## 2 Materials and Methods
### Forecasting Methodology  
Following the preprocessing, the first step in the forecasting methodology is the application of the first three years' (2013-2015) data in training (i) a linear regression model and (ii) a feed-forward artificial neural network (FF ANN) with one hidden layer (MLP). The input parameters for both models are in-plane irradiance and backsheet temperature and the single output parameter is AC inverter power output.  
The structure of the FF ANN is shown in Figure 1. It is implemented by the use of the open-source machine learning framework: Tensorflow (Python programming language) [39]. The input layer comprises two input nodes, namely, irradiance (G) and backsheet temperature (T\({}_{\text{p}}\)) (Figure 1). The hidden layer comprises 20 nodes, each one containing a sigmoid activation function [40]. The Levenberg-Marquardt optimization algorithm is employed for training [41; 42].  
Figure 1: Structure of the feed-forward artificial neural network with one hidden layer of 20 nodes, employed in the data processing.  
Training the neural network can be envisaged as the fitting of a complex curve through the training data, until it can approximate it with the highest possible accuracy, by employing loss minimization algorithms and kernels (weights) and biases optimization. Since this complex fitting will be employed in the prediction of the future behavior of the PV park, it is very important to exclude erroneous or noisy information from the dataset. This explains the required careful quality assurance procedure included in the preprocessing of the datasets. The performance of these models is assessed based on the measurements of the last five and a half years in the dataset (2016-2021). As a next step in the forecasting methodology, training of the FF ANN was carried out based on the first five years' (2013-2017) data and the performance of the neural network was assessed based on the measurements of the last three and a half years in the dataset (2018-2021).  
The statistical metrics employed for the assessment of the accuracy of prediction are the root mean square error (RMSE), normalized root mean square error (nRMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), mean bias error (MBE), and Pearson correlation coefficient (COR), which are the most common metrics employed in the literature comparisons [28; 43; 44]. They are defined as follows:  
\[\text{MAE}=\frac{\sum_{i=1}^{\text{N}}\lvert\text{Pm}_{\text{i}}-\text{Pf}_{ \text{i}}\rvert}{\text{N}} \tag{1}\]  
\[\text{MAE}=\frac{\sum_{i=1}^{\text{N}}\lvert\text{Pm}_{\text{i}}-\text{Pf}_{ \text{i}}\rvert}{\text{N}} \tag{2}\]  
\[\text{nRMSE}=\frac{\sqrt{\sum_{i=1}^{\text{N}}(\text{Pm}_{\text{i}}-\text{Pf} _{\text{i}})^{2}}}{\sqrt{\sum_{i=1}^{\text{N}}(\text{Pm}_{\text{i}})^{2}}} \tag{3}\]  
\[\text{MAPE}=\frac{100\%}{\text{N}}\sum_{i=1}^{\text{N}}\frac{\lvert\text{Pm} _{\text{i}}-\text{Pf}_{\text{i}}\rvert}{\text{Pm}_{\text{i}}} \tag{4}\]  
\[\text{MBE}=\frac{\sum_{i=1}^{\text{N}}(\text{Pm}_{\text{i}}-\text{Pf}_{ \text{i}})}{\text{N}} \tag{5}\]  
\[\text{COR}=\frac{\text{COV}(\text{Pm}_{\text{i}},\text{Pf}_{\text{i}})}{\sqrt {\text{V}(\text{Pm}_{\text{i}})}\sqrt{\text{V}(\text{Pf}_{\text{i}})}}100\% \tag{6}\]  
where N is the number of samples in the time series, \(\text{Pm}_{\text{i}}\) and, \(\text{Pf}_{\text{i}}\) denote the measured and predicted value of the modeled variable at the time step i (i = 1, N). In the definition of the Pearson correlation coefficient, (COR), COV denotes the covariance of the two variables (measured and modeled values), and V is the variance of each respective variable.  
Another important metric that will be computed in our study is the yearly performance ratio (PR) which is defined in Appendix B.