## 6 Simulation and Analysis
### Analysis of Simulation Results
#### 6.2.3 Unmeasured Load Branch Test  
Using feeder B\({}_{4}\)B\({}_{5}\) as the protected section and adding the ULB inside it, the performance of the ACDP in case of internal and external faults is tested, and the simulation results are shown in Table 6.  
It can be seen from Table 6 that when fault point \(f_{1}\) is located inside the protected section, the ADP can trip correctly and has high sensitivity. When the fault point \(f_{3}\) is located outside the protected section and is upstream of the ULB, the amplitude ratio of the PSCFCs on both sides of the protected section is greater than 1, which is consistent with the theoretical analysis of Section 4. When the AB-phase-to-phase fault occurs at feeder B\({}_{1}\)B\({}_{4}\) or the ABC-3-phase fault occurs at the first end (5% from B\({}_{1}\)) and middle (50% from B\({}_{1}\)) of feeder B\({}_{1}\)B\({}_{4}\), the ACDP of feeder B\({}_{4}\)B\({}_{5}\) will misjudge. At this time, the protection malfunction can be avoided with the auxiliary criterion. When the fault point \(f_{2}\) is located outside the protected section and is downstream of the ULB, \(K_{\text{sen}}\) is tiny, the action impedance \(Z_{\text{act}}<0\), and the proposed protection is reliably not tripped.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multirow{2}{*}{**Fault Location**} & \multirow{2}{*}{\(\varepsilon\)} & \multirow{2}{*}{\(\delta\)**(/rad)**} & \multicolumn{3}{c}{\(K_{\text{sen}}\)} & \multicolumn{3}{c}{**Trip or Not**} \\ \cline{5-8}  & & & & **ACDP** & **TCDP** & **ACDP** & **TCDP** \\ \hline \multirow{3}{*}{AB} & 5\% & 2.21 & 0.21 & 3.79 & 3.65 & Yes & Yes \\  & 50\% & 1.23 & 0.22 & 9.33 & 9.33 & Yes & Yes \\  & 95\% & 0.73 & 0.21 & 7.68 & 7.68 & Yes & Yes \\ \hline \multirow{3}{*}{ABG} & 5\% & 2.22 & 0.22 & 3.77 & 3.63 & Yes & Yes \\  & 50\% & 1.20 & 0.24 & 9.44 & 9.44 & Yes & Yes \\  & 95\% & 0.72 & 0.23 & 7.18 & 7.18 & Yes & Yes \\ \hline \multirow{3}{*}{ABC} & 5\% & 2.26 & 0.25 & 3.70 & 3.53 & Yes & Yes \\  & 50\% & 1.25 & 0.23 & 8.89 & 8.89 & Yes & Yes \\ \cline{1-1}  & 95\% & 0.72 & 0.21 & 7.40 & 7.40 & Yes & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulation results of metallic multi-phase faults at feeder B\({}_{7}\)B\({}_{8}\).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multirow{2}{*}{**Fault Location**} & \multirow{2}{*}{\(\varepsilon\)} & \multirow{2}{*}{\(\delta\)**(/rad)**} & \multicolumn{3}{c}{\(K_{\text{sen}}\)} & \multicolumn{3}{c}{**Trip or Not**} \\ \cline{5-8}  & & & & **ACDP** & **TCDP** & **ACDP** & **TCDP** \\ \hline \multirow{3}{*}{AB} & 5\% & 5.10 & \(-\)0.77 & 2.13 & 1.89 & Yes & Yes \\  & 50\% & 3.34 & \(-\)0.63 & 2.65 & 2.30 & Yes & Yes \\  & 95\% & 2.21 & \(-\)0.46 & 3.79 & 3.23 & Yes & Yes \\ \hline \multirow{3}{*}{ABG} & 5\% & 5.45 & \(-\)0.65 & 2.07 & 1.91 & Yes & Yes \\  & 50\% & 3.36 & \(-\)0.48 & 2.64 & 2.42 & Yes & Yes \\  & 95\% & 2.18 & \(-\)0.25 & 3.85 & 3.64 & Yes & Yes \\ \hline \multirow{3}{*}{ABC} & 5\% & 5.02 & 0.16 & 2.14 & 2.13 & Yes & Yes \\  & 50\% & 2.82 & \(-\)5.75 & 3.00 & 2.63 & Yes & Yes \\ \cline{1-1}  & 95\% & 2.00 & \(-\)5.60 & 4.29 & 2.97 & Yes & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation results of metallic multi-phase faults at feeder B\({}_{4}\)B\({}_{5}\).