# Performance Analysis of a Stand-Alone PV/WT/Biomass/Bat System in Alrashda Village in Egypt
## 6 Results and Discussion  
In this work, a novel HBO technique is suggested to determine the optimal sizing of four alternatives off-grid hybrid system scenarios based on PV, WT, biomass, and battery units. These four scenarios of the hybrid system are namely PV/WT/biomass/Bat, PV/biomass/Bat, WT/biomass/Bat, and PV/WT/Bat. In order to validate the effectiveness of this HBO as a way to provide optimal reliability and least cost, the results achieved by the suggested algorithms are compared with other recent optimization techniques CFA, GWO and STOA. The control parameters used in the optimization process for each algorithm are listed in Appendix A. Figure 8 presents the graphic form of the final values of the target function over the 50 executes for the four analyzed configurations scenarios utilizing the optimization techniques namely, HBO, CFA, GWO, and STOA. It can be noted that, the fitness values for the suggested HBO method in the four system cases were within a limited range, which demonstrated the stability of the suggested technique over the other techniques. Therefore, parametric and nonparametric metric values are superior using the HBO method compared to the rest of the optimization techniques. Figure 9 displays the best optimal solution convergence curve for each scenario utilizing HBO, CFA, GWO, and STOA. For Case (1), the best solution achieved by using HBO technique which is 0.0643767 after 27 iterations, followed by CFA technique with 0.06437783 after 44 iterations. For Case (2), the best solution achieved by using HBO technique which is 0.0703404 after 49 iterations, followed by best solution achieved by CFA technique with 0.07034462 after 32 iterations. For Case (3), the best solution achieved by using HBO technique with 0.0705909 after 41 iterations, followed by best solution achieved by CFA technique with 0.0651240320 after 39 iterations. Finally for Case (4), the best solution achieved by using HBO technique with 0.151991724 after 41 iterations, followed by best solution achieved by CFA technique with 0.152001799 after 58 iterations. It can be noticed that the HBO method provides a good convergence characteristic over the other optimization algorithms CFA, GWO, and STOA in all suggested cases. Figure 8: _Cont._  
Figure 8: End values of the fitness function for 50 executions using HBO, CFA, GWO, and STOA methods: case-1: PV/WT/Biomass/Bat system, case-2: PV/Biomass/Bat system, case-3: WT/Biomass/Bat system, case-4: PV/WT/ Bat system. Figure 9: _Cont._  
Figure 9: The Convergence curves for 100 iterations using HBO, CFA, GWO, and STOA methods: case-1: PV/WT/Biomass/Bat system, case-2: PV/Biomass/Bat system, case-3: WT/Biomass/Bat system, case-4: PV/WT/ Bat system. Tables 6-9 illustrate the results of the optimization properties for the four system scenarios proposed, which is based on many factors including the best value of the objective function, the decision variables (\(\rm{N_{PV}}\), \(\rm{N_{WT}}\), \(\rm{N_{g}}\) and \(\rm{N_{Bat}}\)), the COE, LPSP, and NPC of the suggested optimization algorithms (HBO, CFA, GWO and STOA). which based on WT/biomass/Bat units produces the minimum value of COE and NPC, but it is not the optimal and efficient system for use. As the design of this case is based on batteries and biomass generators only, which have the highest yearly sharing of the capital cost, operating and maintenance cost. While the first scenario which is consists of PV/WT/biomass/Bat units considered an appropriate solution with minimal investment cost for the suggested case study area. Parametric and non-parametric statistical measurements were performed for a more accurate comparison between the four optimization methods (HBO, CFA, GWO and STOA) on the basis of the acquired values of the objective function across a hundred individual runs for all analyzed cases. Parametric measurements comprise the lower value (Min. ), maximum value (Max.)