A high-resistance fault locating method and system based on SPWVD and sub-pixel level image

Abstract

The application discloses a high-resistance fault positioning method and system based on SPWVD and sub-pixel level images, and belongs to the technical field of power distribution network fault positioning. The method comprises the following steps: performing time-frequency analysis on a zero sequence current through an SPWVD algorithm and drawing a two-dimensional time-frequency image; based on filtering and denoising, contrast enhancement, frequency axis convex region detection and time axis sub-pixel level positioning analysis on the time-frequency image, the wave head arrival time in the time-frequency image is positioned through multi-directional fusion positioning of a peak value detection method, a Gaussian fitting method and a gravity center method, and the distance between the fault point and the measuring point is calculated through a proportional algorithm. The application performs SPWVD time-frequency analysis on the zero sequence current signal extracted by a low sampling frequency device, uses frequency axis convex detection and adopts spline interpolation to perform sub-pixel level positioning on the time axis, and significantly improves the high-resistance grounding fault positioning accuracy of a 35kV and above voltage level power line system which is only provided with a low sampling frequency detection device.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network fault location technology, and more specifically, relates to a high-resistivity fault location method and system based on SPWVD and sub-pixel level images. Background Technology

[0002] Distribution networks with voltage levels of 35kV and above are a crucial link in the power system connecting the main grid with a wide range of users, undertaking the important tasks of power distribution and transmission. Due to their wide coverage and complex operating environment, the risk of line faults is relatively high. Among them, high-resistance faults (such as conductors falling into dry ground, contacting trees or concrete poles, etc.) have always been a technical challenge in the field of distribution network protection and location because of their weak fault current and inconspicuous characteristics. Quickly and accurately locating such faults is of paramount importance for improving power supply reliability, shortening power outage time, and reducing operation and maintenance costs.

[0003] Currently, high-resistivity fault location methods in distribution networks can be mainly divided into three categories: traveling wave method, impedance method, and artificial intelligence-based methods. The traveling wave method utilizes the time difference between the arrival of transient traveling wave surges generated by the fault at the measurement point for distance measurement. Theoretically, it has high accuracy, but traditional implementations require extremely high sampling frequencies (usually above MHz), resulting in expensive equipment. Furthermore, wavefront identification is susceptible to interference from noise, line branches, and reflected waves. The impedance method measures distance based on the relationship between the measured impedance of the fault loop and the distance. It is simple in principle and easy to implement, but its accuracy is greatly affected by transition resistance, load changes, and system operating conditions, making it difficult to meet the reliable location requirements in high-resistivity fault scenarios. In recent years, with the development of artificial intelligence technology, data-driven deep learning methods have been gradually introduced. By extracting the time-frequency features of fault signals and training neural network models, intelligent identification of fault sections can be achieved, improving the adaptability of fault location to a certain extent.

[0004] However, existing methods still face a series of technical bottlenecks: the high sampling frequency requirement leads to high hardware deployment costs, making it difficult to promote on a large scale in distribution networks; traditional signal processing methods struggle to accurately capture fault traveling wavefronts under limited sampling rates; and deep learning methods often rely on a large number of high-quality labeled samples, resulting in limited model generalization ability and a lack of physical interpretability, which restricts their application in practical engineering. Therefore, how to overcome the performance bottlenecks of existing methods in low sampling rates and complex environments without excessively increasing hardware costs, and improve the accuracy and reliability of high-resistivity fault location in 35kV and above voltage level distribution networks, remains a key technical challenge that urgently needs to be addressed.

[0005] Prior art document 1 (CN121027709A) discloses a method, system, device, and medium for feature extraction of fault traveling wave signals. Its limitation is that this document primarily focuses on feature extraction of fault traveling wave signals through variational mode decomposition (VMD) combined with Hilbert transform and Wigner-Willi distribution (WVD). Although it can extract amplitude, time-frequency, and energy features, its method still falls within the scope of traditional signal analysis. It requires a high signal sampling frequency, and when fault features are weak or the signal-to-noise ratio is low, the effective signal is easily submerged by noise, making it difficult to accurately capture the arrival time of the wavefront.

[0006] Prior art document 2 (CN120177926A) discloses a fault location method for active distribution networks based on an improved convolutional neural network. Its shortcomings lie in its reliance on a large amount of offline simulation data to train a CPCA-CNN model. This model converts one-dimensional zero-sequence current into two-dimensional time-frequency graph samples, which are then processed by a deep learning model to output the probability of faulty lines and sections. While this method improves feature representation capabilities, it is essentially a data-driven black-box model, requiring a large sample set to cover various fault conditions, and its generalization ability is limited by the completeness of the training data. Furthermore, the resolution and feature extraction capabilities of this method for time-frequency graphs depend on the network structure and training quality; at low sampling frequencies, the amount of information in the time-frequency graphs decreases, potentially leading to a significant drop in model performance. In addition, deep learning methods have high computational complexity, making real-time deployment on edge computing devices difficult. Summary of the Invention

[0007] To address the shortcomings of existing technologies in fault location for 35kV and above voltage level power line systems equipped only with low-sampling-frequency detection devices, such as insufficient accuracy, weak anti-interference capability, and poor location reliability, this invention provides a sub-pixel-level image analysis method and system for high-resistivity fault location in distribution networks based on smoothed pseudo-Wigner-Ville distribution (SPWVD). This method can accurately determine the arrival time of wavefronts and the distance of the fault location from the detection device in 35kV and above voltage level power line systems equipped only with low-sampling-frequency detection devices, and possesses strong robustness. It provides a fast and reliable location solution for 35kV and above voltage level power line systems equipped only with low-sampling-frequency detection devices.

[0008] The present invention adopts the following technical solution.

[0009] The first aspect of the present invention provides a high-resistivity fault location method based on SPWVD and sub-pixel level images, comprising the following steps: The zero-sequence current is collected and decomposed into time and frequency in the time-frequency domain. A two-dimensional time-frequency graph is plotted with time as the horizontal axis and frequency as the vertical axis. The convex vertex of the two-dimensional time-frequency plot is determined along the time axis. Based on the convex vertex, the range of the convex region along the frequency axis is determined by searching outward to the point where the gradient is zero. Within the frequency axis convex region, a continuous function is obtained by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph, and then sub-pixel level curves are generated through sub-pixel level resampling. The arrival time of the wavefront is located from the subpixel-level curve, and the location of the fault point is calculated based on the arrival time of the wavefront using double-ended ranging.

[0010] Preferably, plotting a two-dimensional time-frequency graph includes: The collected zero-sequence current is smoothed into a pseudo-Wigner-Vell distribution to generate energy density distributions in time and frequency. Based on the energy density distribution over time and frequency, a two-dimensional time-frequency diagram is plotted with time as the horizontal axis and frequency as the vertical axis.

[0011] Preferably, determining the range of the frequency axis protrusion region includes: The two-dimensional time-frequency graph is preprocessed, and the maximum value of each row along the time axis is taken from the preprocessed two-dimensional time-frequency graph and aggregated into a one-dimensional frequency axis projection curve. The one-dimensional frequency axis projection curve is smoothed using a Gaussian filter to generate a smooth frequency axis curve; the gradient of the smooth frequency axis curve is calculated, and the region where the absolute value of the gradient is greater than a set gradient threshold is set as the region where the gradient changes significantly. Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the convex vertex. Using the convex vertex as the center, the search extends outward to the frequency point where the gradient is zero, generating the initial convex region. Extend the initial left boundary of the initial region by 2 frequency points in the direction of decreasing frequency points, and extend the initial right boundary of the initial region by 2 frequency points in the direction of increasing frequency points to determine the range of the frequency axis convex region.

[0012] Preferably, the preprocessing of the two-dimensional time-frequency graph includes: The two-dimensional time-frequency graph is converted into a grayscale image, and the pixel values ​​of the grayscale image are normalized to the range of [0,1] to generate a normalized image. The image is smoothed and normalized using a Gaussian convolution kernel. The smoothed image is then contrast-stretched so that the pixel values ​​are linearly mapped to the [0,1] interval, generating a preprocessed two-dimensional time-frequency map.

[0013] Preferably, the initial region for generating the protrusion includes: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. The search proceeds outward from the peak point until a frequency point with a gradient value of zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

[0014] Preferably, generating sub-pixel level curves includes: Within the defined frequency axis protrusion region, the preprocessed two-dimensional time-frequency plot is summed along the frequency axis to obtain a one-dimensional time axis projection curve. Gaussian filtering is applied to the one-dimensional time axis projection curve to smooth it, resulting in a smoothed time axis curve. Perform cubic spline interpolation on discrete points on a smoothed time axis curve to output a continuous function; By resampling the continuous function at sub-pixel intervals, sub-pixel level curves are obtained.

[0015] Preferably, locating the wavefront arrival time from the sub-pixel level curve includes: Calculate the first-order difference for the sub-pixel level curve, find the time point when the first-order difference changes from positive to negative and set it as the peak point. Take n points to the left and right of the peak point to determine the wavefront candidate region. Based on the wavefront candidate region, determine the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region; The arrival time of the wavefront is determined based on the Gaussian fitting of the wavefront time and the center x-coordinate.

[0016] Preferably, determining the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region includes: Extract the data point set within the candidate wavefront region, transform the standard Gaussian model into a quadratic polynomial through linearization, solve the coefficients of the quadratic polynomial using the least squares method to restore the Gaussian parameters, and generate the Gaussian fitted wavefront time using the Gaussian fitting method. Find the minimum value of the ordinate of all data points in the wavefront candidate region, calculate the effective amplitude of each point relative to the minimum value, normalize the effective amplitude with weights to obtain the normalized weight of each data point in the range [0,1], and use the normalized weight as the coefficient to perform a weighted average on the abscissa of the data point set to obtain the center abscissa of the subpixel-level curve in the wavefront candidate region.

[0017] Preferably, determining the wavefront arrival time based on the Gaussian fitted wavefront time and the center abscissa includes: When the absolute value of the Gaussian fitted wavefront time minus the center abscissa is less than the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed valid. The Gaussian fitted wavefront time and center abscissa are then weighted and fused to obtain the wavefront arrival time. If the absolute value of the Gaussian fitted wavefront time minus the center abscissa is greater than or equal to the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed invalid. The peak point in the peak detection method is selected, and the wavefront arrival time is calculated by Lagrange interpolation.

[0018] A second aspect of the present invention provides a high-resistivity fault location system based on SPWVD and subpixel-level images, which, when running the high-resistivity fault location method based on SPWVD and subpixel-level images described in the first aspect, includes: The two-dimensional time-frequency plotting module is used to collect zero-sequence current, decompose it into time and frequency in the time-frequency domain, and plot a two-dimensional time-frequency plot with time as the horizontal axis and frequency as the vertical axis. The convex region determination module is used to determine the convex vertices along the time axis of the two-dimensional time-frequency graph, and to determine the range of the convex region along the frequency axis by searching outward from the convex vertices to the point where the gradient is zero. The subpixel-level curve generation module is used to obtain a continuous function by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph within the frequency axis convex region, and then generate a subpixel-level curve through subpixel-level resampling. The fault location module is used to locate the arrival time of the wavefront from the sub-pixel level curve, and calculate the location of the fault point based on the arrival time of the wavefront through dual-end ranging.

[0019] Preferably, plotting a two-dimensional time-frequency graph includes: The collected zero-sequence current is smoothed into a pseudo-Wigner-Vell distribution to generate energy density distributions in time and frequency. Based on the energy density distribution over time and frequency, a two-dimensional time-frequency diagram is plotted with time as the horizontal axis and frequency as the vertical axis.

[0020] Preferably, determining the range of the frequency axis protrusion region includes: The two-dimensional time-frequency graph is preprocessed, and the maximum value of each row along the time axis is taken from the preprocessed two-dimensional time-frequency graph and aggregated into a one-dimensional frequency axis projection curve. The one-dimensional frequency axis projection curve is smoothed using a Gaussian filter to generate a smooth frequency axis curve; the gradient of the smooth frequency axis curve is calculated, and the region where the absolute value of the gradient is greater than a set gradient threshold is set as the region where the gradient changes significantly. Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the convex vertex. Using the convex vertex as the center, the search extends outward to the frequency point where the gradient is zero, generating the initial convex region. Extend the initial left boundary of the initial region by 2 frequency points in the direction of decreasing frequency points, and extend the initial right boundary of the initial region by 2 frequency points in the direction of increasing frequency points to determine the range of the frequency axis convex region.

[0021] Preferably, the preprocessing of the two-dimensional time-frequency graph includes: The two-dimensional time-frequency graph is converted into a grayscale image, and the pixel values ​​of the grayscale image are normalized to the range of [0,1] to generate a normalized image. The image is smoothed and normalized using a Gaussian convolution kernel. The smoothed image is then contrast-stretched so that the pixel values ​​are linearly mapped to the [0,1] interval, generating a preprocessed two-dimensional time-frequency map.

[0022] Preferably, the initial region for generating the protrusion includes: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. The search proceeds outward from the peak point until a frequency point with a gradient value of zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

[0023] Preferably, generating sub-pixel level curves includes: Within the defined frequency axis protrusion region, the preprocessed two-dimensional time-frequency plot is summed along the frequency axis to obtain a one-dimensional time axis projection curve. Gaussian filtering is applied to the one-dimensional time axis projection curve to smooth it, resulting in a smoothed time axis curve. Perform cubic spline interpolation on discrete points on a smoothed time axis curve to output a continuous function; By resampling the continuous function at sub-pixel intervals, sub-pixel level curves are obtained.

[0024] Preferably, locating the wavefront arrival time from the sub-pixel level curve includes: Calculate the first-order difference for the sub-pixel level curve, find the time point when the first-order difference changes from positive to negative and set it as the peak point. Take n points to the left and right of the peak point to determine the wavefront candidate region. Based on the wavefront candidate region, determine the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region; The arrival time of the wavefront is determined based on the Gaussian fitting of the wavefront time and the center x-coordinate.

[0025] Preferably, determining the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region includes: Extract the data point set within the candidate wavefront region, transform the standard Gaussian model into a quadratic polynomial through linearization, solve the coefficients of the quadratic polynomial using the least squares method to restore the Gaussian parameters, and generate the Gaussian fitted wavefront time using the Gaussian fitting method. Find the minimum value of the ordinate of all data points in the wavefront candidate region, calculate the effective amplitude of each point relative to the minimum value, normalize the effective amplitude with weights to obtain the normalized weight of each data point in the range [0,1], and use the normalized weight as the coefficient to perform a weighted average on the abscissa of the data point set to obtain the center abscissa of the subpixel-level curve in the wavefront candidate region.

[0026] Preferably, determining the wavefront arrival time based on the Gaussian fitted wavefront time and the center abscissa includes: When the absolute value of the Gaussian fitted wavefront time minus the center abscissa is less than the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed valid. The Gaussian fitted wavefront time and center abscissa are then weighted and fused to obtain the wavefront arrival time. If the absolute value of the Gaussian fitted wavefront time minus the center abscissa is greater than or equal to the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed invalid. The peak point in the peak detection method is selected, and the wavefront arrival time is calculated by Lagrange interpolation.

[0027] Compared with the prior art, the beneficial effects of the present invention include at least the following: This invention combines a smooth pseudo-Wigner-Vell distribution with subpixel-level image analysis technology to process low-sampling-frequency zero-sequence current signals collected for high-resistivity faults. It effectively suppresses cross-term interference through the dual smoothing window of SPWVD, generating a high-resolution two-dimensional time-frequency graph. Image processing techniques are introduced to denoise and enhance the contrast of the time-frequency graph. Subpixel-level positioning of the time axis is achieved through frequency axis convex region detection and cubic spline interpolation and subpixel-level resampling. Under the condition of limited hardware sampling frequency (low sampling rate), subpixel-level curves are generated, overcoming the bottleneck of traditional signal processing methods' inability to accurately capture the fault traveling wave front under limited sampling rate conditions. It also overcomes the bottleneck of insufficient time resolution in traditional methods, achieving subpixel-level accurate positioning of the arrival time of weak and ambiguous traveling wave fronts. This avoids the technical problem of high hardware deployment costs and difficulty in large-scale promotion caused by high sampling frequency requirements, thus improving the accuracy of high-resistivity fault location.

[0028] Discrete pixel-level data is converted into continuous high-resolution curves. A multi-directional fusion positioning strategy using peak detection, Gaussian fitting, and centroid method is employed to accurately determine the arrival time of the wavefront and finally calculate the fault distance. This reduces the dependence on sampling frequency and enables high-precision fault positioning under low sampling rate conditions. The positioning accuracy for high-resistance faults is improved, overcoming the limitation of weak high-resistance grounding fault signals that make identification difficult. A multi-method fusion positioning strategy is adopted to enhance the robustness and noise resistance of the algorithm, maintaining high positioning accuracy even in weak signal scenarios.

[0029] This invention employs SPWVD to perform time-frequency analysis on low-sampling-frequency zero-sequence currents collected during high-resistance faults. After generating a two-dimensional time-frequency image, image processing techniques are directly used for denoising and enhancement. Furthermore, a multi-directional fusion localization strategy combining peak detection, Gaussian fitting, and centroid method is employed to determine the arrival time of wavefronts in the time-frequency image. This fusion localization strategy fully leverages the intuitiveness of peak detection, the accuracy of Gaussian fitting, and the noise resistance of the centroid method. By combining the results of these three methods, the accuracy and robustness of wavefront time identification are significantly improved. The method integrates peak detection, Gaussian fitting and centroid method for localization, and realizes multi-angle comprehensive determination of wavefront arrival time. It overcomes the defect of single method being prone to failure under noise interference. It has low complexity, high computational efficiency, and is easy to implement in real time fault location on embedded devices or field terminals. It has a definite physical mechanism, strong adaptability to different system parameters and fault types, no need for frequent model updates, and low maintenance cost.

[0030] The present invention is applicable to signal processing and analysis of high-resistance faults and fault zero-sequence currents collected by low-sampling-frequency detection devices. Its application field is wider. In this technical field, unless high-resistance faults are specifically mentioned, the related technologies are assumed to be only applicable to traditional low-resistance faults within 500 ohms, while high-resistance faults are generally considered to meet the level of 3000 ohms and above, the latter being a noise amplification effect caused by a larger transition resistance.

[0031] Time-frequency analysis of the original low-sampling frequency signal was performed using SPWVD time-frequency dual smoothing windows to obtain the energy density distribution in time and frequency, and a two-dimensional time-frequency graph was plotted. Image recognition methods were used to identify regions with significant gradient changes and convex regions. Cubic spline interpolation was used to improve resolution, converting discrete pixel-level data into continuous high-resolution curves. Finally, a multi-directional fusion positioning strategy using peak detection, Gaussian fitting, and centroid method was employed to determine the arrival time of the wavefront. The distance from the fault point to the detection device was calculated using a dual-end ranging formula. This method enables rapid, accurate, and robust fault location in 35kV and above voltage level power line systems equipped only with low-sampling frequency detection devices, providing reliable technical support for the safe operation and efficient maintenance of 35kV and above voltage level power lines. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of a high-resistivity fault location process based on SPWVD and sub-pixel level images provided in accordance with an embodiment of the present invention; Figure 2 This is a schematic diagram of a power line topology for testing a 35kV voltage level, provided according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the low-sampling-frequency zero-sequence current waveform upstream of the fault point, provided according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the low-sampling-frequency zero-sequence current waveform downstream of the fault point provided in accordance with an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the determination of the arrival time of the wavefront for locating the upstream of the fault point according to an embodiment of the present invention; Figure 6 This is a schematic diagram of determining the arrival time of the wavefront for locating the fault point using a two-dimensional time-frequency diagram provided in an embodiment of the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0034] like Figure 1 As shown, Embodiment 1 of the present invention provides a high-resistivity fault location method based on SPWVD and sub-pixel level images, comprising the following steps: Step 1: Based on the smooth pseudo-Wigner-Weil distribution, the collected zero-sequence current is decomposed in the time-frequency domain to generate a two-dimensional time-frequency graph. The sampling frequency of the zero-sequence current is set to be greater than 10kHz and less than 500kHz.

[0035] In a preferred but non-limiting embodiment of the present invention, step 1 includes: Step 1.1: Collect the zero-sequence current at each measurement point upstream and downstream of the fault point on the faulty feeder. Analyze the collected zero-sequence current... Smooth the pseudo-Wigner-Vell distribution to generate the energy density distribution SPWVD(t,f), which is expressed by the following formula:

[0036] In the formula, Indicates time and frequency Energy density distribution on For time The zero-sequence current, For For the time smoothing window of the independent variable, Represents the time offset variable. For For the frequency smoothing window of the independent variable, Represents the time delay variable. Indicates time The zero-sequence current, express The complex conjugate, It is the kernel of the Fourier transform.

[0037] Step 1.2, based on time and frequency The energy density distribution over time was plotted. The x-axis represents frequency. This is a two-dimensional time-frequency graph with the vertical axis as the ordinate. The brightness of the colors in the two-dimensional time-frequency graph represents the energy density; the brighter the color, the greater the energy density value.

[0038] Traditional traveling wave positioning generally requires a sampling rate higher than 1MHz, which results in higher technical requirements for communication. However, this technical solution can be applied to the identification of traveling wave-level fault characteristics under the premise of low sampling rate, fundamentally solving the constraint of traditional solutions being too dependent on the performance of communication equipment. This represents a significant advancement and fundamental innovation compared to existing technical solutions.

[0039] Step 2: Preprocess the two-dimensional time-frequency graph to obtain the preprocessed two-dimensional time-frequency graph.

[0040] In a preferred but non-limiting embodiment of the present invention, step 2 includes: Step 2.1: Convert the two-dimensional time-frequency image to a grayscale image, normalize the pixel values ​​of the grayscale image to the range of [0, 1], and generate a normalized image. Color information interference is eliminated by unifying the image format, thus standardizing the pixel values.

[0041] Step 2.2: Use a Gaussian convolution kernel (sigma=1.0) to smooth and normalize the image, suppress high-frequency noise while preserving edge information, smooth the image, and reduce the interference of scattered noise on subsequent analysis.

[0042] Step 2.3: The smoothed image is contrast stretched, and the image pixel values ​​are linearly mapped to the entire [0, 1] interval to generate a preprocessed two-dimensional time-frequency map, which enhances the contrast between high grayscale areas and low grayscale background.

[0043] By employing a targeted and optimized signal preprocessing mechanism, interference components can be effectively filtered out, laying the foundation for the accurate extraction of high-impedance fault characteristics in the future.

[0044] Step 3: Determine the convex vertex along the time axis of the two-dimensional time-frequency graph preprocessed in Step 2, and search outward from the convex vertex to the point where the gradient is zero to determine the range of the convex region on the frequency axis.

[0045] In a preferred but non-limiting embodiment of the present invention, step 3 includes: Step 3.1: Take the maximum value of each row along the time axis of the preprocessed two-dimensional time-frequency graph and aggregate them into a one-dimensional frequency axis projection curve. Compress the two-dimensional image into one dimension to highlight the brightness changes along the frequency axis.

[0046] Step 3.2: Smooth the one-dimensional frequency axis projection curve using a Gaussian filter with a window size of 5 to generate a smooth frequency axis curve. This eliminates minor fluctuations and highlights the main trends.

[0047] Step 3.3: Calculate the gradient of the smoothed frequency axis curve to locate the boundary of energy abrupt change, and set the region where the absolute value of the gradient is greater than the set gradient threshold as the region of significant gradient change.

[0048] Step 3.4: Within the region of significant gradient change, find the frequency point where the gradient changes from positive to negative and set it as the convex vertex. Using the convex vertex as the center, search outwards (in both directions of decreasing and increasing frequency) to the frequency point where the gradient is zero, generating the initial convex region, including: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. Using the peak point as the center, the search continues to both sides until a frequency point with a gradient value close to zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

[0049] Step 3.5: To ensure that the preliminary region contains complete convex features, extend the preliminary left boundary of the preliminary region by 2 frequency points in the direction of decreasing frequency points, and extend the preliminary right boundary of the preliminary region by 2 frequency points in the direction of increasing frequency points, thereby determining the range of the convex region along the frequency axis.

[0050] Assuming the pixel number k on the frequency axis ranges from 1 to 100, and a convex vertex is detected at k=50, searching to the left, we find that the gradient at k=35 is close to zero, which is the initial left boundary. Searching to the right, we find that the gradient at k=65 is close to zero, which is the initial right boundary. The initial region is the index region [35, 65]. Expanding the initial region by 2 pixels both in front and behind: the left boundary 35 is expanded forward by 2 pixels to 33, and the right boundary 65 is expanded backward by 2 pixels to 67. The range of the convex region on the frequency axis is now [33, 67].

[0051] Step 4: Within the frequency axis protrusion region determined in Step 3, a continuous function is obtained by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph. After sub-pixel level resampling, a sub-pixel level curve is generated.

[0052] In a preferred but non-limiting embodiment of the present invention, step 4 includes: Step 4.1: Within the frequency axis protrusion region determined in step 3, sum the two-dimensional time-frequency graphs preprocessed in step 2 along the frequency axis to obtain a one-dimensional time axis projection curve.

[0053] The one-dimensional time axis projection curve reflects the total energy of the main frequency components of the wavefront at each time point, with the peak point corresponding to the arrival time of the wavefront.

[0054] Step 4.2: Apply Gaussian filtering to smooth the one-dimensional time axis projection curve to generate a smoothed time axis curve; Step 4.3 involves performing cubic spline interpolation on the discrete points on the smoothed time axis curve to output a continuous function. This interpolation improves the time axis resolution to sub-pixel level, achieving sub-pixel level positioning accuracy.

[0055] Step 4.4: Resample the continuous function at sub-pixel intervals to obtain sub-pixel level curves.

[0056] Step 5: Locate the wavefront arrival time from the subpixel-level curve.

[0057] In a preferred but non-limiting embodiment of the present invention, step 5 includes: Step 5.1: For the sub-pixel curve y = f(x), calculate the first-order difference △yi = yi+1 - yi, and find the time point when the first-order difference changes from positive to negative, that is, when △yi > 0 and △yi+1 < 0. Set this time point of changing from positive to negative as the peak point xmax, and the corresponding maximum amplitude is ymax. Take n points on both the left and right sides centered on the peak point xmax, where n = 5, so as to determine the wavefront candidate region [xleft, xright]. In the formula: xleft = xmax - n; xright = xmax + n; Step 5.2: Extract the data point set (xi, yi) within the wavefront candidate region. Transform the standard Gaussian model into a quadratic polynomial through linearization transformation, use the least squares method to solve the coefficients of the quadratic polynomial, restore the Gaussian parameters, and generate the Gaussian fitting wavefront moment xgauss through Gaussian fitting method; Step 5.3: Find the minimum value ymin of the ordinates of all data points within the wavefront candidate region, subtract ymin from each point one by one, calculate the effective amplitude yrel,i of each point relative to the minimum value, perform weight normalization on the effective amplitude yrel,i, and obtain the normalized weight ωi with a range of [0, 1] for each data point. Use the normalized weight ωi as the coefficient to perform weighted averaging on the abscissas xi of the data point set, and the obtained result is the central abscissa xcenter of the sub-pixel curve within the wavefront candidate region.

[0058] Step 5.4: Determine the wavefront arrival time based on the Gaussian fitting wavefront moment and the central abscissa.

[0059] Further preferably, Step 5.4 includes: Set 50 times the sub-pixel interval as the interval threshold T; When the absolute value |xgauss - xcenter| of the difference between the Gaussian fitting wavefront moment and the central abscissa is less than the interval threshold T, that is, |xgauss - xcenter| < T, it is determined that the data of the Gaussian fitting wavefront moment and the central abscissa are valid, and the Gaussian fitting wavefront moment and the central abscissa are weighted and fused to obtain the wavefront arrival time xfinal = 0.7 × xgauss + 0.3 × xcenter; If the absolute value of the difference between the Gaussian fitting wavefront moment and the central abscissa is greater than or equal to the interval threshold T, that is, |xgauss - xcenter| ≥ T, it is determined that the data of the Gaussian fitting wavefront moment and the central abscissa are invalid, and the peak point in the peak detection method is selected, and the wavefront arrival time is calculated through Lagrange interpolation method.

[0060] Step 6: Based on the wavefront arrival time in Step 5, determine the wavefront arrival time measured by the A-end detection device and the wavefront arrival time measured by the B-end detection device, and calculate the distance of the fault point from the detection device through double-end ranging, which is expressed by the following formula:

[0061] In the formula, This indicates the distance from the fault point to end A. Indicates the arrival time of the wavefront at end A. Indicates the arrival time of the wavefront at end B. Indicates the traveling wave velocity. Indicates the total length of the line.

[0062] Embodiment 2 of the present invention provides a high-resistivity fault location system based on SPWVD and subpixel-level images, which runs the high-resistivity fault location method based on SPWVD and subpixel-level images described in Embodiment 1, including: The two-dimensional time-frequency plotting module is used to collect zero-sequence current, decompose it into time and frequency in the time-frequency domain, and plot a two-dimensional time-frequency plot with time as the horizontal axis and frequency as the vertical axis. The convex region determination module is used to determine the convex vertices along the time axis of the two-dimensional time-frequency graph, and to determine the range of the convex region along the frequency axis by searching outward from the convex vertices to the point where the gradient is zero. The subpixel-level curve generation module is used to obtain a continuous function by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph within the frequency axis convex region, and then generate a subpixel-level curve through subpixel-level resampling. The fault location module is used to locate the arrival time of the wavefront from the sub-pixel level curve, and calculate the location of the fault point based on the arrival time of the wavefront through dual-end ranging.

[0063] Preferably, plotting a two-dimensional time-frequency graph includes: For the collected zero-sequence current Perform smoothing of pseudo-Wigner-Vell distribution, generation time and frequency Energy density distribution on; Based on time and frequency The energy density distribution over time was plotted. x-axis, frequency A two-dimensional time-frequency graph with the vertical axis as the ordinate.

[0064] Preferably, determining the range of the frequency axis protrusion region includes: The two-dimensional time-frequency graph is preprocessed, and the maximum value of each row along the time axis is taken from the preprocessed two-dimensional time-frequency graph and aggregated into a one-dimensional frequency axis projection curve. The one-dimensional frequency axis projection curve is smoothed using a Gaussian filter to generate a smooth frequency axis curve; the gradient of the smooth frequency axis curve is calculated, and the region where the absolute value of the gradient is greater than a set gradient threshold is set as the region where the gradient changes significantly. Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the convex vertex. Using the convex vertex as the center, the search extends outward to the frequency point where the gradient is zero, generating the initial convex region. Extend the initial left boundary of the initial region by 2 frequency points in the direction of decreasing frequency points, and extend the initial right boundary of the initial region by 2 frequency points in the direction of increasing frequency points to determine the range of the frequency axis convex region.

[0065] Preferably, the preprocessing of the two-dimensional time-frequency graph includes: The two-dimensional time-frequency graph is converted into a grayscale image, and the pixel values ​​of the grayscale image are normalized to the range of [0,1] to generate a normalized image. The image is smoothed and normalized using a Gaussian convolution kernel. The smoothed image is then contrast-stretched so that the pixel values ​​are linearly mapped to the [0,1] interval, generating a preprocessed two-dimensional time-frequency map.

[0066] Preferably, the initial region for generating the protrusion includes: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. The search proceeds outward from the peak point until a frequency point with a gradient value of zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

[0067] Preferably, generating sub-pixel level curves includes: Within the defined frequency axis protrusion region, the preprocessed two-dimensional time-frequency plot is summed along the frequency axis to obtain a one-dimensional time axis projection curve. Gaussian filtering is applied to the one-dimensional time axis projection curve to smooth it, resulting in a smoothed time axis curve. Perform cubic spline interpolation on discrete points on a smoothed time axis curve to output a continuous function; By resampling the continuous function at sub-pixel intervals, sub-pixel level curves are obtained.

[0068] Preferably, locating the wavefront arrival time from the sub-pixel level curve includes: Calculate the first-order difference for the sub-pixel level curve, find the time point when the first-order difference changes from positive to negative and set it as the peak point. Take n points to the left and right of the peak point to determine the wavefront candidate region. Based on the wavefront candidate region, determine the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region; The arrival time of the wavefront is determined based on the Gaussian fitting of the wavefront time and the center x-coordinate.

[0069] Preferably, determining the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region includes: Extract the data point set within the candidate wavefront region, transform the standard Gaussian model into a quadratic polynomial through linearization, solve the coefficients of the quadratic polynomial using the least squares method to restore the Gaussian parameters, and generate the Gaussian fitted wavefront time using the Gaussian fitting method. Find the minimum value of the ordinate of all data points in the wavefront candidate region, calculate the effective amplitude of each point relative to the minimum value, normalize the effective amplitude with weights to obtain the normalized weight of each data point in the range [0,1], and use the normalized weight as the coefficient to perform a weighted average on the abscissa of the data point set to obtain the center abscissa of the subpixel-level curve in the wavefront candidate region.

[0070] Preferably, determining the wavefront arrival time based on the Gaussian fitted wavefront time and the center abscissa includes: When the absolute value of the Gaussian fitted wavefront time minus the center abscissa is less than the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed valid. The Gaussian fitted wavefront time and center abscissa are then weighted and fused to obtain the wavefront arrival time. If the absolute value of the Gaussian fitted wavefront time minus the center abscissa is greater than or equal to the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed invalid. The peak point in the peak detection method is selected, and the wavefront arrival time is calculated by Lagrange interpolation.

[0071] Embodiment 3 of the present invention applies the high-resistivity fault location method based on SPWVD and sub-pixel level images described in Embodiment 1, taking a single-phase grounding fault in a 35kV power line as an example: This test case is based on the parameters of an actual 35kV power line in Jiangsu Province. A corresponding simulation model was built on the PSCAD / EMTDC simulation platform for specific testing. The overall overview of this 35kV power line is as follows: it includes 10 outgoing lines with a total length of 71.9km, of which 45.2km are cable lines, forming a typical cable-line hybrid structure. The overhead line type is LGJ-240 / 30; the cable types are mainly YJV32-26 / 35-3×400, YJSV-26 / 35-3×400, and YJSV-26 / 35-3×300.

[0072] To facilitate algorithm testing, two typical routes are selected for demonstration; their topology details can be found in [link to documentation]. Figure 2 As shown in the diagram, the three test lines are drawn from the 35kV busbar and include both buried cables and overhead lines. The closed-loop design is operated in open-loop mode. The installation locations of the current sensors are clearly marked in the diagram, numbered M1 to M6. The fault point is planned to be located between M4 and M5. Figure 3The low-sampling-frequency zero-sequence current at measurement point M4 upstream of the fault point, including the fault occurrence time, is displayed at 0.1 s. Figure 4 The low-sampling-frequency zero-sequence current at measurement point M5 downstream of the fault point at 0.1s, including the time of the fault occurrence, is shown.

[0073] Figure 5 This diagram illustrates the determination of the arrival time of the wavefront at the upstream fault point using a two-dimensional time-frequency graph. The two-dimensional time-frequency graph of the low-sampling frequency (100kHz) zero-sequence current is analyzed for time-frequency characteristics. The image recognition of the raised area is performed, and multiple methods are used to fuse and determine the arrival time of the wavefront at the upstream measurement point. The arrival time of the wavefront at the upstream measurement point is calculated to be 23.65307304ms using the double-end ranging formula. Figure 6 A schematic diagram for determining the arrival time of the wavefront at the downstream two-dimensional time-frequency diagram is provided. Using the same method, the arrival time of the wavefront at the downstream measurement point is calculated to be 23.65700018 ms. Since the upstream of the fault point is an overhead line and the downstream is a cable line, the total length of the line is calculated to be 2781.5723 m through normalization, and the wave velocity is 3 × 10⁸ m / s. The final calculated fault location is 801.72 m away from the upstream measurement point of the fault point, with an error of 198.28 m from the actual fault location, as shown in Table 1.

[0074] Table 1

[0075] The simulation results above verify the effectiveness and practicality of the fault location algorithm constructed in this invention. This paper describes a sub-pixel-level image analysis method for high-resistance fault location in distribution networks based on smooth pseudo-Wigner-Vell distribution (SPWVD), providing a fast and reliable location solution for high-resistance faults in 35kV power line systems equipped only with low-sampling-frequency detection devices.

[0076] Compared with the prior art, the beneficial effects of the present invention include at least the following: This invention combines a smooth pseudo-Wigner-Vell distribution with sub-pixel-level image analysis technology to process low-sampling-frequency zero-sequence current signals collected for high-resistivity faults. It effectively suppresses cross-term interference through the double smoothing window of SPWVD, generating a high-resolution two-dimensional time-frequency graph. Image processing techniques are introduced to denoise and enhance the contrast of the time-frequency graph. Sub-pixel-level positioning of the time axis is achieved through frequency axis convex region detection and cubic spline interpolation, converting discrete pixel-level data into a continuous high-resolution curve. A multi-directional fusion positioning strategy using peak detection, Gaussian fitting, and centroid method is employed to accurately determine the wavefront arrival time and finally calculate the fault distance, reducing dependence on sampling frequency and enabling high-precision fault location under low sampling rate conditions. This improves the positioning accuracy for high-resistivity faults, overcoming the limitation of weak high-resistivity grounding fault signals leading to identification difficulties. The multi-method fusion positioning strategy enhances the algorithm's robustness and noise resistance, maintaining high positioning accuracy even in weak signal scenarios.

[0077] This invention employs SPWVD to perform time-frequency analysis on low-sampling-frequency zero-sequence currents collected during high-resistance faults. After generating a two-dimensional time-frequency image, image processing techniques are directly used for denoising and enhancement. Furthermore, a multi-directional fusion localization strategy combining peak detection, Gaussian fitting, and centroid method is employed to determine the arrival time of wavefronts in the time-frequency image. This fusion localization strategy fully leverages the intuitiveness of peak detection, the accuracy of Gaussian fitting, and the noise resistance of the centroid method. By combining the results of these three methods, the accuracy and robustness of wavefront time identification are significantly improved. The method integrates peak detection, Gaussian fitting and centroid method for localization, and realizes multi-angle comprehensive determination of wavefront arrival time. It overcomes the defect of single method being prone to failure under noise interference. It has low complexity, high computational efficiency, and is easy to implement in real time fault location on embedded devices or field terminals. It has a definite physical mechanism, strong adaptability to different system parameters and fault types, no need for frequent model updates, and low maintenance cost.

[0078] The present invention is applicable to signal processing and analysis of high-resistance faults and fault zero-sequence currents collected by low-sampling-frequency detection devices. Its application field is wider. In this technical field, unless high-resistance faults are specifically mentioned, the related technologies are assumed to be only applicable to traditional low-resistance faults within 500 ohms, while high-resistance faults are generally considered to meet the level of 3000 ohms and above, the latter being a noise amplification effect caused by a larger transition resistance.

[0079] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A high-resistivity fault location method based on SPWVD and sub-pixel level images, characterized in that: The zero-sequence current is collected and decomposed into time and frequency in the time-frequency domain. A two-dimensional time-frequency graph is plotted with time as the horizontal axis and frequency as the vertical axis. The convex vertex of the two-dimensional time-frequency plot is determined along the time axis. Based on the convex vertex, the range of the convex region along the frequency axis is determined by searching outward to the point where the gradient is zero. Within the frequency axis convex region, a continuous function is obtained by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph, and then sub-pixel level curves are generated through sub-pixel level resampling. The arrival time of the wavefront is located from the subpixel-level curve, and the location of the fault point is calculated based on the arrival time of the wavefront using double-ended ranging.

2. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 1, characterized in that: Drawing a two-dimensional time-frequency graph includes: The collected zero-sequence current is smoothed into a pseudo-Wigner-Vell distribution to generate energy density distributions in time and frequency. Based on the energy density distribution over time and frequency, a two-dimensional time-frequency diagram is plotted with time as the horizontal axis and frequency as the vertical axis.

3. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 1, characterized in that: Determining the range of the frequency axis bulge region includes: The two-dimensional time-frequency graph is preprocessed, and the maximum value of each row along the time axis is taken from the preprocessed two-dimensional time-frequency graph and aggregated into a one-dimensional frequency axis projection curve. The one-dimensional frequency axis projection curve is smoothed using a Gaussian filter to generate a smooth frequency axis curve; the gradient of the smooth frequency axis curve is calculated, and the region where the absolute value of the gradient is greater than a set gradient threshold is set as the region where the gradient changes significantly. Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the convex vertex. Using the convex vertex as the center, the search extends outward to the frequency point where the gradient is zero, generating the initial convex region. Extend the initial left boundary of the initial region by 2 frequency points in the direction of decreasing frequency points, and extend the initial right boundary of the initial region by 2 frequency points in the direction of increasing frequency points to determine the range of the frequency axis convex region.

4. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 3, characterized in that: Preprocessing of the two-dimensional time-frequency graph includes: The two-dimensional time-frequency graph is converted into a grayscale image, and the pixel values ​​of the grayscale image are normalized to the range of [0,1] to generate a normalized image. The image is smoothed and normalized using a Gaussian convolution kernel. The smoothed image is then contrast-stretched so that the pixel values ​​are linearly mapped to the [0,1] interval, generating a preprocessed two-dimensional time-frequency map.

5. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 4, characterized in that: The initial region for generating the protrusion includes: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. The search proceeds outward from the peak point until a frequency point with a gradient value of zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

6. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 1, characterized in that: Generating subpixel level curves includes: Within the defined frequency axis protrusion region, the preprocessed two-dimensional time-frequency plot is summed along the frequency axis to obtain a one-dimensional time axis projection curve. Gaussian filtering is applied to the one-dimensional time axis projection curve to smooth it, resulting in a smoothed time axis curve. Perform cubic spline interpolation on discrete points on a smoothed time axis curve to output a continuous function; By resampling the continuous function at sub-pixel intervals, sub-pixel level curves are obtained.

7. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 1, characterized in that: Locating the wavefront arrival time from a sub-pixel level curve includes: Calculate the first-order difference for the sub-pixel level curve, find the time point when the first-order difference changes from positive to negative and set it as the peak point. Take n points to the left and right of the peak point to determine the wavefront candidate region. Based on the wavefront candidate region, determine the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region; The arrival time of the wavefront is determined based on the Gaussian fitting of the wavefront time and the center x-coordinate.

8. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 7, characterized in that: Determining the Gaussian fitting wavefront time and the center x-coordinate of the subpixel-level curve within the wavefront candidate region includes: Extract the data point set within the candidate wavefront region, transform the standard Gaussian model into a quadratic polynomial through linearization, solve the coefficients of the quadratic polynomial using the least squares method to restore the Gaussian parameters, and generate the Gaussian fitted wavefront time using the Gaussian fitting method. Find the minimum value of the ordinate of all data points in the wavefront candidate region, calculate the effective amplitude of each point relative to the minimum value, normalize the effective amplitude with weights to obtain the normalized weight of each data point in the range [0,1], and use the normalized weight as the coefficient to perform a weighted average on the abscissa of the data point set to obtain the center abscissa of the subpixel-level curve in the wavefront candidate region.

9. The high-resistivity fault location method based on SPWVD and sub-pixel level images according to claim 8, characterized in that: Determining the wavefront arrival time based on Gaussian fitting of the wavefront time and the center x-coordinate includes: When the absolute value of the Gaussian fitted wavefront time minus the center abscissa is less than the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed valid. The Gaussian fitted wavefront time and center abscissa are then weighted and fused to obtain the wavefront arrival time. If the absolute value of the Gaussian fitted wavefront time minus the center abscissa is greater than or equal to the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed invalid. The peak point in the peak detection method is selected, and the wavefront arrival time is calculated by Lagrange interpolation.

10. A high-resistivity fault location system based on SPWVD and sub-pixel level images, characterized in that, include: The two-dimensional time-frequency plotting module is used to collect zero-sequence current, decompose it into time and frequency in the time-frequency domain, and plot a two-dimensional time-frequency plot with time as the horizontal axis and frequency as the vertical axis. The convex region determination module is used to determine the convex vertices along the time axis of the two-dimensional time-frequency graph, and to determine the range of the convex region along the frequency axis by searching outward from the convex vertices to the point where the gradient is zero. The subpixel-level curve generation module is used to obtain a continuous function by performing cubic spline interpolation along the frequency axis on the preprocessed two-dimensional time-frequency graph within the frequency axis convex region, and then generate a subpixel-level curve through subpixel-level resampling. The fault location module is used to locate the arrival time of the wavefront from the sub-pixel level curve, and calculate the location of the fault point based on the arrival time of the wavefront through dual-end ranging.

11. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 10, characterized in that: Drawing a two-dimensional time-frequency graph includes: The collected zero-sequence current is smoothed into a pseudo-Wigner-Vell distribution to generate energy density distributions in time and frequency. Based on the energy density distribution over time and frequency, a two-dimensional time-frequency diagram is plotted with time as the horizontal axis and frequency as the vertical axis.

12. The high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 10, characterized in that: Determining the range of the frequency axis bulge region includes: The two-dimensional time-frequency graph is preprocessed, and the maximum value of each row along the time axis is taken from the preprocessed two-dimensional time-frequency graph and aggregated into a one-dimensional frequency axis projection curve. The one-dimensional frequency axis projection curve is smoothed using a Gaussian filter to generate a smooth frequency axis curve; the gradient of the smooth frequency axis curve is calculated, and the region where the absolute value of the gradient is greater than a set gradient threshold is set as the region where the gradient changes significantly. Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the convex vertex. Using the convex vertex as the center, the search extends outward to the frequency point where the gradient is zero, generating the initial convex region. Extend the initial left boundary of the initial region by 2 frequency points in the direction of decreasing frequency points, and extend the initial right boundary of the initial region by 2 frequency points in the direction of increasing frequency points to determine the range of the frequency axis convex region.

13. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 12, characterized in that: Preprocessing of the two-dimensional time-frequency graph includes: The two-dimensional time-frequency graph is converted into a grayscale image, and the pixel values ​​of the grayscale image are normalized to the range of [0,1] to generate a normalized image. The image is smoothed and normalized using a Gaussian convolution kernel. The smoothed image is then contrast-stretched so that the pixel values ​​are linearly mapped to the [0,1] interval, generating a preprocessed two-dimensional time-frequency map.

14. The high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 13, characterized in that: The initial region for generating the protrusion includes: Within a region where the gradient changes significantly, the frequency point where the gradient changes from positive to negative is set as the peak point. The search proceeds outward from the peak point until a frequency point with a gradient value of zero is found. The frequency point with a gradient value of zero to the left of the peak point is set as the initial left boundary, and the frequency point with a gradient value of zero to the right of the peak point is set as the initial right boundary. The region from the initial left boundary to the initial right boundary is set as the initial region of the convexity.

15. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 10, characterized in that: Generating subpixel level curves includes: Within the defined frequency axis protrusion region, the preprocessed two-dimensional time-frequency plot is summed along the frequency axis to obtain a one-dimensional time axis projection curve. Gaussian filtering is applied to the one-dimensional time axis projection curve to smooth it, resulting in a smoothed time axis curve. Perform cubic spline interpolation on discrete points on a smoothed time axis curve to output a continuous function; By resampling the continuous function at sub-pixel intervals, sub-pixel level curves are obtained.

16. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 10, characterized in that: Locating the wavefront arrival time from a sub-pixel level curve includes: Calculate the first-order difference for the sub-pixel level curve, find the time point when the first-order difference changes from positive to negative and set it as the peak point. Take n points to the left and right of the peak point to determine the wavefront candidate region. Based on the wavefront candidate region, determine the Gaussian fitting wavefront time and the center x-coordinate of the sub-pixel level curve within the wavefront candidate region; The arrival time of the wavefront is determined based on the Gaussian fitting of the wavefront time and the center x-coordinate.

17. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 16, characterized in that: Determining the Gaussian fitting wavefront time and the center x-coordinate of the subpixel-level curve within the wavefront candidate region includes: Extract the data point set within the candidate wavefront region, transform the standard Gaussian model into a quadratic polynomial through linearization, solve the coefficients of the quadratic polynomial using the least squares method to restore the Gaussian parameters, and generate the Gaussian fitted wavefront time using the Gaussian fitting method. Find the minimum value of the ordinate of all data points in the wavefront candidate region, calculate the effective amplitude of each point relative to the minimum value, normalize the effective amplitude with weights to obtain the normalized weight of each data point in the range [0,1], and use the normalized weight as the coefficient to perform a weighted average on the abscissa of the data point set to obtain the center abscissa of the subpixel-level curve in the wavefront candidate region.

18. A high-resistivity fault location system based on SPWVD and sub-pixel level images according to claim 17, characterized in that: Determining the wavefront arrival time based on Gaussian fitting of the wavefront time and the center x-coordinate includes: When the absolute value of the Gaussian fitted wavefront time minus the center abscissa is less than the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed valid. The Gaussian fitted wavefront time and center abscissa are then weighted and fused to obtain the wavefront arrival time. If the absolute value of the Gaussian fitted wavefront time minus the center abscissa is greater than or equal to the interval threshold, the Gaussian fitted wavefront time and center abscissa data are deemed invalid. The peak point in the peak detection method is selected, and the wavefront arrival time is calculated by Lagrange interpolation.

Images