# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
## 4 Simulation and Experimental Results  
In this section, we account how simulation and experimental tests were carried out to validate the performance of the proposed control method and compare the results with the conventional one. The simulation model was prepared in MATLAB/Simulink with parameters as close as possible to the real power system. The control and system parameters are given in Table 3.  
Based on that, various analyses and tests were carried out to reveal system performance under different conditions, which might not be possible by experiments due to some practical limitations (e.g., large inductors values, power, and current limitations). Finally, analytical and simulation results were validated by conducting experiments on a laboratory setup. It is worth noting that a downscaled power system is designed to emulate weak grid  
Figure 10: Impact of grid SCR variations on critical mode locations of a grid-connected VSC in the complex s-plane (\(P=P_{n}\) and \(f_{PLL}=10\) Hz (conventional controller) and \(50\) Hz (proposed controllers)). \begin{table}
\begin{tabular}{l l l l} \hline \hline \multicolumn{2}{c}{**Power System Parameters**} & \multicolumn{2}{c}{**Control Parameters**} \\ \hline Nominal power (\(P_{n}\)) & 10 (kW) & \multicolumn{2}{c}{Conventional control method} \\ \hline Nominal line voltage (\(v_{g}\)) & 400 (V) & \(k_{pc}\), \(k_{i\epsilon}\), & 9.425, 4.4 \(\times\) 10\({}^{3}\) \\ \hline Grid frequency (\(f_{1}\)) & 50 (Hz) & \(k_{pp}\), \(k_{ip}\) & 0.22, 9.9 \\ \hline Filter capacitor (\(C_{f}\)) & 10 (\(\mu\)F) & \(k_{pu}\), \(k_{ii}\) & 0, 4.8 \\ \hline Inverter-side inductor (\(L_{d}\)) & 2 (mH) & \(k_{a}\), \(\omega_{a}\) & 1, 6.6 \(\times\) 10\({}^{3}\) \\ \hline Grid-side inductor (\(L_{g}\)) & 5–50 (mH) & \(k_{pd}\), \(k_{id}\) & 0.13, 2.91 \\ \hline Grid SCR & 1–10 & \(k_{ig}\) & 6.1 \\ \hline The series resistance of \(C_{f}\) (\(r_{c}\)) & 0.5 (m\(\Omega\)) & \multicolumn{2}{c}{Proposed control method} \\ \hline The series resistance of \(L_{f}\) (\(r_{g}\)) & 1 (m\(\Omega\)) & 1.5, 1 \(\times\) 10\({}^{4}\) & \(r,q_{1}\) \\ \hline The series resistance of \(L_{g}\) (\(r_{g}\)) & 1 (m\(\Omega\)) & 1, 5 & \(q_{2}\), \(q_{3}\) \\ \hline DC-link capacitor (\(C_{dc}\)) & 1.5 [mF] & 0.22, 9.9 & \(k_{pp}\), \(k_{ip}\) \\ \hline DC-link voltage (\(v_{dc}\)) & 700 (V) & \multicolumn{2}{c}{Control delay} \\ \hline Sampling and switching frequencies & 10 (kHz) & 150 (\(\mu\)s) & \(T_{d}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main system and control parameters. conditions and reduce the required inductors in practice. Table 4 shows the parameters that differ from the main circuit parameters. The common parameters by the main circuit are not repeated in this table. The experimental setup includes two 5 kW Danfoss voltage source converters operating back-to-back, LCL filters, a grid simulator (Chroma 61845), and a DS1007 dSPACE system, as shown in Figure 11.  
The first VSC acts as a constant power source, emulating a primary source such as PV or wind turbine and supplies the second three-phase grid-connected VSC. The second VSC is connected to a grid simulator through an LCL filter and transfers the received power to the power grid. It contains CC, VFF, PLL, AVC, and DVC. A DS1007 dSPACE system platform is used to realize both control methods and drive VSCs. Figure 12 shows the steady-state performance of the proposed control method under strong and ultra-weak grid conditions (SCR = 10 and 1). This figure confirms a robust and stable operation over a wide range of grid SCR variations, especially critical scenario (SCR = 1), while a high-performance PLL is implemented. The system responses of the conventional and the proposed control methods under different grid SCRs are shown in Figure 13. As it can be seen, the performance of the conventional control method is degraded under a weaker grid, and it becomes unstable under the weakest one (SCR = 1.25). In comparison, the proposed control method can provide a stable response under weak grids.