A method and system for calibrating a fault traveling wave front for a power transmission line

Abstract

The application discloses a kind of methods and systems for calibrating fault traveling wave head of transmission line, the method is to obtain the sampling frequency and traveling wave current component sequence of transmission line measurement end, according to the sampling frequency, construct several scales, obtain the morphological gradient waveform and spectral entropy under each scale;According to spectral entropy and morphological gradient waveform, the modal component of fault current component sequence and fault current component sequence is intercepted to obtain instantaneous energy curve, instantaneous frequency curve, energy threshold and frequency mutation threshold;According to energy threshold, frequency mutation threshold, instantaneous energy and instantaneous frequency curve, extract fault sampling point;According to the sampling point sequence number of starting sampling time and fault sampling point, the wave head arrival time is obtained.The present application combines multiscale morphology and spectral entropy to realize scale adaptive matching, and combines energy and frequency double feature joint criterion to solve the problem of existing technology analysis tool fixation and decision criterion singularity, improve the accuracy of wave head calibration.

Description

Technical Field

[0001] This invention relates to the field of power system fault detection technology, and in particular to a method and system for calibrating the traveling wave head of a fault in a transmission line. Background Technology

[0002] High-voltage transmission lines, as the core carriers of the power system, directly determine the reliability of the power grid's supply. Transmission lines often stretch for hundreds of kilometers and operate in complex environments, leading to frequent faults. Therefore, accurate fault location is crucial for ensuring line operational safety. Among the various fault location methods, traveling wave ranging (TWR) has become the primary method due to its theoretical advantage of being unaffected by transition resistance, system operating modes, and current transformer (CT) saturation. Its principle involves accurately measuring the arrival time of the transient traveling wave surge at the measurement end, and then combining wave velocity and propagation time to invert the fault location. Therefore, the ability to accurately determine the arrival time of the initial traveling wave front from strong noise and complex transient signals directly determines the success rate and accuracy of fault location.

[0003] Currently, there are three main types of methods for calibrating the arrival time of traveling wavefronts. The first type is the wavelet transform modulus maxima method, which decomposes the linear mode signal into multi-scale wavelet components and calibrates the arrival time of the wavefront at the first zero-crossing moment of the modulus maxima of the detail coefficients at each scale. The second type is the Hilbert-Huang transform method, which sieves the signal into intrinsic mode functions through empirical mode decomposition, selects high-frequency components to construct an analytic signal, and calibrates the arrival time of the wavefront at the first significant peak moment of the instantaneous amplitude curve. The third type is the energy operator method, which calculates the instantaneous energy using nonlinear energy operators such as Teager and calibrates the arrival time of the wavefront at the first abrupt change point in the energy sequence that crosses an empirical threshold.

[0004] The methods described above all suffer from the drawbacks of fixed analytical tools and singular decision criteria. On the one hand, wavelet basis, EMD decomposition termination conditions, and energy operator thresholds all need to be pre-set manually, making it impossible to adaptively match based on changes in signal kurtosis, which can easily lead to feature extraction distortion. On the other hand, the methods mentioned above rely solely on modulus maxima, instantaneous energy peak values, or single threshold exceedances for judgment, and a single criterion can easily lead to misjudgment or missed judgment in the presence of strong noise or high-impedance grounding. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention discloses a method and system for calibrating the fault traveling wave head of transmission lines. This method solves the technical problem that existing technologies cannot accurately calibrate wave heads due to poor adaptability and susceptibility to noise interference, thereby improving the accuracy of traveling wave head calibration.

[0006] To achieve the above technical objectives, the present invention provides a method for fault traveling wave front calibration of transmission lines, comprising: The sampling frequency and traveling wave current component sequence of the measurement end of the transmission line are obtained, and several scales are constructed based on the sampling frequency. Obtain the morphological gradient waveforms of the traveling wave current component sequence at each of the stated scales and the spectral entropy corresponding to each of the stated morphological gradient waveforms; The fault current component sequence is extracted from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform. Obtain the modal components corresponding to the fault current component sequence, and obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence based on the modal components; Based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve, fault sampling points are extracted from the fault current component sequence; The arrival time of the wavefront at the measurement end of the transmission line is obtained based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence.

[0007] This invention discloses a method for calibrating the wavefront of a traveling wave in a transmission line fault. First, it acquires the sampling frequency and traveling wave current component sequence at the measurement end of the transmission line and constructs several scales based on the sampling frequency to obtain the morphological gradient waveform of the traveling wave current component sequence at each scale and the corresponding spectral entropy. This achieves adaptive matching of the analysis scale through multi-scale morphological analysis and quantitative evaluation of spectral entropy. Second, based on the spectral entropy and the morphological gradient waveform, a fault current component sequence is extracted from the traveling wave current component sequence, effectively reducing the data range for subsequent analysis to the suspected local region of the wavefront and improving overall processing efficiency. Simultaneously, by acquiring the modal components corresponding to the fault current component sequence, the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence are obtained. This allows for the extraction of the modal components to obtain the high-frequency impact characteristics at the wavefront arrival time. The system achieves the most concentrated manifestation of the transient wave characteristics and transforms the original waveform data into time-domain energy features and frequency-domain frequency features with clear physical meaning based on instantaneous energy and instantaneous frequency. This allows for adaptive calculation of energy thresholds and frequency mutation thresholds using the statistical characteristics of the instantaneous energy curve and instantaneous frequency curve, respectively, achieving automatic matching of threshold settings with the signal background noise level. Next, fault sampling points are extracted from the fault current component sequence based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve. This dual feature of energy and frequency effectively distinguishes the true wavefront from noise interference, avoiding misjudgments and omissions in strong noise or high-resistance grounding scenarios using a single criterion, thus improving the accuracy of fault sampling and location. Finally, based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence, the arrival time of the wavefront at the measurement end of the transmission line is obtained, achieving precise location of the traveling wavefront.

[0008] As a preferred example, the step of acquiring the sampling frequency and traveling wave current component sequence of the transmission line measurement end, and constructing several scales based on the sampling frequency, includes: When a transient fault is detected in the transmission line, the sampling frequency and three-phase transient current signal at the measurement end of the transmission line are acquired. The three-phase transient current signal is converted from analog to digital according to the sampling frequency to obtain the discrete sampling sequence of the three-phase current corresponding to the measurement end of the transmission line. The three-phase current discrete sampling sequence is subjected to phase mode transformation to obtain the traveling wave current component sequence corresponding to the measurement end of the transmission line; The upper limit of the scale corresponding to the measurement end of the transmission line is obtained according to the sampling frequency, and several scales corresponding to the measurement end of the transmission line are obtained according to the upper limit of the scale and the preset lower limit of the scale.

[0009] The above scheme acquires three-phase transient current signals after detecting a fault transient start-up, and performs analog-to-digital conversion on the three-phase transient current signals according to the sampling frequency to obtain a discrete sampling sequence of three-phase currents. This discrete sampling sequence is then subjected to phase-mode transformation to obtain a traveling wave current component sequence, thereby decoupling the three-phase coupled signal into line-mode components and eliminating the influence of zero-mode component wave velocity variation on the traveling wave propagation time. Simultaneously, based on the sampling frequency, an upper scale value is obtained, and combined with a preset lower scale value, several scales are derived. This ensures that the scale range for subsequent morphological analysis matches the actual sampling rate of the signal, effectively covering wavefront features at different sampling rates and providing an accurate and complete data foundation for subsequent multi-scale morphological analysis.

[0010] As a preferred example, the traveling wave current component sequence includes a plurality of discrete sampling points and the instantaneous amplitude of the traveling wave current corresponding to each discrete sampling point; the step of obtaining the morphological gradient waveform of the traveling wave current component sequence at each scale and the spectral entropy corresponding to each morphological gradient waveform includes: For any one of the several scales and any discrete sampling point in the traveling wave current component sequence, obtain the number of sampling points corresponding to that scale, and use the number of sampling points as the window length; Centered on the discrete sampling point, several neighboring discrete sampling points corresponding to the discrete sampling point are obtained from the traveling wave current component sequence according to the window length. The largest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood is selected as the expansion data corresponding to the discrete sampling point, and the smallest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood is selected as the corrosion data corresponding to the discrete sampling point. Subtracting the erosion data from the dilation data yields the morphological gradient magnitude of the discrete sampling point at that scale. By traversing all the discrete sampling points in the traveling wave current component sequence and the morphological gradient magnitude corresponding to each discrete sampling point, the morphological gradient waveform of the traveling wave current component sequence at this scale is obtained. The spectral entropy of the traveling wave current component sequence at this scale is obtained based on the morphological gradient waveform.

[0011] The above scheme obtains the number of sampling points corresponding to each scale as the window length, and takes the maximum value of the instantaneous amplitude of the traveling wave current within the window length as the dilation data and the minimum value as the erosion data, with each discrete sampling point as the center. The morphological gradient amplitude is obtained by subtracting the erosion data from the dilation data, so as to highlight the edge feature of the traveling wave head as the steep rising edge of the signal through morphological gradient operation. By traversing all discrete sampling points, the morphological gradient waveforms at each scale are obtained, and the spectral entropy at each scale is further obtained to construct a morphological gradient spectrum containing three-dimensional information including scale, time and gradient amplitude. This provides a complete data foundation for subsequent adaptive selection of the scale that best matches the steepness of the signal, thereby improving the accuracy of wave head localization.

[0012] As a preferred example, obtaining the spectral entropy of the traveling wave current component sequence at this scale based on the morphological gradient waveform includes: For any given scale corresponding to the morphological gradient waveform, obtain the upper limit value and the lower limit value of the morphological gradient amplitude in the morphological gradient waveform; Based on the upper limit value and the lower limit value of the morphological gradient amplitude, several amplitude intervals corresponding to the morphological gradient waveform are obtained; For any given amplitude interval, the frequency of the morphological gradient amplitude falling into that amplitude interval in the morphological gradient waveform is obtained, so as to obtain the probability corresponding to that amplitude interval based on the frequency and the total number of amplitude intervals; Obtain the logarithm corresponding to the probability, and use the product of the probability and the logarithm as the subspectral entropy corresponding to the amplitude interval; Obtain the sum of the sub-spectral entropies of all amplitude intervals corresponding to the morphological gradient waveform, and use the sum as the spectral entropy corresponding to the morphological gradient waveform.

[0013] The above scheme divides the amplitude range into several amplitude intervals by obtaining the upper and lower limits of the morphological gradient amplitude, and counts the frequency of amplitude occurrence in each interval. The frequency is divided by the total number of amplitude intervals to obtain the probability corresponding to each interval. Then, the spectral entropy is calculated based on the negative of the sum of the products of each probability and its logarithm. The magnitude of the spectral entropy value is used to quantitatively evaluate the concentration of the gradient waveform probability distribution. The smaller the spectral entropy value, the more concentrated the gradient waveform energy is in a few amplitude intervals and the more prominent the wavefront feature. This provides an objective and quantitative mathematical basis for automatically selecting the optimal scale that best matches the morphological characteristics of the current fault signal, ensuring the accuracy of wavefront identification.

[0014] As a preferred example, the step of extracting the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform includes: From all the scales corresponding to the transmission line, select the scale corresponding to the minimum spectral entropy as the target scale; Obtain the target morphological gradient waveform corresponding to the target scale, and take the discrete sampling point corresponding to the upper limit of the morphological gradient amplitude in the target morphological gradient waveform as the center sampling point; Centered on the central sampling point, the wavefront suspicious interval corresponding to the target morphological gradient waveform and the starting sampling point number of the wavefront suspicious interval are obtained according to the preset extension length. Based on the starting sampling point number and the suspected wavefront interval, the fault current component sequence is extracted from the traveling wave current component sequence.

[0015] The above scheme achieves adaptive matching of the analysis scale by selecting the scale with the minimum spectral entropy as the target scale. By obtaining the point with the largest amplitude in the morphological gradient waveform at the target scale as the central sampling point, the initial location of the wavefront is achieved by utilizing the characteristic that the amplitude of the morphological gradient reaches its peak at the wavefront. The suspected wavefront interval is delineated with the central sampling point as the center, and the fault current component sequence is extracted from the traveling wave current component sequence. This reduces the amount of data used for fine analysis from a complete long sequence to a local segment, improving the overall processing efficiency. At the same time, it focuses the analysis on the local area where the wavefront may appear, providing high-quality data input for subsequent mode decomposition and dual-feature criterion analysis, thus ensuring the accuracy of the mode decomposition and dual-feature criterion analysis.

[0016] As a preferred example, obtaining the mode components corresponding to the fault current component sequence, and obtaining the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence based on the mode components, includes: The fault current component sequence is subjected to mean-removal processing to obtain a zero-mean current component sequence. Variational mode decomposition is performed on the zero-mean current component sequence to obtain several candidate mode components; The candidate mode component with the highest center frequency is selected from all the candidate mode components corresponding to the zero-mean current component sequence as the mode component corresponding to the fault current component sequence. Perform Hilbert transform on the modal components to obtain the analytical signal corresponding to the fault current component sequence; The instantaneous energy and instantaneous frequency corresponding to each discrete sampling point in the fault current component sequence are obtained based on the analytical signal. By traversing all the discrete sampling points in the fault current component sequence and the instantaneous energy and instantaneous frequency corresponding to each discrete sampling point, the instantaneous energy curve and instantaneous frequency curve corresponding to the fault current component sequence are obtained. The energy threshold corresponding to the fault current component sequence is obtained from the instantaneous energy curve, and the frequency change threshold corresponding to the fault current component sequence is obtained from the instantaneous frequency curve.

[0017] The above scheme overcomes the problems of mode aliasing and endpoint effects by performing variational mode decomposition on the fault current component sequence after mean removal processing. This is achieved by non-recursively decomposing the signal into several mode components with sparse frequency bands. By selecting the mode component with the highest center frequency, the high-frequency impact energy at the arrival time of the wavefront is most concentrated. An analytical signal is constructed by performing a Hilbert transform on the highest frequency mode component. The instantaneous energy and instantaneous frequency are calculated based on the analytical signal, transforming the original waveform data into time-domain energy characteristics and frequency-domain frequency characteristics with clear physical meaning. Based on the statistical characteristics of the instantaneous energy curve and instantaneous frequency curve, adaptive matching energy thresholds and frequency change thresholds are obtained to improve the accuracy of wavefront calibration.

[0018] As a preferred example, the step of obtaining the energy threshold corresponding to the fault current component sequence based on the instantaneous energy curve and obtaining the frequency change threshold corresponding to the fault current component sequence based on the instantaneous frequency curve includes: Obtain the median energy corresponding to the instantaneous energy curve, and obtain the energy threshold corresponding to the fault current component sequence based on the median energy and the preset energy coefficient; Obtain the frequency difference sequence of the instantaneous frequency curve and calculate the standard deviation of the frequency difference sequence; The frequency mutation threshold corresponding to the fault current component sequence is obtained based on the standard deviation and the preset frequency mutation coefficient.

[0019] The above scheme obtains the median of the instantaneous energy curve and uses the product of the median and a preset energy coefficient as the energy threshold. It leverages the median's insensitivity to extreme peaks at wavefronts to robustly reflect the background energy level. It also obtains the difference sequence of the instantaneous frequency curve and calculates its standard deviation, using the product of the standard deviation and a preset frequency mutation coefficient as the frequency mutation threshold to objectively reflect the background level of frequency fluctuations. All of these thresholds are calculated online based on the actual statistical characteristics of the instantaneous features within the suspicious interval, achieving adaptive matching between the threshold setting and the signal background noise level, without the need for pre-setting fixed empirical thresholds.

[0020] As a preferred example, the step of extracting fault sampling points from the fault current component sequence based on the energy threshold, the frequency change threshold, the instantaneous energy curve, and the instantaneous frequency curve includes: For any discrete sampling point in the fault current component sequence, the adjacent sampling points corresponding to the discrete sampling point are obtained from the fault current component sequence according to the preset scanning order. The difference between the instantaneous frequency of the discrete sampling point and the adjacent sampling points is obtained, and the difference is used as the instantaneous frequency change corresponding to the discrete sampling point. When the instantaneous energy of the discrete sampling point is greater than the energy threshold and the instantaneous frequency change is greater than the frequency change threshold, the discrete sampling point is regarded as a candidate fault sampling point. According to the scanning order, the first candidate fault sampling point is selected from all the candidate fault sampling points corresponding to the fault current component sequence, and the first candidate fault sampling point is used as the fault sampling point corresponding to the fault current component sequence.

[0021] The above scheme scans the fault current component sequence in a preset scanning order to obtain the instantaneous frequency difference between each discrete sampling point and its adjacent sampling points as the instantaneous frequency change. When the instantaneous energy is greater than the energy threshold and the instantaneous frequency change is greater than the frequency change threshold, the sampling point is selected as a candidate fault sampling point. This is achieved by mutually verifying the dual characteristics of energy and frequency. The instantaneous energy reflects the amplitude impact intensity when the wavefront arrives, and the instantaneous frequency change reflects the phase step change when the wavefront arrives. Only when both conditions are met simultaneously is it determined to be the arrival of a true wavefront, effectively distinguishing between a true wavefront and noise interference. By selecting the first candidate fault sampling point according to the scanning order, it is ensured that the calibrated wavefront time is the arrival time of the initial traveling wave. This overcomes the shortcomings of a single criterion being prone to misjudgment or omission in strong noise or high-resistance grounding scenarios, thus improving the accuracy of wavefront calibration.

[0022] As a preferred example, obtaining the wavefront arrival time at the measurement end of the transmission line based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence includes: Obtain the starting sampling time of the traveling wave current component sequence, and determine the time interval between any two discrete sampling points according to the sampling frequency; The sampling point number of the fault sampling point in the traveling wave current component sequence is obtained, so as to obtain the wavefront arrival time of the measurement end of the transmission line according to the sampling point number, the starting sampling time and the time interval.

[0023] The above scheme obtains the initial sampling time of the traveling wave current component sequence and determines the sampling interval according to the sampling frequency to obtain the sampling point number of the fault sampling point in the original traveling wave current component sequence. Based on the sampling point number, the initial sampling time, and the sampling interval, the wavefront arrival time is calculated. This achieves accurate restoration from local detection results to global time coordinates, giving the output results a clear physical time meaning, which can be directly used for subsequent wave velocity-time calculations in traveling wave ranging. In turn, the accuracy of fault ranging is improved by improving the accuracy of wavefront calibration.

[0024] On the other hand, the present invention discloses a fault traveling wave front calibration system for transmission lines, including a parameter acquisition module, a spectral entropy calculation module, a current interception module, a multi-threshold extraction module, a fault identification module, and a wave front calibration module; The parameter acquisition module is used to obtain the sampling frequency and traveling wave current component sequence of the measurement end of the transmission line, and to construct several scales based on the sampling frequency; The spectral entropy calculation module is used to obtain the morphological gradient waveforms of the traveling wave current component sequence at each scale and the spectral entropy corresponding to each morphological gradient waveform. The current extraction module is used to extract the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform. The multi-threshold extraction module is used to obtain the modal components corresponding to the fault current component sequence, so as to obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold and frequency change threshold corresponding to the fault current component sequence based on the modal components. The fault identification module is used to extract fault sampling points from the fault current component sequence based on the energy threshold, the frequency change threshold, the instantaneous energy curve, and the instantaneous frequency curve. The wavefront calibration module is used to obtain the wavefront arrival time of the measurement end of the transmission line based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence.

[0025] This invention discloses a fault traveling wave wavefront calibration system for transmission lines. First, it acquires the sampling frequency and traveling wave current component sequence at the measurement end of the transmission line and constructs several scales based on the sampling frequency to obtain the morphological gradient waveforms of the traveling wave current component sequence at each scale and the corresponding spectral entropy. This achieves adaptive matching of analysis scales through multi-scale morphological analysis and quantitative evaluation of spectral entropy. Second, based on the spectral entropy and the morphological gradient waveforms, a fault current component sequence is extracted from the traveling wave current component sequence, effectively reducing the data range for subsequent analysis to the suspected local region of the wavefront, improving overall processing efficiency. Simultaneously, by acquiring the modal components corresponding to the fault current component sequence, the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence are obtained based on the modal components. This allows for the extraction of the high-frequency impact characteristics at the wavefront arrival time. The system achieves the most concentrated manifestation of the transient wave characteristics and transforms the original waveform data into time-domain energy features and frequency-domain frequency features with clear physical meaning based on instantaneous energy and instantaneous frequency. This allows for adaptive calculation of energy thresholds and frequency mutation thresholds using the statistical characteristics of the instantaneous energy curve and instantaneous frequency curve, respectively, achieving automatic matching of threshold settings with the signal background noise level. Next, fault sampling points are extracted from the fault current component sequence based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve. This dual feature of energy and frequency effectively distinguishes the true wavefront from noise interference, avoiding misjudgments and omissions in strong noise or high-resistance grounding scenarios using a single criterion, thus improving the accuracy of fault sampling and location. Finally, based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence, the arrival time of the wavefront at the measurement end of the transmission line is obtained, achieving precise location of the traveling wavefront. Attached Figure Description

[0026] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating a method for calibrating the traveling wave front of a fault in a transmission line, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of a fault traveling wave head calibration system for power transmission lines provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0029] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0030] In the description of the embodiments in this application, "a plurality of" means two or more, unless otherwise expressly specified. The reference to "embodiment" herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0031] In the description of the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0032] See Figure 1 To address the technical problem of existing technologies failing to accurately calibrate wavefronts due to poor adaptability and susceptibility to noise interference, an embodiment of the present invention provides a method for calibrating the wavefront of a traveling wave in a transmission line fault, thereby improving the accuracy of traveling wavefront calibration; wherein, the method includes: Step 101: Obtain the sampling frequency and traveling wave current component sequence of the transmission line measurement end, and construct several scales based on the sampling frequency.

[0033] Step 102: Obtain the morphological gradient waveforms of the traveling wave current component sequence at each of the stated scales and the spectral entropy corresponding to each of the stated morphological gradient waveforms.

[0034] Step 103: Extract the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform.

[0035] Step 104: Obtain the modal components corresponding to the fault current component sequence, so as to obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold and frequency change threshold corresponding to the fault current component sequence based on the modal components.

[0036] Step 105: Extract fault sampling points from the fault current component sequence based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve.

[0037] Step 106: Based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence, obtain the wavefront arrival time of the measurement end of the transmission line.

[0038] In this embodiment, the traveling wave current component sequence is a discrete sequence of line-mode currents obtained by decoupling the three-phase transient current signals collected by the transmission line measurement terminal after a fault occurs. This sequence reflects the transient current variation characteristics of the traveling wave propagating along the transmission line. The "several scales" refer to a family of structuring elements with different numbers of sampling points constructed based on the sampling frequency, used to detect abrupt changes in the signal from multiple dimensions. The morphological gradient waveform refers to the difference waveform obtained after performing morphological dilation and erosion operations on the traveling wave current component sequence, used to highlight the position of the steep rising edge of the traveling wave. The spectral entropy refers to the information entropy calculated after statistically analyzing the probability distribution of the amplitude of the morphological gradient waveform, used to quantitatively evaluate the degree of determinism of the gradient waveform at each scale. The fault current component sequence refers to a signal segment extracted from the traveling wave current component sequence based on the spectral entropy and morphological gradient waveform, used to process subsequent signals. The analysis focuses on the local region where the wavefront may occur; the modal components refer to the components obtained by decomposing the fault current component sequence according to frequency components, used to extract high-frequency impulse components in the signal; the instantaneous energy curve and instantaneous frequency curve refer to the characteristic curves calculated after constructing an analytical signal based on the modal components, used to reflect the energy intensity and frequency changes of the signal at each moment; the energy threshold and frequency change threshold refer to the judgment criteria calculated based on the statistical characteristics of the instantaneous energy curve and instantaneous frequency curve, respectively, used to provide a reference standard for the joint judgment of dual features; the fault sampling point refers to the sampling point in the fault current component sequence that simultaneously satisfies the energy condition and the frequency change condition, used to accurately locate the local position of the wavefront arrival time; the wavefront arrival time refers to the absolute time coordinate value obtained by restoring the fault sampling point to the time axis of the original signal, used to directly input the traveling wave ranging formula to invert the fault location.

[0039] The method provided in this embodiment first obtains the sampling frequency and traveling wave current component sequence of the transmission line measurement end, and constructs several scales based on the sampling frequency to obtain the morphological gradient waveform of the traveling wave current component sequence at each scale and the spectral entropy corresponding to each morphological gradient waveform. This achieves adaptive matching of the analysis scale through multi-scale morphological analysis and quantitative evaluation of spectral entropy. Secondly, based on the spectral entropy and the morphological gradient waveform, the fault current component sequence is extracted from the traveling wave current component sequence, effectively reducing the data range for subsequent analysis to the suspected local region of the wavefront, thus improving overall processing efficiency. Simultaneously, by obtaining the modal components corresponding to the fault current component sequence, the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence are obtained. This extraction of modal components allows for the most concentrated representation of the high-frequency impact characteristics at the wavefront arrival time. The original waveform data is transformed into time-domain energy features and frequency-domain frequency features with clear physical meaning based on instantaneous energy and instantaneous frequency. Energy thresholds and frequency mutation thresholds are adaptively calculated using the statistical characteristics of the instantaneous energy curve and instantaneous frequency curve, respectively, achieving automatic matching of threshold settings with the signal background noise level. Next, fault sampling points are extracted from the fault current component sequence based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve. This allows for effective differentiation between the true wavefront and noise interference through the mutual verification of energy and frequency characteristics, avoiding misjudgments and omissions under strong noise or high-resistance grounding scenarios using a single criterion, and improving the accuracy of fault sampling and location. Finally, the arrival time of the wavefront at the measurement end of the transmission line is obtained based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence, achieving precise location of the traveling wavefront.

[0040] In this embodiment, step 101 includes: Step 1011: When a transient fault is detected in the transmission line, the sampling frequency and three-phase transient current signal of the measurement end of the transmission line are acquired; Step 1012: Perform analog-to-digital conversion on the three-phase transient current signal according to the sampling frequency to obtain the three-phase current discrete sampling sequence corresponding to the measurement end of the transmission line; Step 1013: Perform phase mode transformation on the three-phase current discrete sampling sequence to obtain the traveling wave current component sequence corresponding to the measurement end of the transmission line; Step 1014: Obtain the upper limit value of the scale corresponding to the measurement end of the transmission line according to the sampling frequency, so as to obtain several scales corresponding to the measurement end of the transmission line according to the upper limit value of the scale and the preset lower limit value of the scale.

[0041] In this embodiment, a detection device pre-installed on the measurement end of the transmission line, such as a strong isolation device or a fault recording device, monitors the three-phase current signal at the measurement end of the transmission line in real time and continuously detects whether a fault transient occurs. Preferably, the detection of the fault transient can be achieved through a current change criterion. For example, when the instantaneous rate of change of any phase current or the change in phase current exceeds a preset threshold value, it is determined that a fault transient has been detected.

[0042] When a transient fault is detected in a transmission line, the sampling frequency and three-phase transient current signals at the measurement end of the transmission line are acquired. The sampling frequency is a pre-set time sampling rate used for analog-to-digital conversion of the analog current signal, measured in Hertz (Hz) or Megahertz (MHz). In this embodiment, the value of the sampling frequency can be determined based on the sampling configuration of the fault recording device or protection device at the measurement end. For example, for traveling wave ranging applications on high-voltage transmission lines, a sampling frequency of 1MHz or higher is typically used. The three-phase transient current signals are the A-phase, B-phase, and C-phase analog current signals output from the secondary side of the current transformer, used to reflect the instantaneous current state flowing in the line after the fault occurs.

[0043] In this embodiment, when a transient fault is detected, waveform recording is initiated and three-phase current data are continuously collected for a period of time before and after the fault to ensure complete recording of the transient waveform of the initial traveling surge of the fault reaching the measurement end. Then, the three-phase transient current signal is converted from analog to digital according to the sampling frequency to obtain the discrete sampling sequence of the three-phase current corresponding to the measurement end of the transmission line.

[0044] In this embodiment, the three-phase transient current signal is sampled at equal intervals using a preset sampling frequency, converting the analog continuous signal into a digital discrete sequence. After analog-to-digital conversion, a three-phase current discrete sampling sequence is obtained. The time interval between adjacent sampling points in the three-phase current discrete sampling sequence is the reciprocal of the sampling frequency. Each sampling point in the three-phase current discrete sampling sequence includes the instantaneous current amplitude at the corresponding moment and the sampling point number in the sequence. The sampling point number is used to uniquely identify the sequential position of each sampling point on the time axis.

[0045] Traveling waves propagating on transmission lines exhibit complex coupling characteristics. Electromagnetic coupling exists between the three phases, causing the three-phase current signals to influence each other. This embodiment employs phase-mode transformation to convert the discrete sampling sequence of the three-phase currents from the phase domain to the mode domain to eliminate the influence of three-phase coupling and extract the effective components of traveling wave propagation. Each sampling point in the resulting traveling wave current component sequence contains the instantaneous amplitude of the line-mode current at that moment and the sampling point number within the sequence. By extracting the line-mode components through phase-mode transformation, the influence of zero-mode component wave velocity variations on the traveling wave propagation time is eliminated, providing a stable and reliable analysis signal for subsequent wavefront calibration.

[0046] Considering that the steepness of the traveling wave front varies due to factors such as fault distance, transition resistance, and line dispersion characteristics, a single scale cannot accommodate all fault scenarios. Therefore, this implementation constructs a set of flat structural elements with different scales to detect abrupt changes in signal characteristics from multiple scale dimensions. The structural element is the most basic probe in mathematical morphology, and its shape and scale determine the performance of morphological transformations. Given that the traveling wave front represents a transient change in signal amplitude, belonging to the geometric edge features of the signal, this implementation selects flat structural elements that only focus on the time width without changing the amplitude.

[0047] In this embodiment, the scale corresponds to the coverage width of the structural element on the time axis, and is measured in units of the number of sampling points. Specifically, let the scale parameter be λ, where λ is a positive integer representing the number of sampling points contained in the structural element. Then, the flat structural element corresponding to the scale λ... (used for expansion) and (For corrosion) is defined as: Wherein, n represents the nth sampling point in the traveling wave current component sequence; in this embodiment, the scale has a lower limit value, preferably, the preset lower limit value of the scale is 3; wherein, the significance of setting the minimum scale to 3 is to ensure that the structural element can cover the local abrupt change interval composed of at least three consecutive sampling points, thereby effectively detecting the minimum scale abrupt change feature in the signal and avoiding the inability to capture effective wavefront information due to the window being too small.

[0048] The upper limit value L of the scale is obtained based on the sampling frequency, and is typically taken as the number of sampling points per microsecond corresponding to the sampling rate (MHz) multiplied by the typical duration of the traveling wavefront (usually 5-10 μs). For example, for a 1MHz sampling rate, L can be taken as 10~20; for higher sampling rates, L increases accordingly. This results in a set of scales with different time widths. This is used for subsequent multiscale analysis.

[0049] The above implementation method acquires three-phase transient current signals after detecting a fault transient start-up, and performs analog-to-digital conversion on the three-phase transient current signals according to the sampling frequency to obtain a three-phase current discrete sampling sequence. This three-phase current discrete sampling sequence is then subjected to phase-mode transformation to obtain a traveling wave current component sequence, thereby decoupling the three-phase coupled signal into line-mode components and eliminating the influence of zero-mode component wave velocity changes on the traveling wave propagation time. Simultaneously, based on the sampling frequency, an upper scale value is obtained, and combined with a preset lower scale value, several scales are derived. This ensures that the scale range for subsequent morphological analysis matches the actual sampling rate of the signal, effectively covering wavefront features at different sampling rates and providing an accurate and complete data foundation for subsequent multi-scale morphological analysis.

[0050] In this embodiment, step 102 includes: Step 1021: For any one of the several scales and any discrete sampling point in the traveling wave current component sequence, obtain the number of sampling points corresponding to that scale, and use the number of sampling points as the window length; Step 1022: Using the discrete sampling point as the center, obtain several neighboring discrete sampling points corresponding to the discrete sampling point from the traveling wave current component sequence according to the window length; Step 1023: Select the largest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood as the expansion data corresponding to the discrete sampling point, and select the smallest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood as the corrosion data corresponding to the discrete sampling point; Step 1024: Subtract the erosion data from the dilation data to obtain the morphological gradient magnitude of the discrete sampling point at that scale; Step 1025: Traverse all the discrete sampling points in the traveling wave current component sequence and the morphological gradient magnitude corresponding to each discrete sampling point to obtain the morphological gradient waveform of the traveling wave current component sequence at this scale. Step 1026: Obtain the spectral entropy of the traveling wave current component sequence at the specified scale based on the morphological gradient waveform; wherein, for any morphological gradient waveform corresponding to any given scale, obtain the upper limit and lower limit of the morphological gradient amplitude in the morphological gradient waveform; obtain several amplitude intervals corresponding to the morphological gradient waveform based on the upper limit and lower limit of the morphological gradient amplitude; for any amplitude interval, obtain the frequency of the morphological gradient amplitude falling into the amplitude interval in the morphological gradient waveform, and obtain the probability corresponding to the amplitude interval based on the frequency and the total number of amplitude intervals; obtain the logarithm corresponding to the probability, and use the product of the probability and the logarithm as the sub-spectral entropy corresponding to the amplitude interval; obtain the sum of the sub-spectral entropies of all amplitude intervals corresponding to the morphological gradient waveform, and use the sum as the spectral entropy corresponding to the morphological gradient waveform.

[0051] In this embodiment, after constructing several scales, a multi-scale morphological gradient transformation is performed on the traveling wave current component sequence. The morphological gradient, by calculating the difference between the dilation and erosion results, highlights the rising and falling edges of the signal, and the local maxima of the output waveform correspond to the abrupt changes in the original signal.

[0052] In this embodiment, for any one of the plurality of scales λ and the traveling wave current component sequence For any discrete sampling point in (n=1, 2, ..., N, where N is the signal length), obtain the number of sampling points corresponding to the scale λ, and use the number of sampling points as the window length. Specifically, the scale λ can be any value in the constructed scale set, where λ is a positive integer representing the number of sampling points contained in the structuring element at that scale, which is also the window length for the current morphological operation.

[0053] Centered on any discrete sampling point, the traveling wave current component sequence is obtained according to the window length λ. The method obtains several neighboring discrete sampling points corresponding to the discrete sampling point. Specifically, for the current scale λ, all sampling points within a window of length λ centered on the current sampling point are taken as the neighboring discrete sampling points corresponding to the discrete sampling point. The sampling point range covered by the window is a total of λ sampling points from the left to the right of the current sampling point. To ensure that boundary points (i.e., sampling points near the start or end of the sequence) can obtain complete window data, this embodiment performs boundary extension on the original signal. Preferably, the boundary extension can adopt a mirror extension method, that is, supplementing sampling points symmetrical to the signal near the start point before the signal start point, and supplementing sampling points symmetrical to the signal near the end point after the signal end point, so that each sampling point (including boundary points) can obtain λ neighboring sampling points centered on the current sampling point.

[0054] In this embodiment, the dilation operation takes the local maximum value within the neighborhood defined by the structuring element, and its mathematical definition is: Where ⊕ represents the dilation operator, and m is the local offset within the structuring element window, with a value range of m=0, 1, ..., λ-1. For each current sampling point, the maximum signal value within a window of length λ, centered on the current sampling point, is taken as the dilation result.

[0055] The erosion operation finds a local minimum within the neighborhood defined by the structuring element, and its mathematical definition is: in, This represents the erosion operator; for each sampling point, the minimum signal value within a window of length λ is taken as the erosion result.

[0056] In this embodiment, the morphological gradient magnitude of the discrete sampling point at this scale is obtained by subtracting the erosion data from the dilation data. Specifically, the formula for calculating the morphological gradient magnitude is: in, This represents the morphological gradient amplitude at sampling point n at scale λ. In this embodiment, in regions where the signal changes gradually, the difference between local maxima and minima is small, so the difference between dilation and erosion data is close to zero, resulting in a small morphological gradient amplitude. At the rising edge of the signal, i.e., the wavefront, the dilation data takes a larger value near the wave crest, while the erosion data takes a smaller value near the wave trough, significantly increasing the difference and forming a sharp positive pulse. At the falling edge of the signal, a negative pulse is formed. Therefore, the magnitude of the morphological gradient amplitude directly reflects the degree of signal change in the neighborhood of that sampling point; the larger the amplitude, the more likely it is to be a traveling wavefront.

[0057] In this embodiment, for the current scale λ, the dilation, erosion, and gradient calculations are performed sequentially on each sampling point in the traveling wave current component sequence to obtain the morphological gradient amplitude corresponding to each sampling point. The morphological gradient amplitudes of all sampling points are arranged in order of their sampling point numbers to form a one-dimensional sequence of length N, thus obtaining the morphological gradient waveform at scale λ. .

[0058] In this embodiment, the spectral entropy of the traveling wave current component sequence at that scale is obtained based on the morphological gradient waveform. The process of calculating the spectral entropy of the morphological gradient waveform corresponding to any scale λ is as follows: First, obtain the upper and lower limits of the morphological gradient magnitude in the morphological gradient waveform. Specifically, iterate through all sampling points in the morphological gradient waveform to determine the maximum value of the gradient magnitude at that scale. and minimum value .

[0059] Secondly, based on the upper limit and lower limit of the morphological gradient amplitude, several amplitude intervals corresponding to the morphological gradient waveform are obtained. Specifically, the intervals are... The amplitude is uniformly divided into M intervals (M is usually between 50 and 100, ensuring sufficient statistical samples in each interval); where the i-th amplitude interval is denoted as . , i=1,2,……,M.

[0060] Then, for any one of the amplitude intervals Obtain the frequency of the morphological gradient amplitude falling within the specified amplitude range in the morphological gradient waveform. Based on the frequency and the total number M of the amplitude intervals, the probability corresponding to the amplitude interval is obtained. : in, This represents the probability that the morphological gradient waveform amplitude falls within the i-th amplitude interval at scale λ, where N is the signal length. This yields the probability distribution vector at that scale. .

[0061] Next, the probability is obtained. Corresponding logarithm The product of the probability and the logarithm is taken as the subspectral entropy corresponding to the amplitude interval. It should be noted that when the... To avoid the logarithm calculation being undefined, a very small positive number can be set to make the logarithm... Become ; wherein, the It is a very small positive number.

[0062] Finally, the sum of the sub-spectral entropies of all amplitude intervals corresponding to the morphological gradient waveform is obtained, and this sum is used as the spectral entropy corresponding to the morphological gradient waveform. Specifically, the spectral entropy... Defined as: In this embodiment, the magnitude of the spectral entropy reflects the degree of concentration of the probability distribution of the morphological gradient waveform. The smaller the spectral entropy value, the more concentrated the gradient waveform energy is in a few amplitude ranges, the higher the waveform determinism, and the more prominent the wavefront features. The larger the spectral entropy value, the more dispersed the waveform probability distribution, indicating that the waveform is disordered and the wavefront features are submerged by noise.

[0063] In this embodiment, the above steps are repeated to traverse all constructed scales λ∈[3,L], obtaining the morphological gradient waveform and its corresponding spectral entropy at each scale. The morphological gradient waveforms at each scale are arranged in ascending order of scale λ to form a two-dimensional data matrix, which is the multi-scale morphological gradient spectrum. The rows of this matrix correspond to different analysis scales, the columns correspond to time sampling points, and the values ​​of the matrix elements represent the morphological gradient amplitude at a specific scale and a specific time. The spectral entropy corresponding to each scale is then used for optimal scale selection in subsequent steps.

[0064] The above implementation method acquires three-phase transient current signals after detecting a fault transient start-up, and performs analog-to-digital conversion on the three-phase transient current signals according to the sampling frequency to obtain a three-phase current discrete sampling sequence. This three-phase current discrete sampling sequence is then subjected to phase-mode transformation to obtain a traveling wave current component sequence, thereby decoupling the three-phase coupled signal into line-mode components and eliminating the influence of zero-mode component wave velocity changes on the traveling wave propagation time. Simultaneously, based on the sampling frequency, an upper scale value is obtained, and combined with a preset lower scale value, several scales are derived. This ensures that the scale range for subsequent morphological analysis matches the actual sampling rate of the signal, effectively covering wavefront features at different sampling rates, and providing an accurate and complete data foundation for subsequent multi-scale morphological analysis. At that time, the number of sampling points corresponding to each scale is obtained as the window length, and the maximum value of the instantaneous amplitude of the traveling wave current within the window length is taken as the dilation data and the minimum value is taken as the erosion data, with each discrete sampling point as the center. The morphological gradient amplitude is obtained by subtracting the dilation data from the erosion data, so as to highlight the edge feature of the traveling wave head as the steep rising edge of the signal through morphological gradient operation. The morphological gradient waveform at each scale is obtained by traversing all discrete sampling points, and the spectral entropy at each scale is further obtained to construct a morphological gradient spectrum containing three-dimensional information including scale, time and gradient amplitude. This provides a complete data foundation for subsequent adaptive selection of the scale that best matches the steepness of the signal, thereby improving the accuracy of wave head localization.

[0065] In this embodiment, step 103 includes: Step 1031: From all the scales corresponding to the transmission line, select the scale corresponding to the minimum spectral entropy as the target scale; Step 1032: Obtain the target morphological gradient waveform corresponding to the target scale, and take the discrete sampling point corresponding to the upper limit of the morphological gradient amplitude in the target morphological gradient waveform as the center sampling point; Step 1033: Using the central sampling point as the center, obtain the wavefront suspicious interval corresponding to the target morphological gradient waveform and the starting sampling point number of the wavefront suspicious interval according to the preset extension length; Step 1034: Extract the fault current component sequence from the traveling wave current component sequence according to the starting sampling point number and the wavefront suspicious interval.

[0066] In this embodiment, the optimal scale is selected based on the spectral entropy value corresponding to each scale. Specifically, from all scales λ∈[3,L] corresponding to the transmission line, the spectral entropy H(λ) corresponding to each scale λ is obtained, resulting in a curve showing the change of spectral entropy with scale. This curve typically shows a trend of first decreasing and then increasing, and the scale corresponding to its trough is the optimal scale that best matches the morphological characteristics of the current fault traveling wave signal. The scale corresponding to the minimum spectral entropy is selected as the target scale, which is the optimal scale, and its selection formula is: Among them, the The optimal scale to be selected is the target scale.

[0067] Obtain the target morphological gradient waveform corresponding to the target scale, which is the morphological gradient waveform obtained at the target scale; use the discrete sampling points corresponding to the upper limit of the morphological gradient amplitude in the target morphological gradient waveform as the center sampling points. Specifically, in the target morphological gradient waveform... The algorithm iterates through all sampling points to search for the location of the global maximum value of the morphological gradient magnitude. Since the traveling wave front usually corresponds to the first significant peak of the gradient waveform (for single-ended measurements, the initial traveling wave of the fault arrives earliest), the location of the global maximum value of the gradient waveform is taken as the candidate point for the initial wave front, denoted as . ; wherein, the central sampling point That is, the discrete sampling point corresponding to the upper limit of the morphological gradient magnitude, which represents the moment when the wavefront feature is most significant.

[0068] With the central sampling point Centered on the target morphological gradient waveform, the wavefront suspicious interval and the starting sampling point number of the wavefront suspicious interval are obtained according to the preset extension length.

[0069] Specifically, with peak point Centered on the wavefront, extend time windows to the left and right by a certain length to form intervals of suspected wavefronts. The determination of the extension length must take into account two principles: the interval must completely contain the entire process of the rising edge of the wavefront; the interval should be as small as possible to eliminate interference from distant locations and reduce the computational load of subsequent steps.

[0070] This implementation adopts an adaptive expansion strategy, where the expansion length W is related to the target scale. Positive correlation: Where k is the expansion coefficient, ranging from 3 to 5, which can be adjusted according to the sampling rate. Where k is the expansion coefficient, with a value ranging from 3 to 5, which can be adjusted according to the sampling rate. When the sampling rate is high, the value of k can be increased appropriately to cover a more complete rising edge of the wavefront; when the sampling rate is low, the value of k can be decreased appropriately to eliminate interference and reduce the amount of computation. The sampling point number at the left boundary of the suspicious interval. This is the sampling point number at the right boundary of the suspicious interval.

[0071] The suspicious wavefront interval and its starting sampling point number can be obtained from the above formula. If the calculated starting sampling point number is less than 1, then the starting sampling point number is 1; if the ending sampling point number of the suspicious wavefront interval is greater than N, then the ending sampling point number is N, so as to ensure that the suspicious interval does not exceed the range of the original signal sequence.

[0072] In this embodiment, a signal segment corresponding to the suspected wavefront interval is extracted from the traveling wave current component sequence and denoted as s(t). This yields the fault current component sequence s(n) to be analyzed in detail. This signal segment reduces the data range for subsequent analysis from a complete long sequence to a suspected local region of the wavefront. This significantly reduces the computational load of subsequent variational mode decomposition and dual-feature criterion processing, and focuses the analysis on the local interval where the wavefront may appear, providing high-quality data input for subsequent mode decomposition and precise wavefront localization.

[0073] The above implementation achieves adaptive matching of the analysis scale by selecting the scale with the minimum spectral entropy as the target scale. By obtaining the point with the largest amplitude in the morphological gradient waveform at the target scale as the central sampling point, the initial location of the wavefront is achieved by utilizing the characteristic that the amplitude of the morphological gradient reaches its peak at the wavefront. The suspected wavefront interval is delineated with the central sampling point as the center, and the fault current component sequence is extracted from the traveling wave current component sequence. This reduces the amount of data used for fine analysis from a complete long sequence to a local segment, improving the overall processing efficiency. At the same time, the focus of analysis is concentrated on the local area where the wavefront may appear, providing high-quality data input for subsequent mode decomposition and dual-feature criterion analysis, thus ensuring the accuracy of the mode decomposition and dual-feature criterion analysis.

[0074] In this embodiment, step 104 includes: Step 1041: Perform mean-removal processing on the fault current component sequence to obtain a zero-mean current component sequence; Step 1042: Perform variational mode decomposition on the zero-mean current component sequence to obtain several candidate mode components; Step 1043: Select the candidate mode component with the highest center frequency from all the candidate mode components corresponding to the zero-mean current component sequence as the mode component corresponding to the fault current component sequence; Step 1044: Perform Hilbert transform on the modal components to obtain the analytical signal corresponding to the fault current component sequence; Step 1045: Obtain the instantaneous energy and instantaneous frequency corresponding to each discrete sampling point in the fault current component sequence based on the analytical signal; Step 1046: Traverse all the discrete sampling points in the fault current component sequence and the instantaneous energy and instantaneous frequency corresponding to each discrete sampling point to obtain the instantaneous energy curve and instantaneous frequency curve corresponding to the fault current component sequence; Step 1047: Obtain the energy threshold corresponding to the fault current component sequence based on the instantaneous energy curve and the frequency mutation threshold corresponding to the fault current component sequence based on the instantaneous frequency curve; wherein, obtain the energy median corresponding to the instantaneous energy curve, and obtain the energy threshold corresponding to the fault current component sequence based on the energy median and a preset energy coefficient; obtain the frequency difference sequence of the instantaneous frequency curve and calculate the standard deviation of the frequency difference sequence; obtain the frequency mutation threshold corresponding to the fault current component sequence based on the standard deviation and a preset frequency mutation coefficient.

[0075] This embodiment performs mean-removal processing on the fault current component sequence to obtain a zero-mean current component sequence. Specifically, the fault current component sequence is... Where t = 1, 2, ..., T, and T is the length of the suspicious interval. To eliminate the influence of possible trend terms (DC bias or low-frequency drift) on the subsequent variational mode decomposition results, s(t) is mean-reduced. The mean-reducing method is as follows: in, The zero-mean current component sequence; The mean of the fault current component sequence s(t) is used; by removing the mean, the mean in the sequence is set to zero, thus eliminating the influence of DC bias on the decomposition results.

[0076] This embodiment employs Variational Mode Decomposition (VMD) to analyze the zero-mean current component sequence. The decomposition is performed; wherein, the variational mode decomposition is a non-recursive signal decomposition method that decomposes the signal into several mode components with sparse frequency bands by solving variational problems. It has a rigorous mathematical theoretical basis and can effectively overcome the mode aliasing and endpoint effects problems existing in empirical mode decomposition.

[0077] Specifically, after executing the variational mode decomposition algorithm, K candidate mode components are obtained, denoted as... K is the preset number of decomposition layers, which is pre-set according to signal characteristics and sampling frequency. The K candidate mode components are arranged according to the center frequency, with the high-frequency mode components mainly reflecting the abrupt change characteristics of the arrival time of the traveling wave front, while the low-frequency mode components mainly reflect the steady-state components after the fault or the low-frequency oscillations formed by multiple reflections of the traveling wave between the busbars.

[0078] Since the impact energy at the arrival time of the traveling wave front is mainly concentrated in the high-frequency band, the modal component with the highest center frequency most concentratedly reflects the abrupt change characteristics at the arrival time of the wave front. Therefore, in this embodiment, the candidate modal component with the highest center frequency is selected from the K candidate modal components as the modal component for subsequent analysis. Specifically, for the K candidate modal components obtained by decomposition, the center frequency of each modal component is calculated, and the modal component with the largest center frequency value is selected as the target signal, denoted as h(t): in, The candidate mode component with the highest center frequency is represented. This mode component most concentratedly reflects the high-frequency impact energy at the arrival time of the traveling wave front, while the other mode components mainly reflect low-frequency components and are not used as target signals for subsequent analysis.

[0079] In this embodiment, the Hilbert transform can transform a real signal into its orthogonal components, thereby constructing an analytic signal to extract the instantaneous amplitude and instantaneous phase of the signal. Specifically, the Hilbert transform is performed on the high-frequency mode component h(t) to obtain its orthogonal components. In practical discrete computing, the Hilbert transform is implemented through a fast Fourier transform: h(t) is transformed to the frequency domain, the positive frequency components are multiplied by -j, the negative frequency components are multiplied by +j, and then an inverse Fourier transform is performed to construct the analytic signal z(t): in, Original high-frequency modal components; for Hilbert transform; The instantaneous amplitude; The formula for calculating is: The For instantaneous phase, the The calculation formula is: Where j is the imaginary unit, and z(t) is the analytical signal corresponding to the fault current component sequence.

[0080] In this embodiment, the instantaneous amplitude and instantaneous phase of each discrete sampling point are calculated based on the analytic signal z(t), wherein the instantaneous amplitude... Let φ(t) be the magnitude of the analytic signal, φ(t) be the instantaneous phase of the analytic signal, and E(t) be the instantaneous energy, defined as the square of the instantaneous amplitude, reflecting the energy intensity of the signal at each moment. When the traveling wave front arrives, the amplitude of the high-frequency modal components increases sharply, resulting in a significant peak in the instantaneous energy. This peak is one of the important bases for wave front calibration.

[0081] instantaneous frequency Defined as the derivative of the instantaneous phase with respect to time: In practical discrete computing, the phase difference method is used to determine the instantaneous frequency. : in, The sampling interval is denoted by Δt. To prevent jumps caused by phase winding, the phase sequence needs to be unwound. Here, Δt is the sampling interval, i.e., the time interval between two adjacent discrete sampling points, Δt = 1 / , The sampling frequency is defined as follows. The instantaneous frequency reflects the frequency variation characteristics of the signal at various moments. Before the wavefront arrives, the high-frequency modal components are mainly background noise or weak precursor waves, and their instantaneous frequency fluctuates greatly and irregularly. At the instant the wavefront arrives, due to the addition of the impact component, the instantaneous frequency will undergo a step-like change, usually manifested as a sudden jump from chaotic fluctuations to a certain higher frequency value. This abrupt change characteristic is another important basis for wavefront calibration.

[0082] By traversing all the discrete sampling points in the fault current component sequence and the instantaneous energy and instantaneous frequency corresponding to each discrete sampling point, the instantaneous energy curve and instantaneous frequency curve corresponding to the fault current component sequence are obtained.

[0083] Specifically, the instantaneous energy and instantaneous frequency calculations are performed on each discrete sampling point in the fault current component sequence s(t) to obtain the instantaneous energy value E(t) and instantaneous frequency value corresponding to each sampling point. Arrange the instantaneous energy values ​​of all sampling points in order of sampling point number t to form a positive real number sequence of length T, which is the instantaneous energy curve corresponding to the fault current component sequence; arrange the instantaneous frequency values ​​of all sampling points in order of sampling point number to form a real number sequence of length T, which is the instantaneous frequency curve corresponding to the fault current component sequence.

[0084] To overcome the drawback of fixed thresholds' poor adaptability to different fault conditions, this implementation constructs an adaptive energy threshold based on the statistical characteristics of instantaneous energy within the suspected interval. Specifically, the median energy corresponding to the instantaneous energy curve is obtained. : This embodiment uses the median instead of the mean because the median is not sensitive to extreme peaks that may occur at the wavefront and can more robustly reflect the background energy level. Based on the median energy The energy threshold corresponding to the fault current component sequence is obtained by using a preset energy coefficient α. : Here, α is the energy coefficient, ranging from 3 to 8, which can be adjusted according to the ambient noise level. A larger value is used when the noise level is high, and a smaller value is used when the noise level is low. The energy threshold represents an energy level significantly higher than the background noise; only when the instantaneous energy exceeds this threshold is it considered likely to be a true wavefront arrival.

[0085] The frequency abrupt change threshold corresponding to the fault current component sequence is obtained based on the instantaneous frequency curve. When the traveling wave front arrives, the instantaneous frequency of the high-frequency mode component undergoes a step abrupt change. To quantify this abrupt change, the difference sequence of instantaneous frequencies is calculated: Calculate the standard deviation of the difference series as a measure of the background level of frequency fluctuations: The frequency mutation threshold is set as follows: in, The frequency mutation coefficient, with a value range of 3 to 5; It is a difference sequence of instantaneous frequencies; The standard deviation of the difference sequence represents the standard deviation of the difference sequence; The frequency mutation threshold represents the amount of frequency change that is significantly higher than the background frequency fluctuation level. When the amount of frequency change at a certain moment exceeds the threshold, it is considered that a significant frequency step has occurred.

[0086] The above implementation method performs variational mode decomposition on the fault current component sequence after mean removal, non-recursively decomposing the signal into several mode components with sparse frequency bands, thus overcoming the problems of mode aliasing and endpoint effects. By selecting the mode component with the highest center frequency, the high-frequency impact energy at the wavefront arrival time is most concentratedly represented. By performing Hilbert transform on the highest frequency mode component to construct an analytical signal, the instantaneous energy and instantaneous frequency are calculated based on the analytical signal, transforming the original waveform data into time-domain energy characteristics and frequency-domain frequencies with clear physical meaning. Based on the statistical characteristics of instantaneous energy and frequency curves, adaptive matching energy thresholds and frequency mutation thresholds are obtained to improve the accuracy of wavefront calibration. Simultaneously, by obtaining the median of the instantaneous energy curve and using its product with a preset energy coefficient as the energy threshold, the median's insensitivity to extreme peaks at the wavefront is utilized to robustly reflect the background energy level. Similarly, by obtaining the difference sequence of the instantaneous frequency curve and calculating its standard deviation, the product of the standard deviation and a preset frequency mutation coefficient is used as the frequency mutation threshold to objectively reflect the background level of frequency fluctuations. All of these thresholds are calculated online based on the actual statistical characteristics of instantaneous features within the suspicious interval, achieving adaptive matching between threshold settings and signal background noise levels without the need for pre-setting fixed empirical thresholds.

[0087] In this embodiment, step 105 includes: Step 1051: For any discrete sampling point in the fault current component sequence, obtain the adjacent sampling points corresponding to the discrete sampling point from the fault current component sequence according to the preset scanning order. Step 1052: Obtain the difference between the instantaneous frequency of the discrete sampling point and the adjacent sampling points, and use the difference as the instantaneous frequency change corresponding to the discrete sampling point; Step 1053: When the instantaneous energy of the discrete sampling point is greater than the energy threshold and the instantaneous frequency change is greater than the frequency change threshold, the discrete sampling point is designated as a candidate fault sampling point. Step 1054: Select the first candidate fault sampling point from all the candidate fault sampling points corresponding to the fault current component sequence according to the scanning order, and take the first candidate fault sampling point as the fault sampling point corresponding to the fault current component sequence.

[0088] In this embodiment, for any discrete sampling point in the fault current component sequence, the adjacent sampling points corresponding to that discrete sampling point are obtained from the fault current component sequence according to a preset scanning order. In this embodiment, the preset scanning order is a point-by-point scanning order from front to back, that is, starting from t=1, incrementing sequentially to t=T, and judging each discrete sampling point in the fault current component sequence one by one. For the current discrete sampling point t, its corresponding adjacent sampling point is t+1, that is, the next sampling point in the fault current component sequence immediately adjacent to this sampling point.

[0089] Specifically, for the current discrete sampling point t, the instantaneous frequency value of the sampling point and the instantaneous frequency values ​​of its adjacent sampling points are obtained, and the difference between the two is calculated as the instantaneous frequency change corresponding to the discrete sampling point; the instantaneous frequency change reflects the magnitude of the instantaneous frequency change at the discrete sampling point and is used to quantify the degree of frequency abrupt change.

[0090] Specifically, for the current discrete sampling point t, we simultaneously determine whether the following two conditions are true: Condition A (Energy Condition): E(t) > ; Condition B (Frequency mutation condition): ; When both of the above conditions are met, it indicates that the discrete sampling point has both an energy intensity exceeding the background noise level and a significant frequency step change, which is consistent with the physical characteristics of the arrival of the traveling wave front. In this case, the discrete sampling point is regarded as a candidate fault sampling point.

[0091] Specifically, following a point-by-point scanning order from front to back, all discrete sampling points in the fault current component sequence are traversed, and the above-mentioned judgment process is performed to record all candidate fault sampling points that simultaneously satisfy condition A and condition B. Among these candidate fault sampling points, the one that appears first in the scanning order is selected as the fault sampling point corresponding to the fault current component sequence. Since the traveling wave signal propagates from the fault point to the measurement end at a speed close to the speed of light after the fault occurs, the time when the initial traveling wave arrives at the measurement end corresponds to the time when the traveling wave signal first arrives. Therefore, the first sampling point that simultaneously satisfies both characteristics is taken as the final fault sampling point, which corresponds to the time when the initial traveling wave front arrives at the measurement end.

[0092] In this implementation, if no sampling point simultaneously satisfying conditions A and B is found after traversing the entire fault current component sequence, a special case handling strategy is initiated: the energy condition is prioritized, and the first sampling point satisfying the energy condition E(t) > 0 is selected. The sampling point is taken as the fault sampling point; if no point satisfies the energy condition, the position corresponding to the peak point of the gradient waveform is taken as the fault sampling point. If multiple consecutive sampling points simultaneously satisfy the dual characteristics, the first one is taken as the fault sampling point. This special case handling mechanism ensures that a clear fault sampling point can be output under any operating condition, guaranteeing the robustness of the method.

[0093] The above implementation scans the fault current component sequence in a preset scanning order to obtain the instantaneous frequency difference between each discrete sampling point and its adjacent sampling points as the instantaneous frequency change. When the instantaneous energy is greater than the energy threshold and the instantaneous frequency change is greater than the frequency change threshold, the sampling point is selected as a candidate fault sampling point. This is achieved by mutually verifying the dual characteristics of energy and frequency. The instantaneous energy reflects the amplitude impact intensity when the wavefront arrives, and the instantaneous frequency change reflects the phase step change when the wavefront arrives. Only when both conditions are met simultaneously is it determined to be the arrival of a true wavefront, effectively distinguishing between a true wavefront and noise interference. By selecting the first candidate fault sampling point according to the scanning order, it is ensured that the calibrated wavefront time is the arrival time of the initial traveling wave. This overcomes the shortcomings of a single criterion being prone to misjudgment or omission in strong noise or high-resistance grounding scenarios, thus improving the accuracy of wavefront calibration.

[0094] In this embodiment, step 106 includes: Step 1061: Obtain the starting sampling time of the traveling wave current component sequence, and determine the time interval between any two discrete sampling points according to the sampling frequency; Step 1062: Obtain the sampling point number of the fault sampling point in the traveling wave current component sequence, so as to obtain the wavefront arrival time of the transmission line measurement end according to the sampling point number, the starting sampling time and the time interval.

[0095] This embodiment obtains the starting sampling time of the traveling wave current component sequence. The starting sampling time is the initial time at which the fault recording device begins recording data after detecting a transient fault start-up. This time is the time origin of the entire traveling wave current component sequence, and the physical time of all sampling points is converted relative to this origin.

[0096] Next, the time interval between any two discrete sampling points is determined based on the reciprocal of the sampling frequency; the time interval between two adjacent discrete sampling points is uniquely determined by the sampling frequency, and the higher the sampling frequency, the shorter the time interval and the higher the time resolution.

[0097] In this embodiment, the sampling point number of the fault sampling point in the traveling wave current component sequence is obtained. The fault sampling point is the first sampling point extracted from the fault current component sequence that simultaneously satisfies the energy condition and the frequency change condition, and its position in the fault current component sequence is... , which is the relative offset relative to the starting point of the suspicious interval.

[0098] Considering this location It is the relative position with respect to the starting point of the fault current component sequence, and it needs to be restored to the time axis of the original signal: ;in, The starting sampling point number of the defined fault current component sequence; This refers to the precise time point at which the traveling wave signal first propagates from the fault point to the measurement point after the fault occurs. It represents the position number of the sampling point within the fault current component sequence that simultaneously satisfies the energy condition and the frequency condition.

[0099] The arrival time of the wavefront at the measurement end of the transmission line is obtained based on the location number, the starting sampling time, and the time interval.

[0100] The above implementation method obtains the initial sampling time of the traveling wave current component sequence and determines the sampling interval according to the sampling frequency to obtain the sampling point number of the fault sampling point in the original traveling wave current component sequence. The wavefront arrival time is then calculated based on the sampling point number, the initial sampling time, and the sampling interval. This achieves accurate restoration from local detection results to global time coordinates, giving the output results a clear physical time meaning. This allows for direct use in subsequent traveling wave ranging wave velocity-time calculations, thereby improving the accuracy of fault ranging by increasing the accuracy of wavefront calibration.

[0101] like Figure 2As shown, based on the above-mentioned method embodiments, an embodiment of the present invention provides a fault traveling wave front calibration system for transmission lines, including a parameter acquisition module 201, a spectral entropy calculation module 202, a current interception module 203, a multi-threshold extraction module 204, a fault identification module 205, and a wave front calibration module 206.

[0102] The parameter acquisition module 201 is used to acquire the sampling frequency and traveling wave current component sequence of the transmission line measurement end, and to construct several scales based on the sampling frequency.

[0103] The spectral entropy calculation module 202 is used to obtain the morphological gradient waveforms of the traveling wave current component sequence at each scale and the spectral entropy corresponding to each morphological gradient waveform.

[0104] The current extraction module 203 is used to extract the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform.

[0105] The multi-threshold extraction module 204 is used to obtain the modal components corresponding to the fault current component sequence, so as to obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold and frequency change threshold corresponding to the fault current component sequence based on the modal components.

[0106] The fault identification module 205 is used to extract fault sampling points from the fault current component sequence based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve.

[0107] The wavefront calibration module 206 is used to obtain the wavefront arrival time of the measurement end of the transmission line based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence.

[0108] This embodiment provides a method and system for fault traveling wave wavefront calibration in transmission lines. Leveraging the advantage of mathematical morphology in measuring the local shape of signals, a multi-scale flattened family of structured elements is constructed to perform morphological gradient transformation on the traveling wave current component sequence. The spectral entropy of the morphological gradient waveform at each scale is calculated to quantitatively evaluate the certainty of the wavefront characteristics at each scale. This allows for the adaptive selection of the optimal structured element scale that best matches the steepness of the current fault signal based on the minimum spectral entropy criterion. The global maximum value of the gradient waveform at the optimal scale is used to delineate the suspicious interval, thereby extracting the fault current component sequence from the traveling wave current component sequence. This achieves adaptive matching between the structured element scale and the signal morphology during coarse wavefront localization, avoiding the subjectivity and uncertainty of traditional methods that require pre-selection of the analysis scale. Simultaneously, it reduces the data range for subsequent fine analysis to the suspicious local region of the wavefront, improving overall processing efficiency. Furthermore, combining the non-recursive decomposition characteristics of variational mode decomposition, variational mode decomposition is performed on the extracted fault current component sequence to extract the mode with the highest center frequency. The modal components are used to concentrate the high-frequency impact energy at the arrival time of the traveling wave front. Based on these modal components, an analytical signal is constructed, and the instantaneous energy and frequency are calculated. This transforms the original waveform data into time-domain energy and frequency characteristics with clear physical meaning, providing multi-dimensional quantitative evidence for wave front determination. Finally, using a dual-feature criterion of instantaneous energy and instantaneous frequency, the first fault sampling point in the fault current component sequence that simultaneously satisfies both an instantaneous energy greater than the adaptive energy threshold and an instantaneous frequency change greater than the adaptive frequency mutation threshold is extracted. This allows for effective differentiation between the real wave front and noise interference through mutual verification of energy and frequency characteristics. The arrival time of the wave front is calculated based on the absolute position of the fault sampling point on the time axis of the original signal. This solves the problems of feature extraction distortion, misjudgment under strong noise, and missed detection of slowly changing wave fronts under high impedance grounding caused by the fixed analysis tools and singular decision criteria in existing technologies. It achieves accurate locking of the arrival time of the traveling wave front in line-mode current, significantly improving the adaptive capability, anti-interference capability, and positioning accuracy of traveling wave front calibration.

[0109] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calibrating the fault traveling wave front of a transmission line, characterized in that, include: The sampling frequency and traveling wave current component sequence of the measurement end of the transmission line are obtained, and several scales are constructed based on the sampling frequency. Obtain the morphological gradient waveforms of the traveling wave current component sequence at each of the stated scales and the spectral entropy corresponding to each of the stated morphological gradient waveforms; The fault current component sequence is extracted from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform. Obtain the modal components corresponding to the fault current component sequence, and obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence based on the modal components; Based on the energy threshold, the frequency mutation threshold, the instantaneous energy curve, and the instantaneous frequency curve, fault sampling points are extracted from the fault current component sequence; The arrival time of the wavefront at the measurement end of the transmission line is obtained based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence.

2. The method for calibrating the fault traveling wave front of a transmission line according to claim 1, characterized in that, The process involves acquiring the sampling frequency and traveling wave current component sequence at the measurement end of the transmission line, and constructing several scales based on the sampling frequency, including: When a transient fault is detected in the transmission line, the sampling frequency and three-phase transient current signal at the measurement end of the transmission line are acquired. The three-phase transient current signal is converted from analog to digital according to the sampling frequency to obtain the discrete sampling sequence of the three-phase current corresponding to the measurement end of the transmission line. The three-phase current discrete sampling sequence is subjected to phase mode transformation to obtain the traveling wave current component sequence corresponding to the measurement end of the transmission line; The upper limit of the scale corresponding to the measurement end of the transmission line is obtained according to the sampling frequency, and several scales corresponding to the measurement end of the transmission line are obtained according to the upper limit of the scale and the preset lower limit of the scale.

3. The method for calibrating the fault traveling wave front of a transmission line according to claim 2, characterized in that, The traveling wave current component sequence includes several discrete sampling points and the instantaneous amplitude of the traveling wave current corresponding to each discrete sampling point; The step of obtaining the morphological gradient waveforms of the traveling wave current component sequence at each of the aforementioned scales and the corresponding spectral entropy of each of the aforementioned morphological gradient waveforms includes: For any one of the several scales and any discrete sampling point in the traveling wave current component sequence, obtain the number of sampling points corresponding to that scale, and use the number of sampling points as the window length; Centered on the discrete sampling point, several neighboring discrete sampling points corresponding to the discrete sampling point are obtained from the traveling wave current component sequence according to the window length. The largest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood is selected as the expansion data corresponding to the discrete sampling point, and the smallest instantaneous amplitude of the traveling wave current among all the discrete sampling points in the neighborhood is selected as the corrosion data corresponding to the discrete sampling point. Subtracting the erosion data from the dilation data yields the morphological gradient magnitude of the discrete sampling point at that scale. By traversing all the discrete sampling points in the traveling wave current component sequence and the morphological gradient magnitude corresponding to each discrete sampling point, the morphological gradient waveform of the traveling wave current component sequence at this scale is obtained. The spectral entropy of the traveling wave current component sequence at this scale is obtained based on the morphological gradient waveform.

4. The method for calibrating the fault traveling wave front of a transmission line according to claim 3, characterized in that, The step of obtaining the spectral entropy of the traveling wave current component sequence at this scale based on the morphological gradient waveform includes: For any given scale corresponding to the morphological gradient waveform, obtain the upper limit value and the lower limit value of the morphological gradient amplitude in the morphological gradient waveform; Based on the upper limit value and the lower limit value of the morphological gradient amplitude, several amplitude intervals corresponding to the morphological gradient waveform are obtained; For any given amplitude interval, the frequency of the morphological gradient amplitude falling into that amplitude interval in the morphological gradient waveform is obtained, so as to obtain the probability corresponding to that amplitude interval based on the frequency and the total number of amplitude intervals; Obtain the logarithm corresponding to the probability, and use the product of the probability and the logarithm as the subspectral entropy corresponding to the amplitude interval; Obtain the sum of the sub-spectral entropies of all amplitude intervals corresponding to the morphological gradient waveform, and use the sum as the spectral entropy corresponding to the morphological gradient waveform.

5. A method for calibrating the fault traveling wave front of a transmission line according to claim 4, characterized in that, The step of extracting the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform includes: From all the scales corresponding to the transmission line, select the scale corresponding to the minimum spectral entropy as the target scale; Obtain the target morphological gradient waveform corresponding to the target scale, and take the discrete sampling point corresponding to the upper limit of the morphological gradient amplitude in the target morphological gradient waveform as the center sampling point; Centered on the central sampling point, the wavefront suspicious interval corresponding to the target morphological gradient waveform and the starting sampling point number of the wavefront suspicious interval are obtained according to the preset extension length. Based on the starting sampling point number and the suspected wavefront interval, the fault current component sequence is extracted from the traveling wave current component sequence.

6. The method for calibrating the fault traveling wave front of a transmission line according to claim 1, characterized in that, The step of obtaining the modal components corresponding to the fault current component sequence, and obtaining the instantaneous energy curve, instantaneous frequency curve, energy threshold, and frequency change threshold corresponding to the fault current component sequence based on the modal components, includes: The fault current component sequence is subjected to mean-removal processing to obtain a zero-mean current component sequence. Variational mode decomposition is performed on the zero-mean current component sequence to obtain several candidate mode components; The candidate mode component with the highest center frequency is selected from all the candidate mode components corresponding to the zero-mean current component sequence as the mode component corresponding to the fault current component sequence. Perform Hilbert transform on the modal components to obtain the analytical signal corresponding to the fault current component sequence; The instantaneous energy and instantaneous frequency corresponding to each discrete sampling point in the fault current component sequence are obtained based on the analytical signal. By traversing all the discrete sampling points in the fault current component sequence and the instantaneous energy and instantaneous frequency corresponding to each discrete sampling point, the instantaneous energy curve and instantaneous frequency curve corresponding to the fault current component sequence are obtained. The energy threshold corresponding to the fault current component sequence is obtained from the instantaneous energy curve, and the frequency change threshold corresponding to the fault current component sequence is obtained from the instantaneous frequency curve.

7. A method for calibrating the fault traveling wave front of a transmission line according to claim 6, characterized in that, The steps of obtaining the energy threshold corresponding to the fault current component sequence based on the instantaneous energy curve and obtaining the frequency change threshold corresponding to the fault current component sequence based on the instantaneous frequency curve include: Obtain the median energy corresponding to the instantaneous energy curve, and obtain the energy threshold corresponding to the fault current component sequence based on the median energy and the preset energy coefficient; Obtain the frequency difference sequence of the instantaneous frequency curve and calculate the standard deviation of the frequency difference sequence; The frequency mutation threshold corresponding to the fault current component sequence is obtained based on the standard deviation and the preset frequency mutation coefficient.

8. A method for calibrating the fault traveling wave front of a transmission line according to claim 6, characterized in that, The step of extracting fault sampling points from the fault current component sequence based on the energy threshold, the frequency change threshold, the instantaneous energy curve, and the instantaneous frequency curve includes: For any discrete sampling point in the fault current component sequence, the adjacent sampling points corresponding to the discrete sampling point are obtained from the fault current component sequence according to the preset scanning order. The difference between the instantaneous frequency of the discrete sampling point and the adjacent sampling points is obtained, and the difference is used as the instantaneous frequency change corresponding to the discrete sampling point. When the instantaneous energy of the discrete sampling point is greater than the energy threshold and the instantaneous frequency change is greater than the frequency change threshold, the discrete sampling point is regarded as a candidate fault sampling point. According to the scanning order, the first candidate fault sampling point is selected from all the candidate fault sampling points corresponding to the fault current component sequence, and the first candidate fault sampling point is used as the fault sampling point corresponding to the fault current component sequence.

9. A method for calibrating the fault traveling wave front of a transmission line according to claim 1, characterized in that, The step of obtaining the wavefront arrival time at the measurement end of the transmission line based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence includes: Obtain the starting sampling time of the traveling wave current component sequence, and determine the time interval between any two discrete sampling points according to the sampling frequency; The sampling point number of the fault sampling point in the traveling wave current component sequence is obtained, so as to obtain the wavefront arrival time of the measurement end of the transmission line according to the sampling point number, the starting sampling time and the time interval.

10. A fault traveling wave front calibration system for transmission lines, characterized in that, It includes a parameter acquisition module, a spectral entropy calculation module, a current interception module, a multi-threshold extraction module, a fault identification module, and a wavefront calibration module; The parameter acquisition module is used to obtain the sampling frequency and traveling wave current component sequence of the measurement end of the transmission line, and to construct several scales based on the sampling frequency; The spectral entropy calculation module is used to obtain the morphological gradient waveforms of the traveling wave current component sequence at each scale and the spectral entropy corresponding to each morphological gradient waveform. The current extraction module is used to extract the fault current component sequence from the traveling wave current component sequence based on the spectral entropy and the morphological gradient waveform. The multi-threshold extraction module is used to obtain the modal components corresponding to the fault current component sequence, so as to obtain the instantaneous energy curve, instantaneous frequency curve, energy threshold and frequency change threshold corresponding to the fault current component sequence based on the modal components. The fault identification module is used to extract fault sampling points from the fault current component sequence based on the energy threshold, the frequency change threshold, the instantaneous energy curve, and the instantaneous frequency curve. The wavefront calibration module is used to obtain the wavefront arrival time of the measurement end of the transmission line based on the starting sampling time corresponding to the traveling wave current component sequence and the sampling point number of the fault sampling point in the traveling wave current component sequence.

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