# A Method of Discriminating Between Power Swings and Faults Based on Principal Component Analysis
## 4 Simulation Tests  
### Test Results Based on Two-End System  
For testing the performance of the proposed method, a two-end system is built in PSCAD/EMTDC. The sketch of the system is shown in Figure 6. In this figure, \(\dot{E}_{\rm m}\) and \(\dot{E}_{\rm n}\) are the equivalent power sources at two ends, where \(\dot{E}_{\rm m}=500\)\(\angle\)33 \({}^{\circ}\)kV and \(\dot{E}_{\rm n}=500\)\(\angle\) 0 \({}^{\circ}\)kV. \(Z_{\rm m}\) and \(Z_{\rm n}\) are the equivalent impedances of the systems on the two sides, where \(Z_{\rm m}=Z_{\rm n}=28.07\)\(\angle\) 86 \({}^{\circ}\Omega\). M is the measuring point. The length of the transmission line is 300 km, and the detail of its parameters are given in Table 1.  
During the simulation, the power frequency is 50 Hz and the sampling frequency is 4 kHz. The value of the threshold \(C_{\rm set}\) is set to avoid the fault occurring at the end of the line, while considering a certain margin upwards. Since the value of \(C_{\rm avr}\) after a three-phase shorting fault occurs at the end of the line is 61.57, \(C_{\rm set}\) in (19) is set to 70. In addition, the value of the threshold \(P_{\rm set}\) is set based on the corresponding calculation result of \(\Delta P\) under the fault occurring at the end of the line, while considering a certain margin downwards. Since the value of \(\Delta P\) after a three-phase shorting fault occurs at the end of the line during a power swing is 204.89, \(P_{\rm set}\) is set to 100. In addition, \(I_{\rm set}\) in (22) is set to 1.1 times the peak value of the current during normal operation. Based on the two-end system shown above, power swings of different oscillation frequencies and different three-phase shorting fault situations are simulated to test the performance of the proposed method. The frequency of the system on the right side is gradually changed from 50 Hz to 48 Hz, resulting in a power swing with an oscillation frequency of 2 Hz. Taking the distance protection with directional circle characteristics as an example, the setting value of the distance protection I is set to 80% of the line length. The impedance circle is shown in Figure 7. The blue line in the figure indicates the trajectory of the measured impedance after the power swing occurs, with the direction of movement being from right to left. From Figure 7, it can be seen that the measured impedance enters the operation zone of Zone I of the distance protection, and remains there for 138.3 ms after the power swing, resulting in a mal-operation of the distance protection. Therefore, there is a necessity to identify oscillations to prevent mal-operation of the distance protection. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Positive Sequence** & **Zero Sequence** \\ \hline \(R\) (\(\Omega\))/km) & 0.0196 & 0.1828 \\ \(L\) (mH/km) & 0.8917 & 2.739 \\ \(C\) (\(\mu\)F/km) & 135 & 92 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of transmission line. Figure 6: Sketch of simulation system. Figure 8 shows the waveform of the three-phase voltage under the power swing of 2 Hz. The corresponding value of \(C\) is shown in Figure 9. The power swing occurs at 1.2 s; 6 ms later (1.206 s, \"\(t_{1}\)\" in Figure 9), the instantaneous current value exceeds the set threshold, and PSB is activated. After a delay of 10 milliseconds (1.216 s, \"\(t_{2}\)\" in Figure 9), based on the three-phase voltage data of three sampling points after \(t_{2}\) and matrix \(P\) shown in (14), the horizontal and vertical coordinates \(x_{\text{U}}\) and \(y_{\text{U}}\) in the new two-dimensional coordinate system, corresponding to the three-phase voltage, can be obtained. After obtaining \(x_{\text{U}}\) and \(y_{\text{U}}\), they can be substituted into (18) to obtain index \(C\) as 95.85, 95.77, and 95.70. According to the definition of \(C_{\text{avr}}\) in (19), the value of \(C_{\text{avr}}\) is 95.77. In such a case, (19) is satisfied, and the PSBU will block the protection relay. More test results are shown in Tables 2-4.