# A Fault Section Location Method for Distribution Networks Based on Divide-and-Conquer
## 1 Introduction
Reference [18] proposes applying logical operations to express the causal relationship between FTU fault information and faulty equipment and proposes a mathematical model of fault location based on the state approximation principle, which transforms fault location into a combinatorial optimization problem. Since then, scholars have successively used the genetic algorithm (GA) [19], binary particle swarm optimization algorithm (BPSO) [20], ant colony algorithm (AC) [21], harmony search algorithm (HS) [22], and other intelligent algorithms to implement the solution of this model. The intelligent optimization algorithm has a strong information fault tolerance capability. However,  
Figure 1: The basic working principle of the fault location method based on FTUs. the method requires iterative search operations in a high-dimensional solution space, which affects the speed of fault location [23]. Moreover, its search process has a certain degree of randomness, which leads to a certain probability of local convergence. Therefore, this method has the inherent defect of insufficient convergence stability [24]. 3. Fault location methods based on the linear integer programming model. The basic principle of this method is to transform the mathematical model of fault location into a linear integer programming model (LIP) using algebraic operation substitution [25], ascending dimension [26], etc. Then, classical LIP methods (such as the branch and bound method, cut plane method, and implicit enumeration method) are applied to solve the model to locate the fault. The \"optimality checking\" step in the LIP solution method enables it to gradually approximate and eventually converge to the global optimal solution through iterations and thus has good convergence stability. However, the solution of the LIP model involves the computation of its continuous relaxed linear programming model (LP) several times, resulting in high time complexity for the algorithm [27]. Tests have shown that the fault location time of small and medium-sized distribution networks is in the range of seconds [26], which does not meet the requirements of rapidity. 4. Fault location methods based on the hierarchical optimization model. Reference [28] proposes that the branch of the network is externally equivalent to a two-port based on the equivalence principle and constructs a hierarchical optimization model of fault location. The basic idea is to solve the mathematical model of fault location in a reduced dimension: first, locate the branch where the fault is located, then determine the faulty device from the faulty branch. Since then, scholars have successively used the multiverses optimization algorithm (MVO) [29], quantum computing and immune optimization algorithm(QIOA) [30], bald eagle search algorithm (BES) [31], and other intelligent algorithms to implement the solution of hierarchical optimization models. This method converts effectively reduces the size of solution space and improves the speed and accuracy of fault location. However, the method requires high soundness of FTU fault information at the branch port, which may produce misjudgment when the port information is distorted, and it cannot completely eradicate the defect of insufficient convergence stability of the intelligent algorithm. The characteristics of the aforementioned various distribution network fault location methods are shown in Table 1.  
In summary, a large number of results have been achieved in distribution network fault location methods, but the following problems still exist: on one hand, the traditional fault location model contains logical operations; thus, it is difficult to obtain a high efficient solution to the model through strict mathematical derivation; on the other hand, the current fault location methods are still difficult to use simultaneously. Furthermore, current fault location methods are not yet able to meet the requirements of accuracy and speed simultaneously.