# Fault Location in Double Circuit Medium Power Distribution Networks Using an Impedance-Based Method
## 1 Introduction
### Literature Review and Challenges  
Since 1980, fault location algorithms have seen substantial development, particularly methods that are based on impedance. At the beginning of these developments, power systems were modeled based on symmetric geometric lines and analyzed based on symmetric parts which were specifically used for underground systems (e.g., the method used in [1; 2]). Reference [3] uses symmetric factors based on the line's parallel admittance which is also used only for underground distribution networks. In [4], the accuracy was improved significantly by considering the effect of capacitors. However, this can only be used for underground systems. In [5], a method was proposed for determining the distance to a single-phase fault in overhead distribution cables based on the base frequency, voltage, and current at the beginning of the feeder. In this method, by using the short line model and series and parallel analysis, the impedance of different routes were evaluated. [PERSON] [6] proposed a new method for fault location by considering a \(\pi\) line model. This method uses the corrected impedance, and a quadratic equation in accordance with the fault distance is obtained. By using this method, the fault detection accuracy was improved and maximum error percentage was reported to be 1.58%. In [7], a new and precise fault location algorithm was provided by considering the effect of capacitors. This method has a higher accuracy than previous methods. The downside of this method is that it can only be used for single circuit distribution networks.  
In [8], special attention was given to the dynamic model. In this work, the fault distance was estimated through the load amount. The load amount was calculated from the load factor and power factor. In [9], a method was given to determine the specific fault location since there might be more than one fault in the system. As a result, two approaches were used to determine the real fault's location. The first approach compares the measured and recorded voltage samples, and the second approach uses the voltage's frequency spectrum.  
A hybrid fault location method is presented for single line to ground fault in [15]. At first, the possible fault locations are determined using an impedance-based fault location method. Then, the faulty section or the main fault location among the determined possible fault locations is strongminded using a voltage sag matching algorithm. In [16], the fault location in the four-wire lines is determined by improving the algorithm presented in [15].  
A time domain technique is presented for locating faults in a power distribution network (PDN) [17]. It uses the voltage and current at the beginning of the feeder and distributed generator DG place. Furthermore, an iterative method is presented to solve the fault location problem. The need for a high sampling rate is the drawback of this method.  
The self-healing concept is used for locating faults in PDN with DG in [18]. In this paper, the fault location algorithm requires the transient and steady state of signals, load flow algorithm, and synchronization angle.  
Furthermore, the important papers in this topic are reviewed and the characteristics and details are shown in Table 1.