Estimation of the Power Loss of a Soiled Photovoltaic Panel Using Image Analysis Techniques

Abstract

Soiling is one of the main problems of photovoltaic power. It is estimated that some areas could accumulate up to $0.6\%$ of soil per day. This, along with the lack of rainfall in arid zones, produces a considerable energy loss. Soil detection has been studied previously in the literature using artificial intelligence methods that require an extensive amount of images to train. Here, we propose an algorithmic approach that focuses on the characteristics of the images to discriminate different levels of soiling. Our method requires the construction of a soiling simulator to deposit layers of soil over a module while measuring the electric variables. From the datasets obtained, a calibration vector is established, which allows for the estimation of the power produced by the soiled panel from a captured image of it. We have found that the maximum error is approximately $3\%$ when applying the model to images of its own dataset. The error then varies from $3\%$ to $10\%$ when determining power from another dataset and up to $10\%$ when applying the model to an external dataset. We believe this work is a pioneer in the estimation of power produced by a soiled panel by examining only a picture.

1. Introduction

Solar panels, whether they are photovoltaic, concentrated, or thermal, are typically installed in arid regions with high levels of insolation and low annual rainfall. These locations offer optimal conditions for solar energy generation due to the abundance of sunlight. However, these zones are prone to considerable dust accumulation [1,2,3,4]. The presence of dust on the panels can lead to a decrease in performance [5,6] and, more critically, a reduction in their lifetime [7]. The extent of these effects depends on the specific area (if it is arid or not) and weather conditions, such as wind or rain [8].

The performance of photovoltaic plants is significantly affected by dust accumulation, resulting in reduced profitability, as reported by the the International Energy Agency-Photovoltaic Power Systems Program [9]. It is essential to note that as technology advances, with increased efficiency per panel, the same levels of dust result in even greater energy losses and subsequent economic losses. Furthermore, although the deposition of dust may not be recognized as a failure in a photovoltaic module, it can ultimately lead to a decrease in the panel’s useful life. The research conducted by Jamil et al. [10] demonstrates through modeling that the energy loss in a photovoltaic system due to dust accumulation can be as high as 26.22% each year in areas with adverse characteristics. A research of soiling in Chile [11] has established that even though in two different locations the soiling rates per day could be comparable (i.e., $0.6\%$ per day) in the north (desert area), the annual energy loss could peak up to $39\%$, while in the central zone (with higher rainfall rates) this number diminishes to $7\%$.

In general, there is little interest in detecting and cleaning in small and residential PV systems, and it is often considered an additional cost in PV farms [9]. Usually, the cleaning frequency is not entirely established; however, it can be economically scheduled when the cost of energy loss outweighs the cost of cleaning [12]. Many solar farm owners and operation and maintenance companies perform two cleanings per year, applying a case-by-case criterion, even though new algorithms are now available to establish a cleaning frequency [13]. The “duck curve” phenomenon in solar photovoltaics is slowly diminishing due to the increase in the installation of BESSs. Given this trend, selling energy at a higher cost would be more attractive to power plant owners, and then the soiling would become even more costly than the actual scenario.

There are several methods for automatic detection, mostly based on artificial intelligence [14,15,16,17,18] and very few based on regular algorithms [18,19]. In our previous work [19], we proposed an algorithm based on CIELAB color space that is able to determine the percentage of soiling over a module by using a sample of dust and the clean panel. In this work, we propose a method based on algorithms that generates an empirical model to estimate the power produced by a uniformly soiled photovoltaic panel based on image analysis. In the first part, the algorithm uses artificial intelligence only to crop and reshape the images. After that, we created a series of databases with soil from three different solar farm locations: Lambert (LA), Llanos de Potroso (LP), and Lo Miranda (LM). The soiling is determined and classified using the CIELAB channel b, and the results are correlated with the measured power and radiation. This creates a calibration vector that can be used to estimate power from an unknown source. We believe that our method can have a positive impact on the performance and lifespan of solar panels, serving as a diagnostic tool for implementing efficient cleaning strategies.

2. Materials and Methods

This section describes the materials and methods used to develop an experimental system designed to uniformly soil photovoltaic panels, intending to evaluate their performance under controlled contamination conditions. The system includes the design and construction of specialized hardware to generate uniform soiling on the panel surface, enabling the replication of degradation scenarios caused by dust accumulation. A visible-spectrum camera is used to capture images, providing precise visual data of the panels under different soiling conditions. These images are stored and organized in a dataset specifically designed for analyzing power reduction based on soiling levels. Image processing and the extraction of relevant features allow for the development of a model designed to estimate the power generated by solar panels from a photograph. To achieve this, computer vision and machine learning techniques are implemented using image processing tools.

The materials used in the construction of the system are detailed below, along with the methods employed for generating dirt, capturing images, and developing the dataset, ensuring the reproducibility of the experiments and the reliability of the results obtained.

2.1. Dust Simulator

To obtain soiled photovoltaic panels using soil from different locations, we constructed a soiling simulator based on models from other researchers [20,21,22]. Some key differences in our soiling simulator method are that it can work in outdoor conditions and supports a module of 62 cm × 32 cm, and since the dust chamber is assembled aside from the simulator, it can be arranged to support bigger modules. Figure 1 shows a conceptual diagram of the device, which aims to generate dust contamination that settles on the surface of a photovoltaic panel. The equipment is used outdoors, but within an enclosed space. The structure must be robust enough to operate outdoors while also being lightweight for easy transport. It is constructed from aluminum profiles and covered with tin sheets to prevent interference from external wind. Actual figures of the device are presented in Appendix A.

The device has a container for the soil that acts as a sieve with a pore size of 1.5 mm, in which the soil particles settle into dust. It uses four 12-volt fans to generate an airflow, which impacts and displaces the smallest soil particles that fall from the sieve, creating a dust flow that impacts a deflector. It has a 40-degree inclined surface that allows debris to be displaced from the soil, facilitating its removal. This creates a dust cloud that settles on the surface of the photovoltaic panel, resulting in a homogeneous distribution of particles. The fans feature pulse-width modulation speed control and are battery-powered, allowing portability and flexibility for use in a harsh environment. Photographs and dimensions are shown in Figure A1 and Figure A2 of Appendix A.

2.2. Instrumentation Used for Data Acquisition

Various measuring instruments were used during the experimental tests to record key parameters at the time the photographs were captured: a Fluke IRR1-SOL irradiance meter with a resolution of 1 W/m², Fluke 117 multimeter, and a drone camera model Sony IMX477R (Sony Semiconductor Solutions Corporation, Atsugi-shi, Kanagawa, Japan) with 12.3 megapixels, with a 16mm C-mount telephoto lens from CGL Electronics Co., Ltd. (Shenzhen, Guangdong, China) The camera is located approximately 2 m within the line of sight.

2.3. Equipment Setup in Experimental Tests

To ensure reproducible experiments, the tests were carried out in a controlled environment designed to minimize the influence of external factors. An enclosed space was used to contain the dust cloud generated during the fouling phase. This workspace is insulated by movable panels that cover both the perimeter and the top, ensuring that external wind does not interfere with the deposition of dust particles, thus achieving a homogeneous distribution of particulate matter on the photovoltaic panel. Figure 2 shows the structure described above with the PV panel inside. To the left of the workspace is the dust simulator, along with the solar radiation, voltage, and current measuring instruments. Figure 2 also shows the visible-light camera mounted on a lectern. The workstation features six movable panels, closed at the edges, with removable top covers that are used when capturing photographs.

The tests were conducted during the Southern Hemisphere summer at a latitude of −33.408162 and a longitude of −70.503075, in the Las Condes district of the Santiago Metropolitan Region, Chile. Days with clear skies were selected to avoid variations in solar irradiance caused by cloud cover. The test schedule was between 11:00 a.m. and 2:00 p.m., when solar radiation is most stable and the incidence of projected shadows is minimized. The maximum radiation reached 1060 W/${\mathrm{m}}^2$, while on average reached approximately 975.22 W/${\mathrm{m}}^2$.

For the experiments, we used a 30 watts polycrystalline panel (Ps30 enertik) and a monocrystalline (SFM-29.8W) panel for the final test. Details of the modules are provided in Appendix B. It was strategically placed within the workspace, ensuring direct sunlight fell on its surface without interference from shadows or reflections from the walls of the enclosed space.

2.4. Methodology for Systematic Image Capture

The dataset creation procedure involves systematically capturing images of the solar panel at different levels of soiling, from its cleanest to its most soiled state. This process was designed to ensure a controlled progression of soiling accumulation, allowing for subsequent correlation between the level of soiling and the power generated by the panel.

The protocol followed for image capture is as follows:

• Preparation of the soiling system: The particulate material is introduced into the dust simulator container.
• Isolation of the test environment: The enclosure housing the solar panel is sealed to prevent interference from external air currents.
• Activation of the dispersion system: The fans are turned on to generate controlled movement of the dust within the workspace.
• Distribution of the particulate material: The sieve is activated to disperse the dust in a controlled manner, where small particles are displaced by the airflow, which impacts the inclined surface, generating a cloud of suspended particles.
• Settling time: The system is run for 30 s to ensure homogeneous coverage of the particulate matter.
• Dust settling: The fans are turned off and the system waits another 30 s to allow the suspended particles to settle on the panel surface completely.
• Exposure to solar radiation: The enclosure’s top cover is removed, allowing direct sunlight to hit the panel.
• Image capture: A photograph of the panel is captured using the camera with a resolution of 1600 × 1200 pixels, ensuring standardized lighting conditions.
• Measurement: The instantaneous current and voltage are recorded, along with the radiation in which the image is captured.

2.5. Dataset Construction

In this study, a series of datasets was generated under controlled conditions, each corresponding to a distinct experimental campaign. These campaigns were meticulously designed to capture the images and electrical variables of photovoltaic panels subjected to varying degrees of surface soiling. The datasets differed from each other primarily due to the origin of the soil utilized in the PV panel soiling process. The collection of each soil sample was rigorously executed from diverse real solar plants, thereby ensuring the representation of soiling conditions with physical and colorimetric compositions that are specific to each site. From now on, we will refer to these datasets as Lambert (15 images), Miranda (10 images), and Potroso (12 images), which represent the soil from these respective plant locations.

Each dataset consists of images in RGB format, captured under controlled conditions after the soil was applied. In conjunction with each image, the temporal occurrence of the image’s capture was documented, along with the values of short circuit current ($I_{sc}$), open circuit voltage ($V_{oc}$), and incident irradiance ($G_m$). This methodology enabled the association of a precise quantitative measurement of the generated power with each image. It is important to note that each image was saved using the following format according to the time of capture and its respective dataset: “LA_hour_minute.png” for image from the Lambert dataset, “LP_hour_minute.png” from the Potroso dataset, and “LM_hour_minute.png” from the Miranda dataset.

3. Empirical Model

3.1. Estimation Based on Image Analysis

Following our previous work [19], we utilized the CIELAB color space to develop an empirical model for automatic detection of soil and power production estimation. The use of channel b of CIELAB is particularly beneficial for determining dust and clean conditions in photovoltaic panels. Most panels are blue or dark blue, while dust typically appears in brown to yellow tones, providing a natural distinction between the two states.

The dataset images were captured in outdoor conditions, making it necessary to segment the photovoltaic panel from the background. To accomplish this, we utilize a computer vision algorithm that automatically segments images using the YOLOv8 model [23,24]. This algorithm was trained using our own dataset with manually labeled photovoltaic panel images [25]. It is to be noted that this is the only use of artificial intelligence in this work. After performing the inference and successfully segmenting the panel, a perspective correction algorithm is applied. Finally, the images are resized to $2000\times 3500$ px to manage a resolution that does not delay the processing.

The processing steps for setting up the model are depicted in a flowchart in Figure 3. Initially, the black arrow path is followed; for analysis, the dashed line must be chosen. First, the pre-processed images are converted into CIELAB-b, and it is necessary to check if the images follow a trend while soiling is deposited. The selection is made using a graph that relates the current in each image to its mean value in channel b. An inversely proportional relationship is anticipated: the lower the current (i.e., the greater the soiling), the higher the mean value in channel B. Samples that do not conform to this relationship were discarded.

Following the filtering of the curve, images representing each soiling level are selected. Since soil deposition is very gradual, with a small amount of dust added in each iteration, many images appear quite similar when analyzed by a histogram. To validate the histogram-based thresholding mentioned above, the boxplots of the five selected images were reviewed. It has been established that the overlap between the interquartile ranges of two consecutive images must not exceed 80%. If the condition above is met, the level thresholds are defined; otherwise, new samples are selected, and the process is repeated. This step establishes boundary values in the CIELAB channel that delimit the levels of soiling. This criterion will be revisited in Section 3.2 with the actual values of overlapping.

To establish a correlation between the soiled images and the actual power at the time of capture, we used a matrix whose lines are constructed from the histograms of the images (here, the bins are reduced to five levels of soiling). Each image generates a vector indicating the proportion of pixels at each soil level, which is then normalized to the total pixel count. We will call these vectors $P{V}_{soiled}$. These vectors are then organized into a matrix (m × n), where n denotes the number of soiling levels and the m rows are the $P{V}_{soiled}$ vectors. The matrix, denoted by $M_{m\times n}$, is expected to approximate an identity matrix, with the highest value of each vector matching its designated level. Below is an example of a matrix for the LA dataset:

$${\mathbf{M}}_{5\times 5}=\left(\begin{array}{c}P{V}_{soiled}1\\ P{V}_{soiled}2\\ P{V}_{soiled}3\\ P{V}_{soiled}4\\ P{V}_{soiled}5\end{array}\right),{\mathbf{M}}_{5\times 5}\left(\begin{array}{ccccc}0.56& 0.19& 0.06& 0.05& 0.12\\ 0.20& 0.28& 0.11& 0.14& 0.24\\ 0.02& 0.15& 0.17& 0.18& 0.45\\ 0& 0.03& 0.08& 0.26& 0.6\\ 0& 0& 0.01& 0.09& 0.83\end{array}\right),$$

(1)

where there is a tendency to mark the diagonal. This will be explained further on.

Following the construction of the aforementioned matrix, a column vector of measured power is generated for each sample. The rows of the vector herein represent the measured power corresponding to their respective sample in the m × n matrix M. To properly relate the power vector to the soiling matrix, it is necessary to normalize both. Consequently, the power vector is normalized using its maximum value, which corresponds to the cleanest panel and is the first measurement.

Another critical factor is radiation, which, even under clear sky conditions, changes during the day due to the Air Mass factor (AM0, AM1.5, etc.). Then, the power values obtained are adjusted based on the irradiance recorded during the initial sample record. This process involves defining the irradiance of the initial sample as the baseline and then adjusting the power values of the others with respect to the original. With this calibration, if the radiation level increases or decreases, the power is always matched to the initial value. This is possible only in the case of the uniform distribution of soiling, which is the case for all the samples prepared.

The equation for the power estimation is a simple linear trend expressed as follows:

$$P_{\mathrm{adj}}=P_{\mathrm{m}}·{\displaystyle \frac{G_{\mathrm{ref}}}{G_{\mathrm{m}}}},$$

(2)

where $P_{\mathrm{m}}$ is the measured power (W), $G_{\mathrm{m}}$ is the measured radiation (W/${\mathrm{m}}^2$), $G_{\mathrm{ref}}$ is the reference radiation (W/${\mathrm{m}}^2$), and $P_{\mathrm{adj}}$ (W) is the power adjusted to the reference irradiance.

Finally, once the normalized matrix M and power have been obtained, it is necessary to find a multiple linear regression model that establishes a relationship between the two. The objective of this study is to determine a vector ($\lambda$) containing the coefficients specific to each soiling level. The regression coefficients are determined by replacing the estimated power with the experimentally obtained power values. Subsequently, by solving for the parameter $\lambda$, we arrive at the following result:

$$\lambda ={\mathbf{M}}_{m\times n}^{-1}·{\mathbf{P}}_{n\times 1}.$$

(3)

To apply this model, a soiling vector from a soiled panel is required. This vector is obtained utilizing the CIELAB b boundaries for each of the soiling levels to produce a vector of the image. To obtain the estimated power, this vector is multiplied by the $\lambda$ vector and finally denormalized by the base power $P_{base}$ (Equation (4)). To analyze a set of images, the procedure is the same except for the use of the M matrix containing the set of $P{V}_{soiled}$ vectors (Equation (5)):

$$P_{\mathrm{estimate}}\left[\mathrm{W}\right]=(P{V}_{soiled}·\lambda )P_{\mathrm{base}}\left[\mathrm{W}\right],$$

(4)

$$P_{\mathrm{estimate}}{\left[\mathrm{W}\right]}_{m\times 1}=({\mathbf{M}}_{m\times n}·{\lambda }_{n\times 1})P_{\mathrm{base}}\left[\mathrm{W}\right].$$

(5)

This, of course, depends on the light absorption of the dust over the panel, which is why we investigated three types of dust coming from the different plant locations. The objective is to find a common trend in soil absorption without the need to determine soil composition. It is important to mention that $P_{base}$ is the base power related to $P{V}_{soiled}$.

3.2. Data Analysis

This section illustrates the implementation of the algorithms, using images from the database generated with soil from the Llanos de Potroso Solar PV farm. The initial procedure entails the automatic segmentation of the photovoltaic panel by implementing a computer vision algorithm, as shown in Figure 4. The original captured image is depicted in Figure 4a, while panel detection and isolation can be seen in Figure 4b. The model demonstrates a high degree of efficacy in identifying cells, attaining an approximate probability of detection of 94%. After the cells are segmented, any pixel outside the segmentation mask is defined as a null value. The result, in which the background and the panel frame are eliminated, is shown in image Figure 4c, since the background information is irrelevant for this study. Subsequently, the perspective of the segmented object is corrected to normalize its shape using a perspective correction algorithm. The resultant image is displayed in Figure 4d. This procedure is repeated for each image in the dataset, with the relevant information being filtered to allow for analysis of the subject’s behavior in the CIELAB b spectrum.

Following the segmentation of all images and their conversion to CIELAB b-space, specific samples are selected to represent each of the five levels of soiling. To accomplish this objective, the complete dataset is subjected to evaluation. Images that do not follow the current vs. channel b value trend are subsequently discarded as mentioned in the previous section. For the three datasets used, no pictures were eliminated from the Lambert dataset, but 43.75% were discarded from the Miranda dataset, and 17.65% from the Potroso dataset. These exclusions are due to experimental inconsistencies caused by camera movements or displacement.

The images selected to illustrate the dirt levels are then subjected to analysis. This analysis involves the visualization of the histograms and boxplots of each sample, followed by processing using an empirical formula. The analysis of the graphs in Figure 5 establishes the intervals where each image concentrates the highest number of pixels, thereby defining the range corresponding to each level of soiling. As illustrated in Figure 5a, the combined histogram of images 1, 2, and 3 is presented. Figure 5b presents the histogram of images 3, 4, and 5, illustrating the distribution of image data and facilitating data analysis.

To ensure that the images do not present a similar pixel distribution, the overlapping percentages between the interquartile ranges of consecutive images are calculated using boxplots. The objective of this part is to determine whether the observed differences between them are statistically significant. To formalize this criterion, the percentage of overlap between the interquartile ranges was calculated, obtaining a range from $39.1\%$ to a maximum of $70.3\%$. From this, we can estimate the average overlap for each set, resulting in $54.8\%$ for LA, $55.1\%$ for LP, and $49.1\%$ for LM. With these results, a threshold of $80\%$ maximum overlap was established. If the overlap between two consecutive images exceeds this limit, the pair is considered too similar, and one must be replaced to ensure proper contrast between dirt levels. In this case, as seen in Figure 6, it has been confirmed that the selected images accurately represent each of the dirt levels according to the established resolution threshold. It is important to note here that soil accumulation is not linear, and this is reflected in the CIELAB values for the different soil levels obtained. For example, the limits for the LA dataset are $(-37.1,-18.0,-14.2,-12.1,-9.1,22.9)$. These limits are obtained directly from the boxplots and histogram comparison (see Figure 5 and Figure 6).

Following the validation of this step, Equation (3) is implemented to relate the information contained in the images of the five samples, according to the previously defined intervals, with the corresponding power for each of them. Then, the values of $\lambda$ for each dataset are obtained. The results of this step are shown in Equation (6):

$$\begin{array}{cc}\hfill {\lambda }_{\mathrm{LA}}& =\left(\begin{array}{ccccc}1.0229& 1.1976& 0.9053& 1.0828& 0.6067\end{array}\right),\hfill \\ \hfill {\lambda }_{\mathrm{LP}}& =\left(\begin{array}{ccccc}1.0204& 1.1008& 0.6931& 1.5554& 0.6213\end{array}\right),\hfill \\ \hfill {\lambda }_{\mathrm{LM}}& =\left(\begin{array}{ccccc}0.9899& 1.0250& 1.2803& 0.7243& 0.8086\end{array}\right).\hfill \end{array}$$

(6)

Following the acquisition of the regression coefficients, either Equation (4) or (5) can be used to estimate the power of a new image or dataset. To perform this estimation, it is sufficient to obtain the vector containing the pixel information of the image whose power needs to be estimated. It is essential to note that a clean level is required for an unknown dataset or image.

4. Results

This chapter presents the experimental results acquired by applying the proposed method to estimate the power generated by photovoltaic panels under different soiling conditions. The specific results obtained for each dataset are presented, including real and estimated power values, as well as the accuracy levels achieved. Additionally, a meticulous analysis of the results is employed when applying the regression vectors generated in external datasets to evaluate the accuracy and consistency of the predictions made by the proposed model.

4.1. Accuracy Assessment of Datasets—Images of the Same Dataset

The initial analysis involved assessing the accuracy of power estimation for images from a shared dataset, including those used to obtain the $\lambda$ vector. This assessment consisted of estimating the power of images from the same dataset and then estimating power from images of other datasets.

The results from the Lambert dataset indicate a high degree of accuracy in estimating power when applied to its own dataset (Figure 7a). The average estimation error corresponds to $1.14\%$, indicating a highly accurate correspondence between the estimated power and the actual power. Error bars, on the other hand, exhibit a greater range than the exact estimation. This is because the error bars originated from the error in estimating $\lambda$, which would be addressed later. Figure 7b shows the Lambert dataset power estimated with the other $\lambda$s. For this case, the discrepancies are higher with an average error of $9.89\%$ using LM$\lambda$ and $3.46\%$ using LP$\lambda$.

The estimation of the Miranda dataset, using its own $\lambda$, is shown in Figure 7c. In this case, there is a discrepancy for the first images (which have less soiling) and an excellent correspondence for the images that have more soiling. In this case, the average estimation error corresponds to $3.05\%$. Figure 7d shows the estimation of the LM dataset using LA$\lambda$ and LP$\lambda$, resulting in $3.38\%$ and $2.37\%$ errors, respectively.

Finally, the empirical results obtained from samples of the Potroso dataset are shown in Figure 7e,f. The self-estimation shows an excellent correspondence with an error of $1.17\%$, whereas the cross-estimation resulted in a certain offset. The error in power estimation with LA$\lambda$ was $5.08\%$ and with LM$\lambda$ was $2.32\%$.

In general, the results are good, except for a few cases. However, the Potroso $\lambda$ vector undoubtedly performed better in both self-estimation and cross-estimation. A comparison of all average errors is presented in

Table 1. Comparison of average errors of all datasets.

	LA	LM	LP
Self-estimation (%)	1.14	3.05	1.17
Cross-estimation (%)	3.38	9.89	3.46
Cross-estimation (%)	5.08	2.32	2.37

.

Regarding the error bars, they were calculated assuming that the matrix M could be an identity matrix. This is, of course, an ideal scenario, where each image has a disjoint histogram distribution, which is clearly not real. Nevertheless, even though the error bars are quite significant, we believe that this error is more representative of the real error. This occurs when the histogram is segmented into specific levels, making it more difficult to quantify. Ignoring the segmentation, there is another error contributing to $\lambda$, which is the experimental error of the power measurement, which is extremely low.

4.2. Model Testing

To evaluate the efficacy of the vectors on images that deviate from the original, a new dataset was created, featuring a diverse range of characteristics, including a different module and dust collected from the university campus. The new PV module is a $29.8$ Wp monocrystalline module with an estimated Fill Factor of 0.778. The new dataset, which we refer to as Validation or VAL, comprises four images of the solar panel with varying degrees of soiling. The log data are presented in

Table 2. New panel dataset data.

Soiling Level	Image	${\mathit{G}}_{\mathit{m}}$ (W/${\mathbf{m}}^{\mathbf{2}}$)	${\mathit{I}}_{\mathit{sc}}$ [A]	${\mathit{V}}_{\mathit{oc}}$ [V]	${\mathrm{P}}_{\mathbf{adj}}$ [W]
1	$11\_48$	732	1.392	19.85	21.497
2	$11\_53$	770	1.357	19.69	19.760
3	$11\_57$	778	1.350	19.80	19.570
4	$12\_05$	782	1.380	19.57	19.667

, where level 1 soiling represents a completely clean panel and level 4 soiling represents the dirtiest.

As this dataset contains completely different images, after segmenting and correcting perspectives, the procedure follows the dashed line of Figure 3. The only caveat is that the clean range must be adjusted to the range of the other datasets. This is because the $\lambda$ vectors were calculated using a different panel, and consequently, the blue minimum value in CIELAB-b differs. Equation (4) is used to assess the power estimation when applied to new images. This evaluation enables a comparative analysis, presenting insights into the performance characteristics of each coefficient vector. The results of this analysis are presented in Figure 8.

Finally, the precision of the power estimation in each image was calculated, obtaining an average accuracy of $9.60\%$ for the Llanos de Potroso vector, $7.05\%$ for Lo Miranda, and $7.28\%$ for the Lambert vector. All relative errors for this dataset can be seen in

Table 3. Relative errors in power estimation for VAL dataset.

	1	2	3	4	Average
LA (%)	0.51	9.57	9.81	9.25	7.28
LM (%)	0.25	10.84	8.88	8.23	7.05
LP (%)	2.53	12.24	12.12	11.51	9.06

. It is noteworthy that the estimations show an error of around $10\%$ of the real power, even with a completely different module and another kind of soil. Clearly, the soil could absorb a greater quantity of radiation, resulting in a greater mismatch between the estimated and actual power.

5. Conclusions

This work presents an empirical model that estimates the power loss in a photovoltaic (PV) panel caused by soiling, using only visual data from images of both soiled and clean panels. Our approach avoids the need for large machine learning datasets by employing a physically based, image-processing method that uses CIELAB color space analysis along with a calibrated regression model. The results show that, when tested on its own dataset, the model achieves high accuracy with power estimation errors below 3%. Cross-dataset testing—using soil from different geographic locations—produces an error range of 3% to 10%. Even in the most challenging scenario, with a completely different module and soil type, the model maintains an average estimation error of about 10%. This validates the broad applicability of the approach, making it a promising tool for non-invasive power diagnostics and remote monitoring of PV systems, especially in arid regions where soiling is a significant concern.

Despite certain experimental limitations, including environmental disturbances, camera misalignment, and measurement variability, our method performs well with a small image set (about 30 images), unlike deep learning models that typically require thousands of labeled images (at least 5000). This significantly lowers the barrier to deploying it in real-world solar farms.

Future work will include integrating temperature compensation with back-panel thermocouples to enhance voltage-based power estimates, expanding the model to cover various soiling patterns and panel technologies, and developing a user-friendly application for on-site or drone-based diagnostics.