Effect of Sand and Dust Shading on the Output Characteristics of Solar Photovoltaic Modules in Desertification Areas

Abstract

Photovoltaic power generation is rapidly developing as a kind of renewable energy that can protect the ecological environment. The establishment of photovoltaic power stations in desertification areas can play a very important role in desert windbreaks and sand fixation as well as improve the ecological environment. The realization of the effective integration of photovoltaics and deserts can have multiple benefits for the economy, society, and ecology. However, the deposition of sand and dust caused by environmental factors in desertification areas can seriously affect the power generation efficiency of PV modules. In this study, the output characteristics of photovoltaic modules were tested under three wind speed conditions (5 m/s, 10 m/s, and 15 m/s), with different sand densities, sand particle sizes, and inclination angles. The experimental study showed that the module’s output power gradually decreased with an increase in the density of accumulated sand; the sand accumulation density on the surface of the photovoltaic module increased from 0 to 40 g/m², and the maximum output power decreased by 32.2%. As the sand particle size increased, the maximum output power of the module rose and was gradually stabilized in the three wind speed groups. As the sand particle size increased, the maximum output power of the module increased and gradually stabilized in the three wind speed groups. When the wind speed was 15 m/s, the component output power of the angle had the largest drop; the tilt angle was 60° when the relative output power rate reached the minimum (i.e., 86.5%); that is, there was electrical energy loss of approximately 13.7%. The sand particle size and accumulated sand density were the control variables related to the module temperature and the transmittance of the proportion of the impact of the module filling factor differences. According to the curve analysis of the filling factor in different sand accumulation densities, the filling factor first increased and then decreased. In this test, the filling factor at the sand accumulation density of 35 g/m² (module temperature valley) reached the peak value. The change trend for the component filling factor under different sand particle sizes fluctuated.

1. Introduction

Photovoltaic power generation systems not only generate clean energy but also play a role in promoting land restoration and ecological conservation, as well as in slowing land degradation and water consumption. The construction of photovoltaic systems in desertified areas can improve desert land coverage and the desert environment. Thus, the formation of dust storms can be prevented, and the ability to cure the land can be improved. The Inner Mongolia region of China has a large desert area with rich solar radiation resources. These resources are conducive to the development of photovoltaic power generation bases and industries; however, solar photovoltaic power generation technology is highly susceptible to the influences of the climatic environment, such as solar radiation, environmental temperature, humidity, wind speed, dust accumulation, etc. [1]. Therefore, it is important to understand the causes of the effects and to provide a reference for the study of PV module performance output in desertification areas.

Hosseini et al. [2] identified the mass density and dust properties as pivotal in dictating their effect on PV module performance. Striving to decipher a mathematical correlation between mass deposition density and its global influence on photovoltaic modules, the team introduced a novel mathematical method. This method seamlessly integrates a double-diode photovoltaic model with a pre-existing mathematical relationship; this integration serves as a predictive tool to determine the effects of dust on PV performance. Zhang et al. [3] investigated the implications of ash accumulation in relation to the power generation capabilities of photovoltaic (PV) modules. Their data suggest a marked decline in power at the maximum power point as dust accumulates. Zhang et al. [4] assessed the impact of dust accumulation on the efficacy of rooftop PV power plants. Their findings underscore that power generation disruption due to dust is primarily a result of changes in solar transmittance at the module surface. However, a comprehensive theoretical analysis is lacking. Wu et al. [5] measured the PV modules’ output power in the Dali region before and after dust accumulation. Between January and May, without rainfall interference, the decrease in PV module output power attributable to sand and dust was consistent, resulting in an 11.4–13.3% reduction in power generation efficiency. Conversely, from June to October, the seasonal rainfall in Dali substantially mitigated the dust accumulation on the PV module surfaces. This led to an enhancement in the PV modules’ relative power generation efficiency.

Nevertheless, natural cleaning processes fail to eliminate the adverse effects of sand and dust particles. Wang et al. [6] examined the dust accumulation patterns on PV modules in the Hohhot region. They revealed that for dust accumulation levels of 2.75 g/m², 4.59 g/m², and 5.86 g/m², the corresponding average daily attenuation rates were 1.29%, 3.42%, and 4.71%. Chen et al. [7] implemented controlled dust deposition experiments on PV modules, establishing three distinct sand and dust coverage densities: 10 g/m², 20 g/m², and 30 g/m². Their results demonstrated that a dust density of 10 g/m² led to a 34% reduction in the PV module’s peak output power. As the dust density increased progressively, there was a consistent decline in component output power, which eventually plateaued upon reaching a specific sand and dust accumulation threshold. Dida et al. [8] examined the accumulation of sand and dust on photovoltaic (PV) modules in a Sahara desert environment through experimental methods. After eight weeks of exposure, the modules amassed approximately 4.36 g/m² of sand and dust. The maximum output power, short-circuit current, and open-circuit voltage experienced reductions of 8.41%, 6.10%, and 0.51%, respectively, compared to clean modules.

Furthermore, the power generation from grid-connected PV plants in the vicinity was assessed before and after a sandstorm, revealing a 32% decline in power generation due to the sandstorm. Lasfar et al. [9] embarked on an experimental investigation of the influence of sand and dust particles on the electrical performance of PV modules in the Nouakchott region. Parameters, such as the I-V and P-V curves, open-circuit voltage (Voc), short-circuit current (Isc), and maximum power currents and voltages (Imp and Vmp), were measured. Significant perturbations of the I-V and P-V curves were observed when the modules were covered with sand and dust. This led to reductions in the Isc and Imp values for the dusty modules compared to their clean counterparts. Sadat et al. [10] gathered authentic sand and dust particles from the vicinity of a power plant in an Iranian region. This collected matter was uniformly distributed on a single PV module for experimental analysis. The particle size distribution of the samples predominantly ranged from 1 μm to 30 μm, with an average size of 8 μm. As the density of the sand and dust increased from 0.1 μg/m² to 3.3 μg/m², there was a substantial decline of ~98.0% in the output efficiency of the PV module. Elemental analysis of the local sand dust revealed a composition mainly consisting of Si, O, Al, and Ca. Rached [11] and colleagues assessed the impact of seasonal variations on dust and PV performance losses over 15 weeks in the summer of 2018 for the Sharjah region. The dust samples, obtained using a customized device from glass sheets, were predominantly carbon-, oxygen-, calcium-, and silica-rich, suggesting a silica and calcite presence. During UV tests, a 30% decline in light transmission was observed after 15 weeks of dust buildup. Various determinants influencing the sand and dust particle deposition on the PV module surfaces were explored to mitigate this deposition. Yang [12] and their team undertook an indoor artificial dust-laying experiment to address dust accumulation in agricultural photovoltaic devices. Their findings revealed that 0–38, 38–75, 75–110, and 110–150 μm sand and dust particles curtailed the module’s power output by 16.0%, 12.5%, 8.2%, and 5.4%, respectively. Mostefaoui et al. [13] evaluated four photovoltaic modules, focusing on their current–voltage characteristics, to determine the impact of sand and dust. Their results demonstrated that sandstorms and dust accumulation diminished module performance primarily due to decreased transmittance. They emphasized that during sandstorms, particle deposition density substantially increases. Furthermore, in Saharan conditions, the PV modules that were not cleaned showcased a significant decline in power output, with the exception of a shading mismatch in the partially cleaned modules. Said et al. [14] studied dust accumulation on a PV module’s glass cover tilted at 26° and exposed for 45 days. Their findings indicated a 20% reduction in glass transmittance and a dust accumulation of 5 g/m². Notably, the transmittance reduction was less pronounced for the anti-reflective coated glass than its uncoated counterpart. The adhesion of particles to the flat surface increased with particle size; this was attributed to a larger contact area. Furthermore, increased vertical adhesion was noted at elevated humidity levels, resulting from the centrifugal force between the dust particles and glass. Wanxiang et al. [15] and associates established test stands in Tianjin with orientations in four cardinal directions accompanied by six tilt angles (15°, 30°, 45°, 60°, 75°, and 90°) in each. The data indicated that the PV modules facing south were the most impacted and that the tilt angle’s influence on the modules was significant. Ndeto et al. [16] studied the influence of mounting height, tilt angle, and a southward wind on the sand and dust deposition on photovoltaic modules. Under a southward wind, the modules mounted less than 2.0 m in height and, facing north, exhibited a heightened dust deposition rate compared to their southern counterparts at equivalent heights and tilts. Nearly horizontal tilts (5°) manifested increased dust particle deposition. The optimal mounting height and tilt for the Kenyan region were 2.5 m and 15°. Khodakaram-Tafti [17] and their team examined PV modules at various tilt angles (0°, 15°, 30°, and 45°) in a semi-arid setting. Their data suggested a strong correlation between dust accumulation and tilt angle. PV module output power declined by 58.2%, 27.8%, 21.7%, and 20.7% under the respective tilt angles. It was inferred that incorrect tilt settings affect the output power of PV modules.

Moreover, external environmental conditions influence sand and dust particle deposition. Xu et al. [18] found that the effect of dust deposition on the lower surface temperature was greater than on the upper surface temperature. Meanwhile, the maximum temperature of the PV glass panels decreased exponentially with the increase in wind speed under light and windy conditions. The final temperature of the clean glass panels tended to be consistent with the ambient temperature, while the temperature of the dusty glass panels was much higher than the air temperature. In a separate study, Bouraiou et al. [19] explored the performance of PV modules in desert conditions, focusing on daily weather variations. The experimental results revealed a degradation in key performance parameters, including Imax, Vmax, Pmax, Voc, Isc, and FF.

In the above studies, considerable experimental analyses have been conducted on dust accumulation, while relatively little research has been conducted on solar PV modules in desertification areas. PV modules in desertification areas have unique regional environmental differences compared with ordinary areas, and the environmental factors in desertification areas greatly influence the deposition of sand and dust. For the special desert environment, the effect of different sand densities and particle sizes on dust accumulation at different wind speeds and inclination angles should be studied.

2. Model Formulation and Boundary Conditions

In this study, a desert photovoltaic power station in the Inner Mongolia region was used as the research background; concerning the power station, fixed photovoltaic arrays were installed to simplify the model required for computational simulation, as shown in Figure 1. For numerical simulation, the realizable turbulence model for particulate matter description was selected as the most relevant to the actual situation of the DPM model; a random collision model was added [20,21].

In the simulation setup, the airflow was regarded as an incompressible constant flow. The numerical simulation of the gas–solid two-phase flow at different tilt angles and wind speeds was carried out with the side facing the PV module as the inlet of the flow field and the back side of the PV module as the outlet; the pressure outlet was adopted as the boundary condition. The surface of the PV module and the interior of the computational domain were set as the no-slip wall surfaces. The boundary condition settings are shown in

Table 1. Boundary condition settings.

Boundary Condition	Parameterization
Sand particle incidence mode	Surface
PV module surface particle deposition method	Trap
Inlet speed	5 m/s, 10 m/s, 15 m/s
Gravity acceleration	9.81 m/s−2

.

3. Experimental Tests

3.1. Experimental Setup

The experiment was conducted in a DC boundary layer wind tunnel located in Beijing. The photovoltaic modules employed were identical to those utilized in the field desert study. The wind tunnel’s cross-section measures 3.0 m × 2.5 m, with an overall length of 20 m. The designed wind speed for the experimental section can reach up to 30 m/s and is continuously adjustable. The sand utilized in the experiments, which had mixed granular sizes, was sourced directly from the field experimental sites. The research focused on assessing the impact of sand and dust on the output performance and temperature of the photovoltaic system under the varied densities of accumulated sand, wind speeds, and inclination angles. The experimental outline is shown in Figure 2.

To simulate generally weak, moderate, and strong sandstorms, as described in references, experiments were conducted using varying densities of accumulated sand at wind speeds of 5 m/s, 10 m/s, and 15 m/s to assess the influence of the accumulated sand density on the transmission rate. Subsequently, for the sand accumulation study, the module tilt angle was adjusted to 0°, 15°, 30°, 45°, 60°, 75°, and 90°. Lastly, the density of the accumulated sand on the PV module surface was varied from 0 to 40 g/m². The aim of this was to observe the alterations in the PV module’s fill factor value and the density of the accumulated sand on its surface over time, as well as to track the module’s temperature response to the changing density of the accumulated sand (Figure 3).

The particle size distribution of the dust sampled from the desert surface was determined using a Neopartek Helos particle size analyzer from Germany; this analyzer has an accuracy of σ ± 1%. The findings are detailed in

Table 2. Particle size parameters of sand and dust samples.

Particle Size D/mm	Percentage%	Particle Size D/mm	Percentage%
0.00–0.02	0.00	0.40–0.50	0.02
0.02–0.04	0.05	0.50–0.60	0.02
0.04–0.06	0.36	0.60–0.70	0.02
0.06–0.08	1.01	0.70–0.80	0.02
0.08–0.10	13.90	0.80–0.90	0.01
0.10–0.20	82.51	0.90–1.00	0.01
0.20–0.30	1.92	>1.00	0.00
0.30–0.40	0.15

, showing that the particle sizes of the sand dust from this desert region are predominantly between 0.05 mm and 0.30 mm. Consequently, for experimental analysis, the sand dust samples were segregated into seven consecutive particle size intervals: <0.04 mm, 0.04–0.06 mm, 0.06–0.08 mm, 0.08–0.10 mm, 0.10–0.20 mm, 0.20–0.30 mm, and 0.30–0.40 mm.

The particle size intervals for the sand and dust particles were determined using the sieving method, which employs sieves of varying sizes. Equal masses of sand particles from each size interval were uniformly distributed across the surfaces of the seven PV modules, as illustrated in Figure 4. The experimental setup remained consistent with that of the prior experimental phase.

For operational PV modules, the maximum output power dictates the capacity benefit, while the fill factor is pivotal in determining energy conversion efficiency. This study aims to holistically analyze the output characteristics of the PV modules, factoring in these crucial parameters and integrating the findings from experiments investigating the impact of sand and dust on the temperature performance of PV modules [22].

3.2. Analysis of Experimental Results

3.2.1. Effect of Different Sand Densities on the Maximum Output Power of Photovoltaic Modules

Figure 5 depicts the correlation between the PV module’s maximum output power and the sand density on its surface over time. As the sand density on the PV module’s surface escalates, there is a corresponding decline in its maximum output power. Beyond a certain sand density threshold, the fluctuation in the maximum output power diminishes, converging to a stable state. Notably, as the density of accumulated sand on the module’s surface increases from 0 to 40 g/m², there is a 32.2% reduction in the maximum output power. This highlights the profound influence of sand and dust on the PV module’s output capacity [23,24].

Figure 6 illustrates the influence of sand accumulation on the transmittance of PV modules. When sand is present on the module surface, the light intensity, denoted as U, is scattered and absorbed by the sand particles. The absorbed light energy, ΔU₁, is converted into thermal energy. The resultant scattered light intensity is ΔU₂. A fraction of this scattered light is redirected to the module surface. The light, U₁, is scattered onto the module glass plate by the sand particles and undergoes another cycle of transmission and reflection. Due to the interference of sand and dust, the light intensity intended to reach the module surface through the glass cover plate, originally U, diminishes to (U − ΔU₁ + ΔU₂). This decrease results in reduced power. This observation aligns with the notion that the primary effect of sand accumulation on the module output power is attributed to decreased transmittance on the module surface.

3.2.2. Effect of Different Sand Particle Sizes on the Maximum Output Power of Photovoltaic Modules with the Same Sand Quality

Figure 7 shows the relationship between different dust particle sizes and the variation in the maximum output power of the PV modules with the same sand quality at different moments. The maximum output power of the clean PV module is larger than that of the module when there is sand and dust, and the maximum output power increases gradually with an increase in the particle size and finally stabilizes. When the particle size is 0.04–0.06 mm, the maximum output power of the module appears to have the lowest value, and the maximum drop is 0.5 W. The reason is that when sand accumulates on the surface of the PV module, the shading effect formed by the sand and dust weakens the total energy of the radiation received by the PV module, i.e., it reduces the transmittance of the glass cover plate on the surface of the PV module. This leads to a 6.0% decrease in its output power with a minimum drop as low as 0.2%. This is because when the total mass of sand and dust covering the surface of the module is the same, the larger the particle size of the sand and dust, the smaller the number of particles; the larger the particle gap, the smaller the relative effect on the transmittance of the PV module. The relative transmittance of the module when the particle size is 0.06–0.10 mm is 1.17% higher than the relative transmittance of the module when the particle size is 0.04–0.06 mm; hence, the maximum output power of the module at this time is relatively recovered [25,26,27,28,29].

3.2.3. Experimental Results and Analysis of the Relationship between Mounting Inclination Angle and Sand Accumulation on the Surface of Photovoltaic Modules

In Inner Mongolia, the optimal tilt angle for PV modules is determined to be approximately 45°. The simulations were conducted on PV modules with a tilt angle of 45° under varying wind speeds. As depicted in Figure 8, the minimum dust accumulation occurs at a wind speed of 5 m/s, while the maximum accumulation is observed at 15 m/s.

Figure 9 illustrates the accumulation of sand on the photovoltaic (PV) modules at various inclination angles under the same wind speed. With an increase in the inclination angle, the adherence of sand and dust progressively increases, peaking at 60°. Beyond 60°, the accumulation diminishes, yet the PV panel surface exhibits non-uniform distribution, with certain areas accumulating more dust than others. Three sets of experiments were performed with sand densities of 5 g/m³, 10 g/m³, and 15 g/m³, coupled with wind speeds of 5 m/s, 10 m/s, and 15 m/s. As presented in Figure 10, under the same wind speed but with varying sand concentrations, the power generation rate generally decreases and then ascends. At a wind speed of 5 m/s and inclination angles between 0° and 90°, the relative power generation rates are comparable. This similarity arises because, at 0° inclination, the PV panel surface aligns with the wind and sand flow direction, resulting in minimal sand deposition due to the negligible horizontal force acting on the sand particles. Conversely, at an inclination of 90°, the panel surface is perpendicular to the sand flow, causing most sand particles to slide off due to combined gravitational and elastic forces. Between inclination angles of 0° and 60°, an increased inclination correlates with a declining power generation rate. At 60°, the relative power generation rate drops to its lowest, 94.2%, marking a 5.8% energy loss compared to the peak rate. The minimal fluctuations in the ratio can be attributed to the low wind speed, which prevents larger sand particles from adhering to the module.

Relative output power is the ratio of the output power of the PV cell after dust accumulation to the output power of the clean PV cell, as detailed in the following equations.

$${\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}={\mathrm{P}}_{\mathrm{s}\mathrm{a}\mathrm{n}\mathrm{d}}/{\mathrm{P}}_{\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{n}}$$

(1)

At a wind speed of 10 m/s, with a sand and dust concentration of 15 g/m³, the relative output power rate remains relatively stable, reaching its lowest value at an inclination angle of 60°. When the inclination angle is below 30°, the influence of increased sand and dust concentration on the relative output power rate becomes more pronounced. When the wind speed is elevated to 15 m/s, the component output power across the varying tilt angles demonstrates greater stability than at wind speeds of 5 m/s and 10 m/s. At a 60° tilt angle, the relative output power rate declines to its nadir of 86.5%, resulting in a 13.7% energy reduction relative to the peak relative output power rate. These experimental observations are consistent with the simulation outcomes.

The effects of the various factors on the photovoltaic (PV) modules differ. Specifically, under different wind speeds, sand and dust concentrations, and installation inclination angles, the impact on the PV modules varies. With varying installation inclination angles, the force exerted on the sand particles during their settlement process changes, leading to alterations in the amount of sand settling on the PV module’s surface. Moreover, the inclination angle influences the scouring effect on the PV module surface. Given a certain precipitation level, different PV module installation tilt angles result in varying scouring intensities and rain flow diameters on the module surface, subsequently affecting the scouring outcome [30].

The experimental results discussed above were analyzed based on the various forces acting on the sand particles on the surface of the PV module. These forces include Fv, representing the force exerted by the PV module on the sand particles; Fu, denoting the frictional resistance of the module against the sand; and G, which signifies the intrinsic gravitational force of the sand. The mounting inclination of the PV cell, represented by $\mathsf{\theta }$, also plays a pivotal role, as depicted in Figure 11. Ga and Gb represent the gravitational forces of the sand particles in the directions parallel and perpendicular to the PV module surface, respectively, as detailed in the following equation:

$${\mathrm{G}}_{\mathrm{a}}=\mathrm{G}\sin \mathsf{\theta }$$

(2)

$${\mathrm{G}}_{\mathrm{b}}=\mathrm{G}\cos \mathsf{\theta }$$

(3)

Figure 11 illustrates the force exerted by sand particles on the surface of the PV module. It is evident that without accounting for intermolecular forces such as electrostatic forces, the force exerted by the sand particles on the module surface varies with the mounting inclination $\mathsf{\theta }$ of the PV module. This variation subsequently influences the settlement of sand particles on the module surface. Consequently, the characteristics related to the quantity of sand and dust settling on the PV module surface are altered, leading to corresponding changes in the module’s external output characteristics.

In the experiment, it was observed that as the wind speed and the angle of the plate surface increased, more sand particles came into contact with the component. This led to an enhanced force, Fv, exerted by the component on the sand and dust. As the interaction force between sand particles intensified, it surpassed the frictional resistance between the sand and the plate pieces. Consequently, an increased upward force was noted, making sand and dust particles more likely to deposit on the component. Furthermore, due to the intrinsic gravity, G, some sand and dust particles exhibited greater sizes than others, reducing the relative power generation rate. This can be attributed to the increased elasticity of the component toward sand and dust and the amplified interaction force among the sand particles. However, with an increasing inclination angle θ, the horizontal component of gravity, Ga, increases, causing a decrease in Gb. This scenario facilitates the easier slipping of sand and dust particles, resulting in some particles accumulating on the component’s edge. These particles cannot readily adhere to the component surface, leading to an increased ratio of particles present on the surface [31].

3.2.4. Influence of Sand Accumulation Density on the Filling Factor of Photovoltaic Modules

The fill factor (FF) is the ratio of the product of the current and voltage when the cell has maximum output power to the product of the short-circuit current and open-circuit voltage, which is a measure of the quality of the sun on that cell and determines the energy conversion efficiency [12]. In addition to the voltage and current, the fill factor is also related to the temperature of the solar cell panel; the fill factor of silicon solar cells in the 25 °C test environment has the following relationship equation:

$$\mathrm{F}\mathrm{F}=\frac{{\mathrm{I}}_{\mathrm{m}}{\mathrm{V}}_{\mathrm{m}}}{{\mathrm{I}}_{\mathrm{s}\mathrm{c}}{\mathrm{V}}_{\mathrm{o}\mathrm{c}}}$$

(4)

$$\frac{1}{\mathrm{F}\mathrm{F}}\frac{\mathrm{d}\mathrm{F}\mathrm{F}}{\mathrm{d}\mathrm{T}}\approx \left[\frac{1}{{\mathrm{V}}_{\mathrm{o}\mathrm{c}}}\frac{\mathrm{d}{\mathrm{V}}_{\mathrm{o}\mathrm{c}}}{\mathrm{d}\mathrm{T}}-\frac{1}{\mathrm{T}}\right]/6\approx -0.0015/\mathrm{°C}$$

(5)

From the equations, it can be seen that the value of the fill factor decreases by a factor of 0.0015 for every 1 °C increase in temperature.

Sand deposition also has a certain indirect effect on the filling factor. First, the effect of the sand deposition on the temperature of the PV components was observed. Utilizing the 1 g/m² density gradient from 30 g/m² to 40 g/m², the corresponding density of the sand accumulation under the component temperature change was tested. From the data shown in Figure 12, it can be seen that the component temperature changes with the density of sand in the inflection point at the density value of ~35 g/m².

Figure 13 shows the variation in the filling factor value of the PV module with the density of sand accumulation on the surface of the module at different moments. For the density interval in which the module temperature size changes with the density of the accumulated sand and an inflection point occurs, the density value was refined for supplementary experiments. Figure 14 shows the corresponding change in the fill factor under the value of the density of accumulated sand set in the supplementary experiments.

Figure 13 illustrates that as the density of the sand accumulation is augmented, the fill factor of the PV module initially increases and subsequently decreases. The intrinsic determinants influencing the silicon solar cells’ fill factor include the module’s open-circuit voltage and short-circuit current. The analysis of the experimental data reveals a pronounced difference in the sensitivity of the open-circuit voltage and short-circuit current to the component temperature. The variation trend of the fill factor with the component temperature aligns closely with that of the open-circuit voltage in relation to temperature. With an increase in the density of the accumulated sand from 0 to 30 g/m², the component temperature reduces in line with the escalating density of the accumulated sand, leading to a consistent increment in the computed fill factor value. Coinciding with the inflection point in Figure 12, an abrupt alteration in the fill factor value is discerned at an accumulated sand density of 30 g/m². As the density of the accumulated sand rises from 30 g/m² to 40 g/m², there is a marked reduction in the fill factor, which reaches its nadir at an accumulated sand density of 40 g/m². Furthermore, the data from the supplementary experiment depicted in Figure 14 indicate a nadir in the component temperature at a sand accumulation density of 35 g/m², while the fill factor peaks at this density. Based on the trends from both datasets, it is deduced that when the sand accumulation density on the PV module surfaces is ≤35 g/m², the fill factor ascends progressively, whereas for densities >35 g/m², the fill factor for the PV modules diminishes gradually [32,33,34].

3.2.5. Influence of Different Sand Particle Sizes on the Filling Factor of Photovoltaic Modules with the Same Sand Quality

The decline in output power observed in Figure 7 for the particle size range of 0.08–0.10 mm was evaluated alongside the findings related to the temperature characteristics of the photovoltaic modules under varying degrees of particle size coverage (Figure 15). Upon comparative analysis, the congruence between the power decrease at the specific particle size intervals in Figure 7 and the corresponding temperature peaks in Figure 15 becomes evident. Notably, while a slight increase in dust particle size within this range leads to enhanced relative transmittance of the glass cover plate, a concurrent temperature peak emerges for the PV module covered by the dust of this particle size. As the module conversion efficiency is inversely related to its temperature, the resultant decline in combined module output power can be attributed to the significant temperature increase adversely affecting the module conversion efficiency, which becomes the predominant factor influencing power [35].

Figure 16 illustrates the correlation between diverse particle sizes and the filling factor of PV modules across various time points, given a consistent dust mass. A comparative examination of Figure 15 and Figure 16 reveals that the trend in the module filling factor as a function of sand dust particle size is almost inversely proportional to the trend in PV module temperature with respect to particle size.

In the experiment considering seven predefined sand particle size intervals, the filling factor reveals two pronounced peaks. Specifically, these peaks appear within the particle size intervals where the PV module temperature experiences its minimum values. The most elevated filling factor is discerned within the 0.04–0.06 mm particle size range, reflecting a 4% enhancement relative to a pristine module. In contrast, the most diminished filling factor arises within the 0.08–0.10 mm particle size interval, which corresponds with the zenith of the module temperature. Upon thorough analysis, it becomes evident that the filling factor exhibits a trend of a nearly monotonic decrease in relation to the increasing module temperature. This analytical observation underscores the fact that the magnitude of the filling factor for PV modules, when covered by sand and dust of different particle sizes, hinges profoundly on the prevailing module temperature. Notably, this module temperature is amplified with the sand and dust particle size augmentation. This relationship unfolds as an intriguing pattern of initial ascent followed by a descent and culminating in an ascent. Such a dynamic can be attributed to the variations inherent in the particle sizes of the sand and dust, which engender diverse blockage areas and spacings. These disparities consequently mediate the irradiance of the PV modules when they are cloaked by these particles. Predominantly, desert dust is characterized by its quartz sand composition, which intrinsically possesses low thermal conductivity coupled with a diminutive heat capacity. Such inherent properties inhibit the module’s heat dissipation efficiency. Consequently, a pronounced thermal resistance effect emerges when layers of sand dust settle on the module’s surface. The distinct temperature effects induced by the varying dust particle sizes upon the module are manifested in the differentiated magnitudes and proportions. This results in the module temperature’s relationship with particle size delineating a fluctuating trajectory. Subsequently, the filling factor of the PV module, as influenced by the dust particle size, also follows a wavering trajectory, which contrasts intriguingly with the aforementioned temperature trend [36].

4. Conclusions

The output characteristics of the PV modules were assessed under three distinct wind speeds: 5 m/s, 10 m/s, and 15 m/s. These assessments were conducted at varying sand and dust densities and inclination angles. The detailed simulation and experimental observations facilitated the following conclusions:

(1)

The output power of the module gradually decreases with the increase in sand accumulation density. The density of the sand accumulation on the surface of the PV module increases from 0 to 40 g/m², and the maximum output power decreases by 32.2%. Thus, it can be seen that sand and dust affect the output power of the PV module by significantly affecting the transmittance rate.

(2)

The maximum output power of the module increases and stabilizes as the particle size of the dust increases. When the particle size is 0.04–0.06 mm, the maximum output power of the module appears to be the lowest, and the maximum decrease is 0.5 W, at which time the relative transmittance of the module decreases by 26.7%. The maximum output power of the PV module decreases according to the influence of the particle size change on the module’s transmittance and temperature.

(3)

The wind tunnel experiment revealed that when the wind speed is 5 m/s, the relative output power of each angle module is below 5%. When the inclination angle is 60°, the relative output power rate reaches the minimum, i.e., 94.2%, with a relative output power loss of 5.8%. Compared with the experimental wind speed, when the wind speed is 15 m/s, the output power of each angle module exhibits the greatest decrease, while the relative output power rate reaches the minimum when the inclination angle is 60°; the minimum value is 86.5%, with an ~13.7% relative output power loss compared with the maximum value.

(4)

There are differences in the effects of the two control variables, the density of the accumulated sand and the sand particle size, on the component temperature; unlike the role of accumulated sand density on the fill factor curve, the trend in the component fill factor under different sand particle sizes fluctuates. The trend of component fill factor with a density of accumulated sand is divided into two stages: at 0–35 g/m², with the increase of sand density, component temperature decreases, the fill factor increases and peaks at 35 g/m² (component temperature valley); meanwhile, at 35–45 g/m², with an increase in accumulated sand density, the component surface temperature increases and the fill factor decreases.