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Article

Quantification of Dust Accumulation on Solar Panels Using the Contact-Characteristics-Based Discrete Element Method

1
Department of Electrical Engineering, National Taitung Junior College, 911, Jhengci N. Rd., Taitung 95045, Taiwan
2
Department of Electrical Engineering, National Chin-Yi University of Technology, 57, Section 2, Chungshan Road, Taiping District, Taichung 41107, Taiwan
*
Author to whom correspondence should be addressed.
Energies 2023, 16(6), 2580; https://doi.org/10.3390/en16062580
Submission received: 2 November 2022 / Revised: 29 December 2022 / Accepted: 1 March 2023 / Published: 9 March 2023
(This article belongs to the Topic IOT, Communication and Engineering)

Abstract

:
Dust comprises particles usually present in the atmosphere. The deposition of dust on the surface of the solar panel seriously affects the light transmittance, resulting in lower pow-er generation efficiency and shortening the service life of the solar panel. Therefore, it is important to understand the dust distribution on the surface of solar panels and discuss the influence of dust on the power generation efficiency of solar panels for the efficient prevention of dust deposition on the panel. In this study, to analyze the dust distribution on the surface of the solar panel, the discrete element method was used to establish the contact mechanics model between dust particles and the solar panel. The number of dust particles on the surface of solar panels was calculated at different solar panel inclination angles, wind speeds, and wind directions. The wind speed of 1 and 3 m/s did not affect the dust deposition significantly but the speed over 5 m/s reduced the dust particles from the surface of the solar panel. The inclination angle of 23° influenced dust deposition on the surface of the solar panel. Wind direction did not show a significant effect on dust deposition. The longer the deposition time, the more particles remained on the surface due to the increased force between the particles and the surface of the solar panel. The results from calculation and measurement from transmittance were similar with a different rate of 3.41%. Thus, the result of the proposed calculation in this study provides a basis for de-signing the solar power generation plant and decision-making on the maintenance of the solar panel.

1. Introduction

The increasing demand for energy causes the "energy security crisis" more prominent than before. "Global warming" caused by using fossil fuels also emerges more seriously [1]. Renewable energy source, especially, solar energy is ideal for sustainable development with the advantages of inexhaustibility and easier expansion of generation capacity. Solar energy is an appropriate power source for remote areas and emergency power backup, too. It does not require labor-intensive mining and is environment friendly allowing ecological conservation and suppression of carbon dioxide emission [2,3].
Therefore, researchers have researched solar cells from varius perspectives. With a huge investment, the power generation of solar cells has improved considerably but it still is limited by natural causes such as dust deposition [4,5,6]. Even in remote areas where solar power plants are built, dust problems are unavoidable as dust is produced from natural sources (wind, volcanic activity, and so on) as well as anthropogenic sources (construction, transportation, and other human activities). Dust deposition on the solar panel is one of the most important factors in managing solar power production [7]. The size, composition, and shape of dust vary a lot as dust may contain pollens, human and animal cells, hairs, textile fibers, and minerals [8]. Dust and other various environmental factors including irradiance, rain, and wind affects solar panel temperature and light transmittance which again influences power production [9]. Especially, the efficiency of solar power production is greatly affected by a layer of dust (usually less than 10 μm) as dust hinders the radiation onto the solar cell. The deposition of dust particles on the surface of the solar panel seriously affects the power generation efficiency of the solar panel, decreasing power generation efficiency and shortening the service life of the solar panel.
Hertz [10] proposed the theory of contact related to the static interaction of particles. He found a relationship between the contact area and elastic deformation between particles. Recently, research on the adhesion of dust particles to the surface has been conducted based on his theory. Cundall and Strack [11] proposed the concept of the soft sphere model to describe the adhesion between microscopic particles and proposed the discrete simulation analysis of the particulate matter numerically.
To analyze the distribution of dust on the surface of solar panels over time and explore its influence on the efficiency of power generation, we established a contact model with the discrete element method to explain the interaction between dust particles and solar panels, considering the inclination angles of the solar panel, wind speed, and direction, the distribution of dust on the surface of solar panels. In the research, it was assumed that the surface of the solar panel was exposed to the atmosphere and received dust particles falling from the air. For modeling, a micro weather station and an automatic dust measurement platform were designed and installed. The atmospheric parameters and the dust deposition on the surface were measured to verify the accuracy of the proposed model and compare the simulation results to the measured distribution of dust particles. The result provides the basic information for the design of the solar power plant and the maintenance of the solar panel.

2. Contact Mechanism Model Based on the Discrete Element Method

The discrete element method was proposed by Cundall based on the principle of molecular dynamics for the analysis of discrete particle behavior [12]. The discrete element method was analogous to the process of motion of particles spreading in the air. The motion of particles inevitably causes collisions and generates various forces between particles. The process of the collision described by the discrete element method describes the basic process of contact generation and the following motions of particles.
To quantify the impact of dust deposition on solar panel power generation, a model was established to evaluate the impact based on the data on the amount of dust and wind intensity. For the model, the contact mechanism model was adopted with the following assumptions.
(1)
The distribution of dust particles was uniform in the surrounding environment of the solar panel. The particle shape was spherical and the particle sizes were randomly distributed. A friction coefficient was used to compensate for the error caused by the irregular shapes of dust particles.
(2)
Gravity and van der Waals forces were considered between dust particles.
Based on the above two assumptions, the physical parameters of the contact between dust particles and solar panels were named as shown in Table 1 [13].
The normal force Fn between dust particles or between the particles and the solar panel is expressed as follows [13].
F n = 4 π γ E * α 3 + 4 E * α 3 3 R *
where γ is the surface energy of solar energy, E* is the comprehensive elastic modulus, R* is the comprehensive radius of particles, and α is the normal overlap.
The tangential force Ft between dust particles or between the particles and the solar panel is expressed as Equation (2) [13].
F t = S t δ
where St is the tangential stiffness and δ is the tangential overlap.
The St tangential stiffness is expressed as the following equation [13].
S t = 8 G * R * α
where G* is the equivalent shear modulus, R* is the comprehensive radius of the particle, and α is the normal overlap amount.
The friction force f between dust particles or between the particles and the solar panel is expressed as Equation (4) [13].
f = μ s F n
where Fn is the normal force and µs is the static friction coefficient.
The rolling friction is extremely important in the analysis. The rolling friction is calculated by the moment Ti between the dust particles or the contact surface between the dust particles and the solar panel, which is expressed as the following equation [13].
T i = μ r F n R i ω i
where µr is the coefficient of rolling friction, ωi is the angular velocity of particle i at the point of contact, and Ri is the distance from the center of mass of particle i to the contact point.

3. Solar Panel Dust Accumulation Experiment

3.1. Parameters and Equations

Figure 1 shows the simulation model of solar panel dust accumulation, and the particle factory above simulated the falling surface of dust particles. The size of the solar panel glass in the model was 375 × 340 mm, which is the standard size for commercial use. The width of the aluminum alloy frame was 20 mm. The material for the surface of the solar panel was glass.
The physical parameters of the glass panel of the solar panel surface, aluminum alloy frame, and dust particles for simulation are shown in Table 2. Table 3 presents the characteristic parameters of contacts between dust particles and between the particles and the glass or frame (aluminum allow) of the solar panel [13].
According to the data provided by the automatic dust measurement system in Taichung City (installed and managed by the Environmental Protection Agency of Taiwan), the flux of atmospheric dust on the surface was estimated as 2.29 tons/km2∙month [14]. It was equivalent to 8.834 × 10−16 kg/mm2∙s. For the size of 375 × 340 mm of a solar panel, the flux of the dust on the panel was estimated to be 1.1264 × 10−10 kg/s. To have the amount of 1.1264 × 10−6 kg of dust particles (7951 particles) on the panel, 2.778 h were required. The number of dust particles is calculated based on the density of dust particles on the solar panel, which is 1400 kg/m3 (Table 2). The volume of a dust particle is 3.0352 × 10−13 m3 and the mass of a particle is 4.25 × 10−10 kg. As there are three particle factories in the model design, the total mass of dust particles is 1.1264 × 10−10 kg × 3 = 3.3792 × 10−6 kg, so the number of dust particles is calculated as the total mass of dust particles/the mass of a single dust particle (3.3792 × 10−6 kg/4.25 × 10−10 kg) = 7951.
When the flux of dust particles does not change over time, the simulation time can be set as the actual accumulation time (T) for dust deposition on the panel. Thus, the following equation is proposed.
T = ( T M ÷ G s ) × D f
where T is the actual dust accumulation time on the solar panel, TM is the total weight of dust, Gs is the area of the solar panel, and Df is the dust deposition flux in Taichung City.

3.2. Calculation of Dust Deposition

Assuming that dust particles falled on the solar panel surface randomly, we divided the surface into 25 sections. The distribution of dust particles was measured in each section, as shown in Figure 2. For the convenience of analysis, the glass surface was divided into five areas from top to bottom, namely, upper, middle-upper, middle, middle-lower, and lower. Each area contained five sections and the average weight of the dust particles in each area was calculated. After deducting the dust particles on the aluminum alloy, the number of dust particles in each section was calculated.
Wind direction and speed data were provided by the Environmental Protection Agency of Taiwan. The location of the actual measurement site was Taichung City, Taiwan. The monthly average wind speed was between 1 and 2 m/s [15].
The inclination angle of the solar panel affects the light absorption of the solar panel dust deposition. In Taiwan (23° N latitude), the inclination angle of solar panels is generally 23°, which gives the maximum solar radiation. Four different inclination angles (10°, 15°, 20°, and 23°) were chosen to compare the dust deposition on the solar panels in simulation. The average wind speed was about 1–2 m/s and the highest wind speed reached about 5–6 m/s in Taichung. To simulate the greatest dust deposition, rain was not considered. In summary, the parameters for simulation in this study included different solar panel inclination angles (10°, 15°, 20°, and 23°), wind speed (1, 3, and 5 m/s), and wind direction (northeast and southwest).

4. Results

4.1. Number of Dust Particles in Each Area

The flux of dust particles varied under different solar panel inclination angles and changed the distribution on the surface of the solar panel regardless of wind direction and speed. In the simulation for 3.5 days, a total of 7951 dust particles were assumed to fall from the particle factory.
Figure 3a depicts the simulation results of particle distribution on the surface of the solar panel at an inclination angle of 10°. A total of 7535 particles were counted on the surface, with 416 not deposited on the solar panel. The dust particles were almost evenly distributed on each section of the surface. The upper area had 50 particles on average less than the middle area. Figure 3b shows the average number of particles over time in five areas (the upper, middle-upper, middle, middle-lower, and lower areas) of the panel. At the inclination angle of 10°, dust particles deposited more on the upper middle and lower middle areas.
Figure 4a shows the simulation results of particle distribution on the surface of the solar panel at an inclination angle of 15°. The distribution of dust particles on the surface changed significantly compared to that at the angle of 10°. The particles in the lower areas and the middle area accumulated more than in other areas. The total number of dust particles was 7397, while 554 dust particles did not land on the surface. The number of particles in each area over time was presented in Figure 4b.
Figure 5a presents the particle distribution on the surface of the solar panel at an inclination angle of 20°. More dust particles deposited on the upper-middle, middle, and lower-middle areas. There were 7263 dust particles on the glass. Figure 5b shows the number of particles in each area over time.
Figure 6a shows the particle distribution on the surface of the solar panel at an inclination angle of 23°. As the inclination angle increased, dust particles tended to move down from the upper area. Therefore, the upper area had the smallest number of particles. The particles seemed to gather in the upper and lower-middle areas. There were 7065 dust particles on the surface and 886 dust particles were not deposited. More particles were removed at the inclination angle of 23° than at the other angles. Figure 6b presents that more particles were deposited in the other areas than in the upper area. Instead, more particles were deposited on the lower area than at the other inclination degrees.
Table 4 presents the statistics of dust deposition at different inclination angles for 3.5 days. More particles were not deposited with the increase of the inclination angle. The ratio of non-deposited particles to the total number of particles from the particle factory increased accordingly, and the steeper the angle was, the less particles were deposited. The difference in the proportion of non-deposited particles at the inclination angles of 23° and 20° was 2.49%. The differences between the inclination angles of 20° and 15° and between the inclination angles of 15° and 10° were 1.68 and 1.74%.

4.2. Influence of Wind Direction and Speed

The unevenly distributed particles on the surface affected the power generation of the solar panel. The wind blows dust particles, which cleans the surface to a certain extent. The stronger the wind, the more particles are blown away from the surface regardless of wind direction. It was found in this study that the northeast wind removed more dust particles on the surface of the solar panel than the southwest wind at the speed of 5 m/s. Therefore, wind direction rarely affected the dust deposition while wind speed does significantly. The result is shown in Table 5.

4.3. Dust Deposition for 1 Month

The simulation was carried out for 1 month at an inclination angle of 10° with the wind. The result is shown in Table 6. The proportion of non-deposited particles decreased significantly when compared to that in the simulation for 3.5 days. With no wind, the proportion for 3.5 days was 5.23% while that for 1 month was 3.85%. With the wind, the proportion ranged from 6.09−7.65% in the northeast wind and 5.48−6.49% in the southwest wind for 3.5 days. The proportion in the simulation for 1 month decreased to 4.32−6.27% in the northeast wind and 4.31−4.70% in the southwest wind. The effect of wind direction at the wind speed of 5 m/s became more obvious (6.27% in the northeast wind and 4.70% in the southwest wind). The main reason was that more dust particles were deposited on the surface, which increased the force between the particles and between the particles and the surface of the solar panel, and the force held them on the surface.

4.4. Dust Deposition for 3 Months

In the simulation for 3 months at an inclination angle of 10° with the wind, the total number of dust particles was 204,961. The proportion of non-deposited particles decreases when compared with that in the simulation of 1 month. In the northeast wind, the proportion in the simulation for 1 month was 4.32–6.27% in the northeast wind and 4.31–4.70% in the southwest wind, while that in the simulation for 3 months was 3.96–5.66% in the northeast wind and 3.63–4.39% in the southwest wind. Without wind, the proportion was similar: 3.99% for 3 months and 3.85% for 1 month. The forces seemed to increase to hold the particles on the surface of the solar panel.

4.5. Particle Deposition Model

In this study, the discrete element method was used to treat the dust particle as multiple discrete units. Ech particle or an aggregate (block) of dust particles is called a unit, and the contact force between units is calculated according to Newton’s law of motion. The motion parameters of the unit are calculated to realize the prediction of the motion of the object. As a unit is a particle or an aggregate, the particle model and block method need to be considered for understanding their movements on the surface.
In the particle model, the motion of a particle is independent, and when the particles collide with each other, they interact at the point of contact. The dispersive characteristics of particles produce complex movements under various forces. In practical applications, it is necessary to treat particles as discs and spheres, that is, two-dimensional circular particles and three-dimensional spherical particles. Figure 7 shows the contact between particles (assumed to be spheres) and the contact between particles and surface, where Pn represents a particle. The contact is regarded as a Hertz contact unit including particles and particles and particles and boundaries, where R1 and R2 are the contact radii of particles Z1 and Z2 respectively, A is the radius of the contact circle, and δ is the deformation of the contact (Figure 8) [16].
In the block model, the main object is an aggregate of particles. At present, the commonly used spherical particle contact mechanism in discrete aggregates is explained by the hard-sphere model and the soft-sphere model to simplify the contact problem [17]. The hard-sphere model does not consider the contact force and contact deformation during the particle contact process, simplifying the entire contact process into a collision that occurs in a very short time. The soft-sphere model is simpler than the hard-sphere model as a simplified contact force is considered between soft-ball particles. The force on particles is described with a damper and spring, and the tangential force is simplified as a damper, sliding machine, and spring.
In this study, we assumed that the aggregation of dust particles followed the hard-sphere model, and the force between particles was assumed to be gravity and Van der Waals force. Therefore, particles and aggregates of particles were affected by such forces, which were related to the different numbers of particles on the surface of the solar panel with different inclination angles of the solar panel.

5. Experiment for Verifying the Calculation Result

To verify the result of the simulation, an automatic dust measurement platform was designed for the experiment. Figure 9 and Figure 10 depict the design and appearance of the platform, in which the inclination angle of the solar panel was fixed at 10°. The platform was exposed to the sun for 3.5 days in the open air and the light transmittance on the surface was measured. The light transmittance was measured with LH-220, a high-precision optical transmittance measuring instrument following “Optical Performance Test Method for Automotive Safety Glass” (the standard of GB5137.2-2002), which is professionally used for glass, heat insulation film, and PVC. Table 7 shows the technical parameters of LH-220 (Table 8). The distribution of dust on the surface of the solar panel was analyzed from the transmittance data. The greater the decrease in transmittance, the more dust that was deposited at the transmittance measurement point. Through the initial measurement of light transmittance, it was confirmed that dust was evenly distributed on the surface. Then, the light transmittance of the solar panel was measured by the platform at nine measurement points. The average value was calculated from the data of the points to obtain the average daylight transmittance.
First, the light transmittance of the solar panel was measured. There were 25 measurement points in each section. Figure 11 shows an example of the measured light transmittance at each point. It was observed that dust was evenly distributed on the surface, with similar transmittance of 86–88%. When the surface was clean, the light transmittance was 94%. Taking 94% of the light transmittance as the criteria, the light transmittance with dust particles on the surface was estimated. The result showed that, when the average transmittance decreased to 6.6%, the average number of dust particles was 302. Therefore, it was assumed that 46 particles decreased by 1% of the light transmittance. Thus, at point 13 (the middle of the surface) as an example, with a decrease in the light transmittance from 94 to 88.2%, a 5.8% decrease pertained to 273 dust particles at the point. The average difference between the measured and calculated light transmittance was 3.41%. The average error rate was 5.37%. The accuracy of automatic measurement was verified by manual measurement, and the results were similar to each other (Table 9).
Figure 12 presents the result of the automatic measurement of the light transmittance after 3.5 days of dust accumulation. The slide motor of the automatic measurement platform moved in one direction. Therefore, automatic measurement was conducted only in one direction, and the average light transmittance of the measurement was 86.01%. The light transmittance was 1.38% different from the average light transmittance of 87.39% at 25 measurement points. Therefore, in the future, the results of automatic measurement can be used to represent the transmittance of the solar panel.

6. Conclusions

Since solar power plants are usually located in open areas such as grasslands and deserts, the surface of the solar panel was prone to dust deposition. Thus, it is important to remove and prevent the deposited dust in solar power generation. Therefore, we studied factors affecting dust deposition on the surface of the solar panel and the relationship between light transmittance and the number of dust particles through calculation based on the weather data and measured transmittance with an automated dust measurement platform. The result showed that dust deposition was effectively predicted considering the wind speed and direction, inclination angles of the solar panel, and time for dust deposition. In Taichung, Taiwan, the northeast wind could remove more dust particles at a wind speed of 5 m/s than the southwest wind. At the wind speed of 1 and 3 m/s, the wind direction did not influence the dust deposition significantly. Wind speed of less than 5 m/s did not affect dust deposition considerably but the wind speed over 5 m/s reduced the dust particles from the surface of the solar panel significantly. The inclination angle also influenced dust deposition when the angle was steeper than 23°. Dust particles tended to gather around the middle part of the surface at this inclination angle. The longer the deposition time, the more particles remained on the surface due to the increased force among the particles and between the particles and the surface of the solar panel. The wind speed of over 5 m/s removed more particles from the surface. The calculated results were compared with the measurement based on transmittance with the proposed dust measurement platform, which showed a difference of only 3.41%. The result of the proposed method in this study provides an important basis for designing the solar power generation plant and decision-making on the maintenance of the solar panel.

Author Contributions

Conceptualization, S.-L.W. and H.-C.C.; Methodology, S.-L.W., H.-C.C. and K.-J.P.; Software, S.-L.W., H.-C.C. and K.-J.P.; Validation, S.-L.W., H.-C.C. and K.-J.P.; Formal analysis, S.-L.W. and H.-C.C.; Data curation, S.-L.W., H.-C.C. and K.-J.P.; Writing—original draft, S.-L.W., H.-C.C. and K.-J.P.; Writing—review & editing, S.-L.W. and H.-C.C. All authors have read and agreed to the published version of the manuscript.

Funding

The study was supported by Ministry of Science and Technology of Republic of China, under Grant No. MOST 111-2221-E-167-005-MY2.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Dust accumulation on a solar panel.
Figure 1. Dust accumulation on a solar panel.
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Figure 2. Schematic diagram showing the position of the glass side of the solar panel.
Figure 2. Schematic diagram showing the position of the glass side of the solar panel.
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Figure 3. Dust particle distribution at an inclination angle of 10°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
Figure 3. Dust particle distribution at an inclination angle of 10°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
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Figure 4. Dust particle distribution at an inclination angle of 15°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
Figure 4. Dust particle distribution at an inclination angle of 15°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
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Figure 5. Dust particle distribution at an inclination angle of 20°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
Figure 5. Dust particle distribution at an inclination angle of 20°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
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Figure 6. Dust particle distribution at an inclination angle of 23°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
Figure 6. Dust particle distribution at an inclination angle of 23°. (a) The total number of particles in each area and (b) that over time on the solar panel surface.
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Figure 7. Particle-to-particle contact and particle-to-surface contact.
Figure 7. Particle-to-particle contact and particle-to-surface contact.
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Figure 8. Hertz contact element [16].
Figure 8. Hertz contact element [16].
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Figure 9. Design of the automatic dust measurement platform.
Figure 9. Design of the automatic dust measurement platform.
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Figure 10. Appearance of the automatic dust measurement platform.
Figure 10. Appearance of the automatic dust measurement platform.
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Figure 11. Manual measurement result of light transmittance after 3.5 days of dust deposition.
Figure 11. Manual measurement result of light transmittance after 3.5 days of dust deposition.
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Figure 12. Automated measurement result of light transmittance after 3.5 days of dust deposition.
Figure 12. Automated measurement result of light transmittance after 3.5 days of dust deposition.
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Table 1. Parameters for two spherical particles.
Table 1. Parameters for two spherical particles.
Dust Particles 1Dust Particles 2 or Solar Panels
RadiusR1R2
Sphere Center Position Vectorr1r2
Elastic ModulusE1E2
Poisson’s Ratioγ1γ2
Qualitym1m2
Pre-Collision Velocity Vectorv1v2
Shear ModulusG1G2
Table 2. Solar panel and dust physical parameters.
Table 2. Solar panel and dust physical parameters.
ParameterGlassAluminum AlloyDust Particle
Poisson’s Ratio0.230.38970.4
Shear Modulus/Pa2.8 × 10102.7 × 10102 × 106
Density/(kg/m3)245827001400
Table 3. Collision characteristic parameters.
Table 3. Collision characteristic parameters.
ParameterDust Particle-to-Particle Contact CoefficientCoefficient of Contact
between Dust Particles and Glass
Coefficient of Contact
between Dust Particles and Aluminum Alloys
Coefficient of Recovery0.50.40.4
Static Friction Coefficient0.50.70.7
Rolling Friction Coefficient0.10.50.5
Table 4. Simulation result of dust deposition for 3.5 days at different inclination angles.
Table 4. Simulation result of dust deposition for 3.5 days at different inclination angles.
Total Number of
Particles
Number of Deposited
Particles
Number of Non-Deposited ParticlesProportion of Non-Deposited Particles (%)
Inclination Angle
10°75354165.23
15°73975546.97
20°72636888.65
23°706588611.14
Table 5. Simulation result of dust deposition for 3.5 days with the wind at an inclination angle of 10°.
Table 5. Simulation result of dust deposition for 3.5 days with the wind at an inclination angle of 10°.
Total Number of
Particles
Number of Deposited
Particles
Number of Non-Deposited ParticlesProportion of
Non-Deposited Particles (%)
Wind Direction and Speed
No Wind75354165.23
Northeast wind1 m/s74674846.09
3 m/s73825697.16
5 m/s73436087.65
Southwest wind1 m/s75154365.48
3 m/s74764755.97
5 m/s74355166.49
Table 6. Simulation result of dust deposition for 1 month with the wind at an inclination angle of 10°.
Table 6. Simulation result of dust deposition for 1 month with the wind at an inclination angle of 10°.
Total Number of
Particles
Number of Deposited
Particles
Number of
Non-Deposited Particles
Proportion of
Non-Deposited Particles (%)
Wind Direction and Speed
No Wind76,40830623.85
Northeast wind1 m/s76,03634344.32
3 m/s75,60538654.86
5 m/s74,49149796.27
Southwest wind1 m/s76,04634244.31
3 m/s75,88635844.51
5 m/s75,73337374.70
Table 7. Simulation result of dust deposition for 3 months with the wind at an inclination angle of 10°.
Table 7. Simulation result of dust deposition for 3 months with the wind at an inclination angle of 10°.
Total Number of
Particles
Number of Deposited
Particles
Number of
Non-Deposited Particles
Proportion of
Non-Deposited Particles (%)
Wind Direction and Speed
No Wind196,77581863.99
Northeast wind1 m/s196,83881233.96
3 m/s195,25897034.73
5 m/s193,36511,5965.66
Southwest wind1 m/s197,53074313.63
3 m/s197,36875933.70
5 m/s195,97189904.39
Table 8. Measurement parameters of LH-220.
Table 8. Measurement parameters of LH-220.
Wavelength of light source380–760 nm
Measurement range0–100%
Resolution0.1%
Measurement error≤1%
Thickness for measurement≤50 mm
Table 9. Results of the simulation and measurement of transmittance and the number of dust particles in each section.
Table 9. Results of the simulation and measurement of transmittance and the number of dust particles in each section.
Section 1Section 2Section 3Section 4Section 5
Measured transmittance88.588.887.287.387.6
Simulated number of particles287244300295283
Measured number of particles250236309305291
Difference (%)12.873.113.053.262.82
Section 6Section 7Section 8Section 9Section 10
Measured transmittance85.887.686.587.186.8
Simulated number of particles342309311298316
Measured number of particles373291341314327
Difference (%)9.015.839.645.273.59
Section 11Section 12Section 13Section 14Section 15
Measured transmittance86.887.888.286.387.8
Simulated number of particles328290273331298
Measured number of particles327282264350282
Difference (%)0.22.83.415.765.41
Section 16Section 17Section 18Section 19Section 20
Measured transmittance86.987.586.686.887.5
Simulated number of particles317303320314304
Measured number of particles323296336327296
Difference (%)1.832.475.144.252.79
Section 21Section 22Section 23Section 24Section 25
Measured transmittance89868887.688.2
Simulated number of particles267331288299290
Measured number of particles227364273291264
Difference (%)14.869.885.282.689.07
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Wu, S.-L.; Chen, H.-C.; Peng, K.-J. Quantification of Dust Accumulation on Solar Panels Using the Contact-Characteristics-Based Discrete Element Method. Energies 2023, 16, 2580. https://doi.org/10.3390/en16062580

AMA Style

Wu S-L, Chen H-C, Peng K-J. Quantification of Dust Accumulation on Solar Panels Using the Contact-Characteristics-Based Discrete Element Method. Energies. 2023; 16(6):2580. https://doi.org/10.3390/en16062580

Chicago/Turabian Style

Wu, Shing-Lih, Hung-Cheng Chen, and Kai-Jun Peng. 2023. "Quantification of Dust Accumulation on Solar Panels Using the Contact-Characteristics-Based Discrete Element Method" Energies 16, no. 6: 2580. https://doi.org/10.3390/en16062580

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