CN105699855A

CN105699855A - Single-ended traveling fault location calculation method and location method insusceptible to traveling wave speed

Info

Publication number: CN105699855A
Application number: CN201610209799.4A
Authority: CN
Inventors: 高洪雨; 宋卫平; 王磊; 马士聪; 赵义奎; 赵衍恒; 李经纬
Original assignee: State Grid of China Technology College
Current assignee: State Grid of China Technology College
Priority date: 2016-04-06
Filing date: 2016-04-06
Publication date: 2016-06-22
Anticipated expiration: 2036-04-06
Also published as: CN105699855B

Abstract

The invention provides a single-ended traveling fault location method insusceptible to traveling wave speed and a single-ended traveling fault location calculation method insusceptible to traveling wave speed. According to the invention, the fault occurrence time is set to be t0; the time when initial current traveling waves reach an M end is set to be T1M, the time when first or second type travelling waves reach the M end is set to be t2M, and the time when first, second or third type travelling waves reach the M end is set to be t2M, t4M...; L is set to be the total length of a line; x is set to be the distance between a fault point and a bus M; when 0<=x<=L/3, L/2<=x<=2L/3 and 2L/3<=x<=L, calculation is performed in said three conditions and only incidence relation with time exists while no incidence relation with traveling wave speed exists. Therefore, limits caused by implementation conditions are removed and location accuracy is improved.

Description

Based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed and distance-finding method

Technical field

Patent of the present invention relates to a kind of single-ended traveling wave fault location computational methods, especially a kind of based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed and distance-finding method。

Background technology

After power circuit breaks down, judging the trouble point of power circuit exactly, be conducive to rapidly removing faults, recovering line powering, therefore single-ended traveling wave fault location is a kind of important high-voltage line protection method。In existing single-ended traveling wave fault location computational methods, utilize the traveling wave spread speed estimated to calculate fault distance, due to the deviation of wave velocity, cause that the degree of accuracy of range finding is low。

Summary of the invention

The object of the present invention is a kind of based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed degree；

The object of the present invention is a kind of based on the single-ended traveling wave fault location method not affected by traveling wave speed degree。

In order to overcome above-mentioned technical disadvantages, the purpose of patent of the present invention is to provide based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed and distance-finding method, is therefore no longer limited by implementation condition, improves the degree of accuracy of range finding。

For reaching above-mentioned purpose, patent of the present invention adopts the technical scheme that:

A kind of based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed；Its step: during line failure, is sent fault traveling wave to M bus, N bus by trouble point simultaneously。If fault occurs the moment to be t₀, the moment of initial current traveling wave arrival M end is t_1M, thereafter first or second class traveling wave arrive M end moment be t_2M, and first, second or the 3rd class traveling wave arrive M end moment be t_3M、t_4M..., if L is the total length of circuit, x is the distance that bus M is arrived in trouble point,

When 0 < x < during L/3:

Usually, if t_pIn (p >=4) moment, the transmitted wave of the 1st echo of opposite end bus arrives bus monitoring side,

t₀=(3t₁-t₂)/2

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

t₀=(3t₁-t₂)/2

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

t₀=(3t₁-t₃)/2

As 2L/3, < x is < during L

t₀=(3t₁-t_p)/2

Owing to devising point computational methods for different sections, the time only arriving monitoring side with traveling wave surge is relevant, no longer has relation with traveling wave spread speed, is therefore no longer limited by implementation condition, improves the degree of accuracy of range finding。

The present invention devises based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed, its step:

3.1 phase-model transformations

There is coupling in three-phase high-voltage, medium-voltage line, in order to eliminate the impact of coupling between three-phase, need first traveling-wave component to be carried out phase-model transformation, it is separate 0, α, β component by the phase component decoupling intercoupled, converting according to triumphant logical sequence Bel (Karrenbauer), three-phase current decoupling is:

Wherein: I_α、I_β、I₀Respectively phase current I_a、I_b、I_cTriumphant human relations Bel convert under α mold component, β mold component and zero _exit, wherein zero _exit is propagated between three-phase conductor and the earth, and α mold component is propagated between A phase and B phase line, and β mold component is propagated between A phase and C phase line。α mold component and β mold component are only propagated between the conductors, so also known as Aerial mode component。

Zero _exit is very serious along with frequency raises decay, does not generally select zero _exit as the object of wavelet transformation；And line mould transient state travelling wave signal can ensure that enough sensitivity as measurement signal, it is possible to carry out wavelet analysis as measuring signal。Adopt the α mold component of fault current as measuring signal。

3.2 location algorithms

Fault current travelling wave signal is gathered at M end。MN circuit diverse location fault, traveling wave process is as Figure 2-Figure 5。

When line failure, trouble point send fault traveling wave to M bus, N bus simultaneously。If fault occurs the moment to be t₀, the moment of initial current traveling wave arrival M end is t_1M, thereafter first or second class traveling wave arrive M end moment be t_2M, and first, second or the 3rd class traveling wave arrive M end moment be t_3M、t_4M……

If L is the total length of circuit, x is the distance that bus M is arrived in trouble point。

According to arrive M end the 2nd traveling wave belonging to dissimilar, the total length L of circuit can be divided into (0, L/2), (L/2, L) two sections；According to arrive M end the 3rd traveling wave belonging to dissimilar, (0, L/2) section is sub-divided into (0, L/3), (L/3, L/2) two sub-segments, (L/2, L) section is sub-divided into (L/2,2L/3), (2L/3, L) two sub-segments。In sum, the total length L of circuit, it is possible to be divided into 4 sub-segments by L/3, L/2,2L/3 point, respectively 0 < x < L/3, L/3 < x < L/2, L/2 < x < 2L/3,2L/3 < x < L。

Three (four) the individual moment that wavefront arrives M end are utilized to calculate traveling wave speed and fault distance。

Each section location algorithm is derived as follows。

3.2.10 < x < L/3 section

At 0 < x < L/3 section, fault transient travelling wave is as in figure 2 it is shown, simultaneous below equation:

In formula, traveling wave propagates average speed v, moment t occurs fault₀, x be unknown number, t₁、t₂、t₃Trying to achieve with the wavelet modulus maxima correspondence moment, observe visible, above simultaneous equations are mutually ratio, it is impossible to try to achieve v, x, from grid chart 2, introduce second class traveling wave due in t₄, below equation group can be obtained:

Simultaneous above equation, tries to achieve:

t₀=(3t₁-t₂)/2

Usually, if t_pIn (p >=4) moment, the transmitted wave of the 1st echo of opposite end bus arrives bus monitoring side, then exist:

3.2.2L/3 < x < L/2 section

At L/3 < x < L/2 section, fault transient travelling wave as it is shown on figure 3,

At t≤3 τ time interval, list equation:

Simultaneous above equation, solves:

t₀=(3t₁-t₂)/2

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

At L/2 < x < 2L/3 section, fault transient travelling wave as shown in Figure 4,

At t≤3 τ time interval, list equation:

Simultaneous above equation, solves:

t₀=(3t₁-t₃)/2

3.2.42L/3 < x < L section

At 2L/3 < x < L section, fault transient travelling wave as it is shown in figure 5,

At t≤3 τ time interval, list equation:

Simultaneous above equation, without solving。

Utilize the 1st class traveling wave due in t_p, obtain below equation:

Simultaneous above equation, solves:

t₀=(3t₁-t_p)/2

Result according to above 4 sectional analyses, in fault distance function x expression formula, independent variable is without row wave speed v, only with total track length and t₁、t₂、t₃、t₄(t_p) etc. relevant, it is possible to be directly used in circuit fault location range finding。

The present invention devises: a kind of based on the single-ended traveling wave fault location method not affected by traveling wave speed,

Its step:

A, it is three class buses and opposite end is that a class bus carries out traveling wave record ripple and starts according to measuring end local terminal, detection primary fault current traveling wave and carry out triumphant human relations Bel conversion；

B, to I_αCarry out One Dimension Continuous Wavelet Transform, extract t₁、t₂、t₃、t₄(t_p)；

C, corresponding wavelet modulus maxima moment t₁、t₂、t₃、t₄(t_p), read wavelet coefficient polarity, size, it is determined that wavefront polarity；

D, carrying out combinations of polarities according to following principle: with the polarity of initial wavefront wavelet coefficient for reference polarity, if recording first, to arrive wave head wavelet coefficient be negative, then second arrival wave head wavelet coefficient be then "+"；If recording first to arrive wave head wavelet coefficient for just, then second arrives wave head wavelet coefficient then respectively "-"；

If e, when record first arrive wave head wavelet coefficient for just with the second arrive wave head wavelet coefficient be "-" time, then x < L/2,

According to:

Formula one:

Determine whether to meet 0 < x < L/3,

Formula two:

Determine whether to meet L/3 < x < L/2；

F, when record first arrive wave head wavelet coefficient for negative, second arrive wave head wavelet coefficient for "+" time, then x > L/2,

According to:

Formula one:

Determine whether to meet L/2 < x < 2L/3,

Formula two:

Determine whether to meet 2L/3 < x < L。

In the technical program, sectional based on triumphant logical sequence Bel conversion is calculated as important technical characteristic, based on the single-ended traveling wave fault location not affected by traveling wave speed degree and distance-finding method, having novelty, creativeness and practicality, the term in the technical program is all can make an explanation with patent documentation in the art and understand。

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, the accompanying drawing used required in embodiment or description of the prior art will be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings。

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

Fig. 2 is for inventing at 0 < x < L/3 section, fault transient travelling wave figure；

Fig. 3 is for inventing at L/3 < x < L/2 section, fault transient travelling wave figure；

Fig. 4 is for inventing at L/2 < x < 2L/3 section, fault transient travelling wave figure；

Fig. 5 is for inventing at 2L/3 < x < L section, fault transient travelling wave figure；

Fig. 6 is the faulted phase current transients fault compoment oscillogram of 3 circuits (containing faulty line interior) on the same bus in Kang Jin side in inventive embodiments；

Fig. 7 is the wavelet transformation curve chart of invention Fig. 6；

Fig. 8 is that in invention example, B phase earth fault, wherein Kang Jin side faulty line current temporary state fault component oscillogram occur Kang Sui A-wire；

Fig. 9 is the wavelet transformation curve chart of invention Fig. 8。

Detailed description of the invention

Below in conjunction with embodiment, the present invention being further described, following example are intended to illustrate the present invention rather than limitation of the invention further。

A kind of based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed degree, its step:

Single-ended traveling wave fault location algorithm

3.1 phase-model transformations

There is coupling in three-phase high-voltage, medium-voltage line, in order to eliminate between three-phase the impact of coupling, it is necessary to first traveling-wave component is carried out phase-model transformation, is separate 0, α, β component by the phase component decoupling intercoupled。Converting according to triumphant logical sequence Bel (Karrenbauer), three-phase current decoupling is:

Wherein: I_α、I_β、I₀Respectively phase current I_a、I_b、I_cTriumphant human relations Bel convert under α mold component, β mold component and zero _exit。Wherein zero _exit is propagated between three-phase conductor and the earth, and α mold component is propagated between A phase and B phase line, and β mold component is propagated between A phase and C phase line。α mold component and β mold component are only propagated between the conductors, so also known as Aerial mode component。

3.2 location algorithms

From Fig. 2-Fig. 5, when line failure, trouble point send fault traveling wave to M bus, N bus simultaneously。If fault occurs the moment to be t₀, the moment of initial current traveling wave arrival M end is t_1M, thereafter first or second class traveling wave arrive M end moment be t_2M, and first, second or the 3rd class traveling wave arrive M end moment be t_3M、t_4M……

Three (four) the individual moment arriving M end are utilized to calculate traveling wave speed and fault distance。

Each section location algorithm is derived as follows:

3.2.10 < x < L/3 section

At 0 < x < L/3 section, fault transient travelling wave is as shown in Figure 2。Simultaneous below equation:

In formula, traveling wave propagates average speed v, moment t occurs fault₀, x be unknown number, t₁、t₂、t₃Try to achieve with the wavelet modulus maxima correspondence moment。Observing visible, above simultaneous equations are mutually ratio, it is impossible to try to achieve v, x。From grid chart 2, introduce second class traveling wave due in t₄, below equation group can be obtained:

Simultaneous above equation, tries to achieve:

t₀=(3t₁-t₂)/2(11)

3.2.2L/3 < x < L/2 section

At L/3 < x < L/2 section, fault transient travelling wave is as shown in Figure 3。

At t≤3 τ time interval, list equation:

Simultaneous above equation, solves:

t₀=(3t₁-t₂)/2(15)

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

At L/2 < x < 2L/3 section, fault transient travelling wave is as shown in Figure 4。

At t≤3 τ time interval, list equation:

Simultaneous above equation, solves:

t₀=(3t₁-t₃)/2(17)

3.2.42L/3 < x < L section

At 2L/3 < x < L section, fault transient travelling wave is as shown in Figure 5。

At t≤3 τ time interval, list equation:

Simultaneous above equation, without solving。

Utilize the 1st class traveling wave due in t_p, obtain below equation:

Simultaneous above equation, solves:

t₀=(3t₁-t_p)/2(19)

Result according to above 4 sectional analyses, fault distance function x, independent variable is without row wave speed v, only with total track length and t₁、t₂、t₃、t₄(t_p) etc. relevant, it is possible to be directly used in circuit fault location range finding。

3.3 fault localization flow processs

It is example with " 31 class " bus (for three class buses, opposite end is a class bus to measurement end local terminal) structure, lists fault localization flow process, be illustrated in fig. 4 shown below。Wherein, combinations of polarities link, with the polarity of initial wavefront wavelet coefficient for reference polarity, namely in figure first arrive wave head wavelet coefficient be negative, then second arrival wave head wavelet coefficient be then "+"；If recording first to arrive wave head wavelet coefficient for just, then second arrives wave head wavelet coefficient then respectively "-"。

Fault produce in the line before with midpoint after, arriving bus, to measure second traveling wave classification of end different, one of criterion of composition figure below fault location。In the process being subdivided into four fault zones, it is possible to wave head polarity is combined with range finding formula, verifies each other。

Fault localization flow process is as shown in Figure 1。

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

D, carrying out combinations of polarities according to principle once: with the polarity of initial wavefront wavelet coefficient for reference polarity, if recording first, to arrive wave head wavelet coefficient be negative, then second arrival wave head wavelet coefficient be then "+"；If recording first to arrive wave head wavelet coefficient for just, then second arrives wave head wavelet coefficient then respectively "-"；

If e, when record first arrive wave head wavelet coefficient for just with the second arrive wave head wavelet coefficient, respectively during "-", then x < L/2, according to:

Formula one:

Determine whether to meet 0 < x < L/3,

Formula two:

Determine whether to meet L/3 < x < L/2；

F, when record first arrive wave head wavelet coefficient be negative, then second arrival wave head wavelet coefficient be then "+" time, then x > L/2, according to:

Formula one:

Determine whether to meet L/2 < x < 2L/3,

Formula two:

Determine whether to meet 2L/3 < x < L。

One of the present embodiment: B phase earth fault occurs the 220kV Kang Sui A-wire of fault localization example on April 5th, 1: 2002 14:33:07, Heilungkiang Suihua Electric Power Bureau administered total length 64.3km。Wherein on the same bus in Kang Jin side, the faulted phase current transients fault compoment waveform of 3 circuits (containing faulty line interior) is as shown in Figure 6。Faulty line two ends bus is all connected to other circuit a plurality of, is the 3rd class bus。

Fault current traveling wave carries out triumphant human relations Bel conversion, and α mold component electric current is such as shown in Fig. 7 the first row waveform。To α mold component electric current application One Dimension Continuous Wavelet Transform, the db10 small echo adopting vanishing moment exponent number to be 10 decomposes, yardstick j=1～100, the then such as figure shown in Fig. 7 the second row of the wavelet coefficient under each yardstick；Wavelet coefficient during yardstick j=50 is waveform shown in Fig. 7 the third line such as；The maximum of the wavelet coefficient of yardstick 1～100 is waveform shown in Fig. 7 fourth line such as, and modulus maximum position is obvious。Amplifying along sampled point direction, the sampling number reading each wave head corresponding is as follows:

t₁=62, t₂=258, t₃=327, t₄=435

Fault is positioned at (L/3, L/2) section, brings formula (16) into, and range measurement is 27.34km, is 0.06km with physical fault distance 27.4km error。

One of the present embodiment: on April 16th, 2002 4:29:39, above-mentioned fault diagnosis example one Kang Sui A-wire occur B phase earth fault, wherein Kang Jin side faulty line current temporary state fault component waveform is as shown in Figure 8。

Fault current traveling wave carries out triumphant human relations Bel conversion, and α mold component electric current is such as shown in Fig. 9 the first row waveform。To α mold component electric current application One Dimension Continuous Wavelet Transform, the db10 small echo adopting vanishing moment exponent number to be 10 decomposes, yardstick j=1～100, then the wavelet coefficient under each yardstick, j=50 time wavelet coefficient figure as shown in 9 second and third row respectively。The maximum of yardstick j=1～100 wavelet coefficient is waveform shown in 9 fourth lines such as, and the sampling number reading each wave head corresponding along sampled point direction is as follows:

t₁=70, t₂=133, t₃=445, t₄=454

Fault is positioned at (0, L/3) section, brings formula (14) into, range measurement is 9.062km, being 0.107km with physical fault distance 8.955km error, compared with the position of failure point 9.2km that D type traveling wave range measurement principle obtains, range measurement is more accurate。

Patent of the present invention has lower feature:

1, owing to devising point computational methods for different sections, only relevant for the time of advent with wavelet coefficient polarity, wave head, no longer there is relation with traveling wave spread speed, therefore no longer limited by implementation condition, improve the degree of accuracy of range finding。

2, owing to devising single-ended traveling wave fault location computational methods, no longer traveling wave spread speed is required, extend the use scope of Single Terminal Traveling Wave Fault Location device。

3, owing to devising the restriction that high-tension line length is carried out numerical range, technical characteristic in the technical scheme making numerical range be patent of the present invention, calculate or tested by limited number of time the technical characteristic drawn not by formula, test shows that the technical characteristic of this numerical range achieves good technique effect。

4, owing to devising the technical characteristic of patent of the present invention, effect in the set individually and each other of technical characteristic, by test show, the property indices of patent of the present invention be existing property indices be at least 1.7 times, by assess there is good market value。

Above-described embodiment is a kind of way of realization based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed degree and distance-finding method provided by the present invention; other deformation according to scheme provided by the present invention; increase or reduce composition therein or step; or the present invention is used for other the technical field close with the present invention, belongs to protection scope of the present invention。

Claims

1. one kind based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed, it is characterised in that: the steps include:

During line failure, trouble point send fault traveling wave to M bus, N bus, if fault occurs the moment to be t simultaneously₀, the moment of initial current traveling wave arrival M end is t_1M, thereafter first or second class traveling wave arrive M end moment be t_2M, and first, second or the 3rd class traveling wave arrive M end moment be t_3M、t_4M..., if L is the total length of circuit, x is the distance that bus M is arrived in trouble point,

When 0 < x < during L/3:

t₀=(3t₁-t₂)/2

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{p}}

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

t₀=(3t₁-t₂)/2

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

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

t₀=(3t₁-t₃)/2

x = \frac{(t_{3} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

As 2L/3, < x is < during L

t₀=(3t₁-t_p)/2

x = \frac{(t_{p} - t_{1}) L}{t_{2} + t_{p} - 2 t_{1}} .

2. as claimed in claim 1 based on the single-ended traveling wave fault location computational methods not affected by traveling wave speed, it is characterised in that:

The steps include:

3.1 phase-model transformations

[\begin{matrix} I_{α} \\ I_{β} \\ I_{0} \end{matrix}] = \frac{1}{3} [\begin{matrix} 1 & - 1 & 0 \\ 1 & 0 & - 1 \\ 1 & 1 & 1 \end{matrix}] [\begin{matrix} I_{a} \\ I_{b} \\ I_{c} \end{matrix}]

Wherein: I_α、I_β、I₀Respectively phase current I_a、I_b、I_cTriumphant human relations Bel convert under α mold component, β mold component and zero _exit, wherein zero _exit is propagated between three-phase conductor and the earth, α mold component is propagated between A phase and B phase line, β mold component is propagated between A phase and C phase line, α mold component and β mold component are only propagated between the conductors, so also known as Aerial mode component

Zero _exit is very serious along with frequency raises decay, does not generally select zero _exit as the object of wavelet transformation；And line mould transient state travelling wave signal can ensure that enough sensitivity as measurement signal, it is possible to carry out wavelet analysis as measuring signal, adopt the α mold component of fault current as measuring signal；

3.2 location algorithms

M end gather fault current travelling wave signal, MN circuit diverse location fault, traveling wave process as Figure 2-Figure 5,

When line failure, trouble point send fault traveling wave to M bus, N bus, if fault occurs the moment to be t simultaneously₀, the moment of initial current traveling wave arrival M end is t_1M, thereafter first or second class traveling wave arrive M end moment be t_2M, and first, second or the 3rd class traveling wave arrive M end moment be t_3M、t_4M……

If L is the total length of circuit, x is the distance that bus M is arrived in trouble point,

According to arrive M end the 2nd traveling wave belonging to dissimilar, the total length L of circuit can be divided into (0, L/2), (L/2, L) two sections；According to arrive M end the 3rd traveling wave belonging to dissimilar, (0, L/2) section is sub-divided into (0, L/3), (L/3, L/2) two sub-segments, (L/2, L) section is sub-divided into (L/2,2L/3), (2L/3, L) two sub-segments, in sum, the total length L of circuit, it is possible to be divided into 4 sub-segments by L/3, L/2,2L/3 point, respectively 0 < x < L/3, L/3 < x < L/2, L/2 < x < 2L/3,2L/3 < x < L

Utilize three (four) the individual moment arriving M end to calculate fault and moment and fault distance occur,

Each section location algorithm is derived as follows:

3.2.10 < x < L/3 section

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 3 x \\ v (t_{3} - t_{0}) = 5 x \end{matrix}

In formula, traveling wave propagates average speed v, moment t occurs fault₀, x be unknown number, t_1、t_2、t₃Trying to achieve with the wavelet modulus maxima correspondence moment, observe visible, above simultaneous equations are mutually ratio, it is impossible to try to achieve v, x, from grid chart 2, introduce second class traveling wave due in t₄, below equation group can be obtained:

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 3 x \\ v (t_{4} - t_{0}) = 2 L - x \end{matrix}

Simultaneous above equation, tries to achieve:

t₀=(3t₁-t₂)/2

v = \frac{2 L}{- 2 t_{1} + t_{2} + t_{4}}

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{4}}

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{p}}

3.2.2L/3 < x < L/2 section

At t≤3 τ time interval, list equation:

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 3 x \\ v (t_{3} - t_{0}) = 2 L - x \end{matrix}

Simultaneous above equation, solves:

t₀=(3t₁-t₂)/2

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

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

At t≤3 τ time interval, list equation:

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 2 L - x \\ v (t_{3} - t_{0}) = 3 x \end{matrix}

Simultaneous above equation, solves:

t₀=(3t₁-t₃)/2

x = \frac{(t_{3} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

3.2.42L/3 < x < L section

At t≤3 τ time interval, list equation:

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 2 L - x \\ v (t_{3} - t_{0}) = 4 L - 3 x \end{matrix}

Simultaneous above equation, without solving。

Utilize the 1st class traveling wave due in t_p, obtain below equation:

\{\begin{matrix} v (t_{1} - t_{0}) = x \\ v (t_{2} - t_{0}) = 2 L - x \\ v (t_{p} - t_{0}) = 3 x \end{matrix}

Simultaneous above equation, solves:

t₀=(3t₁-t_p)/2

x = \frac{(t_{p} - t_{1}) L}{t_{2} + t_{p} - 2 t_{1}}

3. based on the single-ended traveling wave fault location method not affected by traveling wave speed,

Its step:

D, carry out combinations of polarities according to following principle: with the polarity of initial wavefront wavelet coefficient for reference polarity, if recording first to arrive wave head wavelet coefficient for " ", then second arrive wave head wavelet coefficient be then "+"；If recording first to arrive wave head wavelet coefficient for just, then second arrives wave head wavelet coefficient then respectively " "；

If e records first arrival wave head wavelet coefficient, second arrival wave head wavelet coefficient opposite polarity, then x < L/2, according to:

Formula one:

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{4}}

Determine whether to meet 0 < x < L/3,

Formula two:

x = \frac{(t_{2} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

Determine whether to meet L/3 < x < L/2；

F, when record first arrive wave head wavelet coefficient, second arrive wave head wavelet coefficient polarity identical time, then x > L/2, according to:

Formula one:

x = \frac{(t_{3} - t_{1}) L}{- 2 t_{1} + t_{2} + t_{3}}

Determine whether to meet L/2 < x < 2L/3,

Formula two:

x = \frac{(t_{p} - t_{1}) L}{t_{2} + t_{p} - 2 t_{1}}

Determine whether to meet 2L/3 < x < L。