of solar plants, it was required that the CFD simulations were based on suitable and concrete data, such as realistic atmospheric conditions and characteristic values, for instance, the parameters of solar cells, dimensions of the PV modules and the support system designs. In what wind speeds are concerned, as there are multiple sources of meteorological information, it was taken into account data made available by Instituto Portugues do Mar e da Atmosfera (IPMA) and Meteored. After analysing the maximum and average wind speed values for the Lisbon district throughout the year 2020, two final values were established: *W*_{avg} = 4.06 m/s – Average Average Wind Speed – and *W*_{max} = 17.55 m/s – Average Maximum Wind Speed. Since that all module temperature prediction models consider *T*_{a} and *G* – ambient temperature and irradiance, respectively – and that NOCT conditions require *G*_{NOCT} = 800 W/m^{2} and *T*_{a,NOCT} = 20 °C, the values chosen for the in-plane irradiance and ambient temperature are the same as the NOCT ones so that *G* = *G*_{NOCT} = 800 W/m^{2} and *T*_{a} = *T*_{a,NOCT} = 20 °C.
Given that there are many PV cells technologies, it is imperative to simulate the most convenient ones. With this purpose, p-Si, CdTe and CIGS technologies were the ones selected. Being that different technologies behave differently due to their intrinsic characteristics and, as beforesaid, aiming to the most accurate real-life simulation results, three distinct solar panels datasheets were collected – one for each technology. These datasheets can be found in [25,26,27], respectively. Their main characteristics (that are fundamental for the calculations) are expressed in Table 1.**Table 1. **Main parameters for each solar cell technology.Before proceeding to the computational simulations, a CAD geometry of the PV arrays had to be created having in mind its real dimensions. Understanding that each company produces PV modules of distinct sizes, it would not be adequate to simulate different geometries and then compare the results obtained, given that the design of each structure influences the aerodynamics hence the wind speeds around solar panels, which would lead to misleading results. For this reason, only one geometry was considered, having in mind that the Temperature Coefficient of *P*_{mpp}, *β*_{STC}, and the remaining parameters accounted in every cell temperature prediction model are technology/material-specific and their value is not dictated by module’s dimension. The dimensions used for constructing the CAD models were 1645 × 992 × 35 mm, that correspond to the p-Si panels. That being said, two geometries were created, as seen in Figure 1 and Figure 2 – arrays of three and nine panels, respectively, in two parallel rows, distancing 2140 mm from each other.
For the purpose of studying wind flow around the panels, CFD simulations demand that the geometries created have to be inside a wind tunnel. Assuming h as the total height of the CAD model, w its total width and l its total length, tunnels were created respecting the following rules proposed by Autodesk, the company that developed Autodesk CFD [26]: 3h < th < 4h – model sitting on the floor (z = 0) and th being the tunnel height; 5w < tw < 7w – model in the center and being tw the tunnel width; tunnel length from the front (inlet) to the object equal to 2l (in the direction of flow); tunnel length from the object to the back (outlet) and equal to 4l (in the direction of flow).**Figure 1. **Two rows of arrays (3 by 2).**Figure 2. **Two rows of arrays (9 by 2).Before running simulations, the geometries created had to go through a process called meshing, which is the process of dividing a CAD model into multiple small cells (mathematically defined shapes) that can be used to discretize a domain in order to simplify a geometry’s complexity and to whom the governing equations are applied when solving simulations.
The final step before proceeding to simulations was to setup the solver. It was where fluid material properties, boundaries and the flow physics model were defined. As a thermal analysis was not performed, the materials assigned to the rows of PV panels were neglected – the geometry was only defined as a solid. However, the fluid inside the wind tunnel must be air, obviously. Wind tunnel structure does not present any requirement in what concerns materials; in spite of that, it inevitably needed boundaries designation, which is a process based on imputing physical conditions to the boundaries of the flow domain – the so-called boundary conditions. They are inherent to the wind model applied to the wind tunnel, that is detailed right away. That being said, the boundary conditions set were: inlet – velocity type, with magnitudes of *W*_{max} and *W*_{avg} (steady-state); outlet – pressure type, equal to zero (steady-state); top and sides – slip/symmetry type. Once the front of the PV geometry is facing the inlet, wind flow is parallel to planes xOy and yOz and perpendicular to xOz.
Finally, with the understanding that wind is a fluid flow, when simulation the wind influence on photovoltaic panels, it was decided to neglect its laminar phase, since it is well known that the laminar phase of a flow (smooth path with no disruption between adjacent paths) is much smaller than its turbulent one (chaotic path that comprises eddies, swirls and flow instabilities) in the type of problem studied here. Thereby, a turbulent flow k-ε (which is the default turbulence model in Autodesk CFD) was applied as an external flow in the longitudinal direction of the wind tunnel, at the inlet. The standard model was chosen by virtue of its characteristics: it gives accurate predictions on distribution of speed around CAD geometries [29] and it is a general purpose model (the most used) that performs well for a large number of applications. The model is part of the Reynolds-Average Navier Stokes (RANS) family of turbulence models and both letters that name it refer to two transport equations that are solved upon its usage: turbulent kinetic energy – energy in turbulence – and turbulent dissipation rate – rate of dissipation of turbulent kinetic energy –, respectively.

Wind flow around the PV arrays was analysed for each geometry, taking into consideration the two aforementioned wind velocities at the inlet: *W*_{avg} = 4.06 m/s and *W*_{max} = 17.55 m/s. In order to extract valuable information about turbulent flow behaviour, a vertical plane – parallel to yOz and perpendicular to xOz – was applied to the wind tunnel, for each geometry and for each inlet wind speed. This generated a cross section inside the tunnel’s volume, where it can be observed the wind flow pattern. With the purpose of obtaining a general wind flow distribution around the whole geometries, a rectangular grid of points was defined at the inlet. Each of these points generates a path across the tunnel for the corresponding wind element point, creating a continuous line.
In what the first CAD model is concerned (3 by 2 geometry), its simulations results for *W*_{avg} are shown in Figure 3 and Figure 4. For the first one, the vertical plane is aligned with the central module of both rows, given that they are parallel (x and z coordinates are equal). For the later one, the plane is aligned with the tip module of each array. The left side scale indicates the velocity magnitude in cm/s, starting in 0 cm/s and ending in 514.366 cm/s for all the figures that refer to this wind speed value. It was observed that the wind shadow phenomenon introduced earlier occurs, which implies a decrease in wind speed right after the first array, thus leading to a lower wind intensity for the second row. When inspecting the wind behaviour close to the front PV module, it was possible to verify that wind has higher speed magnitudes in the upper portion of its face. Although this also happens to the equivalent panel of the second row, the magnitudes are much different, which will cause disparities between temperatures of the modules.
It can be said that despite the fact that turbulent flows are not likely to be perfectly predictable, there is approximately a symmetry of wind flow distribution thus wind speed distribution from the middle of each row to each of its extremities.
Consequently, there is no need to show wind flow simulations for both of them. By examination of the cross section that represents wind flow for the surroundings of the tip modules of each row, it was seen that the wind shadow effect is attenuated, hence the rear panel presents higher speed values near its face if compared to the central module. At the same time, it is clear that wind has a not so different behaviour for all the front row modules when compared to the rear set.
Figure 5, which is also a side view that allows the perception of wind movement along the wind tunnel when crossing the whole PV structure, made evident the appearance of swirls that differ from the common motion of the fluid, as they are represented mostly by blue lines after each array. These swirls are the so-called eddies in fluid mechanics. Their energy is successively transferred from large eddies to smaller ones until it is dissipated [30]. This figure confirms wind shadowing between rows of panels by two factors: reduction of lines density and mitigation of wind speed.
The same procedure was repeated for *W*_{max}, where similar results were obtained proportionally, i.e., the wind behaviour was verified as identical, but wind speeds presented higher magnitudes and turbulent events were enhanced.
Next, wind velocity values were collected for a very close vicinity of the panels’ faces. These values are shown in Table 2, in which the parcel Ratio indicates the ratio between the wind speed collected and the inlet speed value. Note that the numbering of panels is done from left to right and it starts in the left tip panel of the first row.**Figure 3. **Wind flow for a vertical panel aligned with central module of the 3 by 2 geometry – *W*_{avg}.**Figure 4. **Wind flow for a vertical plane aligned with tip module of the 3 by 2 geometry – *W*_{avg}.**Figure 5. **Side view of wind flow for the 3 by 2 geometry – *W*_{avg}.**Table 2. **Main parameters for each solar cell technology.By comparison of the values for both wind speed values, their similarity in what the ratio is concerned is truly evident. There is a significant decrease of wind speed for the central module of the second row (panel 5) but the effective difference between panel 1 and 4 and between 3 and 6 is almost unnoticeable; although the distribution of wind speed may not be so alike, the average wind speed values are.
The 3 by 2 geometry presents a reduced complexity when compared to the geometry covered in this subsection. Although it can represent a real-life situation in such a manner that the simulations results detailed before are a very coherent starting point for what can be expected for other arrangements, the most common designs found in solar plants are clearly more similar to this second one. This being said, each of the tasks performed for the simpler CAD model were replicated to the 9 by 2 geometry.
Starting by the analysis of simulations related to *W*_{avg}, a vertical plane was applied to the wind tunnel, as it can be seen in Figure 6, generating a cross section along the PV structure and the tunnel. This figure depicts the wind flow for the area represented by the plane. The scale displayed in the left side of the figures that illustrate the average average wind speed at the inlet indicates the velocity magnitude, starting in 0 cm/s and goes up to 645.984 cm/s. As it was done for the previous geometry, the plane is aligned with the central module of the 9 by 2 geometry. Once again, the wind shadow effect can be observed due to the much lower wind speed verified for the surroundings of the rear module.
Figure 7 shows wind flow when the vertical plane is aligned with the tip modules. By its inspection, it was possible to confirm that just like with the preceding geometry, wind shadowing effect is almost null for the modules at the extremities.**Figure 6. **Wind flow for a vertical panel aligned with central module of the 9 by 2 geometry – *W*_{avg}.**Figure 7. **Wind flow for a vertical panel aligned with tip module of the 9 by 2 geometry – *W*_{avg}.Wind velocity values were also collected for this geometry respecting to each of the velocities at the inlet, *W*_{avg} and *W*_{max}. These values are exhibited in Table 3. By its inspection, it was noticed an abrupt difference between the wind speeds registered for the tip modules of the rear row (panels 18 and 10) and the remaining, as expected. There is a clear difference between both scenarios: for a lower velocity at the inlet, the ratios observed for the tip panels of each row (1 and 10, 9 and 18) decrease substantially from the front to the rear row, but for a higher wind velocity at the inlet, the wind shadow effect is reduced for the tip panels, which leads to a similar ratio when comparing wind speed for panel 1 with 10 and panel 9 with 18 for this velocity – relations that are closer to what was verified for the first geometry.**Table 3. **Wind speed for each panel (9 by 2 geometry).Temperature predictions were only performed for the second geometry (9 by 2), which depicts a more common case in solar plants. In addition to that, due to the similarities verified for wind flow for both of the geometries under study, it would be almost redundant to calculate the temperatures for each geometry. That being so, the calculations for the 9 by 2 geometry were done according to the following: module temperature forecast according to each prediction model; for each prediction model, each PV Having said that, Table 4 shows the values of temperature (in °C) predicted by each model, taking into account each PV technology and the two distinct wind speed values used in CFD simulations, *W*_{avg} = 4.06 m/s and *W*_{max} = 17.55 m/s. Each of the values displayed refers to a single average temperature value for each set of 18 panels. As it was aforesaid, it is important to mention that models Skoplaki 1, Skoplaki 2, Koehl, Mattei 1 and Mattei 2 take into consideration technology-relative parameters, whereas Kurtz and Tamizhmani do not. This is the reason why the temperatures are the same for the same values of wind speed, disregarding technologies.
Remembering that the Standard Approach is the reference model, which does not account with wind data (it just has an implicit wind velocity of 1 m/s associated), the variation of the temperatures predicted by the models that take wind data into account compared with the standard model is very significant: the maximum absolute variation (worst case) between the results predicted by the complex models is 8.18 °C, but it is increased to 18.73 °C when compared with the SA – this type of discrepancy is much more common throughout all the comparisons between the other models with the Standard Approach than with one another. By inspection of Table 4, it is visible that the Skoplaki models predict lower temperatures than the other models for every technology; the Koehl model is the one that exhibits higher variations with the various technologies; the Mattei models present very similar temperatures across all the technologies and the results they generated are identical between both models, never showing a variation of more than 1.04 °C; the Kurtz and Tamizhmani models predicted close temperatures between them for *W*_{avg}, but differ for higher wind speeds. One interesting case that deviates from all the others is the prediction performed by the Koehl model for the CIGS technology at *W*_{avg}, which is slightly higher than the value expected by the NOCT formula.
It was noticed that the predicted temperatures are always lower for *W*_{max} in contrast to *W*_{avg}, which clarifies the influence that wind has as a cooling mechanism for solar photovoltaic modules. The higher the speed, the lower the temperature predicted according to the module temperature prediction models. These variations in temperature can make all the difference in the output power of the panels, since high temperatures reduce modules efficiency.
Taking into consideration the temperatures predicted in the previous section, the corresponding output power variations were calculated. Knowing that the SA is the reference model, it can be assumed that its predictions correspond to the temperatures commonly expected and these temperatures correspond to a certain power output variation. Being that all the temperatures predicted by the different models are lower than the ones foreseen by the NOCT formula, except for the case mentioned above, the values displayed in Table 5 are the difference between the temperatures predicted by the models that take wind data into account and the values anticipated by the Standard Approach multiplied by the temperature coefficient of Pmpp. Given that βSTC units are %/°C, the results obtained are in percentage.
The interpretation of Table 5 is that wind speed (*W*_{avg} or *W*_{max}) has an influence such that its flow increases/decreases output power in x% when compared with the output power variation normally expected by the SA, in which wind is not taken into consideration.**Table 4. **Values of temperature in °C for each set of 18 PV panels.**Table 5. **Output power variation in percentage (%) for each set of 18 PV panels.

This paper was developed with the main purpose of studying the influence of wind in energy generation of solar plants. To accomplish this task, several parameters were analysed, which culminated in the decision of giving preference to the investigation of how wind could perform as a natural cooling mechanism for solar photovoltaic modules in solar plants look-alike arrangements of PV arrays. Delving into the several methods one could use to examine the interaction between wind flow and modules temperature, it was decided to follow empirical models that predict panels temperature according to various wind speeds and technology-based parameters (for most of them). Given that individual technologies present intrinsic properties, the temperatures that would be foreseen would tend to vary from technology to technology. The understanding of this fact led to the choice of three technologies in vogue worldwide (by distinct factors). Due to the fact that it would not be plausible to compare wind flow around geometries of different sizes, it was assumed that all three had exactly the same proportions, but with different parameters that would characterise each of them; since the variables used in the temperature prediction models are technology-related, dimensions could be neglected.
That being said, a Computational Fluid Dynamics analysis of the wind flow around PV geometries was done with the intention of collecting data on wind speeds close to the solar photovoltaic panels. It was observed that for the direction of wind studied, the front rows of photovoltaic arrays always show higher wind velocity magnitudes, which are similar to the ones registered for the tip panels of the rear rows; the occurrence of wind shadowing between rows of panels imply lower wind speeds for most back panels. The referred data were used in the calculations related to the modules temperature predictions that were subsequently crucial to the output power variation results calculated for each scenario. To execute this assignment, it was imperative to use factual wind information that was gathered from reliable sources, thus empowering simulations of concrete circumstances, mimetizing a real-life approach.
The results achieved expose that higher wind speeds are directly related to decreases in modules temperature: for the average wind speeds verified for Lisbon in 2020, variations of output power reached 3.19 percentage points, which expresses a very significant amount of electrical energy production when talking about solar plants. For the highest wind velocities, a maximum variation of 6.85 percentage points in power output was registered. Despite the fact that these last are not the most common values for wind velocities, they are always recorded at some moment, hence their relevance in this research.
One decisive factor that has to be taken into account is that the results attained are highly dependent on the values of wind speeds collected through simulations, on the parameters found in solar panels datasheets and, finally, on the accuracy of the temperature prediction modules employed. To what the wind speeds collected are concerned, the abrupt differences in velocity around the panels influence the calculations made in a critical way. In order to interpret the calculations results displayed in this paper correctly, it must be foreknown that the wind speed value collected for each solar photovoltaic panel involves an area right after the surface of the PV panels, where wind speeds have lower magnitudes. This procedure leads to lower temperatures variation and lower output power variations. With this in mind, it can be said that the results here achieved allude to the worst case (although its just-proven benefits), from an electrical engineering perspective.
Taking into consideration the results obtained, it can be said that, in fact, wind works as a natural cooling mechanism for solar panels, thereby improving their productivity, which can lead to significant benefits respecting electrical energy production in solar plants. Nevertheless, several other factors that are correlated with wind loads must be investigated and should not be neglected when thinking about wind’s influence on solar plants.
To the extent of the reliances explained for the final results herein presented, this work cannot be considered a dogma for projects with the same technologies here studied or for every scenario, but it is manifested as a general approach that certainly contributes to a strong insight on how wind influences the electrical energy production in solar plants through its cooling effects.

This work was supported in part by FCT/MCTES through national funds and in part by cofounded EU funds under Project UIDB/50008/2020. Also, this work was supported by FCT under the research grant UI/BD/151091/2021.

C.B.: Conceptualization, software, methodology, formal analysis; R.A.M.L.: Conceptualization, Writing – Review & Editing; C.P.C.V.B.: Conceptualization, Writing – Review & Editing; J.P.N.T.: Conceptualization, software, methodology, investigation, formal analysis, supervision. All authors have read and agreed to the published version of the manuscript.

Not applicable.

Not applicable.

This research received no external funding.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Bernardo C, Marques Lameirinhas R, P. Correia V. Bernardo C, N. Torres J. Wind Influence on the Electrical Energy Production of Solar Plants. *Clean Energy and Sustainability* **2024**, *2*, 10004. https://doi.org/10.35534/ces.2024.10004

Bernardo C, Marques Lameirinhas R, P. Correia V. Bernardo C, N. Torres J. Wind Influence on the Electrical Energy Production of Solar Plants. *Clean Energy and Sustainability*. 2024; 2(1):10004. https://doi.org/10.35534/ces.2024.10004

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