The proposed method is described us

The proposed method is described using a sample distribution system shown in Fig. 1. This system includes a main feeder and several laterals with different lengths. The 3-phase voltages are recorded only in the substation. Fig. 2 shows the frequency spectrum of the first aerial mode of the voltage (V1), generated by simulation of 3-phase symmetrical faults on the main feeder, locate at different distances of 6, 7, 9, and 10 km from the substation. All frequency components of the voltages in Fig. 2 are generated by reflections of high frequency transients between the fault location and the substation (main components). Fig. 2 indicates that by increasing the fault distance, frequency of the main components in voltage V1 decreases. For instance, frequency of the first component of TW (component with maximum amplitude named dominant main component (DMC) in this paper) for 3-phase faults located at 6, 7, 9, and 10 km form the substation is 14,450, 12,720, 10,020, and 9058 Hz, respectively. Simulation results for 3-phase faults in different locations of the test system, confirm the decreasing trend of the frequency versus the increase of the fault distance. Hence this criterion can be used to calculate the exact location of the fault. Fig. 3 illustrates the dominant main component frequency (DMCF) versus distance, obtained from simulation of the 3-phase faults with 1 km distance step. Simulations of the 3-phase faults in different locations of the laterals for each path in the distribution system of Fig. 1 yield to a curve similar to Fig. 3. Thus, by using recorded curves related to each path in a database and calculating the DMCF of V1, exact distance of the fault can be calculated. It should be noted that in order to reach a higher accuracy for fault distance calculation, the distance step between simulated faults can be chosen as small as needed. In addition to determination the location of fault, the faulted section in the distribution system should be identified. Analysis of various faults shows that when a fault happens on a branch, there will be one or more subordinate components in addition to the main components. As shown in Fig. 4, when a fault happens on a branch, fault-generated transients travel toward the substation. Parts of these transients are reflected from substation toward fault point (Rm waves) and the other part propagates away from substation toward the main feeder (R waves). Part of transients which are traveling between fault point and substation, generates main components in frequency spectrum (similar to Fig. 2), while the other part which are reflected between junctions and substation, produces subordinate components. As shown in Fig. 4, by closing the faulted section to the substation, number of nodes between fault point and substation decreases. The amplitude of TW reduces by passing through nodes. So, when the number of nodes between fault location and substation increases, traveling wave amplitude decreases more at the substation [17]. In Fig. 4 all of TW from Rm1–Rm6 that reaches to substation, can generate reflections R1–R5 which induce subordinate components in frequency spectrum of V1. Researches in this field show that usually the first subordinate component has considerable amplitude in comparison to the main components in frequency spectrum of V1. In this paper, the first subordinate component is called dominant subordinate component (DSC). The more amplitude of TW at substation produces R waves which pass more distance over the main feeder and therefore reflect from a farther node. The farther node means increasing the oscillation period and decreasing the frequency of DSC, and vice versa. Hence, it is concluded that when fault happens on farther branch regarding to substation, frequency of generated DSC increases. Based on the above discussions, difference between the frequencies of the DSC and DMC of TW can be used to determine faulted branch. Thus DF is defined as follows: