Modelling of Photovoltaic Modules Optical Losses Due to Saharan Dust Deposition in Dakar, Senegal, West Africa

This study aims to evaluate the optical losses of photovoltaic modules due to Saharan dust deposition in Dakar, Senegal, West Africa. For this purpose, an air-dust-glass system is modeled to simulate optical losses in transmittance and reflectance. To do this, we have collected dust samples from Photo-Voltaic (PV) surface in Dakar area (14 ̊42'N latitude, 17 ̊28'W longitude), Senegal. X-ray fluorescence reveals that silicon (Si), iron (Fe), calcium (Ca) and potassium (K) mainly composed these dust samples. Then, dust refractive indices obtained from an ellipsometer were used as an input to be used in the model. Simulations show that for radiation (at normal incidence) arriving on a dust layer of 30 μm-thick (corresponding to a dust deposit of 1.63 g/m), 79% of the visible spectrum is transmitted; 19% is reflected and 2% is absorbed. Overall, the transmittance decreases by more than 50% as of dust layer of 70 μm-thick corresponding to a dust deposit of 3.3 g/m.

energy worldwide. In 2016, the International Energy Agency (IEA) [1] affirmed that approximately 315 GW of photovoltaic power was installed worldwide. On the other hand, the projections for 2017 and 2022 were 385 GW and 500 GW respectively [2]. In Africa, solar production is expected to reach 70 GW by 2030 [3]. Since 2015, Senegal has increased its solar capacity with the installation of new plants according to Aidara et al. [4]. However, the efficiency of PV module production in arid and semi-arid regions is strongly influenced by dust deposition [5]. For example, Darwish et al. [6] studied 15 types of dust and concluded that six of them (ash, calcium, limestone, soil, sand and silica) significantly reduce the PV modules efficiency. Similarly, results based on theoretical models have shown the effect of dust deposition by considering three types of dust: red earth, limestone and ash. These works show that the performance of PV is highly dependent on both composition and source of these particles [7]. Indeed, the nature of the dust is one of main causes of arriving radiation attenuation on PV modules surface (Qasem et al. [8], Makkar et al. [9], Mackey et al. [10]). Other studies carried out in Asia have shown the importance of taking into account dust deposits on photovoltaic installations (Nahar and Gupta [11], Hasan and Sayigh [12], Gürtürk et al. [13], El-Shobokshy and Hussein [14], Javed et al. [15], Paudyal et al. [16], Zarei and Abdolzadeh [17], Guo and Pan [18]). Consequently, dust deposition effect on yields of photovoltaic cells has been highlighted by experimental methods (Mani and Pillai [19]) but also by empirical calculations (Hegazy et al. [20]).
In south Sahara, initial studies have shown that dust reduces the efficiency of solar panels (Ndiaye et al. [21], Ansmann et al. [22], Rao et al. [23], Saidan et al. [24]). Moreover, this region is the world largest source of dust according to Marticorena et al. [25].
However, these kinds of experimental studies are still limited in West Africa, particularly in Senegal. This is due to the lack of technical devices to carry out the characterizations but also to determine optical properties such as transmittance, reflectance and absorbance. Indeed, the data obtained through characterization techniques will make it possible to know the source, the optical properties and the composition of the dust. This study characterizes the dust samples collected in Dakar and also evaluates the transmission and reflection losses of the air-dust-glass system. The paper is subdivided into three parts. The first part presents the experimental (characterization techniques) and theoretical (modeling) approaches. Then, the second part presents the results of dust characterization and the simulations resulting from the modeling of the losses in transmittance and reflectance of solar radiation. Finally, the last section draws the main conclusions of this work.

Experimental Approach
In this work, we collect samples directly from PV surfaces in Dakar (14˚44'N la-titude and 17˚27'28''W longitude). These samples are collected in vials as shown in Figure 1(b). The samples are then analyzed by X-ray fluorescence (EDXRF) to determine the different chemical elements. The instrument used to determine these elementary compositions is a Horiba Jobin Yvon XGT-5000. It is equipped with a tungsten X-ray tube, a beryllium window and a high-purity Si detector; it operates at 50 kV-max/1mA-max. Next, thin layers of dust are made on glass plates (see Figure 1(c)) with a spin coater according to the spin coating technique using an isopropanol solution as described by Lawrence et al. [26]. A digital microscope (Keyence, VHX1000) with a magnification of 100 -1000 nm or 500 -5000 nm is used to determine the thickness of dust layer. In addition, a SOPRA GES-5 type ellipsometer with a spectral ranging from 190 to 2500 nm is used to obtain real and imaginary dust indices (Pristinski et al. [27]). These optical indices obtained from the ellipsometer are used as input parameters for the proposed model. To ensure the reliability of the ellipsometer results, refractions index are compared with those measured by the AERONET sunphotometer stationed in Dakar (Holben et al. [28]). Indeed, the same particles measured by the sunphotometer were deposited on PV modules surface in Dakar. And finally, UV-Visible spectrophotometer is used to validate the model.

Theoretical Approach
The approach consists of simulating an electromagnetic wave with oblique or normal incidence on dust layer deposited on glass as shown in Figure 2. Electromagnetic wave passes through a multilayer optical system (Air-Dust-Glass). This wave can be reflected, transmitted or partially absorbed at each interface by the different constituents of the layers. Air and glass are characterized by their refractive index: n 0 and n 2 respectively. The dust is characterized by its optical index (n 1 ) which varies as a function of wavelength according to Equations (1) and (2) described by Bashara and Azzam [29].  n, k, α and λ respectively represent the refractive index (real index) of dust, the dust extinction coefficient (imaginary index), the dust absorption coefficient and the solar radiation wavelength. Next, we calculate the Fresnel reflection and transmission coefficients at the layer interfaces for p and s polarization by applying electric E and magnetic B field conservation and Descartes' formulas as described by Mahdjoub et al. [30], Berthier and Lafait [31]. We use the equations of Macleod [32], Born and Wolf [33] and McCrackin et al. [34]: For the air-dust interface: And for the dust-glass interface the equation becomes: where β is the phase difference introduced by the reflection and d 1 is the dust layer thickness. The overall reflection (r p , r s ) and transmission (t s , t p ) coefficients of the system for a p or s polarization are shown in the equations below: T, R and A are the mean reflectance, mean transmittance and absorbance of the system, respectively. Figure 3 shows the dust samples elemental analysis by X-ray fluorescence (XRF). It indicates that the dust is dominated by elements such as: Si, Fe, Ca, K, Ti, P, S, Zn, Mn, Zr. Some elements such as Cr, Cd, Br, Pb, Cu and Hg are minority or trace elements. Figure 4 shows the detected element mass concentration in Dakar dust. It determines the mass proportions of each chemical element. The analysis reveals that this powder is mainly composed of Silicon (Si) with a rate of more than 50.1% of the total mass. The remainder consists of 16.8% of Fe, 10.6% of Ca, 1.5% of K, 1.4% of Ti, 0.98% of P and 0.5% of S. Trace elements such as Cu, Zn, Sr, Zr were also detected. However, X-ray fluorescence diffraction (XRF) does not detect very light elements such as aluminum.

X-Ray Fluorescence (XRF) Analysis of Dust Samples
These two materials are used as reference and validation elements to determine the concentrations of sand elements. We find the same chemical elements for these three samples, which proves that the dust collected in Dakar is of sandy nature. However, main elements such as Si, Ca, Fe, S and P are more important in mass in Saharan dust rather than the other samples ( Figure 5).

Optical Index Validation
The model developed uses real and imaginary refractive indices as input parameters. Consequently, the indices of the dust samples collected in Dakar were obtained from an ellipsometer. To validate the ellipsometer data, the refractive indices are compared with those measured by AERONET sunphotometer stationed in Dakar. Indeed, we use AERONET data corresponding to the same periods. Figure 6 shows a comparison between the dust real ( Figure 6 left) and imaginary (Figure 6 right) indices obtained from the ellipsometer and the sunphotometer. Firstly, it clearly shows that the same atmospheric particles over Dakar were deposited on solar panels surface. The curves are in good agreement especially in the visible spectrum. Smart Grid and Renewable Energy From the indices obtained, we will now simulate the losses in transmittance and reflectance of solar radiation.

Transmittance Validation
To validate the model outputs, a comparison with experimental measurements from a UV-visible spectrophotometer was a conducted. Indeed, electromagnetic radiation is sent by an UV-visible spectrophotometer over a thin layer of dust 35 μm-thick (corresponding to a deposit of 1.63 g/m 2 ) deposited on a glass substrate. Then we compare the measured and simulated transmittance. Figure 7 illustrates this comparison between these two transmittances (simulated in red and measured in black) and that of clean glass in cyan color. First of all, the results show that a thin layer of dust of 35 μm lets through (transmittance) on average 75% of solar radiation, which corresponds to a loss of almost 21% compared to clean glass. Then the comparison shows a good agreement between the transmittances measured by the spectrophotometer and simulated by the model especially in the visible range between 450 and 800 nm. The correlation coefficient between these two curves is more than 88%.

Solar Radiation Transmittance Losses
In this section, we perform the model sensitivity studies and then assess the impact of dust on radiation components.
The first step is to simulate the influence of dust layers on solar radiation transmission (transmittance) through an air-dust-glass system. For this purpose, the model is executed with different layer sizes. Figure 8 shows the transmittance for an air-dust-glass system for different dust layer sizes. These values are Smart Grid and Renewable Energy  30 µm (corresponding to a dust deposit of 1.4 g/m 2 ), 45 µm (corresponding to a dust deposit of 2.1 g/m 2 ), 55 µm (corresponding to a dust deposit of 2.6 g/m 2 ) and 70 µm (corresponding to a dust deposit of 3.3 g/m 2 ) respectively.
The correspondence between layer size in µm and dust deposition in g/m 2 is made by considering a dust density about 2.6 g/cm 3 according to Ansmann et al. [22]. The cyan curve in Figure 8 corresponds to the transmittance for clean glass (without dust), which is considered as absolute reference. Overall, a clean glass allows all the radiation to pass through with a transmittance of around 95%.
Next, Figure 8 shows that a dust deposit of 1.4 g/m 2 (corresponding to a layer size of 30 µm) causes 18% loss of transmittance. Then, we note that the transmittance decreases inversely with the layer thickness. Indeed, for thickness of 45, 55 and 70 µm, the mean transmittance is of 70%, 64.7% and 58% respectively. Overall, the results show that the transmittances decrease in short wavelengths. This is due to the Mie scattering of these particles (Xie et al. [35]). These results are in good agreement with those of Yun-Yun and Zhang [36]. However, these losses are greater than those found by Mastekbayeva and Kumar [37]. They showed that for a period of 30 days and for 3.72 g/m 2 of dust deposition, transmission losses were about 24.2%. These differences are due to the nature of the dusts considered. In summary, half of the radiation is lost when the dust layer thickness reaches 70 µm. This radiation is blocked by dust, as shown by Hegazy et al. [20]. Figure 9 shows the reflectance losses (of the air-dust-glass system) for different dust layers considered in the model. Indeed, this figure represents the reflectance as a function of wavelength for four dust layer thicknesses (30,45, 55 and 70 µm). Overall, we note that the average reflectance increases from 26% to 53% if the layer thickness increases from 30 to 70 µm.

Solar Reflectance Losses
Reflectance is more important for short wavelengths between 400 and 600 nm.
According to Kaufman et al. [38], the high reflectance at wavelengths 462 -500 nm is due to the presence of iron atoms in the dust. Other studies such as that of Müller et al. [39] confirm these radiative properties of Saharan dust. Figure 10 shows the transmission losses as a function of different dust layers with thicknesses ranging from 0 to 70 μm. We note that the transmittance decreases as the thickness of the dust layer increases. These results are in good agreement  with those of Said and Walwil [40], Al-Hasan [41], Ebert and Bhushan [42], Duell et al. [43], Chaouki et al. [44] who showed the negative impact of dust layers on transmittances. Thus, this figure shows that the transmittance of solar radiation of a clean glass compared to an unclean glass could decrease by up to 58% for a layer of 70 μm.

Conclusion
This work investigated the optical losses of solar radiation caused by dust deposition on solar panels surface. The objective was to characterize the dust collected on PV surface in Dakar (Senegal) and then to evaluate the impact of this dust layer on solar radiation. Firstly, the experimental study showed that Dakar dust is composed of 50.1% Si, 16.8% Fe, 10.6% Ca, 1.5% K, 1.4% Ti, 0.98% P, 0.5% S and the rest is traces such as Cu, Zn, Sr. An ellipsometer was used to obtain the dust refractive indices which will serve as input for the model. The model implemented was validated by transmittance measurements obtained with a UV-visible spectrophotometer. And secondly, simulations reveal that transmittance is reduced by half for dust layer about 70 μm (corresponding to a dust deposit of 3.3 g/m 2 ).