## 2 Hybrid System Components
### PV Plant  
The power produced by the PV installation can be estimated very accurately from the ambient temperature and irradiance, data that can be easily obtained using the PVGIS programme [66]. Factors influencing the actual irradiance value (such as air clarity index and atmosphere mass) are already considered in the irradiance predictions of the PVGIS programme. The wind speed influences the cell temperature, but for moderate winds (up to 3 m/s), the influence is very small. The average annual wind speed at the chosen site is 2.4 m/s at 10 m above the ground, so no correction for wind will be applied in this study.  
\[P_{M}(G)=\frac{P_{M1}\cdot V_{0}(G)\cdot I_{cc}(G)}{V_{01}\cdot I_{cc1}} \tag{3}\]  
\[P_{M1}=P_{M0}\cdot\left(1+C_{p}\cdot\left(T_{cell}-25\right)\right) \tag{4}\]  
Applying the standard model, the following equation is obtained:  
\[T_{cell}=T_{out}+\frac{G}{800}\cdot\left(T_{NOCT}-20\right)-v(v) \tag{5}\]  
\[V_{01}=V_{0}\cdot\left(1+C_{v}\cdot\left(T_{cell}-25\right)\right) \tag{6}\]  
\[V_{0}(G)=V_{01}+\frac{n\cdot k_{B}\cdot\left(T_{cell}-273\right)}{e}\cdot \ln\left(\frac{G}{1000}\right) \tag{7}\]  
\[I_{cc}(G)=I_{cc1}\cdot\frac{G}{1000} \tag{8}\]  
\[I_{cc1}=I_{cc0}\cdot\left(1+C_{I}\cdot\left(T_{cell}-25\right)\right) \tag{9}\]  
In these equations:  
\(P_{M}(G)\) is the maximum panel's power in W.  
\(P_{M1}\) is the maximum panel's power in W with \(G=1000\) W/m\({}^{2}\).  
\(P_{M0}\) is the standard maximum panel's power in W in standard test conditions (STC).  
\(G\) is the irradiance in W/m\({}^{2}\) normal to the panel.  
\(V_{0}(G)\) is the open-circuit voltage of the panel in V.  
\(V_{01}\) is the open-circuit voltage of the panel in V with \(G=1000\) W/m\({}^{2}\).  
\(V_{0}\) is the standard open-circuit voltage of the panel in V (STC).  
\(I_{cc}(G)\) is the short-circuit current of the panel in A.  
Figure 1: BG plant diagram flow.  
\(l_{cc1}\) is the short-circuit current of the panel in A with \(G\) = 1000 W/m\({}^{2}\).  
\(l_{cc0}\) is the standard short-circuit current of the panel in A (STC).  
\(C_{p}\) is the power/temperature coefficient of the panel in \({}^{\circ}\)C\({}^{-1}\).  
\(T_{out}\) is the outside air temperature in \({}^{\circ}\)C.  
\(T_{NOCT}\) is the temperature of the cell in NOCT (normally operated condition test) conditions in \({}^{\circ}\)C.  
\(v(v)\) is the correction of the temperature with the wind speed in \({}^{\circ}\)C. A value of \(v(v)=0\) m/s is assumed.  
\(C_{v}\) is the voltage/temperature coefficient of the panel.  
\(n\) is a factor dependent on the panel (\(n\cong 1.2\)).  
\(k_{B}\) is the Boltzmann constant (1.380 649 \(\times\) 10\({}^{-23}\) J K\({}^{-1}\)).  
\(e\) is the electron charge (1.6 \(\times\) 10\({}^{-19}\) C).  
\(C_{I}\) is the current/temperature coefficient of the panel in \({}^{\circ}\)C\({}^{-1}\).  
With these equations, using the measured irradiance and temperature data, the generated power curves for two different situations (a sunny day and a cloudy day) are performed. The sunny day corresponds to 29 March 2021, whereas the cloudy day corresponds to 7 October 2021. These generation profiles are shown in Figure 2.