## 7 Conclusions  
A novel CDP scheme for active distribution networks is proposed in this paper. The adaptive phase angle compensation coefficient is introduced to deal with the negative impact of IBDGs on TCDP. The polarity information of action impedance is used as an auxiliary criterion to effectively solve the problem that unmeasurable load branches may \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Resistance**} & \multirow{2}{*}{**Fault Location**} & \multicolumn{2}{c}{**Delay Time (ms)**} & \multirow{2}{*}{\(\varepsilon\)} & \multirow{2}{*}{\(\beta\)**(rad)**} & \multirow{2}{*}{\(\mathbf{K_{sen}}\)} & \multirow{2}{*}{**Trip or Not**} \\ \cline{3-3} \cline{5-10}  & & & & & & **ACDP** & & **TCDP** & **ACDP** & **TCDP** \\ \hline \multirow{3}{*}{\(25\,\Omega\)} & 5\% & 0.1 & 3.6 & 6.15 & 2.46 & 1.98 & 1.11 & Yes & Yes \\  & 50\% & 0.1 & 4.1 & 5.36 & 2.72 & 2.08 & 1.02 & Yes & Yes \\  & 95\% & 0.1 & 2.1 & 3.04 & \(-\)3.72 & 2.83 & 0.83 & Yes & NO \\ \hline \multirow{3}{*}{\(30\,\Omega\)} & 5\% & 0.1 & 4.6 & 6.71 & 2.84 & 1.93 & 1.07 & Yes & Yes \\  & 50\% & 0.1 & 4.2 & 4.58 & 2.96 & 2.23 & 0.92 & Yes & NO \\ \cline{1-1}  & 95\% & 0.1 & 2.1 & 3.03 & \(-\)3.29 & 2.84 & 0.72 & Yes & NO \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulation results of time synchronization error test. \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}{*}{\(\beta\)**(rad)**} & \multirow{2}{*}{\(\mathbf{K_{sen}}\)} & \multirow{2}{*}{**Trip or Not**} \\ \cline{3-3} \cline{5-10}  & & & & **ACDP** & & **TCDP** & **ACDP** & **TCDP** \\ \hline \multirow{3}{*}{AB} & 5\% & 34.2 & \(-\)0.75 & 1.51 & 1.49 & Yes & Yes \\  & 50\% & 23.6 & \(-\)0.79 & 1.55 & 1.52 & Yes & Yes \\  & 95\% & 18.0 & \(-\)0.79 & 1.60 & 1.54 & Yes & Yes \\ \hline \multirow{3}{*}{ABG} & 5\% & 33.2 & \(-\)0.78 & 1.52 & 1.49 & Yes & Yes \\  & 50\% & 22.5 & \(-\)0.80 & 1.56 & 1.52 & Yes & Yes \\  & 95\% & 16.9 & \(-\)0.81 & 1.61 & 1.55 & Yes & Yes \\ \hline \multirow{3}{*}{ABC} & 5\% & 24.4 & \(-\)0.72 & 1.55 & 1.52 & Yes & Yes \\  & 50\% & 16.6 & \(-\)0.73 & 1.61 & 1.56 & Yes & Yes \\ \cline{1-1}  & 95\% & 12.7 & \(-\)0.75 & 1.67 & 1.61 & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Simulation results of DG\({}_{4}\) out of operation during metallic multi-phase faults occur at feeder B\({}_{7}\)B\({}_{8}\). lead to protection misjudging. The simulation results show that the proposed protection scheme has superior action performance in the following aspects:  
1. In the case of different types of DG access, when various types of multi-phase faults occur, the proposed ACDP can trip correctly, and the sensitivity is higher than that of the TCDP;
2. The proposed ACDP has a strong ability to withstand fault resistance and can still trip sensitively under 150\(\Omega\) fault resistance, while TCDP cannot trip correctly under 100 \(\Omega\) fault resistance;
3. The proposed protection scheme can effectively deal with the negative impact of unmeasured load branches and has high reliability;
4. Without strict time synchronization, the proposed ACDP can still trip sensitively when the time synchronization error is 4.6 ms;
5. The proposed ACDP is not affected by DG random output and has high reliability. Compared with TCDP, the proposed ACDP has apparent advantages in terms of sensitivity, reliability, and time synchronization requirements. Conceptualization, C.Y. and Z.G. ; data curation, C.Y. and Z.L. ; formal analysis, C.Y., Z.G. and Z.T. ; funding acquisition, Z.G. ; methodology, C.Y., Z.G. and Z.L. ; project administration, Z.G. ; software, C.Y. ; validation, C.Y. and Z.G. ; visualization, C.Y. and Z.T. ; writing--original draft, C.Y. ; writing--review and editing, C.Y., Z.G. and Z.L. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the Science and Technology Project of the State Grid Corporation of China (NO. 520600190011H).