# Novel Faulted-Section Location Method for Active Distribution Networks of New-Type Power Systems
## 5 Simulation Analysis
### Test Case 3: Multiple Faults with T-Connected Sections  
Multiple faults with T-connected sections are simulated in the distribution network shown in Figure 7, assuming that \(L_{9}\), \(L_{11}\), and \(L_{28}\) are faulty. This involves attaining the protection \(e_{4}\), \(e_{5}\), and \(e_{12}\) action information and the equipment status information \(I=[1\;1\;1\;1\;0\;1\;1\;1\;1\;1\;1\;0-1\;0\;-1\;-1\;-1\;0\;-1\;-1\;-1\;-1\;0 \;0\;0\;-1\;-1\;-1\;1\;0\;0\;0\;-1\;-1]\). The boundary nodes are \(S_{1}\), \(S_{12}\), \(S_{28}\), \(S_{33}\), and \(S_{34}\). The matrix \(I=[1\;1\;1\;1\;1\;1\;1\;1\;0\;-1\;-1\;-1\;-1\;-1\;0\;0\;-1\;-1\;-1\;-1\;-1]\).  
The improved matrix calculation is carried out to obtain the matrix \(L=[0\;0\;0\;0\;0\;0\;0\;1\;0\;1\;0\;0\;0\;0\;0\;0\;0\;0\;0\;0\;0\;1]\). Non-T-connected sections \(l_{11}=1\) and \(l_{28}=1\) illustrate that the two sections are fault sections. For the T-connected section \(l_{9}=1\), search for the other fault sections; otherwise, it is judged as a non-fault section. The fault section location result is \(L_{11}\) and \(L_{28}\). \(I^{*}=[1\;1\;1\;1\;1\;1\;1\;1\;0\;-1\;-1\;-1\;-1\;-1\;-1\;1\;1\;-1\;-1\;-1 \;1\;-1\;-1]\). Because \(I^{*}\
eq I\), the positioning result is wrong. The suspicious fault sections are: \(L_{4}\), \(L_{8}\), \(L_{9}\), \(L_{10}\), \(L_{11}\), \(L_{12}\), \(L_{13}\), \(L_{17}\), \(L_{20}\), \(L_{22}\), \(L_{24}\), and \(L_{28}\). According to the operation rules of the GTA, the optimization process is shown in Figure 9.  
According to the calculation, the fault sections are \(L_{9}\), \(L_{11}\), and \(L_{28}\), and the fitness function value is 3. Multiple simulation experiments are carried out on multiple faults with T-connected sections. The results in Table 10 show that GTA can accurately locate multiple faults with T-connected sections.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Sections** & **Boundary Nodes** & **Location Result** & **Correct or Not** \\ \hline \(L_{8}\), \(L_{28}\) & \(S_{1}\), \(S_{28}\), \(S_{33}\), \(S_{34}\) & \(L_{8}\), \(L_{28}\) & correct \\ \(L_{14}\), \(L_{19}\) & \(S_{1}\), \(S_{14}\), \(S_{33}\), \(S_{34}\) & \(L_{14}\), \(L  
In summary, the proposed algorithm can accurately locate various fault conditions. The algorithm proposed in this paper fully combines the advantages of the fast calculation speed of the improved matrix algorithm and the high tolerance performance of the GTA. The improved matrix algorithm is used to reduce the dimension of the optimization of the GTA, and the GTA is used to solve the problem that the improved matrix algorithm cannot accurately locate multiple faults with T-connected sections and faults with fault information errors. The simulation results show that the positioning algorithm can correctly locate the fault section in complex fault conditions with higher accuracy and solve the problem of fault information errors with better tolerance performance. The accuracy, tolerance performance, and rapidity of the location algorithm will be further verified by a large number of comparative experiments in the next section.