Numerical study of the effect of wind on the cooling of photovoltaic panels

. The main objective of this study is to optimize the production of electricity from a photovoltaic (PV) plant with a capacity of 50MWc. The power plant is located near the city of KITA, Mali, in an area whose climate is characterized by high temperatures. However, the temperature of photovoltaics cells plays a key role in their performance, which deteriorates when the temperature increases. In this study we focus on the analysis of laminar forced convection flow around a PV panel, main element of a photovoltaic plant, considering the ambient temperature, irradiation as well as the velocity and the direction of the wind. Several operating configurations were analysed in relation to the specific climatic conditions of Mali for a typical day of sunshine with a daily irradiation of a duration of 12 hours between 6:00 and 18:00. The mass transport, momentum and energy equations are solved numerically using the finite volume method. This method is based on the spatial integration of transport equations with respect to elementary control volumes. Computer simulations are performed with ANSYS Fluent® CFD commercial software. Our results show that considering the effect of wind plays an important role in the temperature estimates of photovoltaic cells and that accurate knowledge of this behaviour is essential for optimizing production. conditions is colder than 3K. Our results show that considering the effects of wind and PV panel inclination plays an important role in the temperature estimates of photovoltaic cells. Work continues on electrical modelling to find a physical relationship between the temperature of the PV cell, the irradiation received and the wind velocity and direction.


Introduction
Solar energy is the cleanest and most sustainable source of energy available to a large majority of the world's population. The solar energy received by the Earth is abundant and inexhaustible. Approximately, the solar continuous power reaching the earth's surface is about 120000 TW [1]. Each year, it corresponds to a potential 6,500 times greater than the amount of energy yearly required in the world. Indeed, in 2014, world primary energy consumption stood at 13684 Mtoe that are equivalent to 159000 TWh [2]. Only a small part of this energy is exploited by man for his daily needs. The industrial production of solar electricity falls into two sectors: solar photovoltaic production and solar thermal generation. The photovoltaic sector contributes exclusively to the generation of electrical energy by means of photovoltaic solar panels while the thermal sector contributes not only to the generation of electric power by means of a superheated steam turbine but also to the production of water hot sanitary or heat production to warm the buildings. The electrical performance of the photovoltaic generators (PV) are strongly dependent on the operating temperature. It is known that the no-load voltage decreases with the temperature rise of the PV cell, and that, to a lesser extent, the photovoltaic current increases with it. This results in a significant decrease in the maximum power available when the temperature of the PV cell increases. The technical documentation of the photovoltaic panels indicates two coefficients making it possible to correct the principal characteristics in a proportional way. These characteristics are defined under standard test conditions (STC) including, among others, ambient temperature. This approach makes it possible to obtain results which are ordinarily satisfactory although not very precise. Indeed, the photoelectric phenomenon is very sensitive to the temperature of the semiconductor crystal in which it occurs. The cell is trapped between different layers of materials, achieving among other things, the optical treatment and giving it its mechanical strength. It is therefore proposed to precede the electrical simulation of the generator with a thermal study, in order to evaluate the temperature of the photovoltaic cells more precisely. Therefore, we focus in this study on the analysis of laminar forced convection flow around a PV panel, the main component of a photovoltaic power plant. Regardless of the accuracy improvement in the estimation of cell temperature, this approach will also allow us to consider the influence of wind on the performance of PV panels, which is not possible with the classic approach based on the ambient temperature.
During the operation of the PV modules, their cells heat up due to a number of phenomena such as thermalization, charge carrier recombination, the Joule effect, the Peltier effect and the Thomson effect. Knowledge of photovoltaic cell temperature is of significant importance in predicting the efficiency that the PV system can achieve during operation. Zondag et al. [3] found that a lower temperature of the PV module improves its efficiency. Moreover, the heating of the PV panels can be attenuated by the flow of air around the panel, windinduced flow [4]. Edgar et al. [5] show that passive convection cooling of PV modules can improve electrical power by 2% under nominal operating conditions. Goverde et al [6] conducted an experimental study varying the irradiation of the PV panel and the wind speed between 1 and 5 m/s. They found that the temperature of the module as well as the coefficient of convective heat transfer were significantly affected by the wind. In addition, analytical models have been proposed to evaluate cell temperature as a function of wind velocity [7][8]. Stropnik and Stritih [9] focused on increasing electrical efficiency and power output of photovoltaic (PV) panel with the use of a phase change material (PCM). They found that the maximum temperature difference on the surface of PV panel without PCM was 35.6 °C higher than on a panel with PCM in a period of one day. Our work is part of a program of scientific cooperation with Mali, with the objective of optimizing the electricity production of a 50 MWp photovoltaic power plant located in KITA in the area Sahel-Saharan Africa, where the climate is characterized by high temperatures. To achieve this objective, it is suitable to set the physical relationship between the temperature of the PV cell, the illumination and the relevant meteorological parameters such as wind is the most important factor influencing the cell temperature.

Problem setup
In this study, we focus on the analysis of laminar forced convection flow around a PV panel, main element of a photovoltaic plant, considering the ambient temperature, irradiation as well as the velocity and the direction of the wind. Several operating configurations were analysed in relation to the specific climatic conditions of Mali for a typical day of sunshine with a daily irradiation of a duration of 12 hours between 6:00 and 18:00.

Geometry
The photovoltaic panel (Fig. 1) used for the numerical simulations has the following dimensions: length L = 1.65 m, width l = 0.992 m and thickness H = 6.243 mm. The PV panel consists of 9 layers (Table 1) and is placed at the top of an aluminium frame 40 mm high, 35 mm width and 8 mm thick (Fig. 2).
In the case of the KITA photovoltaic plant, the climatic conditions in Mali require the installation of PV panels at 2 m from the ground with an inclination of 15° relative to the horizontal as well as with an orientation of 7° East compared to south in the horizontal plane (xy). The fluid domain around the PV panel (Fig. 3) is constructed to ensure the independence of the solution from the boundaries and extends 3 m upstream, left, right and top and 9 m downstream [10].    In order to validate the mesh, we tested 3 different meshes ( Table 2). Finally, we chose the mesh n° 2 which represents a good compromise between solution accuracy and the computation time. The structured mesh of the fluid domain (Fig. 4) comprising 39 million cells is, on the one hand, of boundary layer type near the PV panel and, on the other hand, progressive away from the PV panel.
 Energy equation: The fluid is considered to be newtonian, and the physical properties (ρ, Cp, k, μ) of the fluid are temperature dependent. Indeed, the Boussinesq approximation is not valid for air with temperature variations higher than 10 K [11]. The radiation heat transfer is not considered in the physical model because the location of the PV panels in the solar track with no surrounding reflective surfaces, makes this mode of heat transfer insignificant. Moreover, on the overall irradiation received by the PV panel, only 31.9% of this energy is converted into heat and will contribute to the heating of the PV cell [12]. The soil temperature was taken 2K higher than the ambient temperature to consider its heating due to direct solar radiation [5]. The boundary conditions corresponding to the several cases studied for a typical day (01 April 2013) consider the specific climatic conditions of Mali (Table 3). The choice of the typical date was made after analysis of the meteo data over 20 years between 1994 and 2014 for this geographical area. The daily irradiation of a duration of 12 hours is between 6:00 and 18:00.

Numerical method
Transport equations of mass, momentum and energy (1) -(5) are solved numerically using the finite volume method [13]. This method is based on the spatial integration of transport equations on control volumes. The coupling between velocity and pressure is achieved with the coupled algorithm that solves the equations of continuity and momentum simultaneously and gives an advantage to treat flows with a strong interdependence between dynamic and thermal fields. Central-Differenced Schemes and Second-Order Upwind Schemes are used for the spatial discretization for diffusive terms and convective terms respectively. The convergence criteria were based on the absolute residuals resulting from the integration of the conservation equations over finite control volumes. For all simulations performed in this study, converged solutions were achieved after a residuals decrease lower than 10 for all the governing equations. 3D numerical simulations are performed with ANSYS Fluent® CFD commercial software.

Results and discussion
The efficiency of the PV cell is generally measured under standard test conditions (STC) with a PV cell temperature of 25 °C and an irradiation of 1000 . These conditions are rarely met in outdoor facilities. The numerical model developed in this study represents a tool for the analysis of the operating temperature of photovoltaic generators.
In this study, we present the results for a typical day using the specific climatic conditions of Mali, the ambient temperature, the irradiation as well as the velocity and direction of the wind. The typical day of sunshine in Mali with a daily irradiation of a duration of 12 hours between 6:00 and 18:00. For example, the solar radiation at 6:30 and 17:30 on the city of Kita is respectively 174 and 49 .
Figures 5, 6 and 7 show the PV module isotherms for 3 representative cases of a typical day, that is to say, 7:30, 11:30 and 15:30. The temperature of the PV cell, which can be assumed to be identical to the temperature of the PV module [14], shows great variability under changing outdoor conditions. During a cloudless summer day in Mali in the town of Kita, the cell temperature is between 309K and 341K over a day. The maximum temperature of 341K is reached at 11h30 when the daily irradiation is maximum and when the wind blows from the south-east direction (328°) with a velocity close to the average day velocity. This heating of the PV cells can lead to a considerably reduced energy efficiency. It is also observed that despite a substantially constant ambient temperature from 11:30 to 15:30, the temperature of the PV panel at 15:30 is only 324K. The cooling of the PV cell is due to the higher wind velocity and its more favorable orientation compared to prevailing winds. In a second part, two additional inclinations of the PV panel (10° and 20° relative to the horizontal) were tested in order to study the influence of the inclination of the PV panel with respect to its heating, knowing that initially the PV panel was tested for à 15° inclination. These inclinations relative to the horizontal were tested for the most adverse climatic conditions, i.e. at 11:30 during a typical day.  Figure 9 represents the evolution of the temperature during the typical day of April 01, 2013 for the corresponding irradiations and an inclination of 15° of PV panel. In addition, the influence of the inclination of the PV panel relative to the horizontal is displayed for 2 inclinations (10° and 20°). One may note that the temperature evolution follows local irradiation with a maximum reached at 11:30. Moreover, it is found that, for a greater inclination (20°) relative to the horizontal than that initially tested (15°), the PV panel subjected to the same climatic conditions is colder than 3K.

Conclusion
A 3D numerical study of laminar forced convection airflow around a photovoltaic panel was conducted. Several operating configurations were analysed compared to changing climatic conditions in Mali for a typical day. During a cloudless summer day in the city of Kita in Mali and for an inclination of the PV panel relative to the horizontal of 15°, the cell temperature changes from 309K and 341K. For these climatic conditions, the maximum temperature is reached at 11:30. Despite the fact that the ambient temperature remains high until 15:30, the temperature of the PV cell drops thanks to the airflow generated by the wind around PV panel. Moreover, it is found that, for a greater inclination (20°) relative to the horizontal than that initially tested (15°), the PV panel subjected to the same climatic conditions is colder than 3K. Our results show that considering the effects of wind and PV panel inclination plays an important role in the temperature estimates of photovoltaic cells. Work continues on electrical modelling to find a physical relationship between the temperature of the PV cell, the irradiation received and the wind velocity and direction.