## 2 Materials and Methods
### Monitored Data and Specifications of the Analysed PV System  
A set of 36 PV modules connected to an inverter were the elements used to carry out the analysis shown in this paper. They belong to a PV installation located on the rooftop of a building in the city of Cordoba (37 deg53'00'' N, 4 deg46'00'' O), in the south of Spain. The modules, from BP, are made of polycrystalline silicon and have a peak power of 165 W. Their characteristics are listed in Table 1. The modules are configured as three strings in parallel, with 12 modules connected in series in each of them, and they are mounted on an open frame with 30 deg of inclination and 18 deg of azimuth. The inverter to which the modules are connected is from SMA, model SMC-100, and its specifications are shown in Table 2. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Specifications**} \\ \hline Number of modules per inverter & 36 = 12 × 3 \\ \hline Module model & BP-3165 \\ \hline PV module peak power & 165 W \\ \hline Number of cells per module & 72 \\ \hline Surface area of each module & 1,573,790 mm\({}^{2}\) \\ \hline PV cell surface & 125 mm-125 mm \\ \hline Useful module area & 1125 m\({}^{2}\) \\ \hline Power of modules per inverter & 5940 W \\ \hline Power temperature coefficient & \(-\)(0.5 \(\pm\) 0.005) \%/°C \\ \hline Temperature coefficient of Isc & (0.065 \(\pm\) 0.015) \%/°C \\ \hline Temperature coefficient of Voc & \(-\)(160 \(\pm\) 20) mV/°C \\ \hline NOCT & 47°C \(\pm\) 2 °C \\ \hline Open-circuit voltage (Voc) & 44.2 V \\ \hline Voltage at maximum power (Vmax) & 35.2 V \\ \hline Short-circuit current (Isc) & 5.2 A \\ \hline Current maximum power (Imax) & 4.7 A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: General characteristics of the installation and its PV modules. The data acquisition system of the PV installation is integrated in the inverter. The measured parameters were stored with a frequency of 5 min, and they correspond to an average value of each parameter in this time interval. The irradiance values analysed in this work, which correspond to the global tilted irradiance (GTI), were collected by an equipment called Sunny SensorBox, from the company SMA, to which the sensor of this parameter was connected, which was a calibrated PV ASI amorphous cell, with a measurement range of 0 to 1500 W/m\({}^{2}\), an accuracy of \(\pm\)8% and a resolution of 1 W/m\({}^{2}\). This irradiance sensor was installed next to the PV modules, with the same orientation and inclination, so that the recorded irradiance values would represent those received by the PV panels. During the nine years of operation, a degradation of the cell was detected, resulting in a decrease of 1.8% in the recorded irradiance data, which is a percentage lower than the accuracy given by the sensor manufacturer. In addition, this equipment also collected measurements from two temperature sensors. One of them, a PT-100M sensor, with a range of \(-\)20 to +110 \({}^{\circ}\)C, was used to measure the temperature of the modules. Its accuracy and its resolution specified by the manufacturer were \(\pm\)0.5 \({}^{\circ}\)C and 0.1 \({}^{\circ}\)C, respectively. The other, a PT-100M-NR sensor, was used for measuring the ambient temperature, which had the same characteristics as the previous one, but with an accuracy of \(\pm\)0.7 \({}^{\circ}\)C given by the manufacturer. Assuming effects of decoupling and stability for these sensors, the error in temperature measurements can be considered \(\pm\)1 \({}^{\circ}\)C.  
The SensorBox and the inverter were connected via RS485 to a device called Sunny-Webbox from SMA. It is a device with a central communications unit that continuously collects all the data from the inverters and the SensorBox and is a multifunctional, energy-saving data logger. The measurement data were transmitted via a GSM modem from remote locations where there was no telephone or ADSL connection, so it was read directly from a computer, and connected to the network, consuming between 4 and 12 W of power.