## 6 Conclusions  
This work has analyzed several progressive faults presented in Table 1 and has been able to conclude the following:  
* The differential voltage in the affected modules will always be higher than the differential voltage in the faulty module. * The relative percentage difference (\(\Delta_{V}\)) always increases in proportion to the severity (power loss) of the fault wherever operational points of the array. Figure 4: Power loss of the modules versus \(\Delta_{V}\) at mpp for the studied faults. * The power loss per module is proportional to the \(\Delta_{V}\) if the PV system works at maximum power-point. The criteria proposed to detect permanent and progressive faults are based on estimating the power degradation in the faulty PV module. This is done with the differential voltages of the modules. This new detection criterion is suitable for real-time online analysis in PV arrays, which is part of the additional work, to experimentally demonstrate the simplicity of this fault detection criterion, running on a real-time system with several faulty modules. Conceptualization, L.D.M.-S.; methodology, L.D.M.-S.; software, L.D.M.-S.; validation, L.D.M.-S. and C.M. ; formal analysis, L.D.M.-S.; investigation, L.D.M.-S. and C.M. ; resources C.M. ; data curation, L.D.M.-S.; writing--original draft preparation, L.D.M.-S.; writing review and editing, C.M. ; visualization, L.D.M.-S.; supervision, C.M. ; project administration, C.M. ; funding acquisition, C.M. All authors have read and agreed to the published version of the manuscript. This work was supported by the scholarship program of the Costa Rica Institute of Technology and the VIE project 5402-1360-4201. Not applicable. Special thanks to [PERSON] from the University of Salerno, Italy, for his comments on this work. The authors declare no conflict of interest. The following abbreviations are used in this manuscript. \begin{tabular}{l l} PV & PhotoVoltaic \\ SRD & Series Resistor Degradation \\ OD & Optical Homogeneous Degradation \\ OHD & Optical Heterogeneous Degradation \\ PID1 & Potential Induced Degradation variant one \\ PID2 & Potential Induced Degradation variant two \\ MC & Micro-cracks \\ LID & Light Induced Degradation \\ TPL & Total Power loss \\ MPL & Module Power loss \\ \end{tabular}   
Figure 12: Optical heterogeneous degradation faults. This figure shows four charts as following: (**a**) the current of the affected string versus the operation voltage of the array, (**b**) the differential voltage for all the modules in the affected string, (**c**) the relative percentage difference versus the operating voltage of the array, (**d**) peak behavior of output power in the array. Figure 13: Potential induced degradation faults type 1. This figure shows four charts as following: (**a**) the current of the affected string versus the operation voltage of the array, (**b**) the differential voltage for all the modules in the affected string, (**c**) the relative percentage difference versus the operating voltage of the array, (**d**) peak behavior of output power in the array. Figure 14: Potential induced degradation faults type 2. This figure shows four charts as following: (**a**) the current of the affected string versus the operation voltage of the array, (**b**) the differential voltage for all the modules in the affected string, (**c**) the relative percentage difference versus the operating voltage of the array, (**d**) peak behavior of output power in the array. Figure 13: Micro cracks faults. This figure shows four charts as following: (**a**) the current of the affected string versus the operation voltage of the array, (**b**) the differential voltage for all the modules in the affected string, (**c**) the relative percentage difference versus the operating voltage of the array, (**d**) peak behavior of output power in the array. Figure 16: Light induced degradation faults.