## 4 Case Study
### Results  
Through the application of the fault location algorithm proposed in this paper in the IEEE-37 node and IEEE-123 node, the following results can be obtained. (1) _Results of the proposed method applied to IEEE-37 nodes_  
It can be seen from Table 4 that when the tested line has an interphase short-circuit or three-phase short-circuit faults, the fault section location accuracy can reach 100%. When a single-phase-to-ground short circuit occurs in the test line and the transition resistance is less than 500 \(\Omega\), the accuracy of the fault section location is 100%. When the transition resistance of the single-phase-to-ground fault continues to increase to 500 \(\Omega\), there is the misjudgment of one line. The reason is that with the increase in the transition resistance value, the characteristic quantity of the system fault becomes smaller and smaller, and the fault section location accuracy reduces. In addition, when a single-phase-to-ground short circuit, phase-to-phase short circuit, or three-phase short circuit occur in the four distribution power supply areas in the example, the proposed fault location method can accurately locate the fault. In the tested four typical lines and two distribution power supply areas, there are not only network trunk branches such as lines 17-22, but also network end branches such as 34-35, which indicate that the proposed fault section location method has high adaptability at different positions of the distribution network. The accuracy of the fault judgment results for branches 34-35 and the power supply area near node 36 shows that the method can effectively distinguish short branches with common nodes. From Table 5, the proposed single-phase-to-ground fault line selection method for an active distribution network has high adaptability to the level of DG permeability. Because this method does not need to perform complex equivalent processing on DG, but adopts the idea of least squares estimation to solve the system state as a whole for fault line selection, it avoids the error caused by the inaccurate model in principle and improves the fault line selection as well as applicability and effectiveness of the method in high-permeability DG access scenarios. (2) _Results of the proposed method applied to IEEE-123 nodes_  
It can be seen from Table 7 that both the fault location algorithms are not affected by the magnitude of the grounding impedance, and the location accuracy is high in most cases. The lines involved in the fault scenario set up in this paper include not only key trunk branches such as branches (67, 72), but also network end branches such as branches (49, 50); it includes both three-wire lines and single-phase lines such as branches (8, 9); including both overhead lines and cable lines (64, 65) which reflect the proposed high adaptability of the fault section location method in the large-scale three-phase distribution network. By comparing the method proposed in this paper with that proposed in Reference [2], it can be seen that the former has higher accuracy. This also means that the algorithm proposed in this paper is more effective in judging the fault category. It can be seen from Figure 12 that the changing trend is consistent with the fault propagation characteristics. However, in Table 7, when a single-phase ground fault occurs at line (105, 108) and the grounding impedance is 0.001 p.u., the fault location accuracy is low. Although most of the fault section location results at this time indicate that the single-phase-to-ground fault occurs at line (105, 108), there are still some results that determine that the fault occurs at its adjacent line (108, 300). One reason is that the average length of the line in the example is short; another reason is that since node 300 has no load, the actual value of the node voltage is almost the same as that of node 108, resulting in a lack of distinction between its fault characteristics and adjacent nodes.