Photovoltaic (PV) Thermal Fault Monitoring Using the Catadioptric Device

Large photovoltaic (PV) generations are vulnerable to thermal faults where the location is difficult to determine. The pre-existing thermal fault detection method (mostly manual visual inspection) is time-consuming and non-continuously monitoring. It may lead to more defects, such as degrading the faulted PV cell or putting the PV farm on fire. We propose a novel PV thermal fault monitoring and detection method using a catadioptric device (CD), which promises quick and continuous detection. In this paper, as an early stage in CD development, we focus on constructing a model involving some parameters to identify the object image formation. Then, through the model, a simulation case study of the PV farm monitoring proses was performed where the CD is ostensibly placed in front of the PV arrays. We variated the model parameters and selected the combination that resulted in a symmetrical and non-overlapped PV array image, which was then analyzed to see the sensor requirements of the CD. The results showed that the developed model could simulate PV image formation on CD with good validity. Also, the case result found that nine parameter combinations produce symmetrical and non-overlapped PV images where the image ratio is more affected by the camera position than the focal length. Finally, the minimum sensor requirement is determined by the center length of the farthest PV image to monitor all of the PV arrays.


I. INTRODUCTION
Solar power generation, especially photovoltaic (PV), is currently developing technology and is widely used in various countries because it has flexibility in terms of capacity and produces sustainable energy [1]. It is estimated that the use of solar energy has reached 100 GW worldwide. This increase in use is not yet at its maximum point and continues to grow along with the cheaper and easier installation of PV. It is reinforced by the green environment issue by reducing fossil fuels and replacing them with renewable energy sources [2].
Economically, a PV plant is feasible if the solar modules installed in the field can operate appropriately for more than 30 years [3]. However, in the realization of PV maintenance in the field, generally, PV modules are only cleaned regularly, so potential damage to the module is challenging to detect [4].
The associate editor coordinating the review of this manuscript and approving it for publication was Baoping Cai .
Several failure modes can appear on the PV module: cracking, encapsulation material damage, interconnection failure, delamination, corrosion, mismatch fault, bypass diode failure, and arc fault [5], [6]. Most of these disturbances result in thermal fault in the PV module, such as hotspots and electrical arc [7]. Hotspot disturbances in PV have a harmful impact, especially the degradation of the module material [8], [9]. It can cause accelerated aging and reduce PV energy production to about 70% within 15 years of operation [10].
The health monitoring of PV modules (against thermal fault) is essential to ensure PV works optimally [11], [12], [13], [14]. It needs to be a concern, especially in large-scale PV plants that contain millions of PV cells [15]. Currently, two pre-existing methods are used to monitor thermal hotspots in PV, namely the electrical and visual methods [16], [17], [18]. The electrical method utilizes the value of current and voltage to identify the occurrence of disturbances in PV [19], [20]. Meanwhile, the visual PV monitoring method is performed using a camera carried out by an operator or mounted on a drone [21], [22], [23]. The operator/drone goes around the PV field and records images from the PV, which are then analyzed to determine any disturbance [13], [24], [25]. The two methods cannot monitor hotspot disturbances continuously, so they probably leave the thermal fault unattended. It may lead to other defects in the faulted cell, such as degrading the cell or even putting the PV farm on fire [7], [26]. For example, on the 60 MW PV farms (with 120 hectares of area and 252000 modules), the preexisting method requires up to 420 days to detect the thermal fault.
This study proposes a method of detecting a thermal fault in a large PV farm using the catadioptric device (CD). It can monitor more PV modules in one detection time due to its wide angle of view characteristic, promising quick and continuous detection processes [27]. Nevertheless, the PV array image formation on a CD is still challenging due to its non-linear projection [28]. In this paper, as an early stage in CD development, we focus on constructing a model involving some parameters to identify the object image formation. Then, through the model, a simulation case study of the PV farm monitoring proses was performed where the CD is ostensibly placed in front of the PV arrays. We variated the model parameters and selected the combination that resulted in a symmetrical and non-overlapped PV array image, which was then analyzed to see the sensor requirements of the CD.
The paper presentation is divided into four sections. Section 1 explains the background of the hotspot problems that arise in PV, the weaknesses of the current monitoring method, and the potential use of CD in dealing with the weaknesses of the previous method. Section 2 discusses the mathematical modeling of image formation in CD. Section 3 is a case study simulation of the PV monitoring process with a capacity of 1 MW, including analysis and discussion. Section 4 is the conclusion.

II. CATADIOPTRIC SYSTEM
A catadioptric is an optical device that combines the components of reflection (mirror) and refraction (lens) in one unit. In this detection concept, the mirror device used is an ellipsoid mirror, while the camera is a thermal type. This combination produces an optical device capable of observing wide viewing angles to model a PV module thermal fault monitoring system.

A. MODELING
The proposed CD consists of an ellipsoid mirror and a camera with the arrangement in Figure 1. The basic mathematical modeling to see the process of image formation in the CD is given by [28]. In this paper, the model is extended to identify the characteristic of the PV module image when the catadioptric coordinate is transformed. The modeling is carried out for a catadioptric system equipped with a single ellipsoid mirror and camera. The mirror's center is on one axis with the center of the camera lens [29]. With this arrangement, the catadioptric system can observe the objects at an angle of more than 90 • . The expectation is that all PV modules in front of the device can be monitored. However, due to the non-linearity of the ellipsoid mirror, modeling and simulation are needed to see the characteristics of the PV module image formation. Figure 1 shows a beam of light from object M (located at the x, y, and z coordinate with distances of X, Y, and Z from the focal point of the ellipsoid mirror, respectively) reflected on an elliptical mirror at pointM q . The lens surface receives the reflected light and is forwarded to the image sensor (with an effective focal length of f ). O is the center point of the mirror on the xyz coordinate so that it forms the oxyz coordinates as a reference in the modeling process. ρ is the distance from the center of the mirror o to the directrix of the elliptical mirror. p is the focal length of the ellipsoid mirror. dc is the distance from point o to the camera. The image coordinates (x and y) are determined by the characteristics of the CD (e, p, f, dc) and the object's coordinate position (X, Y, Z) concerning the ellipsoid mirror. The relationship is determined by (1).
The image coordinates of the object on the surface of the ellipsoid mirror (M q ) are given in (2).
Assuming that the camera has an image projection with pinhole characteristics, the projection matrix (K ) is given in (3).
When viewed relative to the image plane on the camera, the position changes (M I ) with the transformation value in (4).
So that the overall projection experienced byM q on the camera image plane is given by (5).
Thus, the image projection equation on the sensor plane (in internal camera construction) is obtained in (6) and (7).
x and y are the object coordinates in the image plane. X andỲ are object coordinates relative to the CD. Their values are the same as X and Y if the position of the CD does not change. In the simulation, it is required to see the effect of changing the catadioptric position (translation and rotation), so to accommodate this, the positions of Y and X change relative to the CD with a rotational transformation matrix (R Y(θ) R X(ϕ) ) and the translation matrix (T (X,Y,Z) ) as given in (8) and (9).
Therefore, the object coordinates are obtained as in (10).

B. MODEL VALIDATION
After obtaining the mathematical equations used to obtain the image characteristics of the CD, validation was carried out using the scheme in Figure 2.
In Figure 2, the CD consists of an ellipsoid mirror with e = 0.3 and p = 290 mm. The ellipsoid mirror is made of steel material coated with chromium metal to ensure that visible light and infrared waves can be reflected at more than 90%. In this validation, a visible camera (f = 8 mm) is used with 6 spherical objects (Obj 1 to Obj 6 in Figure 2) with white color and 6 cm in diameter to facilitate the identification of object shapes. The six objects are located at relative coordinates to the mirror center point with values as shown in Table 1. The ball is placed in a black area/environment so that when the camera captures the image, there is a color contrast between black (environment) and white (balls). The characteristic we use to identify faults is the difference in color/contrast of the hotspot to its environment. In actual conditions, when using a thermal camera, the hotspot will generate more heat than its surroundings; the contrast of black and white also represents this.
The contrast color is then entered into the image processing application to measure the distance x and y, as shown in Table 2. The object image was measured three times, and the measurement used specific CD parameter values, namely dc = 34cm, ϕ = 0, and θ = 0. After measuring the object image with CDs, simulations are performed for the same conditions as the measurement process. The measured image and the simulated image are compared in one exact figure to see the suitability of the measurement and simulation results.
With the object coordinates as given in Table 1, based on the simulation results (according to (6) and (7)) and 3 times measurement results, the object image positions are shown in Figure 3.
In Figure 3, circle M is an ellipsoid mirror image, and in the mirror image, there are six object images used for the validation process. Figure 3 shows that the simulation and measurement results are at the corresponding point. 75548 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  Quantitatively, the image coordinates of the measured object and the simulation results are given in Table 2, where the value of x and y is measured from M's center. A statistical t-test was completed (for each pair of x,y-values from the simulation results to x,y-values from the measurement results) to quantify the suitability of the measurement and the simulation results. For this reason, prerequisite testing is finished before performing the t-test in the form of normality testing (using the Kolmogorov-Smirnov method) [30]. The normality test was performed to the ''error'' between the x and y values pairs from the simulation and measurement results. The normality test result shows that the error between the pairs of x and y values in the simulation and measurement results has a significancy of 0.2 (more than 0.05) so that the data is normally distributed with 95% of confidence level. After the normality prerequisites are met, a t-test is carried out for the x and y from the measurement and simulation results. The results of the t-test for the values of x and y, respectively, have a significance of 0.94 and 0.99 (more than 0.05), which means that the simulation results are not significantly different from the measurement results (with a confidence level of 95%). Thus, the formed model for CD can appropriately simulate a PV monitoring system.

III. CASE STUDY A. BACKGROUND
Indonesia is an archipelago whose primary utility grid does not cover many islands. For this reason, electricity needs in the archipelago are supplied mainly by PV and diesel generators. In future planning, diesel generators will be reduced and fully supplied by PV, where most islands have a peak electricity load of around 300 kW to 900 kW. In this case study, we try to simulate the hotspot monitoring process on PV with a capacity of 1 MW peak. However, for continuous development, the method is also expected could be used to monitor PV with a capacity greater than 10 MW, so in this case, optimization is needed in determining the number and location of CD placement and also the remaining useful life (RUL) of the CD should be calculated. The current method for optimizing the location and number of the sensor is using a discrete particle swarm that can improve the detection accuracy [31]. On the other hand, a novel method of RUL with a new definition of failure mode is revealed in [32], where the result can reduce the maintenance cost by 84%.

B. MONITORING SCHEME
The simulation scheme is carried out as given in Figure 4. Ten PV rows are used where the ''PV row 1'' is the PV row with the smallest distance from the CD, while the ''PV row 10'' is the PV row with the longest distance from the CD. Each PV row in the model has a length of 100 m and a width of 2 m. The projection created by the ellipsoid mirror on the CD has a non-linear image projection so that to determine the characteristics of the image on the CD, several simulations are completed with varying parameter values. In this simulation, a combination of f , ϕ, θ, xed, yed, and zed values are carried out, which respectively state the value of the effective focal length of the lens, the angle of rotation in the y and x-axes, and the translational distance in the X, Y, and Z axes of the CD against the PV rows.
The distance values for xed, yed, and zed refer to the origin point in Figure 4. The value of yed, xed, zed, f , ϕ, and θ are given in Table 3.

1) COMBINATION PARAMETERS THAT CREATE SYMMETRICAL AND NON-OVERLAP PV ARRAYS IMAGE
By using the parameter variations described in Table 3, 3240 parameter combinations are obtained. Then, parameter combinations that produce symmetrical and non-overlapped images are selected. The purpose of using non-overlapped images is to ensure the observability of the entire PV module surface. Thus, if a thermal fault occurs anywhere on the PV module section, the CD can detect it. On the other hand, the thermal fault cannot be detected with an overlapped PV image, leaving it to create more damage. The simulation results show that the combinations of parameter values, as shown in Table 4, give symmetrical and non-overlapped module images. The parameters combination for each value of f, ϕ, θ, xed, yed, and zed are denoted by ''Comb.1'' to ''Comb. 9'' in Table 4. In the nine parameter combinations in Table 4, only two quantities have changed, namely the zed and the f quantity. Each value of xed, yed, ϕ, and θ has only one value because changes in the value of each of these quantities cause asymmetrical and overlapping images.
For further analysis, the image display of PV rows on a catadioptric device with the combination in Table 4 and the  Table 4. In the image, the center length and edge length of the PV row is defined as CL and EL, respectively. measurement scheme in Figure 4 is shown in Figure 5 and Figure 6.
The PV row with a straight shape in the actual condition ( Figure 4) is transferred to a curved shape in a catadioptric perspective view ( Figure 5 and Figure 6). ''PV Row 1'' represent the nearest PV array to the CD, and ''PV Row 10'' represents the farthest PV array. ''Point A'', ''Point B'', ''EL1'', ''EL2'', ''CL1'', and ''CL2'' in Figure 5 correspond to the description in Figure 4. Parameter combination ''Comb. 1'' produce images as given in Figure 5, as well as ''Comb. 2'' to ''Comb. 9'' produce images in Figure 6 (a) to Figure 6 (h), respectively. ''x values'' and ''y values'' are the image coordinates (in mm). EL 1 and CL1 represent the edge length and center length of the image in ''PV row 1'', EL 2 and CL2 represent the edge length and center length of the image in ''PV row 2'', and so on until the last is EL 10 and CL10 which represents the edge length and the center length of the image in ''PV row 10''. The same explanation and definition in Figure 5 also apply to Figure 6. In addition, Figure 8 and Figure 9 also use the same definitions of CL and EL. Figure 4 is the same as point A in Figure 5. This point marks the center point of land under the PV. Meanwhile, point B is the endpoint of the corresponding ground plane in Figures 4 and Figure 5. Points A and B are used as references to determine the effect of changes in the magnitude of the f and zed distance on the image ratio, with the results given in Table 5.

Point A in
xa and ya are respectively the distance of the image of point A in the x and y direction, are in the field of the catadioptric device sensor, and xb and yb are the distance of the point B image. The ratio in Table 5 is the ratio between the difference in the image length of point B and point A on the x-axis to the y-axis. The ratio value is used as a marker of the effect of 75550 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.   changes in the f and zed values. If plotted in an image, the results in Table 5 appear in Figure 7. In Figure 7, it can be seen that the change in the f value for each zed value does not change the ratio of the image distance. This result shows that the change/scale of the image in the x and y directions is the same. So that the resulting image experiences a proportional enlargement/reduction in the x and y direction; however, for each value of the same f , a change in the zed value results in a change in the ratio value. It means image change in the x and y direction is not proportional. Increasing the zed linearly creates a non-linear increase in image ratio.

3) IMAGE PROJECTION LENGTH
All row modules in Figure 5 to Figure 6 can be observed by CDs. Therefore, if a thermal camera is used on the CD, the emission of infrared waves from the entire modules are received by the CD. However, the camera detection capability is determined by the sensitivity of the thermal sensor. In digital sensors, if the sensor size is larger than the object image, the sensor cannot accurately distinguish the object image. In addition, the object requires more energy to ensure that the camera sensor can capture the object.
The EL and CL values from Figure 5 to Figure 6 are displayed in graphs (as shown in Figure 8 and Figure 9) to facilitate the sensor requirement determination.
Each combination parameter ''Comb. 1'' to ''Comb. 9'' in Table 4 represents each line in Figure 8 and Figure 9. The x-axis in Figure 8 and Figure 9 represents the row number of the module in each Figure 5 and Figure 6 (a) to Figure 6 (h).
Meanwhile, the y-axis in Figure 8 and Figure 9, respectively, states the value of EL and CL from each row for each parameter combination contained in Table 1. For example, Figure 8 states that the image formed with the parameters combination of ''Comb.3'' produces a CL of 0.25 mm for ''PV row 1'', about 0.17 mm for ''PV row 2'', and so on, finally 0.025 mm for ''PV row 10''. The same reading way is used for different rows in Figure 8 and Figure 9 (edge length reading).  Based on the results in Figure 8, it is known that the farther the PV row from the CD (the change in the distance between the rows is linear) causes a non-linear decrease in the CL where the changes range from 0.02 mm to 0.32 mm. Meanwhile, based on the results in Figure 9, the changes in EL are less than those in CL. The changes are close to linear characteristics, ranging from 0.03 mm to 0.06 mm. This changing pattern is then used to determine the sensor requirements on the CD.

4) SENSOR SENSITIVITY REQUIREMENT
According to Figure 8 and Figure 9, the PV row farthest from the CD produces an image of the smallest length. This condition occurs when a parameter combination ''Comb. 9'' is used, with CL and EL values of 0.013 mm and 0.026 mm, respectively. The thermal sensor's ability to capture objects is significantly influenced by the pixel size and thermal intensity produced by the object. 75552 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. Therefore, the smallest module length limits thermal sensor sensitivity for the same thermal intensity. An array of pixels constructs thermal sensors. Sensor design depends on the pixel design, which has a tradeoff in deciding the pixel size. A smaller pixel is needed to create a higher resolution, but the larger pixel is needed for a high dynamic range [33], [34]. It is still a challenge, but in the practical area, the image quality is determined by pixel density. Pixel density is the number of pixels present in an object space dimension with the unit of pixel per meter (ppm) [35]. As an illustration, one ppm states that one pixel is to cover a one-meter object in length in actual conditions. There are three scales used in defining image quality based on pixel density (Johnson criteria), namely detection (2 ppm), recognition (8 ppm), and identification (16 ppm) [36], [37].
As an example, if it is needed to get a clear image of all PV rows, as given in Figure 4, the ability to capture an image with 0.013 mm length is mandatory for the sensor (Figure 8). To monitor the PV module with a width at actual coordinates is 2 m and an image length of 0.013 mm, at least a sensor with a pixel size of 3.25 µm is required (referring to the detection quality of 2 ppm).

IV. CONCLUSION
The CD equipped with an ellipsoid mirror is promising to detect the thermal fault quickly and continuously because it has a wide angle of view. The modeling and simulation were performed to identify the image characteristic of the catadioptric. The results showed that the developed model could simulate PV image formation on CD with good validity. Also, the case result found that nine parameter combinations produce symmetrical and non-overlapped PV images where the image ratio is more affected by the camera position than the focal length. Finally, the minimum sensor requirement is determined by the center length of the farthest PV image to monitor all of the PV arrays. Future work will be performed to identify the prediction accuracy of thermal fault location coordinates.