# Early Detection of Photovoltaic Panel Degradation through Artificial Neural Network
## 2 Single Diode Model for Describing Degradation Phenomena  
The SDM, shown in Figure 1, is the most used PV model due to the trade-off between simplicity and accuracy [17]. It is described by Equation (1) and has a set of five parameters to be identified:  
* \(I_{ph}\): Photo-generated current (A). * \(I_{sat}\): Dark saturation current (A). * \(\eta\): Diode ideality factor. * \(R_{s}\): Series resistance (\(\Omega\)). * \(R_{sh}\): Shunt resistance (\(\Omega\)). The number of PV cells in the module (\(n_{s}\)) and the thermal voltage (\(V_{t}=\frac{k\cdot T}{q}\)) are known once the cells temperature (\(T\)), the Boltzman's constant (\(k\)) and electron charge (\(q\)) are given. \[I_{pv}=I_{ph}-I_{sat}\cdot[exp\left(\frac{V_{pv}+I_{pv}\cdot R_{s}}{\eta\cdot n _{s}\cdot V_{t}}\right)-1]-[\frac{V_{pv}+I_{pv}\cdot R_{s}}{R_{sh}}] \tag{1}\]  
Figure 1: Single-diode model of PV devices. The parameters identification is a relevant task since they are not available on the manufacturer data sheet. There are variations associated with the operating conditions, non-linear nature, and degradation phenomena [18]. Methodologies for solving this task are commonly grouped into three categories [19]: iterative (numerical), non-iterative (analytical), and AI-based optimization approaches. _Analytical methods_ use equations solved symbolically or explicitly by using key-points information from data sheets or _I-V_ curve data. These approaches are characterized by the simplicity of their implementation and computational efficiency [20]. _Numerical methods_ seek to fit the points of the _I-V_ curve by using systems of equations that are solved numerically. Commonly, trial and error approaches or numerical solvers, such as Newton-Raphson and curve-fitting methods, are used. The accuracy, reliability, and convergence of these methodologies are strongly linked to the selection of the initial conditions [19; 21]. _Optimization approaches_ group different kinds of algorithms based on artificial intelligence and heuristics methods. The development of computational intelligence has improved the implementation of these algorithms to solve highly non-linear and complex problems. Many advantages are associated with these approaches, as preliminary identification of the search space of parameters, high accuracy, and in some cases, a mathematical model, are not needed. Nevertheless, it requires high computational complexity [8]. In this last category, artificial neural networks are proven to be an effective tool for SDM parameters identification. In [22], a multilayer perceptron (MLP) for identifying the \(I_{ph},R_{s}\), and \(I_{sat}\) parameters is implemented. This work uses an input vector of five inputs composed by \(I_{sc},V_{oc},I_{mpp},V_{mpp}\) and \(P_{mpp}\) from the data sheet at the panel level. Another study [23] focuses on identifying some important points of the _I-V_ curve, such as \(V_{oc},I_{sc},P_{max},V_{max}\), and \(I_{max}\) at the panel level. For this purpose, it uses as inputs the irradiance and temperature in a two-hidden layer configuration. In [24], a recurrent neural network is implemented for predicting the output current of the cell by using temperature, irradiance, and voltage as inputs. In [25], the input vector carries out a mix among environmental and electrical variables, such as irradiance, temperature, \(V_{oc},I_{sc},V_{mpp},I_{mpp}\), and \(P_{mpp}\). In this case, the parameters identified are \(R_{s},R_{sh}\), and \(\eta\) for an application at the panel level. Finally, authors in [26] and [27] propose configurations based on feed-forward neural networks for identifying the full set of five parameters by means of two-stage identification. Both works only use irradiance and temperature as inputs, but the work in [27] is focused on a single cell, while the other [26] concentrates on an entire PV panel. In this paper, a numerical method is presented that combines _I-V_ curve fitting and ANN optimization to estimate the variation in PV panels' SDM parameters when the PV panels are subject to degradation.