# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
## 4 Simulation and Experimental Results
The simulation results also confirm the robustness analysis in the previous section. \begin{table}
\begin{tabular}{l l l l} \hline \hline \multicolumn{2}{c}{**Power System Parameters**} & \multicolumn{2}{c}{**Control Parameters**} \\ \hline Nominal power (\(P_{n}\)) & 5 (kW) & Conventional control method \\ \hline Nominal line voltage (\(v_{g}\)) & 172 (V) & \(k_{pc},k_{ic}\) & 7.068, 3.3 \(\times\) 10\({}^{3}\) \\ \hline Filter capacitor (\(C_{f}\)) & 30 (\(\mu\)F) & \(k_{pp},k_{ip}\) & 0.51, 22.95 \\ \hline Inverter-side inductor (\(L_{t}\)) & 1.5 (mH) & \(k_{pa},k_{ia}\) & 0, 30 \\ \hline Grid-side inductor (\(L_{g}\)) & 1.9–19 (mH) & \(k_{ig}\) & 3 \\ \hline DC-link voltage (\(v_{dc}\)) & 600 (V) & \multicolumn{2}{c}{Proposed control method} \\ \hline \(r,q_{1}\) & \(2,1\times 10^{4}\) & \(k_{pp},k_{ip}\) & 0.51, 22.95 \\ \hline \multicolumn{2}{c}{} & \(q_{2},q_{3}\) & 1, 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Downscaled system and control parameters. Figure 11: Experimental setup. The system performance under different PLL bandwidths is investigated in Figure 14. As shown, under the conventional control method, it is impossible to implement fast PLL in weak grids. In contrast, the proposed control method can facilitate the implementation of high-performance and fast PLL. Moreover, the system is stable over a wide range of PLL bandwidth selections. Therefore, the PLL bandwidth can be selected based on the other performance requirements, such as fault ride-through (FRT) capability, large-signal stability, and ancillary services such as virtual inertia, and not only restricted limitations imposed by small-signal stability. Figure 12: Time-domain simulations showing steady-state performance of the proposed state-feedback control method under different grid SCRs (\(P=10\) kW, \(f_{PLL}=50\)Hz): (**a**) SCR = 1 and (**b**) SCR = 10. Figure 13: Time-domain simulations showing the system response under different grid SCR (SCR = 1.5, 1.35, and 1.25; \(P=10\) kW): (**a**) the conventional control method and (**b**) the proposed control method. The dynamic response of the VSC under 20% voltage sag at the grid voltage is depicted in Figure 15.  
The conventional control method has a larger rise time. However, it can be expected when outer voltage control loops are considered, and the system operates under a very weak grid connection, as discussed in References [23; 32], where a rise time equal to or smaller than 100 ms was suggested for AVC as a compromise between the system stability and performance. In contrast, the proposed control method shows an excellent transient performance and disturbance-rejection capability that are even higher than the required levels by standards. Furthermore, the transient performance of both control methods under step changes in the dc voltage reference is shown in Figure 16. Both control methods can provide a good transient response; however, the proposed one can respond a little faster with lower oscillations. Finally, the feasibility of the proposed control method is examined in practice. The performance of both control methods under weak grid conditions (SCR = 1.21) is shown in Figures 17 and 18. Experiments show their capability under different PLL bandwidths and 20% voltage sag. As shown, the proposed control method can employ a fast and high-performance PLL under weak grids, while the conventional one cannot. Moreover, the conventional one becomes unstable under a 20% voltage sag. In contrast, the proposed control method has an excellent disturbance rejection and fault ride-through capability. Figure 14: Time-domain simulations showing the system response under different PLL bandwidths (\(P=10\) kW, SCR = 1.5): (**a**) the conventional control method and (**b**) the proposed control method. Figure 15: Time-domain simulations showing the system response under 20% voltage sag at the grid voltage (\(P=10\) kW, SCR = 2): (**a**) the conventional control method and (**b**) the proposed control method.