Method and system for locating partial discharges of a cable

Abstract

The application discloses a positioning method and system for partial discharge of a cable, and comprises the following steps: collecting a node position parameter, a cable propagation speed parameter and a partial discharge pulse sequence, and preprocessing to obtain a node pulse sequence; slidingly embedding the node pulse sequence to obtain a Hankel matrix, performing eigenvalue decomposition on the Hankel matrix, and calculating a second-order statistical quantity sequence; determining the number of effective propagation components by using a SORTE algorithm, writing the number of effective propagation components into an improved Matrix Pencil algorithm containing an adaptive model order constraint mechanism and a pseudo-time delay elimination mechanism, and obtaining a matrix pencil constraint parameter set; estimating candidate time delay components according to the matrix pencil constraint parameter set, calculating the stability of candidate time delay components with the same sequence number, and calculating the position of the partial discharge after eliminating the pseudo-time delay. The application can reduce the influence of the fluctuation of time delay extraction caused by attenuation, dispersion and phase velocity frequency variation on the positioning result.

Description

Technical Field

[0001] This invention relates to the field of smart grid technology, and in particular to a method and system for locating partial discharge in cables. Background Technology

[0002] During long-term operation, insulation defects, joint aging, and localized electric field concentration in power cables can trigger partial discharges. When a partial discharge pulse propagates along the cable, it can be collected by monitoring nodes deployed at different locations. The location of the discharge source can be estimated based on the pulse arrival time difference, cable propagation speed, and the location of the monitoring nodes. Existing location technologies mainly employ threshold triggering, peak detection, cross-correlation analysis, waveform matching, and traveling wave time difference calculation to extract the pulse arrival time, and then combine this with dual-end monitoring data to complete the location inversion. Some schemes also identify multipath propagation components through time-frequency analysis, parameter estimation, and signal subspace decomposition to reduce the interference of background noise and reflected waves on the arrival time determination.

[0003] Cable propagation channels exhibit frequency-dependent attenuation and dispersion characteristics, with different frequency components showing varying amplitude attenuation and phase delay after long-distance propagation. Partial discharge pulses may also be affected by reflections and superpositions from joints, terminations, and impedance discontinuities, resulting in multiple closely spaced propagating components within the same discharge pulse. Arrival time extraction methods based on fixed thresholds or single peak values ​​are susceptible to amplitude variations, while cross-correlation and waveform matching methods rely on the consistency between the reference waveform and the actual received waveform. When the pulse shape changes with propagation distance and operating conditions, the position of the correlation peak may shift.

[0004] When identifying propagation components using matrix factorization and parameter estimation, the model order directly affects the distinction between effective and noise components. A model order that is too low will miss time delay components related to partial discharge propagation, while a model order that is too high may include components corresponding to noise, reflection disturbances, and numerical errors in the estimation results. Existing methods often determine the number of components based on a fixed order, empirical thresholds, or single-shot spectral characteristics, making it difficult to adapt to variations in the number and stability of propagation components across different pulse segments. Furthermore, candidate time delays obtained from single-shot parameter estimation may contain pseudo-time delays with significant fluctuations across pulse segments; if directly used for location calculation, this can lead to deviations in the propagation time difference between nodes and the location inversion results.

[0005] Therefore, how to provide a method and system for locating partial discharge in cables is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose a method and system for locating partial discharge in cables. This invention reduces the impact of propagation attenuation, dispersion, and phase velocity frequency variation on the location results of partial discharge by using adaptive model order constraints and pseudo-delay elimination.

[0007] A method for locating partial discharge in a cable according to an embodiment of the present invention includes: The monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences of the cable monitoring nodes are collected and preprocessed to obtain the node pulse sequence. The node pulse sequence is subjected to sliding embedding processing according to the number of rows and columns of the matrix to obtain the Hankel matrix; The Hankel matrix is ​​subjected to eigenvalue decomposition, and the second-order statistics of the interval between adjacent eigenvalues ​​are calculated to obtain a sequence of second-order statistics. The number of effective propagation components is determined based on the local minimum locations in the second-order statistic sequence. The effective propagation component number is written into the improved Matrix Pencil algorithm, which includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism, to obtain the matrix bundle constraint parameter set. Based on the set of matrix bundle constraint parameters, matrix bundle parameter estimation is performed on the Hankel matrix to obtain a set of candidate time delay components; According to the arrangement order of the node pulse sequence, read the candidate delay components with the same sequence number from the candidate delay component set, calculate the change amplitude of the delay component, and determine the stability of the delay component; Candidate time delay components whose stability did not reach the time delay component stability threshold were removed from the matrix bundle constraint parameter set to obtain the effective time delay component set. The partial discharge location was then calculated based on the effective time delay component set, the monitoring node location parameters, and the cable propagation speed parameters.

[0008] Optionally, the monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences of the collected cable monitoring nodes are preprocessed, specifically as follows: Collect the monitoring node location parameters and cable propagation speed parameters of the cable monitoring nodes, and establish a propagation reference table between cable nodes; A partial discharge pulse sequence was collected, and the pulse rising edge interval, peak sampling point, and pulse energy centroid sampling point corresponding to each cable monitoring node were extracted to obtain a node pulse index table. Based on the propagation reference table between cable nodes, cross-node pulse timing matching is performed on the node pulse index table, and node sampling offset is established based on the index offset difference between the matched peak sampling point and the pulse energy centroid sampling point. The propagation reference table between cable nodes is corrected based on the node sampling offset, and a matching time window is established; Candidate segments are collected from the node pulse index table according to the matching time window to obtain a set of candidate node pulse segments. Segment alignment is performed on the pulse energy centroid sampling points in the candidate node pulse segment set, and amplitude normalization is performed to obtain the node pulse sequence.

[0009] Optionally, the sliding embedding process of the node pulse sequence according to the number of matrix rows and columns is specifically as follows: Calculate the amplitude difference between adjacent sampling points of the node pulse sequence according to the sampling order, and mark the sampling points where the amplitude difference changes from positive to non-positive to obtain the pulse main peak index set; Centered on the pulse main peak index set, the monotonically increasing sampling length before the peak is counted forward, and the monotonically decreasing sampling length after the peak is counted backward, thus obtaining the main response width set; Based on the set of main response widths, partial discharge pulse segments with main response widths smaller than the preset embedding reference width are filtered out to obtain the pulse sequence of the node to be embedded. The number of rows and columns of the matrix are determined based on the sampling length of the pulse sequence of the node to be embedded; The pulse sequence of the node to be embedded is sampled point by point according to the number of rows and columns of the matrix, and the same sampling number and corresponding sampling value are written to the same anti-diagonal position to obtain the Hankel matrix.

[0010] Optionally, the step of performing eigenvalue decomposition on the Hankel matrix and calculating the second-order statistic of the interval between adjacent eigenvalues ​​specifically involves: Multiplying the transpose of the Hankel matrix with the Hankel matrix yields the eigencorrelation matrix; The eigenvalue correlation matrix is ​​decomposed to extract the magnitude of each eigenvalue, and then sorted in descending order of eigenvalue magnitude to obtain the eigenvalue sequence. The difference between the amplitudes of adjacent eigenvalues ​​in the eigenvalue sequence is calculated sequentially and then normalized to obtain the eigenvalue interval sequence. Starting from each sequence position in the eigenvalue interval sequence, extract the eigenvalue interval from the current sequence position to the last sequence position to obtain the tail interval subsequence; Calculate the mean interval of each tail interval subsequence, and calculate the mean squared difference between each feature value interval and the corresponding mean interval to obtain the tail discrete quantity sequence; Replace the zero values ​​in the tail discrete quantity sequence with preset positive lower limit values, and calculate the ratio of the next tail discrete quantity to the previous tail discrete quantity in turn to obtain the second-order statistical quantity sequence.

[0011] Optionally, determining the number of effective propagation components based on the local minimum locations in the second-order statistic sequence specifically involves: Select the current second-order statistic sequentially from the second-to-last position of the second-order statistic sequence; The SORTE algorithm is used to compare the current second-order statistic with the previous and next second-order statistics respectively, and the sequence positions where the current second-order statistic is less than both the previous and next second-order statistics are marked as candidate minimum positions. Starting from the position after the minimum position of each candidate, extract the second-order statistics up to the end of the second-order statistics sequence to obtain the candidate tail subsequence, and calculate the tail discreteness of each candidate tail subsequence. Calculate the mean of the first and second order statistics corresponding to each candidate minimum position and the mean of the first and second order statistics, and calculate the difference between the mean and the current second order statistic to obtain the minimum concave amplitude. Candidate minimum positions that are filtered out based on the tail dispersion and the minimum concave amplitude, where the tail dispersion exceeds a preset dispersion threshold and the minimum concave amplitude does not reach a preset concave threshold, are obtained as a set of effective minimum positions. The SORTE algorithm is used to select the effective minimum location with the smallest corresponding second-order statistic from the set of effective minimum locations, and to determine the number of effective propagation components.

[0012] Optionally, the improved Matrix Pencil algorithm includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism, specifically: By setting the number of effective propagation components to the matrix bundle decomposition order through an adaptive model order constraint mechanism, the first matrix bundle constraint parameters are obtained. The adaptive model order constraint mechanism sets the positions of several sequences of the first effective propagation components as reserved positions and the remaining sequence positions as truncated positions according to the arrangement order of the eigenvalue sequences, thus obtaining the second matrix bundle constraint parameters; Based on the first and second matrix bundle constraint parameters, the eigenvalues ​​and eigenvectors corresponding to the retained positions are set as matrix bundle parameter estimation objects, and the number of matrix bundle parameter estimation objects is limited to the matrix bundle decomposition order, thus obtaining the order constraint parameter set; The pseudo-delay elimination mechanism sets the condition for eliminating candidate delay components when the stability of the delay component does not reach the stability threshold, and sets the condition for retaining candidate delay components when the stability of the delay component reaches the stability threshold, thus obtaining the first pseudo-delay screening parameters. The pseudo-delay elimination mechanism sets adjacent partial discharge pulse segments as comparison objects for candidate delay components with the same sequence number according to the arrangement order of partial discharge pulse segments in the node pulse sequence, and sets the number of groups of adjacent partial discharge pulse segments as the number of comparisons to obtain the second pseudo-delay screening parameters. Based on the first pseudo-delay screening parameter and the second pseudo-delay screening parameter, the ratio of the number of times the change amplitude of the delay component does not exceed the change amplitude threshold to the number of comparisons is set as the screening criterion for candidate delay components and screening is performed to obtain the pseudo-delay elimination parameter group. The order constraint parameter set and the pseudo-delay elimination parameter set are combined to obtain the matrix bundle constraint parameter set.

[0013] Optionally, the step of estimating the matrix bundle parameters of the Hankel matrix based on the matrix bundle constraint parameter set specifically involves: Based on the sampling range of the partial discharge pulse segment, the matrix elements corresponding to the anti-diagonal positions are extracted from the Hankel matrix to obtain the segment Hankel matrix; Based on the second matrix bundle constraint parameters in the matrix bundle constraint parameter set, the Hankel matrix of each segment is decomposed into eigenvalues, and several eigenvalues ​​and corresponding eigenvectors of the first effective propagation component are retained to obtain the segment constraint signal subspace. Based on the first matrix bundle constraint parameters in the matrix bundle constraint parameter set, the dimension of each segment constraint signal subspace is limited to the matrix bundle decomposition order, and the last row and the first row of each segment constraint signal subspace are deleted respectively to obtain the first shift subspace matrix set and the second shift subspace matrix set. According to the arrangement order of partial discharge pulse segments, the first shift subspace matrix set and the second shift subspace matrix set are longitudinally spliced ​​to obtain the first joint shift matrix and the second joint shift matrix; The number of generalized eigenvalues ​​of the joint matrix bundle formed by the first joint shift matrix and the second joint shift matrix is ​​limited to the order of matrix bundle decomposition, and the generalized eigenvalue decomposition is performed on the joint matrix bundle to obtain the reference propagation pole. The time delay components are assigned serial numbers according to the phase angle ascending order of the reference propagation poles, and the first and second shift subspace matrices corresponding to each partial discharge pulse segment are subjected to generalized eigenvalue decomposition to obtain the segment propagation poles. Each segment propagation pole is assigned a corresponding time delay component number in the manner that the phase angle difference with the reference propagation pole is minimized. The segment propagation poles are then converted into candidate time delay components based on the sampling time interval of the node pulse sequence, thus obtaining a set of candidate time delay components.

[0014] Optionally, the step of reading candidate delay components with the same sequence number from the candidate delay component set according to the arrangement order of the node pulse sequence, calculating the change amplitude of the delay component, and determining the stability of the delay component specifically involves: The candidate time delay components are grouped according to their sequence numbers, and the candidate time delay components in each group are sorted according to the order of their corresponding node pulse sequences to obtain the candidate time delay component trajectories. Two candidate time delay components corresponding to adjacent partial discharge pulse segments are extracted sequentially from the trajectory of each candidate time delay component to obtain the adjacent time delay comparison group; Calculate the absolute difference between two candidate time delay components in each adjacent time delay comparison group to obtain the first change amplitude sequence; From the second sequence position to the second-to-last sequence position of the first change amplitude sequence, extract the first change amplitude corresponding to the previous sequence position, the current sequence position, and the next sequence position respectively, and take the maximum value of the three as the change amplitude of the time delay component corresponding to the current sequence position; Extract the first change amplitude corresponding to the first and second positions in the first change amplitude sequence, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the first position. Extract the first change amplitude corresponding to the second to last position and the last position, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the last position. Arrange the time delay component changes corresponding to the current sequence position, the first position, and the last position in sequence according to their corresponding first changes in the first change magnitude sequence to obtain the second change magnitude sequence; The number of times the change amplitude of the time delay component in the second change amplitude sequence does not exceed the change amplitude threshold is counted to obtain the number of stable comparisons. The number of stable comparisons is then divided by the number of comparisons to obtain the stability of the time delay component.

[0015] Optionally, the calculation of the partial discharge location specifically involves: The initial set of effective time delay components is determined based on the first pseudo-delay screening parameter in the matrix bundle constraint parameter set; The initial effective time delay component set is grouped according to the time delay component sequence number and cable monitoring node. The difference between the corresponding retained components of two cable monitoring nodes under the same time delay component sequence number is calculated to obtain the propagation time difference set between nodes. Based on the set of propagation time differences between nodes, the location parameters of monitoring nodes, and the cable propagation speed parameters, the candidate partial discharge locations corresponding to each time delay component number are calculated respectively. Based on the cable path distance and cable propagation speed parameters between each candidate partial discharge location and the corresponding cable monitoring node, the reconstruction propagation time difference of the corresponding node pair is calculated, and the absolute difference between the reconstruction propagation time difference and the propagation time difference between nodes is calculated to obtain the reconstruction time difference residual. Candidate partial discharge locations and their corresponding retained components that have reconstructed time difference residuals exceeding the reconstructed time difference residual threshold are removed to obtain the effective time delay component set and the effective partial discharge location set. The stability of the time delay component corresponding to each effective partial discharge location in the effective partial discharge location set is normalized to obtain the location fusion weight. The effective partial discharge locations are calculated by weighting the location fusion weights to obtain the partial discharge locations.

[0016] Optionally, a locating system for partial discharge in cables includes: The data processing module is used to collect monitoring node location parameters, cable propagation speed parameters, and partial discharge pulse sequences, and to preprocess them to obtain node pulse sequences; The matrix construction module is used to perform sliding embedding processing on the node pulse sequence to obtain the Hankel matrix; The propagation component determination module is used to perform eigenvalue decomposition on the Hankel matrix, obtain a second-order statistic sequence, and determine the number of effective propagation components. The constraint parameter generation module is used to generate a matrix bundle constraint parameter set based on the effective propagation component number and time delay. The time delay component estimation module is used to estimate the matrix bundle parameters of the Hankel matrix based on the matrix bundle constraint parameter set, and obtain a set of candidate time delay components. The stability calculation module is used to calculate the stability of the time delay components based on the candidate time delay component set. The positioning module is used to calculate the location of partial discharge based on the candidate time delay component set, the stability of the time delay components, the monitoring node position parameters, and the cable propagation speed parameters.

[0017] The beneficial effects of this invention are: (1) This invention establishes a propagation reference table between cable nodes, corrects the propagation time difference reference based on the node sampling offset, and uses a matching time window to complete cross-node pulse timing matching, segment alignment and amplitude normalization processing, thereby realizing the time correspondence and waveform scale uniformity of partial discharge pulse segments of different cable monitoring nodes, thereby reducing the impact of hardware sampling offset and node matching error on subsequent time delay estimation.

[0018] (2) This invention performs second-order statistics on the eigenvalue intervals of the Hankel matrix and uses the SORTE algorithm to determine the number of effective propagation components. The number of effective propagation components is written into the adaptive model order constraint mechanism, which jointly limits the matrix bundle decomposition order, eigenvalue retention position and matrix bundle parameter estimation object. This achieves adaptive matching between the number of propagation components and the range of matrix bundle parameter estimation, thereby reducing the omission of effective components and the mixing of noise components caused by improper model order setting.

[0019] (3) The improved Matrix Pencil algorithm in this invention achieves the screening of cross-partial discharge pulse segment fluctuation components by combining matrix bundle estimation, construction of candidate time delay component trajectories with the same sequence number, calculation of time delay component stability and elimination of pseudo time delay, and combining reconstruction time difference residual screening and position fusion weight for positioning calculation. This reduces the impact of attenuation, dispersion and phase velocity frequency change on the partial discharge positioning results during long-distance cable propagation. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Fig. 1 This is a flowchart of the method for locating partial discharge in cables proposed in this invention; Fig. 2 This is a system structure block diagram of the positioning system for partial discharge of cables proposed in this invention; Fig. 3 This is a flowchart of the improved Matrix Pencil algorithm for locating partial discharge in cables, as proposed in this invention. Detailed Implementation

[0021] Example 1: Reference Figs. 1-3 Methods for locating partial discharge in cables include: The monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences of the cable monitoring nodes are collected, and the partial discharge pulse sequences are preprocessed to obtain the node pulse sequences. The node pulse sequence is subjected to sliding embedding processing according to the number of rows and columns of the matrix to obtain the Hankel matrix corresponding to the node pulse sequence; The Hankel matrix is ​​subjected to eigenvalue decomposition. The eigenvalue sequence is arranged in descending order of eigenvalue magnitude, and the second-order statistics of the interval between adjacent eigenvalues ​​are calculated to obtain the second-order statistics sequence. The SORTE algorithm is used to process the second-order statistics sequence, and the number of effective propagation components is determined based on the local minima in the second-order statistics sequence. The number of effective propagation components is incorporated into the improved Matrix Pencil algorithm, which includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism. The adaptive model order constraint mechanism limits the matrix bundle decomposition order to the number of effective propagation components, and the pseudo-delay elimination mechanism uses the stability threshold of the delay components as the screening condition for candidate delay components, thus obtaining the matrix bundle constraint parameter set. Based on the adaptive model order constraint mechanism in the matrix bundle constraint parameter set, matrix bundle parameter estimation is performed on the Hankel matrix to obtain the candidate delay component set corresponding to the number of effective propagation components; According to the arrangement order of the node pulse sequence, the candidate time delay components with the same sequence number corresponding to adjacent partial discharge pulse segments are read from the candidate time delay component set, the change amplitude of the time delay component is calculated, and the proportion of the number of times the change amplitude of the time delay component does not exceed the change amplitude threshold to the number of comparisons is determined as the stability of the time delay component. The pseudo-delay elimination mechanism in the matrix bundle constraint parameter set eliminates candidate delay components whose delay component stability does not reach the delay component stability threshold, thus obtaining the effective delay component set. The partial discharge location is then calculated based on the effective delay component set, monitoring node location parameters, and cable propagation speed parameters.

[0022] In this embodiment, the acquisition of monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences from the cable monitoring nodes, followed by preprocessing, specifically involves: Collect the monitoring node location parameters and cable propagation speed parameters of the cable monitoring nodes, and establish a propagation reference table between cable nodes; In Example 1, the node number, monitoring node location parameters, and cable propagation speed parameters of each cable monitoring node are collected; node pairs are formed by combining the node numbers, and the node spacing is determined based on the cable path distance between the two monitoring node location parameters; the propagation time difference reference value is obtained by dividing the node spacing by the cable propagation speed parameter; the node pairs, node spacing, and propagation time difference reference value are written into the table entries in the order of node numbers to obtain the propagation reference table between cable nodes. A partial discharge pulse sequence was collected, and the pulse rising edge interval, peak sampling point, and pulse energy centroid sampling point corresponding to each cable monitoring node were extracted to obtain a node pulse index table. Based on the propagation reference table between cable nodes, cross-node pulse timing matching is performed on the node pulse index table, and node sampling offset is established based on the index offset difference between the matched peak sampling point and the pulse energy centroid sampling point. In Example 1, the cable monitoring node with the smallest node number is selected as the reference node; the reference node pulse record is extracted from the node pulse index table in ascending order of peak sampling points; the peak sampling points of the reference node pulse record are added to the propagation time difference reference value of the corresponding node pair in the cable node propagation reference table to form the target node predicted peak sampling point; the target node pulse record with the smallest distance to the target node predicted peak sampling point is found in the node pulse index table, and the reference node pulse record and the target node pulse record are grouped into the same matching group; for each matching group, the sampling sequence number difference between the peak sampling point and the pulse energy centroid sampling point is calculated; the average of the sampling sequence number differences of the same cable monitoring node in each matching group is used to obtain the node sampling offset; The propagation reference table between cable nodes is corrected based on the node sampling offset, and a matching time window is established with the corrected propagation reference table between cable nodes as the center and the node sampling offset as the boundary. In Example 1, the node sampling offset of the target node in the node pair is subtracted from the node sampling offset of the reference node to obtain the node pair offset correction value; the propagation time difference reference value in the cable node propagation reference table is added to the node pair offset correction value to obtain the corrected propagation time difference reference value; the corrected propagation time difference reference value is written into the cable node propagation reference table to obtain the corrected cable node propagation reference table; the larger of the absolute values ​​of the node sampling offsets at both ends of the node pair is selected as the half-width of the time window; the corrected propagation time difference reference value is subtracted from the half-width of the time window to obtain the start point of the time window, and the corrected propagation time difference reference value is added to the half-width of the time window to obtain the end point of the time window, thus obtaining the matching time window; Candidate segments are collected from the node pulse index table according to the matching time window to obtain a set of candidate node pulse segments. Perform segment alignment on the pulse energy centroid sampling points in the candidate node pulse segment set, and perform amplitude normalization on the segment-aligned candidate node pulse segment set to obtain the node pulse sequence.

[0023] In this embodiment, the sliding embedding process of the node pulse sequence according to the number of matrix rows and columns is specifically as follows: Calculate the amplitude difference between adjacent sampling points of the node pulse sequence according to the sampling order, and mark the sampling points where the amplitude difference changes from positive to non-positive to obtain the pulse main peak index set; In Example 1, the node pulse sequence is arranged in ascending order of sampling time. Starting from the second sampling point, the amplitude of the previous sampling point is subtracted from the amplitude of the current sampling point to obtain the amplitude difference sequence between adjacent sampling points. Starting from the second item in the amplitude difference sequence between adjacent sampling points, the previous item is compared with the current item. When the current item is positive and not greater than 0, the sequence number of the back-end sampling point corresponding to the previous item is marked as the pulse main peak index. All pulse main peak indices are summarized in ascending order of sampling time to obtain the pulse main peak index set. Centered on the pulse main peak index set, the monotonically increasing sampling length before the peak is counted forward, and the monotonically decreasing sampling length after the peak is counted backward, thus obtaining the main response width set; In Example 1, for each pulse main peak index in the pulse main peak index set, the amplitudes of adjacent sampling points are compared point by point along the decreasing sampling sequence number. When the amplitude of the current sampling point is less than the amplitude of the subsequent sampling point, the monotonically increasing sampling length before the peak is included; the statistics stop when the condition is not met. The amplitudes of adjacent sampling points are compared point by point along the increasing sampling sequence number. When the amplitude of the current sampling point is greater than the amplitude of the subsequent sampling point, the monotonically decreasing sampling length after the peak is included; the statistics stop when the condition is not met. The monotonically increasing sampling length before the peak and the monotonically decreasing sampling length after the peak are added together to obtain the main response width of the corresponding pulse main peak index. All main response widths are summarized to obtain the main response width set. Partial discharge pulse segments with main response widths smaller than the preset embedding reference width are filtered out from the main response width set to obtain the pulse sequence of the node to be embedded. The preset embedding reference width is a segment screening threshold determined by the ascending quantile sampling length of the main response width set. The main response width set is arranged in ascending order of value. The number of main response widths in the set is multiplied by 0.3 and rounded up to obtain the reference number. The main response width corresponding to the sorted reference number is taken as the preset embedding reference width. When the reference number is less than 1, the reference number is set to 1. The number of rows and columns of the matrix are determined based on the sampling length of the pulse sequence of the node to be embedded, and the sum of the number of rows and columns of the matrix is ​​equal to the sampling length of the pulse sequence of the node to be embedded plus 1. The pulse sequence of the node to be embedded is sampled point by point according to the number of rows and columns of the matrix, and the same sampling number and corresponding sampling value are written to the same anti-diagonal position to obtain the Hankel matrix corresponding to the node pulse sequence.

[0024] In Example 1, a blank matrix is ​​created with the same number of rows and columns as the matrix. For each position in the blank matrix, the row number and column number are added together and then subtracted by 1 to obtain the target sampling number. The sampling value corresponding to the target sampling number is extracted from the pulse sequence of the node to be embedded and written into the corresponding matrix position. Matrix positions with the same sum of row number and column number form the same anti-diagonal line. After writing all matrix positions, the Hankel matrix corresponding to the node pulse sequence is obtained.

[0025] In this embodiment, the eigenvalue decomposition of the Hankel matrix and the calculation of the second-order statistic of the interval between adjacent eigenvalues ​​specifically involve: Multiplying the transpose of the Hankel matrix with the Hankel matrix yields the eigencorrelation matrix; The eigenvalue correlation matrix is ​​decomposed to extract the magnitude of each eigenvalue, and then sorted in descending order of eigenvalue magnitude to obtain the eigenvalue sequence. In Example 1, the feature correlation matrix is ​​used as a real symmetric matrix for QR iterative decomposition. In each iteration, the feature correlation matrix is ​​decomposed into an orthogonal matrix and an upper triangular matrix, and the feature correlation matrix is ​​updated according to the product of the upper triangular matrix and the orthogonal matrix. The iteration stops when the absolute value of all off-diagonal elements is less than 10 to the power of -12. The diagonal elements of the updated feature correlation matrix are extracted as eigenvalues, and the absolute value of each eigenvalue is calculated as the eigenvalue magnitude. The corresponding eigenvalues ​​are arranged in descending order of eigenvalue magnitude to obtain the eigenvalue sequence. The difference between the amplitudes of adjacent eigenvalues ​​in the eigenvalue sequence is calculated sequentially and then normalized to obtain the eigenvalue interval sequence. Starting from each sequence position in the eigenvalue interval sequence, extract the eigenvalue interval from the current sequence position to the last sequence position to obtain the tail interval subsequence; In Example 1, the sequence positions in the feature value interval sequence are numbered sequentially from 1 to N; starting from number 1, the feature value intervals corresponding to number N are arranged in their original order to form the first tail interval subsequence; the starting number is incremented by 1 each time, and the feature value intervals corresponding to each starting number are arranged in their original order to form tail interval subsequences; when the starting number reaches N, the truncation stops, resulting in N tail interval subsequences; Calculate the mean interval of each tail interval subsequence, and calculate the mean squared difference between each feature value interval and the corresponding mean interval to obtain the tail discrete quantity sequence; The zero values ​​in the tail discrete quantity sequence are replaced with a preset positive lower limit value, and the ratio of the next tail discrete quantity to the previous tail discrete quantity is calculated in turn to obtain a second-order statistical quantity sequence. The preset positive lower limit value is a positive number obtained by multiplying the minimum value of all non-zero tail discrete quantities in the tail discrete quantity sequence by 10 to the power of -6. When there are no non-zero tail discrete quantities in the tail discrete quantity sequence, the preset positive lower limit value is set to 10 to the power of -12.

[0026] In this embodiment, determining the number of effective propagation components based on the local minimum position in the second-order statistic sequence specifically involves: Select the current second-order statistic sequentially from the second-to-last position of the second-order statistic sequence; The SORTE algorithm is used to compare the current second-order statistic with the previous and next second-order statistics respectively, and the sequence positions where the current second-order statistic is less than both the previous and next second-order statistics are marked as candidate minimum positions. In Example 1, the positions from the second to the second-to-last sequence in the second-order statistic sequence are sequentially set as the current sequence position. The SORTE algorithm is used to extract the second-order statistics corresponding to the current sequence position, the previous sequence position, and the next sequence position. When the current second-order statistic is less than both the previous and next second-order statistic, the current sequence position is recorded as a candidate minimum position. When any comparison condition is not met, the current sequence position is not recorded. After comparing all sequence positions, the candidate minimum positions are obtained. Starting from the position after the minimum position of each candidate, extract the second-order statistics up to the end of the second-order statistics sequence to obtain the candidate tail subsequence, and calculate the tail discreteness of each candidate tail subsequence. In Example 1, for each candidate tail subsequence, the arithmetic mean of all second-order statistics is calculated to obtain the tail mean; the difference between each second-order statistic and the tail mean is calculated, and the difference is squared to obtain a sequence of squared differences; the sum of all squared differences in the sequence of squared differences is obtained by dividing the sum of squared differences by the number of second-order statistics contained in the candidate tail subsequence to obtain the tail discreteness of the corresponding candidate tail subsequence; Calculate the mean of the first and second order statistics corresponding to each candidate minimum position and the mean of the first and second order statistics, and calculate the difference between the mean and the current second order statistic to obtain the minimum concave amplitude. Candidate minimum positions are filtered out based on the tail dispersion and the minimum concave amplitude, where the tail dispersion exceeds a preset dispersion threshold and the minimum concave amplitude does not reach a preset concave threshold, thus obtaining a set of effective minimum positions. The preset dispersion threshold is the value corresponding to the median position after arranging the tail dispersion corresponding to all candidate tail subsequences in ascending order; when the number of tail dispersions is even, the arithmetic mean of the two middle values ​​is taken. The preset concave threshold is the value corresponding to the median position after arranging the minimum concave amplitude corresponding to all candidate minimum positions in ascending order; when the number of minimum concave amplitudes is even, the arithmetic mean of the two middle values ​​is taken. The SORTE algorithm is used to select the effective minimum position with the smallest corresponding second-order statistic from the set of effective minimum positions, and the sequence position corresponding to the selected effective minimum position is determined as the number of effective propagation components.

[0027] In Example 1, the SORTE algorithm is used to extract the second-order statistics corresponding to each effective minimum position in the effective minimum position set; the effective minimum positions are arranged in ascending order according to the second-order statistics values, and if the second-order statistics values ​​are the same, they are arranged in ascending order according to the sequence position; the first effective minimum position is selected; the sequence position value of the selected effective minimum position in the second-order statistics sequence is determined as the number of effective propagation components.

[0028] In this embodiment, the improved Matrix Pencil algorithm includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism, specifically: The effective propagation component number is set as the matrix bundle decomposition order through an adaptive model order constraint mechanism to obtain the first matrix bundle constraint parameters. The adaptive model order constraint mechanism receives the effective propagation component number, eigenvalue sequence and corresponding eigenvector, and labels the sequence position in descending order of eigenvalue amplitude. The eigenvalues ​​and corresponding eigenvectors whose sequence position is not greater than the effective propagation component number are marked as retained objects, and the remaining eigenvalues ​​and corresponding eigenvectors are marked as truncated objects. The truncated objects are deleted, and only the retained objects constitute the matrix bundle parameter estimation objects. The number of retained objects is written into the matrix bundle decomposition order to complete the order synchronization constraint. The adaptive model order constraint mechanism sets the positions of several sequences of the first effective propagation components as reserved positions and the remaining sequence positions as truncated positions according to the arrangement order of the eigenvalue sequences, thus obtaining the second matrix bundle constraint parameters; Based on the first and second matrix bundle constraint parameters, the eigenvalues ​​and eigenvectors corresponding to the retained positions are set as matrix bundle parameter estimation objects, and the number of matrix bundle parameter estimation objects is limited to the matrix bundle decomposition order, thus obtaining the order constraint parameter set; A pseudo-delay elimination mechanism is used to set the condition for candidate delay components whose stability does not reach the stability threshold as the condition for elimination, and the condition for candidate delay components whose stability reaches the stability threshold as the condition for retention, thus obtaining the first pseudo-delay screening parameters. The pseudo-delay elimination mechanism receives a set of candidate delay components, a change amplitude threshold, a delay component stability threshold, and the order of the node pulse sequences. According to the order of the partial discharge pulse segments, candidate delay components with the same sequence number in adjacent partial discharge pulse segments are grouped into comparison groups, and the number of comparison groups is recorded as the number of comparisons. The absolute difference between the two candidate delay components in each group is calculated to obtain the change amplitude of the delay component. The number of comparison groups whose change amplitude does not exceed the change amplitude threshold is counted, and the results are then compiled. The stability of the time delay component is obtained by performing a division operation using the number of times the component is counted as the dividend and the number of comparisons as the divisor. Candidate time delay components whose stability does not reach the time delay component stability threshold are marked as elimination objects, and candidate time delay components that reach the time delay component stability threshold are marked as retention objects. The elimination objects are deleted and the retention objects are summarized to complete the pseudo-time delay elimination. The time delay component stability threshold is a screening boundary determined by the time delay component stability corresponding to all candidate time delay components. All time delay component stability values ​​are arranged in ascending order of value. When the number of time delay component stability values ​​is odd, the value corresponding to the middle position is taken as the time delay component stability threshold. When the number of time delay component stability values ​​is even, the arithmetic mean of the two middle values ​​is taken as the time delay component stability threshold. The pseudo-delay elimination mechanism sets adjacent partial discharge pulse segments as comparison objects for candidate delay components with the same sequence number according to the arrangement order of partial discharge pulse segments in the node pulse sequence, and sets the number of groups of adjacent partial discharge pulse segments as the number of comparisons to obtain the second pseudo-delay screening parameters. Based on the first pseudo-delay screening parameter and the second pseudo-delay screening parameter, the ratio of the number of times the change amplitude of the delay component does not exceed the change amplitude threshold to the number of comparisons is set as the screening criterion for candidate delay components and screening is performed to obtain a pseudo-delay elimination parameter group. The change amplitude threshold is a comparison boundary determined by the change amplitude of all delay components. The change amplitudes of all delay components are arranged in ascending order of value. When the number is odd, the value corresponding to the middle position is taken as the change amplitude threshold. When the number is even, the arithmetic mean of the two middle values ​​is taken as the change amplitude threshold. The order constraint parameter set and the pseudo-delay elimination parameter set are combined to obtain the matrix bundle constraint parameter set.

[0029] In Example 1, the first matrix bundle constraint parameter, the second matrix bundle constraint parameter, and the matrix bundle parameter estimation object in the order constraint parameter group are sequentially written into the front field, and the first pseudo-delay filtering parameter, the second pseudo-delay filtering parameter, and the candidate delay component filtering criteria in the pseudo-delay elimination parameter group are sequentially written into the back field; a unified parameter group number is set for the front field and the back field to form a matrix bundle constraint parameter set.

[0030] In this embodiment, the step of estimating the matrix bundle parameters of the Hankel matrix based on the matrix bundle constraint parameter set specifically involves: Based on the sampling range of the partial discharge pulse segment, the matrix elements corresponding to the anti-diagonal positions are extracted from the Hankel matrix to obtain the segment Hankel matrix; Based on the second matrix bundle constraint parameters in the matrix bundle constraint parameter set, the Hankel matrix of each segment is decomposed into eigenvalues, and several eigenvalues ​​and corresponding eigenvectors of the first effective propagation component are retained to obtain the segment constraint signal subspace. In Example 1, the transpose of the Hankel matrix of each segment is multiplied by the corresponding segment Hankel matrix to obtain the segment feature correlation matrix; QR iterative decomposition is performed on the segment feature correlation matrix to extract eigenvalues ​​and corresponding eigenvectors; the eigenvalues ​​and corresponding eigenvectors are arranged in descending order of eigenvalue amplitude; according to the second matrix bundle constraint parameters, the eigenvalues ​​and eigenvectors corresponding to several sequence positions of the previous effective propagation components are retained, and the remaining eigenvalues ​​and eigenvectors are truncated to obtain the segment constraint signal subspace; Based on the first matrix bundle constraint parameters in the matrix bundle constraint parameter set, the dimension of each segment constraint signal subspace is limited to the matrix bundle decomposition order, and the last row and the first row of each segment constraint signal subspace are deleted respectively to obtain the first shift subspace matrix set and the second shift subspace matrix set. According to the arrangement order of partial discharge pulse segments, the first shift subspace matrix set and the second shift subspace matrix set are longitudinally spliced ​​to obtain the first joint shift matrix and the second joint shift matrix; The number of generalized eigenvalues ​​of the joint matrix bundle formed by the first joint shift matrix and the second joint shift matrix is ​​limited to the order of matrix bundle decomposition, and the joint matrix bundle is decomposed into generalized eigenvalues ​​to obtain the reference propagation poles corresponding to the number of effective propagation components. In Example 1, the first joint shift matrix is ​​decomposed into singular values, and a generalized inverse matrix is ​​constructed based on the reciprocals of the non-zero singular values. The generalized inverse matrix is ​​multiplied by the second joint shift matrix to obtain the matrix bundle transformation matrix. QR iteration is performed on the matrix bundle transformation matrix to extract all eigenvalues. The eigenvalues ​​are sorted in descending order of magnitude, and the eigenvalues ​​of the first matrix bundle decomposition order are retained. The retained eigenvalues ​​are determined as the generalized eigenvalues ​​of the joint matrix bundle. The time delay components are assigned serial numbers according to the phase angle ascending order of the reference propagation poles, and the first and second shift subspace matrices corresponding to each partial discharge pulse segment are subjected to generalized eigenvalue decomposition to obtain the segment propagation poles. In Example 1, the phase angle of each reference propagation pole is calculated, arranged in ascending order of phase angle values, and numbered consecutively starting from 1 to obtain the time delay component number; for each partial discharge pulse segment, the corresponding first shift subspace matrix is ​​decomposed into singular values, and a generalized inverse matrix is ​​constructed based on the reciprocal of the non-zero singular values; the generalized inverse matrix is ​​multiplied by the corresponding second shift subspace matrix to obtain the segment matrix bundle transformation matrix; QR iteration is performed on the segment matrix bundle transformation matrix to extract the matrix bundle decomposition order eigenvalues ​​to obtain the segment propagation poles; Each segment propagation pole is assigned a corresponding time delay component number in the manner that the phase angle difference with the reference propagation pole is minimized. The segment propagation poles are then converted into candidate time delay components according to the sampling time interval of the node pulse sequence, resulting in a set of candidate time delay components corresponding to the number of effective propagation components.

[0031] In Example 1, the phase angles of each segment propagation pole and each reference propagation pole are calculated, and the absolute difference of the phase angle between each segment propagation pole and all reference propagation poles is calculated. Unoccupied reference propagation poles are matched to segment propagation poles in ascending order of absolute phase difference, and a time delay component index is assigned to each matched reference propagation pole. When the absolute phase differences are the same, the reference propagation pole with the smaller time delay component index is selected. The phase angles of the ordered segment propagation poles are expanded, and the absolute value of the expanded phase angle is divided by twice pi to obtain the sampling point offset. The sampling point offset is multiplied by the sampling time interval of the node pulse sequence to obtain the candidate time delay component.

[0032] In this embodiment, the step of reading candidate delay components with the same sequence number from the candidate delay component set according to the arrangement order of the node pulse sequence, calculating the change amplitude of the delay component, and determining the stability of the delay component specifically involves: The candidate time delay components are grouped according to their sequence numbers, and the candidate time delay components in each group are sorted according to the order of their corresponding node pulse sequences to obtain the candidate time delay component trajectories. In Example 1, the candidate time delay components in the candidate time delay component set are classified according to their time delay component numbers; candidate time delay components with the same time delay component number are grouped into the same group; based on the arrangement position of the partial discharge pulse segment corresponding to each candidate time delay component in the node pulse sequence, the candidate time delay components in the same group are sorted in ascending order according to their arrangement position; the sorted candidate time delay components are connected in sequence to obtain the candidate time delay component trajectory with the corresponding time delay component number. Two candidate time delay components corresponding to adjacent partial discharge pulse segments are extracted sequentially from each candidate time delay component trajectory to obtain adjacent time delay comparison groups, and the number of adjacent time delay comparison groups is determined as the number of comparisons. Calculate the absolute difference between two candidate time delay components in each adjacent time delay comparison group to obtain the first change amplitude sequence; From the second sequence position to the second-to-last sequence position of the first change amplitude sequence, extract the first change amplitude corresponding to the previous sequence position, the current sequence position, and the next sequence position respectively, and take the maximum value of the three as the change amplitude of the time delay component corresponding to the current sequence position; Extract the first change amplitude corresponding to the first and second positions in the first change amplitude sequence, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the first position. Extract the first change amplitude corresponding to the second to last position and the last position, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the last position. Arrange the time delay component changes corresponding to the current sequence position, the first position, and the last position in sequence according to their corresponding first changes in the first change magnitude sequence to obtain the second change magnitude sequence; In Example 1, consecutive position numbers are assigned to each sequence position of the first variation amplitude sequence; the variation amplitude of the time delay component corresponding to the first position is written into number 1; the variation amplitude of the time delay component corresponding to the second to last sequence position is written into the corresponding position number; the variation amplitude of the time delay component corresponding to the last position is written into the last position number; all the variation amplitudes of the time delay component are connected in ascending order of position number to obtain the second variation amplitude sequence. The number of time delay components whose change amplitude in the second change amplitude sequence does not exceed the change amplitude threshold is counted to obtain the number of stable comparisons. The number of stable comparisons is then divided by the number of comparisons to obtain the stability of the time delay component corresponding to each time delay component number.

[0033] In this embodiment, calculating the partial discharge location specifically involves: Based on the first pseudo-delay screening parameter in the matrix bundle constraint parameter set, candidate delay components whose delay component stability does not reach the delay component stability threshold are marked as discarded components, and candidate delay components whose delay component stability reaches the delay component stability threshold are marked as retained components, thus obtaining the initial set of effective delay components. The initial effective time delay component set is grouped according to the time delay component sequence number and cable monitoring node. The difference between the corresponding retained components of two cable monitoring nodes under the same time delay component sequence number is calculated to obtain the propagation time difference set between nodes. Based on the set of propagation time differences between nodes, the location parameters of monitoring nodes, and the cable propagation speed parameters, the candidate partial discharge locations corresponding to each time delay component number are calculated respectively. In Example 1, the first and second nodes are determined in ascending order of cable monitoring node numbers; the propagation time difference between nodes is obtained by subtracting the corresponding retained component of the first node from the corresponding retained component of the second node; the cable path length between the two nodes is calculated based on the monitoring node position parameters; the propagation time difference between nodes is multiplied by the cable propagation speed parameter to obtain the propagation path difference; the propagation path difference is subtracted from the cable path length between the two nodes, and then the path is divided into two equal parts to obtain the cable path distance from the candidate partial discharge location to the first node; the first node position parameter is added to the cable path distance to obtain the candidate partial discharge location with the corresponding time delay component number. Based on the cable path distance and cable propagation speed parameters between each candidate partial discharge location and the corresponding cable monitoring node, the reconstruction propagation time difference of the corresponding node pair is calculated, and the absolute difference between the reconstruction propagation time difference and the propagation time difference between nodes is calculated to obtain the reconstruction time difference residual. In Example 1, for each candidate partial discharge location, the cable path distance from the candidate partial discharge location to the first node and the second node are calculated respectively; the cable propagation speed parameter is used as a divisor to perform division operations on the two cable path distances respectively to obtain the first propagation time and the second propagation time; the second propagation time is subtracted from the first propagation time to obtain the reconstruction propagation time difference of the corresponding node pair. Candidate partial discharge locations and their corresponding retained components that have reconstruction time difference residuals exceeding the reconstruction time difference residual threshold are removed to obtain an effective time delay component set and an effective partial discharge location set. The reconstruction time difference residual threshold is twice the sampling time interval of the node pulse sequence. The time difference between adjacent sampling points of the node pulse sequence is calculated to obtain the sampling time interval. The sampling time interval is multiplied by 2 to obtain the reconstruction time difference residual threshold. The stability of the time delay component corresponding to each effective partial discharge location in the effective partial discharge location set is normalized to obtain the location fusion weight. The effective partial discharge locations are calculated by weighting the location fusion weights to obtain the partial discharge locations.

[0034] In this embodiment, the positioning system for partial discharge of cables includes: The data processing module is used to collect monitoring node location parameters, cable propagation speed parameters, and partial discharge pulse sequences, and to preprocess them to obtain node pulse sequences; The matrix construction module is used to perform sliding embedding processing on the node pulse sequence to obtain the Hankel matrix; The propagation component determination module is used to perform eigenvalue decomposition on the Hankel matrix, obtain a second-order statistic sequence, and determine the number of effective propagation components. The constraint parameter generation module is used to generate a matrix bundle constraint parameter set based on the effective propagation component number and time delay. The time delay component estimation module is used to estimate the matrix bundle parameters of the Hankel matrix based on the matrix bundle constraint parameter set, and obtain a set of candidate time delay components. The stability calculation module is used to calculate the stability of the time delay components based on the candidate time delay component set. The positioning module is used to calculate the location of partial discharge based on the candidate time delay component set, the stability of the time delay components, the monitoring node position parameters, and the cable propagation speed parameters.

[0035] Example 2: To verify the feasibility of this invention in practice, it was applied to a 1800-meter-long cross-linked polyethylene insulated cable test line for locating partial discharge pulses. Four cable monitoring nodes were set up along the cable at locations of 0 meters, 600 meters, 1200 meters, and 1800 meters, with a sampling frequency of 100 MHz and a cable propagation velocity of 1.68 x 10⁸ meters per second. After long-distance propagation, partial discharge pulses exhibit attenuation, broadening, peak shift, and reflection superposition. Using fixed thresholds and fixed model orders can easily lead to fluctuations in arrival time and the inclusion of invalid components. Twenty partial discharge pulses were triggered at five known locations, and 100 sets of partial discharge pulse sequences were collected.

[0036] During implementation, the monitoring node location parameters and cable propagation velocity parameters of each cable monitoring node are collected. Any two cable monitoring nodes are paired, and the cable path distance between nodes is calculated. The path distance is divided by the cable propagation velocity parameter to obtain the propagation time difference benchmark, establishing a propagation benchmark table between cable nodes. For each trigger record, the pulse rising edge interval, peak sampling point, and pulse energy centroid sampling point are extracted to obtain a node pulse index table. Using the cable monitoring node with the smallest number as the reference node, the propagation time difference benchmark is converted into sampling point offset to form the predicted peak sampling point for the target node. The pulse record with the smallest distance is selected to complete cross-node pulse timing matching. The index offset difference between the peak sampling point and the pulse energy centroid sampling point is calculated, and the average value is taken for the same node to obtain the node sampling offset. The difference between the node sampling offsets of the target node and the reference node is superimposed on the propagation time difference benchmark to obtain the corrected propagation benchmark table between cable nodes.

[0037] Using the node sampling offset with the largest absolute value as the half-width of the matching time window, candidate segments are collected from the node pulse index table according to the matching time window to obtain a set of candidate node pulse segments. Segment alignment is performed on the sampling points of the pulse energy centroid, and amplitude normalization is performed according to the maximum absolute amplitude of the segment to obtain the node pulse sequence. The amplitude difference between adjacent sampling points is calculated according to the sampling order, and sampling points that change from positive to non-positive values ​​are marked to obtain the pulse main peak index set. The monotonically increasing sampling length before the peak and the monotonically decreasing sampling length after the peak are counted to obtain the main response width set. The main response width set is sorted in ascending order, and the main response width corresponding to the number multiplied by 0.3 and rounded up is used as the preset embedding reference width. Partial discharge pulse segments that do not meet the conditions are filtered out to obtain the node pulse sequence to be embedded. The sampling length of the node pulse sequence to be embedded is 128, the number of matrix rows is 64, and the number of matrix columns is 65. They are written in the same anti-diagonal position according to the same sampling sequence number to obtain the Hankel matrix.

[0038] Multiplying the transpose of the Hankel matrix with the Hankel matrix yields the eigenvalue correlation matrix. Eigenvalue decomposition is performed using orthogonal triangular iteration, stopping when the absolute values ​​of all off-diagonal elements are less than 10 to the power of -12. Eigenvalue amplitudes are extracted and sorted in descending order to obtain the eigenvalue sequence. The difference in amplitude between adjacent eigenvalues ​​is calculated and normalized to obtain the eigenvalue interval sequence. Each sequence position is truncated to the last position, and the mean interval and mean squared difference of the tail interval subsequences are calculated to obtain the tail discrete quantity sequence. Zero values ​​are replaced with a preset positive lower limit value, and the ratio of adjacent tail discrete quantities is calculated to obtain the second-order statistic sequence. The SORTE algorithm is used to select candidate minimum positions, calculating the tail discrete quantity and the minimum concave amplitude. The median of these two values ​​is used as the corresponding threshold for screening, and the sequence position with the smallest second-order statistic is determined as the number of effective propagation components. The number of effective propagation components is between 3 and 5.

[0039] The number of effective propagation components is incorporated into the improved Matrix Pencil algorithm. An adaptive model order constraint mechanism limits the matrix bundle decomposition order to the number of effective propagation components. The first few eigenvalues ​​and corresponding eigenvectors of the effective propagation components are retained, and the remaining positions are set as truncation positions, forming an order constraint parameter set. The segment Hankel matrix is ​​extracted according to the sampling range of the partial discharge pulse segment. After eigenvalue decomposition, the segment constraint signal subspace is obtained. The last and first rows of the segment constraint signal subspace are deleted to obtain the first and second shift subspace matrix sets, which are then vertically concatenated to obtain the first and second joint shift matrices. Generalized eigenvalue decomposition is performed on the joint matrix bundle, limiting the number of generalized eigenvalues ​​to the matrix bundle decomposition order, yielding the reference propagation poles. The time delay components are assigned in ascending order of phase angle according to the reference propagation poles. The same processing is then applied to each partial discharge pulse segment to obtain the segment propagation poles. Indication matching is performed according to the minimum phase angle difference, and the components are converted into candidate time delay components based on the sampling time interval, resulting in a candidate time delay component set.

[0040] The candidate time delay components are grouped according to their sequence numbers, and their trajectories are formed according to the order of the node pulse sequences. The absolute difference between candidate time delay components with the same sequence number corresponding to adjacent partial discharge pulse segments is calculated to obtain the first amplitude variation sequence. For the middle sequence position, the maximum value of the previous, current, and next positions is taken, and the larger value of the two adjacent positions for the first and last positions is taken to obtain the second amplitude variation sequence. The median amplitude variation of the time delay components is used as the amplitude variation threshold, and the median stability of the candidate time delay components is used as the stability threshold. The stability of the time delay components is obtained by the ratio of the number of stability comparisons to the number of comparisons. Candidate time delay components whose stability does not reach the stability threshold are eliminated through a pseudo-time delay elimination mechanism, resulting in the initial effective time delay component set.

[0041] Table 1 Comparison of Partial Discharge Localization Treatment Results

[0042] The initial effective time delay component set is grouped according to the time delay component index and cable monitoring nodes. The difference between the corresponding retained components of two cable monitoring nodes under the same time delay component index is calculated to obtain the inter-node propagation time difference set. Candidate partial discharge locations are calculated based on the inter-node propagation time difference set, monitoring node position parameters, and cable propagation velocity parameters. The reconstructed propagation time difference is calculated based on the cable path distance from the candidate partial discharge location to the two cable monitoring nodes. The absolute difference between the reconstructed propagation time difference and the inter-node propagation time difference is determined as the reconstructed time difference residual. Twice the sampling time interval, i.e., 20 nanoseconds, is set as the reconstructed time difference residual threshold. Candidate partial discharge locations and their corresponding retained components that exceed the threshold are removed to obtain the effective time delay component set and the effective partial discharge location set. The stability of the time delay component corresponding to each effective partial discharge location is normalized to obtain the location fusion weight, which is then weighted and calculated to output the partial discharge location.

[0043] As shown in Table 1, the absolute error of the fixed-order processing method in the five samples ranged from 31.7 meters to 47.8 meters, while the corresponding absolute error of the present invention ranged from 6.8 meters to 8.6 meters. Sample S3 had nine candidate delay components, the SORTE algorithm determined the effective propagation components to be five, the adaptive model order constraint mechanism limited the matrix bundle decomposition object to five propagation components, and the pseudo-delay elimination mechanism retained five delay components, thus adjusting the positioning result from 873.5 meters to 838.6 meters. The average delay component stability of the five samples was not lower than 0.81, and the maximum reconstruction time difference residual was less than 20 nanoseconds, indicating that the retained components have continuity and conform to the corresponding propagation relationship.

[0044] The results of this embodiment show that node sampling offset correction, pulse energy centroid sampling point alignment, and amplitude normalization can form a consistent node pulse sequence corresponding to the monitoring nodes across the cable; the number of effective propagation components determined by the SORTE algorithm is used to improve the adaptive model order constraint of the Matrix Pencil algorithm, which can reduce the invalid propagation components introduced by the fixed order; the continuous screening of candidate delay component trajectories, delay component stability, and reconstruction time difference residuals can eliminate pseudo-delays with large fluctuations, and output the partial discharge position according to the position fusion weight, thereby reducing the impact of attenuation, dispersion, and phase velocity frequency variation on the positioning results.

[0045] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for locating partial discharge in cables, characterized in that, include: The monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences of the cable monitoring nodes are collected and preprocessed to obtain the node pulse sequence. The node pulse sequence is subjected to sliding embedding processing according to the number of rows and columns of the matrix to obtain the Hankel matrix; The Hankel matrix is ​​subjected to eigenvalue decomposition, and the second-order statistics of the interval between adjacent eigenvalues ​​are calculated to obtain a sequence of second-order statistics. The number of effective propagation components is determined based on the local minimum locations in the second-order statistic sequence. The effective propagation component number is written into the improved Matrix Pencil algorithm, which includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism, to obtain the matrix bundle constraint parameter set. Based on the set of matrix bundle constraint parameters, matrix bundle parameter estimation is performed on the Hankel matrix to obtain a set of candidate time delay components; According to the arrangement order of the node pulse sequence, read the candidate delay components with the same sequence number from the candidate delay component set, calculate the change amplitude of the delay component, and determine the stability of the delay component; Candidate time delay components whose stability did not reach the time delay component stability threshold were removed from the matrix bundle constraint parameter set to obtain the effective time delay component set. The partial discharge location was then calculated based on the effective time delay component set, the monitoring node location parameters, and the cable propagation speed parameters.

2. The method for locating partial discharge in cables according to claim 1, characterized in that, The monitoring node location parameters, cable propagation velocity parameters, and partial discharge pulse sequences of the cable monitoring nodes are collected and preprocessed, specifically as follows: Collect the monitoring node location parameters and cable propagation speed parameters of the cable monitoring nodes, and establish a propagation reference table between cable nodes; A partial discharge pulse sequence was collected, and the pulse rising edge interval, peak sampling point, and pulse energy centroid sampling point corresponding to each cable monitoring node were extracted to obtain a node pulse index table. Based on the propagation reference table between cable nodes, cross-node pulse timing matching is performed on the node pulse index table, and node sampling offset is established based on the index offset difference between the matched peak sampling point and the pulse energy centroid sampling point. The propagation reference table between cable nodes is corrected based on the node sampling offset, and a matching time window is established; Candidate segments are collected from the node pulse index table according to the matching time window to obtain a set of candidate node pulse segments. Segment alignment is performed on the pulse energy centroid sampling points in the candidate node pulse segment set, and amplitude normalization is performed to obtain the node pulse sequence.

3. The method for locating partial discharge in cables according to claim 1, characterized in that, The sliding embedding process of the node pulse sequence according to the number of matrix rows and columns is specifically as follows: Calculate the amplitude difference between adjacent sampling points of the node pulse sequence according to the sampling order, and mark the sampling points where the amplitude difference changes from positive to non-positive to obtain the pulse main peak index set; Centered on the pulse main peak index set, the monotonically increasing sampling length before the peak is counted forward, and the monotonically decreasing sampling length after the peak is counted backward, thus obtaining the main response width set; Based on the set of main response widths, partial discharge pulse segments with main response widths smaller than the preset embedding reference width are filtered out to obtain the pulse sequence of the node to be embedded. The number of rows and columns of the matrix are determined based on the sampling length of the pulse sequence of the node to be embedded; The pulse sequence of the node to be embedded is sampled point by point according to the number of rows and columns of the matrix, and the same sampling number and corresponding sampling value are written to the same anti-diagonal position to obtain the Hankel matrix.

4. The method for locating partial discharge in cables according to claim 1, characterized in that, The eigenvalue decomposition of the Hankel matrix and the calculation of the second-order statistic of the interval between adjacent eigenvalues ​​are specifically as follows: Multiplying the transpose of the Hankel matrix with the Hankel matrix yields the eigencorrelation matrix; The eigenvalue correlation matrix is ​​decomposed to extract the magnitude of each eigenvalue, and then sorted in descending order of eigenvalue magnitude to obtain the eigenvalue sequence. The difference between the amplitudes of adjacent eigenvalues ​​in the eigenvalue sequence is calculated sequentially and then normalized to obtain the eigenvalue interval sequence. Starting from each sequence position in the eigenvalue interval sequence, extract the eigenvalue interval from the current sequence position to the last sequence position to obtain the tail interval subsequence; Calculate the mean interval of each tail interval subsequence, and calculate the mean squared difference between each feature value interval and the corresponding mean interval to obtain the tail discrete quantity sequence; Replace the zero values ​​in the tail discrete quantity sequence with preset positive lower limit values, and calculate the ratio of the next tail discrete quantity to the previous tail discrete quantity in turn to obtain the second-order statistical quantity sequence.

5. The method for locating partial discharge in cables according to claim 1, characterized in that, The determination of the number of effective propagation components based on the local minimum position in the second-order statistic sequence is specifically as follows: Select the current second-order statistic sequentially from the second-to-last position of the second-order statistic sequence; The SORTE algorithm is used to compare the current second-order statistic with the previous and next second-order statistics respectively, and the sequence positions where the current second-order statistic is less than both the previous and next second-order statistics are marked as candidate minimum positions. Starting from the position after the minimum position of each candidate, extract the second-order statistics up to the end of the second-order statistics sequence to obtain the candidate tail subsequence, and calculate the tail discreteness of each candidate tail subsequence. Calculate the mean of the first and second order statistics corresponding to each candidate minimum position and the mean of the first and second order statistics, and calculate the difference between the mean and the current second order statistic to obtain the minimum concave amplitude. Candidate minimum positions that are filtered out based on the tail dispersion and the minimum concave amplitude, where the tail dispersion exceeds a preset dispersion threshold and the minimum concave amplitude does not reach a preset concave threshold, are obtained as a set of effective minimum positions. The SORTE algorithm is used to select the effective minimum location with the smallest corresponding second-order statistic from the set of effective minimum locations, and to determine the number of effective propagation components.

6. The method for locating partial discharge in cables according to claim 1, characterized in that, The improved MatrixPencil algorithm includes an adaptive model order constraint mechanism and a pseudo-delay elimination mechanism, specifically: By setting the number of effective propagation components to the matrix bundle decomposition order through an adaptive model order constraint mechanism, the first matrix bundle constraint parameters are obtained. The adaptive model order constraint mechanism sets the positions of several sequences of the first effective propagation components as reserved positions and the remaining sequence positions as truncated positions according to the arrangement order of the eigenvalue sequences, thus obtaining the second matrix bundle constraint parameters; Based on the first and second matrix bundle constraint parameters, the eigenvalues ​​and eigenvectors corresponding to the retained positions are set as matrix bundle parameter estimation objects, and the number of matrix bundle parameter estimation objects is limited to the matrix bundle decomposition order, thus obtaining the order constraint parameter set; The pseudo-delay elimination mechanism sets the condition for eliminating candidate delay components when the stability of the delay component does not reach the stability threshold, and sets the condition for retaining candidate delay components when the stability of the delay component reaches the stability threshold, thus obtaining the first pseudo-delay screening parameters. The pseudo-delay elimination mechanism sets adjacent partial discharge pulse segments as comparison objects for candidate delay components with the same sequence number according to the arrangement order of partial discharge pulse segments in the node pulse sequence, and sets the number of groups of adjacent partial discharge pulse segments as the number of comparisons to obtain the second pseudo-delay screening parameters. Based on the first pseudo-delay screening parameter and the second pseudo-delay screening parameter, the ratio of the number of times the change amplitude of the delay component does not exceed the change amplitude threshold to the number of comparisons is set as the screening criterion for candidate delay components and screening is performed to obtain the pseudo-delay elimination parameter group. The order constraint parameter set and the pseudo-delay elimination parameter set are combined to obtain the matrix bundle constraint parameter set.

7. The method for locating partial discharge in cables according to claim 1, characterized in that, The matrix bundle parameter estimation of the Hankel matrix based on the matrix bundle constraint parameter set is specifically as follows: Based on the sampling range of the partial discharge pulse segment, the matrix elements corresponding to the anti-diagonal positions are extracted from the Hankel matrix to obtain the segment Hankel matrix; Based on the second matrix bundle constraint parameters in the matrix bundle constraint parameter set, the Hankel matrix of each segment is decomposed into eigenvalues, and several eigenvalues ​​and corresponding eigenvectors of the first effective propagation component are retained to obtain the segment constraint signal subspace. Based on the first matrix bundle constraint parameters in the matrix bundle constraint parameter set, the dimension of each segment constraint signal subspace is limited to the matrix bundle decomposition order, and the last row and the first row of each segment constraint signal subspace are deleted respectively to obtain the first shift subspace matrix set and the second shift subspace matrix set. According to the arrangement order of partial discharge pulse segments, the first shift subspace matrix set and the second shift subspace matrix set are longitudinally spliced ​​to obtain the first joint shift matrix and the second joint shift matrix; The number of generalized eigenvalues ​​of the joint matrix bundle formed by the first joint shift matrix and the second joint shift matrix is ​​limited to the order of matrix bundle decomposition, and the generalized eigenvalue decomposition is performed on the joint matrix bundle to obtain the reference propagation pole. The time delay components are assigned serial numbers according to the phase angle ascending order of the reference propagation poles, and the first and second shift subspace matrices corresponding to each partial discharge pulse segment are subjected to generalized eigenvalue decomposition to obtain the segment propagation poles. Each segment propagation pole is assigned a corresponding time delay component number in the manner that the phase angle difference with the reference propagation pole is minimized. The segment propagation poles are then converted into candidate time delay components based on the sampling time interval of the node pulse sequence, thus obtaining a set of candidate time delay components.

8. The method for locating partial discharge in cables according to claim 1, characterized in that, The step involves reading candidate delay components with the same sequence number from the candidate delay component set according to the arrangement order of the node pulse sequence, calculating the change amplitude of the delay component, and determining the stability of the delay component. Specifically: The candidate time delay components are grouped according to their sequence numbers, and the candidate time delay components in each group are sorted according to the order of their corresponding node pulse sequences to obtain the candidate time delay component trajectories. Two candidate time delay components corresponding to adjacent partial discharge pulse segments are extracted sequentially from the trajectory of each candidate time delay component to obtain the adjacent time delay comparison group; Calculate the absolute difference between two candidate time delay components in each adjacent time delay comparison group to obtain the first change amplitude sequence; From the second sequence position to the second-to-last sequence position of the first change amplitude sequence, extract the first change amplitude corresponding to the previous sequence position, the current sequence position, and the next sequence position respectively, and take the maximum value of the three as the change amplitude of the time delay component corresponding to the current sequence position; Extract the first change amplitude corresponding to the first and second positions in the first change amplitude sequence, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the first position. Extract the first change amplitude corresponding to the second to last position and the last position, and take the larger of the two values ​​as the time delay component change amplitude corresponding to the last position. Arrange the time delay component changes corresponding to the current sequence position, the first position, and the last position in sequence according to their corresponding first changes in the first change magnitude sequence to obtain the second change magnitude sequence; The number of times the time delay component change amplitude in the second change amplitude sequence does not exceed the change amplitude threshold is counted to obtain the number of stable comparisons. The number of stable comparisons is then divided by the number of comparisons to obtain the stability of the time delay component.

9. The method for locating partial discharge in cables according to claim 1, characterized in that, The calculation of the partial discharge location specifically involves: The initial set of effective time delay components is determined based on the first pseudo-delay screening parameter in the matrix bundle constraint parameter set; The initial effective time delay component set is grouped according to the time delay component sequence number and cable monitoring node. The difference between the corresponding retained components of two cable monitoring nodes under the same time delay component sequence number is calculated to obtain the propagation time difference set between nodes. Based on the set of propagation time differences between nodes, the location parameters of monitoring nodes, and the cable propagation speed parameters, the candidate partial discharge locations corresponding to each time delay component number are calculated respectively. Based on the cable path distance and cable propagation speed parameters between each candidate partial discharge location and the corresponding cable monitoring node, the reconstruction propagation time difference of the corresponding node pair is calculated, and the absolute difference between the reconstruction propagation time difference and the propagation time difference between nodes is calculated to obtain the reconstruction time difference residual. Candidate partial discharge locations and their corresponding retained components that have reconstructed time difference residuals exceeding the reconstructed time difference residual threshold are removed to obtain the effective time delay component set and the effective partial discharge location set. The stability of the time delay component corresponding to each effective partial discharge location in the effective partial discharge location set is normalized to obtain the location fusion weight. The effective partial discharge locations are calculated by weighting the location fusion weights to obtain the partial discharge locations.

10. A system for locating partial discharge in cables, used to perform the method for locating partial discharge in cables according to any one of claims 1 to 9, characterized in that, include: The data processing module is used to collect monitoring node location parameters, cable propagation speed parameters, and partial discharge pulse sequences, and to preprocess them to obtain node pulse sequences; The matrix construction module is used to perform sliding embedding processing on the node pulse sequence to obtain the Hankel matrix; The propagation component determination module is used to perform eigenvalue decomposition on the Hankel matrix, obtain a second-order statistic sequence, and determine the number of effective propagation components. The constraint parameter generation module is used to generate a matrix bundle constraint parameter set based on the effective propagation component number and time delay. The time delay component estimation module is used to estimate the matrix bundle parameters of the Hankel matrix based on the matrix bundle constraint parameter set, and obtain a set of candidate time delay components. The stability calculation module is used to calculate the stability of the time delay components based on the candidate time delay component set. The positioning module is used to calculate the location of partial discharge based on the candidate time delay component set, the stability of the time delay components, the monitoring node position parameters, and the cable propagation speed parameters.

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