## 5 Results and Discussion
### Results for the 33-Node AC MG Operating in Grid-Connected Mode
#### 5.1.3 Statistical Analysis of the Objective Function \(Fo_{3}\) (\(Co_{2}\) Emissions)  
When comparing the analyzed metaheuristic techniques regarding \(CO_{2}\) emissions in the 33-node MG during grid-connected operation, an average decrease of 57.9576% is observed among the best solutions provided by each algorithm in relation to the base case (12541.1958 \(kgCO_{2}\)). Figure 15 presents the average reductions achieved by each technique after 100 executions. In this analysis, PGA stands out with a reduction of 65.8319%, representing improvements of 35.2939%, 2.0183%, 0.8879%, 14.4529%, and 4.9379% compared with MC, PSO, JAYA, GNDO, and MVO.  
Figure 16 presents the 100 solutions obtained by each methodology, with the purpose of analyzing their dispersion. PGA achieves a standard deviation of 0.0673%, which translates into improvements of 0.6723%, 2.2018%, 1.7188%, 6.0265%, and 1.8921% compared with MC, PSO, JAYA, GNDO, and MVO, respectively. These results, along with the average solutions obtained, position the PGA as the most effective technique for \(CO_{2}\) emissions reduction in this case, standing out not only for the quality of its solutions but also for its repeatability and consistency.  
For \(FO_{3}\), JAYA reported the best computation time, completing the optimization in 227.4124 s. Close behind, the proposed PGA achieved a processing time of 235.4538 s, positioning it among the fastest and confirming its consistently efficient performance across all objective functions. Once again, GNDO registered the highest processing time (369.1405 s), reinforcing the advantages of more lightweight and stable algorithms such as PGA for this type of optimization problem.  
Figure 14: Boxplot of the solutions for \(FO_{2}\) in the 33-node AC MG operating in grid-connected mode.  
Figure 15: Average emissions reduction in the 33-node MG operating in grid-connected mode.  
In general terms, the average processing time of all strategies with regard to \(FO_{3}\) was approximately 278.7691 s, making PGA's performance not only competitive but clearly below the average, which reinforces its potential as a reliable and time-efficient tool for tasks involving the environmental optimization of MGs.  
Furthermore, it was essential to ensure that the results obtained with each methodology adhered to the technical constraints of the MG, particularly regarding voltage levels and line loading capacity. This compliance is demonstrated in Figures 17 and 18, which illustrate the evolution of the worst voltage variation and the maximum current level throughout the 24-hour operation period. In both figures, it is graphically verified that all methodologies respect the established technical limits for the analyzed MG.  
Incorporating the reactive power injected by the WTs into this MG requires ensuring that their apparent power does not exceed the nominal capacity. To this effect, Figure 19 presents the active power dispatch of the three WTs for each of the objective functions considered. In parallel, Figure 20 shows the reactive power of the WTs under the same scenarios. Finally, Figure 21 illustrates the apparent power of the WTs, as calculated from the previously presented active and reactive powers. This final analysis was only conducted for PGA since our proposal achieved the best performance. In this figure, it can be observed that at no point during the 24 h period does the apparent power exceed the nominal capacity of the power converters (1300 kW for each of the WTs).  
Figure 16: Boxplot of the solutions for \(FO_{3}\) in the 33-node AC MG operating in grid-connected mode.  
Figure 17: Maximum voltage variations for the 33-node AC distribution network operating in grid-connected mode.  
Figure 19: Active power dispatched by the WTs within the 33-node AC MG operating in grid-connected mode.  
Figure 20: Reactive power dispatched by the WTs within the AC MG with 33 nodes during grid-connected operation.  
Figure 18: Line loadability for the 33-node AC MG operating in grid-connected mode.