CN112083272A - 10kV cable fault location method based on sheath current traveling wave natural frequency difference method - Google Patents

10kV cable fault location method based on sheath current traveling wave natural frequency difference method Download PDF

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CN112083272A
CN112083272A CN202010833469.9A CN202010833469A CN112083272A CN 112083272 A CN112083272 A CN 112083272A CN 202010833469 A CN202010833469 A CN 202010833469A CN 112083272 A CN112083272 A CN 112083272A
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fault
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traveling wave
phase
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CN112083272B (en
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束洪春
李航
宋建
董俊
袁小兵
梁雨婷
于永波
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Kunming University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/083—Locating faults in cables, transmission lines, or networks according to type of conductors in cables, e.g. underground
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/088—Aspects of digital computing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/11—Locating faults in cables, transmission lines, or networks using pulse reflection methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/52—Testing for short-circuits, leakage current or ground faults
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
    • G01R31/58—Testing of lines, cables or conductors

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Abstract

The invention relates to a 10kV cable fault location method based on a sheath current traveling wave natural frequency difference method, and belongs to the technical field of power system relay protection. Firstly, extracting three-phase sheath current and I after phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the FFT-MUSIC is utilized to carry out fault ranging on the signal I∑Carrying out frequency spectrum transformation to extract each frequency component in the traveling wave signal; and finally, carrying out fault location by using a natural frequency difference method. The invention utilizes the frequency domain characteristic of the traveling wave, does not need to identify the traveling wave head, even if the polarity of the traveling wave head changes in the transmission process or the traveling wave head is gradually deformed along with the attenuation wave, and utilizes the frequency differenceThe method can obtain the fault distance only by extracting the natural frequency of the traveling wave and acquiring the stable frequency difference delta f, and the distance measurement result is accurate and reliable.

Description

10kV cable fault location method based on sheath current traveling wave natural frequency difference method
Technical Field
The invention relates to a 10kV cable fault location method based on a sheath current traveling wave natural frequency difference method, and belongs to the technical field of power system relay protection.
Background
The power cable is an important component of the urban power grid, and the power supply reliability of the urban power grid is directly influenced by the fault detection and repair efficiency of the power cable. At present, about 80% of the fault types of the power distribution network cable are single-phase ground faults, and the fault occurrence rate is far higher than that of two-phase short-circuit faults, two-phase ground faults and three-phase short-circuit faults. When a single-phase earth fault occurs in the cable, in order to avoid multi-point faults such as two-phase (earth) short circuit, three-phase short circuit and the like caused by the earth fault, the fault position is quickly and accurately found, and the fault is quickly eliminated, so that the method has important significance for maintaining the safe and stable operation of the power distribution network.
Disclosure of Invention
The invention aims to solve the technical problem of providing a 10kV cable fault location method based on a sheath current traveling wave natural frequency difference method, which is used for solving the problem.
The technical scheme of the invention is as follows: a10 kV cable fault location method based on a sheath current traveling wave natural frequency difference method comprises the steps of firstly, extracting the sum I of three-phase sheath currents subjected to phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the FFT-MUSIC is utilized to carry out fault ranging on the signal I∑Carrying out frequency spectrum transformation to extract each frequency component in the signal; and finally, carrying out fault location by using a natural frequency difference method.
The method comprises the following specific steps:
step 1: obtaining the sum I of three-phase sheath currents∑As a fault ranging signal;
firstly, a Clarke transformation matrix is used for decoupling a three-phase conductor system signal, the Clarke matrix needs to be expanded before decoupling to obtain a voltage transformation matrix S and a current transformation matrix Q after expansion, and then the three-phase core current and the sheath current are decoupled into six independent moduli through phase-mode transformation.
Since the outer modulus ( modulus 1, 2 and 3) is not the main component of fault travelling wave, and the three inner moduli ( modulus 4, 5 and 6) are similar to the overhead line mode, and the travelling wave signal mutation characteristic of modulus 4 is obvious and stable, the method can be used for cable fault location. However, in the tunnel or channel-laid system, since the three-phase sheath includes three internal moduli and the propagation velocities of the moduli 5 and 6 are higher than the modulus 4, the three internal moduli interfere with each other.
Figure BDA0002638830200000011
In the formula (1), Ia、Ib、IcRespectively three-phase sheath current i1～i6Six modulus currents.
Adding the three-phase sheath currents can find that the external modulus 2 and 3 and the internal modulus 5 and 6 are mutually offset, and the final formula only contains the modulus 1 and the modulus 4, namely the sum I of the three-phase sheath currents∑Comprises the following steps:
Figure BDA0002638830200000021
the sum I of three-phase sheath currents∑As a fault-ranging signal.
Step 2: utilizing FFT-MUSIC algorithm to carry out fault ranging on the fault ranging signal I in Step1∑Carrying out frequency spectrum transformation, extracting each frequency component in the signal, and obtaining the accurate frequency of each group of components of the signal according to the spectral peak position of the MUSIC pseudo-spectrum, wherein the normalized frequency is as follows:
Figure BDA0002638830200000022
in the formula (2), wiIs the signal frequency to be estimated.
Aiming at the traveling wave signals with short signal length and high attenuation speed, the MUSIC algorithm can be used for extracting the real frequency. However, the MUSIC algorithm has the defects of parameter transition dependence, long time consumption and pseudo spectrum. The FFT algorithm is used for carrying out spectrum analysis in a signal period, and meets the sampling theorem f when carrying out the MUSIC algorithms≥2fmaxIn the case of (2), the data row vector is sampled N times, and the entire spectrum of the signal can be obtained in principle. However, when performing spectrum transformation, because the period of the signal cannot be accurately obtained, performing FFT transformation directly on N samples can only obtain an approximate value of the signal spectrum. Therefore, the invention adopts the frequency estimation combining the FFT and the MUSIC algorithm, firstly, the FFT is used for pre-estimating the frequency, the search domain is reduced, and then the MUSIC is used for frequency refinement.
The time for searching the spectral peak is shortened in the whole frequency domain range, the frequency of the fault transient signal is more accurately and effectively extracted, and the frequency leakage phenomenon is avoided.
Step 3: the initial traveling wave generated by the fault propagates to both sides along the line, and the measuring end senses the superposition of the measuring end M and the traveling waves reflected by the fault point and the tail end for multiple times, and the superposition shows that the frequency is a series of high-frequency components with natural frequency. Considering the non-negativity of the actual frequency, the frequency of the fault traveling wave can be obtained as follows:
Figure BDA0002638830200000023
in formula (4): thetaFAnd thetaMThe reflection angles of the fault point and the measuring end are shown, and therefore, the frequency spectrum of the fault traveling wave is related to the reflection angle of the fault point, the reflection angle of the system measuring end and the fault distance. Changing tau to xfThe calculation formula of the fault distance obtained by substituting/v into the above formula is as follows:
changing tau to xfSubstituting/v into equation (4) above, the available fault distance is:
Figure BDA0002638830200000031
when the power cable is subjected to fault location using the formula (5), the fault location is not only related to the traveling wave frequency but also related to the fault point reflection angle θFAnd the measurement end reflection angle thetaMIt is related. Therefore, the travelling wave natural frequency ranging needs to accurately extract natural frequency components and accurately estimate the fault point reflection angle and the measurement end reflection angle. Therefore, the frequency method is difficult to find the fault distance, a high-precision frequency spectrum analysis technology is needed, and the practicability is not high. Therefore, the invention changes the angle consideration and utilizes the frequency difference delta f between adjacent frequency components in the frequency domain to carry out fault distance measurement. According to the natural frequency ranging formula (5), the frequency difference Δ f between adjacent frequency components is:
Figure BDA0002638830200000032
the invention utilizes the frequency domain characteristic of the traveling wave, does not need to identify the wave head of the traveling wave, even if the polarity of the wave head of the traveling wave is changed in the transmission process or the wave head is gradually deformed along with the attenuation wave, the fault distance can be obtained by extracting the natural frequency of the traveling wave and acquiring the stable frequency difference delta f by utilizing the frequency difference method for ranging, and the ranging result is accurate and reliable.
The invention has the beneficial effects that:
1. the invention utilizes the sum I of three-phase sheath currents∑The fault distance measuring signal can eliminate modulus interference and strengthen mutation characteristics so as to achieve the purpose of optimizing the fault distance measuring signal.
2. The frequency difference method is used for ranging, the frequency domain characteristic of the traveling wave is utilized, the traveling wave head does not need to be identified, even if the polarity of the traveling wave head changes in the transmission process or the traveling wave head is gradually deformed along with the attenuation wave, the fault distance can be obtained by only extracting the inherent frequency of the traveling wave and acquiring the stable frequency difference delta f by utilizing the frequency difference method for ranging.
3. The invention utilizes the frequency difference method to carry out fault location without calculating fault pointsAngle of reflection thetaFAnd the measurement end reflection angle thetaMOnly the natural frequency component needs to be accurately extracted, and the ranging reliability is higher than that of a traveling wave time domain method.
Drawings
FIG. 1 is a diagram of a 10kV cable simulation model according to the present invention;
FIG. 2 is a diagram of a Thevenin equivalent model of a transmission system fault attachment network and two-terminal systems thereof according to the present invention;
FIG. 3 is a branch L of FIG. 1 according to the present invention1Middle 3km fault ranging signal I∑A spectrogram;
FIG. 4 shows branch L of FIG. 1 according to the present invention1Middle 5km fault ranging signal I∑A spectrogram;
FIG. 5 is a branch L of FIG. 1 according to the present invention1Middle 8km fault ranging signal I∑A spectrogram;
FIG. 6 is a branch L of FIG. 1 according to the present invention1Middle 10km fault ranging signal I∑A spectrogram;
FIG. 7 is a branch L of FIG. 1 according to the present invention1Middle 13km fault ranging signal I∑And (4) a spectrogram.
Detailed Description
The invention is further described with reference to the following drawings and detailed description.
A10 kV cable fault location method based on a sheath current traveling wave natural frequency difference method comprises the steps of firstly, extracting the sum I of three-phase sheath currents subjected to phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the FFT-MUSIC is utilized to carry out fault ranging on the signal I∑Carrying out frequency spectrum transformation to extract each frequency component in the traveling wave signal; and finally, carrying out fault location by using a natural frequency difference method.
The method comprises the following specific steps:
step 1: obtaining the sum I of three-phase sheath currents∑As fault location signals
In the practical engineering, a Clarke transformation matrix is commonly used for decoupling signals of a three-phase conductor system, and the decoupling matrix is as follows:
Figure BDA0002638830200000041
in order to realize the phase-mode transformation of the three-phase cable six-conductor system, a Clarke matrix needs to be expanded, and the expanded voltage transformation matrix S and current transformation matrix Q are as follows:
Figure BDA0002638830200000042
the three-phase core current and the sheath current are decoupled into six independent moduli through phase-mode transformation, and analysis on the characteristics of each modulus of a cable system can find that the external moduli ( moduli 1, 2 and 3) are not main components of fault traveling waves, and because the external moduli are closely connected with the ground, the traveling waves are quickly attenuated in the transmission process, stable traveling wave transient signals cannot be obtained, and the traveling waves are difficult to apply to cable fault location, which is similar to the ground mode of an overhead line. And the three internal moduli (4, 5 and 6) are similar to the overhead line mode, and the traveling wave signal mutation characteristic of the modulus 4 is obvious and stable, so that the method can be used for cable fault location. However, in the tunnel or channel-laid system, since the three-phase sheath includes three internal moduli and the propagation velocities of the moduli 5 and 6 are higher than the modulus 4, the three internal moduli interfere with each other. The invention therefore proposes a method for optimizing a fault-ranging signal according to this idea.
Figure BDA0002638830200000043
In the above formula (3)a、Ib、IcRespectively three-phase sheath current i1～i6Six modulus currents. Adding the three phase sheath currents as described above, it can be seen that the outer mold quantities 2, 3 and the inner moduli 5, 6 cancel each other out, and the final formula contains only modulus 1 and modulus 4, i.e.:
Figure BDA0002638830200000051
step 2: utilizing FFT-MUSIC algorithm to carry out fault ranging on the fault ranging signal I in the step one∑And carrying out spectrum transformation to extract each frequency component in the signal. The method comprises the following specific steps:
1. multiple signal classification (MUSIC)
Let the time series y (n) be a complex sinusoidal signal with noise signals, i.e.:
Figure BDA0002638830200000052
in the above formula: w (n) is the added noise signal;
Figure BDA0002638830200000053
is a random initial phase; w is aiIs the signal frequency to be estimated; a isiIs the complex harmonic signal amplitude.
For the (M +1) -dimensional observation signal vector y (n), if:
y(n)＝[y(0),y(1)…y(M)]T (6)
y(n)＝[1,eiwj,ei2wj,…,eiMwj]T (7)
a (M +1) × (M +1) -dimensional correlation matrix obtained by the equations (6) and (7):
Figure BDA0002638830200000054
for matrix Ry(τ) singular value decomposition to give:
Ry(τ)＝VAUH (9)
in formula (9): a is a diagonal matrix composed of frequency energy; in the formula, the upper corner H is expressed by a unitary matrix, and V and U are respectively RyA unitary matrix of left and right singular vectors of (τ), the expression being as follows:
Figure BDA0002638830200000055
let R ═ E (R)yRy H)＝HA2VHFrom this, it can be seen that the singular vector V is a feature vector of R, and V is made to be [ V ]s,VN]And thus may be represented by matrix RySingular value decomposition of (τ) to obtain a signal subspace VsSum noise subspace VNThe spatial spectrum constructed by the MUSIC principle is as follows:
Figure BDA0002638830200000056
therefore, the precise frequency of each group of components of the signal can be obtained according to the peak position of the MUSIC pseudo spectrum, and the normalized frequency is as follows:
Figure BDA0002638830200000061
according to research, the MUSIC algorithm can be used for extracting the real frequency aiming at the traveling wave signals with short signal length and high attenuation speed. However, the MUSIC algorithm has the disadvantages of being dependent on parameter transition, and the MUSIC needs to perform spectrum peak search in the whole frequency domain, which takes long time, and in addition, due to the existence of pseudo-spectrum, the application of the MUSIC algorithm in practice is seriously influenced. Therefore, the invention adopts the frequency estimation combining the FFT and the MUSIC algorithm, firstly, the FFT is used for pre-estimating the frequency, the search domain is reduced, and then the MUSIC is used for frequency refinement.
2. Frequency estimation method of FFT-MUSIC
The FFT algorithm is a spectral analysis performed in one signal period, which is expressed as:
Figure BDA0002638830200000062
in formula (13): the sampling sequence and its corresponding harmonic coefficients are x (n) and x (k), respectively, and in practical applications, nonlinear, non-periodic, and unsteady signals with limited length are usually encountered. To apply equation (13) to the signal to be analyzed for fourier transformation, the data needs to be truncated into N, and then the N-point sequence is treated as a periodic sequence of a periodic signal.
Satisfying the sampling theorem f when performing the MUSIC algorithms≥2fmaxIn the case of (2), the data row vector is sampled N times, and the entire spectrum of the signal can be obtained in principle. However, when the spectrum transform is performed by using equation (5), since the period of the signal cannot be accurately obtained, performing the FFT transform on the N samples directly can only obtain an approximate value of the signal spectrum. It proved to be as follows:
suppose that when performing a MUSIC analysis, the sampling data of a certain signal is N0The data sequence is x (n). If the sampled data in one signal period is N0N is (r + m) N0Wherein m is a non-negative integer, and r is more than or equal to 0 and less than 1. According to the periodicity of the signal: x (N) ═ x (N + N)0) Then, FFT is performed using data with length N, and the spectrum is:
Figure BDA0002638830200000063
the second part in equation (14) can be regarded as N formed by zero padding after being cut by a window0The DFT of the point data has certain leakage; mx (k) is the exact spectrum of the signal. Therefore, the equation (14) includes a frequency spectrum of the periodic signal and a pseudo spectrum due to leakage. On the other hand, in the formula (14), the frequency corresponding to the k-th spectral line is fk＝k/N0(ii) a The frequency of the (r + m) th line is given by:
Figure BDA0002638830200000064
as can be seen from the above equation (15), the FFT can directly perform spectrum transformation on the data sequence of any signal length, so as to obtain an approximate value of the corresponding frequency. By the spectral analysis combining the FFT and the MUSIC algorithm, the spectral peak searching time can be shortened in the whole frequency domain range, the frequency of the fault transient signal can be extracted more accurately and effectively, and the frequency leakage phenomenon is avoided.
Step 3: and D, performing fault location by using a frequency difference method according to the frequency components extracted in the step two, wherein the specific method comprises the following steps:
the initial traveling wave generated by the fault propagates to both sides along the line, and the measuring end senses the superposition of the measuring end M and the traveling waves reflected by the fault point and the tail end for multiple times, and the superposition shows that the frequency is a series of high-frequency components with natural frequency.
For the measurement end M, the natural frequency of the fault transient traveling wave is determined by the characteristic formula of formula (16):
1-M(s)F(s)p2(s)＝0 (16)
by solving the equation using the euler equation, equation (15) can be transformed into:
Figure BDA0002638830200000074
this is obtained by the following equation (17):
Figure BDA0002638830200000071
according to the physical meaning of the pole of the laplace function, the imaginary part of the equation (18) is the oscillation degree of the fault traveling wave frequency, and the real part represents the attenuation degree of the fault traveling wave frequency. According to equation (18), considering the non-negativity of the actual frequency, the frequency of the fault traveling wave is obtained as follows:
Figure BDA0002638830200000072
in formula (19): thetaFAnd thetaMThe reflection angles of the fault point and the measuring end are shown, and therefore, the frequency spectrum of the fault traveling wave is related to the reflection angle of the fault point, the reflection angle of the system measuring end and the fault distance. Changing tau to xfThe calculation formula of the fault distance obtained by substituting/v into the above formula is as follows:
Figure BDA0002638830200000073
is represented by formula (20)) It can be seen that, when the power cable is subjected to fault location by the formula (20), the fault distance is not only related to the traveling wave frequency but also related to the fault point reflection angle θFAnd the measurement end reflection angle thetaMIt is related. Therefore, the travelling wave natural frequency ranging needs to accurately extract natural frequency components and accurately estimate the fault point reflection angle and the measurement end reflection angle. Therefore, the frequency method is difficult to find the fault distance, a high-precision frequency spectrum analysis technology is needed, and the practicability is not high. Therefore, the invention changes the angle consideration and utilizes the frequency difference delta f between adjacent frequency components in the frequency domain to carry out fault distance measurement. According to the natural frequency ranging formula (20), the frequency difference Δ f between adjacent frequency components is:
Figure BDA0002638830200000081
example 1: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at the position 3km away from the head end of the line, the total length of the line is 15km, the transition resistance is 0.01 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that the time window data of 10ms after the fault occurs is taken as an analysis signal. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 3.
The invention utilizes a frequency stabilization difference method delta f to carry out fault location, as shown in figure 3, the stable delta f is approximately 3.125 multiplied by 104Hz,. DELTA.f can be substituted for formula (21):
Figure BDA0002638830200000082
according to the distance measurement result, the absolute error is 0.152km, the relative error is 1.01%, the distance measurement result does not meet the requirement that the distance measurement error of the frequency method is within 5% of the real fault distance, the actual line patrol requirement is not influenced, and the distance measurement result is reliable.
Example 2: 10kV distribution network power supply as shown in figure 1A cable simulation model with a branch L1The single-phase earth fault occurs at the position 5km away from the head end of the line, the total length of the line is 15km, the transition resistance is 10 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that the time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 4.
The invention utilizes a frequency stabilization difference method delta f to carry out fault location, as shown in figure 4, the stable delta f is approximately 1.875 multiplied by 104Hz,. DELTA.f can be substituted for formula (21):
Figure BDA0002638830200000083
according to the ranging result, the absolute error is 0.253km, the relative error is 1.69%, the ranging result does not meet the requirement that the ranging error of the frequency method is within 5% of the real fault distance, the actual line patrol requirement is not influenced, and the ranging result is reliable.
Example 3: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at a position 8km away from the head end of the line, the total length of the line is 15km, the transition resistance is 20 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 5.
The invention utilizes a frequency stabilization difference method delta f to carry out fault location, as shown in figure 4, the stable delta f is approximately 1.25 multiplied by 104Hz,. DELTA.f can be substituted for formula (21):
Figure BDA0002638830200000091
according to the distance measurement result, the absolute error is 0.120km, the relative error is 0.8%, the distance measurement result meets the requirement that the distance measurement error of the frequency method is within 5% of the real fault distance, the actual line patrol requirement is met, and the distance measurement result is accurate and reliable.
Example 4: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at a position 10km away from the head end of the line, the total length of the line is 15km, the transition resistance is 30 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 6.
The invention utilizes a frequency stabilization difference method delta f to carry out fault location, as shown in figure 6, the stable delta f is approximately 0.974 multiplied by 104Hz,. DELTA.f can be substituted for formula (21):
Figure BDA0002638830200000092
according to the ranging result, the absolute error is 0.113km, the relative error is 0.75%, the ranging result meets the requirement that the ranging error of the frequency method is within 5% of the real fault distance, the actual line patrol requirement is met, and the ranging result is accurate and reliable.
Example 5: as shown in FIG. 1, a 10kV power distribution network cable simulation model is provided with a branch L1The single-phase earth fault occurs at the position 13km away from the head end of the line, the total length of the line is 15km, the transition resistance is 50 omega, the sampling frequency is 800kHz, and due to the occurrence of the earth fault, the duration time of the traveling wave is 0.5-0.7 power frequency periods, so that time window data of 10ms after the fault occurs are taken as analysis signals. Fault ranging signal I using FFT-MUSIC algorithm∑(sum of three-phase cable sheath currents) is subjected to spectrum analysis, and the corresponding spectrum is shown in fig. 7.
The invention utilizes a frequency stabilization difference method delta f to carry out fault location, as shown in figure 7, the stability delta f is approximately 0.751 multiplied by 104Hz,. DELTA.f can be substituted for formula (21):
Figure BDA0002638830200000093
according to the ranging result, the absolute error is 0.116km, the relative error is 0.77%, the ranging result meets the requirement that the ranging error of the frequency method is within 5% of the real fault distance, the actual line patrol requirement is met, and the ranging result is accurate and reliable.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.

Claims (2)

1. A10 kV cable fault location method based on a sheath current traveling wave natural frequency difference method is characterized by comprising the following steps: firstly, extracting the sum I of three-phase sheath currents after phase-mode conversion by an expanded Clarke matrix∑As a fault ranging signal; secondly, the FFT-MUSIC is utilized to carry out fault ranging on the signal I∑Carrying out frequency spectrum transformation to extract each frequency component in the signal; and finally, carrying out fault location by using a natural frequency difference method.
2. The 10kV cable fault location method based on the sheath current traveling wave natural frequency difference method according to claim 1, which is characterized by comprising the following specific steps:
step 1: obtaining the sum I of three-phase sheath currents∑As a fault ranging signal;
firstly, decoupling a three-phase conductor system signal by using a Clarke transformation matrix, before decoupling, expanding the Clarke matrix to obtain a voltage transformation matrix S and a current transformation matrix Q, and then decoupling a three-phase core current and a sheath current into six independent moduli by phase-mode transformation;
Figure FDA0002638830190000011
in the formula (1), Ia、Ib、IcRespectively three-phase sheath current i1～i6Current of six moduli;
the sum I of the currents of the three-phase sheath can be obtained by adding the currents of the three-phase sheath∑Comprises the following steps:
Figure FDA0002638830190000012
the sum I of three-phase sheath currents∑As a fault ranging signal;
step 2: utilizing FFT-MUSIC algorithm to carry out fault ranging on the fault ranging signal I in Step1∑Carrying out frequency spectrum transformation, extracting each frequency component in the signal, and obtaining the accurate frequency of each group of components of the signal according to the spectral peak position of the MUSIC pseudo-spectrum, wherein the normalized frequency is as follows:
Figure FDA0002638830190000013
in the formula (2), wiIs the signal frequency to be estimated;
step 3: and (3) fault location is carried out by using a frequency difference method according to each frequency component extracted in Step2, wherein the frequency of the fault traveling wave is as follows:
Figure FDA0002638830190000014
in formula (4): thetaFAnd thetaMThe reflection angles at the fault point and the measuring end are obtained;
changing tau to xfSubstituting/v into equation (4) above, the available fault distance is:
Figure FDA0002638830190000021
and (3) carrying out fault distance measurement by using the frequency difference delta f between adjacent frequency components in the frequency domain, wherein the frequency difference delta f between the adjacent frequency components can be obtained according to the natural frequency distance measurement formula (5) as follows:
Figure FDA0002638830190000022
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