Introduction to the Principle of A-type Modern Traveling Wave Fault Location

0 Introduction
Transmission line traveling wave fault distance measurement technology has always attracted the attention of relay protection professionals due to its advantages such as high distance measurement accuracy and wide application range [1]. As early as the 1950s, foreign countries developed four basic types of traveling wave fault distance measurement devices, namely A, B, C, and D. However, due to problems such as poor reliability, complex structure and high price, they were not widely used.
In the 1980s, based on the early traveling wave fault distance measurement principle of type A, domestic and foreign countries proposed the traveling wave distance protection principle that integrates protection and distance measurement [2,3]. However, due to the unreliability of the distance measurement algorithm and the limitations of field test conditions, the traveling wave distance protection has not been further developed.
In the 1990s, China proposed the principle, algorithm and implementation scheme of transmission line traveling wave fault location using current transient components [4-8], which promoted the development of modern traveling wave fault location (MTWFL) technology [9], and successively developed modern traveling wave fault location devices and systems integrating multiple principles such as A, D, and E, and their absolute location error has been able to reach within 200 m [10,11]. In the field of applied research, in order to further improve the accuracy of traveling wave fault location, wavelet modulus maximum detection theory has been increasingly widely used in single-end and double-end traveling wave fault location research [12-15].
In recent years, domestic scholars have begun to apply the type A modern traveling wave fault location principle to relay protection, and proposed a distance-based traveling wave distance protection principle based on wavelet transform [16,17].
In order to better apply the type A modern traveling wave fault location principle to measured waveform analysis, this paper divides it into three independent operating modes, namely standard mode, extended mode and comprehensive mode, and gives typical examples of each mode for measured current transient waveform analysis.

1 Operation mode of type A modern traveling wave fault distance measurement principle
type A modern traveling wave distance measurement principle is a single-ended principle. According to the different properties of the detected reflected waves, type A modern traveling wave distance measurement principle can be divided into three operation modes, namely standard mode, extended mode and comprehensive mode. In standard mode, it is necessary to detect the reflected wave at the fault point, in extended mode, it is necessary to detect the reflected wave of the opposite busbar, and in comprehensive mode, it is necessary to detect the second reverse traveling wave surge and identify its nature.
1.1 Standard mode
The type A modern traveling wave fault distance measurement principle in standard mode uses the time delay between the first positive traveling wave surge felt at the measuring end when the line fails and its reflected wave at the fault point to calculate the distance between the measuring point and the fault point. Its basic principle is the same as the early type A traveling wave fault distance measurement principle. In order to realize the type A modern traveling wave fault distance measurement principle in standard mode, the reflected wave of the first positive traveling wave surge caused by the fault at the fault point must be accurately and reliably detected at the measuring end.
1.2 Extended Mode
The A-type modern traveling wave fault distance measurement principle in the extended mode uses the time delay between the first reverse traveling wave surge felt at the measuring end when the line fails and the reflected wave of the initial traveling wave surge of the fault transmitted through the fault point on the opposite bus to calculate the distance between the opposite bus and the fault point.
In order to realize the A-type modern traveling wave fault distance measurement principle in the extended mode, the reflected wave of the initial traveling wave surge of the fault transmitted through the fault point on the opposite bus must be accurately and reliably detected at the measuring end.
When the reflection coefficient of the fault point to the transient traveling wave is small, the reflected wave of the first forward traveling wave surge at the fault point at the measuring end may not be detected, resulting in the failure of the A-type modern traveling wave fault distance measurement principle in the standard mode. However, in this case, the A-type modern traveling wave fault distance measurement principle in the extended mode can work well.
1.3 Comprehensive mode
The A-type modern traveling wave fault distance measurement principle in the comprehensive mode uses the time delay between the first positive traveling wave surge and the second reverse traveling wave surge felt at the measuring end when the line fails to calculate the distance between the measuring point at the local end or the opposite end busbar and the fault point.
Analysis shows that no matter how the busbar is connected, the initial traveling wave surge of the fault can generate a reflection wave with a relatively obvious amplitude when it reaches the busbar [4]. It can be seen that when a line fault occurs, the time when the measuring end feels the first positive traveling wave surge and the first reverse traveling wave surge is the same. The second reverse traveling wave surge felt by the measuring end can be either the reflection wave of the first positive traveling wave surge at the fault point (when the fault point is within the midpoint of the line), or the reflection wave of the initial traveling wave surge of the fault transmitted through the fault point at the opposite end busbar (when the fault point is outside the midpoint of the line), or the superposition of the two (when the fault point is exactly at the midpoint of the line). For high-resistance faults (weak reflected waves at the fault point), even if the fault point is within the midpoint of the line, the second reverse traveling wave surge felt at the measurement point may be a reflected wave from the opposite bus. For faults where the arc at the fault point is extinguished prematurely (no reflected wave exists at the fault point), regardless of the location of the fault point, the second reverse traveling wave surge felt at the measurement point is a reflected wave from the opposite bus.
Therefore, when a line fault occurs, if the nature of the second reverse traveling wave surge felt can be correctly identified at the measurement end, single-end traveling wave fault ranging can be achieved. Specifically, when the second reverse traveling wave surge is a reflected wave of the first forward traveling wave surge at this end at the fault point, the time delay between the two corresponds to the distance between the measurement point at this end and the fault point; when the second reverse traveling wave surge is a reflected wave from the opposite bus, the time delay between it and the first forward traveling wave surge at the measurement point at this end corresponds to the distance between the opposite bus and the fault point.
It can be seen that in order to realize the type A modern traveling wave fault ranging principle in the integrated mode, the second reverse traveling wave surge caused by the fault must be accurately and reliably detected at the measuring end and its nature must be identified.

2 Direct waveform analysis method for realizing type A traveling wave ranging principle using current transient components
2.1 Basic relationship of traveling wave fault ranging
From the perspective of traveling wave fault ranging, busbars can be divided into two types of connection [4], where the first type of busbar is connected to multiple lines of the same voltage level, while the second type of busbar is only connected to one line. Most of the buses in the power system are type 1 buses. With respect to the traveling wave from the line MN direction, the equivalent wave impedance of the busbar M at the measuring end is equal to the parallel impedance of all line wave impedances on the busbar except line MN and the busbar distributed capacitance. Assuming that all lines connected to bus M have the same wave impedance, the time domain reflection coefficient KMR and time domain transmission coefficient KMT of bus M to the voltage transient traveling wave from line MN can be expressed as:

Where: F-1 represents the inverse Fourier transform; K is the number of lines connected to bus M other than line MN (assuming K≥2); C is the distributed capacitance of bus M; ZC is the line wave impedance.
Assuming that the positive direction of the current at terminal M is from bus to line, the transient fault component of the current in this line caused by the initial traveling wave surge generated by the fault in line MN reaching this end can be expressed as: The transient fault component of the current in this

line caused by the reflected wave of the first positive traveling wave surge eF(t) at terminal M (i.e., the reflected wave of the initial traveling wave surge of the fault on bus M) at the fault point reaching bus M can be expressed as:

Where: KFR is the reflection coefficient of the voltage transient traveling wave at the fault point (assuming it is a constant).
The transient fault component of the line current caused by the reflected wave of the initial fault wave surge at the bus N at the opposite end of line MN passing through the fault point to reach the bus M can be expressed as:

where: KFT is the transmission coefficient of the voltage transient traveling wave at the fault point (assumed to be a constant); KNR is the reflection coefficient of the voltage transient traveling wave at the opposite end bus N; is the propagation time of the transient traveling wave from the fault point to the opposite end bus N.
Comparing equations (3) to (5), we can obtain that

the reflection coefficient of the transient traveling wave at bus M and fault point F is always negative, and the transmission coefficient at the fault point is always positive. Therefore, the transient fault components Δi1(t) and Δi2(t) of the current in line MN caused by the initial fault traveling wave surge and the reflected wave at the fault point reaching bus M have the same polarity, and the time delay between the two is equal to the propagation time of the transient traveling wave between the measurement point at the M end and the fault point. The transient fault components Δi1(t) and Δi′2(t) of the current in the line caused by the initial fault traveling wave surge and the reflected wave at the opposite end bus N of the fault line reaching the M end bus have opposite polarities in a certain initial period (depending on the wiring mode of the opposite end bus N) [4], and the time delay between the two is equal to the propagation time of the transient traveling wave between the fault point and the opposite end bus N.
It can be seen that when a line fault occurs, the reflected waves from the fault point and the busbar at the opposite end of the line can be identified by comparing the initial polarity of the transient component of the fault line current caused by the traveling wave surge from the fault direction reaching the measuring end busbar. In this case, as long as the transient component of the current caused by the traveling wave surge from the positive direction and the reverse direction of the fault line reaching the measuring end busbar can be correctly distinguished, the A-type modern traveling wave fault distance measurement principle under various operation modes can be realized.
2.2 Identification of the transient component of the current caused by the traveling wave surge
from the fault direction The transient component of the current of the fault line and the adjacent sound lines caused by the traveling wave surge from any point X in the fault direction reaching the busbar M can be expressed as:

Where: is the propagation time of the transient traveling wave from point X to the busbar M; K is the number of adjacent sound lines (assuming K≥2).
Since the reflection coefficient KMR is always less than 0, equation (9) shows that there is an opposite polarity relationship between the transient component of the fault line current caused by any traveling wave surge from the fault direction reaching the busbar M and the transient components of the current of all other adjacent sound lines.
Similarly, when a traveling wave surge from the positive direction of any line reaches the busbar M, the transient current component of the line caused by the current surge of the line and the transient current components of all other lines (including the fault line) have an opposite polarity relationship. Therefore, by comparing the polarities of the transient current components of each line caused by the traveling wave surge reaching the busbar M, the transient current component caused by the traveling wave surge from the fault direction can be identified.
When there are many outgoing lines on the busbar, the amplitude of the transient current components of each healthy line caused by the traveling wave surge from the fault direction reaching the busbar is very small, and can even be ignored, thereby simplifying the fault distance measurement process.
It should be pointed out that the line loss and the frequency-dependent characteristics of the line parameters are not taken into account in the above analysis. These influencing factors will cause the attenuation and distortion of the traveling wave during the propagation process, but the polarity relationship between the above-mentioned traveling wave surges still holds.
2.3 Implementation steps of direct waveform analysis method
The specific steps of using direct waveform analysis method of current transient component to realize the principle of type A modern traveling wave fault location are as follows (taking comprehensive mode as an example):
1) Select the fault line by comparing the polarity of the first wave head component in the current transient component waveform
of each line on the same bus; 2) For each wave head component in the current transient waveform of the fault line, determine the second wave head component caused by the traveling wave surge from the fault direction by comparing it with the polarity of the current transient components of other lines at the same time;
3) By comparing the initial polarity of the second wave head component in the current transient waveform of the fault line caused by the traveling wave surge from the fault direction with the first wave head component, determine whether the second wave head component is caused by the reflected wave of the fault point (the two have the same polarity) or caused by the reflected wave of the opposite bus (the two have opposite polarities), and then determine the location of the fault point. [page]

3 Measured fault analysis
3.1 Both the local and opposite busbars are Class 1 busbars
At 2:17:49 on December 14, 1997, a phase A ground fault occurred on the 330 kV Longma line (total length 311 km) under the jurisdiction of the Tianshui Power Supply Bureau of Gansu Province. The transient fault component waveforms of the fault phase currents of the three lines on the same busbar including the fault line on the Longxi side are shown in Figure 1. Obviously, the local busbar is a Class 1 busbar. On the fault line, the second wave head component caused by the wave surge from the fault direction always has the opposite polarity to the initial wave head component, so it must be caused by the reflected wave of the opposite busbar, and the opposite busbar is also a Class 1 busbar, so the distance measurement result in the extended and comprehensive modes can be directly obtained as 75.8 km, as shown in Figure 1 (a). The distance measurement result in the standard mode can be obtained indirectly (it is difficult to obtain directly in this case), which should be equal to the difference between the actual conductor length of the fault line and the distance measurement result in the extended or comprehensive mode, and can be approximately expressed as (km). From the transient component waveform of the fault line current, it can be found that there is no transient wave head component at the position corresponding to the approximate distance measurement result, but there is a transient wave head component caused by the wave surge from the fault direction in its neighborhood at 235.6 km away from this end, as shown in Figure 1(b), so the distance measurement result in the standard mode can be corrected to 235.6 km. The actual fault point is located at (235-236) km away from this end. In this case, the reflected wave of the opposite bus reaches the measurement point at this end before the reflected wave of the fault point, so the fault point is located outside the midpoint of the line (close to the opposite end).

At 14:33:07 on April 5, 2002, a phase B ground fault occurred on the 220 kV Kangsui A line (total length 64.3 km) under the jurisdiction of Heilongjiang Suihua Electric Power Bureau. The transient fault component waveforms of the fault phase currents of the three lines on the same bus including the fault line on the Kangjin side are shown in Figure 2. The busbars at both ends of the fault line are connected to multiple other lines, so the busbars at both ends are Class 1 busbars. On the fault line, the second wave head component caused by the wave surge from the fault direction always has the same polarity as the initial wave head component, so it must be caused by the reflected wave at the fault point, so the distance measurement results of 27.4 km in the standard and comprehensive modes can be directly obtained, as shown in Figure 2(a). On the fault line, the third wave head component (superimposed on the second transient component of the transient waveform) caused by the wave surge from the fault direction always has the opposite polarity to the initial wave head component, so it must be caused by the reflected wave of the busbar at the opposite end of the line, so the distance measurement result in the extended mode can be directly obtained as 36.9 km, as shown in Figure 2(b). The actual fault point is located 37 km away from the opposite end. In this case, the reflected wave from the fault point reaches the measurement point at this end before the reflected wave from the busbar at the opposite end, so the fault point is located within the midpoint of the line (close to this end).

3.2 The local and opposite busbars are Class 1 and Class 2 busbars respectively.
At 13:46:47 on October 2, 1997, a B-phase grounding fault occurred on the 110 kV Linyu line (total length 43 km) under the jurisdiction of Shandong Dezhou Electric Power Bureau. The transient fault component waveforms of the fault phase currents of the three lines on the same busbar including the fault line on the Linyi side are shown in Figure 3. It can be seen that the waveform is relatively complex. A careful analysis shows that there is a wave head component caused by the traveling wave surge from the fault direction at a fault distance of 26.9 km. Its initial polarity is opposite to the polarity of the initial wave head component of the fault, but the two quickly become the same polarity. Therefore, it must be caused by the reflected wave of the opposite busbar of the line, and the opposite busbar must be a Class 2 busbar. Therefore, the distance measurement result in the extended mode can be directly obtained as 26.9 km, as shown in Figure 3 (a). The distance measurement results in the standard and comprehensive modes can be obtained indirectly and are approximately (km). From the transient component waveform of the fault line current, it can be found that there is a transient wave head component caused by the traveling wave surge from the fault direction at a distance of 16.5 km from the local end in the neighborhood corresponding to the approximate position, as shown in Figure 3(b), so the distance measurement results in the standard and comprehensive modes can be corrected to 16.5 km. The actual fault point is located 16 km from the local end (within the midpoint of the line).

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At 4:03:25 on April 29, 2001, a phase A ground fault occurred on the 220 kV Sui-Tie line (96.4 km in total length) under the jurisdiction of the Suihua Electric Power Bureau in Heilongjiang Province. The transient fault component waveforms of the fault phase currents of the three lines on the same bus including the fault line on the Suihua side are shown in Figure 4. At the fault distance of 34 km, there are two wave head components caused by the traveling wave surge from the fault direction. Their initial polarity is opposite to that of the initial wave head component of the fault, but the two quickly become the same polarity. Therefore, they must be caused by the reflected wave of the bus at the opposite end of the line, and the bus at the opposite end must be a Class 2 bus. Therefore, the distance measurement result of 34 km in the extended and comprehensive mode can be directly obtained, as shown in Figure 4(a). At the fault distance of 62.4 km, there is a third wave head component caused by the traveling wave surge from the fault direction. Its polarity is always the same as the polarity of the initial wave head component of the fault, so it must be caused by the reflected wave of the fault point, so the distance measurement result of the standard mode can be directly obtained as 62.4 km, as shown in Figure 4(b). The actual fault point is located 62.525 km away from the local end (outside the midpoint of the line).

4 Conclusion
This paper divides the A-type modern traveling wave fault distance measurement principle into three independent operation modes: standard, extended and comprehensive. The various operation modes are used for the analysis of the current transient waveform generated by the actual fault by using the direct waveform analysis method of the current transient component. The measured fault analysis shows that the absolute distance measurement error of the A-type modern traveling wave fault distance measurement principle does not exceed 500 m.
Due to the complexity of some fault transient waveforms, reliable distance measurement results cannot be directly obtained in all operation modes. In order to further improve the reliability of the A-type modern traveling wave fault distance measurement principle, it is very necessary to combine the actual fault transient waveform and conduct in-depth research on the real-time and reliable modern traveling wave detection and identification algorithm.