# Early Detection of Photovoltaic Panel Degradation through Artificial Neural Network
## 2 Single Diode Model for Describing Degradation Phenomena
### Effect of PV Degradation on the _I-V_ Characteristic and the SDM Parameters  
In [28], the most common degradation effects and failures that are detectable by the inspection of the _I-V_ curve and the related SDM parameters variations are described. They are visually shown in Figure 2. A brief comment on these effects is also reported in the following. * **S1 effect:** The _I-V_ curve exhibits a lower short-circuit current (\(I_{sc}\)) than expected. This degradation effect may be caused by the following: loss of transparency of the encapsulation, due to browning or yellowing; glass corrosion, which reduces the light trapping of the module; or delamination, which causes optical uncoupling of the layers. This is mainly reflected in the reduction of the photoinduced current (\(I_{ph}\)) parameter. * **S2 and S3 effects:** The _I-V_ curve has an open circuit voltage (\(V_{\infty}\)) lower than expected, and all points shift homogeneously to the left, while the _I-V_ curve preserves its slope around \(V_{\infty}\). This anomaly may be due to failed cell interconnections, short circuits from cell to cell or a failure of the bypass diode. Such failure can be associated to the SDM ideality factor (\(\eta\)) because the number of cells (\(n_{s}\)) in a PV module directly appears in the SDM Equation (1). Thus, the effects of cells failures can be expressed as follows: \[\eta=\eta_{H}\frac{n_{H}}{n_{s}}\] (2) where \(\eta_{H}\) is the healthy ideality factor and \(n_{H}\) is the number of healthy cells inside the PV panel made of \(n_{s}\) cells. For example, if \(n_{s}=36\), one failed cell has an impact of almost \(-3\%\) on the \(\eta\) parameter. The open-circuit voltage of the module can be reduced also by the light-induced degradation (LID) of crystalline silicon modules or potential induced degradation (PID). Since the leakage current inside the PV cell is an indicator of such phenomena, they can be directly associated to the variation of saturation current \(I_{sat}\) parameter. Small variation of \(I_{sat}\) does not affect significantly the _I-V_ characteristic. It can be observed that the impact of \(I_{sat}\) and \(\eta\) is directly opposite. This can cause a multi-modal problem in the parameter identification, which means that the same _I-V_ curves may be reproduced with different pairs of the \(I_{sat}\) and \(\eta\). Therefore, in some cases, the same degradation phenomena can be associated almost indifferently in the \(I_{sat}\) variation or \(\eta\) variation. * **S4 effect:** The slope of the _I-V_ curve near \(V_{\infty}\) is lower, indicating an increase in the series resistance \(R_{s}\) in the PV module. \(R_{s}\) in the module could rise by the increase in interconnections resistance, corrosion in junction box or interconnects and slacks joints. Figure 2: Module failures detectable from the _I-V_ curve. * **S5 effect:** The slope around \(I_{sc}\) is mostly associated to the parallel resistance \(R_{sh}\). The variation of this parameter is due to shunt paths in the PV cells and/or the interconnections. Slight cell mismatch or slight non-uniform yellowing may be additional causes. * **S6 effect:** The presence of steps in the curve is likely caused by the activation of one or more bypass diodes that are connected in parallel to a block of cells to protect them from inverse polarization under mismatched operating conditions. It can be due to irregular soiling, the shadow affecting only a few cells in the PV module, or the breakage of one or more cells protected by the same bypass diode. This effect cannot be reproduced with a single diode model, and thus the variations of the SDM parameters associated to this effect do not have a physical meaning.