## 3 Results and Discussion  
### Annual Output of Tested Photovoltaic System  
For all photovoltaic installations operating in the temperate zone, some relationship can be seen between the energy generated in summer and winter [50]. The course of daily energy consumption for the purpose of designing an installation adapted to the investor's consumer needs was assumed to be constant. As can be seen from the below diagram, Figure 1, during the summer period, excess energy is generated and can be returned to the grid. The installation was intentionally slightly oversized. There was an overproduction of 766 kWh of energy per year. From the analyzed data, the year 2020 was quite unusual in terms of solar conditions in Poland. The highest amount of energy was produced in April. Usually, the sunniest month of the year is June or July, less often August or May. The 8.8 kWp installation produced more than 60 kWh of daily energy four times per year. The highest value was recorded on 1 June 2020 (61.714 kWh). From October to February, it was observed six times that the installation did not work during the day, and net energy production was zero due to weather conditions. According to the manufacturer of the modules, solar radiation of 1000 \(\frac{W}{m^{2}}\) generates a current of 9.35 A and a voltage of 39.6 V. In order to reduce the influence of shading on individual cells, so-called power optimizers were installed at each module. A module produces a higher amount of energy if it operates at a higher power. This is highest when voltage and current values are high and very close to each other. The performance characteristics can be shown for a given amount of solar energy falling on the module. PV cells have been designed to operate under optimal conditions, which are considered to be rated conditions (in this case STC). As shown in Figure 2, the amount of generated power can be represented by a rectangle. The area of the rectangle that is the ideal operating point is limited by the values of current and voltage. An ideal characteristic has been designated as a product of the voltage of the open circuit and the short circuit current of the solar cell [51]. The FF (fill factor) has the greatest value if it is defined as the ratio of an ideal characteristic to the point of maximum power. The FF corresponds to the voltage drop by the module during operation. The shadowing of parts of the module cells results in the flow of a much lower current and  
Figure 1: Characteristics of annual electricity generation by a photovoltaic installation. Figure 2: Performance characteristics of the module for different solar irradiance values. a shift of the operating point toward 0 [52]. The function of the optimizer is to find and enforce the work in the so-called maximum power point, allowing the system to work with the highest possible efficiency. For the analyzed case, the FF reached a value of 0.79. The results of the fill factor depend on the technology used and its durability. The operation of a photovoltaic panel with this efficiency is a satisfying result [53; 54]. The device responsible for adapting the voltage and current to the requirements of the distribution network operator is the inverter. Due to this device, the generated energy can be transmitted to the grid and consumed by the prosumer at any time. The adaptation of the generated energy consists of changing the DC voltage to AC voltage with an effective value of 230 V (phase to neutral) and a frequency of 50 Hz. In addition, the inverter divides the voltage into 3 phases shifted by 120\({}^{\circ}\) and synchronizes them to the grid voltage. The used inverter has an efficiency as high as 99.5%. According to the datasheet, the modules are very well adapted to exposure to external conditions.