## 3 Results  
The first part of the study was focused on the identification of optimal tilt angle for southern Slovakia region. In this section the time relations for different tilt angles (\(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\)) were evaluated. At first, data from autonomous model solar system (1 PV module) were detected, then the results were processed and the data were recalculated on the experimental PV power plant. The dependencies of energy produced by  
Figure 5: **(a)** The azimuth orientation of the model PV system; (b) The recommended orientation (azimuth angle marked in blue color) for southern Slovakia. the PV system for tilt angle range from 0\({}^{\circ}\) to 90\({}^{\circ}\) in different calendar months are presented in Figure 6. Especially for tilt angle 35\({}^{\circ}\) was measured the amount of produced electrical energy not only by the model PV system but also by the PV power plant. The correlation between the calculated values and the experimentally obtained results was from 99.18% to 99.89% during the year. The output power of the system was the highest for the tilt angle 30\({}^{\circ}\) and the optimal energy balance was detected for tilt angle from 15\({}^{\circ}\) to 30\({}^{\circ}\). A very small difference of about 0.9% in energy production of PV system was identified for range (30-35\({}^{\circ}\)). If the tilt angle is greater than the 35\({}^{\circ}\), the power decreases. The group data analysis and data extraction were carried out for identifying the model equation within the observed experimental dependence. For mathematical description of power energy balance for different tilt angle \(\beta\) was found mathematical Equation (4), which is a polynomial function of the second degree with the coefficient of determination R\({}^{2}\) = 0.9999. \[E_{m}(\beta)=-0.9\ \beta^{2}+61.929\ \beta+7514.3 \tag{4}\]  
where: \(E_{m}(\beta)\) is the energy produced by the PV system per month (kWh), \(\beta\) is the tilt angle (\({}^{\circ}\)). Figure 7 shows a more general relation which represents the result of the evaluation of the PV module tilt angle influence on the electricity production. The simulation in software Matlab(r) was used for detection of the optimal tilt angle for examined PV system installed in southern Slovakia region. The maximum of energy production was obtained for the tilt angle 34.5\({}^{\circ}\). A part of the model equation verification has the polynomial function form described by Equation (4). An analytical model was created by using of iterative method for system modelling. Finally, both models (polynomial and analytical) were compared. A 3 rd order differential equation with constant coefficients--Equation (5)--was used to create the analytical model. Figure 6: Dependencies of energy produced by the PV system for tilt angle range from 0\({}^{\circ}\) to 90\({}^{\circ}\). The differential equation describes the behavior of the output variable. From the physical point of view, it represents the amount of energy produced by the PV system, which is characterized by a transfer function in a complex plain--Equation (6). \[\frac{d^{3}\;E(\beta)}{d\beta^{3}}+0.02644\cdot\frac{d^{2}\;E(\beta)}{d\beta^{2} }+0.007259\cdot\frac{d\;E(\beta)}{d\beta}+5.472\cdot 10^{-11}\cdot E(\beta)=-0.004562 \cdot\beta \tag{5}\]  
\[G(s)=\;\frac{-0.004562}{s^{3}+0.02644\cdot s^{2}+0.007259\cdot s+5.472\cdot 10^{ -11}} \tag{6}\]  
This is based on the values of the independent variable, which was the tilt angle of PV modules \(\beta\). The 95.96% reliability of the transfer function with respect to the experimental data was determined (Figure 8). Figure 8: Comparison of the experimental curve and the curve of the analytical model expressed by the transfer function. Figure 7: Dependence of the energy produced by the PV system for the different tilt angles. General solution of the differential Equation (7) has the form expressed as follows-Equation (7):  
\[