CN105699855B - Based on the single-ended traveling wave fault location calculation method not influenced by traveling wave speed and distance measuring method - Google Patents

Abstract

A single-terminal traveling wave fault location method based on the unaffected by traveling wave velocity, a single-terminal traveling wave fault location calculation method based on the unaffected by traveling wave velocity; assuming the fault occurrence time is t ₀ , the initial electric current The time when the prevailing wave arrives at the M terminal is t _1M , and then the time when the first or second type of traveling wave arrives at the M terminal is t _2M , and the time when the first, second or third type of traveling wave arrives at the M terminal is t _3M , t _4M ... ..., let L be the total length of the line, x be the distance from the fault point to the bus M, when 0<x<L/3, when L/2<x<2L/3 and when 2L/3<x<L When the three states are calculated, it is only related to the time and no longer related to the propagation speed of the traveling wave, so it is no longer limited by the implementation conditions, and the accuracy of ranging is improved.

Description

Calculation method and distance measurement based on single-ended traveling wave fault location not affected by traveling wave velocity method

technical field

The patent of the present invention relates to a single-end traveling wave fault ranging calculation method, in particular to a single-end traveling wave fault ranging calculation method and ranging method based on the single-end traveling wave fault not affected by the traveling wave velocity.

Background technique

When a power line fails, accurately determining the fault point of the power line is conducive to quickly troubleshooting and restoring line power supply. Therefore, single-ended traveling wave fault location is an important method for high-voltage line protection. In the existing single-ended traveling wave fault location calculation method, the fault distance is calculated by using the estimated traveling wave propagation velocity, but the accuracy of distance measurement is low due to the deviation of wave velocity.

Contents of the invention

The object of the present invention is a calculation method based on single-ended traveling wave fault distance measurement which is not affected by traveling wave velocity;

The object of the present invention is a single-end traveling wave fault location method which is not affected by traveling wave velocity.

In order to overcome the above-mentioned technical shortcomings, the purpose of the patent of the present invention is to provide a single-ended traveling wave fault ranging calculation method and a ranging method based on the single-ended traveling wave that is not affected by the traveling wave velocity, so it is no longer limited by the implementation conditions and improves the accuracy of ranging .

In order to achieve the above object, the technical scheme adopted by the patent of the present invention is:

The invention relates to a single-ended traveling wave fault location calculation method which is not affected by traveling wave velocity; the steps are: when a fault occurs on a line, a fault traveling wave is simultaneously sent from a fault point to an M bus and an N bus. Assuming that the time of fault occurrence is t ₀ , the moment when the initial current traveling wave arrives at terminal M is t _1M , and then the time when the first or second type of traveling wave arrives at M terminal is t _2M , and the time when the first, second or third type of traveling wave arrives at The moment at the M terminal is t _3M , t _4M ..., let L be the total length of the line, x be the distance from the fault point to the bus M,

When 0<x<L/3:

Generally, if at time t _p (p≥4), the transmitted wave of the first reflected wave of the bus at the opposite end reaches the bus monitoring end,

t ₀ =(3t ₁ -t ₂ )/2

When L/3<x<L/2:

t ₀ =(3t ₁ -t ₂ )/2

When L/2<x<2L/3:

t ₀ =(3t ₁ -t ₃ )/2

When 2L/3<x<L

t ₀ =(3t ₁ -t _p )/2

Due to the design of the calculation method divided into different sections, it is only related to the time when the traveling wave surge arrives at the monitoring end, and is no longer related to the propagation speed of the traveling wave, so it is no longer limited by the implementation conditions, and the accuracy of distance measurement is improved. .

The present invention designs a calculation method based on a single-ended traveling wave fault distance measurement not affected by traveling wave velocity, the steps of which are as follows:

3.1 Phase mode transformation

There is a coupling effect in the three-phase high-voltage and medium-voltage lines. In order to eliminate the influence of the coupling between the three phases, it is necessary to perform phase-mode transformation on the traveling wave component first, and decouple the coupled phase components into mutually independent 0, α, and β components. According to the Karrenbauer transformation, the three-phase current decoupling is:

Among them: I _α , I _β , I ₀ are the α-mode component, β-mode component and zero-mode component under the Karen Bell transformation of the phase currents I _a , I _b , I _c respectively, and the zero-mode component is between the three-phase conductor and the ground The α-mode component propagates between the A-phase and B-phase lines, and the β-mode component propagates between the A-phase and C-phase lines. The α mode component and the β mode component only propagate between conductors, so they are also called line mode components.

The zero-mode component attenuates seriously with the increase of frequency, and the zero-mode component is generally not selected as the object of wavelet transformation; while the line-mode transient traveling wave signal can ensure sufficient sensitivity as the measurement signal, and can be used as the measurement signal for wavelet analysis. The α-mode component of the fault current is used as the measurement signal.

3.2 Ranging Algorithm

The fault current traveling wave signal is collected at the M terminal. Figure 2-Figure 5 shows the traveling wave transmission process of faults at different locations on the MN line.

When a fault occurs on the line, the fault point sends fault traveling waves to the M bus and N bus at the same time. Assuming that the time of fault occurrence is t ₀ , the moment when the initial current traveling wave arrives at terminal M is t _1M , and then the time when the first or second type of traveling wave arrives at M terminal is t _2M , and the time when the first, second or third type of traveling wave arrives at The time at the M terminal is t _3M , t _4M ......

Let L be the total length of the line, and x be the distance from the fault point to the bus M.

According to the different types of the second traveling wave arriving at the M terminal, the total length L of the line can be divided into two sections (0,L/2) and (L/2,L); according to the third traveling wave arriving at the M terminal Belonging to different types, the (0,L/2) section is subdivided into two subsections (0,L/3) and (L/3,L/2), and the (L/2,L) section is further subdivided It is divided into two subsections (L/2,2L/3) and (2L/3,L). To sum up, the total length L of the line can be divided into 4 sub-sections by points L/3, L/2, and 2L/3, respectively 0<x<L/3, L/3<x<L/ 2. L/2<x<2L/3, 2L/3<x<L.

Use the three (four) moments when the traveling wave head arrives at the M terminal to calculate the traveling wave velocity and fault distance.

The ranging algorithm of each section is derived as follows.

3.2.1 0<x<L/3 segment

In the 0<x<L/3 section, the fault transient traveling wave is shown in Figure 2, and the following equations are simultaneously established:

In the formula, the average speed of traveling wave propagation v, the time of fault occurrence t ₀ and x are unknowns, and t ₁ , t ₂ , t ₃ are obtained from the time corresponding to the maximum value of wavelet transform modulus. It can be seen from observation that the above simultaneous equations are proportional to each other , v and x cannot be obtained, as can be seen from the grid diagram 2, introducing the arrival time t ₄ of the second type of traveling wave, the following equations can be obtained:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₂ )/2

Generally, if at time t _p (p≥4), the transmitted wave of the first reflected wave of the opposite bus arrives at the monitoring end of the bus, then there exists:

3.2.2 L/3<x<L/2 segment

In the L/3<x<L/2 section, the fault transient traveling wave is shown in Figure 3.

In the t≤3τ time interval, list the equation:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₂ )/2

3.2.3 L/2<x<2L/3 section

In the L/2<x<2L/3 section, the fault transient traveling wave is shown in Figure 4.

In the t≤3τ time interval, list the equation:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₃ )/2

3.2.4 2L/3<x<L section

In the 2L/3<x<L section, the fault transient traveling wave is shown in Figure 5.

In the t≤3τ time interval, list the equation:

Combining the above equations, there is no solution.

Using the arrival time t _p of the first type of traveling wave, the following equation is obtained:

Combining the above equations, we get:

t ₀ =(3t ₁ -t _p )/2

According to the results of the analysis of the above four sections, in the expression of the fault distance function x, the independent variable does not include the traveling wave velocity v, but only related to the total length of the line and t ₁ , t ₂ , t ₃ , t ₄ (t _p ), etc. It can be directly used for fault location and distance measurement of lines.

The present invention designs: a method based on a single-ended traveling wave fault location not affected by traveling wave velocity,

Its steps:

a. Start traveling wave recording according to the fact that the local end of the measurement terminal is a three-type busbar and the opposite end is a first-class busbar, detect the initial fault current traveling wave and perform Karen Bell transformation;

b. Perform one-dimensional continuous wavelet transform on I _α to extract t ₁ , t ₂ , t ₃ , t ₄ (t _p );

c. Corresponding to the wavelet transform modulus maximum time t ₁ , t ₂ , t ₃ , t ₄ (t _p ), read the polarity and magnitude of the wavelet coefficients, and determine the polarity of the traveling wave head;

d. Carry out polarity combination according to the following principle: take the polarity of the initial traveling wave wavelet coefficient as the reference polarity, if the measured first arriving wavelet coefficient is negative, then the second arriving wavelet coefficient is " +"; if the first arriving wavelet coefficient is positive, then the second arriving wavelet coefficient is "-" respectively;

e. If the measured first arrival wavelet coefficient is positive and the second arrival wavelet coefficient is "-", then x<L/2,

according to:

Formula 1:

Determine whether it meets 0<x<L/3,

Formula 2:

Determine whether it meets L/3<x<L/2;

f. When the first arrival wavelet coefficient is negative and the second arrival wavelet coefficient is "+", then x>L/2,

according to:

Formula 1:

Determine whether it meets L/2<x<2L/3,

Formula 2:

Determine whether 2L/3<x<L is met.

In this technical solution, the calculation based on the division of Kellenbell transform is an important technical feature, which is novel, creative and practical in the single-ended traveling wave fault location and ranging method that is not affected by the speed of traveling waves , the terms in this technical solution can be explained and understood with the patent documents in this technical field.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is the flow chart of invention based on the single-ended traveling wave fault location method not affected by traveling wave velocity;

Fig. 2 is a fault transient traveling wave diagram of the invention in the 0<x<L/3 section;

Fig. 3 is the fault transient traveling wave diagram of the invention in the L/3<x<L/2 section;

Fig. 4 is a fault transient traveling wave diagram of the invention in the L/2<x<2L/3 section;

Fig. 5 is a fault transient traveling wave diagram of the invention in the 2L/3<x<L section;

Fig. 6 is the waveform diagram of the fault phase current transient fault component of 3 lines (including the fault line) on the same bus on the Kangjin side in the embodiment of the invention;

Fig. 7 is the wavelet transform curve diagram of Fig. 6 of the invention;

Fig. 8 is a waveform diagram of the current transient fault component of the fault line on the Kang-Jin side where a B-phase ground fault occurs on the Kangsui Line A in the example of the invention;

Fig. 9 is a graph of wavelet transformation of Fig. 8 according to the invention.

Detailed ways

The present invention will be further described below in conjunction with the examples, and the following examples are intended to illustrate the present invention rather than further limit the present invention.

A single-ended traveling wave fault location calculation method based on the fact that it is not affected by traveling wave velocity, its steps:

Single-ended traveling wave fault location algorithm

3.1 Phase mode transformation

Three-phase high-voltage and medium-voltage lines have coupling effects. In order to eliminate the influence of coupling between the three phases, it is necessary to perform phase-mode transformation on the traveling wave components first, and decouple the coupled phase components into mutually independent 0, α, and β components. According to the Karrenbauer transformation, the three-phase current decoupling is:

Among them: I _α , I _β , I ₀ are the α-mode component, β-mode component and zero-mode component under Karen Bell transformation of the phase currents I _a , I _b , I _c respectively. Among them, the zero-mode component propagates between the three-phase conductor and the ground, the α-mode component propagates between the A-phase and B-phase lines, and the β-mode component propagates between the A-phase and C-phase lines. The α mode component and the β mode component only propagate between conductors, so they are also called line mode components.

The zero-mode component attenuates seriously with the increase of frequency, and the zero-mode component is generally not selected as the object of wavelet transformation; while the line-mode transient traveling wave signal can ensure sufficient sensitivity as the measurement signal, and can be used as the measurement signal for wavelet analysis. The α-mode component of the fault current is used as the measurement signal.

3.2 Ranging Algorithm

The fault current traveling wave signal is collected at the M terminal. Figure 2-Figure 5 shows the traveling wave transmission process of faults at different locations on the MN line.

It can be seen from Fig. 2-Fig. 5 that when a fault occurs on the line, the fault point sends a fault traveling wave to the M bus and the N bus at the same time. Assuming that the time of fault occurrence is t ₀ , the moment when the initial current traveling wave arrives at terminal M is t _1M , and then the time when the first or second type of traveling wave arrives at M terminal is t _2M , and the time when the first, second or third type of traveling wave arrives at The time at the M terminal is t _3M , t _4M ......

Let L be the total length of the line, and x be the distance from the fault point to the bus M.

According to the different types of the second traveling wave arriving at the M terminal, the total length L of the line can be divided into two sections (0,L/2) and (L/2,L); according to the third traveling wave arriving at the M terminal Belonging to different types, the (0,L/2) section is subdivided into two subsections (0,L/3) and (L/3,L/2), and the (L/2,L) section is further subdivided It is divided into two subsections (L/2,2L/3) and (2L/3,L). To sum up, the total length L of the line can be divided into 4 sub-sections by points L/3, L/2, and 2L/3, respectively 0<x<L/3, L/3<x<L/ 2. L/2<x<2L/3, 2L/3<x<L.

Use the three (four) moments of arrival at the M terminal to calculate the traveling wave velocity and fault distance.

The ranging algorithm of each section is derived as follows:

3.2.1 0<x<L/3 segment

In the 0<x<L/3 section, the fault transient traveling wave is shown in Figure 2. Simultaneously the following equations:

In the formula, the average speed of traveling wave propagation v, the fault occurrence time t ₀ , x are unknowns, and t ₁ , t ₂ , t ₃ are obtained from the corresponding time of wavelet transform modulus maximum. It can be seen from observation that the above simultaneous equations are proportional to each other, and v and x cannot be obtained. It can be seen from the grid diagram 2 that the following equations can be obtained by introducing the arrival time t ₄ of the second type of traveling wave:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₂ )/2 (11)

Generally, if at time t _p (p≥4), the transmitted wave of the first reflected wave of the opposite bus arrives at the monitoring end of the bus, then there exists:

3.2.2 L/3<x<L/2 segment

In the L/3<x<L/2 section, the fault transient traveling wave is shown in Figure 3.

In the t≤3τ time interval, list the equation:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₂ )/2 (15)

3.2.3 L/2<x<2L/3 section

In the L/2<x<2L/3 section, the fault transient traveling wave is shown in Figure 4.

In the t≤3τ time interval, list the equation:

Combining the above equations, we get:

t ₀ =(3t ₁ -t ₃ )/2 (17)

3.2.4 2L/3<x<L section

In the 2L/3<x<L section, the fault transient traveling wave is shown in Figure 5.

In the t≤3τ time interval, list the equation:

Combining the above equations, there is no solution.

Using the arrival time t _p of the first type of traveling wave, the following equation is obtained:

Combining the above equations, we get:

t ₀ =(3t ₁ -t _p )/2 (19)

According to the analysis results of the above four sections, the independent variable of the fault distance function x does not include the traveling wave velocity v, which is only related to the total length of the line and t ₁ , t ₂ , t ₃ , t ₄ (t _p ), etc., which can be directly It is used for fault location and distance measurement of lines.

3.3 Fault location process

Taking the structure of "three types of busbars" (the measuring end is a type three busbar, and the opposite end is a type one busbar) structure as an example, the fault location process is listed, as shown in Figure 4 below. Among them, in the polarity combination link, the polarity of the initial traveling wave wavelet coefficient is used as the reference polarity, that is, the first arriving wavelet coefficient in the figure is negative, and the second arriving wavelet coefficient is "+". ; If the first arriving wavelet coefficient is positive, then the second arriving wavelet coefficient is “-”.

The fault occurs before and after the midpoint of the line, and the type of the second traveling wave arriving at the bus measurement end is different, which constitutes one of the criteria for fault location in the figure below. In the process of subdividing into four fault areas, the polarity of the wave head and the ranging formula can be combined to verify each other.

The fault location process is shown in Figure 1.

A method for fault location based on single-ended traveling waves not affected by traveling wave speed, the first embodiment of the present invention, its steps:

a. Start traveling wave recording according to the fact that the local end of the measurement terminal is a three-type busbar and the opposite end is a first-class busbar, detect the initial fault current traveling wave and perform Karen Bell transformation;

b. Perform one-dimensional continuous wavelet transform on I _α to extract t ₁ , t ₂ , t ₃ , t ₄ (t _p );

c. Corresponding to the wavelet transform modulus maximum time t ₁ , t ₂ , t ₃ , t ₄ (t _p ), read the polarity and magnitude of the wavelet coefficients, and determine the polarity of the traveling wave head;

d. Carry out polarity combination according to the following principles: take the polarity of the initial traveling wave wavelet coefficient as the reference polarity, if the measured first arriving wavelet coefficient is negative, then the second arriving wavelet coefficient will be " +"; if the first arriving wavelet coefficient is positive, then the second arriving wavelet coefficient is "-" respectively;

e. When the measured first arriving wavelet coefficient is positive and the second arriving wavelet coefficient is "-", then x<L/2, according to:

Formula 1:

Determine whether it meets 0<x<L/3,

Formula 2:

Determine whether it meets L/3<x<L/2;

f. When the first arrival wavelet coefficient is negative and the second arrival wavelet coefficient is "+", then x>L/2, according to:

Formula 1:

Determine whether it meets L/2<x<2L/3,

Formula 2:

Determine whether 2L/3<x<L is met.

One of the present embodiments: Fault location Example one: At 14:33:07 on April 5, 2002, a phase B ground fault occurred on the 64.3km-long 220kV Kangsui Line A under the jurisdiction of Heilongjiang Suihua Power Industry Bureau. Among them, the transient fault component waveforms of the fault phase current of the three lines (including the fault line) on the same bus on the Kangjin side are shown in Figure 6. The busbars at both ends of the faulty line are connected to multiple other lines, all of which are category 3 busbars.

Carry out Karen Bell transform on the traveling wave of the fault current, the α-mode component current is shown as the waveform in the first row of Figure 7. Apply one-dimensional continuous wavelet transform to the α-mode component current, use the db10 wavelet whose vanishing moment order is 10 to decompose, and scale j=1～100, then the wavelet coefficients at each scale are shown in the second row of Figure 7; the scale The waveform of the wavelet coefficient when j=50 is shown in the third row of Figure 7; the maximum value of the wavelet coefficient with a scale of 1 to 100 is shown in the fourth row of Figure 7, and the position of the modulus maximum value is obvious. Zoom in along the direction of the sampling point, and read the number of sampling points corresponding to each wave head as follows:

t ₁ =62, t ₂ =258, t ₃ =327, t ₄ =435

The fault is located in the (L/3, L/2) section, which is brought into Equation (16). The distance measurement result is 27.34km, and the error with the actual fault distance of 27.4km is 0.06km.

One of the present examples: at 4:29:39 on April 16, 2002, the above-mentioned fault example, a phase B ground fault occurred on the Kangsui Line A, and the current transient fault component waveform of the fault line on the Kangjin side is shown in Figure 8 .

Carry out Karen Bell transformation on the fault current traveling wave, the α-mode component current is shown in the first row of waveform in Figure 9. Apply one-dimensional continuous wavelet transform to the α-mode component current, use the db10 wavelet whose vanishing moment order is 10 to decompose, and scale j=1～100, then the wavelet coefficients at each scale and the wavelet coefficient when j=50 are respectively as 9 The graphics shown in the second and third lines. Scale j=1～100 The maximum value of the wavelet coefficient is as shown in the fourth row of 9, and the number of sampling points corresponding to each wave head is read along the sampling point direction as follows:

t ₁ =70, t ₂ =133, t ₃ =445, t ₄ =454

The fault is located in the (0, L/3) section, brought into the formula (14), the distance measurement result is 9.062km, and the actual fault distance is 8.955km, the error is 0.107km, and the fault point position obtained by the principle of D-type traveling wave distance measurement Compared with 9.2km, the ranging result is more accurate.

The invention patent has the following characteristics:

1. Due to the design of the calculation method divided into different sections, it is only related to the polarity of the wavelet coefficient and the arrival time of the wave head, and is no longer related to the propagation speed of the traveling wave. Therefore, it is no longer limited by the implementation conditions, and the distance measurement is improved. the accuracy.

2. Due to the design of the single-end traveling wave fault distance calculation method, there is no longer a requirement for the propagation speed of the traveling wave, which expands the scope of use of the single-end traveling wave distance measuring device.

3. Due to the limitation of the numerical range of the length of the high-voltage line, the numerical range is the technical feature in the technical solution of the patent of the present invention, not the technical feature obtained through formula calculation or limited number of tests. The test shows that the numerical range The technical characteristics have achieved very good technical results.

4. Due to the design of the technical features of the patent of the present invention, the effects of the individual technical features and the combination of each other, it has been shown through tests that the performance indicators of the patent of the present invention are at least 1.7 of the existing performance indicators times, with good market value through appraisal.

The above-mentioned embodiment is only an implementation form of the single-ended traveling wave fault distance measurement method and distance measurement method provided by the present invention, and according to other variations of the solution provided by the present invention, add or Reducing the components or steps therein, or applying the present invention to other technical fields close to the present invention all belong to the protection scope of the present invention.

Claims (3)

1. A single-ended traveling wave fault ranging calculation method based on not being affected by traveling wave velocity is characterized in that: its steps are: When a fault occurs on the line, the fault point sends a fault traveling wave to the M bus and the N bus at the same time, assuming that the fault occurrence time is t ₀ , the time when the initial current traveling wave arrives at the M terminal is t _1M , and then the first or second type of traveling wave arrives at The time at the M terminal is t _2M , and the time when the first, second or third type of traveling wave arrives at the M terminal is t _3M , t _4M ..., let L be the total length of the line, and x be the distance from the fault point to the bus M, When 0<x<L/3: Generally, if at time t _p (p≥4), the transmitted wave of the first reflected wave of the bus at the opposite end reaches the bus monitoring end, t ₀ =(3t ₁ -t ₂ )/2 When L/3<x<L/2: t ₀ =(3t ₁ -t ₂ )/2 When L/2<x<2L/3: t ₀ =(3t ₁ -t ₃ )/2 When 2L/3<x<L t ₀ =(3t ₁ -t _p )/2 2. the single-ended traveling wave fault ranging calculation method based on not being affected by traveling wave velocity as claimed in claim 1, characterized in that: The steps are: 3.1 Phase mode transformation There is a coupling effect in the three-phase high-voltage and medium-voltage lines. In order to eliminate the influence of the coupling between the three phases, it is necessary to perform phase-mode transformation on the traveling wave component first, and decouple the coupled phase components into mutually independent 0, α, and β components. According to the Karrenbauer transformation, the three-phase current decoupling is: Among them: I _α , I _β , I ₀ are the α-mode component, β-mode component and zero-mode component under the Karen Bell transformation of the phase currents I _a , I _b , I _c respectively, and the zero-mode component is between the three-phase conductor and the ground The α-mode component propagates between the A-phase and B-phase lines, the β-mode component propagates between the A-phase and C-phase lines, and the α-mode component and β-mode component only propagate between the conductors, so they are also called line conductors. modulus component, The zero-mode component attenuates seriously with the increase of frequency, and the zero-mode component is generally not selected as the object of wavelet transformation; while the line-mode transient traveling wave signal can ensure sufficient sensitivity as the measurement signal, and can be used as the measurement signal for wavelet analysis. The α-mode component of the fault current is used as the measurement signal; 3.2 Ranging Algorithm The fault current traveling wave signal is collected at the M terminal, and the MN line is faulty at different locations. The traveling wave transmission process is shown in Figure 2-Figure 5. When a line fault occurs, the fault point sends fault traveling waves to the M bus and N bus at the same time, assuming that the time of fault occurrence is t ₀ , the time when the initial current traveling wave reaches the M terminal is t _1M , and then the first or second type of traveling wave The moment of arrival at the M terminal is t _2M , and the moment of the first, second or third type of traveling wave arriving at the M terminal is t _3M, t _4M ... Let L be the total length of the line, x be the distance from the fault point to the bus M, According to the different types of the second traveling wave arriving at the M terminal, the total length L of the line can be divided into two sections (0,L/2) and (L/2,L); according to the third traveling wave arriving at the M terminal Belonging to different types, the (0,L/2) section is subdivided into two subsections (0,L/3) and (L/3,L/2), and the (L/2,L) section is further subdivided It is divided into two subsections (L/2,2L/3) and (2L/3,L). In summary, the total length L of the line can be divided by L/3, L/2, and 2L/3 points It is 4 sub-sections, respectively 0<x<L/3, L/3<x<L/2, L/2<x<2L/3, 2L/3<x<L, Use the three (four) moments of arrival at the M terminal to calculate the fault occurrence time and fault distance, The ranging algorithm of each section is derived as follows: 3.2.1 0<x<L/3 segment In the 0<x<L/3 section, the fault transient traveling wave is shown in Figure 2, and the following equations are simultaneously established: In the formula, the average speed of traveling wave propagation v, the time of fault occurrence t ₀ , x are unknowns, t _1, t _2, t ₃ are obtained from the time corresponding to the maximum value of wavelet transform modulus, it can be seen from observation that the above simultaneous equations are proportional to each other , v and x cannot be obtained, as can be seen from the grid diagram 2, introducing the arrival time t ₄ of the second type of traveling wave, the following equations can be obtained: Combining the above equations, we get: t ₀ =(3t ₁ -t ₂ )/2 Generally, if at time t _p (p≥4), the transmitted wave of the first reflected wave of the opposite bus arrives at the monitoring end of the bus, then there exists: 3.2.2 L/3<x<L/2 section In the L/3<x<L/2 section, the fault transient traveling wave is shown in Figure 3. In the t≤3τ time interval, list the equation: Combining the above equations, we get: t ₀ =(3t ₁ -t ₂ )/2 3.2.3 L/2<x<2L/3 section In the L/2<x<2L/3 section, the fault transient traveling wave is shown in Figure 4. In the t≤3τ time interval, list the equation: Combining the above equations, we get: t ₀ =(3t ₁ -t ₃ )/2 3.2.4 2L/3<x<L section In the 2L/3<x<L section, the fault transient traveling wave is shown in Figure 5. In the t≤3τ time interval, list the equation: Simultaneously the above equations have no solution; Using the arrival time t _p of the first type of traveling wave, the following equation is obtained: Combining the above equations, we get: t ₀ =(3t ₁ -t _p )/2 According to the results of the analysis of the above four sections, in the expression of the fault distance function x, the independent variable does not include the traveling wave velocity v, but only related to the total length of the line and t ₁ , t ₂ , t ₃ , t ₄ (t _p ), etc. It can be directly used for fault location and distance measurement of lines. 3. A fault location method based on single-ended traveling waves that is not affected by traveling wave velocity, Its steps: a. Start traveling wave recording according to the fact that the local end of the measurement terminal is a three-type busbar and the opposite end is a first-class busbar, detect the initial fault current traveling wave and perform Karen Bell transformation; b. Perform one-dimensional continuous wavelet transform on I _α to extract t ₁ , t ₂ , t ₃ , t ₄ (t _p ); c. Corresponding to the wavelet transform modulus maximum time t ₁ , t ₂ , t ₃ , t ₄ (t _p ), read the polarity and magnitude of the wavelet coefficients, and determine the polarity of the traveling wave head; d. Carry out polarity combination according to the following principles: take the polarity of the initial traveling wave wavelet coefficient as the reference polarity, if the measured first arriving wavelet coefficient is “—”, then the second arriving wavelet coefficient is then is "+"; if the measured first arriving wavelet coefficient is positive, then the second arriving wavelet coefficient is "-" respectively; e. If the polarity of the first arrival wavelet coefficient and the second arrival wavelet coefficient are opposite, then x<L/2, according to: Formula 1: Determine whether it meets 0<x<L/3, Formula 2: Determine whether it meets L/3<x<L/2; f. When the first arriving wavelet coefficient and the second arriving wavelet coefficient are measured to have the same polarity, then x>L/2, according to: Formula 1: Determine whether it meets L/2<x<2L/3, Formula 2: Determine whether 2L/3<x<L is met.