## 5 Results and Discussion
### Validating the Proposed Methodology on a 69-Node MG
#### 5.3.1 PGA Performance in the Grid-Connected 69-Node MG  
Table 8 presents the results obtained by applying the PGA to the 69-node MG operating in grid-connected mode. This table includes the different objective functions used in this work, along with the base cases for each of the seven days of the week and the corresponding results achieved by PGA on each day. Regarding \(FO_{1}\), PGA achieved a weekly average cost reduction of USD 8180.6846. When compared with the base case, this corresponds to an average economic improvement of 114.8964%, with daily absolute reductions ranging from USD 8122.9397 to USD 8315.0187. The standard deviation throughout the week is approximately 1.9558%, indicating PGA's stable and consistent performance under varying operating conditions. It is worth noting that reduction values exceeding 100% indicate that the MG not only satisfies its own energy demand but also generates surplus energy that can be exported to the main grid. This surplus leads to additional economic benefits, thereby enhancing the overall profitability of wind-based MG operations. Such outcomes are directly related to the interaction between power demand patterns and the availability of wind generation within the MG, which, under favorable conditions, allows for both self-sufficiency and energy sales. In addition, the average execution time required by the proposed methodology to solve the cost minimization problem (\(FO_{1}\)) is 437.3418 s per day, i.e., approximately 7.2890 min, which demonstrates its practicality for day-ahead or short-term operation planning. As for \(FO_{2}\), PGA achieved a weekly average reduction of 1592.3923 kWh compared with the base scenario. This corresponds to an average improvement of 92.5971%, with daily absolute reductions ranging from 1455.7406 kWh to 1643.6205 kWh. The standard deviation is approximately 0.2696%, indicating a highly stable and consistent performance under varying load and wind generation conditions. This high level of loss reduction significantly improves the overall efficiency of the MG, minimizing unnecessary energy dissipation along the distribution lines. The consistency observed throughout the week reinforces PGA's robustness in managing technical constraints and optimizing power flows, even when the system operates in different modes or under fluctuating generation profiles. Moreover, the average computation time required to solve the energy losses minimization problem was 432.1599 s per day, equivalent to approximately 7.2027 min. Finally, regarding \(FO_{3}\), PGA reported a weekly average reduction of 10782.4538 \(kgCO_{2}\) compared with the base scenario. This corresponds to an average improvement of 119.9285%, with daily absolute reductions ranging from 10720.0819 to 10877.8816 \(kgCO_{2}\) \begin{table}
\begin{tabular}{l l c c c c c c c} \hline \hline
**Objective Function** & **Case** & **Monday** & **Tuesday** & **Wednesday** & **Thursday** & **Friday** & **Saturday** & **Sunday** \\ \hline \multirow{3}{*}{\(FO_{1}\) (USD)} & Base case & 7210.8434 & 7210.8434 & 7066.6091 & 7210.8434 & 7210.8434 & 7063.7285 & 6878.1870 \\  & PGA & \(-\)912.9585 & \(-\)1104.1753 & \(-\)1048.6528 & \(-\)979.4717 & \(-\)912.0963 & \(-\)1233.0386 & \(-\)1222.5005 \\  & Time & 442.7379 & 435.6855 & 437.8046 & 440.8969 & 437.0812 & 432.0471 & 435.1390 \\ \hline \multirow{3}{*}{\(FO_{2}\) (kWh)} & Base Case & 1771.9870 & 1771.9870 & 1690.1724 & 1771.9870 & 1771.9870 & 1678.4614 & 1580.8471 \\  & PGA & 133.4848 & 128.3665 & 120.6716 & 131.1342 & 133.4666 & 118.4529 & 125.1065 \\  & Time & 445.6671 & 439.2460 & 421.9443 & 436.7708 & 437.915 & 411.7367 & 432.2634 \\ \hline \multirow{3}{*}{\(FO_{3}\) (\(kgCO_{2}\))} & Base case & 9105.5029 & 9105.5029 & 8923.3709 & 9105.5029 & 9105.5029 & 8919.7335 & 8685.4406 \\  & PGA & \(-\)1624.3047 & \(-\)1730.2292 & \(-\)1797.4812 & \(-\)1772.3787 & \(-\)1627.1358 & \(-\)1940.4494 & \(-\)2034.6413 \\ \cline{1-1}  & Time & 438.4596 & 432.3273 & 436.4479 & 436.9342 & 436.3788 & 429.8061 & 430.5589 \\ \hline \hline \end{tabular}
\end{table}