New Method for Locating Traveling Wave Faults in Rural Distribution Networks of Power Grids

Abstract

Rural distribution networks have complex structures and numerous branches, making it difficult to locate the fault point when a fault occurs. This article studies the precise positioning problem of single-phase grounding faults in complex rural distribution networks. A new method for locating multi-terminal traveling wave faults based on the principle of time information matching is proposed. Firstly, according to the distribution network structure, a time database of the traveling wave arrival time of each detection device is established in advance. Then, after the fault occurs, the time of detection device is compared with the database, and the section of the fault point is screened. Finally, the double-terminal traveling wave positioning method is used to determine the precise location of the fault. The simulation results show that this method could be applied to all kinds of complex fault situations. It is easy to achieve, with high accuracy and fewer errors, and it is not affected by the type of short circuit, transition resistance, initial phase angle of the fault, or fault location. It effectively solves the problem of fault location in rural distribution networks of a power grid.

1. Introduction

With the continuous expansion of the power grid’s scale and complexity, the users’ requirements for the security of the power grid are becoming higher and higher, and it is critical to ensure the power supply. The distribution network is the final power transmission link, which directly undertakes the mission of supplying power to customers [1,2,3]. China’s rural power grid has the characteristics of a complex line structure, lots of branch structures, and low distribution automation. At present, after the power grid fails, the manual line patrol is generally used. Once a distribution line failure occurs, a lot of manpower will be consumed to find the fault point, which is time-consuming, laborious, and inefficient. Therefore, it is urgent to establish an intelligent distribution network and then conduct centralized monitoring to accurately locate the faults on the distribution lines. To reflect the line conditions, facilitate the elimination of hidden dangers, and change passive emergency repair into active monitoring, it is necessary to achieve the controlled maintenance of distribution lines in a timely manner [4,5,6].

Domestic and foreign experts have conducted in-depth research on rural distribution networks. Currently, sectional circuit breakers are mainly installed in branch lines at the distribution line site. However, after the circuit breakers are disconnected, the fault points are manually found at a distance from the line, and the specific location of the fault points cannot be accurately determined [7]. The fault location is implemented by configuring the overhead remote fault indicator. This method could determine the faulty section effectively. However, there are many disadvantages to this method (such as the installation of more equipment, high cost, and difficult maintenance) [8,9]. The impedance method calculates the position of the fault point by using the impedance change caused by faults. But accuracy and reliability are greatly affected by the measurement environment and line parameters. In addition, there are a number of positioning errors in actual use [10]. Relevant research on fault locations in distribution lines is mainly focused on artificial neural networks, Petri networks, fuzzy set theory, etc. An artificial neural network can predict and fit data rules, but the convergence speed of the network algorithm is slow, and the large amount of computation requires high computing ability [11]. A Petri network can process discrete information, but the system structure should not be too complex, and the scale should not be large. The algorithm is subject to the power grid structure [12]. Fuzzy set theory is applicable to the analysis of uncertain problems, but its fault tolerance is not high, and it easily outputs wrong results [13]. In terms of the theory and method of fault diagnosis, a systematic method system and formed engineering practice are rarely applied. In the area of distribution line fault monitoring, there is no global informative, efficient, reliable, and intelligent fault identification system. Currently, the fault monitoring data of distribution lines are isolated, the function is single, and the degree of intelligence is low [14]. Many fault location methods for distribution lines cannot achieve ideal results in application.

To solve the problem of difficult fault location on rural distribution lines and to achieve the intelligent monitoring of distribution lines, this paper studies a multi-terminal fault location method based on the time information matching of complex rural distribution lines. This method is based on the distribution network structure, and it establishes the distribution network traveling wave arrival sampling device database. The detection data and the comprehensive fault section are compared. We also use the double-terminal traveling wave positioning method to determine the accurate location of the fault point on the fault section. The method then carries out intelligent fault monitoring of the rural distribution network and accurate fault location.

2. Principles and Methods of Fault Location in Distribution Networks

2.1. The Fault Location Principle of Distribution Networks

2.1.1. Principle of the Fault Traveling Time Database

The propagation speed of traveling wave signals in a uniform distribution network is the same, and the time taken for the initial traveling wave to reach the detection device is proportional to the length of the line. Firstly, the distribution network is divided into multiple sections based on nodes and intersections. The fault point can occur at any position in the line section. Then, the distances from the beginning and end of all line sections to each detection device are calculated, and the traveling wave speed is converted to the time database from the fault point to each detection device. Finally, the arrival times of the traveling waves from all detection devices are compared to determine the section where the fault point is located.

The initial traveling wave of the fault propagates at the same speed v, with the distance from the beginning of the section to a certain detection device l_s, the time t_s, the distance from the end of the section to the detection device l_t, and the time t_t.

$$t_{\mathrm{s}}={\displaystyle \frac{l_{\mathrm{s}}}{V}}$$

(1)

$$t_t={\displaystyle \frac{l_t}{V}}$$

(2)

The time from the beginning and end of the line section to the same detection device is divided into t_s, t_t. The time t_s from the beginning of all sections to a detection device is the lower limit of a time array, and the time t_t from the end of all sections to a detection device is the upper limit of a time array. Then, the distance between all sections of the distribution network through wave velocity and the time of all detection devices are converted to obtain a time array from each section to each detection device, thus constructing a traveling wave transmission time database.

2.1.2. The Double-Terminal Traveling Wave Positioning Principle

The double-terminal traveling wave method for fault location uses the initial traveling wave signal generated by the fault point of the line to calculate the distance between the fault point and the detection points at both ends of the line, based on the time difference when it reaches the detection points.

In Figure 1, it can be seen that the initial traveling wave of the fault reaches the line m and n detection devices at the same propagation speed v, and the time is Tm and Tn, respectively. The following equations exist:

$$\left\{\begin{array}{l}{\displaystyle \frac{L_{mf}}{V}}-{\displaystyle \frac{L_{nf}}{V}}=T_m-T_n\\ L_{mf}+L_{nf}=L\end{array}\right.$$

(3)

where L_mf and L_nf are, respectively, the distances between the two detection devices and the fault point and L is the length of the line mn. The equation system can be solved as follows:

$$\left\{\begin{array}{l}{L}_{mf}={\displaystyle \frac{1}{2}}\left[v(T_m-T_n)+L\right]\\ L_{nf}={\displaystyle \frac{1}{2}}\left[v(T_n-T_m)+L\right]\end{array}\right.$$

(4)

The double-terminal traveling wave method requires the accurate arrival time of the initial traveling wave at the fault point to the two detection devices; then, the distance from the fault point to the detection device is calculated. The detection devices at both ends of the distribution network can be installed at both ends of the main line. The double-terminal traveling wave method for positioning requires ensuring time synchronization at both ends of the detection device. Only the initial traveling wave needs to be identified for fault location, without considering the influence of multiple refracted and reflected waves during the traveling wave transmission process. This method has high positioning accuracy.

2.2. Fault Location Method for Distribution Networks

The distribution network fault location is divided into two parts. Firstly, the time array database is established according to the actual data of the distribution network, the time is recorded when the fault traveling wave signal is transmitted to the detection device according to different sections. If the recording time of the measuring device meets the set requirements, it is determined that the fault occurred in the specific preset section. Then, double-terminal traveling wave positioning of the detection device at both ends of the main line is used to calculate the distance from the fault point to the detection device and achieve fault point positioning.

A schematic diagram of the distribution network topology is shown in Figure 2, where A, B, C, D, E, F, G, and H are the nodes at the end of the distribution network and a, b, c, d, e, and f are the branch points on the distribution network line. The numbers represent the line length, and the unit is km. When a fault occurs in the distribution network, a traveling wave will be generated at the fault point and propagate towards both ends of the line. Based on the hyperbolic positioning principle, the hyperbolic equation system with the fault point as the focus is solved. At least three traveling wave positioning devices are required to uniquely determine the location of the fault point [15].

In this paper, the topology method based on graph theory is used for initial configuration, and the basic structure of the distribution network is analyzed. The specific configuration principles of the traveling wave detection device of the distribution network are as follows:

1.

Traveling wave detection devices must be installed at both ends of the main line of the distribution network.

2.

On a single branch connected to the main line, there is no need to install a detection device.

3.

On the multiple branches connected with the main line, one branch line should be selected to install the traveling wave detection device at the end side.

According to the analysis of the three configuration principles, the configuration principle follows 1, where traveling wave detection devices should be configured at both ends of main lines A and F. According to configuration principle 2, in a single branch line, nodes B, D, E, H, and G do not need to be equipped with traveling wave detection devices. According to configuration principle 3, we can select the C configuration traveling wave detection device on the aC branch. Therefore, three sampling points A, C, and F, can selected as the distribution network traveling wave signal detection device.

The traveling wave location method mainly adopts single-terminal and double-terminal fault traveling wave location methods. The two methods can facilitate fault location for transmission lines, but it is difficult to achieve accurate fault location for complex rural distribution networks [16,17]. Distribution network fault location needs to consider the special complex structure of the power grid and adopt the multi-terminal installation detection device, matched with the appropriate positioning method, to realize the accurate fault location of the distribution network [18].

The direct application of multi-terminal positioning may lead to multiple fault points at the same distance, so it is difficult to judge the branch on which the true fault occurs [19,20,21]. Therefore, considering the problem of branch location, it is necessary to establish a fault time database, simulate the fault on the line, calculate the distance between the fault point and detection devices A, C, and F, and then calculate the time when the traveling wave arrives at the detection device according to the traveling wave transmission speed. When the distribution line really breaks down, the specific section of the fault point is determined by comparing it with the established time database.

To establish a traveling wave arrival time database, it is necessary to calculate the distances between the terminal node (A–H) and branch intersection point (a–f) of the distribution line. By adding distribution line distances, the distance between the branch intersection point and the distribution line terminal node from the detection device distance is calculated. The topology of distribution network branch intersections is shown in Figure 3.

The distance between a node and detection devices A, C, and F is calculated by adding the distribution line length, as shown in

Table 1. Distance between nodes and the detection devices.

Starting Point	End Point	Distance (km)	Starting Point	End Point	Distance (km)	Starting Point	End Point	Distance (km)
A	A	0	C	A	20	F	A	23.5
A	B	19.2	C	B	10.4	F	B	20.5
A	C	20	C	C	0	F	C	21.3
A	D	18	C	D	6.2	F	D	19.3
A	E	15.9	C	E	13.7	F	E	10
A	F	23.5	C	F	21.3	F	F	0
A	G	23.3	C	G	21.1	F	G	4.4
A	H	19.2	C	H	17	F	H	15.7

. The distance between the intersection of each branch and the detection devices is shown in

Table 2. Distance between branch intersections and the detection devices.

Starting Point	End Point	Distance (km)	Starting Point	End Point	Distance (km)	Starting Point	End Point	Distance (km)
A	a	11.1	C	a	8.9	F	a	12.4
A	b	14.4	C	b	5.6	F	b	15.7
A	c	15.9	C	c	4.1	F	c	17.2
A	d	13.5	C	d	11.3	F	d	10
A	e	14.7	C	e	12.5	F	e	8.8
A	f	21.2	C	f	19	F	f	2.3

.

The starting point and ending point represent the beginning and end of the line measurement, respectively. Table 2 divides the distribution network into different sections. In this paper, U₁–U₁₃ in Figure 2 are divided into fault point occurrence section positions. U₁ indicates that the fault occurs between A and a, and the possible range of the fault is 0~11.1 km from point A. U₂ indicates that the fault occurs between a and d, and the possible range of the fault is 11.1~13.5 km from point A. U₃ indicates that the fault occurs between a and b, and the possible range of the fault is 11.1~14.4 km from point A; the same applies to U₄–U₁₃. By adding up the line distances, the distance range table between a fault point and the detection devices is established, as shown in

Table 3. Distance range between fault points and the detection devices.

Location of Fault Point	Distance from Point A (km)	Distance from Point C (km)	Distance from Point F (km)
U1	0–11.1	8.9–20	12.4–23.5
U2	11.1–13.5	8.9–11.3	10–12.4
U3	11.1–14.4	5.6–8.9	12.4–15.7
U4	14.4–19.2	5.6–10.4	15.7–20.5
U5	14.4–15.9	4.1–5.6	15.7–17.2
U6	15.9–20	0–4.1	17.2–21.3
U7	13.5–19.2	11.3–17	10–15.7
U8	13.5–14.7	11.3–12.5	8.8–10
U9	14.7–15.9	12.5–13.7	8.8–10
U10	14.7–21.2	12.5–19	2.3–8.8
U11	21.2–23.3	19–21.1	2.3–4.4
U12	21.2–23.5	19–21.3	0–2.3
U13	15.9–18	4.1–6.2	17.2–19.3

.

The time required for the traveling wave signal to propagate on the distribution line is proportional to the line length. By simulating different fault points, the corresponding propagation time of different fault points is calculated. Taking the fault point “a” of line U₁ as an example, assume that the distribution network is all overhead lines, and the traveling wave propagation speed is set to 3 × 10⁸ m/s. When the fault point occurs at point A of the detection device, the time required is at least 0 s. The longest time required for a traveling wave transmitted to point A can be calculated as follows:

$$t_t={\displaystyle \frac{l_t}{V}}={\displaystyle \frac{11.1\times {10}^3}{3\times {10}^8}}\times {10}^6=37 \mathrm{\mu }\mathrm{s}$$

(5)

The time for a traveling wave signal at a fault point to be transmitted to point C of the detection device is between

$$t_s={\displaystyle \frac{l_s}{V}}={\displaystyle \frac{8.9\times {10}^3}{3\times {10}^8}}\times {10}^6=29.66 \mathrm{\mu }\mathrm{s}$$

(6)

and

$$t_t={\displaystyle \frac{l_t}{V}}={\displaystyle \frac{20\times {10}^3}{3\times {10}^8}}\times {10}^6=66.66 \mathrm{\mu }\mathrm{s}$$

(7)

The time of fault traveling wave transmission to point F of the detection device is between

$$t_s={\displaystyle \frac{l_s}{V}}={\displaystyle \frac{12.4\times {10}^3}{3\times {10}^8}}\times {10}^6=41.33 \mathrm{\mu }\mathrm{s}$$

(8)

and

$$t_t={\displaystyle \frac{l_t}{V}}={\displaystyle \frac{23.5\times {10}^3}{3\times {10}^8}}\times {10}^6=78.33 \mathrm{\mu }\mathrm{s}$$

(9)

In the same way, the arrival schedule of U₂–U₁₃ fault traveling wave transmission to the detection device can be obtained, as shown in

Table 4. Arrival time of a fault traveling wave at the detection devices.

Location of Fault Point	Time of Propagation to Point A (μs)	Time of Propagation to Point C (μs)	Time of Propagation to Point F (μs)
U1	0–37	29.66–66.66	41.33–78.33
U2	37–45	29.66–37.66	33.33–41.33
U3	37–48	18.66–29.66	41.33–52.33
U4	48–64	18.66–34.66	52.33–68.33
U5	48–53	13.66–18.66	52.33–57.33
U6	53–66.66	0–13.66	57.33–71
U7	45–64	37.66–56.66	33.33–52.33
U8	45–49	37.66–41.66	29.33–33.33
U9	49–53	41.66–45.66	29.33–33.33
U10	49–70.66	41.66–63.66	7.66–29.33
U11	70.66–77.66	63.33–70.33	7.66–14.66
U12	70.66–78.33	63.33–71	0–7.66
U13	53–60	13.66–20.66	57.33–64.33

.

The time database of the fault traveling wave arrival detection device is established through analysis and calculation. Assume that the fault occurs in the “de” section, 1 km away from d branch point. Three detection devices are used to measure the arrival time of the traveling wave; then, the fault distance from the fault point to A, C, and F is calculated, and the fault point is determined by the intersection of the fault distance. Through the intersection of the distances measured by the three detection devices, the exact fault point at U₈ is finally determined. However, this method has a large amount of calculation, which requires manual analysis and comparison to eliminate false fault points, and it cannot automatically locate the fault points.

Therefore, this paper directly measures the time taken by the fault traveling wave to reach monitoring points A, C, and F and does not need to convert the time into the traveling wave transmission distance. The fault location is carried out in the fault occurrence section that meets the requirements, and then the accurate location of the fault point is determined through double-terminal traveling wave location. The diagram of the fault location process for rural distribution networks is shown in Figure 4.

3. Program Design of Distribution Network Fault Location

Firstly, the traveling wave detection devices A, C, and F detect the arrival time and list the arrival time into six double-type arrays, such as D, E, F, G, H, and I. In these six arrays, D and E, respectively, represent the upper and lower limits of the time when the traveling wave arrives at the monitoring point A. Arrays F and G, respectively, represent the upper and lower limits of the time when the traveling wave reaches monitoring point C. Arrays H and I, respectively, represent the upper and lower limits of the time when the traveling wave reaches monitoring point F. Secondly, a function is used to define three input variables of double-types X, Y and Z, which are used to input the time taken for the fault traveling wave to arrive at A, C, and F. Finally, a loop statement can be used to traverse the array with self-addition to find the required interval from the array until the fault can be found in the specific line section by comparing the database. After determining the fault section, combined with the method of double-terminal traveling wave positioning, accurate fault location of rural distribution networks can be realized.

4. Distribution Network Fault Location Simulation

According to the distribution network topology diagram and setting parameters shown in Figure 2, a distribution line simulation model was built in ATP (version 3.5) simulation software, which adopts the distributed parameter model (J. Marti model); the influence of the line on ground capacitance was considered. We selected the overhead line with the conductor model LGJ-240, and the traveling wave velocity was set to V = 3 × 10⁸ m/s, which verified the feasibility of the traveling wave fault location method for distribution lines. Then, we verified the feasibility of the traveling wave fault location method for distribution network faults on branch lines, main lines, and branch intersection nodes.

4.1. Branch Line Fault Location

Assume the fault occurs at the “dH” branch line section, 4.1 km away from H point. The traveling wave detection device is installed at the distribution transformer at the end of the distribution line to extract the voltage traveling wave. The distribution network fault topology is shown in Figure 5. The fault model of the simulated distribution network was drawn in ATP simulation software, as shown in Figure 6.

A, C, and F are the detection points of the three detection devices. The fault is set as a single-phase ground fault, the occurrence time is set to 0 s, the simulation step size is set to 1 × 10⁻⁸ s, and the total simulation time is set to 800 μs. The simulation waveforms of the traveling wave reaching detection points A, C, and F are shown in Figure 7. It can be seen from the figure that the initial wave head time of the waveform is very close, so it is impossible to accurately identify the initial time of the wave head. It is necessary to amplify the initial traveling wave head signal, as shown in Figure 8.

As can be seen from Figure 8, when the traveling wave head signal is calibrated, the initial time for fault traveling wave head transmission to detection point A is 50.3 μs, the transmission time to detection point C is 42.95 μs, and the transmission time to F detection point is 38.65 μs. Then, we input the time when the fault traveling wave arrives at A, C, and F into the program, compare it with the time database traversal of fault traveling wave arrival at the detection device, and filter to match the range of sections. The program simulation fault point is located in the U₇ section, which proves that the fault occurred on this branch.

Detection devices A and F at both ends of the main line are used to extract the initial signal of the wave head and perform double-terminal positioning to calculate the fault distance. The length of l_AF is 23.5 km. The distance from fault point f to node A is:

$$l_{Af}={\displaystyle \frac{1}{2}}\left[3\times {10}^5\times \left(50.3-38.65\right)\times {10}^{-6}+23.5\right]=13.498 \mathrm{km}$$

Because the fault point is located in the U₇ section (dH section), as determined by the program, the time from the intersection point d of the dH section branch to detection device A is 45 μs, and the distance from the fault point f to the intersection point d of the branch is:

$$l_{df}=\left(50.3-45\right)\times 3\times {10}^5\times {10}^{-6}=1.59 \mathrm{km}$$

The distance between the fault point of the branch line and detection device A is the double-terminal positioning value plus the distance from the fault point to the intersection point of the branch line: 13.498 + 1.59 = 15.088 km. The actual distance between the fault point and detection device A is 11.1 + 2.4 + 1.6 = 15.1 km. The positioning calculation error is 12 m.

4.2. Main Line Fault Location

Assuming the fault occurs at a distance of 14 km from point A and 0.5 km from point d on section de of the main line, the simulated distribution network fault model diagram is shown in Figure 9.

The initial wave head is amplified to A, C, and F, as shown in Figure 10. The transmission time of the fault traveling wave to detection point A is 46.67 μs, the transmission time to detection point C is 39.33 μs, and the transmission time to detection point F is 31.65 μs. The time when the fault traveling wave arrives at A, C, and F is entered into the program and compared with the time database of the fault traveling wave arrival detection device. After screening, we determined that the fault point is located in the U₈ section.

The fault distance is calculated using the double-terminal positioning method of detection devices A and f. The distance from fault point f to node A is:

$$l_{Af}={\displaystyle \frac{1}{2}}\left[3\times {10}^5\times (46.67-31.65)\times {10}^{-6}+23.5\right]=14.003 \mathrm{km}$$

The actual fault point distance A is 14 km, and the positioning error is 3 m.

4.3. Branch Intersection Node Fault Location

Assuming the fault occurs at point f of section fG of the branch intersection node 21.2 km away from point A, the simulation model diagram of the distribution network fault is shown in Figure 11.

The initial wave head is amplified to A, C, and F, as shown in Figure 12. The transmission time of the fault traveling wave to detection point A is 70.69 μs, the transmission time to detection point C is 63.34 μs, and the transmission time to detection point F is 7.67 μs. The time when the fault traveling wave arrives at A, C, and F is entered into the program and compared with the time database of the fault traveling wave arrival detection device. After screening, we determined that the fault point is located in the U₁₂ section of the branch line.

When considering a branch intersection node f fault, theoretically, node f belongs to the three connected sections fG, fF, and ef (U₁₀, U₁₁, U₁₂ sections). Because of the existence of time errors in traveling wave detection, the section positioning cannot fully locate the fault point; it can only locate it in a certain section near the node. Database comparison and positioning are only for the U₁₂ line section. Therefore, a certain margin needs to be set for the positioning of the branch intersection node to ensure the fault tolerance of the fault location. The fault distance is calculated through the double-terminal positioning method of the detection device.

The distance from fault point f to detection device A is:

$$l_{Af}={\displaystyle \frac{1}{2}}\left[3\times {10}^5\times (70.69-7.67)\times {10}^{-6}+23.5\right]=21.203 \mathrm{km}$$

The fault point of the traveling wave positioning is the main line U₁₂, and the actual fault point f is 21.2 km away from A. The branch intersection node cannot be accurately identified. There is a positioning deviation at the node, but the traveling wave positioning error is only 3 m. Onsite maintenance personnel can still find the accurate branch intersection node near the fault point, and within the allowable positioning error range, fault positioning can also be achieved.

Based on the simulation experiments, this fault location method has a maximum error of 12 m and a minimum error of 3 m in locating the branch line, main line, and branch intersection node, and it can achieve accurate fault location. Three traveling wave detection devices are used in this article. When a certain traveling wave detection device on the main line loses data and fails to locate due to a fault, it can be switched to another traveling wave detection device, which improves the fault tolerance and reliability of fault location.

Using the branch line fault simulation model as described before, we conducted a simulation analysis of different fault types. Three different short-circuit types, namely, a two-phase short-circuit, a two-phase short-circuit grounding, and a three-phase short-circuit, which occurred 4.1 km away from the H point, were taken as an example. The positioning results are shown in

Table 5. Fault location results of different short circuit types.

Fault Type	Two-Phase Short-Circuit	Two-Phase Short-Circuit Grounding	Three-Phase Short-Circuit
Positioning results	15.075 km	15.08 km	15.086 km
Positioning error	25 m	20 m	14 m

.

The occurrence of a single-phase fault was taken as an example for simulation under different transition resistances. The transition resistances were set from metal grounding to high-resistance grounding from small to large, and different transition resistances, such as 1 Ω, 100 Ω, and 1000 Ω, were used 4.1 km from the H point. The positioning results are shown in

Table 6. Fault location results of different transition resistors.

Transition Resistance	1 Ω	100 Ω	1000 Ω
Positioning results	15.088 km	15.079 km	15.07 km
Positioning error	12 m	21 m	30 m

.

The fault initial phase angles were adjusted to 15°, 30°, and 60°. The positioning results are shown in

Table 7. Fault location results of different fault initial phase angles.

Fault Initial Phase Angle	15°	30°	60°
Positioning results	15.116 km	15.12 km	15.118 km
Positioning error	16 m	20 m	18 m

.

Next, we adjusted the positions of different fault points separately. We selected the ad section of the main line 12 km away from detection device A, the de section of the main line 14 km away, and the Bb section of the branch line 16 km away. The positioning results are shown in

Table 8. Fault location results of different fault points.

Fault Distance	12 km	14 km	16 km
Positioning results	12.005 km	14.003 km	16.01 km
Positioning error	5 m	3 m	10 m

.

According to the above simulation positioning results, the position errors of the rural distribution networks are all within 30 m, which can meet the requirements of fault positioning accuracy.

In addition, after the same number of positioning devices was configured, the time information matching the multi-terminal traveling wave fault positioning method proposed in this paper was compared with the new fault positioning method combined with two traveling wave principles and the D-type positioning method [22]. Fault points were set for the main lines and branch lines, and simulation verification was carried out under different transition resistances and fault initial phase angles. The positioning results are shown in

Table 9. Comparison of the locating results of a single-phase grounding fault in the distribution network.

Fault Location	Transition Resistance/(Ω)	Fault Initial Phase Angle/(°)	Algorithm in This Paper		Combination Algorithm of Two Traveling Wave Principles [22]		D-Type Algorithm [22]
			Positioning Distance/km	Absolute Error/km	Positioning Distance/km	Absolute Error/km	Positioning Distance/km	Absolute Error/km
Line ad, 12 km from end A	20	15	12.028	0.028	12.045	0.045	12.045	0.045
	500	30	12.030	0.030	12.046	0.046	12.046	0.046
	20	60	12.024	0.024	12.042	0.042	12.042	0.042
	500	90	12.022	0.022	12.042	0.042	12.042	0.042
Line Bb, 16 km from end A	20	15	15.965	0.035	15.659	0.341	14.447	1.553
	500	30	15.971	0.033	15.665	0.335	14.445	1.555
	20	60	15.972	0.028	15.665	0.335	14.445	1.555
	500	90	15.974	0.026	15.671	0.329	14.445	1.555

.

As can be seen from the comparison of the location results in Table 9, when a fault occurs in the main line, if the fault point is in the “ad” section of the main line, it is 12 km away from the A detection device. The maximum positioning error of this algorithm is 30 m, and the maximum error of the new fault location method combined with two traveling wave principles and the D-type location method is 46 m. The three methods mentioned above can achieve accurate fault location. However, with the time information matching multi-terminal traveling wave fault location method proposed in this paper, by using multiple sets of time constraints, the fault point can be uniquely determined by comparing and traversing the time array. Then, fault location can be achieved by using double-terminal traveling wave positioning, which has high accuracy and a small error. Overall, the maximum positioning error is reduced by 34.8%.

Table 9 also shows a fault that occurs in the branch line, where the fault point is in the branch line section “Bb”, which is 16 km away from the A detection device. Because of the need to extract zero-mode and linear-mode wave velocities through phase-mode transformation, inaccurate extraction of zero-mode and linear-mode waves can lead to positioning errors. Therefore, the fault location method based on the combination of two traveling wave principles has a large positioning error, and the accuracy is within the range of 0.341 km. The D-type positioning method has a false fault point, and when the fault point is a branch point of the branch line, the absolute error is 1.555 km. In addition, the error value is too large, which made the method fail. In contrast, the positioning error of the method proposed in this paper is within 35 m in all cases, which accurately determines the fault location.

This method is less affected by the fault location, transition resistance, and initial phase angle of the fault, and it has high positioning accuracy. Therefore, the time information matching multi-terminal traveling wave fault location method proposed in this article has the characteristics of a simple process and accurate positioning, which can meet the requirements of precise fault location in rural distribution networks.

However, in actual distribution networks, different types of lines have different wave speeds. The aging of the line and an increase in temperature can lead to an increase in wire resistance, a decrease in wave speed, and intensified signal attenuation and distortion, making it more difficult to accurately detect time and affecting positioning accuracy. It is necessary to combine multi-dimensional methods, such as signal processing and equipment status evaluation, to effectively improve positioning accuracy. The initial wave head signal of a traveling wave has noise interference in detection, which can easily confuse the wave head characteristics and submerge the signal. The interference of the wave head signal can directly lead to measurement errors in the arrival time of the wave head, affecting the accuracy of traveling wave positioning. Filtering and preprocessing are needed to remove noise and interference and improve robustness in noisy environments. The distribution network needs to manually readjust each section to the detection device time database due to changes in line length, but it cannot be automatically updated in real time. There are positioning deviations at the intersection of branches, which affect accuracy and require consideration of fault tolerance. Therefore, further research is needed.

5. Conclusions

Aiming at the problem that it is difficult to find a fault location accurately in rural distribution networks, a fault location method based on time information matching and a multi-terminal traveling wave is proposed. This method is based on the original double-terminal traveling wave location method, combined with an arrival time database comparison method of traveling waves. Thanks to this method, we can determine the fault section and then determine the fault point location, which is easy to realize and has high positioning accuracy. Based on the simulation test, the fault location method is more accurate in locating the fault points of the main line and branch line under different fault conditions, which made up for the shortcomings of the conventional traveling wave location method. So, this method can realize the accurate fault location of the distribution network and solve the problem that the traveling wave location is difficult to locate accurately in the rural distribution networks of a power grid.