## 5 Results and Discussion
### Simulation Results  
To examine and verify the impact of the optimal controllers' parameters of the CPL, PLL, droop, and DGs on the MG stability, different disturbances have been applied. Firstly, a three-phase fault has been applied at CPL3. Figure 9a-d illustrate the active and reactive powers, output voltage, and output current responses of all DGs, respectively, while Figure 9e depicts the DC output voltage of the CPLs. At t = 3.3 s, the measured active powers of DG1, DG2, and DG3 have been increased from 1.4 to 2.4 p.u., from 0.4 to 1.5 p.u. and from 0.4 to 2.48 p.u., respectively. While the measured reactive powers of DG1, DG2, and DG3 have been increased from 0.384 to 1.14 p.u., from \(-\)0.04 to 0.435 p.u., and from 0.0 to 0.54 p.u., respectively. The measured d-axis voltages of DG1, DG2, and DG3 have been increased from 1.0 to 1.14, 1.15, and 1.28 p.u. respectively. The d-axis of the measured output currents of DG1 has been increased from 1.5 to 2.45 p.u. while the d-axis of the measured output currents of DG2 and DG3 have been increased from 0.5 to 1.6 and 3.48 p.u., respectively. The DC voltages of the three CPLs have been increased from 1.17 to 1.47, 1.39, and 1.38 p.u., respectively. As shown in Figure 9, with the high penetration level of CPLs, the system is getting stable within 2 s after the transient has been settled. The proposed controller needs this time to return back to the stable mode because of the high number of CPLs. In terms of overshoot and settling time, the results impressively show an enhanced and adequate damping MG performance under this fault. In addition, the DGs output powers have been tightly increased after occurring the fault directly. The three-phase fault has been relocated at CPL1 to check the controller effectiveness. Figure 10a,b illustrates the responses of the active power of the three DGs and DC output voltage of the CPLs, respectively. At t = 3.3 s, the measured active powers of DG1, DG2, and DG3 have been increased from 1.44 to 3.4 p.u., from 0.44 to 2.7 p.u., and from 0.44 to 1.5 p.u., respectively. Meanwhile, the DC voltages of the three CPLs have been increased from 1.17 to 1.45, 1.38, and 1.37 p.u., respectively. The results display satisfactory damping characteristics of the proposed controller for this disturbance. Moreover, Figure 11 illustrates the MG response when the voltage at CPL3 has been stepped down to 0.25 p.u. The measured active powers of DG1, DG2, and DG3 have been increased from 1.44 to 2.3 p.u., from 0.44 to 1.5 p.u., and from 0.44 to 2.45 p.u., respectively. Meanwhile, the DC voltages of the three \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{5}{c}{**Microgrid Parameters**} \\ \hline Parameter & Value & Parameter & Value \\ \(f_{s}\) & 8 kHz & \(V_{n}\) & 381 V \\ \(L_{f}\) & \(1.35\) mH & \(L_{c}\) & 0.35 mH \\ \(C_{f}\) & \(50\times 10^{-6}\) F & \(C_{b}\) & \(50\times 10^{-6}\) F \\ \(r_{f}\) & \(0.1\,\Omega\) & \(r_{c}\) & 0.03 \(\Omega\) \\ \(\omega_{n}\) & \(314.16\) rad/s & \(\omega_{c}\) & 31.416 rad/s \\ \(r_{1}+jx_{1}\) & \((0.23+j0.1)\,\Omega\) & \(r_{2}+jx_{2}\) & \((0.35+j0.58)\,\Omega\) \\ \hline \multicolumn{5}{c}{**CPL Parameters**} \\ \hline \(L_{f}\) & \(2.3\) mH & \(L_{c}\) & 0.93 mH \\ \(C_{f}\) & \(8.8\times 10^{-6}\) F & \(r_{c}\) & 0.03 \(\Omega\) \\ \(r_{f}\) & \(0.1\,\Omega\) & \(C_{k}\) & \(2040\times 10^{-6}\) F \\ \(R_{dc}\) & \(72\,\Omega\) & \(C_{k}\) & \(2040\times 10^{-6}\) F \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters.