## 6 Results
### Validation of QOBO Algorithm  
The results of the statistical measurements for the modified QOBO, the conventional BO, HHO, AEFA and IWO algorithms are listed in Tables 2 and 3. From Table 2, the reader can find the results of the optimal sizing for the multiple scenarios studied, as well as the convergence time of each simulation, and conclude that the QOBO algorithm finds the best results with a short time compared with the other algorithms. From Table 3, the reader can compare between algorithms and the different scenarios of the proposed hybrid system using multiple factors. Briefly, it is noticed that the hybrid PV/biomass system is highly competitive, mainly using the developed QOBO algorithm, the optimized system is calculated with $110,807, which means an LCOE of 0.1053 $/kWh, the constraints are satisfied and the project is 100% supplied by renewable energy sources. In this scenario, the performances of the QOBO and the BO are almost equal, while in other scenarios, the difference is clearly noticed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Quantity** & **Conversion** \\ \hline \(N\) & Project lifetime & 20 years \\ \(i_{r}\) & Interest rate & 13.25\% \\ \(\mu\) & Escalation rate & 2\% \\ \(\delta\) & Inflation rate & 12.27\% \\ \hline \multicolumn{3}{c}{**PV system**} \\ \(\lambda_{pv}\) & PV initial cost & 300 \$/m\({}^{2}\) \\ \(\theta_{pv}\) & Annual O\&M cost of PV & 0.01 \(\star\lambda_{pv}\) \$/m\({}^{2}\)/year \\ \(\eta_{r}\) & Reference efficiency of the PV & 25\% \\ \(\eta_{t}\) & Efficiency of MPPT & 100\% \\ \(T_{r}\) & PV cell reference temperature & 25 \({}^{\circ}\)C \\ \(\beta\) & Temperature coefficient & 0.005 \({}^{\circ}\)C \\ NOCT & Nominal operating cell temperature & 47 \({}^{\circ}\)C \\ \(N_{pv}\) & PV system lifetime & 20 years \\ \hline \multicolumn{3}{c}{**WT system**} \\ \(\lambda_{wind}\) & Wind initial cost & 125 \$/m\({}^{2}\) \\ \(\theta_{wind}\) & Annual O\&M cost of wind & 0.01 \(\star\lambda_{wind}\) \$/m\({}^{2}\)/year \\ \(C_{p,wind}\) & Maximum power coefficient & 48\% \\ \(\tilde{V}_{ci}\) & Cut-in wind speed & 2.6 m/s \\ \(V_{ca}\) & Cut-out wind speed & 25 m/s \\ \(V_{r}\) & Rated wind speed & 9.5 m/s \\ \(N_{wind}\) & Wind system lifetime & 20 years \\ \hline \multicolumn{3}{c}{**Diesel generator**} \\ \(\lambda_{dg}\) & Diesel initial cost & 250 \$/kW \\ \(\theta_{dg}\) & Annual O\&M cost of diesel & 0.05 \$/h \\ \(R_{dg}\) & Replacement cost & 210 \$/kW \\ \(p_{f}\) & Fuel price in Egypt & 0.43 \$/L \\ \(N_{diesel}\) & Diesel system lifetime & 7 years \\ \hline \multicolumn{3}{c}{**BESS**} \\ \(\lambda_{bat}\) & Battery initial cost & 100 \$/kWh \\ \(\theta_{bat}\) & Annual operation and maintenance cost of battery & 0.03 \(\star\lambda_{bat}\) \$/m\({}^{2}\)/year \\ \(DOD\) & Depth of discharge & 80\% \\ \(\eta_{b}\) & Battery efficiency & 97\% \\ \(SOC_{min}\) & Minimum state of charge & 20\% \\ \(SOC_{max}\) & Maximum state of charge & 80\% \\ \(N_{bat}\) & Battery system lifetime & 5 years \\ \hline \multicolumn{3}{c}{**Inverter**} \\ \(\lambda_{inv}\) & Inverter initial cost & 400 \$/m\({}^{2}\) \\ \(\theta_{inv}\) & Annual O\&M cost of inverter & 20 \$/year \\ \(\eta_{inv}\) & Inverter efficiency & 97\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Units for magnetic properties.