A high-impedance and low-impedance compatible power cable fault location method

Abstract

This invention discloses a fault location method for power cables compatible with both high and low resistance, comprising: connecting to a test terminal to acquire voltage and current responses, determining the initial impedance state, and setting scanning excitation parameters; applying an exponentially increasing scanning excitation signal, calculating the complex impedance gradient characteristics, and determining the threshold energy level range; expanding a fractal excitation sequence within the threshold range, collecting propagation response data, and constructing a response matrix; normalizing the propagation response matrix data, calculating the cross-scale correlation strength, and forming a consistency curve; constructing a propagation consistency vector field, performing density clustering and topology analysis, and determining the fault stability region; and calculating the fault location based on the propagation time at the center of the stability region and the propagation velocity. This invention achieves stable identification and accurate location of faults in both high-resistance and low-resistance power cables through exponentially increasing scanning excitation and fractal energy spectrum multi-scale propagation analysis.

Description

Technical Field

[0001] This invention relates to the field of power cable fault detection and location technology, and in particular to a power cable fault location method compatible with both high and low resistance. Background Technology

[0002] Power cables, as crucial transmission and distribution carriers in power systems, are widely used in urban power grids, industrial power supply systems, and underground utility tunnels. Because power cables operate in complex environments, they are susceptible to insulation aging, mechanical damage, moisture corrosion, and overvoltage surges, leading to various types of faults, including low-resistance short-circuit faults, high-resistance grounding faults, and intermittent discharge faults. To ensure the safe and stable operation of power systems, it is essential to quickly and accurately locate the fault after a power cable fault occurs. Currently, commonly used power cable fault location techniques include the pulse reflection method, traveling wave method, and high-voltage flashover method. These methods typically involve injecting test signals into the cable and analyzing the characteristic changes in the reflected or propagated signals to deduce the location of the cable fault.

[0003] However, in practical applications, existing technologies still have certain limitations when dealing with cable faults with different impedance characteristics. For low-impedance faults, the pulse reflection signal is relatively obvious, and the location accuracy is relatively high. However, for high-impedance faults or nonlinear discharge faults, the fault point often fails to stably trigger a significant reflection signal, resulting in weak signal characteristics and greater noise interference, thus affecting the accuracy of fault location. Traditional methods typically use a single excitation signal or single-scale signal analysis, which is difficult to fully extract fault response characteristics in complex propagation environments. Especially when the cable line is long, signal attenuation is significant, and multipath reflections exist, the location error is likely to increase or misjudgment may occur.

[0004] To address the aforementioned issues, existing technologies still fall short in terms of stability in high-resistance fault identification, utilization of multi-scale propagation signals, and feature extraction capabilities in complex noise environments. Particularly in cable lines where high-resistance and low-resistance faults coexist, traditional methods lack a unified localization mechanism capable of adapting to different fault characteristics simultaneously, making it difficult to achieve stable identification and accurate localization of fault response signals.

[0005] Therefore, how to provide a fault location method for power cables that is compatible with both high and low resistance 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 power cable fault location method compatible with both high and low impedance. This invention utilizes an exponentially increasing scanning excitation signal triggering mechanism, fractal energy spectrum generation and a multi-scale propagation response acquisition structure, and a density peak clustering and persistent homology analysis method based on a propagation consistency vector field. This allows for multi-scale feature extraction and stability domain identification of power cable fault response signals, achieving stable triggering, effective extraction, and accurate location of fault signals from cables with different impedance characteristics. This invention enhances fault response characteristics even when high-impedance faults are unlikely to trigger significant reflection signals. It improves signal identification stability through multi-level propagation response analysis, offering advantages such as high fault triggering stability, strong noise resistance, and high location accuracy.

[0007] A method for locating faults in power cables that is compatible with both high and low resistance according to an embodiment of the present invention includes:

[0008] Connect the power cable fault location device to the test end of the power cable to be tested, obtain the initial voltage response and current response of the power cable, determine the initial impedance state of the power cable, and set the starting energy level, energy level increment step size and scanning range of the scanning excitation signal.

[0009] A scanning excitation signal with an exponentially increasing amplitude is applied to the power cable. The amplitude gradient and phase gradient of the voltage-current complex impedance are calculated in real time. When the two gradients jump synchronously and are accompanied by a current spike, the fault point is determined to trigger the threshold induced discharge, and the corresponding energy level interval is recorded as the threshold energy level interval.

[0010] A fractal energy spectrum generator performs self-similar energy level expansion centered on the threshold energy level interval to generate a fractal excitation sequence. The propagation response of the power cable is collected under the corresponding fractal time sampling window. The propagation response matrix is ​​constructed by mapping the power cable propagation response according to the energy level index and the time index.

[0011] The propagation response matrix is ​​normalized, and the cross-scale correlation coefficient between adjacent energy levels is calculated. The cross-scale consistency curve is formed by iterative accumulation, and the aligned propagation response dataset is obtained.

[0012] Based on the aligned propagation response dataset, a sliding window embedding is performed in the spatial location domain to construct a propagation consistency vector field. Density peak clustering and persistent cohomology analysis are performed on the propagation consistency vector field to extract the persistent main peak cluster and determine the central region of the main peak cluster as the fault stability region.

[0013] The fault response propagation time is determined based on the center moment of the fault stability region on the propagation response time axis, and the location of the power cable fault point is calculated in combination with the power cable signal propagation speed.

[0014] Optionally, determining the initial impedance state of the power cable includes:

[0015] An initial detection signal is applied to the test end of the power cable, and the voltage and current signals of the power cable are collected simultaneously. The equivalent impedance amplitude and impedance phase of the power cable are calculated based on the voltage and current signals.

[0016] The equivalent impedance amplitude is compared with a preset impedance threshold. When the equivalent impedance amplitude is greater than the preset impedance threshold, it is determined to be a high impedance state. When the equivalent impedance amplitude is less than or equal to the preset impedance threshold, it is determined to be a low impedance state. The initial impedance state of the power cable is determined based on the determination result.

[0017] Optionally, the setting of the starting energy level, energy level increment step size, and scan interval of the scan excitation signal includes:

[0018] Obtain the equivalent impedance amplitude and impedance phase corresponding to the initial impedance state. When the power cable is in a low impedance state, set the starting energy level of the scanning excitation signal to the first preset energy level and set the energy level increment step size to the first preset step size.

[0019] When the power cable is in a high impedance state, the starting energy level of the scanning excitation signal is set to the second preset energy level, and the energy level increment step size is set to the second preset step size. The second preset energy level is greater than the first preset energy level, and the second preset step size is less than the first preset step size.

[0020] A scanning interval is constructed with the initial energy level as the lower limit of the scan and the preset maximum allowable energy level as the upper limit of the scan. Scan excitation signals are generated step by step within the scanning interval according to the initial energy level and the energy level increment step size. The energy level difference between two adjacent scan excitation signals is equal to the energy level increment step size. The scanning interval setting is terminated when the scan excitation signal generated step by step reaches the preset maximum allowable energy level.

[0021] Optionally, the scanning excitation signal is generated through a multi-level excitation logic combination structure, which includes a first inductor L1, a second inductor L2, a third inductor L3, and resistors R4, R5, and R6.

[0022] Optionally, the step of determining the fault point trigger threshold induced discharge and recording the corresponding energy level interval as the threshold energy level interval includes:

[0023] According to the set scanning excitation signal parameters, a scanning excitation signal with an amplitude that increases exponentially is continuously applied to the power cable, and a corresponding energy level identifier is assigned to each energy level scanning excitation signal.

[0024] During the application of the scanning excitation signal for each energy level, the voltage and current responses corresponding to the energy level are synchronously acquired. Based on the acquired voltage and current responses, the complex impedance characteristics corresponding to the energy level are obtained, and the amplitude and phase characteristics of the complex impedance characteristics are extracted.

[0025] The difference in amplitude between two adjacent energy levels is used as the amplitude gradient, and the difference in phase between two adjacent energy levels is used as the phase gradient. Peak characteristic parameters are extracted from the current response at each energy level.

[0026] The nonlinear consistency criterion is calculated from the voltage and current responses at each energy level. The nonlinear consistency criterion is composed of the following three conditions being met simultaneously:

[0027] The magnitude gradient characterization exceeds a preset magnitude gradient threshold and the phase gradient characterization exceeds a preset phase gradient threshold;

[0028] The peak feature representation exceeds the preset peak threshold;

[0029] The voltage and current responses exhibit nonlinear loop characteristics within the same sampling window corresponding to the energy level. The nonlinear loop characteristics are determined by the increase in the loop area of ​​the voltage-current phase plane trajectory exceeding a preset loop threshold, and the increase in the loop area changes abruptly relative to the increase in the loop area of ​​the previous energy level.

[0030] When the nth energy level satisfies the nonlinear consistency criterion, the nth energy level is recorded as the threshold trigger energy level. The scanning excitation signal of the (n+1)th energy level is then applied for verification. When both the nth and (n+1)th energy levels satisfy the nonlinear consistency criterion, the power cable fault point is determined to trigger threshold induced discharge, and the energy level range between the nth and (n+1)th energy levels is determined as the threshold energy level interval.

[0031] Optionally, the step of constructing a propagation response matrix by mapping the propagation response of the power cable according to the energy level index and the time index includes:

[0032] Read the determined threshold energy level range and determine the center energy level of the threshold energy level range as the expansion center energy level. At the same time, determine the fractal scaling factor, the number of fractal expansion layers, and the sampling window length corresponding to each layer.

[0033] A fractal excitation sequence is generated using a fractal energy spectrum generator, which consists of a fractal energy level expansion unit, a spectrum folding index unit, and a time window synchronization scheduling unit, wherein:

[0034] The fractal energy level expansion unit takes the expansion center energy level as the reference, and generates each layer of fractal energy level recursively according to the fractal scaling factor to form a fractal energy level sequence.

[0035] The time window synchronization scheduling unit allocates a corresponding sampling time window for each fractal energy level and generates a synchronization trigger signal;

[0036] The spectral folding index unit assigns an energy level index to each fractal energy level and defines the mapping relationship between the energy level index and the sampling window index;

[0037] Fractal energy level excitation is applied to the power cable according to the fractal excitation sequence. During the application of each fractal energy level excitation, the voltage response and current response of the power cable are synchronously collected in the corresponding sampling time window according to the synchronous trigger signal.

[0038] For each fractal energy level excitation, a consistent shaping operation is performed on the voltage and current responses. Specifically, the voltage-current phase plane trajectory is constructed using the in-phase sampling pairs of the voltage and current responses. The loop area features, loop center offset features, and current spike features of the voltage-current phase plane trajectory are extracted and bound to the corresponding fractal energy level index to form a propagation response feature vector.

[0039] According to the mapping relationship defined by the spectral folding index unit, the propagation response feature vectors of each layer are folded and arranged in a two-dimensional coordinate system of energy level index and sampling window index to construct the propagation response matrix.

[0040] Optionally, the step of forming a cross-scale consistency curve through iterative accumulation to obtain the aligned propagation response dataset includes:

[0041] The propagation response matrix is ​​normalized, which includes scaling the propagation response feature vector corresponding to each energy level index in the propagation response matrix according to its own amplitude range.

[0042] The cross-scale correlation coefficient is calculated between adjacent energy level indices, specifically as follows:

[0043] At the same sampling time index, the propagation response feature vectors of two adjacent energy level indices are taken respectively. The components of the two vectors are multiplied and summed to obtain the instantaneous similarity.

[0044] Within the sampling time index range of two adjacent energy level indices, the instantaneous similarity is averaged by a sliding window to obtain the cross-scale correlation coefficient at the sampling time index. The cross-scale correlation coefficients corresponding to all sampling time indices are then combined to form a cross-scale correlation sequence.

[0045] Phase consistency correction is performed on cross-scale correlated sequences, specifically as follows:

[0046] A finite shift search is performed on the sampling time axis for the propagation response feature vectors of two adjacent energy level indices. The sum of instantaneous similarities corresponding to each shift amount is calculated. The shift amount with the largest sum of instantaneous similarities is selected as the alignment shift amount. The alignment shift amount is used to correct the cross-scale correlation sequence to obtain the corrected cross-scale correlation sequence.

[0047] The cross-scale consistency curve is generated based on the corrected cross-scale correlation sequence, specifically as follows:

[0048] The corrected cross-scale correlation coefficient at each sampling time index is used as the consistency accumulation input, and iterative accumulation is performed sequentially from low to high energy level index. Energy level consistency gating conditions are introduced in each iteration accumulation.

[0049] The energy level consistency gating condition is that the cross-scale correlation coefficients of two adjacent energy level indices are allowed to accumulate when they simultaneously satisfy the magnitude consistency threshold and the direction consistency threshold. If they are not satisfied, accumulation is suppressed. After completing the iterative accumulation of all adjacent energy level indices, the cross-scale consistency curve is obtained.

[0050] Based on the sampling time index corresponding to the local maxima of the cross-scale consistency curve, adaptive time alignment processing is performed on the propagation response matrix to obtain the aligned propagation response dataset.

[0051] Optionally, the step of performing density peak clustering and persistent cohomology analysis on the propagation consistency vector field, extracting persistent main peak clusters, and determining the central region of the main peak clusters as the fault stability region includes:

[0052] The sampling time index of the aligned propagation response dataset is converted into a spatial location index according to the propagation speed of the power cable signal, so that the aligned propagation response dataset forms a corresponding propagation response sequence in the spatial location domain;

[0053] In the spatial location domain, the sliding window length and window step size are set, and sliding window embedding is performed on the propagation response sequence. In each sliding window, multi-scale propagation response features are extracted in order of energy level index. The cross-scale correlation strength, energy level consistency gating state and nonlinear loop features between adjacent energy levels are jointly encoded to generate the propagation consistency feature vector corresponding to the spatial location. The propagation consistency feature vectors corresponding to all spatial locations are arranged in order of spatial location index to form a propagation consistency vector field.

[0054] Scale-preserving neighborhood distance calculation is performed on the propagation consistency vector field. For any two spatial locations, the difference between cross-scale correlated components, the difference between energy level gated components, and the difference between nonlinear loop components are calculated respectively. The vector field distance is obtained by weighted summation according to preset weights. Neighborhood relationship is constructed in the spatial location domain based on the vector field distance.

[0055] Density peak clustering is performed on the propagation consistency vector field in terms of neighborhood relations. For each spatial location, the local density value and density gradient distance are calculated. The peak center is determined based on the spatial location where the local density value and density gradient distance both reach the clustering threshold. The remaining spatial locations in the neighborhood are assigned to the corresponding peak center according to the vector field distance to form a peak cluster.

[0056] Persistent cohomology analysis is performed on the peak clusters. Specifically, the neighborhood of the peak clusters is expanded from small to large using the vector field distance as the filtering parameter. The generation and disappearance times of the connected components during the neighborhood expansion process are recorded. Connected components with earlier generation times and later disappearance times are selected as persistent main peak clusters. The central region of the persistent main peak clusters in the spatial location domain is determined as the fault stability region.

[0057] Optionally, the calculation of the power cable fault location based on the power cable signal propagation speed includes:

[0058] Read the fault stability domain, determine the sampling time index corresponding to the center position of the fault stability domain on the propagation response time axis, and record the propagation time corresponding to the sampling time index as the fault response propagation time;

[0059] The fault propagation distance is calculated based on the fault response propagation time and the power cable signal propagation speed. A distance mapping relationship is established based on the calculated fault propagation distance and the power cable line length information, and the fault propagation distance is converted into the fault spatial location on the power cable.

[0060] The fault location is matched with the geographical coordinates of the power cable line to output the fault location result of the power cable.

[0061] The beneficial effects of this invention are:

[0062] Compared with existing power cable fault location technologies, this invention applies a scanning excitation signal with an exponentially increasing amplitude and determines threshold-induced discharge by combining the changes in complex impedance characteristics of voltage and current responses. This allows cable fault points to be triggered under relatively stable excitation conditions, enhancing the observability of high-resistance fault points. Through joint analysis of voltage-current response characteristics, it can effectively distinguish between normal propagation signals and nonlinear discharge signals, improving the reliability of fault triggering identification. This enables stable detection of high-resistance faults even in complex electromagnetic environments, addressing the insufficient sensitivity of traditional single-pulse excitation methods in high-resistance fault detection.

[0063] This invention utilizes a fractal energy spectrum generator to perform self-similar energy level expansion across threshold energy level ranges, forming a multi-scale fractal excitation sequence. Simultaneously, it acquires the propagation response of power cables within the corresponding fractal time sampling window, thereby constructing a propagation response matrix. This enables the acquisition of multi-dimensional propagation features at different energy level scales, resulting in hierarchical signal features in the cable fault response across both energy and time dimensions, effectively improving the resolvability of the propagation signal. By introducing propagation response feature vectors to construct a propagation consistency vector field and embedding it within a sliding window in the spatial location domain, fault-related features can be stably extracted in complex propagation environments, enhancing the robustness of signal analysis.

[0064] This invention utilizes density peak clustering and persistent cohomology analysis of the propagation consistency vector field to identify persistent main peak structures in multi-scale propagation characteristics. The corresponding spatial region is then defined as the fault stability domain. By combining the propagation response time and cable signal propagation velocity, the fault location is calculated, thereby achieving precise localization of power cable faults. This method not only effectively reduces the impact of noise interference and multipath reflection on the localization results but also maintains stable localization performance even when high-resistance and low-resistance faults coexist, significantly improving the accuracy and reliability of power cable fault localization. Attached Figure Description

[0065] 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:

[0066] Figure 1 This is a flowchart of a power cable fault location method that is compatible with both high and low resistance proposed in this invention.

[0067] Figure 2 This is a schematic diagram illustrating the process of constructing the propagation consistency vector field for a power cable fault location method compatible with both high and low resistance proposed in this invention.

[0068] Figure 3 This is a schematic diagram of the high and low voltage logic combination structure of a power cable fault location method that is compatible with both high and low resistance proposed in this invention. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0070] refer to Figure 1 , Figure 2 and Figure 3 A method for locating faults in power cables that is compatible with both high and low resistance includes:

[0071] Connect the power cable fault location device to the test end of the power cable to be tested, obtain the initial voltage response and current response of the power cable, determine the initial impedance state of the power cable, and set the starting energy level, energy level increment step size and scanning range of the scanning excitation signal.

[0072] A scanning excitation signal with an exponentially increasing amplitude is applied to the power cable. The amplitude gradient and phase gradient of the voltage-current complex impedance are calculated in real time. When the two gradients jump synchronously and are accompanied by a current spike, the fault point is determined to trigger the threshold induced discharge, and the corresponding energy level interval is recorded as the threshold energy level interval.

[0073] A fractal energy spectrum generator performs self-similar energy level expansion centered on the threshold energy level interval to generate a fractal excitation sequence. The propagation response of the power cable is collected under the corresponding fractal time sampling window. The propagation response matrix is ​​constructed by mapping the power cable propagation response according to the energy level index and the time index.

[0074] The propagation response matrix is ​​normalized, and the cross-scale correlation coefficient between adjacent energy levels is calculated. The cross-scale consistency curve is formed by iterative accumulation, and the aligned propagation response dataset is obtained.

[0075] Based on the aligned propagation response dataset, a sliding window embedding is performed in the spatial location domain to construct a propagation consistency vector field. Density peak clustering and persistent cohomology analysis are performed on the propagation consistency vector field to extract the persistent main peak cluster and determine the central region of the main peak cluster as the fault stability region.

[0076] The fault response propagation time is determined based on the center moment of the fault stability region on the propagation response time axis, and the location of the power cable fault point is calculated in combination with the power cable signal propagation speed.

[0077] In this embodiment, determining the initial impedance state of the power cable includes:

[0078] An initial detection signal is applied to the test end of the power cable, and the voltage and current signals of the power cable are acquired simultaneously. The equivalent impedance amplitude and impedance phase of the power cable are calculated based on the voltage and current signals. The calculation of the equivalent impedance amplitude and impedance phase is as follows:

[0079] After an initial detection signal is applied to the test end of the power cable, voltage and current signals at the power cable port are simultaneously acquired. These voltage and current signals are obtained through a voltage sampling module and a current sampling module, and are then synchronously sampled and digitized by the signal acquisition unit.

[0080] After obtaining the synchronously sampled voltage and current data, the two signals are preprocessed, including removing DC components, filtering high-frequency noise, and time synchronization correction.

[0081] Based on the amplitude relationship between the voltage signal and the current signal at the corresponding sampling time, the proportional relationship between voltage and current is calculated to obtain the equivalent impedance amplitude of the power cable under the current detection signal.

[0082] Phase analysis is performed on voltage and current signals. By comparing the waveform position differences of the two signals within the same period, the phase offset of the voltage waveform relative to the current waveform is determined, and the impedance phase is obtained.

[0083] The equivalent impedance amplitude is compared with a preset impedance threshold. When the equivalent impedance amplitude is greater than the preset impedance threshold, it is determined to be a high impedance state. When the equivalent impedance amplitude is less than or equal to the preset impedance threshold, it is determined to be a low impedance state. The initial impedance state of the power cable is determined based on the determination result, where the preset impedance threshold is 125Ω.

[0084] In this embodiment, setting the starting energy level, energy level increment step size, and scanning interval of the scanning excitation signal includes:

[0085] Obtain the equivalent impedance amplitude and impedance phase corresponding to the initial impedance state. When the power cable is in a low impedance state, set the starting energy level of the scanning excitation signal to the first preset energy level and set the energy level increment step size to the first preset step size.

[0086] When the power cable is in a high impedance state, the starting energy level of the scanning excitation signal is set to the second preset energy level, and the energy level increment step size is set to the second preset step size. The second preset energy level is greater than the first preset energy level, and the second preset step size is less than the first preset step size.

[0087] A scanning interval is constructed with the initial energy level as the lower limit of the scan and the preset maximum allowable energy level as the upper limit of the scan. Scan excitation signals are generated step by step within the scanning interval according to the initial energy level and the energy level increment step size. The energy level difference between two adjacent scan excitation signals is equal to the energy level increment step size. The scanning interval setting is terminated when the scan excitation signal generated step by step reaches the preset maximum allowable energy level.

[0088] In this embodiment, the scanning excitation signal is generated through a multi-level excitation logic combination structure, which includes a first inductor L1, a second inductor L2, a third inductor L3, and resistors R4, R5, and R6.

[0089] In this embodiment, the step of determining the fault point trigger threshold induced discharge and recording the corresponding energy level interval as the threshold energy level interval includes:

[0090] According to the set scanning excitation signal parameters, a scanning excitation signal with an amplitude that increases exponentially is continuously applied to the power cable, and a corresponding energy level identifier is assigned to each energy level scanning excitation signal.

[0091] During the application of the scanning excitation signal for each energy level, the voltage and current responses corresponding to the energy level are synchronously acquired. Based on the acquired voltage and current responses, the complex impedance characteristics corresponding to the energy level are obtained, and the amplitude and phase characteristics of the complex impedance characteristics are extracted.

[0092] The difference in amplitude between two adjacent energy levels is used as the amplitude gradient, and the difference in phase between two adjacent energy levels is used as the phase gradient. Peak characteristic parameters are extracted from the current response at each energy level.

[0093] The nonlinear consistency criterion is calculated from the voltage and current responses at each energy level. The nonlinear consistency criterion is composed of the following three conditions being met simultaneously:

[0094] The magnitude gradient characterization exceeds a preset magnitude gradient threshold and the phase gradient characterization exceeds a preset phase gradient threshold;

[0095] The peak feature representation exceeds the preset peak threshold;

[0096] The voltage and current responses exhibit nonlinear loop characteristics within the same sampling window corresponding to the energy level. The nonlinear loop characteristic is determined by the increment of the loop area of ​​the voltage-current phase plane trajectory exceeding a preset loop threshold. Furthermore, the increment of the loop area changes abruptly relative to the increment of the loop area of ​​the previous energy level. The increment of the loop area of ​​the voltage-current phase plane trajectory refers to the difference between the area enclosed by the closed loop formed by the voltage-current change trajectory drawn in the phase plane with the voltage response signal as the abscissa and the current response signal as the ordinate within the same sampling window, and the loop area of ​​the voltage-current trajectory formed in the sampling window corresponding to the previous excitation energy level.

[0097] When the nth energy level satisfies the nonlinear consistency criterion, the nth energy level is recorded as the threshold trigger energy level. The scanning excitation signal of the (n+1)th energy level is then applied for verification. When both the nth and (n+1)th energy levels satisfy the nonlinear consistency criterion, the power cable fault point is determined to trigger threshold induced discharge, and the energy level range between the nth and (n+1)th energy levels is determined as the threshold energy level interval.

[0098] In this embodiment, the step of constructing a propagation response matrix by mapping the propagation response of the power cable according to the energy level index and the time index includes:

[0099] Read the determined threshold energy level range and determine the center energy level of the threshold energy level range as the expansion center energy level. At the same time, determine the fractal scaling factor, the number of fractal expansion layers, and the sampling window length corresponding to each layer.

[0100] A fractal excitation sequence is generated using a fractal energy spectrum generator, which consists of a fractal energy level expansion unit, a spectrum folding index unit, and a time window synchronization scheduling unit, wherein:

[0101] The fractal energy level expansion unit uses the expansion center energy level as a reference, and recursively generates each layer of fractal energy levels according to the fractal scaling factor to form a fractal energy level sequence. Specifically, the recursive generation of each layer of fractal energy levels according to the fractal scaling factor to form the fractal energy level sequence is as follows:

[0102] The central energy level is used as the reference energy level for fractal energy level expansion, and the central energy level is used as the initial reference point for the fractal energy level sequence.

[0103] According to the preset fractal scaling factor, the expansion is carried out recursively on both sides of the central energy level: in the high energy level direction, the energy level amplitude is increased layer by layer according to the fractal scaling factor to generate new energy levels, and in the low energy level direction, the energy level amplitude is decreased layer by layer according to the same fractal scaling factor to generate new energy levels, forming a multi-layer fractal expansion structure.

[0104] Arrange the central energy level and the energy levels generated recursively in each layer according to the generation order to obtain a fractal energy level sequence distributed around the unfolded central energy level;

[0105] The fractal scaling factor is a scale parameter used to control the proportional relationship between adjacent energy levels during the fractal energy level expansion process. When performing fractal energy level expansion, each newly generated energy level is based on the previous energy level and the ratio is recursively calculated according to the fractal scaling factor to maintain a stable proportional interval between energy levels. The fractal scaling factor is a scaling parameter greater than 1.

[0106] The time window synchronization scheduling unit allocates a corresponding sampling time window for each fractal energy level and generates a synchronization trigger signal;

[0107] The spectral folding index unit assigns an energy level index to each fractal energy level and defines a mapping relationship between the energy level index and the sampling time window index. This mapping relationship refers to establishing a one-to-one or sequential correspondence between the fractal energy level index and the sampling time window index, specifically:

[0108] Energy level index assignment: The fractal energy levels generated by the fractal energy level expansion unit are numbered according to the generation order to form an energy level index sequence. Each fractal energy level corresponds to a unique energy level index, which is used to identify the excitation state under different detection energy levels.

[0109] Sampling window indexing: The sampling time axis of the voltage response signal and the current response signal is divided into multiple continuous sampling windows of a fixed length. Each sampling window is numbered in chronological order to form a sampling window index sequence.

[0110] Establish index mapping relationship: According to the order of energy level application in the detection process, associate the detection stage corresponding to each fractal energy level with the collected sampling time window, so that each energy level index corresponds to one or more sampling time window indices, forming a mapping relationship between energy level index and sampling time window index;

[0111] Fractal energy level excitation is applied to the power cable according to the fractal excitation sequence. During the application of each fractal energy level excitation, the voltage response and current response of the power cable are synchronously collected in the corresponding sampling time window according to the synchronous trigger signal.

[0112] For each fractal energy level excitation, a consistent shaping operation is performed on the voltage and current responses. Specifically, the voltage-current phase plane trajectory is constructed using in-phase sampling pairs of the voltage and current responses. The loop area features, loop center offset features, and current spike features of the voltage-current phase plane trajectory are extracted and bound to the corresponding fractal energy level index to form a propagation response feature vector, where:

[0113] Loop area characteristic: refers to the area of ​​the loop region enclosed by the voltage-current phase plane trajectories constructed within the same sampling window of the voltage response and current response. It is obtained by performing area statistics on the closed loop formed by the phase plane trajectories and is used to characterize the degree of nonlinear hysteresis of the cable response.

[0114] Return line center offset characteristic: refers to the degree of offset of the return line center position of the voltage-current phase plane trajectory relative to the origin or reference center position of the phase plane. It is obtained by calculating the position of the geometric center of the return line trajectory and comparing it with the reference center. It is used to reflect the DC offset or asymmetric characteristics in the cable response.

[0115] Current spike characteristics: refers to the instantaneous increase or spike change characteristics that appear in the current response signal within the corresponding sampling window. It is extracted by detecting transient points in the current signal where the amplitude rises rapidly and exceeds the preset spike threshold, and is used to characterize fault discharge or transient conduction behavior.

[0116] According to the mapping relationship defined by the spectral folding index unit, the propagation response feature vectors of each layer are folded and arranged in a two-dimensional coordinate system of energy level index and sampling window index to construct the propagation response matrix. The row index of the propagation response matrix is ​​the energy level index, the column index is the sampling window index, and the matrix element is the propagation response feature vector that matches the corresponding energy level index and sampling window index.

[0117] In this embodiment, the step of forming a cross-scale consistency curve through iterative accumulation to obtain the alignment propagation response dataset includes:

[0118] The propagation response matrix is ​​normalized, which includes scaling the propagation response feature vector corresponding to each energy level index in the propagation response matrix according to its own amplitude range.

[0119] The cross-scale correlation coefficient is calculated between adjacent energy level indices, specifically as follows:

[0120] At the same sampling time index, the propagation response feature vectors of two adjacent energy level indices are taken respectively. The components of the two vectors are multiplied and summed to obtain the instantaneous similarity.

[0121] Within the sampling time index range of two adjacent energy level indices, the instantaneous similarity is averaged by a sliding window to obtain the cross-scale correlation coefficient at the sampling time index. The cross-scale correlation coefficients corresponding to all sampling time indices are then combined to form a cross-scale correlation sequence.

[0122] Phase consistency correction is performed on cross-scale correlated sequences, specifically as follows:

[0123] A finite shift search is performed on the sampling time axis for the propagation response feature vectors of two adjacent energy level indices. The sum of instantaneous similarities corresponding to each shift is calculated, and the shift with the largest sum of instantaneous similarities is selected as the alignment shift. The alignment shift is used to correct the cross-scale correlation sequence, resulting in the corrected cross-scale correlation sequence. Specifically, the sum of instantaneous similarities corresponding to each shift is calculated as follows:

[0124] Within a preset finite shift range, the propagation response feature vectors corresponding to two adjacent energy level indices are progressively shifted along the sampling time axis, with each shift corresponding to a candidate shift amount;

[0125] For each candidate shift amount, one of the propagation response feature vectors is shifted along the time axis according to the candidate shift amount, and compared point by point with the other propagation response feature vector in the overlapping sampling interval. For each corresponding sampling point, the instantaneous similarity is calculated based on the degree of difference of the feature components of the two vectors at the sampling point. The instantaneous similarity is used to characterize the degree of matching between the two propagation response features at the sampling time.

[0126] The instantaneous similarity of all corresponding sampling points under the current shift amount is accumulated to obtain the sum of instantaneous similarity corresponding to the candidate shift amount;

[0127] The cross-scale consistency curve is generated based on the corrected cross-scale correlation sequence, specifically as follows:

[0128] The corrected cross-scale correlation coefficient at each sampling time index is used as the consistency accumulation input, and iterative accumulation is performed sequentially from low to high energy level index. Energy level consistency gating conditions are introduced in each iteration accumulation.

[0129] The energy level consistency gating condition is that the cross-scale correlation coefficients of two adjacent energy level indices are allowed to accumulate when they simultaneously satisfy the magnitude consistency threshold and the direction consistency threshold. If they are not satisfied, accumulation is suppressed. After completing the iterative accumulation of all adjacent energy level indices, the cross-scale consistency curve is obtained.

[0130] Based on the sampling time index corresponding to the local maxima of the cross-scale consistency curve, adaptive time alignment processing is performed on the propagation response matrix to obtain the aligned propagation response dataset.

[0131] In this embodiment, the step of performing density peak clustering and persistent cohomology analysis on the propagation consistency vector field, extracting persistent main peak clusters, and determining the central region of the main peak clusters as the fault stability region includes:

[0132] The sampling time index of the aligned propagation response dataset is converted into a spatial location index according to the propagation speed of the power cable signal, so that the aligned propagation response dataset forms a corresponding propagation response sequence in the spatial location domain;

[0133] In the spatial location domain, the sliding window length and window step size are set, and sliding window embedding is performed on the propagation response sequence. In each sliding window, multi-scale propagation response features are extracted in order of energy level index. The cross-scale correlation strength, energy level consistency gating state and nonlinear loop features between adjacent energy levels are jointly encoded to generate the propagation consistency feature vector corresponding to the spatial location. The propagation consistency feature vectors corresponding to all spatial locations are arranged in order of spatial location index to form a propagation consistency vector field.

[0134] Scale-preserving neighborhood distance calculations are performed on the propagation consistency vector field. For any two spatial locations, the differences between cross-scale correlated components, energy level-gated components, and nonlinear loop components of the propagation consistency eigenvectors are calculated, and then weighted and summed according to preset weights to obtain the vector field distance. Neighborhood relationships are constructed in the spatial location domain based on the vector field distance, where:

[0135] The degree of difference between cross-scale correlation components refers to the comparison of cross-scale correlation components corresponding to two spatial locations on a scale-by-scale basis. It is obtained by statistically analyzing the degree of difference between the correlation response values ​​at each scale and is used to characterize the consistency difference in multi-scale propagation response at different spatial locations.

[0136] The difference between energy level gating components refers to the energy level-by-energy level comparison of the energy level gating response sequences corresponding to two spatial locations. It is obtained by calculating the difference in the change of gating state or gating strength of each energy level and is used to reflect the degree of difference in the triggering behavior of excitation energy levels at different spatial locations.

[0137] The degree of difference between nonlinear loop components refers to the comparison of the nonlinear loop characteristic parameters corresponding to two spatial locations. It is obtained by statistically analyzing the differences in changes between the loop area, loop center offset, or related loop indices, and is used to characterize the degree of difference in nonlinear response characteristics at different spatial locations.

[0138] Density peak clustering is performed on the propagation consistency vector field based on neighborhood relationships. For each spatial location, the local density value and density gradient distance are calculated. Peak centers are determined based on spatial locations where both the local density value and density gradient distance simultaneously reach the clustering threshold. The remaining spatial locations in the neighborhood are then assigned to the corresponding peak centers according to the vector field distance to form peak clusters. Specifically, the calculation of the local density value and density gradient distance is as follows:

[0139] Based on the vector field distance, a preset neighborhood range is determined around each spatial location, and the number of neighboring spatial locations within the neighborhood range whose distance from the spatial location is less than the preset neighborhood distance threshold is counted. The statistical results are used as the local density value of the spatial location.

[0140] After obtaining the local density value corresponding to each spatial location, for each spatial location, search for all other spatial locations with local density values ​​higher than the spatial location, and calculate the vector field distance between the spatial location and these high-density spatial locations. Select the minimum distance among the vector field distances as the density gradient distance of the spatial location.

[0141] Persistent cohomology analysis is performed on the peak clusters. Specifically, the neighborhood of the peak clusters is expanded from small to large using the vector field distance as the filtering parameter. The generation and disappearance times of the connected components during the neighborhood expansion process are recorded. Connected components with earlier generation times and later disappearance times are selected as persistent main peak clusters. The central region of the persistent main peak clusters in the spatial location domain is determined as the fault stability region.

[0142] In this embodiment, the calculation of the power cable fault location based on the power cable signal propagation speed includes:

[0143] Read the fault stability domain, determine the sampling time index corresponding to the center position of the fault stability domain on the propagation response time axis, and record the propagation time corresponding to the sampling time index as the fault response propagation time;

[0144] The fault propagation distance is calculated based on the fault response propagation time and the signal propagation speed of the power cable. The fault propagation distance is the product of the signal propagation speed and the fault response propagation time, divided by two. The signal propagation speed represents the speed at which electromagnetic signals propagate in the power cable. Dividing by two eliminates the influence of the round-trip propagation path on the distance calculation. A distance mapping relationship is established between the calculated fault propagation distance and the power cable line length information, converting the fault propagation distance into the spatial location of the fault on the power cable. Specifically, the distance mapping relationship means mapping the calculated fault propagation distance to the physical length information of the power cable line to determine the actual spatial location of the fault point on the power cable line.

[0145] Using the power cable test end as the reference starting point for distance calculation, the calculated fault propagation distance is located along the cable line direction. When the fault propagation distance is less than or equal to the total length of the power cable, the line position corresponding to the distance is determined as the fault location. When the detection system is equipped with multiple test ends, the propagation distance information corresponding to each test end is combined for cross-location to further determine the actual spatial location of the fault point.

[0146] The fault location is matched with the geographical coordinates of the power cable line to output the fault location result of the power cable.

[0147] Example 1: To verify the feasibility of this invention in practice, it was applied to a power supply system in an industrial park. The cable type was YJV22-10kV-3×240mm² cross-linked polyethylene insulated power cable, with a total line length of approximately 3.2 kilometers. The cable was laid in an underground cable trench and had been in operation for approximately 7 years. During testing, a power cable fault location device was connected to the cable test end on the distribution room side. First, the initial voltage and current response data of the power cable were acquired, and the initial impedance state of the cable was calculated based on the voltage and current responses. After determining that the cable was in a high-resistance state, a scanning excitation signal with an exponentially increasing amplitude was applied to the cable according to the set scanning excitation signal parameters. At each excitation energy level, the voltage and current responses were simultaneously acquired, and the trend of complex impedance change was determined based on the voltage and current change characteristics. When the excitation energy level gradually increased to approximately 3.5kV, the voltage-current response characteristics showed a significant change, and a short-time current spike signal was detected. This indicated that the cable fault point had entered the threshold induced discharge state, and the threshold energy level range was determined.

[0148] After determining the threshold energy level range, a fractal energy spectrum generator was used to perform self-similar energy level expansion centered on the threshold energy level, forming a multi-scale fractal excitation sequence. The propagation response of the power cable was synchronously acquired within the corresponding fractal time sampling window. The acquired propagation responses were arranged according to energy level and time indices to construct a propagation response matrix. The propagation response matrix was then normalized, and the cross-scale correlation strength between adjacent energy levels was calculated. Through iterative accumulation, a cross-scale consistency curve was formed, resulting in an aligned propagation response dataset. A sliding window embedding was performed in the spatial domain to construct a propagation consistency vector field. Density peak clustering and persistent cohomology analysis were then performed on the propagation consistency vector field to identify persistent main peak cluster regions, which were then defined as the fault stability region. The propagation time was calculated based on the center moment of the fault stability region on the propagation response time axis. Combined with the propagation speed of the power cable signal in this type of cable, the propagation time was converted into the distance to the fault point. The calculation results show that the distance to the fault point from the test end is approximately 2.07 kilometers. Based on the location results, maintenance personnel conducted an excavation inspection at a location approximately 2.05 kilometers from the power distribution room. They ultimately confirmed that the cable's outer sheath was damaged and that the insulation layer was partially damp, a location that was largely consistent with the inspection results.

[0149] To verify the detection effectiveness of the method of this invention, comparative tests were conducted on the same cable line using both the traditional pulse reflection localization method and the method of this invention. The traditional method, due to the weak reflected signal of high-resistivity faults, resulted in significant fluctuations in localization results across multiple tests. In contrast, the method of this invention, through fractal energy level excitation and multi-scale propagation characteristic analysis, can stably identify fault response signals.

[0150] Table 1. Test Data for Fault Location in Power Cables

[0151] Test number Cable length (km) Excitation energy level trigger range (kV) Detection propagation time (μs) Calculate the distance to the fault (km) Actual location of the fault (km) Positioning error (m) 1 3.2 3.4–3.6 20.9 2.06 2.05 10 2 3.2 3.4–3.6 21.1 2.08 2.05 30 3 3.2 3.3–3.5 20.8 2.05 2.05 5 4 3.2 3.5–3.7 21.0 2.07 2.05 20 5 3.2 3.4–3.6 20.9 2.06 2.05 10

[0152] As shown in Table 1, the experimental data indicates that the fault location results obtained through repeated tests along the same 3.2km power cable line are generally stable. The propagation times detected in the five tests are mostly concentrated between 20.8μs and 21.1μs, with a small fluctuation range of only about 0.3μs. This suggests that by using a scanning excitation signal trigger combined with fractal energy spectrum excitation and propagation consistency analysis, the cable propagation response signal can be stably captured, and the propagation time measurement results have good repeatability.

[0153] Further analysis of the calculated fault distances revealed that the calculated distances for the five tests were 2.05 km, 2.06 km, 2.07 km, and 2.08 km, respectively, with an overall range between 2.05 km and 2.08 km. This deviation from the actual fault location of 2.05 km was relatively small. The calculation result for the third test was completely consistent with the actual fault location, with a positioning error of 5 m. The positioning errors for the remaining test results were 10 m, 10 m, 20 m, and 30 m, respectively. All test results had errors controlled within 30 m, with an average error of approximately 15 m, indicating that this method can maintain high positioning accuracy in practical engineering environments.

[0154] From the perspective of the excitation energy level triggering range, the triggering thresholds in each test were concentrated between 3.3kV and 3.7kV, indicating that the cable fault point can stably generate threshold-induced discharge within this voltage range and be identified by the detection system. This demonstrates that by using exponentially increasing scanning excitation and fractal energy level expansion, high-resistance fault responses can be effectively triggered without applying excessively high test voltages, while avoiding additional damage to the cable insulation. Considering the propagation time stability, fault distance calculation results, and location error, it can be seen that the method of this invention can stably identify fault response characteristics and accurately calculate fault locations under multiple test conditions, verifying the feasibility and reliability of this method in locating high-resistance and low-resistance faults in power cables.

[0155] 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 faults in power cables that is compatible with both high and low resistance, characterized in that, include: Connect the power cable fault location device to the test end of the power cable to be tested, obtain the initial voltage response and current response of the power cable, determine the initial impedance state of the power cable, and set the starting energy level, energy level increment step size and scanning range of the scanning excitation signal. A scanning excitation signal with an exponentially increasing amplitude is applied to the power cable. The amplitude gradient and phase gradient of the voltage-current complex impedance are calculated in real time. When the two gradients jump synchronously and are accompanied by a current spike, the fault point is determined to trigger the threshold induced discharge, and the corresponding energy level interval is recorded as the threshold energy level interval. A fractal energy spectrum generator performs self-similar energy level expansion centered on the threshold energy level interval to generate a fractal excitation sequence. The propagation response of the power cable is collected under the corresponding fractal time sampling window. The propagation response matrix is ​​constructed by mapping the power cable propagation response according to the energy level index and the time index. The propagation response matrix is ​​normalized, and the cross-scale correlation coefficient between adjacent energy levels is calculated. The cross-scale consistency curve is formed by iterative accumulation, and the aligned propagation response dataset is obtained. Based on the aligned propagation response dataset, a sliding window embedding is performed in the spatial location domain to construct a propagation consistency vector field. Density peak clustering and persistent cohomology analysis are performed on the propagation consistency vector field to extract the persistent main peak cluster and determine the central region of the main peak cluster as the fault stability region. The fault response propagation time is determined based on the center moment of the fault stability region on the propagation response time axis, and the location of the power cable fault point is calculated in combination with the power cable signal propagation speed.

2. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, Determining the initial impedance state of the power cable includes: An initial detection signal is applied to the test end of the power cable, and the voltage and current signals of the power cable are collected simultaneously. The equivalent impedance amplitude and impedance phase of the power cable are calculated based on the voltage and current signals. The equivalent impedance amplitude is compared with a preset impedance threshold. When the equivalent impedance amplitude is greater than the preset impedance threshold, it is determined to be a high impedance state. When the equivalent impedance amplitude is less than or equal to the preset impedance threshold, it is determined to be a low impedance state. The initial impedance state of the power cable is determined based on the determination result.

3. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The setting of the starting energy level, energy level increment step size, and scan interval of the scanning excitation signal includes: Obtain the equivalent impedance amplitude and impedance phase corresponding to the initial impedance state. When the power cable is in a low impedance state, set the starting energy level of the scanning excitation signal to the first preset energy level and set the energy level increment step size to the first preset step size. When the power cable is in a high impedance state, the starting energy level of the scanning excitation signal is set to the second preset energy level, and the energy level increment step size is set to the second preset step size. The second preset energy level is greater than the first preset energy level, and the second preset step size is less than the first preset step size. A scanning interval is constructed with the initial energy level as the lower limit of the scan and the preset maximum allowable energy level as the upper limit of the scan. Scan excitation signals are generated step by step within the scanning interval according to the initial energy level and the energy level increment step size. The energy level difference between two adjacent scan excitation signals is equal to the energy level increment step size. The scanning interval setting is terminated when the scan excitation signal generated step by step reaches the preset maximum allowable energy level.

4. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The scanning excitation signal is generated through a multi-level excitation logic combination structure, which includes a first inductor L1, a second inductor L2, a third inductor L3, and resistors R4, R5, and R6.

5. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The determination of the fault point trigger threshold induced discharge, and the corresponding energy level interval recorded as the threshold energy level interval, includes: According to the set scanning excitation signal parameters, a scanning excitation signal with an amplitude that increases exponentially is continuously applied to the power cable, and a corresponding energy level identifier is assigned to each energy level scanning excitation signal. During the application of the scanning excitation signal for each energy level, the voltage and current responses corresponding to the energy level are synchronously acquired. Based on the acquired voltage and current responses, the complex impedance characteristics corresponding to the energy level are obtained, and the amplitude and phase characteristics of the complex impedance characteristics are extracted. The difference in amplitude between two adjacent energy levels is used as the amplitude gradient, and the difference in phase between two adjacent energy levels is used as the phase gradient. Peak characteristic parameters are extracted from the current response at each energy level. The nonlinear consistency criterion is calculated from the voltage and current responses at each energy level. The nonlinear consistency criterion is composed of the following three conditions being met simultaneously: The magnitude gradient characterization exceeds a preset magnitude gradient threshold and the phase gradient characterization exceeds a preset phase gradient threshold; The peak feature representation exceeds the preset peak threshold; The voltage and current responses exhibit nonlinear loop characteristics within the same sampling window corresponding to the energy level. The nonlinear loop characteristics are determined by the increase in the loop area of ​​the voltage-current phase plane trajectory exceeding a preset loop threshold, and the increase in the loop area changes abruptly relative to the increase in the loop area of ​​the previous energy level. When the nth energy level satisfies the nonlinear consistency criterion, the nth energy level is recorded as the threshold trigger energy level. The scanning excitation signal of the (n+1)th energy level is then applied for verification. When both the nth and (n+1)th energy levels satisfy the nonlinear consistency criterion, the power cable fault point is determined to trigger threshold induced discharge, and the energy level range between the nth and (n+1)th energy levels is determined as the threshold energy level interval.

6. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The method of constructing a propagation response matrix by mapping the propagation response of power cables according to energy level index and time index includes: Read the determined threshold energy level range and determine the center energy level of the threshold energy level range as the expansion center energy level. At the same time, determine the fractal scaling factor, the number of fractal expansion layers, and the sampling window length corresponding to each layer. A fractal excitation sequence is generated using a fractal energy spectrum generator, which consists of a fractal energy level expansion unit, a spectrum folding index unit, and a time window synchronization scheduling unit, wherein: The fractal energy level expansion unit takes the expansion center energy level as the reference, and generates each layer of fractal energy level recursively according to the fractal scaling factor to form a fractal energy level sequence. The time window synchronization scheduling unit allocates a corresponding sampling time window for each fractal energy level and generates a synchronization trigger signal; The spectral folding index unit assigns an energy level index to each fractal energy level and defines the mapping relationship between the energy level index and the sampling window index; Fractal energy level excitation is applied to the power cable according to the fractal excitation sequence. During the application of each fractal energy level excitation, the voltage response and current response of the power cable are synchronously collected in the corresponding sampling time window according to the synchronous trigger signal. For each fractal energy level excitation, a consistent shaping operation is performed on the voltage and current responses. Specifically, the voltage-current phase plane trajectory is constructed using the in-phase sampling pairs of the voltage and current responses. The loop area features, loop center offset features, and current spike features of the voltage-current phase plane trajectory are extracted and bound to the corresponding fractal energy level index to form a propagation response feature vector. According to the mapping relationship defined by the spectral folding index unit, the propagation response feature vectors of each layer are folded and arranged in a two-dimensional coordinate system of energy level index and sampling window index to construct the propagation response matrix.

7. A method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The process of iteratively accumulating cross-scale consistency curves to obtain the aligned propagation response dataset includes: The propagation response matrix is ​​normalized, which includes scaling the propagation response feature vector corresponding to each energy level index in the propagation response matrix according to its own amplitude range. The cross-scale correlation coefficient is calculated between adjacent energy level indices, specifically as follows: At the same sampling time index, the propagation response feature vectors of two adjacent energy level indices are taken respectively. The components of the two vectors are multiplied and summed to obtain the instantaneous similarity. Within the sampling time index range of two adjacent energy level indices, the instantaneous similarity is averaged by a sliding window to obtain the cross-scale correlation coefficient at the sampling time index. The cross-scale correlation coefficients corresponding to all sampling time indices are then combined to form a cross-scale correlation sequence. Phase consistency correction is performed on cross-scale correlated sequences, specifically as follows: A finite shift search is performed on the sampling time axis for the propagation response feature vectors of two adjacent energy level indices. The sum of instantaneous similarities corresponding to each shift amount is calculated. The shift amount with the largest sum of instantaneous similarities is selected as the alignment shift amount. The alignment shift amount is used to correct the cross-scale correlation sequence to obtain the corrected cross-scale correlation sequence. The cross-scale consistency curve is generated based on the corrected cross-scale correlation sequence, specifically as follows: The corrected cross-scale correlation coefficient at each sampling time index is used as the consistency accumulation input, and iterative accumulation is performed sequentially from low to high energy level index. Energy level consistency gating conditions are introduced in each iteration accumulation. The energy level consistency gating condition is that the cross-scale correlation coefficients of two adjacent energy level indices are allowed to accumulate when they simultaneously satisfy the magnitude consistency threshold and the direction consistency threshold. If they are not satisfied, accumulation is suppressed. After completing the iterative accumulation of all adjacent energy level indices, the cross-scale consistency curve is obtained. Based on the sampling time index corresponding to the local maxima of the cross-scale consistency curve, adaptive time alignment processing is performed on the propagation response matrix to obtain the aligned propagation response dataset.

8. The method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The process of performing density peak clustering and persistent cohomology analysis on the propagation consistency vector field, extracting persistent main peak clusters, and determining the central region of the main peak clusters as the fault stability region includes: The sampling time index of the aligned propagation response dataset is converted into a spatial location index according to the propagation speed of the power cable signal, so that the aligned propagation response dataset forms a corresponding propagation response sequence in the spatial location domain; In the spatial location domain, the sliding window length and window step size are set, and sliding window embedding is performed on the propagation response sequence. In each sliding window, multi-scale propagation response features are extracted in order of energy level index. The cross-scale correlation strength, energy level consistency gating state and nonlinear loop features between adjacent energy levels are jointly encoded to generate the propagation consistency feature vector corresponding to the spatial location. The propagation consistency feature vectors corresponding to all spatial locations are arranged in order of spatial location index to form a propagation consistency vector field. Scale-preserving neighborhood distance calculation is performed on the propagation consistency vector field. For any two spatial locations, the difference between cross-scale correlated components, the difference between energy level gated components, and the difference between nonlinear loop components are calculated respectively. The vector field distance is obtained by weighted summation according to preset weights. Neighborhood relationship is constructed in the spatial location domain based on the vector field distance. Density peak clustering is performed on the propagation consistency vector field in terms of neighborhood relations. For each spatial location, the local density value and density gradient distance are calculated. The peak center is determined based on the spatial location where the local density value and density gradient distance both reach the clustering threshold. The remaining spatial locations in the neighborhood are assigned to the corresponding peak center according to the vector field distance to form a peak cluster. Persistent cohomology analysis is performed on the peak clusters. Specifically, the neighborhood of the peak clusters is expanded from small to large using the vector field distance as the filtering parameter. The generation and disappearance times of the connected components during the neighborhood expansion process are recorded. Connected components with earlier generation times and later disappearance times are selected as persistent main peak clusters. The central region of the persistent main peak clusters in the spatial location domain is determined as the fault stability region.

9. A method for locating faults in power cables compatible with both high and low resistance according to claim 1, characterized in that, The calculation of the power cable fault location based on the power cable signal propagation speed includes: Read the fault stability domain, determine the sampling time index corresponding to the center position of the fault stability domain on the propagation response time axis, and record the propagation time corresponding to the sampling time index as the fault response propagation time; The fault propagation distance is calculated based on the fault response propagation time and the power cable signal propagation speed. A distance mapping relationship is established based on the calculated fault propagation distance and the power cable line length information, and the fault propagation distance is converted into the fault spatial location on the power cable. The fault location is matched with the geographical coordinates of the power cable line to output the fault location result of the power cable.

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