## 4 Verification and Testing
### Performance Evaluation for Individual PV Modules in Strings  
In this section, three modules in string S6 and twelve modules in string S5 are used in the following experiment. All PV modules have the same mounting angle of 10\({}^{\circ}\) in strings S5 and S6. The detail experiment conditions are described as below:  
_M.Location1_ is [PVS1, Inv3, S5, BG032977, BG033404, BG033061].  
_M.Location2_ is [PVS1, Inv2, S6, BG033162, BG033120, BG032981, BG033419, BG033369, BG033415, BG033218, BG033197, BG033968, BG033269, BG032899, BG032290].  
_M. Time_ is [29.06.2022, 11:01,11:29,11:45,13:00,15:30,16:00].  
Module BG032977 and BG032968 are the reference modules in string S5 and string S6, respectively.  
Figure 14: Performance indicators for three states of PV modules at same time: (**a**) experiment condition; (**b**) power differences for three states; (**c**) performance indicator in current; (**d**) performance indicator in voltage.  
The experiment includes four operating states of PV modules, such as cracks, shadow, broken sensors and normal state. Then, the performance of these modules has been evaluated in two strings, as shown in Figure 15. In the following two heatmaps, the sensor's problem is more prominent, followed by moving shadow and cracks. When the sensors in the junction boxes are damaged, the collected data will have the voltage of 0V, the current of substring and the temperature of \(-273.15^{\circ}\)C. This will result in the \(PI_{\Delta V}\) of 1 and \(PI_{\Delta I}\) of 0.17 being slightly higher than the other PV modules in the same substring. If the voltage of the PV module falls below 10V due to other faults, the sensor does not work properly, which leads to the results such as the above. Therefore, in order to use the proposed approach in this paper, the voltage of the PV module needs to be screened firstly.  
Figure 15: Performance indicators of individual PV module in PV strings: (**a**) performance indicator in current; (**b**) performance indicator in voltage.  
On the other hand, when the voltage of the PV module caused by small shadows and cracks is higher than 10 V, the \(PI_{\Delta I}\) and \(PI_{\Delta V}\) values are very effective in distinguishing the shadows and cracks. The negative effects of shading are usually greater, followed by the cracks of solar cells. \(PI_{\Delta V}\) for shading is about 0.47 with missing one substring in shaded PV module and the \(PI_{\Delta V}\) of cracks is almost 0.22. Furthermore, the cracks evolution of solar cells is a very slow process, and the cracked module has only been installed for 2 years, which is why the evaluation factor is slightly higher than the reference module. However, the difference of \(PI_{\Delta V}\) is enough to identify cracks. The \(PI_{\Delta I}\) and \(PI_{\Delta V}\) of faultless are 0.09 and 0.2, respectively. It can also be seen that the \(PI_{\Delta I}\) in string \(\overline{55}\) is much higher than the value in string S6 where the cracked module and shaded module locate. \(PI_{\Delta I}\) can be used to determine the abnormal strings at string-level. Furthermore, the results of faults detection and the location information of faulty module are shown in Table 2. The faulty modules locate in strings S5 and S6 of the PVS1 system. The module ID for faulty modules with cracks, shadow and broken sensors are BG033404, BG033061 and BG033268. In summary, the \(PI_{\Delta I}\) and \(PI_{\Delta V}\) values of PV modules are useful to quickly pinpoint the ID of the module in data matrix and further find the location of the problematic modules.