## 2 Experimental Set-up  
Figure 1 shows the geographical distribution of fifteen PV systems used in this work. For each system, we provide the location, coordinates, climate, and annual global horizontal irradiation in kWh/m\({}^{2}\) per year. The PV systems are located in Bolzano, Italy (EURAC), Pekanbaru, Indonesia (OTH Amberg-Weiden, maintained by UIN Suska Riau University), Cirata, Indonesia (PJB), and Alice Springs, Australia (Desert Knowledge Australia Solar Center (DKASC), maintained by Ekistica). The PV systems are located at the Southern hemisphere, with the highest irradiation of around 2245 kWh/m\({}^{2}\)/year, near the equator (around 1700 kWh/m\({}^{2}\)/year), and the Northern hemisphere, with the lowest irradiation (1400 kWh/m\({}^{2}\)/year). Basic information about each system is given. The information includes rated power, module technical specification, mounting, tilt angle, and basic configuration. The PR calculation was possible with several months of data, but a minimum of 24 months of recording period is required for the calculation of PLR. Irradiance on a horizontal surface in W/m\({}^{2}\) is represented by several terms. They are beam or direct normal irradiance (DNI), diffuse horizontal irradiance (DHI), and ground-reflected irradiance on a horizontal surface (E\({}_{\text{g}}\)). The sum of all irradiances is global horizontal irradiance (GHI). On the plane of array (POA), also in W/m\({}^{2}\), we use the in-plane terms, namely, in-plane global irradiance (G\({}_{\text{POA}}\)), in-plane beam irradiance (G\({}_{\text{bpCoA}}\)), in-plane diffuse irradiance (G\({}_{\text{dpCoA}}\)), and in-plane ground-reflected irradiance (G\({}_{\text{rpCoA}}\)). The terms used for irradiation in Watt-hours/m\({}^{2}\) are horizontal irradiation (H\({}_{\text{h}}\)) and POA irradiation (H\({}_{\text{i}}\)), which are the irradiance aggregated. Other important variables include T\({}_{\text{amb}}\) in \({}^{\circ}\)C, module temperature (T\({}_{\text{m}}\)) in \({}^{\circ}\)C, and wind speed (\(\
u\)) in m/s. Global irradiance on the plane of array, \(\rm G_{POA}\), is mandatory for PR calculation. If \(\rm G_{FOA}\) was not available, it could be estimated from the global horizontal irradiance, GHI, using available decomposition and transposition models. Various empirical decomposition models that are commonly used have been tested by [38]. In general, they are used to estimate the diffuse horizontal irradiance, DHI, from measured GHI. Thereby, both parameters have the following relation. \[\rm k_{d}=\frac{DHI}{GHI} \tag{2}\]  
Here, \(\rm k_{d}\) is the diffuse fraction and its value depends on the clearness index, \(\rm k_{t}\), and the selected decomposition model. Furthermore, GHI, DHI, and the direct normal irradiance, DNI, can be described by Equation (3). \[\rm GHI=DHI+DNI\times\cos(\theta s) \tag{3}\]  
where \(\rm\theta_{s}\) is the solar elevation angle (\({}^{\circ}\)). All decomposition models use at least the clearness index, \(\rm k_{t}\), as input for computing \(\rm k_{d}\), while the other models require additional variables such as elevation angle, ambient temperature, or relative humidity (RH). All models can estimate both DHI and DNI effectively [38]. In this work, we use the Erbs decomposition model [39] due to simplicity because it requires only \(\rm k_{t}\) as the input variable to compute \(\rm k_{d}\). Next, a transposition model is used to determine \(\rm G_{POA}\) using Equation (4). \[\rm G_{FOA}=G_{\rm bPOA}+G_{\rm rPOA}+G_{\rm dPOA} \tag{4}\]  
where \(\rm G_{bPOA}=DNI\times\cos(\theta)\), with \(\theta\) being the angle of incidence of the sunbeam on the plane of the array surface. The calculation of \(\rm G_{rPOA}\) is implemented using Equation (5) which is based on an isotropic model. \[\rm G_{rPOA}=GHI\times\rho\times\frac{1-\cos(\beta)}{2} \tag{5}\]  
Figure 1: The geographical distribution of the photovoltaic (PV) systems, climate locations, and annual global irradiation on a horizontal surface (\(\rm kWh/m^{2}/year\)).