# A Fault Section Location Method for Distribution Networks Based on Divide-and-Conquer
## 5 Simulation Analysis
### Comparative Analysis of Performance  
In summary, Table 10 gives a comparison of the results of the algorithms' performance.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm Number** & **Algorithm Type** & **Accuracy** & **Computational Efficiency** \\ \hline Algorithm 1 & Algorithm in this paper & Highest & Highest \\ Algorithm 2 & Intelligent optimization algorithm & Low & Low \\ Algorithm 3 & Hierarchical fault location algorithm & Higher & Higher \\ Algorithm 4 & Linear integer programming algorithm & Highest & Lowest \\ \hline \end{tabular}
\end{table}
Table 10: Comparative results of algorithm performance.  
Figure 16: The test results of the IEEE 69-node distribution system. (**a**) Accuracy comparison; (**b**) comparison of computational efficiency.  
In terms of accuracy, as described in Section 5.1.1, all of the algorithms in the comparison output correct localization results, but the difference lies in their ability to maintain the consistency of their output results during repeated testing. In other words, the accuracy of the algorithms is closely related to the convergence stability. The intelligent optimization algorithm represented by Algorithm 2 has a random population generation and update, and the population form tends to be homogeneous with the depth of iteration; thus, it sometimes converges to the \"local extreme value point\" in the process of repeated testing, and it cannot maintain consistency in its output results. When the scale of distribution network is expanded, the scale of solution space increases, and these problems become more prominent. The hierarchical fault location algorithm, represented by Algorithm 3, uses a hierarchical strategy to reduce the size of the solution space and improve the convergence stability. However, this algorithm only uses the FTU information of the branch port in determining the fault area, which may lead to misjudgment when the FTU information of the port is distorted. The linear integer programming algorithm, represented by Algorithm 4, applies the classical integer programming algorithm to locate faults, in which the \"optimality check\" step can make it gradually bound through iteration and eventually converge to the same \"global optimal solution\"; thus, it has higher convergence stability. From the pseudocode DASFL in Section 4.1, we can see that the algorithm proposed in this paper does not contain random operations and has the same execution process and calculation results in the same fault situation; thus, it can maintain the consistency of the results, which makes the algorithm of this paper have high convergence stability.  
The computational efficiency of the algorithm was determined using the time complexity of the algorithm. Assuming that the distribution network contains n sections, as described in Section 5.2, Algorithm 4 had a time complexity of O(\(n^{4}\)), and therefore has the lowest computational efficiency. Algorithm 2 requires iterative search operations in a high-dimensional solution space. If it adopts the convergence condition of \"no update at the global extremum\", it ideally has the asymptotic lower bound of \(\Omega(n^{2})\), and in the extreme case, the number of iterations of Algorithm 2 is the maximum number of iterations, at which time the algorithm has the asymptotic upper bound of \(O(n^{3})\). Therefore, its computational efficiency is higher than that of Algorithm 4. Algorithm 3 applies a hierarchical strategy to transform the single-layer, high-dimensional search operation into a double-layer, low-dimensional search operation; thus, its computational efficiency is higher than that of Algorithm 2. As described in Section 4.2, the algorithm in this paper has a linear level of time complexity \(\Theta(n)\), and it therefore has the highest computational efficiency.