## 6 Simulation and Analysis
### Analysis of Simulation Results
#### 6.2.4 Time Synchronization Errors Test  
Feeder B5B6 is used as a protected section to test the performance of the proposed protection against synchronization errors. The protective startup element adopts a fault detection algorithm based on the mutation of phase current. The startup threshold is set to 0.1 times the rated current. The sampling frequency of the protection device is set to 10 kHz, so the startup delay of protection is at least 0.1 ms. The proposed protection utilizes a fault \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fault Type** & **Fault Point** & **Fault Location** & \(\epsilon\) & \(\delta\)**(rad)** & \(K_{\text{sen}}\) & \(Z_{\text{act}}\) & **Trip or Not** \\ \hline \multirow{8}{*}{AB} & \multirow{4}{*}{\(f_{1}\)} & 5\% & 4.53 & \(-\)0.92 & 2.24 & 0.14 & Yes \\  & & 50\% & 2.35 & \(-\)0.63 & 2.04 & 1.19 & Yes \\  & & 95\% & 2.26 & \(-\)0.28 & 3.70 & 0.47 & Yes \\ \cline{2-7}  & & 5\% & 0.86 & \(-\)3.20 & 0.12 & \(-\)0.27 & NO \\  & & 50\% & 0.86 & \(-\)3.20 & 0.12 & \(-\)1.40 & NO \\  & & 95\% & 0.89 & \(-\)3.19 & 0.09 & \(-\)2.49 & NO \\ \cline{2-7}  & & 5\% & 1.60 & 2.94 & 6.19 & \(-\)2.50 & NO \\  & & 50\% & 1.56 & 2.99 & 6.53 & \(-\)1.62 & NO \\  & & 95\% & 1.52 & 3.07 & 6.92 & \(-\)0.15 & NO \\ \hline \multirow{8}{*}{ABg} & \multirow{4}{*}{\(f_{1}\)} & 5\% & 4.22 & \(-\)0.73 & 2.32 & 0.15 & Yes \\  & & 50\% & 2.78 & \(-\)0.27 & 3.03 & 1.21 & Yes \\  & & 95\% & 2.28 & \(-\)0.13 & 2.56 & 0.47 & Yes \\ \cline{2-7}  & & 5\% & 0.87 & \(-\)3.22 & 0.08 & \(-\)0.27 & NO \\  & & 50\% & 0.88 & \(-\)3.20 & 0.10 & \(-\)1.42 & NO \\  & & 95\% & 0.88 & \(-\)3.20 & 0.10 & \(-\)2.29 & NO \\ \cline{2-7}  & & 5\% & 1.49 & 2.97 & 0.29 & \(-\)2.09 & NO \\  & \(f_{3}\) & 50\% & 1.50 & 3.00 & 0.29 & \(-\)1.46 & NO \\  & & 95\% & 1.43 & 3.11 & 0.24 & \(-\)0.29 & NO \\ \hline \multirow{8}{*}{ABC} & \multirow{4}{*}{\(f_{1}\)} & 5\% & 4.94 & 0.11 & 2.15 & 0.64 & Yes \\  & & 50\% & 2.92 & \(-\)5.90 & 2.92 & 0.43 & Yes \\  & & 95\% & 2.36 & \(-\)5.60 & 3.53 & 0.41 & Yes \\ \cline{2-7}  & & 5\% & 0.85 & \(-\)3.24 & 0.14 & \(-\)0.23 & NO \\  & & 95\% & 0.85 & \(-\)3.24 & 0.14 & \(-\)1.49 & NO \\  & & 95\% & 0.86 & \(-\)3.23 & 0.13 & \(-\)2.50 & NO \\ \cline{2-7}  & & 5\% & 1.61 & 3.22 & 6.12 & \(-\)1.77 & NO \\  & & 50\% & 1.55 & 3.34 & 6.62 & \(-\)1.00 & NO \\  & & 95\% & 1.49 & 3.42 & 0.35 & \(-\)0.19 & NO \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Simulation results of the unmeasured load branch test. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fault Resistance** & **Fault Location** & \(\epsilon\) & \(\delta\)**(rad)** & \(K_{\text{sen}}\) & \multicolumn{2}{c}{**Trip or Not**} \\ \cline{3-8}  & 5\% & 6.16 & 1.36 & 1.98 & 1.53 & Yes & Yes \\
25 \(\Omega\) & 50\% & 5.53 & 1.43 & 2.06 & 1.50 & Yes & Yes \\  & 95\% & 2.89 & \(-\)4.37 & 2.94 & 1.16 & Yes & Yes \\ \hline \multirow{4}{*}{50 \(\Omega\)} & 5\% & 9.61 & \(-\)4.44 & 1.76 & 1.35 & Yes & Yes \\  & 50\% & 4.07 & 1.48 & 2.36 & 1.49 & Yes & Yes \\  & 95\% & 1.85 & 1.73 & 4.79 & 1.25 & Yes & Yes \\ \hline \multirow{4}{*}{100 \(\Omega\)} & 5\% & 5.97 & \(-\)1.96 & 2.00 & 1.26 & Yes & Yes \\  & 50\% & 4.57 & \(-\)3.84 & 2.23 & 1.02 & Yes & Yes \\  & 95\% & 2.47 & \(-\)3.67 & 3.37 & 0.71 & Yes & NO \\ \hline \multirow{4}{*}{150 \(\Omega\)} & 5\% & 6.00 & \(-\)4.11 & 2.00 & 1.19 & Yes & Yes \\  & 50\% & 3.28 & \(-\)3.84 & 2.68 & 0.90 & Yes & NO \\  & 95\% & 7.28 & \(-\)3.91 & 1.88 & 1.17 & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results of ABg faults with high fault resistance at feeder B5B6. data self-synchronization algorithm for synchronous timing. ABg-phase-phase-to-ground faults are set at different positions of feeder B\({}_{5}\)B\({}_{6}\), and the simulation results are shown in Table 7.  
It can be seen from Table 7 that the maximum startup delay time difference value between the two ends of feeder protection is about 4.5 ms. The existence of the startup delay time difference reduces the sensitivity of the TCDP or even makes it refuse to trip.