Power distribution network fault location method based on multi-source synchronous waveforms and traveling wave front

Abstract

The application relates to the technical field of power distribution network fault positioning, in particular to a power distribution network fault positioning method based on multi-source synchronous waveforms and traveling wave wave fronts, which comprises the following steps: power distribution network multi-end synchronous waveform data acquisition and preprocessing; a mathematical morphological gradient operator is used to process the preprocessed waveforms; the arrival time of the traveling wave wave front is detected according to the extreme points of the morphological gradient; a traveling wave propagation path model is established; the theoretical propagation time of each candidate fault point to each measurement node is calculated; the theoretical time is matched with the actually detected wave front arrival time; the section where the fault is located is determined; the preliminary position of the fault point is calculated by using the traveling wave arrival time difference of the two measurement points; the transition resistance value is estimated according to the waveform characteristics; the positioning result is corrected to obtain the fault point position; the confidence of the positioning result is comprehensively evaluated; and the fault position and the confidence level are output. The application can improve the fault detection and positioning accuracy of the power distribution network.

Description

Technical Field

[0001] This application relates to the field of distribution network fault location technology, specifically to a distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts. Background Technology

[0002] The power distribution network is a crucial component of the power system, directly serving users, and its operational reliability directly impacts users' power supply quality and electricity experience. Distribution networks are complex in structure, have numerous branches, and operate in diverse modes, resulting in a relatively high failure rate. Quickly and accurately locating fault points is of great significance for shortening power outage time, improving power supply reliability, and reducing operation and maintenance costs.

[0003] Currently, the main methods for fault location in power distribution networks can be categorized as follows: One method is the impedance method. Based on the voltage and current measured after a fault, the impedance of the faulty circuit is calculated, and then the fault distance is calculated based on the impedance per unit length of the line. This method is simple in principle and easy to implement, but it has significant shortcomings: First, the location accuracy is greatly affected by the transition resistance; for high-resistance faults, the error can reach tens or even hundreds of meters. Second, the distribution network has many branches, and the influence of load current can also lead to errors. Finally, the impedance method can only provide an approximate distance and cannot determine which branch the fault is on.

[0004] The second method is the traveling wave method. This method utilizes the transient traveling wave generated by the fault for location, calculating the fault distance based on the wave's propagation time and velocity. The traveling wave method offers high location accuracy and is unaffected by transition resistance and load, making it a current research hotspot. However, its application in distribution networks faces several challenges: First, distribution networks have numerous branches and complex structures, resulting in significant refraction and reflection of the traveling wave during propagation. This leads to multiple wavefronts detected at the measurement point, making it difficult to accurately distinguish and match which wavefronts correspond to the fault point and which are reflected waves. Second, the number of measurement points in a distribution network is limited, often failing to ensure that both ends of the fault section have measuring devices. Finally, in high-resistance faults, the traveling wave amplitude is small, and high-frequency components attenuate rapidly, making wavefront detection difficult and prone to missed or false detections.

[0005] Third is the fault indicator method. Fault indicators are installed on the power distribution line, and the presence of a fault is determined by the change in current during a fault. The faulty section is identified by the operation of the indicator. This method is simple to install and low in cost, but it can only locate the section, with very low accuracy. It can generally only pinpoint the area between two indicators, and manual line inspection is still required to find the specific fault point, making it inefficient.

[0006] Fourthly, artificial intelligence methods. These methods employ machine learning algorithms such as neural networks and support vector machines to train models using fault data for localization. Theoretically, these methods can handle complex nonlinear problems, but they require a large number of fault samples as a training basis. However, fault samples in distribution networks are often scarce, especially those of different types, locations, and transition resistances. Insufficient samples will seriously affect the accuracy and generalization ability of the model.

[0007] Furthermore, with the large-scale integration of distributed generation sources, the distribution network has transformed from a traditional single-source radial network into a multi-source network. This has significantly altered the distribution and characteristics of fault currents, rendering traditional fault location methods often inapplicable, resulting in decreased accuracy or even failure. Most existing methods do not consider the impact of distributed generation source integration, leading to poor adaptability. Summary of the Invention

[0008] To address the aforementioned technical problems, this application provides a method for fault location in distribution networks based on multi-source synchronous waveforms and traveling wavefronts, thereby resolving the existing issues.

[0009] The fault location method for distribution networks based on multi-source synchronous waveforms and traveling wavefronts in this application adopts the following technical solution: One embodiment of this application provides a method for fault location in a distribution network based on multi-source synchronous waveforms and traveling wavefronts, comprising the following steps: Current traveling wave waveform data after a fault is collected at multiple key nodes of the distribution network and preprocessed. The preprocessed waveform is processed using a mathematical morphological gradient operator, and the arrival time of the traveling wave front is detected based on the extreme points of the morphological gradient. A topology map is established using the topology of the distribution network. The theoretical propagation time from each candidate fault point to each measurement node is calculated. The theoretical time is matched with the actual wavefront arrival time to determine the fault section. Within the determined fault section, the initial location of the fault point is calculated using the time difference of arrival of the traveling waves at the two measuring points. The transition resistance is estimated based on the waveform characteristics, and the location result is corrected to obtain the fault point location. By combining the consistency of the multi-terminal waveforms, the wavefront matching degree, and the dispersion of the positioning results, the confidence level of the positioning results is comprehensively evaluated to obtain the fault location and confidence level.

[0010] Preferably, the preprocessing includes: removing abnormal data points from each traveling wave waveform data and completing them using linear interpolation; removing random noise and power frequency interference using morphological opening-closing combination filtering; and performing amplitude normalization processing on the waveform data of each channel.

[0011] Preferably, the detection of the arrival time of the traveling wave front specifically includes: performing dilation and erosion operations on the preprocessed waveform, subtracting the result of the erosion operation from the result of the dilation operation to obtain the morphological gradient, and the time corresponding to the maximum point of the morphological gradient is the arrival time of the traveling wave front.

[0012] Preferably, the validity of the detected wavefront is verified, which specifically includes: comparing the wavefront's amplitude, steepness, and polarity with the characteristic range of a typical traveling wavefront. If all three characteristics are within the characteristic range, the detected wavefront is determined to be a valid wavefront; otherwise, it is determined to be interference or a pseudo wavefront and is discarded.

[0013] Preferably, the step of establishing a topology graph using the topology of the distribution network and calculating the theoretical propagation time from each candidate fault point to each measurement node specifically includes: establishing a topology graph based on the topology of the distribution network, wherein each device is abstracted as an edge of the graph, and buses, nodes, and branch points are abstracted as vertices of the graph, and the length, model, and wave velocity parameters of each line segment are labeled; each line segment in the distribution network is regarded as a candidate fault segment, and each candidate fault point is pre-set in each candidate fault segment.

[0014] Preferably, determining the faulty section specifically includes: For each candidate fault point, the propagation path and corresponding theoretical propagation time from the candidate fault point to each measurement node are calculated according to the shortest path principle. The theoretical propagation time is equal to the total length of the propagation path divided by the traveling wave speed. The calculated theoretical propagation time of each measurement point is matched with the actual detected wavefront arrival time. The sum of the time residuals of each set of matches is calculated. The candidate fault segment corresponding to the candidate fault point of the set of matches with the smallest sum of time residuals is taken as the fault segment.

[0015] Preferably, the calculation of the preliminary location of the fault point specifically includes: The two measurement nodes at both ends of the fault section are designated as M-end and N-end, respectively. If the wavefront arrives first at M-end, then the distance from the fault point to M-end is... If the wavefront at the N end arrives first, then the distance from the fault point to the M end is... Wherein, the distance x from the fault point to end M is the initial location of the fault point, the total length of the fault section is L, the wave velocity of the traveling wave in this section of the line is v, and the time difference between the arrival times of the initial traveling wave front detected at end M and end N is Δt.

[0016] Preferably, estimating the transition resistance based on waveform characteristics specifically includes: extracting three features—peak amplitude of the wavefront, rise time of the wavefront, and proportion of high-frequency energy of the wavefront—to form a feature vector; matching this feature vector with the feature vectors corresponding to different transition resistances, and using the transition resistance with the highest matching degree as the estimated value of the transition resistance.

[0017] Preferably, the wave velocity of the traveling wave is corrected based on the estimated transition resistance, wherein the correction amount is proportional to the magnitude of the transition resistance; the corrected wave velocity is then substituted back into the precise positioning formula to calculate the fault location, thereby obtaining the corrected precise positioning result.

[0018] Preferably, the confidence level of the comprehensive evaluation positioning result specifically includes: Calculate the wavefront matching degree, expressed as the reciprocal normalized mean residual; calculate the waveform consistency, expressed as the cross-correlation coefficient between waveforms; calculate the dispersion of the positioning results, expressed as the coefficient of variation of the positioning results. The three indicators—wavehead matching degree, waveform consistency, and positioning result dispersion—are normalized separately and then fused using a weighted summation method to obtain a comprehensive confidence score. Based on the confidence score, the positioning results are divided into multiple levels, with different levels corresponding to different positioning error ranges.

[0019] This application has at least the following beneficial effects: (1) This application constructs a five-layer positioning architecture, which includes wavefront detection, wavefront matching, segment location, precise location, and result evaluation. From signal detection to the final output, each layer is progressive and interconnected, forming a complete distribution network fault location solution. Unlike the traditional approach of jumping directly from the wavefront to the location result in one step, this application adopts a layered and progressive strategy. First, topology matching is used to determine the fault segment, then precise location is performed within the segment, and finally, confidence evaluation is conducted. This architecture design not only utilizes topology information to solve the problem of multi-branch wavefront matching, but also narrows the scope of precise location through segment location, and provides the reliability of the result through confidence evaluation. It is more systematic, scientific, and practical than traditional methods.

[0020] (2) Innovative Method for Wavefront Detection Based on Mathematical Morphology. This application introduces mathematical morphology into traveling wave front detection, proposing a wavefront detection method based on morphological gradients. Mathematical morphology is a nonlinear signal processing method that extracts the geometric features of a signal through basic operations such as dilation and erosion. Morphological gradients can effectively highlight abrupt changes in the signal, showing excellent detection performance for step-like abrupt changes in traveling wave fronts. Compared with traditional thresholding and wavelet methods, the morphological method is computationally simple, has strong noise resistance, and is well-adapted to the shape of the wavefront. Especially under conditions where the wavefront is flat due to low signal-to-noise ratio and high impedance faults, it can still accurately detect the wavefront position. This is more robust and more accurate than traditional wavefront detection methods.

[0021] (3) Innovation in Multi-Terminal Wavefront Matching Mechanism under Topological Constraints. Addressing the core challenges of numerous branches, multiple wavefronts, and difficult matching in distribution networks, this application proposes a wavefront matching method under topological constraints. Instead of simply comparing the first wavefront at each end, it uses the distribution network topology as a constraint, traversing all possible fault locations on the topology map, calculating the theoretical propagation time, and then matching it with the actual wavefront time to find the pair with the smallest residual. This method cleverly utilizes topological information, transforming the wavefront matching problem into an optimal matching problem on the topology map, fundamentally solving the problem of chaotic wavefront matching under multiple branches. Furthermore, combining wavefront polarity and amplitude information for auxiliary verification further improves the matching accuracy.

[0022] (4) Innovative Adaptive Correction Method for Transition Resistance. To address the problem of inaccurate fault location in high-resistance faults, this application proposes a transition resistance estimation and adaptive correction method based on waveform characteristics. The transition resistance is estimated using three characteristics: wavefront amplitude, rise time, and high-frequency energy proportion. The equivalent wave velocity is then corrected based on the transition resistance, thereby correcting the location result. Traditional methods often assume a constant wave velocity, neglecting the influence of transition resistance. In reality, transition resistance causes high-frequency component attenuation, reducing the equivalent wave velocity and resulting in location errors. The correction method in this application considers this influence; the larger the transition resistance, the larger the correction, significantly improving the location accuracy under high-resistance faults, with a noticeable correction effect.

[0023] (5) Innovation of Multi-Dimensional Confidence Assessment System. This application does not simply provide a location and then stop, but designs a complete confidence assessment system. Indicators are selected from three dimensions: wavefront matching degree, waveform consistency, and location result dispersion. A comprehensive confidence score is obtained through weighted fusion and divided into levels, each corresponding to a different error range. The introduction of confidence assessment makes the location result no longer an isolated numerical value, but a complete piece of information with quantitative reliability indicators. Maintenance personnel can adopt different response strategies based on the confidence level, improving the engineering practical value of the location result. Attached Figure Description

[0024] Figure 1 The flowchart illustrates the steps of the power distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts provided in this application. Detailed Implementation

[0025] The following description, in conjunction with the accompanying drawings, details the specific scheme of the power distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts provided in this application.

[0026] This application provides an embodiment of a distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts. For details, please refer to [link to relevant documentation]. Figure 1 This includes the following steps: This embodiment uses a 10kV urban distribution network as an example to describe the fault location method in detail. The distribution network has a radial structure, starting from the 10kV outgoing line of a 110kV substation. The main line is approximately 5 kilometers long and has three main branches: an east branch, a west branch, and a south branch, each approximately 2 to 3 kilometers long. The entire line is primarily overhead, with some sections using cables. The conductor type is mainly JKLYJ-185. Two distributed photovoltaic power sources are connected to the distribution network, with a total installed capacity of approximately 2MW.

[0027] This application chose the aforementioned distribution network as an example because such urban distribution networks experience frequent faults in actual operation, and have many branches and complex structures, making traditional fault location methods often ineffective. Recently, this distribution network has experienced multiple single-phase grounding faults with unclear fault locations, making line inspection and locating difficult. Maintenance personnel urgently need a high-precision and high-reliability fault location method.

[0028] The overall technical approach of this embodiment can be summarized as five progressive steps: First, multi-terminal synchronous data acquisition and preprocessing are performed to lay a solid data foundation; then, mathematical morphology is used for precise detection of traveling wave fronts to extract key time information; next, multi-terminal wavefront matching is performed under topological constraints to determine the fault segment; subsequently, precise location is performed within the segment and transition resistance correction is applied to obtain the accurate location; finally, confidence level assessment and result output are performed. The entire process progresses from coarse to fine, forming a complete fault location solution. The specific implementation steps are as follows: Step 1: Collect current traveling wave waveform data after a fault at multiple key nodes of the distribution network and perform preprocessing.

[0029] The accuracy of any fault location method relies on high-quality data, and this is especially true for traveling wave location. Traveling wave signals have high frequencies and change rapidly, placing high demands on data synchronization accuracy and sampling rate. Therefore, in this embodiment, a multi-terminal synchronous data acquisition system is first established, and the raw data is preprocessed to provide reliable data input for subsequent wavefront detection and location calculation.

[0030] S11. Arrangement and synchronization of measuring devices.

[0031] First, we planned the layout of the measuring devices. Considering the radial structure and branching characteristics of the distribution network, we chose to place the measuring devices at key locations such as substation outgoing lines, branch entrances, and distributed power source grid connection points. This ensures measurement coverage of the main lines and major branches while controlling the number of devices and costs.

[0032] In this embodiment, five sets of synchronous traveling wave acquisition devices are deployed, located at: the 10kV outgoing line of the substation (referred to as Station S); the entrance of the east branch (referred to as point D); the entrance of the west branch (referred to as point X); the middle section of the south branch (referred to as point N); and the No. 1 photovoltaic grid connection point (referred to as point G1). All five devices support BeiDou satellite timing, with a time synchronization accuracy better than 500 nanoseconds. This embodiment requires high synchronization accuracy because the propagation speed of traveling waves is close to the speed of light, approximately 300 meters per microsecond. If the synchronization error reaches 1 microsecond, the positioning error could reach several hundred meters, completely negating the accuracy advantage of traveling wave positioning. A synchronization accuracy of 500 nanoseconds ensures that the positioning error caused by synchronization is within 150 meters, meeting the engineering requirements.

[0033] The sampling rate was set to 10MHz, meaning one point was sampled every 0.1 microseconds. This sampling rate was chosen after careful consideration: too low a sampling rate would fail to capture the rapid changes in the traveling wave, reducing wavefront detection accuracy; too high a sampling rate would result in excessive data volume, placing a heavy burden on storage and transmission. 10MHz is sufficient for Nyquist sampling requirements for traveling wave signals below ultra-high frequency, accurately capturing nanosecond-level changes. The recording length for each channel is 2 milliseconds: 0.5 milliseconds before the fault and 1.5 milliseconds after the fault. This ensures a complete record of the fault transient process without generating excessive redundant data.

[0034] S12, Outlier removal and missing value completion.

[0035] After acquiring the raw waveform data, the first step is data cleaning, also known as outlier handling. In actual engineering projects, due to communication interference, momentary device failures, and other reasons, some outliers are inevitable in the raw data. If these outliers are not removed, they will seriously affect the subsequent wavefront detection results.

[0036] Here, the Grubbs criterion is used to identify outliers. The basic idea of ​​the Grubbs criterion is intuitive: calculate the mean and standard deviation of the data series, and then see how far each data point deviates from the mean. If the deviation exceeds a critical value, it is judged as an outlier. The critical value is determined based on the confidence level and the sample size. In this embodiment, the confidence level is set to 95%, which is a commonly used confidence level in engineering.

[0037] The data quality of all channels was found to be generally good, with only a few channels showing a small number of anomalies, mainly caused by communication interference spikes, which were all removed.

[0038] For gaps left after removing outliers, as well as short-term missing data due to other reasons, linear interpolation is used to fill in the gaps. As long as the number of consecutive missing data points does not exceed 5, the error of linear interpolation is very small and will not affect subsequent wavefront detection. The reason for choosing linear interpolation instead of more complex interpolation methods is that the traveling wave signal changes approximately linearly in a very short time, linear interpolation is accurate enough, and it is also simple and efficient to calculate.

[0039] S13, Morphological filtering for noise reduction.

[0040] After data completion, appropriate filtering and noise reduction are required. Here, morphological opening-closing combination filtering is used to denoise the signal.

[0041] The reason for choosing morphological filtering instead of commonly used wavelet filtering or digital filtering is mainly due to two considerations: First, morphological filtering is a nonlinear filtering method, which has a good effect on suppressing impulse noise and can better preserve the abrupt edges of the signal. If the filtering also smooths out the steepness of the wavefront, it will be detrimental to subsequent detection. Second, morphological filtering is simple to calculate and has a fast operation speed, making it suitable for online real-time processing.

[0042] Specifically, opening operations involve erosion followed by dilation, which removes positive impulse noise from a signal; closing operations involve dilation followed by erosion, which removes negative impulse noise. Using opening and closing in combination can remove both positive and negative impulse noise while preserving the original shape and abrupt changes of the signal relatively well.

[0043] In this embodiment, the structuring element is a flat structuring element with a length of 5 sampling points. If the structuring element is too small, the denoising effect is limited; if the structuring element is too large, it will wear down the details of the signal, resulting in the loss of detailed information. 5 sampling points correspond to 0.5 microseconds, which is slightly shorter than the typical rising time of a traveling wave, achieving a good balance between denoising and shape preservation.

[0044] After morphological filtering, random noise is significantly reduced, and the abrupt change characteristics of the traveling wave are more prominent, creating favorable conditions for the next step of wavehead detection.

[0045] S14, Amplitude Normalization.

[0046] The final preprocessing step is amplitude normalization. The waveform of each channel is normalized individually, reducing the maximum absolute value of the waveform to 1.

[0047] The reason for normalization is simple: different measurement devices may have different gains, and the amplitude of the traveling wave at different locations will naturally be different. If the original amplitudes are directly compared, unnecessary biases will be introduced. After normalization, the waveforms of each channel are on the same scale, which facilitates subsequent waveform comparison and feature matching, and also makes the calculation results such as morphological gradients comparable.

[0048] Step 2: The preprocessed waveform is processed using the mathematical morphological gradient operator, and the arrival time of the traveling wave front is detected based on the extreme points of the morphological gradient.

[0049] After preprocessing, the wavefront detection stage begins. Wavefront detection is fundamental to traveling wave localization; if the wavefront timing is inaccurate, subsequent precise localization calculations are meaningless. Traditional wavefront detection methods include thresholding, wavelet analysis, and the AIC criterion, each with its own advantages and disadvantages. This embodiment employs the mathematical morphological gradient method for wavefront detection, primarily because morphological methods are computationally simple, have strong noise resistance, and are sensitive to abrupt changes, making them particularly suitable for detecting step-change signals like traveling waves.

[0050] S21. Selection of structural elements.

[0051] Wavefront detection employs the morphological gradient method, first requiring the determination of the structuring element. Here, a flat structuring element with a length of 5 sampling points is also chosen. This length is determined based on the sampling rate and the typical rise time of the traveling wave; 5 sampling points correspond to 0.5 microseconds, slightly shorter than the typical rise time of a traveling wave, effectively highlighting the wavefront without introducing too much noise.

[0052] S22, Expansion and Erosion Operations.

[0053] After determining the structuring element, dilation and erosion operations are performed on the normalized waveform.

[0054] The dilation operation involves sliding a structuring element across the waveform from left to right. For each position, the maximum signal value within the structuring element's coverage area is taken as the dilation output for that position. The erosion operation is the opposite: the minimum signal value within the structuring element's coverage area is taken as the erosion output for that position. The specific morphological processing procedures are well-known to those skilled in the art and will not be described in detail in this embodiment.

[0055] S23, Calculate morphological gradient.

[0056] With the results of dilation and erosion, the morphological gradient can be calculated. The morphological gradient equals the dilation result minus the erosion result.

[0057] In regions where the signal is relatively flat, the results of dilation and erosion are not significantly different, so the gradient value is small. However, at places where the signal changes abruptly, that is, at the position of the traveling wave front, dilation pushes the wave front forward a little, while erosion pulls it back a little, resulting in a large difference between the two and a noticeable peak in the gradient value.

[0058] Therefore, morphological gradients are equivalent to extracting the abrupt changes in a signal and turning them into obvious peaks. The location with the largest gradient is where the signal changes most dramatically, which is the position where the wavefront arrives. This is much clearer than directly finding abrupt changes on the original waveform.

[0059] S24. Determine the wavefront timing by detecting the maximum point.

[0060] After obtaining the morphological gradient sequence, the next step is to find the peaks. This involves detecting all local maxima in the morphological gradient sequence, with each maximum corresponding to a possible wavefront.

[0061] Preferably, considering that not all small fluctuations can be counted as wavefronts, otherwise small spikes caused by noise would also be misjudged, an amplitude threshold is set. In this embodiment, 10% of the maximum gradient value is taken as the threshold, and maxima below the threshold are ignored. This can filter out small fluctuations caused by noise and retain only truly meaningful wavefronts.

[0062] In this embodiment, 3 to 5 valid wavefronts were detected at each of the 5 measurement points, and the first and largest wavefront was the wavefront at which the initial traveling wave of the fault arrived.

[0063] S25, Wavehead validity verification.

[0064] After detecting a candidate wavefront, it cannot be used directly; its validity must be verified to eliminate interference and spurious wavefronts. There are many transient signals in the distribution network, such as switching operations, load switching, and lightning induction, which can all generate pulses similar to traveling waves. If these are not distinguished, it is easy to cause mislocation.

[0065] Therefore, in this implementation, the wavefront is compared with the characteristic range of a typical traveling wavefront based on its three characteristics: amplitude, steepness, and polarity. If all three characteristics are within the characteristic range, the detected wavefront is determined to be a valid wavefront; otherwise, it is determined to be interference or a pseudo wavefront and is discarded.

[0066] In this embodiment, a typical traveling wave front is manually selected to verify whether the three characteristics are within the set characteristic range. Preferably, the normalized wave front amplitude should be greater than 0.1, as a value that is too small may be noise; wave front steepness: the slope of the rising edge should be greater than 0.05 microseconds, as the rising edge of a real fault traveling wave is relatively steep; wave front polarity: it should be consistent with the theoretical polarity corresponding to the fault type, and the initial wave front polarity of each measurement point should be coordinated with each other.

[0067] If all three characteristics are met, it is determined to be a valid wavehead; if any one of them is not met, it is determined to be invalid and is discarded.

[0068] In this embodiment, the first wavefront detected at each measurement point is verified as a valid wavefront of the initial traveling wave of the fault. The arrival times of the wavefronts at each point are as follows: Station S: 0.0 microseconds (initial reference time); Point D: 12.8 microseconds; Point X: 8.5 microseconds; Point N: 21.3 microseconds; Point G1: 15.6 microseconds. These times are relative to the arrival time of the wavefront at Station S.

[0069] Step 3: Build a topology map using the distribution network topology, calculate the theoretical propagation time from each candidate fault point to each measurement node, match the theoretical time with the actual wavefront arrival time, and determine the fault section.

[0070] After detecting the wavefronts at each end, the next challenge is wavefront matching, the most critical problem in distribution network traveling wave localization. Unlike transmission lines which have only two ends, distribution networks have numerous branches, and each measurement point will detect multiple wavefronts. It's easy to confuse which wavefront corresponds to which path. Traditional methods often only consider the first wavefront, but in complex branching situations, the first wavefront may not be a direct wave but a reflected wave, leading to positioning errors.

[0071] The approach of this embodiment is to use the distribution network topology as a constraint, allowing wavefront matching to be performed within the topology framework, rather than by guesswork. In other words, it first calculates on the topology map when each measurement point should receive the wavefront at various fault locations, then compares this calculation with the actual detected wavefront times; the one that best matches is the correct match.

[0072] S31. Create a topology graph.

[0073] The first step is to abstract the physical structure of the distribution network into a mathematical topological graph. The modeling method is intuitive: substations, branch points, and customer access points are abstracted as nodes, and each line segment is abstracted as an edge connecting the nodes, with each edge labeled with its length and conductor type. With this graph model, graph theory methods can be used to calculate path and propagation time. Each line segment in the distribution network is then considered a candidate fault segment, and candidate fault points are pre-defined within each segment.

[0074] In this embodiment, the main node and line parameters are as follows: the line length from station S to branch node J is 2.5km; the line length from node J to point D at the end of the east branch is 2.0km; the line length from node J to point X at the end of the west branch is 1.5km; the line length from node J to point N at the south branch is 3.0km; the photovoltaic grid connection point G1 is located on the west branch, 0.8km away from node J.

[0075] The speed of travel wave propagation on overhead lines is approximately meters per second, close to the speed of light; approximately [speed in cable] Meters per second. This embodiment mainly uses overhead lines, and approximate values ​​are used for ease of calculation. Meters per second, or approximately 300 meters per microsecond.

[0076] S32, Wave Head Information Compilation.

[0077] After establishing the topology map, the wavefront information of each measurement point, including arrival time, polarity, and amplitude, is compiled as input data for subsequent matching.

[0078] The initial wavefront polarity at all five measurement points is positive, indicating that the traveling wave generated by the fault has the same initial polarity at these measurement points as it propagates in all directions. This information will be used later to help verify the reasonableness of the matching results.

[0079] S33. Topological traversal and theoretical time calculation.

[0080] The next step is the core matching process. This involves traversing all possible fault locations on the topology map and calculating the theoretical propagation time from each location to each measurement point.

[0081] If we traverse point by point, the computational load will be very large. To improve efficiency, we adopt a segment-by-segment traversal method, that is, we treat each segment of the line as a candidate fault segment and write the expression for the theoretical wavefront arrival time of each measurement point when the fault point is located in that segment.

[0082] For each candidate fault point, the propagation path and corresponding theoretical propagation time from the candidate fault point to each measurement node are calculated according to the shortest path principle. The theoretical propagation time is equal to the total length of the propagation path divided by the traveling wave speed. The calculated theoretical propagation time of each measurement point is matched with the actual detected wavefront arrival time. The sum of the time residuals of each set of matches is calculated. The candidate fault segment corresponding to the candidate fault point of the set of matches with the smallest sum of time residuals is taken as the fault segment.

[0083] For example, assuming the fault is located on the main line between station S and node J, x kilometers away from station S, then the time to station S = x ÷ wave speed; the time to node J = (2.5 - x) ÷ wave speed; the time to point D = (2.5 - x + 2.0) ÷ wave speed, and so on, to calculate the time to each node.

[0084] Each segment can be expressed as a time-to-fault-location equation according to the shortest path principle. The reason for using the shortest path is that traveling waves always propagate along the shortest path, and the first wave to reach the measurement point is always the direct wave on the shortest path.

[0085] Specifically, after obtaining the theoretical time expression for each segment, it is further compared with the actual measured arrival time. For each candidate line segment, assuming the fault is located in that segment, the fault location variable is substituted to obtain the expression for the theoretical arrival time of each measurement point. Then, the difference is calculated with the actual measured arrival time to calculate the time residual.

[0086] Because there are 5 measurement points, 5 equations can be established, while there is only one unknown (fault location), forming an overdetermined system of equations. Overdetermined systems of equations do not have exact solutions; only optimal solutions can be found. Here, the least squares method is used to solve this, that is, to find a fault location that minimizes the sum of the squares of the 5 time residuals. The minimum residual sum corresponds to the optimal matching result.

[0087] In this embodiment, the least squares method is considered to have good statistical properties for the error of the normal distribution and is simple to calculate. It is the most commonly used method for solving overdetermined equations in engineering. The specific statistical calculation process is existing technology and will not be described in detail in this embodiment.

[0088] If the fault is indeed in a certain segment, then the theoretical time and the actual time should match best, and the residual will naturally be the smallest. Therefore, calculate the minimum residual sum for all candidate fault segments, and the candidate fault segment with the smallest residual sum is the fault segment.

[0089] In this embodiment, calculations show that: the residual sum of the fault on the SJ main line is approximately 3.2; the residual sum of the fault on the eastern branch is approximately 1.5; the residual sum of the fault on the western branch is approximately 0.3; and the residual sum of the fault on the southern branch is approximately 4.8. The residual sum of the western branch is the smallest and much smaller than the others, indicating that the probability of the fault being located on the western branch is the highest.

[0090] To further confirm the reliability of the results, we cannot rely solely on the residual metric; we must also combine hierarchical search and multi-dimensional information for cross-validation. Multi-dimensional validation can effectively reduce the probability of misjudgment.

[0091] First, consider the polarity: the initial wavefront polarity at all measurement points is positive. For a traveling wave generated at the same fault point, the polarity of the initial direct wave detected at each measurement point should be consistent. The detection results here conform to this rule, indicating that the matching is self-consistent.

[0092] Looking further at the amplitude: the wavefront amplitude at point X is the largest, indicating that point X is closest to the fault point. This is consistent with the judgment that the fault is in the western branch, because the farther the traveling wave travels, the greater the amplitude attenuation. The closer the measurement point is to the fault point, the larger the wavefront amplitude should be.

[0093] By combining information from three dimensions—time residual, amplitude, and polarity—the fault was ultimately determined to be located on the western branch, specifically on the line between node J and point X. The mutual corroboration of information from these three dimensions improved the reliability of the section location.

[0094] Step S4: Within the determined fault section, calculate the preliminary location of the fault point using the arrival time difference of the traveling waves at both ends of the measurement point, estimate the transition resistance based on the waveform characteristics, and correct the location result to obtain the fault point location.

[0095] After identifying the faulty section, this embodiment will locate the fault point. Section location is used to roughly locate the line where the fault is located, but in real-world scenarios, maintenance personnel need to know the exact location of the fault so that they can go directly to the fault point without having to search the entire line slowly. The accuracy of the precise location directly determines the efficiency of the line inspection.

[0096] S41, Preliminary Positioning.

[0097] The basic principle of precise location is actually quite simple: it uses the propagation speed of a traveling wave and the time difference between its two ends to calculate the distance. Two measurement nodes at the two ends of the fault section are designated as M and N, respectively. If the wavefront at M arrives first, the distance from the fault point to M is calculated. If the wavefront at the N end arrives first, then the distance from the fault point to the M end is... Wherein, the distance x from the fault point to end M is the initial location of the fault point, the total length of the fault section is L, the wave velocity of the traveling wave in this section of the line is v, and the time difference between the arrival times of the initial traveling wave front detected at end M and end N is Δt.

[0098] Specifically, in this embodiment, the faulty section is the western branch between node J and point X, with a total length L = 1.5 km. Measurement points at both ends of the faulty section are selected for calculation: station S and point X. The wavefront arrival time at station S is 0.0 microseconds, and at point X it is 8.5 microseconds. It's important to note the physical meaning of the time difference: the distance from station S to node J is 2.5 km, and the distance from node J to the fault point is x. Therefore, the distance from the fault point to station S is 2.5 km plus x, and the distance to point X is 1.5 km minus x. The difference between these distances determines the time difference.

[0099] The time it takes for the traveling wave to travel from the fault point to station S is tS = (2500 + x) ÷ 300 microseconds, and the time it takes to travel to point X is tX = (1500 - x) ÷ 300 microseconds. The time difference between the two is Δt = tS - tX = (2500 + x - 1500 + x) ÷ 300 = (1000 + 2x) ÷ 300. The actual measured time difference is 8.5 microseconds (station S arrives first, and point X arrives later). Substituting these values, we get: (1000 + 2x) ÷ 300 = 8.5, 1000 + 2x = 2550, x = 775 meters. This means the fault point is 775 meters away from node J, and on the western branch, it is 1500 - 775 = 725 meters away from point X.

[0100] This is the preliminary accurate positioning result. This result is calculated under the assumption of a constant wave speed, but in reality, the transition resistance will affect the frequency components of the traveling wave, and thus affect the equivalent wave speed, so correction is still needed.

[0101] S42, Transition resistance correction.

[0102] Traditional traveling wave location methods often assume a constant wave velocity, directly using a fixed value for calculation. However, in reality, when a fault has a transition resistance, the high-frequency components of the traveling wave are severely attenuated, with the remaining energy concentrated in the low-frequency range. Since the wave velocity of the low-frequency components is slightly lower than that of the high-frequency components, using the original high-frequency wave velocity for calculation will introduce errors. The larger the transition resistance, the more pronounced this error.

[0103] To address this issue, this embodiment proposes a transition resistance estimation and adaptive correction method based on waveform characteristics.

[0104] First, estimate the magnitude of the transition resistance. Extract three feature parameters: peak amplitude of the wavefront, rise time of the wavefront, and proportion of high-frequency energy of the wavefront to form a feature vector. Calculate the similarity between this feature vector and the corresponding feature vectors under different transition resistances, and use the transition resistance with the highest similarity as the estimated value of the transition resistance.

[0105] 1. Wavefront peak amplitude: In this embodiment, the normalized value is approximately 0.6 (relative to the typical amplitude of a metallic ground fault).

[0106] 2. Wave rise time: In this embodiment, it is approximately 1.2 microseconds (approximately 0.5 microseconds for metallic faults).

[0107] 3. High-frequency energy percentage of wave head: approximately 35% in this embodiment (approximately 60% for metallic faults).

[0108] Considering that the influence of transition resistance on traveling waves is mainly reflected in three aspects: first, amplitude attenuation—the larger the transition resistance, the smaller the wavefront amplitude; second, slower rise time—the larger the transition resistance, the longer the rise time; and third, faster attenuation of high-frequency components—the larger the transition resistance, the lower the proportion of high-frequency energy. Therefore, this embodiment selects the above three characteristics to reflect the influence of transition resistance from different perspectives, and uses them for comprehensive estimation to improve accuracy.

[0109] Furthermore, the feature vector composed of these three features is matched with a standard template library. The standard template library, established through simulation and experimental testing, contains feature vectors for different transition resistances (0Ω, 50Ω, 100Ω, 200Ω, 500Ω, 1000Ω). In this embodiment, the matching method calculates the Euclidean distance between the feature vector obtained in the above process and the feature vector corresponding to each template. The Euclidean distance is negatively correlated with the matching degree; the smaller the distance, the higher the matching degree. Therefore, the transition resistance of the template with the smallest distance is used as the estimated value of the transition resistance.

[0110] In this embodiment, the template with the highest matching degree is the 100Ω transition resistance, so the estimated transition resistance is about 100Ω.

[0111] Furthermore, wave velocity correction is performed after estimating the transition resistance. When the transition resistance is 100Ω, the high-frequency components are attenuated to some extent, and the equivalent wave velocity decreases by about 0.6%. The original wave velocity is taken as 3×10^8 meters per second, and the corrected wave velocity is approximately 2.982×10^8 meters per second, or about 298.2 meters per microsecond.

[0112] The fault location was recalculated using the corrected wave velocity: the time difference remained at 8.5 microseconds, but the wave velocity became 298.2 meters per microsecond.

[0113] Distance difference = 8.5 × 298.2 ≈ 2534.7 meters, 1000 + 2x = 2534.7, 2x = 1534.7, x ≈ 767.4 meters. After correction, the distance between the fault point and node J is about 767 meters, which is about 8 meters closer than the initial result.

[0114] For longer lines or with larger transition resistances, the correction will be more significant. For example, with a transition resistance of 500Ω, the wave velocity decreases by about 3%, resulting in a correction of tens of meters for a 1.5km line, which can effectively improve positioning accuracy.

[0115] Step 5: Combining the consistency of the multi-terminal waveforms, the wavefront matching degree, and the dispersion of the positioning results, comprehensively evaluate the confidence level of the positioning results to obtain the fault location and confidence level.

[0116] Furthermore, after obtaining the precise location result, this embodiment will conduct a confidence assessment of the fault result. This embodiment designs a multi-dimensional confidence assessment system to score the location result and classify the confidence level, so that maintenance personnel can take different response strategies according to the confidence level. For example, if the confidence level is high, go directly for repair, and if the confidence level is low, conduct further confirmation first.

[0117] S51, Wave head matching degree.

[0118] The first evaluation metric is wavefront matching degree, which measures the degree of agreement between the actual wavefront arrival time and the theoretical propagation time. The higher the matching degree, the more the positioning result conforms to the topological propagation law, and the higher the reliability.

[0119] Wavefront matching degree is measured by the reciprocal of the average residual. In this embodiment, the time residual of each measurement point is calculated using the optimal matching result. The residuals of the five measurement points are approximately 0.2 μs, 0.3 μs, 0.1 μs, 0.4 μs, and 0.2 μs, respectively, and the average residual is approximately 0.24 microseconds.

[0120] The smaller the average residual, the higher the matching degree. In this embodiment, the method for normalizing the average residual is: the matching degree is 1 when the average residual is ≤0.1μs, the matching degree is 0 when the average residual is ≥2μs, and linear interpolation is used in between. This normalization range is set based on engineering experience; a residual of less than 0.1 microseconds is already very good, while a residual of more than 2 microseconds indicates a relatively poor matching degree.

[0121] In this embodiment, the average residual is 0.24 μs, and the normalized matching degree is approximately 0.92, which is a very high level.

[0122] S52, Waveform Consistency.

[0123] The second indicator is waveform consistency, which measures the similarity of the traveling wave waveforms at both ends of the fault section. If the location result is correct, then the traveling waves propagating from the fault point to both ends, although with different propagation distances and attenuations, should have similar basic waveform shapes. If the waveforms at both ends differ significantly, then the location is likely incorrect.

[0124] Waveform consistency is measured by the cross-correlation coefficient between the waveforms at both ends of the fault section. Taking the initial traveling wave waveforms at station S and point X, and extracting 5-microsecond segments before and after the wavefront, the cross-correlation coefficient between the two waveforms is calculated. The closer the cross-correlation coefficient is to 1, the more similar the two waveforms are, and the better the consistency.

[0125] In this embodiment, the cross-correlation coefficient is approximately 0.88, which is also 0.88 after normalization. This indicates that the waveforms at both ends are highly similar, further confirming the correctness of the positioning result.

[0126] S53, Dispersion of positioning results.

[0127] The third indicator is the dispersion of positioning results, which measures whether the results calculated by different combinations of measurement points are consistent. The logic is simple: if the positioning is accurate, then the results calculated by different combinations of measurement points should be similar; if the results calculated by different combinations differ greatly, it means that the results are unstable and have low reliability.

[0128] Specifically, in this embodiment, 5 measurement points are used, and any two of them can be combined, resulting in 10 possible combinations. Each combination yields a positioning result. The mean and standard deviation of these 10 results are then calculated. The standard deviation is divided by the mean to obtain the coefficient of variation, or dispersion. The smaller the coefficient of variation, the more stable and consistent the results.

[0129] In this embodiment, the average of the 10 results is approximately 765 m, the standard deviation is approximately 28 m, and the coefficient of variation is approximately 0.037, or 3.7%. This dispersion is relatively small, indicating that the results of different combinations are quite consistent.

[0130] Dispersion normalization: The dispersion index is 1 when the coefficient of variation is ≤1%, and 0 when the coefficient of variation is ≥10%, with intermediate linear interpolation. In this embodiment, the coefficient of variation is 3.7%, and after normalization, it is approximately 0.70.

[0131] S54, Overall Confidence Score.

[0132] After obtaining the above three indicators, a weighted fusion is performed to obtain the overall confidence score. The weights are 0.4, 0.3, and 0.3, respectively. Wavefront matching score has the highest weight because it directly reflects the quality of time matching and is the most critical indicator. Waveform consistency and dispersion each account for 30% as auxiliary verification.

[0133] In this embodiment, the overall confidence score = 0.92×0.4 + 0.88×0.3 + 0.70×0.3 = 0.842, which, when multiplied by 100 and converted to a percentage, is approximately 84.2 points.

[0134] S55, Confidence level determination.

[0135] Furthermore, in this embodiment, the confidence level is divided according to the comprehensive confidence score: A score of 80 or above indicates high confidence, and the location error should not exceed 2% of the total length of the faulty section. • A score of 50 to 80 indicates a medium confidence level, with the location error not exceeding 5% of the total length of the faulty section; A score below 50 indicates a low confidence level.

[0136] In this embodiment, the overall confidence score is 84.2, which is greater than 80 and belongs to the high confidence level. The faulty section is 1.5km long, and 2% is 30 meters, meaning that the probability of the positioning error being within 30 meters is very high.

[0137] Actual verification also confirmed the above process: after the fault was discovered during line inspection, the fault point was found to be approximately 758 meters from node J on the western branch, with a location result of 767 meters, an error of approximately 9 meters, which was indeed within 30 meters, consistent with the confidence assessment result. This demonstrates that the confidence assessment system is accurate and effective.

[0138] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for fault location in distribution networks based on multi-source synchronous waveforms and traveling wavefronts, characterized in that, Includes the following steps: The current traveling wave waveform data after a fault is collected at multiple measurement nodes in the distribution network and preprocessed. The preprocessed waveform is processed using a mathematical morphological gradient operator, and the arrival time of the traveling wave front is detected based on the extreme points of the morphological gradient. A topology map is established using the topology of the distribution network. The theoretical propagation time from each candidate fault point to each measurement node is calculated. The theoretical time is matched with the actual wavefront arrival time to determine the fault section. Within the determined fault section, the initial location of the fault point is calculated using the time difference of arrival of the traveling waves at the two measuring points. The transition resistance is estimated based on the waveform characteristics, and the location result is corrected to obtain the fault point location. By combining the consistency of the multi-terminal waveforms, the wavefront matching degree, and the dispersion of the positioning results, the confidence level of the positioning results is comprehensively evaluated to obtain the fault location and confidence level.

2. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 1, characterized in that, The preprocessing includes: removing abnormal data points from each traveling wave waveform data and completing them using linear interpolation; removing random noise and power frequency interference using morphological opening-closing combination filtering; and normalizing the amplitude of the waveform data in each channel.

3. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 1, characterized in that, The detection of the arrival time of the traveling wave front specifically includes: performing dilation and erosion operations on the preprocessed waveform, subtracting the result of the erosion operation from the result of the dilation operation to obtain the morphological gradient, and the time corresponding to the maximum point of the morphological gradient is the arrival time of the traveling wave front.

4. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 3, characterized in that, The validity of the detected wavefronts is verified by comparing them with the characteristic range of typical traveling wave wavefronts based on the three characteristics of the wavefront: amplitude, steepness, and polarity. If all three characteristics are within the characteristic range, the detected wavefront is determined to be a valid wavefront; otherwise, it is determined to be interference or a pseudo wavefront and is removed.

5. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 4, characterized in that, The process of establishing a topology graph based on the distribution network topology and calculating the theoretical propagation time from each candidate fault point to each measurement node specifically includes: establishing a topology graph based on the distribution network topology, wherein each device is abstracted as an edge of the graph, and buses, nodes, and branch points are abstracted as vertices of the graph, and the length, model, and wave velocity parameters of each line segment are labeled; each line segment in the distribution network is regarded as a candidate fault segment, and each candidate fault point is pre-set in each candidate fault segment.

6. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 5, characterized in that, The determination of the faulty section specifically includes: For each candidate fault point, the propagation path and corresponding theoretical propagation time from the candidate fault point to each measurement node are calculated according to the shortest path principle. The theoretical propagation time is equal to the total length of the propagation path divided by the traveling wave speed. The calculated theoretical propagation time of each measurement point is matched with the actual detected wavefront arrival time. The sum of the time residuals of each set of matches is calculated. The candidate fault segment corresponding to the candidate fault point of the set of matches with the smallest sum of time residuals is taken as the fault segment.

7. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 1, characterized in that, The calculation of the preliminary location of the fault point specifically includes: The two measurement nodes at both ends of the fault section are designated as M-end and N-end, respectively. If the wavefront arrives first at M-end, then the distance from the fault point to M-end is... If the wavefront at the N end arrives first, then the distance from the fault point to the M end is... Wherein, the distance x from the fault point to end M is the initial location of the fault point, the total length of the fault section is L, the wave velocity of the traveling wave in this section of the line is v, and the time difference between the arrival times of the initial traveling wave front detected at end M and end N is Δt.

8. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 7, characterized in that, The step of estimating the transition resistance based on waveform characteristics specifically includes: extracting three features—peak amplitude of the wavefront, rise time of the wavefront, and proportion of high-frequency energy of the wavefront—to form a feature vector; matching this feature vector with the feature vectors corresponding to different transition resistances, and using the transition resistance corresponding to the highest matching degree as the estimated value of the transition resistance.

9. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 8, characterized in that, The wave velocity of the traveling wave is corrected based on the estimated transition resistance, where the correction amount is proportional to the magnitude of the transition resistance. The corrected wave velocity is then substituted back into the precise location formula to calculate the fault location, thus obtaining the corrected precise location result.

10. The distribution network fault location method based on multi-source synchronous waveforms and traveling wavefronts as described in claim 1, characterized in that, The confidence level of the comprehensive assessment of the positioning results specifically includes: Calculate the wavefront matching degree, expressed as the reciprocal normalized value of the mean residual; calculate the waveform consistency, expressed as the cross-correlation coefficient between waveforms; calculate the dispersion of the positioning results, expressed as the coefficient of variation of the positioning results. The three indicators—wavehead matching degree, waveform consistency, and positioning result dispersion—are normalized separately and then fused using a weighted summation method to obtain a comprehensive confidence score. Based on the confidence score, the positioning results are divided into multiple levels, with different levels corresponding to different positioning error ranges.

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