# Adaptive PI Control Strategy for Optimal Microgrid Autonomous Operation
## 6 Description and Outcomes of the Simulations
### Incident 2 (Load Variations under Islanding Mode)  
In the second Incident, the MGD runs steadily in the islanding operation. The MGD is first designed with a complex load, as shown in Table 1. Then, R\({}_{12}\) is raised to 300 \(\Omega\) at t = 3 s and returned to its previous value of 150 \(\Omega\) at t = 3.4 s. Table 6 shows the optimal PI gains for the DGRs with EBSABA, LMSRE, PSO, and SFO techniques. Figure 6a-c shows the DGR's voltages with EBSABA and the other methods. Figure 7a-c displays the complex power in the DGRs with EBSABA, LMSRE, PSO, and SFO techniques. It is essential to remember that the MPUST for the load variation Incident of the given approach is less than 0.5% in Figure 6a. Moreover, the suggested controller's T\({}_{\text{st}}\) is lowered to zero seconds according to the 2% criteria, and the E\({}_{\text{st}}\) is 0.21%. As a result, the presented optimizer provides the least overshoots, the fastest damping, and the most appropriate E\({}_{\text{st}}\). It is important to remember that in Figure 6a, the active power of DGR1 is lowered to 1.3 MW and effectively returned to the previous level at t = 3.4 s. Nevertheless, the powers of  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **EBSABA** & **LMSRE** & **SFO** & & **PSO** \\ \hline \hline \multicolumn{7}{c}{Incident 1 DGR 1} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{1}\) & 6.421 & U\({}_{1}\) & 2.1472 \\ \cline{3-6}  & & & U\({}_{2}\) & 0.0054 & U\({}_{2}\) & 0.00572 \\ \cline{3-6}  & & & U\({}_{3}\) & 2.952 & U\({}_{3}\) & 1.6791 \\ \cline{3-6}  & & & U\({}_{4}\) & 0.3472 & U\({}_{4}\) & 0.3392 \\ \hline MPUST & 8.21\% & 7.93\% & & 12.93\% & & 20.4\% \\ \hline MPOST & 0\% & 0\% & & 0\% & & 0\% \\ \hline T\({}_{\text{st}}\) & 0.037 s & 0.045 s & & 0.0343 s & & 0.0562 s \\ \hline E\({}_{\text{st}}\) & 0.2\% & 0.34\% & & 0.37\% & & 0.42\% \\ \hline \multicolumn{7}{c}{Incident 1 DGR 2} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{5}\) & 5.982 & U\({}_{5}\) & 1.5692 \\ \cline{3-6}  & & & U\({}_{6}\) & 0.0042 & U\({}_{6}\) & 0.00431 \\ \cline{3-6}  & & & U\({}_{7}\) & 2.5082 & U\({}_{7}\) & 1.2342 \\ \cline{3-6}  & & & U\({}_{8}\) & 0.299 & Y\({}_{8}\) & 0.30572 \\ \hline MPUST & 8.1\% & 7.82\% & & 12.54\% & & 20.21\% \\ \hline MPOST & 0\% & 0\% & & 0\% & & 0\% \\ \hline T\({}_{\text{st}}\) & 0.0353 s & 0.0424 s & & 0.0325 s & & 0.0554 s \\ \hline E\({}_{\text{st}}\) & 0.19 \% & 0.32\% & & 0.36\% & & 0.415\% \\ \hline \multicolumn{7}{c}{Incident 1 DGR 3} \\ \hline \multirow{4}{*}{Optimum size} & \multirow{4}{*}{online} & \multirow{4}{*}{online} & U\({}_{9}\) & 5.5343 & U\({}_{9}\) & 1.07 \\ \cline{3-6}  & & & U\({}_{10}\) & 0.00314 & U\({}_{10}\) & 0.0034 \\ \cline{3-6}  & & & U\({}_{11}\) & 2.0991 & U\({}_{11}\) & 0.995 \\ \cline{3-6}  & & & U\({}_{12}\) & 0.2479 & U\({}_{12}\) & 0.259 \\ \hline MPUST & 7.95\% & 7.64\% & & 12.32\% & & 20.05\% \\ \hline MPOST & 0\% & 0\% & & 0\% & & 0\% \\ \hline T\({}_{\text{st}}\) & 0.03495 s & 0.0418 s & & 0.0319 s & & 0.0551 s \\ \hline E\({}_{\text{st}}\) & 0.187\% & 0.312\% & & 0.354\% & & 0.408\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: The outcomes of the three DGRs for Incident 1 with EBSABA, LMSRE, PSO, and SFO techniques.  
the remaining DGRs' have faster damping and lower swings. It is worth noting that the EBSABA outperforms the LMSRE, PSO, and SFO approaches in MPUST, MPOST, Tst, and Est, proving the rigor, cogency, and practicality of the suggested EBSABA over the LMSRE, PSO, and SFO techniques.  
Figure 4: (**a–c**) The reference voltages for Incident 1 in the three DGRs with EBSABA, LMSRE, PSO, and SFO techniques.  
Figure 5: **(a–c)** The complex load powers for Incident 1 in the three DGRs with EBSABA, LMSRE, PSO, and SFO.