## 2 Materials and Methods  
The study carried out in this work was based on the data monitored by the inverters in six PV installations connected to grid located in the south of Spain, in the province of Cordoba. The main characteristics of these installations are shown in Table 1. Figure 1 shows the geographical distribution of the plants. As they are small nominal power installations, they inject their production into LV distribution networks. The data recorded in the different PV installations were provided by the company that installed them, Solar del Valle, SL, which is responsible for the operation and maintenance of these plants. The data acquisition system of the PV installations is integrated in their inverters. Inverters are connected via RS485 to a device called SunnyWebbox from the manufacturer SMA Solar Technology AG. It is a device with a central communication unit that continuously collects all the data from the inverters of each PV installation. The measurement data were transmitted via a GSM modem from remote locations where there was no telephone or ADSL connection, so they were read directly from a computer, and connected to the network, consuming between 4 and 12 W of power. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Plant 1** & **Plant 2** & **Plant 3** & **Plant 4** & **Plant 5** & **Plant 6** \\ \hline Total power (kW) & 672.0 & 217.6 & 36.7 & 22.2 & 100.2 & 17.8 \\ Number & 3 & 2 & 6 & 3 & 18 & 3 \\ of inverters & 3 & 2 & 6 & 3 & 18 & 3 \\ Inverter model & SMA SC-200 & SMA SC-100 & SMA SMC-5000 & SMA SMC-7000 HV & SMA SMC-5000A & SMA SMC-5000 \\ Number of modules & 1280 & 640 & 36 & 38 & 26 & 36 \\ per inverter & 1280 & 640 & 36 & 38 & 26 & 36 \\ Total number & 3840 & 1280 & 216 & 114 & 468 & 108 \\ Modules & [PERSON], STP & Bursche, STP & Busch, c-8 M48195 & Atersa, A-214P & BP-3165 \\ Module nominal & 1758-24/Ac & 1705-24/Ac & 1705-24/Ac & 195 & 214 & 165 \\ power (W) & 175 & 170 & 170 & 195 & 214 & 165 \\ Single-phase & Three-phase & Three-phase & Single-phase & Single-phase & Single-phase & Single-phase \\  & & & & & & \\ Rooftop and ground & Rooftop & Rooftop & Rooftop & Rooftop & Rooftop & Rooftop \\ Geographical location & Carachuey & Pozoblanco & Carachuey & Hinojosa del Duque & Cordoba & Cordoba \\ Rural or city area & Rural, & Rural, & Rural, & City, & City, \\  & industrial area & industrial area & industrial area & industrial area & industrial area & residential area \\ Latitude & 37.463889 & 38.35939 & 37.446389 & 38.481812 & 37.899167 & 37.896389 \\ Longitude & \(-\)4.286611 & \(-\)4.84436 & \(-\)4.271944 & \(-\)5.123581 & \(-\)4.715278 & \(-\)4.795556 \\ \hline \end{tabular}
\end{table} 
Table 1: Main technical characteristics of PV plants analysed. Figure 1: Geographical distribution of the six PV plants analysed in the province of Cordoba, South Spain. The numbers correspond to the order of the installations shown in Table 1.  
Inverters measure a series of parameters related to the production they receive from the PV panels associated with them, as well as related to the electricity they deliver to the grid and their operating status. They also measure some parameters necessary for their operational management, and for regulating the current to be injected, to correctly synchronise their production with the grid signal. The values of the AC power at inverter output (\(P_{AC}\)), the AC current injected into the grid (\(I_{AC}\)), the AC voltage in the grid phases (\(V_{AC}\)) and the grid frequency (\(f_{grid}\)) measured by the inverters were used in this work. The maximum measurement error in the inverters, at a temperature of 25 \({}^{\circ}\)C, was \(\pm\)1% for the grid voltage \(V_{AC}\), that of the injected power \(P_{AC}\) was \(\pm\)3%, that of the injected current \(I_{AC}\) was \(\pm\)2%, and that of the grid frequency \(f_{grid}\) was \(\pm\)0.1% [40]. The data measured by the inverters were displayed every 5 min, and they correspond to an average value of each parameter in this time interval.