## 1 Introduction  
Distribution networks are becoming more intelligent and complex with the development of the society. According to statistics, almost 80% of faults are observed in distribution networks [1]. More importantly, distribution networks are connected with users directly, so the study on fast and accurate fault location method of distribution networks is particularly important. Various fault location methods have been proposed before. The impedance method is simple in principle and requires less investment, but it is easily affected by transition resistance and branches [2; 3; 4; 5]. The traveling wave method requires high accuracy of the measuring equipments, but the cost of equipment is very high. Moreover, it is necessary to install equipment on multiple branches, and it is difficult to accurately synchronize the multi-terminal traveling wave signals, so this method is also difficult to apply in the distribution network [6; 7; 8]. Other fault location methods that have been proposed include minimum fault reactance methods [9; 10], the genetic algorithm [11; 12], and the pattern recognition method [13; 14]. In [11], the classical genetic algorithm has good fault tolerance, but for the random iteration and lack of guidance, it is easy to fall into a local optimum. Reference [12] improved the classical genetic algorithm proposed in Reference [11], through searching the solution space by multiple-population collaboratively and improving the convergence conditions, meaning that the possibility of falling into a local optimum was reduced. However, when distribution networks are expanded to hundreds or thousands of nodes, the calculation work will increase greatly, and the accuracy of the results will also be reduced. Some researchers use pattern recognition methods, and the already-trained artificial neural networks are applied to judge the faulted section [13; 14]. However, when the topology of distribution network changes, the artificial neural networks will take a lot of time to be retrained. As more and more feeder terminal equipments, such as feeder terminal units (FTUs) and fault indicators (FIs), are applied in power distribution networks, using fault status signals collected by feeder terminal equipments to achieve accurate and fast fault location has become an important research topic. In addition, distributed generations applied in distribution networks and information loss of equipments have put forward higher requirements for the research of fault location [15; 16]. So far, scholars from different countries have proposed some fault location methods based on information of FTUs. In [17], a fault location method based on the measurement of sparse voltage amplitude was proposed, it uses the voltage information of some measuring points. Although the number of required measuring points is reduced by the Bayesian compressed sensing theory, the selection of measuring points is very strict. When the topology of distribution network changes, all measuring points need to be reselected, so this method is not suitable for the distribution network if the topology structure changes frequently. The method of linear integer programming was used to locate the fault point in [18], which improves the fault tolerance performance of swarm intelligence algorithm. But the author only considered single power supply when designing the mathematical model of distribution networks, and the constructed function is not applicable to the distribution networks with distribution generations (DGs). When DG provides a fault current in a reverse direction, this method will not be applicable for this condition. In [19; 20], fault location methods that take DGs into consideration were proposed. Both methods can eliminate the influence of distorted information on the results, so the methods have high fault tolerance performance.