## 4 Proposed Hybrid (InC-DFO) Technique for PV Energy Systems
### Partial Shading Detection Method to Transfer from InC to DFO  
To comprehend the PS detection mechanism of the InC-DFO technique, it is important to figure out the I-V curve relationship of a single diode PV cell. The complete P-V curves of the PV system are shown in Figure 6 that consist of UI, PS1, and PS2 conditions. For this aim, an equivalent circuit model is examined. We calculate the value of \(I_{pv}\) from (5). \[I_{pv}=\frac{G}{G_{STC}}(I_{pv,STC}+K\Delta T) \tag{21}\]  
where '\(K\)' stands for Boltzmann constant, '\(T\)' is expressed as the temperature of the photovoltaic cell and \(G\) represents the irradiance. If the value of \(T\) is remaining constant and \(G\) is assumed to be varying then \(I_{pv}\) rewritten as follow:  
\[\frac{I_{pv}}{I_{pv,STC}}=\frac{G}{G_{STC}} \tag{22}\]  
\(I_{pv,STC}\) is the photovoltaic current at standard testing condition i.e., 1000 W/m\({}^{2}\) at 25 \({}^{\circ}\)C. From [41], taking into consideration that maximum current \(I_{mpp}\) exists in the vicinity of 0.9\(I_{sc}\), Equation (22) can be written as  
\[\frac{I_{sc}}{I_{sc,STC}}\approx\frac{I_{mpp}}{I_{mpp,STC}}\approx\frac{G}{G_ {STC}} \tag{23}\]  
\[G\approx\frac{I_{mpp}}{I_{mpp,STC}}G_{STC}\approx\frac{I_{sc}}{I_{sc,STC}}G_{ STC} \tag{24}\]  
The detection strategy of InC-DFO takes \(I_{mpp}\) and \(I_{sc}\) points on I-V curves of the Sun Power SPR-315E-WHT-D module and their specifications are given in Table 1. The irradiance values that are chosen from the I-V curve are demonstrated in Figure 7.  
Figure 6: Complete P-V curves of PV system. When values of G drops from 1000 W/m\({}^{2}\) to 700 W/m\({}^{2}\), it is noticed that the ratio of \(I_{sc}\) results as  
\[\frac{I_{sc}}{I_{sc,STC}}=\frac{4.202}{6.14}=0.684\approx 0.7 \tag{25}\]  
Respectively, the same outcomes could be drawn during the change in MPP current ratio when G falls from 1000 W/m\({}^{2}\) to 700 W/m\({}^{2}\), i.e.,  
\[\frac{I_{mpp}}{I_{mpp,STC}}=\frac{4.046}{5.867}=0.689\approx 0.7 \tag{26}\]  
It is observed from the (24), that the measured values of irradiance at \(I_{mpp}\) and \(I_{sc}\) are approximately equal. In [41], \(I_{mpp}\) conceals near the 0.8 open-circuit voltage of a selected array \(V_{oc-array}\) and \(I_{sc}\) is in the region of 0.8 open-circuit voltage \(V_{oc}\) of a module. Consequently, \(I_{mpp}\) and \(I_{sc}\) may be denoted as \(I_{0.8 Voc-array}\) and \(I_{0.8 Voc}\), respectively. So, (24) could be written using these terms:  
\[G\approx\frac{I_{0.8 Voc-array}}{I_{mpp,STC}}G_{STC}\approx\frac{I_{0.8 Voc}}{I_{ sc,STC}}G_{STC} \tag{27}\] \begin{table}
\begin{tabular}{l c} \hline \hline
**Description** & **Electric Characteristics of Sun Power** \\  & **SPR-315E-WHT-D** \\ \hline Maximum Power (\(P_{max}\)) & 315.072 W \\ \hline Voltage at MPP (\(V_{max}\)) & 54.7 V \\ \hline Current at MPP (\(I_{max}\)) & 5.76 A \\ \hline Short circuit current (\(I_{sc}\)) & 6.14 A \\ \hline Open circuit voltage (\(V_{oc}\)) & 64.6 V \\ \hline Temperature coefficient of (\(V_{oc}\)) & \(-\)0.176.6 mV/K \\ \hline Temperature coefficient of (\(I_{sc}\)) & 3.5 mA/K \\ \hline Temperature coefficient of power & \(-\)0.38\%/K \\ \hline Peak efficiency & 19.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electric characteristics of Sun Power SPR-315E-WHT-D.  
Figure 7: I-V and P-V curves of the PV system. MPPT records the corresponding currents as \(0.8 Voc-array\) and \(0.8 Voc\) when they take a sample at \(0.8 Voc-array\) and \(0.8 Voc\) respectively. Values of G are determined at \(0.8 Voc-array\) and \(0.8 Voc\) is specified as G-1 and G-2, respectively. In UI condition, values of G-1 and G-2 are almost identical due to the slope current between \(I_{0.8 Voc}\), and \(I_{0.8 Voc-array}\) is very small. This phenomenon is clarified in Figure 7 through the I-V characteristics curve. At 3 different values of G i.e., 1000 W/m\({}^{2}\), 700 W/m\({}^{2}\) and 300 W/m\({}^{2}\) of PV array, corresponding currents are labeled at \(I_{0.8 Voc}\), and \(I_{0.8 Voc-array}\).