## 4 Case Study
### The Improved IEEE-123 Node Distribution Network  
In order to verify the application effect of the algorithm in the large-scale distribution network, this section will verify its performance in the IEEE-123 node system.  
(1) _Introduction to the large-scale distribution network_  
The improved IEEE-123 node three-phase distribution network topology is shown in Figure 11. In this paper, four uPMUs are selected at nodes 1, 35, 76, and 97 to measure the node voltage phasors; the measurement is used to measure the branch flow power and node voltage amplitude. In addition, in order to obtain the more accurate power exchange of the upstream and downstream sub-regions, some FTU devices are installed to measure the branch flow power. Other nodes in the distribution network are pseudo-measurements, usually derived from short-term power predictions to provide the approximate values of active and reactive power injected into the nodes. The three-phase load type, active and reactive power, connection method of each node of the distribution network, and the three-phase parameters of the line and reactive power compensation are detailed in Reference [2]. In this paper, DGs are installed in the different phases of seven nodes in the network as shown in Table 6.  
2. _Comparisons and analysis_ Since it has the same measurement time synchronization and similar fault propagation characteristics of intelligent terminals as the IEEE-37 node power saving system, the results are directly analyzed for the IEEE 123-node. The accuracy of the method proposed in this paper and the method proposed in Reference [2] are compared, and the results are shown in Table 7. The symbol 'A' in the table represents the algorithm proposed in this paper, while the symbol 'B' represents the algorithm proposed in Reference [2]. Additionally, Figure 12 shows the three-phase voltage magnitude and phase angle of the nodes near the fault location when the b-phase-to-ground short circuit occurs at nodes 8-9.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \cline{4-13} \multirow{4}{*}{**Fault Line**} & \multicolumn{4}{c}{**Single-Phase-to-Ground**} & \multicolumn{4}{c}{**Interphase Short Circuit**} & \multicolumn{4}{c}{**Three-Phase Short Circuit**} \\ \cline{3-13}  & & & **0 \(\Omega\)** & **100 \(\Omega\)** & **500 \(\Omega\)** & **0 \(\Omega\)** & **100 \(\Omega\)** & **1 k\(\Omega\)** & **0 \(\Omega\)** & **100 \(\Omega\)** & **1 k\(\Omega\)** \\ \hline \multirow{4}{*}{Fault Line} & 8–9 & A & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% \\  & B & 100\% & 100\% & 99\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% \\  & A & 100\% & 100\% & 98\% & 100\% & 100\% & 99\% & 100\% & 100\% & 100\% \\  & 67–72 & B & 100\% & 100\% & 99\% & 100\% & 100\% & 99\% & 100\% & 100\% & 99\% \\  & A & 100\% & 100\% & 98\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% \\  & 49–50 & B & 100\% & 98\% & 96\% & 100\% & 98\% & 98\% & 100\% & 100\% & 94\% \\  & 64–65 & A & 100\% & 100\% & 99\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% \\  & 61–65 & B & 100\% & 94\% & 92\% & 100\% & 96\% & 94\% & 100\% & 98\% & 94\% \\  & A & 100\% & 100\% & 91\% & 95\% & 90\% & 85\% & 98\% & 95\% & 93\% \\  & 105–108 & B & 100\% & 92\% & 90\% & 100\% & 88\% & 86\% & 100\% & 85\% & 81\% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Fault section location results in different lines and power supply areas in IEEE-123 node network.  
Figure 12: Partial three-phase voltage magnitude and phase angle of nodes near the fault location.