# Performance Analysis of a PEMFC-Based Grid-Connected Distributed Generation System
## 3 Overview of Hybrid Microgrid System
\[f(v)=\frac{2v}{c^{2}}\exp\biggl{[}-\Big{(}\frac{v}{c}\Big{)}^{2}\biggr{]} \tag{2}\]  
\[f(v)=\frac{\Pi v}{2\sigma^{2}}\exp\biggl{[}-\frac{\Pi}{4}\Big{(}\frac{v}{ \vartheta}\Big{)}^{2}\biggr{]} \tag{3}\]  
where \(\vartheta\) is an average wind speed in terms of m/s unit, denoted as 4.78 m/s. According to the Weibull calculations, the wind turbine power curve can be expressed as in Figure 4. The total annual obtained energy from the wind turbine is calculated as 228.493 kWh, as seen in Figure 2.0 \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **Unit** \\ \hline Nominal Power & 400 W \\ Swept Area & 1.07 m2 \\ Cut-in wind speed & 3.58 m/s \\ Cut-off wind speed & 49.2 m/s \\ Rotor diameter & 1.17 m \\ Alternator & Permanent Magnet Brushless \\ \hline \end{tabular}
\end{table} 
Table 1: Wind Turbine Specifications. Figure 4: The DG system component (wind turbine). The parameters of the PV module are reported in Table 3. With regards to geographic location, the coordinates of the aforementioned system are located at 40\({}^{\circ}\)59\({}^{\prime}\) North Latitude, 29\({}^{\circ}\)3\({}^{\prime}\) East Longitude. \[\delta=23,45\sin\left[\frac{360}{365}(n-81)\right] \tag{4}\]  
\[\beta_{A}=90-L+\delta \tag{5}\]  
\[PV_{tilt}=90-\beta_{A} \tag{6}\]  
where \(\delta\) is the solar declination angle, and \(\beta_{A}\) is an altitude angle (the altitude angle is the angle between the sun and the local horizon directly beneath the sun), \(PV_{tilt}\) is the optimum PV module tilt angle, fixed at 30\({}^{\circ}\), \(L\) is the latitude of the site, and \(n\) is number of days. \[I_{total}=I_{beam}+I_{diffuse}+I_{reflected} \tag{7}\]  
\[I_{beam}=I_{BH}R_{B} \tag{8}\]  
\[I_{BH}=I_{H}-I_{DH} \tag{9}\]  
\[H_{SR}=\cos^{-1}(-\tan L\tan\delta) \tag{10}\]  
Figure 4:0  
Figure 4:1  
Figure 4:2  
Figure 4:3  
Figure 4:4  
Figure 4:5  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wind Speed [m/s]** & **Power [W]** & \(f(v)\) & **Hours/Year at \(v\)** & **Energy [Wh/Year]** \\ \hline
1.06 & 0 & 0.065 & 569.4 & 0 \\
2.02 & 0 & 0.1194 & 1045.944 & 0 \\
2.99 & 0 & 0.1512 & 1324.512 & 0 \\
3.58 & 1 & 0.1581 & 1384.956 & 1620.39852 \\
5.00 & 14 & 0.1453 & 1272.828 & 17,921.41824 \\
5.99 & 31 & 0.1196 & 1047.696Figure 4:6  
where \(I_{total}\) is the total daily solar irradiance on the PV module, \(I_{beam}\) is the beam solar irradiance on the PV module, \(I_{diffuse}\) is the diffuse solar irradiance on the PV module, \(I_{reflected}\) is the reflected solar radiation on the PV module, \(I_{H}\) is the total average daily horizontal solar irradiance, \(I_{BH}\) is the beam irradiance on the horizontal surface, \(R_{B}\) is the beam tilt factor, \(H_{SRC}\) is the sunrise hour angle for the collector (when the sun first strikes the collector face, \(\theta\) = 90\({}^{\circ}\)), \(H_{SR}\) is the sunrise hour angle (in radians), \(C\) is the clearness index, \(I_{O}\) is extraterrestrial insolation on a horizontal surface at the site, \(I_{H}\) is insolation on a horizontal surface, and \(\rho\) is ground reflectivity. The total solar irradiance profile is shown in Figure 4:7  
To be aware of the potential of the faculty's location, the 3D Sun-Path program was used to assist in comparing solar altitude, azimuth angles, and zenith angles [22]. The program interface is shown in Figure 4:8  
Figure 4:9  
where \(E_{total}\) is the produced total PV output energy (kWh), \(PR\) is the performance ratio (0.5-0.9), \(A_{module}\) is the module area (m\({}^{2}\)), and \(\eta_{module}\) is the module efficiency (%). \begin{table}
\begin{tabular}{c c} \hline \hline
**Features** & **Values (UOM)** \\ \hline Module Efficiency (\%) & 15.71 \\ Cell Efficiency (\%) & 17.9 \\ Peak Power (\(P\)) & 250 Wp \\ Max Power Voltage (\(Vmp\)) & 30.6 V \\ Max Power Current (\(Imp\)) & 8.17 A \\ Open-Circuit Voltage (\(Voc\)) & 38 V \\ Short-Circuit Current (\(Isc\)) & 8.71 A \\ Number of Cells & 60 \\ Dimensions & 1640 \(\times\) 990 \(\times\) 35 mm \\ \hline \hline \end{tabular}
\end{table}