## 2 Materials and Methods
### Dynamic Electric Model of the Photovoltaic Module  
Electric models of the PV module could be found in several papers [10; 29; 33] as a simple empirical correlation between output power \(P_{\text{DC}}\), solar radiation \(G\) and operating temperature of the PV module \(T\) or as a single/double diode model [34; 35; 36; 37; 38] using the algorithm for a maximum power point tracking (MPPT). In this paper, the dynamic electric model is presented as a double diode model taking into account four parameters (short-circuit current \(I_{\text{SC}}\), open-circuit voltage \(V_{\text{OC}}\), series resistance \(R_{\text{s}}\) and shunt resistance \(R_{\text{sh}}\)) as a function of solar radiation \(G\) and the operating temperature of the PV module \(T\). The double diode model of the PV cell is expressed by (1):  
\[I=I_{\text{ph}}-I_{01}\cdot\left(\exp^{(\frac{V+I\cdot R_{\text{s}}}{\text{Pt -Nb}})}-1\right)-I_{02}\cdot\left(\exp^{(\frac{V+I\cdot R_{\text{s}}}{\text{Pt -Nb}})}-1\right)-\left(\frac{V+I\cdot R_{\text{s}}}{R_{\text{sh}}}\right) \tag{1}\]  
where \(N_{\text{s}}\) is the number of series-connected PV cells, \(I_{\text{ph}}\) is the photocurrent, \(I_{01}\) and \(I_{02}\) are the reverse saturation current of the first and second diode, while \(V_{\text{T1}}\) and \(V_{\text{T2}}\) stand for thermal voltage of the first and second diode. The last five parameters (\(I_{\text{ph}}\), \(I_{01}\), \(I_{02}\), \(V_{\text{T1}}\) and \(V_{\text{T2}}\)) are described in more detail in Appendix A. As mentioned above, a short-circuit current, an open-circuit voltage, a series and shunt resistance [39] of the PV module are calculated as a function of the solar radiation \(G\) and the operating temperature of the PV module \(T\) by (2)-(5), where \(K\) is the Boltzman \begin{table}
\begin{tabular}{c c c} \hline  & **Uncertainty** & **Calibration** \\ \hline Temperature sensor: DS18x20 & \(\pm\)0.5 \({}^{\circ}\)C & 6 years ago \\ Wind speed sensor: VMT107A & \(\pm\)0.5 m/s & 6 years ago \\ Solar radiation sensor—pyranometer: & \(<\)1\% & 6 years ago \\ Kipp\&Zonen SP Lite 2 & \(<\)1\% & 6 years ago \\ Ambient temperature sensor: & \(\pm\)0.15 \({}^{\circ}\)C & 6 years ago \\ TPC 159 (Pt100) & \(\pm\)0.15 \({}^{\circ}\)C & 6 years ago \\ AC measurement—Power Meter: & Current: \(\pm\)0.2\% & \\ Siemens Sentron PAC4200 & Voltage: \(\pm\)0.2\% & 3 months ago \\ DC measurement—Hall Effect Sensor: & Current: \(\pm\)0.5\% & \\ T201 DCH100 & Voltage: \(\pm\)0.5\% & 3 months ago \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristics of measurement devices. Figure 1: Measurement and experimental system: (**1**) Dual-axis PV tracking system; (**2**) Ambient temperature sensor; (**3**) Solar radiation sensor—pyranometer; (**4**) Temperature sensor; and (5) DC/AC inverter. @Laboratory for Applied Electrical Engineering, Faculty of Energy Technology, University of Maribor. n constant (1.38065 \(\times\) 10\({}^{23}\) J/K), \(q\) is the electron charge (1.602 \(\times\) 10\({}^{19}\) C) and \(n\) is the diode ideality factor (dimensionless). Furthermore, \(\mu_{I_{\rm SC}}\) and \(\mu_{V_{\rm OC}}\) are temperature coefficients of \(I_{\rm SC}\) and \(V_{\rm OC}\), while \(I_{\rm SC,STC}\), \(V_{\rm OC,STC}\), \(G_{\rm STC}\) and \(T_{\rm STC}\) presents short-circuit current, open-circuit voltage, solar radiation and temperature of the PV module under STC conditions.