# A Method of Discriminating Between Power Swings and Faults Based on Principal Component Analysis
## 4 Simulation Tests
### Comparison and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(f_{\text{PS}}\) (Hz)} & \multirow{2}{*}{**SNR (dB)**} & \multicolumn{3}{c}{**Proposed Method**} & \multicolumn{3}{c}{**Method in [27]**} \\ \cline{3-8}  & & \(\mathbf{C_{\text{avr}}}\) & **R** & **T (ms)** & **DI** & **R** & **T (ms)** \\ \hline
7.00 & - & 85.24 & \(\surd\) & 10.07 & & \(\surd\) & 10.09 \\
5.00 & - & 88.06 & \(\surd\) & 10.09 & 2.28 \(\times\) 10\({}^{-5}\) & \(\surd\) & 10.08 \\
2.00 & - & 95.55 & \(\surd\) & 10.09 & 1.65 \(\times\) 10\({}^{-5}\) & \(\surd\) & 10.10 \\
1.00 & - & 97.44 & \(\surd\) & 10.07 & 1.50 \(\times\) 10\({}^{-5}\) & \(\surd\) & 10.09 \\
0.40 & - & 98.24 & \(\surd\) & 10.08 & 1.49 \(\times\) 10\({}^{-5}\) & \(\surd\) & 10.10 \\
7.00 & 50 & 85.29 & \(\surd\) & 10.07 & 0.03 & \(\times\) & 10.07 \\
7.00 & 40 & 85.83 & \(\surd\) & 10.08 & 0.25 & \(\times\) & 10.08 \\
7.00 & 30 & 83.06 & \(\surd\) & 10.08 & 3.82 & \(\times\) & 10.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Test results of PSD of proposed method and method in [27]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Distance (Hz)**} & \multirow{2}{*}{**SNR (dB)**} & \multicolumn{3}{c}{**Proposed Method**} & \multicolumn{3}{c}{**Method in [27]**} \\ \cline{3-8}  & & \(\mathbf{C_{\text{avr}}}\) & **R** & **T (ms)** & **DI** & **R** & **T (ms)** \\ \hline
10 & - & 1.57 & \(\surd\) & 10.09 & 0.01 & \(\surd\) & 10.09 \\
70 & - & 16.90 & \(\surd\) & 10.09 & 0.76 & \(\surd\) & 10.08 \\
150 & - & 36.10 & \(\surd\) & 10.08 & 0.31 & \(\surd\) & 10.10 \\
230 & - & 49.32 & \(\surd\) & 10.09 & 0.42 & \(\surd\) & 10.09 \\
290 & - & 58.05 & \(\surd\) & 10.09 & 0.47 & \(\surd\) & 10.10 \\
290 & 50 & 58.12 & \(\surd\) & 10.09 & 0.63 & \(\times\) & 10.07 \\
290 & 40 & 58.41 & \(\surd\) & 10.09 & 1.63 & \(\times\) & 10.08 \\
290 & 30 & 57.46 & \(\surd\) & 10.08 & 14.26 & \(\times\) & 10.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Test results under different fault situations of proposed method and method in [27]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**\(f_{\text{PS}}\) (Hz)**} & \multirow{2}{*}{**Distance (km)**} & \multirow{2}{*}{**\(\mathbf{\delta}\)**} & \multirow{2}{*}{**SNR (dB)**} & \multirow{2}{*}{**\(\mathbf{\Delta P}\)**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**T (ms)**} \\ \cline{3-8}  & & & & & & & \\ \multirow{6}{*}{7.00} & 10 & 50\({}^{\circ}\) & - & 85.24 & \(\surd\) & 0.5 \\  & 150 & 50\({}^{\circ}\) & - & 88.06 & \(\surd\) & 0.75 \\  & 290 & 50\({}^{\circ}\) & - & 94.36 & \(\surd\) & 1.25 \\  & 150 & 120\({}^{\circ}\) & - & 95.55 & \(\surd\) & 0.75 \\
7.00 & 150 & 180\({}^{\circ}\) & - & 96.77 & \(\surd\) & 0.75 \\  & 150 & 220\({}^{\circ}\) & - & 97.44 & \(\surd\) & 0.75 \\  & 150 & 120\({}^{\circ}\) & 50 & 98.30 & \(\surd\) & 0.75 \\  & 150 & 120\({}^{\circ}\) & 40 & 98.24 & \(\surd\) & 0.75 \\  & 150 & 120\({}^{\circ}\) & 30 & 98.50 & \(\surd\) & 0.50 \\ \hline \hline \multirow{6}{*}{0.40} & 10 & 50\({}^{\circ}\) & - & 83.51 & \(\surd\) & 0.50 \\  & 150 & 50\({}^{\circ}\) & - & 84.19 & \(\surd\) & 0.75 \\ \cline{1-1}  & 290 & 50\({}^{\circ}\) & - & 84.89 & \(\surd\) & 1.00 \\ \cline{1-1}  & 150 & 120\({}^{\circ}\) & - & 83.17 & \(\surd\) & 0.75 \\ \cline{1-1}  & 150 & 180\({}^{\circ}\) & - & 83.85 & \(\surd\) & 1.50 \\ \cline{1-1}  & 150 & 220\({}^{\circ}\) & - & 84/89 & \(\surd\) & 0.75 \\ \cline{1-1}  & 150 & 120\({}^{\circ}\) & 50 & 85.24 & \(\surd\) & 0.75 \\ \cline{1-1}  & 150 & 120\({}^{\circ}\) & 40 & 83.85 & \(\surd\) & 0.75 \\ \cline{1-1}  & 150 & 120\({}^{\circ}\) & 30 & 84.53 & \(\surd\) & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Test results for PSD of proposed method. identify power swings of different oscillation frequencies and faults with different fault distances in about 10 ms after the power swing or the fault occurs. In addition, it can be seen that the proposed method is less affected by measurement noise.