## 4 Case Study  
### The Improved IEEE-37 Node Distribution Network  
(1) _Introduction to the distribution network_  
Based on the improved IEEE-37 node three-phase distribution network, the simulation test was carried out, and its topology is shown in Figure 4. The system voltage level is 4.8 kV, the total powers of the three-phase load are 727 + j357 kV\(\cdot\)A, 639 + j314 kV\(\cdot\)A and 1091 + j530 kV\(\cdot\)A, respectively. For the active and reactive power of each node of the distribution network, the connection method, the three-phase parameter, and reactive  
Figure 3: The flowchart of the fault section location and fault phase identification. power compensation, see [31]. In order to verify the applicability of the proposed fault section location method in the active distribution network within the distribution power supply area, distributed power sources with a rated power of 0.5 MW and a rated power of 0.1 MW are connected to nodes 21 and 28, respectively. At the same time, two transformers are installed at nodes 13 and 36, with a transformation ratio of 4.8 kV/0.4 kV, and the Dyn11 wiring mode is used. The load power of the power supply area is shown in Table 2.  
According to the network fault observability analysis, considering the location accuracy requirements of the fault section of the distribution network, intelligent terminals FTU and \(\upmu\)PMU are configured at key nodes 3, 6, 10, 16, 19, 27, 29, 30, and 32 and nodes 13 and 36 that are connected to the transformer. Among them, the measurement error of the node voltage magnitude measured in real-time by FTU obeys a normal distribution with a mean value of zero and a standard deviation of 1% of the true value; the voltage magnitude error measured by \(\upmu\)PMU in real-time obeys a normal distribution with a mean value of zero and a standard deviation of 1% of the true value. Additionally, the voltage angle measurement error follows a normal distribution with a mean of zero and a standard deviation of \(\pm\)0.001\({}^{\circ}\). (2) _Analysis of time synchronization of intelligent terminal measurement_  
Table 3 shows the calculation results of the correlation degree of measurement data of multiple types of intelligent terminals. Taking some FTU and \(\upmu\)PMU measurement data as an example, the maximum value of each row of data almost appears in the fifth column. Based on the correlation degree theory in Section 2.1, it is easy to see that the measurement delay error of the FTU measurement data is set to obey a normal distribution \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Node No.**} & \multicolumn{3}{c}{**Complex Power/kV-A**} \\ \cline{2-4}  & **A-Phase** & **B-Phase** & **C-Phase** \\ \hline
13 & 0 & 140 + 70 j & 21 + 10 j \\
36 & 0 & 0 & 42 + 21 j \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The load power of the power supply area. Figure 4: The improved IEEE-37 distribution network. with a standard deviation of 0.1/s and a mean value of 0, thus ensuring the synchronization and validity of the measurement data of multiple types of intelligent terminals. (3) _Analysis of fault propagation characteristics in distribution power supply area_  
This paper places the b-phase ground fault at the start of lines 12-13 and downstream from the node 13 transformer in order to analyze the fault propagation characteristics of the distribution power supply area. The simulation lasted 0.1 s in total. The fault duration was 0.03 s if the fault occurred in 0.04 s. Figures 5 and 6 depict the downstream power supply area (low voltage side) of node 13 and the fault voltage characteristics of node 12 (medium voltage side), respectively. It can be seen from Figures 5 and 6 that when a single-phase-to-ground fault occurs on the medium voltage side, the fault phase voltage on the medium voltage side decreases, and the non-fault phase voltage increases.