# Adaptive PI Control Strategy for Optimal Microgrid Autonomous Operation
## 6 Description and Outcomes of the Simulations
### Incident 3 (A Three-Phase Fault under Islanding Mode)  
In Incident 3, the MGD runs steadily in the islanding operation. At t = 4 s, a three-phase fault occurs at PCC 1 and then returns to its previous case at t = 4.1 s. Table 7 shows the finest PI gains for the DGRs with EBSABA, LMSRE, PSO, and SFO techniques. Figure 8a-c shows the DGR's voltages with EBSABA and the other methods. Figure 9a-c displays the complex power in the DGRs with EBSABA, LMSRE, PSO, and SFO techniques. It is essential to keep in mind that in Figure 8a, the suggested controller's T\({}_{\text{st}}\) is lowered to 22 ms according to the 2% criteria, and the Est is 0.19%. As a result, the introduced optimizer provides the least MPOST, the fastest damping, and the most appropriate Est. It is worth noting that the EBSABA outperforms the LMSRE, PSO, and SFO approaches in MPUST, MPOST, T\({}_{\text{st}}\), and E\({}_{\text{st}}\), proving the rigor, cogency, and practicality of the suggested EBSABA over the LMSRE, PSO, and SFO techniques. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **EBSABA** & **LMSRE** & **SFO** & & **PSO** \\ \hline \multicolumn{6}{c}{Incident 2 DGR 1} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{1}\) & 6.469 & U\({}_{1}\) & 1.924 \\ \cline{4-6}  & & & U\({}_{2}\) & 0.0125 & U\({}_{2}\) & 0.0118 \\ \cline{4-6}  & & & U\({}_{3}\) & 2.2793 & U\({}_{3}\) & 2.3123 \\ \cline{4-6}  & & & U\({}_{4}\) & 0.238 & U\({}_{4}\) & 0.2315 \\ \cline{4-6}  & MPUST & 0.478\% & 1.91\% & 2.205\% & 3.27\% \\ \hline MPOST & 0.9745\% & 2.216\% & 2.967\% & 3.532\% \\ \hline T\({}_{\text{st}}\) & zero & 0.4015 s & 0.4331 s & 0.453 s \\ \hline E\({}_{\text{st}}\) & 0.21\% & 0.425\% & 0.453\% & 0.496\% \\ \hline \multicolumn{6}{c}{Incident 2 DGR 2} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{5}\) & 6.0246 & U\({}_{5}\) & 1.4025 \\ \cline{4-6}  & & & U\({}_{6}\) & 0.0095 & U\({}_{6}\) & 0.0103 \\ \cline{4-6}  & & & U\({}_{7}\) & 1.8614 & U\({}_{7}\) & 1.7983 \\ \cline{4-6}  & & & U\({}_{8}\) & 0.2074 & U\({}_{8}\) & 0.1999 \\ \hline MPUST & 0.461\% & 1.821\% & 2.15\% & 3.234\% \\ \hline MPOST & 0.96\% & 2.202\% & 2.921\% & 3.457\% \\ \hline T\({}_{\text{st}}\) & zero & 0.4003 s & 0.4284 s & 0.447 s \\ \hline E\({}_{\text{st}}\) & 0.203\% & 0.412\% & 0.441\% & 0.491\% \\ \hline \multicolumn{6}{c}{Incident 2 DGR 3} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{9}\) & 5.4974 & U\({}_{9}\) & 0.8995 \\ \cline{4-6}  & & & U\({}_{10}\) & 0.0069 & U\({}_{10}\) & 0.0656 \\ \cline{4-6}  & & & U\({}_{11}\) & 1.5784 & U\({}_{11}\) & 1.4879 \\ \cline{4-6}  & & & U\({}_{12}\) & 0.1753 & U\({}_{12}\) & 0.1625 \\ \hline MPUST & 0.454\% & 1.813\% & 2.07\% & 3.211\% \\ \hline MPOST & 0.952\% & 2.197\% & 2.906\% & 3.436\% \\ \hline T\({}_{\text{st}}\) & zero & 0.3941 s & 0.4233 s & 0.418 s \\ \hline E\({}_{\text{st}}\) & 0.201\% & 0.403\% & 0.432\% & 0.486\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The outcomes of the three DGRs for Incident 2 with EBSABA, LMSRE, PSO, and SFO techniques. Figure 6: **(a–c)** The reference voltages for Incident 2 in the three DGRs with EBSABA, LMSRE, PSO, and SFO techniques. Figure 7: **(a-c)** The complex load powers for Incident 2 in the three DGRs with EBSABA, LMSRE, PSO, and SFO.