Influence of Dust Deposition on the Electrical Parameters of Silicon-Based Solar Panels Installed in Senegal (Dakar Region)

In recent years, photovoltaic (PV) modules are widely used in many applica-tions around the world. However, this renewable energy is plagued by dust, airborne particles, humidity, and high ambient temperatures. This paper studies the effect of dust soiling on silicon-based photovoltaic panel performance in a mini-solar power plant located in Dakar (Senegal, 14˚42'N latitude, 17˚28'W longitude). Results of the current-voltage (I - V) characteristics of photovoltaic panels tested under real conditions. We modeled a silicon-based PV cell in a dusty environment as a stack of thin layers of dust, glass and silicon. The silicon layer is modeled as a P-N junction. The study performed under standard laboratory conditions with input data of irradiation at 1000 W/m 2 , cell temperature at 25˚C and solar spectrum with Air Mass (AM) at 1.5 for the monocrystalline silicon PV cell (m-Si). The analysis with an ellipsometer of dust samples collected on photovoltaic panels allowed to obtain the refraction indices (real and imaginary) of these particles which will com-plete the input parameters of the model. Results show that for a photon flux arriving on dust layer of 70 μm (corresponding to dust deposit of 3.3 g/m 2 ) deposited on silicon-based PV cells, short circuit current decreases from 54 mA (for a clean cell) to 26 mA. Also, conversion efficiency decreases by 50% compared to clean cell and the cell fill factor decreases by 76% - 50% compared to reference PV cell.


Influence of Dust Deposition on the Electrical Parameters of Silicon-Based Solar Panels
Installed in Senegal (Dakar Region) 1

. Introduction
The rapid growth of photovoltaic technologies in the world is very important and contributed to global electricity generation [1] [2]. Research and development in the field of solar energy continue to focus primarily on optimizing the efficiency of PV cells. With 3.000 hours of sunshine per year and global irradiation of 5.8 kWh/m 2 /day, Senegal has a significant potential for the development of photovoltaic power generation [3] [4] [5]. Solar production is affected by several factors such as local environment, weather conditions, PV panel tilt angle, dust accumulated on PV cells, etc. [1] [2]. Among these different factors, deposition of dust on PV cell surfaces is a crucial element that affects their performances. In fact, after their manufacture, solar panels are installed and exposed in open air for electricity generation. Thus, the accumulation of dust on their surface gives rise to the thin layer. Thus, the layer with some thickness can mask exposure to sun and absorb some incident radiation beam. This led to a significant decrease in the electrical parameters [6] [7]. In addition, solar production is also affected by several factors such as local environment, weather conditions, PV panel tilt angle, dust accumulated on PV cells, etc. [8] [9] [10] [11]. Among these different factors, deposition of dust on PV cell surfaces is a crucial element to study. It is a natural phenomenon and depends on several parameters such as local environment and meteorological parameters [12] [13]. Senegal is close to Sahara Desert and this region is among the largest sources of dust in the world [14]. According to Paudyal and Shakya [15], decrease in electricity production due to dust deposits was 3.16% in one day, reached 10.41% in ten days and finally 15.74% in one month. Thus, Kaldellis and Kapsali [16] and Moehlecke [17] showed that solar energy production decreases significantly in presence of dust.
For example, Chanchangi et al. [18] used a solar simulator and studied the effect of accumulation of 13 different samples (ashes, bird droppings, carpet dust, cement, dust, etc.) on the performance of PV modules. Afterwards, they noted a decrease of about 98% in short circuit current. Similarly, Adıgüzel et al. [19] found 15 g of dust on crystalline silicon modules, power loss of 62%. Moreover, Hachicha et al. (2019) [20] collected dust of different sizes (from 1.61 to 38.40 μm) and various shapes. They concluded that the yield decreases by 1.7% per g/m 2 of accumulated dust. In addition, Jiang and Sun [21] presented monocrystalline silicon (mc-Si), polycrystalline silicon (pc-Si) and amorphous silicon (a-Si) technologies. Their results showed 0% -26% yield reduction for dust deposits increasing from 0 to 22 g/m 2 . In Senegal, Ndiaye et al. [6] exposed PV panels to natural climatic factors for one year and found maximum power decrease of 18% -78% for polycrystalline and monocrystalline modules, respectively. Said and Walwil [22] noted an average reduction in short circuit current of about 13% after 5 weeks of exposure. In fact, several studies on factors affecting photovoltaic energy have been carried out worldwide [23], in Africa and particularly in Senegal. However, modeling studies focusing on interaction of solar radiation with dust deposited on surfaces of these PV cells are still missing. Therefore, a The paper is divided into three parts. The first part presents methodology (modeling). Then, the second part presents the results of simulations resulting from modeling of the losses of electrical parameters of silicon-based solar cell in presence of dust deposit on the surface. Finally, the last part presents the conclusion.

Methods
The monocrystalline silicon cell installed in a dusty environment is modeled as a stack of thin layers (dust/glass/silicon) as shown in Figure   into. They carried the neutral zones on either side of the junction. If the device is insulated, a potential difference appears across the junction and if it is connected to an external electric charge, free electrons must pass through the charge to recombine with positive holes; thus, current can be generated from the cells under illumination [24].
Thus, to study the influence of dust on energy production of silicon-based solar cell, the silicon layer considered as an N-P junction structure as shown in Figure 2. It allows to study the influence of dust on energy production of silicon-based solar cell.
In our study, the surface transport of minority carriers and consequently the surface current is neglected. The continuity equation allows to determine, at any point and at any time, the concentration of carriers in a semiconductor. When light illuminates the surface of the emitter with certain wavelength λ, there is an electron-hole pair generation whose generation rate G(λ) is expressed by Equa- [25]. This model developed by Mahfoud [26].

Density of Excess Minority Holders in the Base
Minority charge carriers generated (electrons) in P-type base of the photopile, under effect of illumination with monochromatic light, are electrons of charge n p − n p0 = δ(x): density of the electrons generated in the base; n p0 : density of electrons generated at equilibrium; D n : minority carriers' diffusion of electrons in base and n: electrons in base.
Indeed, this continuity equation admits for general solution as: where L n is the minority carriers diffusion length in the base and the coefficients A and C are determinated by the following boundary conditions: Thus, density of minority carriers is as follows [28]: Boundary conditions: With x = H e + w and x = H, we have:  In the issuer, the charge carriers obey the following continuity equation: P n − P n0 : density of excess minority carriers and P n0 : density or concentration of excess minority carriers at thermodynamic equilibrium; τ p : lifetime of excess minority shareholders.
Boundary conditions below, the equations below can be solved: At the junction (x = 0); the rear side (x = H e ) and P n − P n0 = 0 S p : front surface recombination velocities and D p : hole diffusion coefficient ; L p : hole diffusion length.

Calculation of the Density of the Photocurrent in the Base
In PN junction cell, photocurrent generated by charge carriers (electrons) is written [29].
q is the electron elementary charge. A: illuminated surface of cell and the corresponding photocurrent density is:

Calculation of Density of the Photo-Current in the Emitter
When we use the Equation (14), we found the photocurrent density in the emitter by using the Equation (15):

Calculation of the Density of the Photo-Current in the Space Charge Zone (ZCE)
In this zone, photocurrent density is given by [27]:

Total Photocurent Density
Total photocurrent density is sum of photocurrent densities of three zones (P-N-ZCE) of photopile and is written as follow [30]: All expressions used to calculate open circuit voltage (V co ), maximum power (P m ), conversion efficiency (η) obtained from [31].

Results and Discussions
In addition to standard parameters, we need the real and imaginary refractive indices of dust to feed our model. For this purpose, we collected samples of dust deposited on surface of the solar module in Dakar. These samples analyzed by ellipsometry to obtain optical indices of particles deposited in Dakar over a period of one year. Thus, Figure 3 shows the variation of real (Figure 3(a)) and imaginary (Figure 3(b)) indices of dust deposited on the PV cell surfaces as a function of wavelength. They will be used as input parameters for the model. Indeed, imaginary refractive indices of the dust collected on the PV cell surfaces over the whole spectrum obtained by the ellipsometer are a bit high compared to the results of Colarco et al. [34]. They found mean imaginary aerosol indices above Dakar at shorter wavelengths. This difference in value is explained by the shift in the collection date and the composition of the dust which varies according to the weather and weather conditions. However, the refraction indices found in this study according to the work [35] [36] [37] [38] show the presence of pure minerals and clays in this composition. These confirm that indices provided by the ellipsometer correspond to dust indices of the locality. Moreover, according to work of Veselovskii et al. [39], the values of real dust indices of Dakar, Senegal could be between 1.35 to 1.65 and those of the imaginary indices between 0 to 0.02 and these values are quite close to those of the ellipsometer.   According to Mahfoud [26], this decrease in short-circuit current is due to decrease in photon flux reaching the cell surface. Consequently, a dust layer 70 μm thick leads to 51% reduction of this current compared to that of the clean cell.
These results were consistent with Chanchangi et al. [18].     mW corresponding to a 53% decrease in production compared to the clean cell.
These losses are quite low compared to results of Nimmo and Said [44] who noted 65% decrease. These differences in value could be due to different compositions of the Kuwaiti dust but also to climatic conditions. For variation of dust layer thickness from 0 to 70 μm, power loss of about 12.614 mW observed.
Overall, this figure confirms results of Jiang and Lu [40] who showed that deposition of dust on PV cell surfaces decreases output power of the cell. According to Ndiaye et al. [6] decrease in cell power is due to the decrease in irradiance.
Indeed, the illumination flux is reflected by dust layers. [45] [46] They concluded that productivity efficiency of photovoltaic cells decreases when dust accumulates on their surfaces. These studies have shown that decrease in performance is due to reduced absorption of solar energy, as a small fraction of the solar radiation passes through the dust layer and reaches the surface of the PV module. Furthermore, according to Klugmann-Radziemska and Hegazy [42] [47], the decrease in efficiency is due to decrease in light transmission through the glass cover when dust accumulates on PV cell surfaces. According to Ndiaye et al. Rao et al. [6] [23] the decrease in efficiency could be due to the increase in temperature above the cell caused by the absorption of light by the dust layers. Figure 8 shows the fill factor of silicon-based cell for different layers of dust deposited on cell surface. Indeed, this parameter provides information on quality of cell. For layer thickness variation from 0 to 70 μm, fill factor decreases from 76% to 50%. This decrease corresponds to 26% compared to clean cell. Thus, this curve confirms degradation caused by dust on surfaces of monocrystalline silicon cells. The reduction of this factor is favored by the increase in temperature on PV cell surface. It is due to absorption of photons and light by dust atoms according to Ahmed et al. [48]. The decrease of the fill factor could be due to the

Conclusions
This work evaluated the influence of dust deposition on the electrical performance of silicon-based photovoltaic cells by a model. Thus, the analysis of loss of electrical characteristics as a function of dust is studied. Indeed, it allowed us to evaluate the losses of electrical characteristics such as production efficiency, power output, short-circuit current and fill factor of monocrystalline silicon-based photovoltaic cells as a function of dust deposited on the surface of these solar modules in Dakar, Senegal. Firstly, this work showed that the deposition of dust on PV cell surfaces does not significantly change open circuit voltage. However, short-circuit current affected by this dust deposit with loss of about 51% for a dust layer of 70 μm (corresponding to dust deposit of 3.3 g/m 2 ) compared to clean cell current. Moreover, the main conclusion is that a cleaning of the cell should be considered in order to optimize its electrical performance from dust layer thickness of 70 μm (corresponding to dust deposit of 3.3 g/m 2 ).
However, it would be interesting to extend this work by introducing into this model, the influence of cell temperature but also by comparing it with experimental studies. In addition, the realization of multi-layers of dust and glass on the silicon cell could allow to measure the electrical parameters in real-time. This study also has limitations because type of dust is not specified and dust layers are assumed to be homogeneous. So, it would also make sense to take into account the binding of dust atoms on the surfaces of PV modules.