## 2 Materials and Methods
### Characterisation of the Behaviour of the PV System Components  
In order to know the performance of the PV installation for each type of irradiance profile, the values of the efficiency of the panels, the efficiency of the inverters, and the performance ratio (_PR_) of the set formed by modules and inverter were determined for each record. These parameters were calculated by using the data recorded by the inverter, corresponding to the current and voltage at the inverter input, and the power at the inverter \begin{table}
\begin{tabular}{c c} \hline \hline  & **Specifications** \\ \hline Inverter model & SMA SMC-5000 \\ \hline Maximum performance & 96\% \\ \hline European performance & \textgreater{}95.1\% \\ \hline Maximum input current & 26 A \\ \hline Maximum dc voltage & 600 V \\ \hline Maximum dc power & 5750 W \\ \hline PV voltage range, MPP & 246–480 V \\ \hline Number of MPPT & 1 \\ \hline Maximum output current & 26 A \\ \hline Maximum nominal ac power & 5000 W \\ \hline Maximum ac power & 5500 W \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inverter characteristics. output, which were also recorded during the indicated period with the same recording frequency of 5 min. The value of the efficiency of the PV modules is given by the expression:  
\[\eta_{G}=(E_{dc}/E_{r})\cdot 100, \tag{3}\]  
where \(E_{dc}\) is the power generated by the PV modules associated with each inverter, which is determined by the expression:  
\[E_{dc}=I_{dc}\cdot V_{dc}\cdot t, \tag{4}\]  
where \(I_{dc}\) is the direct current from the modules, measured in A, \(V_{dc}\) is the voltage at the input of the inverter from the modules, measured in \(V\), and \(t\) is the time corresponding to the monitoring interval expressed in hours. \(E_{r}\) is the reference energy given by:  
\[E_{r}=E_{G}\cdot A_{G}, \tag{5}\]  
where \(E_{G}\) is the in-plane irradiation of the PV panels expressed in \(\mathrm{Wh/m^{2}}\) and given by the product of the irradiance (\(G_{i}\)) multiplied by the monitoring time (\(t\)), and \(A_{G}\) the area of PV panels associated with each inverter. The efficiency of the inverter is determined by the expression:  
\[\eta_{inv}=(E_{ac}/E_{dc})\cdot 100, \tag{6}\]  
where \(E_{ac}\) is the energy obtained at the output of the inverter, given by the expression:  
\[E_{ac}=P_{ac}\cdot t, \tag{7}\]  
in which \(P_{ac}\) is the output power of the inverter and \(t\) is the time, which corresponds to the monitoring interval expressed in hours. Also determined was the parameter known as Performance Ratio (\(PR\)), by means of the expression:  
\[PR=Y_{f}/Y_{r}, \tag{8}\]  
where \(Y_{f}\), named final yield, are given by the expression:  
\[Y_{f}=E_{ac}/P_{0}, \tag{9}\]  
where \(E_{ac}\) is the ac power at the output of the inverter and \(P_{0}\) is the nominal power at standard conditions STC (AM1.5, 1 kW/m\({}^{2}\), 25 \({}^{\circ}\)C) of the PV modules associated to the inverter. \(Y_{r}\) is the reference yield, given by the expression:  
\[Y_{r}=E_{G}/G^{*}, \tag{10}\]  
where \(E_{G}\) is the in-plane total irradiation and \(G^{*}=1000\) W/m\({}^{2}\) is the irradiance at standard conditions STC. \(PR\) is a dimensionless quantity that corresponds to the ratio of the ac energy generated compared to the value of the energy that would be generated with the same irradiation in a system without losses. It would be calculated for the set formed by the inverter and the modules associated with it and gives a value that corresponds to the operation of this set. The average daily values of these parameters were determined for the entire period analysed and grouped for each of the types of days found through the classification process, in order to determine the relationship between the daily irradiance profiles of each type and these three parameters that represent the efficiency of the plant's components.