## 5 Results and Discussion
### Simulation Results
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Power Sharing Parameters of the Three DG Units**} \\ \hline \multirow{3}{*}{\(m_{p}\)} & \(3.79404\times 10^{-7}\) & \multirow{3}{*}{\(n_{q}\)} & \(9.36593\times 10^{-5}\) \\ \cline{2-3}  & \(6.75934\times 10^{-7}\) & & \(1.86121\times 10^{-5}\) \\ \cline{2-3}  & \(1.71857\times 10^{-7}\) & & \(3.21349\times 10^{-5}\) \\ \hline \multirow{3}{*}{\(m_{d}\)} & \(0.2957\times 10^{-5}\) & & \(0.2618\times 10^{-6}\) \\ \cline{2-3}  & \(0.1572\times 10^{-5}\) & & \(0.2374\times 10^{-6}\) \\ \cline{2-3}  & \(-0.0030\times 10^{-5}\) & & \(0.2374\times 10^{-6}\) \\ \hline \multicolumn{3}{c}{**PLL Parameters**} \\ \hline \(K_{p}{}^{PLL}\) & \(1\) & \(K_{l}{}^{PLL}\) & \(50\) \\ \hline \multicolumn{3}{c}{**Controller Parameters of the Three DG Units**} \\ \hline Parameter & Value & Parameter & Value \\ \hline \multirow{3}{*}{\(K_{pc}\) (Amp/Watt)} & \(1.19585\) & \multirow{3}{*}{\(K_{pc}\) (Amp/Watt)} & \(44.1091\) \\ \cline{2-3}  & \(1.43531\) & & \(31.8037\) \\ \cline{2-3}  & \(1.6380\) & & \(40.8816\) \\ \hline \multirow{3}{*}{\(K_{ix}\) (Amp/Joule)} & \(4.4568\) & & \(35.8275\) \\ \cline{2-3}  & \(6.17159\) & \multirow{3}{*}{\(K_{i}\) (Amp/Joule)} & \(26.904\) \\ \cline{2-3}  & \(-0.69434\) & & \(13.4463\) \\ \hline \multicolumn{3}{c}{**CPL Parameters**} \\ \hline \(K_{p\omega\_{,AL}}\) (Amp/Watt) & \(0.331792\) & \(K_{p\omega\_{,AL}}\) (Amp/Watt) & \(33.2732\) \\ \hline \(K_{ip\omega\_{,AL}}\) (Amp/Joule) & \(4.33114\) & \(K_{i\omega\_{,AL}}\) (Amp/Joule) & \(-4.61844\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal parameters. CPLs have been increased from 1.17 to 1.44, 1.37, and 1.35 p.u., respectively. The output responses display the satisfactory damping characteristics of the proposed controller. The DGs output power responses are displayed in Figure (a)a, while Figure (b)b depicts the DC voltage response of CPLs. It has been demonstrated that the system oscillations are highly damped, which shows the effectiveness of the proposed method. Figure 9: Cont. Figure 9: Microgrid response with a three-phase fault at CPL3. (**a**) Measured active powers of DGs. (**b**) Measured reactive powers of DGs. (**c**) Measured d-axis voltages of DGs. (**d**) Measured d-axis currents of DGs. (**e**) DC voltages of CPLs. Additionally, at t = 3.3 s, a three-phase fault is located at line 2. The line has been recovered at t = 3.6 s. During the fault, CPL1 and CPL2 have been fed from DG1 and DG2, while CPL3 has been fed from DG3. The system is getting stable after this disturbance. The DGs capability to support the loads is clearly illustrated in Figure 12. The DGs output power response is depicted in Figure 12a, while Figure 12b shows the DC voltage response of the CPLs. With the optimal settings, the DC reference voltage of CPL1 is stepped up to 1.1 p.u. The proposed controller has been investigated through the time domain simulation. The DGs output power responses are displayed in Figure  
Figure 11: Microgrid response with a voltage step change at CPL3. (**a**) Measured active powers of DGs. (**b**) DC voltages of CPLs. Figure 12: Microgrid response with a fault at TL2. (**a**) Measured active powers of DGs. (**b**) DC voltages of CPLs. For more investigations, the MG performance has been tested when DG1 has been lost. In this case, all CPLs are fed from DG2 and DG3. Figure 14a,b proves the responses of the DGs output power and DC voltage of CPLs for this disturbance. The output responses display the satisfactory damping characteristics of the proposed controller. The output responses show the controller capability for making the system stable after getting disturbance in both cases. With the proposed controller, the MG became stable after getting disturbed and has better dynamic performance. It can be seen from the different applied disturbances that despite variations in the DGs or CPLs side, the system is highly stable with no oscillatory behavior.