## 3 Results of Field Tests
### The First Stage Experiments  
Figure 5 shows the image of a healthy solar module. Figure 5a is the original IR image of this healthy module in normal operation. It shows that basically the panel is of uniform temperature with color of yellowish orange. However, some areas with bright color can also be observed, indicating that higher temperature regions are distributed in the panel. Figure 5b is an image converted to grayscale after Gaussian filtering. The temperature distribution in Figure 5b was calibrated with a thermometer shown in Figure 2. It shows that the whole panel was at around 48 \({}^{\circ}\)C while the normal operating temperature of a healthy solar module is 45 \({}^{\circ}\)C to 49 \({}^{\circ}\)C. However, there is a cell-sized hot spot in the top middle area of this panel and the accurate measurement of the area of this hot spot is 1.67% of the total area with a temperature 55 \({}^{\circ}\)C. The reason is that at the back of the panel, there is a junction box located just opposite to the hot spot region and the temperature in this region is comparatively higher than its neighborhood due to the thermal insulation of the junction box, and therefore it is not a malfunction or abnormality. Solar cells are basic units of a solar panel. Several units of cells are connected in series and parallel, and encapsulated together to form a solar photovoltaic panel module. In this study, the experimental solar module is composed of 6 \(\times\) 10 cells, making one solar module contains 60 cells. Failure of a single cell would account for 1/60 of the fault area (about 1.67%). The aforementioned hot spot occupied 1.67% of the total area, indicating only one cell is at relatively high temperature. As a result, the innovative method of this research can find not only hot spots, but also determine whether it is a hot spot caused by cell failure or contamination. Figure 5c shows a 3-D image of the solar module in normal operation after Gaussian filtering. The temperature variations on the panel surface is converted to a three dimensional hills and valleys to signify the high temperature regions that could not be noticed in the two dimensional figure as shown in Figure 5b. The peak on the upper middle is the hot region caused by the junction box on the opposite side of panel as mentioned before. Figure 5d shows the histogram of the probability density of the calculated temperature value in each pixel. The temperature of a solar module in normal operation is not a normal distribution, but rather it looks like a Beta distribution with \(\alpha\) = 8 and \(\beta\) = 2. The mean temperature is 48 \({}^{\circ}\)C with a deviation of \(-\)7 \({}^{\circ}\)C. The maximum temperature is 55 \({}^{\circ}\)C and the minimum temperature is 35 \({}^{\circ}\)C. The probability density function (PDF) of temperature distribution is a characteristic of a solar panel. In this paper, the PDF and the associated cumulative function are used as an important index to determine the health condition of a solar panel. Figure 5e displays the cumulative distribution function (CDF) of the temperature distribution. It is found that 98.5% of the pixels are under 50 \({}^{\circ}\)C and only 1.5% of pixels exceed 50 \({}^{\circ}\)C. The above description shows that 98.5% of the panel is within the normal area, as displayed in Figure 5d-e. It is noted that the hot spot area caused by the junction box on the back of the solar module is about 1.5%. Since the junction box is not a malfunction of the panel, we may therefore conclude that 1.5% of hot spot might not be a malfunction problem in the CDF curve. Further examination is needed to check if it is a normal operating panel. The second experiment was conducted on three panels that have known defects. The location of these panels is on the GPS coordinates of 24\({}^{\circ}\)12\({}^{\prime}\)31\({}^{\prime}\) N and 120\({}^{\circ}\)29\({}^{\prime}\)40\({}^{\prime\prime}\) E with an altitude of 5 m. The experiment was carried out on April 1, 2020, at 11 am.