## 2 Materials and Methods  
For the performance analysis of PV system operation in the real climatic condition in Nis (Latitude: 43\({}^{\circ}\)19\({}^{\prime}\)28.99\({}^{\prime\prime}\) N, Longitude: 21\({}^{\circ}\)54\({}^{\prime}\)11.99\({}^{\prime\prime}\) E), 10 monocrystalline silicon solar modules (SST-200 WM, Shenzhen Sunco Solar Technology Co., Shenzhen, China), with individual power of 200 W, were mounted right next to each other (in order to minimize cable losses) on the roof of Faculty of Sciences and Mathematics and serially interconnected in a string. The solar modules were set up on the fixed metal construction tilted at an optimal angle of 32\({}^{\circ}\) toward the south (Figure 1). The total PV array (solar modules surface) was 16.59 m\({}^{2}\) (or 1.659 m\({}^{2}\)/module). The minimum distance between the solar modules and the roof surface was 50 cm to ensure natural air circulation, i.e., a passive air-cooling method for the solar modules was used so that the system balance could take place naturally without any additional (mechanical) technique, as can be seen in Figure 1. It should also be noted that the solar modules were free from any shading. By appropriate cables (conductors), the solar modules were connected to a DC junction box (DC-RO), then a 2 kW inverter (SunnyBoy 2000 HF-30, SMASolar Technology AG, Nisetetal, Germany), then to an AC junction box (AC-RO), and finally to a city power grid. The used inverter was a single-phase inverter with a high-frequency (HF) transformer power of 2000 W and an efficiency of 96.3%, providing a single-phase AC voltage of 230 V, 50 Hz. This PV system was connected to the city power grid. However, its effects on the city grid, including the variation of power factor effect of load, PV penetration variation, anti-islanding effect, and introduction of harmonic into the system by the inverter, have not been investigated or considered. It should be noted that over the 10-year period of the PV system operation, there were no problems during the PV electricity transmission to the city network grid. Global solar radiation on the surface of PV modules (POA radiation) was measured by a sensor unit (Sunny SensorBox), which was also placed next to solar modules at an optimal inclination angle of 32\({}^{\circ}\) toward the south. It should be noted that the solar sensor (Sunny  
Figure 1: PV array installed on the roof of the faculty [39]. SensorBox) uses an a-Si solar cell and measures POA radiation with a resolution of 1 W/m\({}^{2}\) and measurement accuracy of \(\pm\)8%. A central communication interface (Sunny WEBBox) was interconnected to the inverter and SensorBox by Bluetooth. The POA radiation data and PV system electrical parameters continuously record every 5 min into the Sunny WEBBox internal memory [10,39]. The SunnyBoy inverter, Sunny WEBBOX, and DC and AC junction boxes were placed indoors in the faculty laboratory, where the optimum room temperature is maintained throughout the year. A schematic of the grid-connected 2 kW\({}_{\rm P}\) PV system in Nis [28] is given in Figure 2.  
An approximate PV module efficiency at STC can be calculated using the Equation (1) [9]:  
\[\eta_{STC}=(I_{SC}\cdot V_{OC}\cdot F\rm{/}\it{I}_{STC} \tag{1}\]  
where I\({}_{\rm{STC}}\) is the reference solar irradiance at STC of 1 kW/m\({}^{2}\), FF is a fill factor of the solar module, I\({}_{\rm{SC}}\) is the short-circuit current of solar module, and V\({}_{\rm{OC}}\) is the open-circuit voltage of solar module [9]. If it is taken into account that FF = 76%, I\({}_{\rm{SC}}\) = 4.64 A, V\({}_{\rm{OC}}\) = 57.12 V, and the inverter efficiency \(\eta_{\rm{inv}}\) = 96.3%, which is based on the specification of the modules and inverter given by the manufactory datasheet and presented in [10], the approximate PV system efficiency at STC (ideally, excluding cable losses) is around 19.4%. Evaluation of the long-term grid-connected PV system operation in real conditions, based on the statistical processing of experimental data, was performed in two phases:  
1.