## 4 Results of Probabilistic Stability and Performance Assessment
### The Grid SCR Impact on System Stability and Performance
#### 4.1.3 Time-Domain Simulations  
Time-domain simulations based on a switching model were also been conducted to validate the previous analytical results. Figure 6c shows results for an inverter current under a 10% voltage sag at grid voltage in three different cases.  
In the third case, the critical mode met the stability and performance requirements and was far from the unstable area. The inverter current had a good transient response with low overshoot and oscillations. In the second case, the critical mode moved to the right, but the stability and performance criteria were still met; as expected, the oscillations grew.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{6}{c}{**SCR**} \\ \hline Indexes & 10 & 5 & 2.5 & 2 & 1.67 \\ Nominal stability (NS) & + & + & + & + & + \\ Nominal performance (NP) & + & + & + & + & + \\ Robust performance (RS) & + & + & + & + & \(-\) \\ Robust stability (RP) & \(-\) & + & + & + & \(-\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Nominal and robust stability and performance comparison for different grid SCRs (\(P=P_{n}\)).  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**SCR** & **10** & **5** & **2.5** & **2** & **1.67** \\ \hline \multicolumn{6}{c}{\(P=0.5P_{n}\)} \\ \hline \multirow{2}{*}{Damping Factor} & \multirow{2}{*}{AVC (0.99)} & \multirow{2}{*}{AVC (0.97)} & \multirow{2}{*}{DVC (0.1), AVC (0.87)} & PLL (0.56), AVC (0.07), DVC (0.13), & CC (0.46), i\({}_{\text{gold}}\) (0.23), \\  & & & & (0.07), DVC (0.13), & PLL (0.08), AVC \\  & & & & APB (0.22) & (0.06), APB (0.08) \\ \hline \multirow{2}{*}{Damping Ratio} & \multirow{2}{*}{HPF (31), Delay (0.27), i\({}_{\text{dq}}\) (0.16)} & HPF (33), Delay (0.22), i\({}_{\text{dq}}\) (0.2), & HPF (34), Delay (0.22), i\({}_{\text{dq}}\) (0.24), & CC (0.45), i\({}_{\text{gold}}\) (0.24), & CC (0.46), i\({}_{\text{gold}}\) (0.23), \\  & & & \(\
u_{\text{cdq}}\) (0.13) & PLL (0.01), AVC (0.05), & PLL (0.08), AVC \\  & & & & APB (0.07) & (0.06), APB (0.08) \\ \hline \multicolumn{6}{c}{\(P=0.75P_{n}\)} \\ \hline \multirow{2}{*}{Damping Factor} & \multirow{2}{*}{AVC (0.99)} & \multirow{2}{*}{AVC (0.97)} & PLL (0.44), AVC (0.08), DVC (0.17), & PLL (0.42), AVC (0.12), DVC (0.16), & PLL (0.4), AVC (0.15), \\  & & & & APB (0.21) & (0.21) \\ \hline \multirow{2}{*}{Damping Ratio} & \multirow{2}{*}{HPF (31), Delay (0.27), i\({}_{\text{dq}}\) (0.17)} & HPF (33), Delay (0.23), i\({}_{\text{dq}}\) (0.24), & HPF (35), Delay (0.24), & CC (0.46), i\({}_{\text{gold}}\) (0.24), \\  & & & \(\
u_{\text{cdq}}\) (0.14) & i\({}_{\text{dq}}\) (0.24), \(\
u_{\text{cdq}}\) (0.14) & PLL (0.08), AVC (0.05), \\  & & & & (0.05), APB (0.07) & APB (0.08) \\ \hline \multicolumn{6}{c}{\(P=p_{n}\)} \\ \hline \multirow{2}{*}{Damping Factor} & \multirow{2}{*}{AVC (0.99)} & \multirow{2}{*}{AVC (0.97)} & PLL (0.37), AVC (0.13), DVC (0.18), & PLL (0.35), AVC (0.16), DVC (0.16), & PLL (0.33), AVC (0.2), \\  & & & & (0.16), DVC (0.14), APB (0.23) & DVC (0.21) \\ \hline \multirow{2}{*}{Damping Ratio} & \multirow{2}{*}{HPF (31), Delay (0.27), i\({}_{\text{dq}}\) (0.22), i\({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.14)} & HPF (33), Delay (0.22), i\({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.22), \({}_{\text{dq}}\) (0.14) & CC (0.45), i\({}_{\text{gold}}\) (0.24), \\  & & & (0.22), i\({}_{\text{dq}}\)In the first case, the system was still stable but very close to an unstable area; therefore, the oscillations increased dramatically, and there was a high overshoot in the outputs.