## 2 Modelling of PV System's Components
### Modelling of Photovoltaic Panel
In addition to that a resistance is connected in series to the aforementioned components so as to represents the internal resistance of the solar cell (see Figure 1), where \(I_{PH}\) is light generated current (\(A\)), \(D\) is diode, \(I_{D}\) is diode current due to the p-n junction under forward bias (\(A\)), \(R_{S}\) is series resistor (\(\Omega\)), and \(R_{SH}\) is shunt resistors (\(\Omega\)). The general I-V characteristic of a PV panel based on the single exponential model is:  
\[i=I_{PH}-I_{O}\left(e^{\frac{v+iR_{S}}{R_{SH}}}-1\right)-\frac{v+iR_{s}}{R_{SH}} \tag{1}\]  
where \(I_{O}\) is dark saturation current in STC, \(A\) is diode quality (ideality) factor, \(k\) is Boltzmann's constant, \(q\) is electron charge, \(n_{s}\) is number of cells in series, and \(T_{sc}\) is temperature at STC. \(V_{t}\) is the thermal voltage and it can be given by,  
\[V_{t}=\frac{Akt_{stc}}{q} \tag{2}\]On the other hand a diagram of a solar cell model using two diodes can be the same as Figure 1 but with additional diode in the parallel to the first diode. The general I-V characteristic of a PV panel based on the two diodes model can be described as,  
\[i=I_{PH}-I_{O1}\left(e^{\frac{p+iB_{n}}{m_{1}T}}-1\right)-I_{O2}\left(e^{\frac{ p+iB_{n}}{m_{1}T}}-1\right)-e^{\frac{p+iB_{n}}{kP}} \tag{3}\]  
However, one of the most important methods used to predict power generated from a photovoltaic panel is using current-voltage characteristic. Some researchers used maximum output power of the PV module to forecast PV system performance, calculated using datasheet's specification under standard test condition (STC). The calculation of maximum power output of a solar cell can be done by,  
\[P_{mp\_stc}=V_{oc}I_{sc}FF \tag{4}\]  
where \(P_{mp\_stc}\) is maximum output power of solar cell (\(W\)), \(V_{oc}\) is solar cell open circuit voltage (\(V\)), \(I_{sc}\) is short circuit current of solar cell (\(A\)) and \(FF\) is fill factor [22]. \(FF\) is a term to show how much energy can be extracted from the module, and calculated as:  
\[FF=\frac{P_{mp}}{V_{oc}I_{sc}}=\frac{I_{mp}V_{mp}}{V_{oc}I_{sc}} \tag{5}\]  
Then, the mathematical model to estimate instantaneous PV module power output under real operating condition in term of \(P_{mp\_stc}\) can be represented by following expression [5]:  
\[P_{pv}(t)=\eta P_{mp\_stc}PSF \tag{6}\]  
where \(PSF\) is peak sun factor (dimensionless) and \(\eta\) is de-rating factor. \(PSF\) was calculated using following expression:  
\[PSF=\frac{G_{array\_plane}}{G_{stc}} \tag{7}\]  
where \(G_{array\_plane}\) is the irradiance measured in array plane, and \(G_{stc}\) is solar irradiance under standard test condition (1000 Wm\({}^{-2}\)). Meanwhile, the mathematical model of a solar cell power output at time \(t\) is:  
\[P_{pv}(t)=V_{pv}(t)I_{pv}(t) \tag{8}\]  
where \(P_{pv}\) is output power of solar cell (\(W\)), \(V_{pv}\) is solar cell operating voltage (\(V\)), and \(I_{pv}\) is output current of solar cell (\(A\)) [23]. In some researches, several authors foresee energy output performance instead of power prediction in their design. As in [24], the authors use energy produced by PV array, \(E_{pv}\) in term of derating factors, \(\eta\), area, \(A\) (m\({}^{2}\)) and solar energy, \(E_{Sun}\) as follows,  
\[E_{PV}(t)=E_{Sun}(t)\eta A \tag{9}\]  
Figure 1: Electrical Equivalent of PV Cell on one-diode model [21]. Moreover, some authors prefer to use energy yield as indicator for system performance. Energy yield in a period of interest can be calculated using equation [25]:  
\[V_{t}=\frac{Akt_{stc}}{q} \tag{2}\]0  
where _PSH_ is peak sun hour at specified tilt angle over a period (h). Here PSH at specific tilt angle means the number of hours that a PV panel that is slanted at a specific tilt angle can receive 1000 W/m\({}^{2}\). This mean that the maximum total energy yield that can be provided by a PV panel at a specific tilt angle. In [26], [PERSON] et al.