CN118050596A - Fault positioning system and method for power transmission line - Google Patents
Fault positioning system and method for power transmission line Download PDFInfo
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Abstract
The invention discloses a fault positioning system of a power transmission line, which comprises: the fault traveling wave acquisition and preprocessing module is used for acquiring three-phase voltage data and preprocessing the three-phase voltage data to obtain fault traveling waves; the fault traveling wave decomposition module is used for decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm; the fault traveling wave arrival time calibration module is used for selecting a mode function IMF with the maximum kurtosis value, and calibrating the time of arrival of the fault initial traveling wave at two ends of the transmission line to be calibrated and the time of arrival of the fault point reflected wave at two ends of the transmission line by adopting a TEO energy operator; the fault positioning module is used for calculating the fault position by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the transmission line to be calibrated and the time when the fault point reflected wave reaches the two ends of the line. The fault position can be calculated only by calibrating the arrival time of the initial fault traveling wave and the fault reflected wave.
Description
Technical Field
The invention relates to the technical field of power line fault removal, in particular to a fault positioning system and method of a power transmission line.
Background
With the continuous development of power systems in China, the requirements on the running safety and reliability of the power grid are higher and higher. After the power transmission line fails, the fault position is quickly and accurately found, the fault is removed in time, the power failure time is reduced, and the method is an important guarantee for safe and stable operation of the power system.
At present, research on fault location of a power transmission line at home and abroad is mature, wherein the principle of a traveling wave location method is simple and reliable, and the method is favored by a plurality of students. According to different sources of the traveling wave data, the traveling wave positioning method can be divided into a single-ended traveling wave positioning algorithm and a double-ended traveling wave positioning algorithm. The single-ended traveling wave positioning algorithm only uses traveling wave data at one end of the line, and calculates the fault position by detecting the time of arrival of the fault traveling wave at one end of the line from the fault point and the arrival time of the fault point reflection traveling wave and combining the traveling wave speed. The double-end traveling wave positioning algorithm calculates the fault position by utilizing the time difference of fault traveling waves reaching the two ends of the line and the traveling wave speed. Therefore, the accuracy of the traveling wave ranging method mainly depends on accurate traveling wave arrival time and traveling wave velocity.
The existing calibration method of the traveling wave arrival time utilizes the maximum value of the wavelet mode to detect the mutation point of the traveling wave signal, and the fault location is realized when the traveling wave arrives at the monitoring point, so that good effect is obtained, but the wavelet transformation method needs to select proper wavelet basis function and decomposition scale, and has poor self-adaptability; the EMD decomposition can have the phenomena of modal aliasing, end-point effect and the like, can have certain influence on the calibration of the arrival time of the traveling wave, has large conversion calculation amount and is difficult to obtain a satisfactory result.
Disclosure of Invention
The invention aims at overcoming the defects of the prior art, and provides a fault positioning system and a fault positioning method for a power transmission line. And secondly, the analysis of the improved double-end traveling wave positioning algorithm finds that the fault positioning result is irrelevant to the transmission speed, the fault position can be calculated only by calibrating the arrival time of the initial traveling wave and the fault reflected wave of the fault without knowing the occurrence time of the fault.
The invention provides a fault positioning system of a power transmission line, which comprises the following components:
the fault traveling wave acquisition and preprocessing module is used for acquiring three-phase voltage data of a power transmission line with faults and preprocessing the three-phase voltage data to obtain fault traveling waves;
the fault traveling wave decomposition module is used for decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
the fault traveling wave arrival time calibration module is used for calculating kurtosis values of the modal functions IMFs, calculating instantaneous energy values of the modal functions IMFs with the largest kurtosis values by adopting a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by utilizing the instantaneous energy values, and obtaining time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and time of the fault reflected wave reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
The fault positioning module is used for calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
Further, in the fault traveling wave obtaining and preprocessing module, the specific method for preprocessing the three-phase voltage data to obtain the fault traveling wave includes:
And carrying out phase-mode transformation on the three-phase voltage data by adopting the Karenebel transformation to obtain line mode voltage and ground mode voltage, and selecting the line mode voltage as fault traveling wave.
Further, in the fault traveling wave decomposition module, the specific method for decomposing the fault traveling wave into a plurality of modal functions IMFs by using the VMD algorithm is as follows:
The calculation formula of the IMF bandwidth of each mode function is as follows:
Wherein k is the number of the mode functions IMF obtained after decomposition, u k is the mode function IMF obtained after decomposition, omega k is the center frequency of the mode function IMF, The partial derivative of t, j is an imaginary unit, t is time, delta (t) is a dirac distribution function, and f is a fault traveling wave;
The constraint problem of traveling wave decomposition is converted into an augmented saddle point problem by introducing a secondary penalty factor alpha and a Lagrange multiplier lambda, and the augmented expression is obtained as follows:
and then carrying out iterative optimization sequence by a multiplication operator alternating direction method, and carrying out alternating iteration on u k n+1、ωk n+1、λk n+1 converted to a frequency domain, wherein the alternating iteration formula is as follows:
wherein, For the mode function IMF obtained by iteration, n is the iteration number, τ is the noise tolerance parameter,/>For the iteratively derived Lagrangian multiplier,/>A representation function for converting the time signal f (t) from the time domain into the frequency domain;
when the iteration result meets the stop condition, an optimal solution is obtained, as shown in the following formula:
where ε is the stop condition.
Further, in the fault traveling wave arrival time calibration module, the specific method for calculating the kurtosis value of each mode function IMF comprises the following steps:
The kurtosis value calculation formula is as follows:
Wherein Ku is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the mode function IMF signal.
Further, in the fault traveling wave arrival time calibration module, the method for calculating the instantaneous energy value of the modal function IMF with the maximum kurtosis value by using the TEO energy operator, respectively obtaining the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated by using the instantaneous energy value, and obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated comprises the following specific steps:
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
Calculating the instantaneous energy value of the mode function IMF with the maximum kurtosis value through a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of a line to be calibrated, wherein the time corresponding to the extreme point of the instantaneous energy value is the traveling wave arrival time, and the specific judging method is as follows:
in an instantaneous energy spectrogram at two ends of a transmission line to be calibrated, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the transmission line is close to the fault position by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, and then judging the time of the fault reflected wave reaching the end of the transmission line to be calibrated, which is close to the fault position, as the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line, which is close to the fault position.
Further, in the fault positioning module, according to the time when the fault initial traveling wave reaches two ends of the transmission line to be calibrated and the time when the fault reflected wave reaches the end of the transmission line to be calibrated, which is close to the fault position, the specific method for calculating the fault position in the transmission line by adopting the improved double-end traveling wave positioning algorithm is as follows:
Firstly, calculating the distance between a fault point and two ends of a power transmission line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
A fault locating method of a power transmission line comprises the following steps:
acquiring three-phase voltage data of a power transmission line with faults, and preprocessing the three-phase voltage data to obtain fault traveling waves;
decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
Calculating kurtosis values of the IMFs of the modal functions, calculating instantaneous energy values of the IMFs of the modal function with the largest kurtosis value by using a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by using the instantaneous energy values, and obtaining time of fault initial traveling waves reaching the two ends of the transmission line to be calibrated and time of fault reflected waves reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
And calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
Further, the method for calculating the kurtosis value of each modal function IMF, then adopting a TEO energy operator to calculate the instantaneous energy value of the modal function IMF with the largest kurtosis value, respectively obtaining the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated by using the instantaneous energy value, and obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated comprises the following specific steps:
The kurtosis value calculation formula is as follows:
Wherein Ku is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the IMF signal of the mode function;
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
Calculating the instantaneous energy value of the mode function IMF with the maximum kurtosis value through a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of a line to be calibrated, wherein the time corresponding to the extreme point of the instantaneous energy value is the traveling wave arrival time, and the specific judging method is as follows:
in an instantaneous energy spectrogram at two ends of a transmission line to be calibrated, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the transmission line is close to the fault position by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, and then judging the time of the fault reflected wave reaching the end of the transmission line to be calibrated, which is close to the fault position, as the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line, which is close to the fault position.
Further, the specific method for calculating the fault position in the power transmission line by adopting the improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part of the power transmission line to be calibrated, which is close to the fault position, comprises the following steps:
Firstly, calculating the distance between a fault point and two ends of a power transmission line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
A computer readable medium having a computer program stored thereon, the computer program, when run, performing a fault location method for a power transmission line as described above.
The beneficial effects of the invention are as follows:
1. The time difference between the fault initial traveling wave and the fault reflected wave at one end of the incoming line is utilized to eliminate the influence of the traveling wave speed. And secondly, the analysis of the improved double-end traveling wave positioning algorithm finds that the fault positioning result is irrelevant to the transmission speed, the fault position can be calculated only by calibrating the arrival time of the initial wave head and the reflected wave without knowing the fault occurrence time. And selecting a corresponding positioning calculation formula according to different fault areas, so that the phenomenon that the detection wave head fails when the transmission of the opposite-end fault reflected wave is overlong when the fault occurs near the line can be avoided.
2. And decomposing fault signals by utilizing a VMD algorithm, selecting proper modal components according to kurtosis, and calibrating the arrival time of the fault traveling wave by using a TEO energy operator. After the fault traveling wave signal is decomposed by the VMD, the traveling wave mutation characteristics of each IMF component with the output length of N are measured by using the kurtosis value K, the larger the kurtosis value is, the more obvious the wave head information is, and therefore the arrival time of the IMF calibration traveling wave with the maximum kurtosis value is selected.
3. The VMD-TEO-based transmission line double-end traveling wave positioning method is small in positioning error at different fault positions, strong in transition resistance tolerance, strong in stability and anti-interference performance, and strong in AC transmission line fault positioning practicality.
Drawings
FIG. 1 is a system block diagram of the present invention;
FIG. 2 is a schematic diagram of the instantaneous energy spectrum at both ends of the line of the present invention;
FIG. 3 is a schematic diagram of fault point location according to the present invention.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved more clear, the application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
Example 1
As shown in fig. 1, a fault location system for a power transmission line includes:
The fault traveling wave acquisition and preprocessing module is used for acquiring three-phase voltage data of a power transmission line with faults and preprocessing the three-phase voltage data to obtain fault traveling waves, wherein the faults comprise single-phase grounding faults, two-phase short-circuit grounding faults, three-phase short-circuit faults and the like;
the fault traveling wave decomposition module is used for decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
the fault traveling wave arrival time calibration module is used for calculating kurtosis values of the modal functions IMFs, calculating instantaneous energy values of the modal functions IMFs with the largest kurtosis values by adopting a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by utilizing the instantaneous energy values, and obtaining time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and time of the fault reflected wave reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
The fault positioning module is used for calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
(1) In the fault traveling wave acquisition and preprocessing module, the specific method for preprocessing the three-phase voltage data to obtain the fault traveling wave comprises the following steps:
And carrying out phase-mode transformation on the three-phase voltage data by adopting the Karenebel transformation to obtain line mode voltage and ground mode voltage, and selecting the line mode voltage as fault traveling wave.
When lightning stroke or short circuit fault occurs, three-phase voltage data (also called transient voltage) are collected: transient voltage = normal operation voltage + additional voltage, line mode voltage is obtained by phase mode conversion of the additional voltage.
Because the ground mode voltage has the problems of chromatic dispersion and attenuation in the transmission process, the fault traveling wave positioning precision is affected, and therefore the line mode voltage is selected for analysis and calculation.
(2) In the fault traveling wave decomposition module, the specific method for decomposing the fault traveling wave into a plurality of modal functions IMFs by using the VMD algorithm is as follows:
The calculation formula of the IMF bandwidth of each mode function is as follows:
Wherein k is the number of the mode functions IMF obtained after decomposition, u k is the mode function IMF obtained after decomposition, omega k is the center frequency of the mode function IMF, The partial derivative of t, j is an imaginary unit, t is time, delta (t) is a dirac distribution function, and f is a fault traveling wave;
The constraint problem of traveling wave decomposition is converted into an augmented saddle point problem by introducing a secondary penalty factor alpha and a Lagrange multiplier lambda, and the augmented expression is obtained as follows:
and then carrying out iterative optimization sequence by a multiplication operator alternating direction method, and carrying out alternating iteration on u k n+1、ωk n+1、λk n+1 converted to a frequency domain, wherein the alternating iteration formula is as follows:
wherein, For the mode function IMF obtained by iteration, n is the iteration number, τ is the noise tolerance parameter,/>For the iteratively derived Lagrangian multiplier,/>A representation function for converting the time signal f (t) from the time domain into the frequency domain;
when the iteration result meets the stop condition, an optimal solution is obtained, as shown in the following formula:
where ε is the stop condition.
In order to enable the TEO energy operator to effectively detect the traveling wave head, fault signals are decomposed through secondary VMD, and most of noise in the signals is filtered.
(3) In the fault traveling wave arrival time calibration module, the kurtosis value of each modal function IMF is calculated, then the transient energy value of the modal function IMF with the largest kurtosis value is calculated by adopting a TEO energy operator, the transient energy value is used for respectively obtaining the transient energy spectrograms at the two ends of the transmission line to be calibrated, and the specific method for obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, is as follows:
The kurtosis value calculation formula is as follows:
Wherein Ku is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the mode function IMF signal. The greater the kurtosis value is, the more obvious the wave head information is, so that the arrival time of the traveling wave is calibrated by the IMF with the maximum kurtosis value is selected.
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
the instantaneous energy value of the mode function IMF with the largest kurtosis value is calculated through a TEO energy operator, so that the instantaneous energy spectrograms at the two ends of the line are respectively obtained, and as shown in fig. 2, the time corresponding to the extreme point of the instantaneous energy value, namely the arrival time of the traveling wave, is specifically judged as follows:
in the instantaneous energy spectrogram at two ends of the line, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the line the fault position is close to by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, wherein the end with the earlier fault initial traveling wave reaching time is the end close to the fault position, and the time of the fault point reflected wave reaching the end of the line is the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line close to the fault position.
The time difference between the fault initial traveling wave and the fault reflected wave at one end of the transmission line close to the fault position is utilized to eliminate the influence of the traveling wave speed. When the power transmission line breaks down, the line end closest to the fault point firstly collects fault traveling waves, and the arrival time of the corresponding traveling waves is minimum, so that the fault position can be judged to be close to the two ends of the power transmission line by comparing the arrival time of the fault initial traveling waves at the two ends of the power transmission line to be calibrated.
(4) In the fault positioning module, the specific method for calculating the fault position of the power transmission line by adopting the improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part of the power transmission line to be calibrated, which is close to the fault position, comprises the following steps:
Firstly, calculating the distance between a fault point and two ends of a line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line, as shown in fig. 3;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
The double-end traveling wave positioning method calculates the fault position by detecting the time when the fault traveling wave reaches the two ends of the line and the propagation speed of the fault traveling wave on the line. From theoretical analysis, the transmission speed calculation formula of the fault traveling wave is as follows(L and C are inductance and capacitance of line unit length respectively), so that the fault traveling wave speeds on different lines are different, and the traveling wave transmission speeds of the same line are not consistent at different moments and different positions due to the influence of the operation environment and the variation of line parameters. In order to solve the problem of influence of uncertainty of wave speed values on fault location, the principle of a single-ended traveling wave location algorithm is combined, the reflected traveling wave of a fault point is utilized to analyze a double-ended traveling wave location algorithm, an improved double-ended traveling wave location algorithm is obtained, the result shows that a fault location result is irrelevant to the transmission speed, the fault occurrence moment is not required to be known, and the fault location can be calculated only by the time when the initial traveling wave of the fault reaches the two ends of the transmission line to be calibrated and the time when the reflected wave of the fault reaches the end part of the transmission line to be calibrated, which is close to the fault location.
Example 2
A fault locating method of a power transmission line comprises the following steps:
Acquiring three-phase voltage data of a power transmission line with faults, and preprocessing the three-phase voltage data to obtain fault traveling waves, wherein the faults comprise single-phase grounding faults, two-phase short-circuit grounding faults, three-phase short-circuit faults and the like;
decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
Calculating kurtosis values of the IMFs of the modal functions, calculating instantaneous energy values of the IMFs of the modal function with the largest kurtosis value by using a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by using the instantaneous energy values, and obtaining time of fault initial traveling waves reaching the two ends of the transmission line to be calibrated and time of fault reflected waves reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
And calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
(1) The specific method for preprocessing the three-phase voltage data to obtain the fault traveling wave comprises the following steps:
And carrying out phase-mode transformation on the three-phase voltage data by adopting the Karenebel transformation to obtain line mode voltage and ground mode voltage, and selecting the line mode voltage as fault traveling wave.
When lightning stroke or short circuit fault occurs, three-phase voltage data (also called transient voltage) are collected: transient voltage = normal operation voltage + additional voltage, line mode voltage is obtained by phase mode conversion of the additional voltage.
Because the ground mode voltage has the problems of chromatic dispersion and attenuation in the transmission process, the fault traveling wave positioning precision is affected, and therefore the line mode voltage is selected for analysis and calculation.
(2) The specific method for decomposing the fault traveling wave into a plurality of modal functions IMFs by using the VMD algorithm comprises the following steps:
The calculation formula of the IMF bandwidth of each mode function is as follows:
Wherein k is the number of the mode functions IMF obtained after decomposition, u k is the mode function IMF obtained after decomposition, omega k is the center frequency of the mode function IMF, The partial derivative of t, j is an imaginary unit, t is time, delta (t) is a dirac distribution function, and f is a fault traveling wave;
The constraint problem of traveling wave decomposition is converted into an augmented saddle point problem by introducing a secondary penalty factor alpha and a Lagrange multiplier lambda, and the augmented expression is obtained as follows:
and then carrying out iterative optimization sequence by a multiplication operator alternating direction method, and carrying out alternating iteration on u k n+1、ωk n+1、λk n+1 converted to a frequency domain, wherein the alternating iteration formula is as follows:
/>
wherein, For the mode function IMF obtained by iteration, n is the iteration number, τ is the noise tolerance parameter,/>For the iteratively derived Lagrangian multiplier,/>A representation function for converting the time signal f (t) from the time domain into the frequency domain;
when the iteration result meets the stop condition, an optimal solution is obtained, as shown in the following formula:
where ε is the stop condition.
In order to enable the TEO energy operator to effectively detect the traveling wave head, fault signals are decomposed through secondary VMD, and most of noise in the signals is filtered.
(3) Calculating kurtosis values of the IMFs of the modal functions, calculating instantaneous energy values of the IMFs of the modal function with the largest kurtosis value by adopting a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by utilizing the instantaneous energy values, and obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated, wherein the specific method comprises the following steps:
The kurtosis value calculation formula is as follows:
Wherein Ku is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the mode function IMF signal. The greater the kurtosis value is, the more obvious the wave head information is, so that the arrival time of the traveling wave is calibrated by the IMF with the maximum kurtosis value is selected.
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
the instantaneous energy value of the mode function IMF with the largest kurtosis value is calculated through a TEO energy operator, so that the instantaneous energy spectrograms at the two ends of the line are respectively obtained, and as shown in fig. 2, the time corresponding to the extreme point of the instantaneous energy value, namely the arrival time of the traveling wave, is specifically judged as follows:
in the instantaneous energy spectrogram at two ends of the line, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the line the fault position is close to by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, wherein the end with the earlier fault initial traveling wave reaching time is the end close to the fault position, and the time of the fault point reflected wave reaching the end of the line is the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line close to the fault position.
The time difference between the fault initial traveling wave and the fault reflected wave at one end of the transmission line close to the fault position is utilized to eliminate the influence of the traveling wave speed. When the power transmission line breaks down, the line end closest to the fault point firstly collects fault traveling waves, and the arrival time of the corresponding traveling waves is minimum, so that the fault position can be judged to be close to the two ends of the power transmission line by comparing the arrival time of the fault initial traveling waves at the two ends of the power transmission line to be calibrated.
(4) The specific method for calculating the fault position of the power transmission line by adopting the improved double-end traveling wave positioning algorithm according to the time of the fault initial traveling wave reaching the two ends of the power transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the power transmission line to be calibrated, which is close to the fault position, comprises the following steps:
Firstly, calculating the distance between a fault point and two ends of a line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line, as shown in fig. 3;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
The double-end traveling wave positioning method calculates the fault position by detecting the time when the fault traveling wave reaches the two ends of the line and the propagation speed of the fault traveling wave on the line. From theoretical analysis, the transmission speed calculation formula of the fault traveling wave is as follows(L and C are inductance and capacitance of line unit length respectively), so that the fault traveling wave speeds on different lines are different, and the traveling wave transmission speeds of the same line are not consistent at different moments and different positions due to the influence of the operation environment and the variation of line parameters. In order to solve the problem of influence of uncertainty of wave speed values on fault location, the principle of a single-ended traveling wave location algorithm is combined, the reflected traveling wave of a fault point is utilized to analyze a double-ended traveling wave location algorithm, an improved double-ended traveling wave location algorithm is obtained, the result shows that a fault location result is irrelevant to the transmission speed, the fault occurrence moment is not required to be known, and the fault location can be calculated only by the time when the initial traveling wave of the fault reaches the two ends of the transmission line to be calibrated and the time when the reflected wave of the fault reaches the end part of the transmission line to be calibrated, which is close to the fault location.
Example 3
A computer readable medium having a computer program stored thereon, which when run performs a fault localization method of an electric transmission line according to embodiment 2.
What is not described in detail in this specification is prior art known to those skilled in the art. It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be finally understood that the foregoing embodiments are merely illustrative of the technical solutions of the present invention and not limiting the scope of protection thereof, and although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that various changes, modifications or equivalents may be made to the specific embodiments of the invention, and these changes, modifications or equivalents are within the scope of protection of the claims appended hereto.
Claims (10)
1. A fault location system for a power transmission line, comprising:
the fault traveling wave acquisition and preprocessing module is used for acquiring three-phase voltage data of a power transmission line with faults and preprocessing the three-phase voltage data to obtain fault traveling waves;
the fault traveling wave decomposition module is used for decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
the fault traveling wave arrival time calibration module is used for calculating kurtosis values of the modal functions IMFs, calculating instantaneous energy values of the modal functions IMFs with the largest kurtosis values by adopting a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by utilizing the instantaneous energy values, and obtaining time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and time of the fault reflected wave reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
The fault positioning module is used for calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
2. A fault location system for a power transmission line according to claim 1, wherein:
in the fault traveling wave acquisition and preprocessing module, the specific method for preprocessing the three-phase voltage data to obtain the fault traveling wave comprises the following steps:
And carrying out phase-mode transformation on the three-phase voltage data by adopting the Karenebel transformation to obtain line mode voltage and ground mode voltage, and selecting the line mode voltage as fault traveling wave.
3. A fault location system for a power transmission line according to claim 1, wherein:
In the fault traveling wave decomposition module, the specific method for decomposing the fault traveling wave into a plurality of modal functions IMFs by using the VMD algorithm is as follows:
The calculation formula of the IMF bandwidth of each mode function is as follows:
Wherein k is the number of the mode functions IMF obtained after decomposition, u k is the mode function IMF obtained after decomposition, omega k is the center frequency of the mode function IMF, The partial derivative of t, j is an imaginary unit, t is time, delta (t) is a dirac distribution function, and f is a fault traveling wave;
The constraint problem of traveling wave decomposition is converted into an augmented saddle point problem by introducing a secondary penalty factor alpha and a Lagrange multiplier lambda, and the augmented expression is obtained as follows:
and then carrying out iterative optimization sequence by a multiplication operator alternating direction method, and carrying out alternating iteration on u k n+1、ωk n+1、λk n+1 converted to a frequency domain, wherein the alternating iteration formula is as follows:
wherein, For the mode function IMF obtained by iteration, n is the iteration number, τ is the noise tolerance parameter,/>For the iteratively derived Lagrangian multiplier,/>A representation function for converting the time signal f (t) from the time domain into the frequency domain;
when the iteration result meets the stop condition, an optimal solution is obtained, as shown in the following formula:
where ε is the stop condition.
4. A fault location system for a power transmission line according to claim 1, wherein:
In the fault traveling wave arrival time calibration module, the specific method for calculating the kurtosis value of each mode function IMF comprises the following steps:
The kurtosis value calculation formula is as follows:
Wherein K u is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the mode function IMF signal.
5. A fault location system for a power transmission line according to claim 1, wherein:
In the fault traveling wave arrival time calibration module, the transient energy value of the modal function IMF with the maximum kurtosis value is calculated by adopting a TEO energy operator, the transient energy value is used for respectively obtaining transient energy spectrograms at two ends of the transmission line to be calibrated, and the specific method for obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, according to the transient energy spectrograms at the two ends of the transmission line to be calibrated is as follows:
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
Calculating the instantaneous energy value of the mode function IMF with the maximum kurtosis value through a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of a line to be calibrated, wherein the time corresponding to the extreme point of the instantaneous energy value is the traveling wave arrival time, and the specific judging method is as follows:
in an instantaneous energy spectrogram at two ends of a transmission line to be calibrated, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the transmission line is close to the fault position by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, and then judging the time of the fault reflected wave reaching the end of the transmission line to be calibrated, which is close to the fault position, as the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line, which is close to the fault position.
6. A fault location system for a power transmission line according to claim 1, wherein:
In the fault positioning module, the specific method for calculating the fault position in the power transmission line by adopting the improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part of the power transmission line to be calibrated, which is close to the fault position, comprises the following steps:
Firstly, calculating the distance between a fault point and two ends of a power transmission line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
7. The fault positioning method for the power transmission line is characterized by comprising the following steps of:
acquiring three-phase voltage data of a power transmission line with faults, and preprocessing the three-phase voltage data to obtain fault traveling waves;
decomposing the fault traveling wave into a plurality of modal functions IMFs by using a VMD algorithm;
Calculating kurtosis values of the IMFs of the modal functions, calculating instantaneous energy values of the IMFs of the modal function with the largest kurtosis value by using a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by using the instantaneous energy values, and obtaining time of fault initial traveling waves reaching the two ends of the transmission line to be calibrated and time of fault reflected waves reaching the end part, close to the fault position, of the transmission line to be calibrated according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated;
And calculating the fault position of the power transmission line by adopting an improved double-end traveling wave positioning algorithm according to the time when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated and the time when the fault reflected wave reaches the end part, close to the fault position, of the power transmission line to be calibrated.
8. The fault location method of a power transmission line according to claim 7, wherein:
Calculating kurtosis values of the IMFs of the modal functions, calculating instantaneous energy values of the IMFs of the modal function with the largest kurtosis value by adopting a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of the transmission line to be calibrated by utilizing the instantaneous energy values, and obtaining the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the transmission line to be calibrated, which is close to the fault position, according to the instantaneous energy spectrograms at the two ends of the transmission line to be calibrated, wherein the specific method comprises the following steps:
The kurtosis value calculation formula is as follows:
Wherein Ku is a kurtosis coefficient, N is the number of data points of the mode function IMF, x i is the signal amplitude corresponding to the ith data point, Is the average value of the amplitude of the IMF signal of the mode function;
For a continuous time signal f (t), the TEO energy operator calculation formula is:
ψ[f(t)]＝f′2(t)-f(t)f"(t)
Wherein, psi is an energy operator, and f' (t) and f "(t) are respectively the first-order derivative and the second-order derivative of the time signal f (t);
For the discrete time signal f (t'), the TEO energy operator calculation formula is:
ψ[f(t′)]＝[f(t′)]2-[f(t′+1)f(t′-1)]；
Calculating the instantaneous energy value of the mode function IMF with the maximum kurtosis value through a TEO energy operator, respectively obtaining instantaneous energy spectrograms at two ends of a line to be calibrated, wherein the time corresponding to the extreme point of the instantaneous energy value is the traveling wave arrival time, and the specific judging method is as follows:
in an instantaneous energy spectrogram at two ends of a transmission line to be calibrated, the time corresponding to the extreme point of the first instantaneous energy value is the time when the fault initial traveling wave reaches the end;
And judging which end of the transmission line is close to the fault position by comparing the time of the fault initial traveling wave reaching the two ends of the transmission line to be calibrated, and then judging the time of the fault reflected wave reaching the end of the transmission line to be calibrated, which is close to the fault position, as the time corresponding to the extreme point of the second instantaneous energy value according to the instantaneous energy spectrogram of the end of the transmission line, which is close to the fault position.
9. The fault location method of a power transmission line according to claim 7, wherein:
the specific method for calculating the fault position in the power transmission line by adopting the improved double-end traveling wave positioning algorithm according to the time of the fault initial traveling wave reaching the two ends of the power transmission line to be calibrated and the time of the fault reflected wave reaching the end part of the power transmission line to be calibrated, which is close to the fault position, comprises the following steps:
Firstly, calculating the distance between a fault point and two ends of a power transmission line according to a double-end traveling wave positioning algorithm, wherein the distance is shown in the following formula:
Wherein L is the length of the line, d m、dn is the distance from the fault point to the two ends of the line, v is the wave velocity of the fault traveling wave, t m、tn is the time for the fault initial traveling wave to reach the two ends of the transmission line to be calibrated, m is the m end of the transmission line, and n is the n end of the transmission line;
according to the transmission process of fault reflected waves on a line, a single-ended traveling wave positioning algorithm is shown as follows:
when the m end of the power transmission line is closer to the fault point, t m1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position, and when the n end of the power transmission line is closer to the fault point, t n1 is the time for the fault reflected wave to reach the end of the power transmission line to be calibrated, which is close to the fault position;
the simultaneous double-end traveling wave positioning algorithm and the single-end traveling wave positioning algorithm are used for eliminating the fault traveling wave velocity v to obtain an improved double-end traveling wave positioning algorithm, and the formula is as follows:
And judging whether the fault point is close to the m end or the n end of the line according to the sequence of time t m、tn when the fault initial traveling wave reaches the two ends of the power transmission line to be calibrated, calculating d m by adopting an improved double-end traveling wave positioning algorithm if the fault point is close to the m end, and calculating d n by adopting the improved double-end traveling wave positioning algorithm if the fault point is close to the n end.
10. A computer readable medium having stored thereon a computer program which, when run, performs a fault localization method of an electrical transmission line as claimed in claims 7-9.
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