1. Introduction
In recent years, photovoltaic power generation has emerged as one of the most promising forms of renewable energy generation. With its advantages of low pollution, high reliability, and wide applicability, the global installed capacity of photovoltaic systems has reached 660 gigawatts. However, solar panels are typically exposed to outdoor environments for long periods, making them highly susceptible to dust contamination. Over time, the accumulated dust layer significantly affects the photoelectric conversion efficiency of the panels. According to statistics, dust accumulation can reduce the power generation efficiency of photovoltaic panels by approximately 2% to 25%. In heavily polluted areas, panels that have not been cleaned for 30 days can lose up to 50% of their generation capacity. Without effective monitoring and timely cleaning, the annual energy loss caused by dust deposition alone can reach nearly 400,000 kWh per megawatt, resulting in enormous economic losses.
Existing dust monitoring systems for photovoltaic panels are mainly limited to measuring the power generation efficiency in isolation. They cannot provide real-time analysis of the dust accumulation condition or offer actionable guidance for cleaning and maintenance scheduling. To address these limitations, this study establishes an online monitoring experimental system for dust accumulation on photovoltaic panels, aiming to provide a reliable basis for determining optimal cleaning cycles.
This research designs an integrated experimental system that combines hardware sensing with software analysis. The hardware components monitor real-time voltage, current, panel temperature, solar irradiance, and high-resolution imagery. The software platform, developed in C#, records all measured parameters and performs image processing and prediction calculations. A simulated dust deposition experiment is conducted to reproduce panels with different dust densities. An improved interpolation algorithm is proposed to remove the silver grid lines from panel images. Finally, a dynamic prediction model describing the relationship between dust density and power loss rate is constructed, and an economic evaluation method is developed to determine the optimal cleaning cycle by minimizing the total annual cost of power loss and cleaning maintenance.
2. Photovoltaic Systems and Dust Characteristics
2.1 Classification of Photovoltaic Power Generation Systems
Photovoltaic power generation systems can be broadly classified into two categories according to their connection to the power grid. The first is the stand-alone photovoltaic system, also known as an off-grid system, which operates independently from the utility grid. It delivers power directly to loads or stores energy in batteries. This type of system is commonly used in remote areas where grid extension is difficult, such as rural electrification projects and telecommunications stations. The second category is the grid-connected photovoltaic system, which converts direct current generated by solar panels into grid-compliant alternating current through an inverter and feeds it into the main power grid. Grid-connected systems are further divided into distributed systems, typically mounted on building rooftops, and centralized systems, which are large-scale photovoltaic power plants. The present study focuses on centralized grid-connected stations, particularly those located in the northwest region of Jilin Province, China, which is characterized by a dry climate, high wind speeds, and substantial dust fallout.
2.2 Influence of Climatic and Environmental Factors on Photovoltaic Panel Performance
Various climatic parameters influence the performance of photovoltaic panels, including solar radiation intensity, wind speed and direction, rainfall, temperature, humidity, and airborne dust concentration. Among these factors, wind exerts a dual influence on dust deposition. On one hand, wind can remove dust particles from the panel surface, thereby reducing the dust layer. On the other hand, high-velocity winds can carry dust and sand from the surrounding area and enhance deposition. Wind tunnel experiments have demonstrated that wind direction has a stronger effect on dust deposition velocity and distribution than wind speed. For particle sizes larger than 75 micrometers, wind speeds greater than 24 m/s tend to degrade the surface mass density of dust deposition to negligible levels. Wind also cools the panel surface through convective heat transfer, which has a beneficial effect on maintaining conversion efficiency because photovoltaic panels lose efficiency as their temperature rises.
Temperature is another critical factor. Manufacturers provide temperature coefficients for open-circuit voltage, short-circuit current, and maximum power. For silicon-based modules, the power temperature coefficient is typically around -0.4% per degree Celsius, meaning that the output power decreases as the panel temperature rises. The band gap of the photovoltaic cell decreases at higher temperature, which may slightly increase the photocurrent, but the significant reduction in open-circuit voltage leads to an overall decrease in the fill factor and thus lower efficiency.
Dust accumulation affects photovoltaic panel performance through two mechanisms. First, suspended dust particles in the atmosphere can scatter solar radiation, reducing the amount of irradiance reaching the panel. Second, a thick dust layer formed on the panel surface modifies the surface optical properties, increases reflectance, decreases transmittance, and thereby reduces the short-circuit current. Studies show that in arid and semi-arid regions, photovoltaic panels exposed outdoors for six months can lose up to 50% of their power generation output.
2.3 Characterization of Dust Particles
The physical and chemical properties of dust particles determine the severity of their impact on photovoltaic performance. Particle size analysis using laser diffraction and scanning electron microscopy reveals that dust deposited on photovoltaic panels typically falls within a size range of 1 to 100 micrometers. Fine particles have a greater impact on reducing transmittance because they cover the surface more effectively for a given mass density. Comparative experiments show that a dust density of 10 g/m² can lower the short-circuit current by approximately 9.89% and reduce the power output by about 15%.
Chemical composition analysis by X-ray diffraction indicates that the dust layer primarily contains quartz, calcite, and trace amounts of dolomite and clay minerals. In humid conditions, dust particles absorb water vapor and form an active mud solution. During the drying process under strong solar radiation, dissolved ions such as Na⁺, K⁺, Ca²⁺, Cl⁻, and SiO⁻ re-crystallize and form a hard scale that is difficult to remove. This phenomenon aggravates the deterioration of panel performance and makes cleaning more difficult.
3. Design of the Online Monitoring Experimental System
3.1 Hardware Architecture
The online monitoring system is composed of two main modules: a field data acquisition subsystem and a central monitoring station. The field subsystem includes a photovoltaic array, a data acquisition module based on a digital signal processor, a power monitoring unit, a temperature sensor array, a high-definition camera, and a meteorological environment monitor. The structural arrangement is shown in Figure 3-1 of the original design, where the photovoltaic array comprises seven identical polycrystalline silicon panels from the same production batch. Each panel contains 60 monocrystalline silicon cells with a dimension of 156 mm by 156 mm, connected in series. The panels are installed at a fixed tilt angle of 43 degrees facing south to operate under uniform solar radiation conditions. The lower edge of the panels is mounted 400 mm above the ground.
One important detail in the system design is the spacing between the panels. Adjacent rows of the photovoltaic array are separated by about 10 meters, which allows small maintenance vehicles to pass between them. This dimensional consideration is essential for field maintenance and cleaning operations. The performance parameters of the photovoltaic panel model used in the experiments are summarized in Table 1 below.
| Parameter | Standard Test Condition | Nominal Operating Cell Temperature Condition |
|---|---|---|
| Maximum Power (W) | 260 | 192 |
| Open-Circuit Voltage (V) | 37.7 | 34.9 |
| Short-Circuit Current (A) | 8.95 | 7.20 |
| Current at Maximum Power Point (A) | 8.58 | 6.82 |
| Module Efficiency (%) | 16.01 | — |
| Temperature Coefficient of Power (%/K) | -0.408 | |
| Temperature Coefficient of Open-Circuit Voltage (%/K) | -0.292 | |
| Temperature Coefficient of Short-Circuit Current (%/K) | +0.045 | |
Three types of sensors are integrated into the hardware system. Temperature monitoring is carried out by DS18B20 digital temperature sensors attached to the backsheet of each panel. These sensors communicate over a single data wire and provide a measurement range of -55°C to +125°C with an accuracy of ±1°C, which is sufficient for the monitoring requirements. The power monitoring module uses a PZ96-DE smart meter to measure the operating voltage and current of each photovoltaic array. The smart meter communicates with the host computer via an RS485 interface using the Modbus-RTU protocol. The communication parameters are configured as 9600 baud, 8 data bits, no parity, and 1 stop bit. The host sends read commands in hexadecimal format to the meter, which then responds with the measured values. For example, the command 0x01 0x03 0x00 0x02 0x00 0x02 0x65 0xCB requests the current reading; the response is decoded to obtain the actual current value.
A meteorological environment monitor is installed at the experimental site to record solar irradiance, wind speed, wind direction, ambient temperature, and humidity. The monitor communicates with the host through RS485 in a request-response mode. Image data is captured by a high-definition camera placed perpendicular to the photovoltaic array. The camera distance is carefully selected to avoid shadowing the panel surface while still providing a complete view of the panel face.
3.2 Software Platform
The monitoring software is developed using the C# programming language with an Access database serving as the data storage backend. The software architecture follows a modular design. The field data acquisition instrument collects the panel operating parameters and meteorological variables. The central station receiver performs data conversion and transmission to the upper computer. The upper computer software processes, displays, and stores the data and executes prediction algorithms.
The operational flowchart of the upper computer software is described as follows. After the USB serial port connection with the data receiver is established, the software waits for incoming data packets. When a complete packet is received, the system performs numerical calculations and digital image processing according to the preset algorithms. The results are then displayed on the main interface and stored to local files for future query. The main interface shows the measured parameters including operating voltage, current, panel temperature, ambient temperature, solar irradiance, and the captured panel image. Additionally, the software calculates the real-time power output and the power loss rate, and it analyzes the dust accumulation image using digital image processing techniques.
3.3 Online Monitoring Method
The online monitoring method is based on maximum power point tracking. A specific photovoltaic array is selected as the detection object, usually consisting of tens of panels connected in series and feeding into a combiner box. The system records the backsheet temperature, operating voltage, current, power, and total solar irradiance simultaneously. The generation efficiency of the panel under dust deposition conditions is calculated according to the national standard DB32T 1831-2011:
$$ \eta_a = \frac{P_{max}}{G \cdot S_r} \times 100\% $$
where \(\eta_a\) is the real-time generation efficiency, \(P_{max}\) is the maximum output power under the corresponding backsheet temperature and irradiance, \(G\) is the total irradiance, and \(S_r\) is the total area of the panel including the frame.
To ensure the accuracy of the efficiency comparison, three influencing factors must be considered. First, the solar incidence angle is eliminated by analyzing data only during the noon period from 11:00 to 13:00. Second, the effect of panel temperature is corrected using the power temperature coefficient. The measured power output is normalized to the value at the nominal operating cell temperature of 45°C. Finally, after these two corrections, the dust accumulation level becomes the sole variable affecting the generation efficiency. The following equations describe the data processing procedure.
The average backsheet temperature is computed as:
$$ T_b = \frac{T_1 + T_2 + \cdots + T_n}{n} $$
where \(T_i\) is the backsheet temperature of the i-th panel in the photovoltaic array. Then, the generation efficiency corrected to the rated operating cell temperature is expressed as:
$$ \eta = \frac{P_{max} – k \cdot (T_b – T_s) \cdot P_{max}}{G_s \cdot A_m} $$
where \(k\) is the power temperature coefficient, \(T_s\) is the standard operating cell temperature, \(G_s\) is the solar irradiance, and \(A_m\) is the panel area. These formulations enable a fair comparison of the generation efficiency of panels with different dust densities.
4. Vision-Based Dust Monitoring Methodology
4.1 Experimental Data Acquisition
To obtain experimental data for different dust accumulation densities, a simulated dust deposition experiment was conducted in the laboratory. Dust samples were collected from the surface of photovoltaic panels in the northwest region of Jilin Province. The samples were analyzed by a laser particle size analyzer, and the results indicated a particle size distribution ranging from approximately 1 to 100 micrometers, with a median diameter around 20 micrometers. The dust samples were ground and sieved through a 150-mesh screen to ensure that all particles were smaller than 100 micrometers.
The simulated dust deposition process followed a natural settlement method. Each photovoltaic panel was placed face up and sealed inside a transparent organic glass enclosure. A blower was used to inject a predetermined mass of dust particles through the single air inlet at the side of the enclosure. The airflow was maintained until the dust was completely dispersed inside the chamber. After blowing stopped, the panels were left undisturbed in a dry environment for six hours to allow natural gravitational settling of the dust particles onto the panel surface. An air humidifier was then used to apply gentle moisture circulation over the panel surface to prevent the dust from being blown away. Seven panels with identical dimensions were prepared with dust densities of 0, 5, 10, 15, 20, 25, and 30 g/m² respectively. The clean panel with zero dust density served as the reference group.
4.2 Image Denoising Based on an Improved Interpolation Algorithm
Multicrystalline photovoltaic panels have parallel silver metal grid lines, known as fingers, uniformly distributed across the surface. These grid lines create periodic interference that significantly disrupts subsequent image analysis. To minimize the interference caused by silver grid lines when calculating the image grayscale values of dusty panels, a preprocessing step is required to remove what are termed stripe noises.
Several classical destriping methods exist, including histogram matching, moment matching, Fourier transform, wavelet transform, and high-order statistics. Histogram matching and moment matching adjust the statistical parameters of the image to a reference range. Fourier transforms and wavelet transforms separate stripe noise in the frequency domain. However, these methods often struggle to balance noise removal and detail preservation. Some methods leave residual stripe noise, while others cause severe blurring of the image. In this research, an improved interpolation algorithm is proposed to overcome the limitations of these existing techniques.
For a two-dimensional image of size \(M \times N\), the two-dimensional Fourier transform is defined as:
$$ F(u,v) = \frac{1}{MN} \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x,y) e^{-j2\pi (ux/M + vy/N)} $$
Frequency domain filtering is performed by multiplying the Fourier transform by a filter function:
$$ F'(u,v) = F(u,v) \cdot H(u,v) $$
The denoised image \(f(x,y)\) is obtained by the inverse Fourier transform. In the frequency domain, the low-frequency components carry the real image information, while stripe noise manifests as high-frequency components. Low-pass filters can attenuate the high-frequency components while preserving the low frequencies. However, this approach also blurs edges and fine details.
The linear interpolation method only processes the rows occupied by stripe noise and leaves non-noise regions unchanged. The key to this approach is accurately locating the stripe noise rows. The silver grid lines on a photovoltaic panel are regularly spaced, and the number of grid lines per panel is known. The location process is described as follows. Suppose the pixel at position \((i,j)\) has a value \(G_{i,j}\). The average of the two neighboring pixels in the same column is computed as:
$$ G = \frac{G_{i-1,j} + G_{i+1,j}}{2} $$
If the ratio satisfies the condition:
$$ \left| G_{i,j} / G \right| > T $$
where \(T\) is a predefined threshold, the pixel is classified as a noise pixel and identified as part of the silver grid line. The drawback of this method is that it may falsely classify image details as noise. To overcome this problem, an improved third-order interpolation algorithm is proposed.
The improved algorithm works as follows. Designate the pixel at coordinate \((i,j)\) as a candidate noise point. Let the pixel above be at \((i-1,j)\) with value \(G(i-1,j)\), and the pixel below be at \((i+1,j)\) with value \(G(i+1,j)\). The absolute difference and the relative error between these two pixels are defined as:
$$ F = |G(i+1,j) – G(i-1,j)| $$
$$ \delta = \left| \frac{F}{G(i-1,j)} \right| $$
A threshold \(d\) is preset. If \(\delta < d\), the two neighboring pixels are considered similar, and the standard linear interpolation method using the upper and lower pixel values is applied. Conversely, if \(\delta \geq d\), the values change rapidly, and a third-order interpolation using sixteen surrounding pixels is performed. Through multiple experiments, the threshold \(d\) was set to 0.25 to achieve the best trade-off between noise removal and detail preservation.
The third-order interpolation is expressed as:
$$ f(i+u, j+v) = A \cdot B \cdot C $$
where the intermediate matrices are:
$$ A = [s(u+1), s(u), s(u-1), s(u-2)] $$
$$ C = [s(v+1), s(v), s(v-1), s(v-2)]^T $$
and the kernel function \(s(\omega)\) is defined as:
$$
s(\omega) =
\begin{cases}
1 – 2|\omega|^2 + |\omega|^3, & 0 \leq |\omega| < 1 \\
4 – 8|\omega| + 5|\omega|^2 – |\omega|^3, & 1 \leq |\omega| < 2 \\
0, & |\omega| \geq 2
\end{cases}
$$
The matrix \(B\) is formed from the sixteen neighboring pixel values centered around the noise point. After obtaining the interpolated values, the least squares method is used to construct a fitting function which replaces the original silver grid line pixel values. This approach effectively removes the stripe noise while preserving the original image details.
4.3 Calculation of the Average Gray Level
After removing the silver grid lines, the average grayscale value of the dust-covered photovoltaic panel image is computed. In MATLAB, a grayscale image is represented by a digital matrix where each element is the grayscale value of the corresponding pixel. Each pixel contains red (R), green (G), and blue (B) color components. The grayscale value for each pixel is calculated as the weighted sum:
$$ Gray_i = 0.3R_i + 0.6G_i + 0.1B_i $$
The average grayscale value of the entire image is then:
$$ Gray_a = \frac{Gray_1 + Gray_2 + \cdots + Gray_n}{n} $$
where \(n\) is the total number of pixels in the image. This average grayscale value serves as a quantifiable indicator of the dust deposition level on the photovoltaic panel surface.
5. Prediction Model and Performance Evaluation
5.1 Experimental Results Analysis
Extensive experiments were conducted at the test site over several months. Table 2 presents a representative set of measured data for a clean photovoltaic panel during the noon period from 11:00 to 12:00. The measured values include total irradiance, operating voltage, current, power, panel temperature, and calculated efficiency. The average generation efficiency of the clean panel is approximately 20.11%, indicating good health status.
| Time | Irradiance (W/m²) | Voltage (V) | Current (A) | Power (W) | Panel Temperature (°C) | Efficiency (%) |
|---|---|---|---|---|---|---|
| 11:00 | 643 | 28 | 6.32 | 176.96 | 3.39 | 20.34 |
| 11:02 | 644 | 28 | 6.31 | 176.68 | 3.34 | 20.28 |
| 11:05 | 643 | 28 | 6.28 | 175.84 | 3.51 | 20.20 |
| 11:08 | 650 | 28 | 6.29 | 176.12 | 3.53 | 20.01 |
| 11:10 | 653 | 28 | 6.33 | 177.24 | 3.17 | 20.07 |
| 11:15 | 656 | 28 | 6.36 | 178.08 | 3.04 | 20.09 |
| 11:20 | 655 | 28 | 6.34 | 177.52 | 2.98 | 20.06 |
| 11:25 | 653 | 28 | 6.34 | 177.52 | 3.14 | 20.11 |
| 11:30 | 655 | 28 | 6.34 | 177.52 | 3.15 | 20.05 |
| 11:35 | 652 | 28 | 6.33 | 177.24 | 3.13 | 20.11 |
| 11:40 | 652 | 28 | 6.35 | 177.80 | 3.08 | 20.18 |
| 11:45 | 641 | 28 | 6.28 | 175.84 | 3.07 | 20.30 |
| 11:50 | 644 | 28 | 6.30 | 176.40 | 2.84 | 20.28 |
| 11:55 | 638 | 28 | 6.21 | 173.88 | 3.20 | 20.15 |
| 12:00 | 637 | 28 | 6.02 | 168.56 | 2.97 | 19.59 |
The generation efficiencies of panels with different dust densities are summarized in Table 3. The data clearly indicate that the generation efficiency of photovoltaic panels decreases as the dust density increases. For a dust density of 5 g/m², the average generation efficiency drops to approximately 19.32%. As the dust density increases to 10 g/m², the efficiency falls to about 17.84%. At a density of 15 g/m², the efficiency is approximately 15.09%. When the dust density reaches 20 g/m², the efficiency falls further to about 14.90%. A dust density of 25 g/m² results in an efficiency of about 12.33%. At the highest tested dust density of 30 g/m², the efficiency plummets to approximately 10.18%.
| Time | 0 g/m² | 5 g/m² | 10 g/m² | 15 g/m² | 20 g/m² | 25 g/m² | 30 g/m² |
|---|---|---|---|---|---|---|---|
| 11:00 | 20.34 | 19.62 | 18.07 | 15.67 | 15.11 | 12.99 | 11.18 |
| 11:05 | 20.20 | 19.15 | 18.50 | 15.68 | 15.32 | 12.93 | 10.81 |
| 11:10 | 20.07 | 19.97 | 18.30 | 15.51 | 15.01 | 12.85 | 10.72 |
| 11:15 | 20.09 | 19.98 | 18.38 | 15.83 | 14.97 | 12.86 | 10.58 |
| 11:20 | 20.06 | 19.41 | 18.57 | 15.31 | 14.69 | 12.68 | 10.47 |
| 11:25 | 20.11 | 19.14 | 18.02 | 15.30 | 14.53 | 12.50 | 10.32 |
| 11:30 | 20.05 | 19.06 | 18.02 | 14.90 | 14.52 | 12.43 | 10.19 |
| 11:35 | 20.11 | 19.06 | 17.79 | 14.98 | 14.79 | 12.29 | 10.09 |
| 11:40 | 20.18 | 19.12 | 17.73 | 14.99 | 14.62 | 12.07 | 9.89 |
| 11:45 | 20.30 | 19.11 | 17.44 | 14.64 | 14.49 | 11.87 | 9.82 |
| 11:50 | 20.28 | 19.06 | 17.15 | 14.77 | 15.01 | 11.84 | 9.57 |
| 12:00 | 19.59 | 19.44 | 16.79 | 14.40 | 15.14 | 11.38 | 9.45 |
The analysis of the image grayscale values yields consistent results. The average grayscale value of the clean panel is approximately 50.21. For dust densities of 5, 10, 15, 20, 25, and 30 g/m², the corresponding average grayscale values are approximately 76.56, 87.58, 94.37, 98.02, 104.06, and 112.11 respectively. Thus the image grayscale value increases monotonically with increasing dust density, demonstrating that the grayscale value is an effective visual indicator of dust accumulation.
5.2 Power Loss Rate Prediction Model
The power loss rate of photovoltaic modules is defined as:
$$ \eta_{pl} = \frac{\eta_c – \eta_d}{\eta_c} \times 100\%, \quad t \geq 0 $$
where \(\eta_c\) is the generation efficiency under clean conditions and \(\eta_d\) is the generation efficiency under dust deposition conditions. Table 4 summarizes the relationship between the power loss rate and dust density at different measurement times.
| Time | 5 g/m² | 10 g/m² | 15 g/m² | 20 g/m² | 25 g/m² | 30 g/m² |
|---|---|---|---|---|---|---|
| 11:00 | 3.54 | 11.16 | 22.96 | 25.71 | 36.14 | 45.03 |
| 11:05 | 5.20 | 8.42 | 22.38 | 24.16 | 36.00 | 46.49 |
| 11:10 | 4.98 | 8.82 | 22.72 | 25.21 | 35.97 | 46.59 |
| 11:15 | 0.55 | 8.51 | 21.20 | 25.49 | 35.99 | 47.34 |
| 11:20 | 3.24 | 7.43 | 23.68 | 26.77 | 36.79 | 47.81 |
| 11:25 | 4.82 | 10.39 | 23.92 | 27.75 | 37.84 | 48.68 |
| 11:30 | 4.94 | 10.12 | 25.69 | 27.58 | 38.00 | 49.18 |
| 11:35 | 5.22 | 11.54 | 25.51 | 26.45 | 38.89 | 49.83 |
| 11:40 | 5.25 | 12.14 | 25.72 | 27.55 | 40.19 | 51.00 |
| 11:45 | 5.86 | 14.09 | 27.88 | 28.62 | 41.53 | 51.63 |
| 11:50 | 6.02 | 15.43 | 27.17 | 25.99 | 41.62 | 52.81 |
| 12:00 | 0.77 | 14.29 | 26.49 | 22.72 | 41.91 | 51.76 |
With a dust density of 5 g/m², the average power loss rate is about 4.11%. At 10 g/m², the power loss rate reaches about 11.34%. For a dust density of 15 g/m², the power loss rate increases to about 24.87%. At 20 g/m², the loss rate is about 26.04%. The power loss rate at 25 g/m² is approximately 38.72%, and at 30 g/m² it reaches about 49.3%. These results demonstrate a clear linear relationship between power loss rate and dust density. The data curves fitted by least squares regression reveal similar trends across all measurement times.
By combining the power loss rate results with the image grayscale analysis, a linear relationship between the average grayscale value and the power loss rate is established:
$$ Gray_a = 49.82 + 0.11268 \times \eta_{pl} \times 100 $$
The relationship between the average grayscale value and dust density is expressed as:
$$ Gray_a = 51.06 + 1.13\rho $$
where \(\rho\) is the dust density in g/m². The statistical analysis shows that a dust density of 10 g/m² causes a power loss of approximately 9.89% and an increase in the grayscale value of about 11.13. This finding is consistent with the experimental results reported in similar studies.
5.3 Power Output Degradation Model
Dust deposition on photovoltaic panels can be treated as a fouling process. The fouling mechanism is a dynamic equilibrium between the deposition and removal of atmospheric suspended particles. Observations suggest that the impact of dust on heat transfer tends to follow a decreasing or asymptotic trend. An asymptotic model for power output degradation is proposed:
$$ \eta_{pl}(t) = \eta_{pl}^* \cdot (1 – e^{-bt}), \quad t \geq 0 $$
where \(\eta_{pl}^*\) is the asymptotic value of the power loss rate and \(b\) is an empirical constant. Figure 5-6 in the original study illustrates the effect of dust deposition time on the power loss rate. When the dust deposition time increases from 7 days to 43 days, the power loss rate increases from 3.25% to 15.32%. According to the model, the power conversion efficiency decreases by approximately 13.31% after 30 days of dust accumulation and by about 17.98% after 60 days. This evolution is consistent with the broadly reported observation that the short-circuit current loss approaches an asymptotic value after 30 to 60 days of outdoor contamination.
It is worth emphasizing that the fast decrease in power generation occurs within the first two months of panel exposure. The asymptotic model enables the prediction of power loss at any given cleaning interval, which serves as the basis for the economic analysis of cleaning cycle optimization.
5.4 Cleaning Cycle Optimization and Cost Evaluation
The cleaning cycle optimization model aims to minimize the total annual cost resulting from dust accumulation. The annual total cost consists of three components: the cumulative electricity loss cost during the cleaning interval, the cleaning and maintenance cost during the cleaning operation, and the residual dust cost after cleaning.
Within a single cleaning cycle, the cumulative electricity loss cost \(E_d\) over the cleaning interval \(t_{ci}\) is expressed as:
$$ E_d = \int_0^{t_{ci}} e_d \, dt $$
where \(e_d\) is the daily loss cost, given by:
$$ e_d = \eta_{pl} \cdot P \cdot t_d \cdot C_e $$
where \(P\) is the installed capacity, \(t_d\) is the average daily utilization time of the photovoltaic system, \(C_e\) is the grid-connected electricity price, \(\eta_{pl}\) is the power loss ratio, and \(t\) is the dust deposition time.
The cleaning and maintenance cost within a single cleaning cycle is calculated as:
$$ E_{cc} = e_c \cdot P $$
where \(e_c\) is the cleaning cost per unit capacity, which can be further expressed as:
$$ e_c = F \cdot C_c $$
where \(F\) is the panel area per unit capacity and \(C_c\) is the cleaning and maintenance cost per unit area.
The residual dust cost after cleaning is expressed as:
$$ E_m = \int_{t_{ci}}^{t_{ci}+t_{cp}} e_m \, dt $$
where \(e_m\) is the marginal loss cost during the cleaning period. The total annual cost \(E\) is then:
$$ E = \frac{\tau}{t_{ci} + t_{cp}} \cdot (E_d + E_c + E_m) $$
where \(\tau\) is the annual operating time in hours. The optimal cleaning interval \(t_{ci}\) corresponds to the minimum total annual cost.
Taking a 50 MWp photovoltaic power plant as a case study, the following parameters are applied: \(P = 50\) MWp, \(\tau = 365\) days, \(t_d = 3.56\) hours per day, \(C_e = 0.95\) yuan per kWh, and \(C_c = 0.25\) yuan per square meter. These values lead to:
$$ E_d = \int_0^{t_{ci}} \eta_{pl}(t) \cdot 50 \times 10^6 \cdot 3.56 \cdot 0.95 \, dt $$
$$ E_c = 25 \cdot F $$
The relationship between cleaning cycle and cost is illustrated in Figure 5-8 of the original study. The total cost curve exhibits a clear minimum at the optimal cleaning interval. The optimization results show that the optimal cleaning cycle for the 50 MWp photovoltaic power plant is 10.14 days, corresponding to 36 cleaning operations per year. The annual power loss cost is 0.782 million yuan, the cleaning and maintenance cost is 1.608 million yuan, and the residual dust cost is 0.335 million yuan. The minimum annual total cost due to dust accumulation reaches 2.725 million yuan. This corresponds to an annual cost of 54,500 yuan per megawatt for the photovoltaic modules, accounting for 5.6% of the expected annual power generation benefit.
At the optimal cleaning cycle, the power loss of the photovoltaic module is calculated as 4.5% according to the power conversion efficiency degradation prediction model. The corresponding average image grayscale value of the dusty panel is 54.89. These results demonstrate that engineers can use image recognition of the photovoltaic module to determine when the cleaning operation should be performed. The methodology therefore provides a visual and quantitative basis for intelligent cleaning scheduling.
6. Conclusion
This research developed a comprehensive online monitoring system for photovoltaic panel dust accumulation, integrated with a vision-based analysis method and a cleaning cycle optimization model. The main conclusions of the study are as follows:
First, through the online monitoring experimental system, real-time operating parameters of photovoltaic panels under dust accumulation conditions were captured. An asymptotic prediction model of the power loss rate under dust conditions was constructed. A method for determining the optimal cleaning cycle was proposed, enabling the quantitative evaluation of both the optimal cleaning cycle and the annual accumulated economic loss for photovoltaic power plants.
Second, the asymptotic prediction model of the power loss rate depends closely on the panel performance parameters and the site-specific environmental and meteorological conditions. By continuously monitoring the operating parameters of dusty panels and updating the asymptotic prediction model, the cleaning cycle optimization method can be extended to photovoltaic stations in different regions and with different module technologies.
Third, the case study of a 50 MWp photovoltaic power plant indicates that the optimal cleaning cycle is 10.14 days. The annual number of cleanings is 36, with a power loss cost of 0.782 million yuan, a cleaning and maintenance cost of 1.608 million yuan, and a residual dust cost of 0.335 million yuan. The power conversion efficiency is reduced by 4.45% at the optimal cleaning interval, and the corresponding grayscale value of the dusty panel image is 54.89.
The proposed method provides a reliable basis for the real-time monitoring of dust accumulation on photovoltaic panels, guidance for cleaning cycle scheduling, improvement of solar energy utilization, and reduction of operation and maintenance costs. Future work should focus on further refining the dust density range, studying the complex effects of mixed dust composition in realistic environments, and developing fully automated cleaning decision systems based on the prediction models proposed in this study.