## 4 Case Study
### The Improved IEEE-37 Node Distribution Network
After it propagates to the low voltage side of the Dyn11 transformer, both the fault phase and lagging phase voltages reduce, which satisfies the propagation relationship of the distribution transformer to fault characteristics described in Section 3.1. It can be seen from Figures 7 and 8 that when a single-phase-to-ground fault occurs on the low-voltage side of the power supply area, because the transformer has a certain electrical isolation effect, it has little influence on the voltage of the remaining nodes of the distribution network system, as well as the low-voltage side of the actual project. The low-voltage side should be tripped directly after a single-phase-to-ground fault to minimize the impact on the overall voltage level of the system. The residuals of the virtual fault state equation at various nodes are shown in Figure 6 in order to demonstrate the viability of the proposed fault section location method. It is shown that the proposed fault section location method is able to achieve the same fault section location method. Figure 8: Voltage characteristics of the LV side when the LV side fails. Figure 6: Voltage characteristics of the LV side when the MV side fails. Figure 7: Voltage characteristics of the MV side when the LV side fails. assumed that a short circuit or ground fault occurs at branches 8-11 of the improved IEEE-37 distribution network. In Figures 9 and 10, the horizontal coordinate represents the node number, and the vertical coordinate represents the residual of the equation. The yellow, green, and red colors represent the three phases, respectively. The grounding impedance corresponding to fault scenario 1 is 0.001 p.u., and the grounding impedance corresponding to fault scenario 2 is 1 p.u. In both scenarios, the smallest state estimation error is at node 8 or 11, which means that the fault occurs near bus 8 or 11, which is consistent with the actual fault location. Additionally, regardless of the value of the grounding impedance, the nodes in the area can be roughly divided into two categories according to the distribution range of the estimation error: one is located in the lower left part of the picture, representing the nodes with smaller state estimation errors, and these nodes are located on the faulty path 1-3-7-8-11. The estimation error corresponding to other types of nodes is larger because they are weakly connected to the fault path and less affected by the fault. At the same time, from the estimation error range in different scenarios, it can be seen that the smaller the grounding impedance is, the larger the residual error difference between the two types of nodes is, which ensures the high accuracy of the fault section location in the distribution network. In order to further verify the accuracy of the proposed fault section location algorithm, four typical line terminals and two different distribution power supply areas were ran  
Figure 10: Residuals of virtual fault state equations at different nodes in scenario 2. Figure 9: Residuals of virtual fault state equations at different nodes in scenario 1.  
domly selected to set up short-circuit faults with different types and different grounding impedances in the improved IEEE-37 distribution network. The results are shown in Table 4. The fault section location accuracy index \(P_{t}\) is defined as:  
\[P_{t}=\frac{\lambda_{\text{t}}}{\lambda}\times 100\% \tag{20}\]  
where \(\lambda_{\text{t}}\) is the number of times for which the faulty section can be accurately identified upon \(\lambda\) tests. It should be noted that the purpose of this paper is to locate the fault section of the distribution network. Considering that the length of the lines used in the example is short (most of them are approximately 100 m), the location point at the beginning or end of the branch falls within the correct results. Moreover, In order to study the influence of the DG permeability on the algorithm, the adaptability of the proposed single-phase-to-ground fault line selection method is verified under different DG permeability scenarios.