## 1 Introduction
According to [23] this parameter decreases its value between \([0,2]\) %/year, for simulation purpose a window of 20 years were simulated. * Optical heterogeneous degradation (OHD) faults. This fault family is similar to the one presented before, but in this case, the level of affectation is not homogeneous in two ways, location and degree of degradation. According to [17] the parasitic parallel resistance \(R_{p}\) decreases, as well as \(I_{ph}\). The variation of \(I_{ph}\) was taken as equivalent to OD faults, and the variation of \(R_{p}\) was taken as the worse case reported in PID faults. * Potential induced degradation (PID) faults. This fault occurs when high potential voltages of the system cause a leakage current between the frame and the solar cells. According to [26], the shunt resistance \(R_{p}\) decreases as well as the short-circuit current \(I_{sc}\), but for this work, we assume that the changes in \(I_{sc}\) are caused by \(I_{ph}\) because these variables are proportional \(I_{sc}\varpropto I_{ph}\). In [27] has proposed that both parameter decrease proportionally, \(\downarrow R_{p}\varpropto\downarrow I_{sc}\). Hence, the range of variation for these parameters are \(R_{p}=[1,100]\%\) and \(I_{ph}=[80,100]\%\). We call this variant as \(PID^{1}\). Also, another PID fault variation, we call \(PID^{2}\), is found in [28], and they show that the parameters \(R_{p}\) moves between \([0.1,100]\%\), \(I_{s}\) varies between \([100,300]\%\) and \(\eta\) moves between \([100,112]\%\). These percentages were calculated by analyzing the maximum and minimum values reported in the graphical results. * Micro cracks (MC) faults. Micro crack can reduce energy production up to 50% of a module with only 40% of the affected area in one cell [29]. For these faults, according to [30], \(I_{s}\) and \(I_{ph}\) decrease proportionally because both parameters are inversely proportional to the affected area; hence the range of variation is \([1,100]\%\). * Light induced degradation (LID) faults. According to [31] LID is defined as the increment of the recombination current in the base in P-type silicon wafers. The effect is also observed in the open-circuit voltage [17]. For a particular module, the saturation current \(I_{s}\) could be moved in a range of \([1,50]\) times; this variation can produce changes of open-circuit voltage \(V_{oc}\) in the range of \([0,18]\%\)[20]. These percentages were calculated by analyzing graphical results. A second contribution is the proposal of new detection criteria based on the measurements of the module voltages. Due to its simplicity, this criterion is suitable for implementation in monitoring strategies such as the one presented in [32]. In fact, several approaches use voltage measurements to detect and diagnose faults in the array, for example [33, 34, 35, 36, 37, 38], but they require other variables like the string current, time, or even the ambient variables, to generate alarms adequately. Also, in those papers, the nature of faults analyzed is different because they focus mainly on faults such as diode short-circuit, open-circuits, partial shadows, and degradation faults represented only as an increase of the serial resistance. Furthermore, a similar indicator based on voltage is presented in [39], which is called \(\Delta V\), but this indicator requires knowing precisely the output voltage of the array and the theoretical voltage at its maximum power. This indicator is quite different from our approach since our criterion is calculated from the voltages of the modules in the PV string. This work presents and analyzes new detection criteria to demonstrate that is capable to detect all the progressive faults only with the module voltage variable in multi-crystal PV modules. This numerical simulation study is divided into the following main sections: Section 2 describes the theoretical framework used to derive the detection criterion. Section 3 links specific fault conditions with changes in the variation of some parameters of the PV array.