## 2 Materials and Methods
### The Proposed Power System
#### 2.1.1 PV Power System  
In order to determine the electrical properties of the PV-SPP, that provides the power to the interconnected system, it is necessary to observe how the current and voltage of the PV cell are affected by a variable load. When a PV cell is modelled, a sufficient number of PV cell groups (\(N_{S}\)) are connected in series, in order to generate the required output voltage. Also, a sufficient number of PV cell groups (\(N_{P}\)) are connected in parallel for generating the required output current. The PV cell variables of the equivalent circuit depend on the light intensity and temperature. Thus, the light and temperature values should be known, in order to calculate the output power [25]. The PV cell is examined, by means of Figure 2. The voltage of the PV cell can be obtained, depending on its current of it by using Equation (1). \"\(I_{0}\)\" is defined as the reverse saturation current of the diode. Definitions of the other symbols are shown in Abbreviations and Nomenclatures. \[V_{cell}=\frac{A\times k\times T_{cell}}{e}\times\ln\left(\frac{I_{ph}+I_{0}+I _{cell}}{I_{0}}\right) \tag{1}\]  
The operating temperature of the PV panel cells, \(T_{cell}\), changes when the climate temperature and the level of solar radiation vary. Therefore, a new photocurrent and a new output voltage are generated. The operating temperature of the PV cells varies, depending on the solar radiation level and the temperature of the environment. The variable ambient temperature, \(T_{x}\), affects the output voltage and the photo current of the cell. The voltage and current coefficients of these effects in the cell model are shown by \(C_{TV}\) and \(C_{TI}\) in Equations (2) and (3), respectively. \[C_{TV}=1+\beta_{T}\times(T_{a}-T_{x}) \tag{2}\]  
\[C_{TI}=1+\frac{\gamma_{T}}{S_{cell}}\times(T_{x}-T_{a}) \tag{3}\]  
where \(T_{a}\) and \(T_{x}\) represent the known reference ambient temperature and the different ambient temperature at different points during the tests, respectively. For the PV-SPP model in this study, the \(T_{x}\) value is taken as 28 \({}^{\circ}\)C. The \(\beta_{T}\) and \(\gamma_{T}\) coefficients represent the slopes of changes in the cell voltage and current due to temperature, respectively. The \(\beta_{T}\) and \(\gamma_{T}\) coefficients vary, depending on the PV cell type, and are determined experimentally. \(\beta_{T}\) is calculated between 0.004 and 0.006, and \(\gamma_{T}\) is calculated between 0.02 and 0.1 [25]. Although the ambient temperature does not significantly change throughout the day, the solar radiation effectively changes because of the amount of sunlight and the cloudiness of the sky. As a result of this, the photo current, operating temperature, and output voltage of the PV cell are affected. These effects are given for the output voltage by \(C_{SV}\) and for the photo-current by \(C_{SI}\), and are defined by Equations (4) and (5), respectively. \[C_{SV}=1+\beta_{T}\times\alpha_{s}(S_{x}-S_{cell}) \tag{4}\]  
\[C_{SI}=1+\frac{\gamma_{T}}{S_{cell}}\times(S_{x}-S_{cell}) \tag{5}\]  
Figure 2: The simplified equivalent circuit of a PV cell. where \(S_{cell}\) is the daylight intensity used as the reference solar radiation level. \(S_{x}\) represents different solar radiation levels at different times, depending on the atmospheric changes. \(\alpha_{s}\) is the coefficient of variation in the solar radiation level, and is defined by Equation (6). \[\alpha_{s}=\ \frac{\Delta T_{cell}}{S_{x}-S_{cell}}=\ \frac{T_{cell}-T_{a}}{S_{x}-S_{ cell}} \tag{6}\]  
The value of \(\alpha_{s}\) is different for PV cells that do not have the same properties and this value is determined experimentally. However, this value is usually between 0.3 and 0.4 \({}^{\circ}\)C cm\({}^{2}\)/mW.