## 3 Results of Field Tests
### The First Stage Experiments
The outdoor temperature is 28 \({}^{\circ}\)C. The surface temperature of the normal operating solar module is 45-49 \({}^{\circ}\)C, and the surface temperature of the abnormal solar module is 50-55 \({}^{\circ}\)C with irradiance of 815 W/m\({}^{2}\). The first panel has a defective cell in the lower middle of the panel. Figure 6a shows the original IR image with a clear and bright area shown in the lower middle that corresponds to the defected cell while a less bright area located in the upper middle is the junction box as mentioned before. Purple lines on the left and right margins are frames of the panel. Figure 6b shows an image converted to grayscale after Gaussian filtering. Grid lines of the panel are blurred due to the filtering effect but the bright region still appears clearly. Figure 6c displays a color image after Gaussian filtering to differentiate temperatures and the image tells that the hot spot is at about 55 \({}^{\circ}\)C and panel frames are at the temperature of 40 \({}^{\circ}\)C while the rest of the panel is at around 45-50 \({}^{\circ}\)C.  
Figure 6d is the histogram of the temperature distribution. The PDF curve still looks like a beta distribution function but a bump can be found at 40 \({}^{\circ}\)C which was not shown in Figure 5d of a normal operating panel because panel frames were not included in Figure 5. The mean temperature of the whole panel is 46 \({}^{\circ}\)C with the deviation of \(-9\)\({}^{\circ}\)C. The maximum temperature is 55 \({}^{\circ}\)C and the minimum temperature is 32 \({}^{\circ}\)C. Figure 6e is the cumulative temperature distribution that the mean temperature, maximum temperature and minimum temperate are very close for a normal operating panel and a panel with a known defected cell. However, hot spots are clearly shown on the solar module in Figure 6a-c. Through the cumulative chart, it is found that the percentage of hot spot area is over 3.1%, indicating there are two cells with high temperature. We already  
Figure 6: Image of first stage experiment 2.1 that the solar module has one cell defective. (**a**) IR origin image. (**b**) Gaussian filtered grayscale image. (**c**) Gaussian filtered color image. (**d**) Histogram of thermal temperature image. (**e**) Cumulative chart of thermal temperature image. (**f**) Cumulative chart-comparison of normal operation and abnormal conditions of solar modules. knew that one of the cells is caused by the junction box and there should be another cell in abnormally high temperature. To highlight the difference between a normal panel and a panel with known defected cell, we have compared the CDF curves of these two panels in Figure 6f. Result shows that the percentage of the area over 50 \({}^{\circ}\)C is a good index to determine cell abnormality or failure. The above description shows that 96.9% of the panel is within the normal area, as displayed in Figure 6d-e. The second panel has two defected cells located in the lower middle of the panel. Figure 7a shows the original IR image with a clear and bright area shown in the lower middle that corresponds to the defected cell. Figure 7b shows an image converted to grayscale after Gaussian filtering. Figure 7c shows a color image after Gaussian filtering that the hot spot is at about 55 \({}^{\circ}\)C. Panel frames are at the temperature of 38 \({}^{\circ}\)C and the rest of the panel is at around 45-50 \({}^{\circ}\)C. Figure 7d displays the histogram after calculating the temperature value of each pixel. The PDF curve still looks like a beta distribution function and the bump with 38 \({}^{\circ}\)C is panel frames. The mean temperature is 43 \({}^{\circ}\)C with the deviation of \(-\)12 \({}^{\circ}\)C. The maximum temperature is 55 \({}^{\circ}\)C and the minimum temperature is 32 \({}^{\circ}\)C. Figure 7e displays the cumulative temperature distribution that the percentage of hot spot area over 50 \({}^{\circ}\)C is 3.4%, indicating there are more than two cells with high temperature.