A method for locating lightning strikes in distribution lines with multiple branches

A lightning strike fault location (FT) method for multi-terminal overhead lines based on 0-mode 1-mode wave velocity difference is proposed to address the shortcomings of current multi-terminal overhead line positioning methods that are difficult to identify due to multi-terminal GPS time synchronization and reflected traveling waves. Based on the wave velocity difference between 0-mode and 1-mode, single-end ranging is performed, and an FT judgment vector is formed based on the ratio of the ranging results of each monitoring terminal to the inherent length of the line. By analyzing the element features in the FT judgment vector, an FT criterion is proposed, and the FT results of the appropriate monitoring terminal are selected as the final FT. After PSCAD/EMTDC simulation verification, this method is suitable for complex multi-branch overhead lines, and can accurately locate the FT without being affected by time synchronization.


Introduction
Power lines are the transmission lifeline of the power grid and play a huge role in the long-distance and high-capacity transmission process in China.High voltage transmission lines not only traverse complex terrain but also have unpredictable climatic conditions, making them the most vulnerable and prone to faults in the power system [1][2].Therefore, quickly and accurately locating faults, and isolating faults after faults can effectively improve the power supply service level of the power grid.
With the development of digital signal technology, the traveling wave method is increasingly widely used in the field of power system protection and fault diagnosis.The traveling wave method is generally divided into six methods: A~E.The dual-end traveling wave method installs monitoring terminals at both ends of the line, relying on the time difference between the traveling waves reaching the monitoring terminals on both sides for positioning.However, this method relies on GPS for clock synchronization, otherwise, the final positioning results will have significant errors [3].In addition, the dual terminal traveling wave method cannot accurately locate the fault location when monitoring terminal packet loss [4][5].Therefore, many experts and scholars have studied the application of the single-ended traveling wave method in Cable fault locations.
The main drawback of the single-ended method is that it cannot determine whether the second reverse traveling wave is a reflection of the fault point or the reflection of the opposite end bus.Many scholars at home and abroad have conducted research on this issue.Initially, scholars used high-pass or bandpass filters for wavefront detection for single-ended ranging, but the time window width of this method is difficult to determine and there are significant errors.Using Mathematical morphology as a filter for this algorithm [6] can improve the reliability, but this method has a poor effect on noise signal processing.Some scholars have proposed using wavelet algorithms to extract effective features from fault current traveling wave signals, but wavelet can only perform binary decomposition on the signal, which may miss useful information in high-frequency signals, making it difficult to accurately identify the second traveling wave head [7][8].With the development of artificial intelligence in recent years, some scholars combine neural networks with single-ended distance measurement, train data samples, and establish models to carry out Cable fault location (FT) [9].However, it is difficult to obtain sample data that meets the model training requirements.
This article proposes a multi-terminal overhead line lightning FT method based on wave velocity difference.This method first performs phase mode transformation on the traveling wave, extracts the time when the 1-mode component and 0-mode component arrive at the monitoring terminal, uses their time difference for single terminal traveling wave location, and forms a fault feature vector based on the ratio of the positioning result to the inherent length of the line branch.The fault area is determined by the characteristics of the fault feature vector, combining appropriate single-ended traveling waveranging results as the final FT.This method is neither affected by clock asynchrony nor has the disadvantage of difficult recognition of fault traveling wave reflection wave heads.After PSCAD simulation verification, this method has a certain degree of reliability and can meet the accuracy requirements of FT.

Single-end positioning principle based on wave velocity difference between 0-mode and 1mode
The 0-mode traveling wave significantly decays due to the influence of distance during transmission, Therefore, there are differences in the time when different modal components arrive at the monitoring terminal.The schematic diagram of a single-ended traveling wave ranging based on 0-mode 1-mode wave velocity difference is shown in Figure 1.If a lightning strike fault occurs at point F, there are: In the formula, S1 is the distance from the fault point F to the monitoring terminal M, v0 and v1 are the 0-mode and 1-mode component velocities, t0 and t1 are the time when the 0-mode and 1-mode arrive at the monitoring terminal, respectively, Δt is the time difference between the 0-mode 1-mode and the monitoring terminal.
Then the Cable FT formula can be obtained as shown in Formula (2).Formula (2) is the traveling wave ranging formula based on the 0-mode linear mode wave velocity difference.

Modeling methods
The simulation topology structure of the multi-terminal overhead line is shown in Figure 2. It is defined as starting from the last level branch line, and the length from the monitoring terminal on the branch line to the first node is the inherent length of the branch line.After the node is selected, it is excluded from the calculation of the length of the upper-level branch line.
Topological structure of overhead lines.As shown in the lightning strike Conditions ①, ②, and ③ marked in Figure 2, the three types of lightning strike conditions are lightning strike branch lines, between lightning strike main nodes, and lightning strike nodes.Below, the characteristics of the lightning FT vector will be analyzed for these three different lightning strike conditions.

Formation of FT judgment vector
When a lightning strike fault occurs on an overhead line, we first perform single-end positioning based on 0-mode 1-mode wave velocity difference for all monitoring terminals that have detected obvious fault waveforms, and calculate the distance from the fault point to the monitoring terminal, as shown in Formula (2).For N1 monitoring terminals, single-end positioning is shown in Formula (3).
1 01 1 10 After obtaining the distance from the lightning fault point to the monitoring terminal, the element of the FT judgment vector is defined as the ratio of the fault distance to the inherent length of the branch line where the monitoring terminal is located, as shown in Formula (4).
In the formula, ai is the i-th element in the FT judgment vector, si is the lightning fault distance calculated by the i-th monitoring terminal, and li is the length of the branch line where the i-th monitoring terminal is located.
After calculating all vector elements, the FT judgment vector is obtained as shown in Formula (5).
Considering factors such as sag and line aging in practical situations, it is necessary to handle the error of elements in the FT judgment vector.The error must be selected based on the line topology and the tolerable error of positioning.Combined with the line topology targeted in this article, it is believed that if the element value is less than 0.97, the element value is less than 1.If the element value is between 0.97 and 1.03, the element value is considered equal to 1.If the element value is greater than 1.03,It is considered that the element value is greater than 1.  2, when a lightning strike fault occurs on the N1T1 branch line, the fault distance sN1 calculated by the N1 monitoring terminal is less than the length of the branch line lN4, while the fault distance calculated by other monitoring terminals is greater than the length of the line where the monitoring terminal is located.Therefore, the elements in the vector behave as a4 less than 1, while other elements are greater than 1.

ISCME-2023
When a lightning strike fault occurs between the main line nodes, as shown in Condition ②.At this point, it can be seen that the fault distance calculated by all monitoring terminals is greater than the length of the branch line, so the elements in the vector represent that all elements are greater than 1.
When a lightning strike fault occurs at node T3 as shown in Condition ③, it can be seen that the fault distance sN2 calculated by the N1 monitoring terminal is equal to the length of the branch line lN1, while the fault distance calculated by other monitoring terminals is greater than the length of the line where the monitoring terminal is located.Therefore, the elements in the vector behave as a2 equals 1, and the other elements are greater than 1.
Propose criteria for different fault conditions in overhead lines: When the value of one element in the FT judgment vector is less than 1 and all other elements are greater than 1, a lightning strike fault occurs on the branch line where the corresponding monitoring terminal of that element is located; When all elements in the FT judgment vector are greater than 1, lightning strikes occur between the main line nodes; When the value of one element in the fault location judgment vector is equal to 1 and all other elements are greater than 1, a lightning strike fault occurs at the corresponding node of the monitoring terminal.
After judging the initial location of the lightning strike fault according to the criteria, take the Cable FT of the corresponding monitoring terminal as the final lightning strike FT.

Simulation results and analysis
A simulation model is built as shown in Figure 2 in the electromagnetic transient simulation program PSCAD/EMTDC to verify the effectiveness of this method.To comply with the actual situation, we set the sampling rate to 10 MHz and input the simulated data into the Python program for relevant calculations.
Three operating conditions in the simulation model are set, as shown in Figure 2, to determine the effectiveness of this algorithm.

Lightning strike branch line
As shown in working Condition ① in Figure 2, the lightning strike fault occurred on the T1N1 line.The FT judgment vector a1 at this time can be obtained as shown in Formula (6).=(0.789，1.949，2.747，1.584，2.303) Performing error processing on Formula (6) to obtain Formula (7).
Observing Formula (10), the criterion for lightning strike branch line land proposed in this article can determine that the lightning strike fault occurred on the N1T1 line, and can be located according to Formula (2), as shown in Formula (8).
The FT calculation shows that the distance between the lightning strike fault point and the N1 monitoring terminal is 1452.1 meters, which is set to 1350 meters in simulation, and the positioning error is 102.1 meters.

Between lightning strike main line nodes
The lightning strike occurs between the main line nodes, as shown in working Condition ② in Figure 2.
The FT judgment vector obtained after error processing is shown in Formula (9).
Observing Formula ( 9), all elements in the FT judgment vector are greater than 1.According to the proposed criterion, the lightning fault occurs on the T1T3 line.Comparing the current amplitudes recorded by the P1 monitoring terminal and the P2 monitoring terminal, a larger P2 monitoring terminal is selected for single-end positioning based on the 0-mode 1-mode wave velocity difference.The positioning result is 3083 meters.In the simulation, the fault distance set to the P2 monitoring terminal is 3000 meters, with an error of 83 meters.

Lightning strike node
The lightning strike occurred at node T2, as shown in Condition ③ in Figure 2. At this point, the FT judgment vector a3 corresponding to lightning strikes on this line can be obtained as shown in Formula (10).
From (10), the element corresponding to the N2 monitoring terminal in the vector is equal to 1.We analyze the circuit topology and connect the N2 monitoring terminal to node T2.Therefore, based on the proposed criteria, it can be concluded that node T2 has a lightning strike fault.

Algorithm accuracy analysis
Lightning faults are set at different locations in the simulation model.Using the lightning strike FT method proposed in this article, the FT results are shown in Table 1.  1, the method proposed in this article can accurately locate the lightning strike conditions along the entire line and has good global observability.Moreover, the error proposed in this method is within two spans of the distribution line, which is within an acceptable range.

Conclusions
This article proposes a multi-terminal network lightning FT method based on the wave velocity difference between 0-mode and 1-mode.This method first utilizes the difference in wave velocity between the 0-mode component and the 1-mode component of the fault current traveling wave for single terminal localization and obtains the distance between the lightning fault and each monitoring terminal.Then compare the fault distance with the inherent line length in the network to obtain the FT judgment vector.A lightning strike FT criterion based on the FT judgment vector was proposed.After preliminarily determining the fault area through criteria, select the appropriate monitoring terminal single-end positioning result as the final lightning strike FT.After PSCAD/EMTDC simulation verification, this method has certain feasibility and can accurately determine the FT and calculate the final fault distance, without being affected by the asynchronous monitoring terminal clock.