A power distribution network fault accurate positioning method based on multi-terminal traveling wave front calibration and wave velocity inversion

Abstract

The application provides a power distribution network fault accurate positioning method based on multi-terminal traveling wave wave head calibration and wave speed inversion, and belongs to the technical field of power distribution network fault positioning. The application comprises the following steps: installing a traveling wave collection terminal at multiple nodes of a power distribution network, and synchronously sampling to obtain a fault traveling wave signal; performing optimal phase-mode transformation to extract optimal line-mode components, and determining an initial traveling wave wave head coarse positioning time; adopting an ESMD-VMD-TEO adaptive method to calibrate the optimal line-mode components with high precision, and obtaining wave head positions of each measuring point; establishing a multi-terminal traveling wave positioning equation group based on the relationship between the wave head arrival time and the wave head position of each measuring point; constructing a weighted least square objective function based on the multi-terminal traveling wave positioning equation group, and inversely calculating a fault position, a traveling wave wave speed and a fault occurrence time by means of a Levenberg-Marquardt algorithm; constructing an energy spectrum correlation degree matrix to distinguish a fault branch; and outputting an accurate fault point position, a traveling wave wave speed and a positioning error confidence interval. The application realizes a tower level accurate positioning of a complex power distribution network fault.

Description

Technical Field

[0001] This invention relates to the technical field of distribution network fault location, and in particular to a method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion. Background Technology

[0002] As the "last mile" of the power system, the reliability of the distribution network directly affects the power quality for end users. Statistics show that distribution network faults account for over 80% of all power system faults, with single-phase grounding faults accounting for the highest proportion. Due to the complex structure, numerous branches, short line lengths, and variable operating environment of the distribution network, fault location is far more difficult than in the transmission network. Existing fault location methods mainly include impedance methods, signal injection methods, and traveling wave methods. Among them, the traveling wave method utilizes the transient traveling wave signal generated by the fault for location, possessing advantages such as being unaffected by transition resistance, unaffected by system operating modes, and high location accuracy, making it a research hotspot for distribution network fault location. However, the traditional traveling wave method still faces the following technical bottlenecks in practical applications:

[0003] Wave velocity uncertainty is a significant issue: the propagation speed of traveling waves is affected by factors such as line parameters (distributed inductance, distributed capacitance), ambient temperature, humidity, and soil resistivity, leading to a substantial discrepancy between theoretically calculated and actual wave velocities. Even along the same line, the propagation speed of traveling waves varies for different frequency components, making it difficult to guarantee the accuracy of positioning methods based on fixed wave velocities. Some studies have attempted to correct wave velocity through frequency analysis, but this still relies on historical data or manually injected signals.

[0004] Wavefront calibration is challenging due to the complex structure of distribution networks. Traveling waves undergo refraction and reflection at branch points and junctions, reducing wavefront singularity and exacerbating noise interference. Traditional thresholding methods and wavelet transform modulus maxima methods are significantly affected by wavelet basis functions and decomposition scales, resulting in insufficient adaptability. In recent years, a method combining variational mode decomposition (VMD) with the Teager energy operator (TEO) has been used for wavefront calibration; however, the selection of the number of VMD decomposition layers and penalty factors relies on experience, and its adaptability needs improvement.

[0005] The adaptability of phase mode transformation: Traditional phase mode transformations (such as Karenbauer transformation and Clark transformation) are designed for ideal transposed lines, and their line mode components only contain two-phase current information. In distribution networks, due to line asymmetry, mixed connection of cables and overhead lines, traditional transformations are difficult to achieve complete decoupling, resulting in the extracted line mode components failing to fully reflect the fault traveling wave characteristics, affecting the accuracy of subsequent location.

[0006] Insufficient multi-end data collaboration: The two-end traveling wave method struggles to pinpoint the faulty branch in multi-branch networks. While the single-end traveling wave method avoids synchronization issues, it is susceptible to interference from reflected waves. Theoretically, the multi-end traveling wave method can comprehensively utilize information from various measurement points, but existing methods often employ a serial strategy of locating the fault first and then identifying the branch, failing to fully leverage the advantages of multi-end data collaboration.

[0007] The time of the fault is unknown: The actual time of the fault is unknown. Traditional methods usually approximate the time of the earliest wavefront arrival as the time of the fault, or eliminate the time of the fault by subtracting the two ends. However, the former has errors, and the latter loses some information. Summary of the Invention

[0008] To address the technical problems in existing technologies, such as uncertain wave velocity, difficult wavefront calibration, poor adaptability of phase mode transformation, and insufficient multi-terminal data coordination, this invention proposes a method for accurate fault location in distribution networks based on multi-terminal traveling wave wavefront calibration and wave velocity inversion. Through optimal phase mode transformation, joint detection of dual-mode derivatives, double-layer decomposition for precise calibration, multi-terminal joint inversion, and energy spectrum clustering discrimination, this method achieves high-precision location and tower-level accurate location of faults in complex distribution networks.

[0009] To achieve the above objectives, the technical solution of this invention is as follows: a method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion, comprising the following steps:

[0010] Step 1: Install traveling wave acquisition terminals at multiple nodes of the distribution network, and achieve nanosecond-level synchronous sampling through Beidou / GPS dual-mode time synchronization to obtain fault traveling wave signals;

[0011] Step 2: Perform optimal phase mode transformation on the acquired fault traveling wave signal to extract the optimal line mode component; perform first-order differentiation on the two optimal line mode components respectively, and take the moment when the absolute value of the first-order derivative of both is greater than the preset threshold and the product of the two is greater than 0 as the initial traveling wave wavefront coarse positioning time; take the initial traveling wave wavefront coarse positioning time as the center, use the ESMD-VMD-TEO adaptive method to perform high-precision calibration on the optimal line mode component to obtain the wavefront position of each measurement point;

[0012] Step 3: Based on the relationship between the arrival time and position of the wavefront at each measurement point, establish a multi-terminal traveling wave localization equation set, with the fault location, traveling wave velocity, and fault occurrence time as variables to be determined;

[0013] Step 4: Construct a weighted least squares objective function based on the multi-terminal traveling wave localization equation set, and use the Levenberg-Marquardt algorithm to jointly invert the fault location, traveling wave velocity, and fault occurrence time;

[0014] Step 5: For multi-dominated power grids, construct an energy spectrum correlation matrix to identify faulty branches;

[0015] Step 6: Output the precise location of the fault point, the inversion wave velocity, and the confidence interval of the positioning error.

[0016] Preferably, traveling wave acquisition terminals are installed at the power supply end, the end of the main line, and the end of each branch line of the distribution network. All traveling wave acquisition terminals are connected to the Beidou / GPS dual-mode timing system. The traveling wave acquisition terminals acquire fault transient traveling wave voltage signals or fault transient traveling wave current signals through high-frequency current transformers.

[0017] The method for extracting the optimal linear modulus components is as follows:

[0018] The optimal phase-mode transformation is performed on the acquired three-phase fault traveling wave current signal. The transformation matrix T of the optimal phase-mode transformation is:

[0019] ;

[0020] We obtain three modulus components:

[0021]

[0022] in, For zero modulus components, , These are the two optimal line mode components. , and These represent the three-phase fault traveling wave current signals a, b, and c, respectively.

[0023] The two optimal line mode components extracted: , ;

[0024] For the optimal linear modulus components and The derivative sequence is obtained by taking the first derivative of each derivative. and Initial traveling wave front coarse positioning time To meet The earliest moment; among them, This is a preset threshold.

[0025] Preferably, the method for achieving high-precision calibration of the optimal linear mode components using the ESMD-VMD-TEO adaptive method to obtain the wavefront position of each measurement point is as follows:

[0026] Coarsely determine the time using the initial traveling wave front. Centered on the front and back windows Optimal linear modulus components within or Pole-symmetric mode decomposition is performed on the optimal linear mode components within the window to obtain several eigenmode function components of the preliminary decomposition.

[0027] The optimal decomposition parameters for variational mode decomposition, including the number of decomposition levels, are adaptively determined using a subtractive averaging optimization algorithm. and penalty factor ;

[0028] Based on the optimal decomposition parameters, a second variational mode decomposition is performed on the high-frequency intrinsic mode function components obtained by pole-symmetric mode decomposition to obtain refined mode components.

[0029] Based on the refined modal components, high-frequency modal components containing fault transient information are selected, and the Teager energy operator sequence is calculated;

[0030] Wavefront position is determined using an adaptive dynamic threshold method. ;in, For threshold coefficient, and These are the Teager energy operator sequences. The mean and standard deviation.

[0031] Preferably, the threshold coefficient is adaptively adjusted according to the signal-to-noise ratio. The implementation method is as follows: at the coarse positioning time Within the preceding and following Δt windows, calculate the adaptive difference step size i and select the optimal step size i. opt The subsequent Teager energy operator sequence ;Calculate the gradient sequence of the energy spectrum within the window And calculate the gradient entropy. The threshold coefficient λ, reflecting the concentration of abrupt changes in the energy spectrum, is determined as follows: ; where λ min and λ max H represents the minimum value and minimum value of the threshold coefficient, respectively. min H max These are the pre-defined upper and lower bounds of the gradient entropy.

[0032] Preferably, the method for calculating the Teager energy operator sequence is as follows:

[0033] The Teager energy operator introduces an adaptive difference step size. According to the signal base frequency and sampling frequency Determine the adaptive difference step size The range of values ​​for: Select the optimal step size within the range of values. This maximizes the peak size of the energy spectrum;

[0034] The formula for calculating the Teager energy operator sequence is: ;in, This represents the discrete sampled value at the current sampling point n in the signal sequence of the high-frequency modal components obtained after decomposition; This indicates that before the current sampling point n, i... opt Discrete sampled values ​​at each sampling point; Indicates i after the current sampling point n opt Discrete sampled values ​​at each sampling point.

[0035] Preferably, the The window value range is 0.5μs ~ 5μs;

[0036] The objective function of the subtraction averaging optimization algorithm is to minimize the energy entropy. ;in, For the first The energy percentage of one IMF component For the first One IMF component of energy, The total energy of the signal. Let the objective function be the subtraction average optimization algorithm;

[0037] The high-frequency mode components are the first 1 to 2 intrinsic mode function components with the highest energy proportion after pole-symmetric mode decomposition and variational mode decomposition;

[0038] The signal base frequency f0 is taken as the rated frequency of the power system, and the sampling frequency f s It is determined by the hardware parameters of the traveling wave acquisition terminal;

[0039] The optimal step size ;in, For adaptive differential step size The corresponding Teager energy operator sequence, and These are the Teager energy operator sequences. The mean and standard deviation;

[0040] The adaptive difference step size The range of values ​​is .

[0041] Preferably, the multi-terminal traveling wave positioning equation set is as follows:

[0042] ;

[0043] Among them, t j Let be the wavefront arrival time at the j-th measurement point. t0 is the distance to the fault, v is the time of fault occurrence, and v is the traveling wave velocity. For the first Calibration error at each measurement point This represents the total number of measurement points.

[0044] Preferably, the multi-terminal traveling wave positioning equations are transformed into a weighted least squares optimization problem, and the objective function is constructed as follows:

[0045] ;

[0046] in, These are the weighting coefficients;

[0047] The objective function is solved using an improved Levenberg-Marquardt algorithm. Introducing a multi-initial-point strategy: randomly generating initial points within the feasible region. Group initial point Optimize separately, and select the objective function. The minimum solution is taken as the global optimal solution. ;

[0048] The first Calibration residuals at each measurement point ;in, To the maximum calibration error, For the first Kuness at each measurement point and These are the Teager energy operator sequences. The mean and standard deviation; φ i For the optimal step size i opt The corresponding Teager energy operator sequence; For the first Signal-to-noise ratio at each measurement point;

[0049] Fault Distance Coordinates of the fault location satisfy: , For the first The coordinates of the measurement points.

[0050] Preferably, the method for constructing the energy spectrum correlation matrix to identify fault branches is as follows:

[0051] The short-time Fourier transform is used to calculate the first... Energy spectrum of the signal near the wavefront at each measurement point The energy spectrum correlation between any two measurement points is calculated using energy spectrum, and a measured energy spectrum correlation matrix is ​​constructed based on the energy spectrum correlation. ;

[0052] Calculate candidate faulty branches The theoretical energy spectrum received at the assumed fault location y. The theoretical energy spectrum correlation between measurement points is calculated using theoretical energy spectra, and a theoretical energy spectrum correlation matrix is ​​constructed. ;

[0053] The problem of minimizing the determination of the exact location of the faulty branch: ;in, These represent the faulty branch and the location of the fault point, respectively. This represents the Frobenius norm.

[0054] Preferably, the signal near the wavefront at the j-th measurement point is obtained after the completion of the first measurement. Wavefront arrival time at each measurement point After calibration, the optimal linear mode component is obtained from the optimal phase mode transformation. or Extract the signal within each Δt window before and after the transient waveform;

[0055] All energy spectrum correlations Constructing the correlation matrix of the measured energy spectrum The diagonal element is 1;

[0056] The theoretical energy spectrum Wherein, the constant S0 is the energy spectral density of the fault traveling wave source within the effective frequency band. The attenuation coefficient per unit length;

[0057] For overhead lines, attenuation coefficient For cable lines, attenuation coefficient ,in, Indicates the frequency of the fault traveling wave signal;

[0058] The theoretical energy spectrum correlation is: ;

[0059] The minimization problem is solved using a two-level search strategy: outer search: traverse each candidate faulty branch l; inner search: for each candidate faulty branch l, perform a golden section search within the range from 0 to the maximum length, calculate the Frobenius norm for each position y, and record the minimum norm value and optimal position of the candidate faulty branch l; branch decision: compare the minimum norm values ​​of all candidate faulty branches, and select the faulty branch with the smallest minimum norm value. As the final faulty branch, the corresponding location is the fault point location. ;

[0060] Output precise location of the fault point Traveling wave velocity When the fault occurred The steps for estimating the confidence interval of positioning error based on residual analysis are as follows:

[0061] Calculate the weighted residual vector of the j-th measurement point. A nonparametric bootstrap method is used to perform B resampling cycles with replacement on n weighted residual vectors, resulting in B bootstrap samples. The perturbed wavefront arrival times are then constructed. For each bootstrap sample, the perturbed measurement time is solved inversely. ,in, For the j-th measurement point and the b-th resampling with replacement, the self-sampled sample is taken at the measurement time. As input, repeat the optimization process in step four to obtain the inversion results of group b. ;in,( () represents the precise location of the fault point retrieved in group b. For the wave velocity inverted in group b , The fault occurrence time is represented by the inversion of group b.

[0062] For a given confidence level , respectively , , , Pick and Quantiles are used to obtain the confidence intervals for each component:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] in, This refers to the statistical term quantile;

[0068] Positioning error radius Project the precise location of the fault point onto the branch mileage and output the confidence interval of the mileage value.

[0069] Synchronous traveling wave acquisition terminals are installed at multiple nodes in the distribution network to collect fault transient traveling wave signals; the optimal line mode component is extracted using optimal phase-mode transformation, and its expression is as follows: , The invention employs a method to coarsely locate the initial wavefront by taking the first derivative of the two optimal mode currents. When the absolute values ​​of both derivatives are greater than a threshold and their product is greater than 0, this moment is used as the initial wavefront coarse location. Centered on the coarse location result, a high-precision calibration is performed using the ESMD-VMD-TEO (Pole Symmetric Mode Decomposition-Variational Mode Decomposition-Teager Energy Operator) adaptive method to obtain the wavefront arrival time at each measurement point. A multi-terminal traveling wave location equation set is established, and a weighted least squares objective function is constructed to jointly invert the fault location, traveling wave velocity, and fault time. For multi-branch networks, an energy spectrum correlation matrix is ​​constructed to identify fault branches. The precise location of the fault point is then output. This invention solves the problems of poor phase mode transformation adaptability, difficult wavefront calibration, uncertain wave velocity, and insufficient multi-terminal coordination in the traditional traveling wave method, achieving precise tower-level location of faults in complex distribution networks with a location error of less than 50m.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] Enhanced adaptability through optimal phase mode transformation: The optimal phase mode transformation, which includes complete three-phase current information, solves the problem of incomplete information in traditional line mode components. It is especially suitable for asymmetrical lines and cable-overhead line hybrid scenarios, laying a solid foundation for subsequent accurate positioning.

[0072] Dual-mode derivative joint detection improves robustness: For the first time, the first derivatives of two optimal mode currents are jointly detected for coarse localization of traveling wave fronts. Both derivatives are required to exceed the threshold simultaneously, which can effectively suppress single-channel noise interference and false wave front misjudgment, and significantly improve detection reliability.

[0073] High precision is achieved through a two-level calibration strategy: By adopting a two-level strategy of "coarse positioning + fine calibration", combined with ESMD-VMD-TEO adaptive decomposition and improved Teager energy operator, the calibration accuracy is better than 0.15μs, and the corresponding distance error is less than 50 meters.

[0074] Wave velocity dynamic inversion eliminates uncertainty: Wave velocity is used as a variable to be determined in the joint inversion, without the need to preset wave velocity or rely on historical data, and is applicable to different line types and environmental conditions.

[0075] Multi-terminal data collaboration and branch identification: By fusing multi-terminal information through weighted least squares and constructing an energy spectrum correlation matrix, fault branch identification is performed, enabling accurate route selection in complex branch networks.

[0076] High positioning accuracy and wide applicability: The positioning error of this invention is less than 50 meters, meeting the engineering requirements for fault location in distribution networks. It is applicable to various complex distribution network topologies, including radial, ring, and mixed cable-overhead line networks, and has good adaptability to different fault types, transition resistances, and noise levels. Attached Figure Description

[0077] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 The overall flowchart of the method of this invention.

[0079] Figure 2 A schematic diagram of the multi-terminal traveling wave acquisition device layout in this invention.

[0080] Figure 3 In Example 2 of this invention, the optimal values ​​of the five measurement points M1-M5 are... A schematic diagram of the modulus component.

[0081] Figure 4 A schematic diagram of the initial wavefront coarse positioning time based on dual-mode derivative joint detection in Embodiment 2 of this invention.

[0082] Figure 5 A schematic diagram of the initial wavefront positioning time of M1 in Embodiment 2 of this invention.

[0083] Figure 6 A schematic diagram of the comparison of the initial wavehead precision positioning time calibrated by M1-M5 in Embodiment 2 of this invention.

[0084] Figure 7 A schematic diagram comparing the correlation between actual measurements and theoretical results in Example 3 of this invention.

[0085] Figure 8 A schematic diagram of the Frobenius calculation results for the fault candidate branch in Embodiment 3 of this invention. Detailed Implementation

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] Example 1

[0088] A method for accurate fault location in distribution networks based on multi-terminal traveling wave wavefront calibration and wave velocity inversion includes the following steps:

[0089] Step 1: Install traveling wave acquisition terminals at multiple nodes of the distribution network, and use the BeiDou / GPS dual-mode timing system to achieve nanosecond-level synchronous sampling to obtain the fault traveling wave signal.

[0090] Traveling wave (TW) acquisition terminals are installed at the power source, the end of the main line, and the end of each branch line in the distribution network. All TW acquisition terminals are connected to the BeiDou / GPS dual-mode timing system to achieve nanosecond-level synchronous sampling. The TW acquisition terminals acquire fault transient traveling wave voltage or current signals through high-frequency current transformers (bandwidth: 10kHz-10MHz), with a sampling frequency of not less than 10MHz. BeiDou / GPS dual-mode timing achieves nanosecond-level synchronization, providing a high-precision time reference for multi-terminal traveling wavefront time difference measurement; the 10kHz–10MHz wideband transformer fully captures the high-frequency components of the fault traveling wave, avoiding signal attenuation; the ≥10MHz sampling rate ensures that the wavefront time domain resolution is better than 0.1μs, supporting a positioning error of <50m. The above configuration together ensures the quality of the raw data from the two-level strategy of "coarse positioning + fine calibration" and multi-terminal joint inversion, which is the key foundation for achieving accurate positioning at the tower level.

[0091] Step 2: Perform optimal phase mode transformation on the acquired fault traveling wave signal to extract the optimal line mode component; perform first-order differentiation on the two optimal line mode components respectively, and when the absolute value of the first-order derivative of both is greater than the preset threshold and the product of the two is greater than 0, take this moment as the initial traveling wave wavefront coarse positioning moment; with the initial traveling wave wavefront coarse positioning moment as the center, use the ESMD-VMD-TEO adaptive method to perform high-precision calibration on the optimal line mode component to obtain the wavefront arrival time of each measurement point.

[0092] This step involves two-stage wavefront calibration based on optimal phase mode transformation and dual-mode derivative joint detection. The specific implementation steps are as follows:

[0093] Step 2.1 Extracting the optimal linear mode component through optimal phase mode transformation

[0094] The optimal phase-mode transformation is performed on the acquired three-phase fault current traveling wave signal to extract the optimal line-mode component. The transformation matrix T of the optimal phase-mode transformation is:

[0095] ;

[0096] This yields three modulus components:

[0097]

[0098] in, For zero modulus components, , These are the two optimal line mode components. , and These represent the fault traveling wave current signals of phases a, b, and c, respectively.

[0099] The acquired fault traveling wave current signal was subjected to optimal phase-mode transformation, and two optimal line-mode components were extracted:

[0100] , ;

[0101] Compared with traditional line-mode components, this optimal line-mode component contains complete information about the three-phase current and can more accurately reflect the fault traveling wave characteristics, making it particularly suitable for unbalanced lines and cable lines.

[0102] Step 2.2 Initial coarse wavefront localization based on dual-mode derivative joint detection

[0103] For the optimal linear modulus components and By taking the first derivative of each derivative, we obtain the derivative sequence. and When the traveling wave front arrives, the mode current... and Dramatic changes will occur, and its derivative will exhibit a significant peak. To effectively suppress noise interference and ensure the reliability of the detection, the initial traveling wavefront coarse positioning time is defined. The earliest time that satisfies the following conditions:

[0104] ;

[0105] in, The preset threshold is set to no less than 5 amps / nanosecond (obtained by calculating the first derivative of the optimal line mode component) based on the actual application scenario. This detection condition requires that the absolute values ​​of the derivatives of the optimal mode currents of the two optimal line mode components simultaneously exceed the threshold, and that they have the same sign (the product is positive). This effectively avoids false detections caused by noise interference in a single mode component, while also eliminating interference from noise with opposite signs, significantly improving detection reliability. This coarse positioning result serves as the center of the search window for subsequent fine calibration.

[0106] Step 2.3: High-precision wavefront calibration based on ESMD-VMD-TEO

[0107] Coarsely determine the time using the initial traveling wave front. Centered on, take the front and back Optimal linear modulus components within the window (or The implementation method of high-precision calibration using the ESMD-VMD-TEO adaptive method is as follows:

[0108] First, pole-symmetric mode decomposition (ESMD) is performed on the signal (optimal linear mode component) within the window to obtain several intrinsic mode function (IMF) components of the preliminary decomposition. ESMD uses extreme point symmetric interpolation instead of envelope fitting in empirical mode decomposition (EMD) to improve decomposition efficiency. To ensure the complete wavefront rising edge is included while effectively eliminating interference from nearby reflected waves, The value range is generally 0.5μs ~ 5μs, and the present invention preferably uses 1μs.

[0109] Secondly, the Subtraction Average Optimizer (SAO) algorithm is used to adaptively determine the optimal decomposition parameters of Variational Mode Decomposition (VMD), including the number of decomposition layers. and penalty factor The objective function of the subtractive averaging optimization algorithm is to minimize the energy entropy.

[0110]

[0111] in, For the first The energy percentage of each IMF component For the first Energy of one IMF component This represents the total energy of the signal. Let p be the objective function of the subtraction averaging optimization algorithm. k The relationship between the decomposition level K and the penalty factor α is as follows: Too small a decomposition level K leads to frequency aliasing and excessively concentrated energy distribution; too large a decomposition level K generates spurious components and disperses energy. Too small a penalty factor α results in excessively wide bandwidth and frequency aliasing; too large a penalty factor α results in excessively narrow bandwidth and loss of transient information. Therefore, the optimal (k, α) should minimize the energy entropy. The objective function should be minimized, even if the transient energy of the fault is concentrated in a few high-frequency intrinsic mode function components. Preferably, the objective function is solved using a subtractive averaging optimization algorithm.

[0112] Furthermore, based on the optimal decomposition parameters, the high-frequency IMF components obtained from ESMD decomposition are subjected to secondary variational mode decomposition (VMD) to obtain refined mode components.

[0113] Finally, high-frequency modal components containing fault transient information are selected, and their improved Teager energy operator (TEO) sequences are calculated. Specifically, the high-frequency modal components refer to the top 1-2 intrinsic mode functions (IMF) components with the highest energy proportion after ESMD-VMD decomposition; these components concentrate the main transient high-frequency energy of the fault traveling wave. The signal fundamental frequency f0 is directly taken as the rated frequency of the power system (e.g., 50Hz), and the sampling frequency f... sDetermined by the hardware parameters of the traveling wave acquisition terminal, the frequency is set to be no less than 10MHz in this invention, and 20MHz is used in the embodiment. The improved Teager energy operator introduces an adaptive differential step size. According to the signal base frequency and sampling frequency Determine the range of adaptive difference step size values:

[0114]

[0115] Select the optimal step size within the range of values. This maximizes the peak intensity of the energy spectrum.

[0116] ;

[0117] in, For adaptive differential step size The corresponding Teager energy operator sequence, and These are the Teager energy operator sequences. The mean and standard deviation.

[0118] Optimal step size The method for determining it is as follows: based on the signal fundamental frequency f0 and the sampling frequency f s Determined range of values Within this process, an traversal search strategy is employed to compute the improved Teager energy operator sequence corresponding to each candidate step size i. And calculate its kurtosis value. The optimal step size is selected as the step size that maximizes the kurtosis value. To improve computational efficiency, a coarse search with a larger step size is preferred to determine the interval with higher kurtosis, followed by a fine search within that interval. This solution process ensures that the Teager energy spectrum is most sensitive to abrupt changes in the traveling wavefront, thus achieving the highest wavefront calibration accuracy.

[0119] The improved formula for calculating the Teager energy operator sequence is as follows:

[0120] ;

[0121] in, It represents the signal amplitude at the current sampling point n in the discrete signal sequence, specifically the discrete sampled value of the high-frequency mode component obtained after ESMD-VMD decomposition; This indicates that before the current sampling point n, i... opt The signal amplitude at each sampling point, i.e., the forward differential point; Indicates i after the current sampling point n opt The signal amplitude at each sampling point, i.e., the backward differential point.

[0122] The abrupt change in the energy spectrum corresponds to the arrival time of the traveling wavefront, denoted as the nth wavefront. Wavefront arrival time at each measurement point To suppress noise interference, an adaptive dynamic threshold method is used to determine the wavefront position.

[0123] ;

[0124] in, The threshold coefficient is adaptively adjusted based on the signal-to-noise ratio. Specifically, it is obtained using an adaptive threshold adjustment method based on the local gradient entropy of the energy spectrum. This eliminates the need for pre-estimation of the absolute noise value; instead, it dynamically determines the threshold coefficient using the morphological characteristics of the energy spectrum near the traveling wavefront. The steps are as follows: at the coarse positioning time Calculate the improved Teager energy operator sequence within the preceding and following Δt windows. Where i is the optimal value of the adaptive difference step size. opt The sequence following; calculate the gradient sequence of the energy spectrum within this window. and through Further calculation of the gradient entropy reflects the concentration of abrupt changes in the energy spectrum (when the wavefront is clear, the gradient is concentrated in a small segment, resulting in low entropy; when there is severe noise, the gradient is dispersed, resulting in high entropy). The threshold coefficient λ is adaptively determined by the following formula: Wherein, λ min =2、λ max =5,H min H max The upper and lower limits of the gradient entropy are pre-calibrated, with values ​​of 0.2 and 1.5, respectively. This mechanism does not require separate calculation of the signal-to-noise ratio; it directly adjusts the threshold using the local waveform complexity of the wavefront, making it less sensitive to amplitude changes and more robust.

[0125] The relationship between wavefront arrival time and wavefront position at each measurement point and the method for obtaining it: Wavefront arrival time t at the j-th measurement point j Distance from Fault The fault occurrence time t0 and the traveling wave velocity v satisfy the following conditions: , To calibrate the residuals, this relationship constitutes the multi-terminal traveling wave positioning equation system (see step three), and v and t0 participate in the joint inversion as unknowns. Therefore, t j The distance to the fault is not calculated in isolation, but rather coupled within the weighted least squares objective function.

[0126] The above-mentioned coarse-fine two-stage calibration strategy can effectively avoid noise interference.

[0127] Step 3: Establish a multi-terminal traveling wave localization equation set, with the fault location, traveling wave propagation speed, and fault occurrence time as variables to be determined.

[0128] Let the time of the fault be... The distance from the fault point to the first The distance between the measurement points is The speed of travel wave propagation is Then there is the first Wavefront arrival time at each measurement point:

[0129] ;

[0130] in, The total number of measurement points. For the first The calibration error of each measurement point, which is a confidence index dynamically estimated based on energy spectral kurtosis and local signal-to-noise ratio during wavefront calibration, is obtained through the following steps: In the fine calibration stage, the optimal step size i is obtained. opt The corresponding Teager energy operator sequence φ i Then, calculate its kurtosis: A higher kurtosis indicates a sharper abrupt change in the energy spectrum, resulting in higher reliability of the wavefront calibration and a lower corresponding calibration error. The smaller the value, the better; take the coarse positioning time t. c Calculate the root mean square of the Teager energy operator sequence within a pure noise window of approximately 0.5 μs in length. Then take the maximum value φ of the energy spectrum within the window near the wavefront. max , Calibration error for ,in, The maximum possible calibration error is set at 0.5 μs. This model allows measurement points with high kurtosis and high signal-to-noise ratio to achieve smaller calibration errors. In subsequent weighted least squares, it will naturally receive a higher weight. .

[0131] distance Coordinates of the fault location satisfy: , For the first The location coordinates of each measurement point are obtained by directly reading the latitude and longitude coordinates of the terminal using the Beidou / GPS dual-mode timing module when deploying the traveling wave acquisition terminal, and then mapping them to the plane coordinate system through Gaussian projection or UTM transformation.

[0132] The multi-terminal traveling wave positioning equations are as follows:

[0133] .

[0134] Step 4: Construct a weighted least squares objective function based on the multi-terminal traveling wave localization equation set, and use the improved Levenberg-Marquardt algorithm to jointly invert the fault location, traveling wave propagation velocity, and fault occurrence time.

[0135] This step involves multi-terminal joint wave velocity inversion and fault location.

[0136] The above multi-terminal traveling wave positioning equations are transformed into a weighted least squares optimization problem, and the objective function is constructed as follows:

[0137]

[0138] in, The weighting coefficient is determined based on the signal-to-noise ratio or kurtosis of the signal at each measurement point. The higher the signal-to-noise ratio and the larger the kurtosis, the larger the weighting coefficient.

[0139] An improved Levenberg-Marquardt algorithm is used to solve this nonlinear optimization problem. To improve convergence speed and avoid local optima, a multi-initial-point strategy is introduced: initial points are randomly generated within the feasible region. Group initial point Optimize them separately and select the one that makes the objective function The minimum solution is taken as the global optimal solution. By introducing a multi-initial-point strategy, multiple initial solutions are randomly generated within the feasible region, optimized separately, and the minimum value of the objective function is obtained. This effectively avoids the single initial point from getting trapped in local optima, significantly improves the global optimization capability and the reliability of the localization results, and enhances the algorithm's adaptability to complex objective function shapes in multi-branch networks.

[0140] Step 5: For multi-dominated power grids, construct an energy spectrum correlation matrix to identify faulty branches.

[0141] For multi-dominated power grids, the method for identifying faulty branches by constructing an energy spectrum correlation matrix is ​​as follows:

[0142] Step 5.1, Calculate the correlation of the measured energy spectrum.

[0143] First, calculate the energy spectrum of the signal near the wavefront at each measurement point. The following information is obtained using Short Time Fourier Transform (STFT):

[0144] ;

[0145] in, Indicates the first The signal near the wavefront at the j-th measurement point, the signal near the wavefront at the j-th measurement point. The wavefront arrival time at the measurement point is obtained in the following way: After high-precision calibration, take time windows of Δt (preferably 2 μs) before and after the optimal phase mode transformation to obtain the optimal linear mode component. or The signal within this window is captured from the transient waveform.

[0146] Secondly, construct any two measurement points and Correlation of energy spectra between them:

[0147] ;

[0148] in, and Representing the measurement points and The correlation coefficient reflects the similarity of the energy spectrum waveforms between two measurement points, ranging from [0,1]. A value closer to 1 indicates a more consistent energy spectrum shape. This correlation is derived from the correlation coefficients of all energy spectra. Constructing the correlation matrix of the measured energy spectrum Its diagonal element is 1.

[0149] Step 5.2: Construct a theoretical energy spectrum correlation matrix based on energy spectrum correlation. .

[0150] For each candidate fault branch in the distribution network (Including the main line segment and each branch), based on the line topology and the traveling wave velocity v obtained from the inversion in step four, calculate the theoretical energy spectrum of each measurement point when the fault point is assumed to be located at different positions y on the branch (y is the distance from the starting point of the branch), and calculate the candidate fault branch. different positions The corresponding theoretical energy spectral attenuation and time delay are used to obtain the theoretical correlation matrix. The details are as follows:

[0151] First, calculate the line frequency-dependent attenuation coefficient. For overhead lines, the attenuation coefficient per unit length is... Approximately For cable lines, , The frequency of the fault traveling wave signal (unit: Hz).

[0152] Secondly, the energy spectrum of the fault source is assumed. The fault traveling wave source can be approximated as a broadband impulse spectrum, and its energy spectral density within the effective frequency band is regarded as a constant S0 (since S0 is canceled in the numerator and denominator when calculating the correlation, there is no need to know its magnitude).

[0153] Next, the theoretical energy spectrum is calculated for the measurement points. For candidate branches... Assuming the fault location is y, and considering the frequency-dependent attenuation during the traveling wave propagation process, the theoretical energy spectrum received at measurement point j is:

[0154] ;

[0155] Next, the theoretical energy spectrum Substituting the above energy spectrum correlation The theoretical relevance can be simplified as follows:

[0156] ;

[0157] Calculate the theoretical correlation for all measurement point pairs (j,k). The theoretical correlation matrix is ​​obtained. .

[0158] Step 5.3: Joint determination of fault branch and location

[0159] The specific location of the faulty branch is determined by minimizing the Frobenius norm:

[0160]

[0161] in, These represent the branch where the fault is located and the precise distance (i.e., location) from the fault point to the starting point of that branch. This represents the Frobenius norm.

[0162] A two-level search strategy is used to solve the above minimization problem:

[0163] First, outer search: traverse each candidate branch l.

[0164] Secondly, inner-layer search: For a fixed branch l, the golden section search is used within the range of 0 to the maximum length to calculate the Frobenius norm corresponding to each position y, and record the minimum norm value and the optimal position of the branch.

[0165] Finally, the branch decision is made by comparing the minimum norm values ​​of all branches and selecting the branch with the smallest value. As the final faulty branch, the corresponding location This is the location of the fault.

[0166] Through the above-described energy spectrum correlation matrix matching method, this invention achieves the following beneficial effects: accurate identification of fault branches: overcoming the shortcomings of the traditional traveling wave method in multi-branch networks, which cannot determine fault branches by relying solely on wavefront time differences, and can still effectively identify them even when the branch length is short and the wavefront time differences are close; strong noise resistance: the energy spectrum correlation is not sensitive to random noise, and the use of frequency band integration further suppresses high-frequency interference; synergistic with wave velocity inversion: the attenuation coefficient in the theoretical matrix and the wave velocity inverted in step four are independent of each other, and their combined use can improve the robustness of localization; high computational efficiency: no need to perform full-waveform electromagnetic transient simulation, only one-dimensional integral calculation is required, which is suitable for real-time engineering applications.

[0167] Step 6: Output the precise location of the fault point, the inversion wave velocity, and the confidence interval of the positioning error.

[0168] Location Result Output and Accuracy Evaluation: As described in step four, output the precise location of the fault point. Inversion wave velocity When the fault occurred Furthermore, a method for estimating the confidence interval of positioning error based on residual analysis is proposed. This method does not require assumptions about the form of the error distribution and is naturally compatible with the aforementioned weighted least squares framework. The specific steps are as follows:

[0169] Step 6.1: Calculate the weighted residual vector. Based on the optimal solution from Step 4, use the formula... Calculate the weighted residuals for each measurement point. This comprehensively reflects both model fitting error and measurement noise.

[0170] Step 6.2: Residual Bootstrap Resampling. A nonparametric bootstrap method is used to resample the residual vector. Perform B resampling cycles with replacement (B=1000 in this invention) to obtain 1000 bootstrap samples. This resampling process preserves the empirical distribution characteristics between residuals without requiring any assumptions about parameter distribution.

[0171] Step 6.3: Construct the arrival time of the perturbed wavefront. For each bootstrap sample... The measurement time after the disturbance is obtained by inverse solving: Measure the time This is considered the "virtual arrival time" of the j-th measurement point in the b-th simulation. The wavefront arrival time t calibrated in step two is maintained. j The original value remains unchanged, and only perturbations that conform to the characteristics of the residual distribution are added within its error range.

[0172] Step 6.4: Re-execute the joint inversion

[0173] To measure time As input, repeat the optimization process in step four (using the same multi-initial-point strategy) to obtain the inversion results of group b. Since each bootstrap sample reflects a possible error pattern, This constitutes the statistical distribution sample of the positioning results.

[0174] Step 6.4: Calculate the confidence interval

[0175] For a given confidence level (Preferred) =5%), respectively for , , , Pick and Quantiles are used to obtain the confidence intervals for each component:

[0176]

[0177]

[0178]

[0179]

[0180] in, This refers to the statistical term quantile. It also defines the radius of positioning error. This intuitively reflects the maximum possible deviation of planar positioning. For cases where the faulty branch has been identified, (x,y) can be projected onto the branch mileage, and the confidence interval of the mileage value can be directly output.

[0181] The confidence interval estimation method does not rely on the assumption of a normal error distribution, and it is consistent with the weighted least squares weight w in step four. j The natural connection (the residuals already include weights) fully demonstrates the originality of this invention in the quantification of multi-source uncertainty. Traditional traveling wave positioning methods only provide a single definite point and cannot assess its reliability; this invention provides statistical error boundaries through a bootstrap method, significantly improving the engineering practical value of the positioning results.

[0182] Example 2

[0183] A method for accurate fault location in distribution networks based on multi-terminal traveling wave front calibration and wave velocity inversion is described in detail in this embodiment using a 10kV radial distribution network as an example. The method includes the following steps:

[0184] Step 1: System Configuration and Traveling Wave Acquisition

[0185] Distribution network topology such as Figure 2As shown: The main line is 15km long, including 3 branch lines: Branch 1 is 2km long, Branch 2 is 3km long, and Branch 3 is 2.5km long. Traveling wave acquisition terminals are installed at the following 5 nodes: power supply terminal (M1), main line end (M2), Branch 1 end (M3), Branch 2 end (M4), and Branch 3 end (M5). All terminals are connected to the BeiDou / GPS dual-mode timing system to achieve nanosecond-level synchronous sampling with a synchronization accuracy ≤100ns. Terminal parameters: sampling frequency 20MHz, A / D conversion accuracy 16-bit, data storage depth 10ms, and high-frequency current transformer bandwidth 10kHz~10MHz.

[0186] Step 2: Wave head calibration

[0187] Assume a phase A ground fault occurs on the line 6.8 km from the power source (located on the main line), with a transition resistance of 100Ω. All terminals synchronously acquire the three-phase fault traveling wave current signal. The two-stage calibration strategy in step two of Example 1 is followed.

[0188] Step 2.1: Perform optimal phase-mode transformation on the three-phase currents collected from each terminal and extract two optimal line-mode components. and .

[0189] Step 2.2: Next, perform coarse localization using joint detection of dual-mode derivatives. Taking the M1 terminal as an example, first, the optimal linear mode components are... and By taking the first derivative, we obtain the derivative sequence. and Set threshold Find the earliest satisfaction , and At that moment, a rough estimate of the time was obtained. Using the same method, the coarse estimated times for terminals M2, M3, M4, and M5 were 30.15 μs, 10.30 μs, 14.60 μs, and 11.55 μs, respectively.

[0190] Step 2.3 High-precision wavefront calibration based on ESMD-VMD-TEO. Taking M1 as an example, the time is roughly estimated. The optimal linear mode component is selected within a ±1μs window centered on the model. Signal (optional) (Both methods are equivalent in effect), and the ESMD-VMD-TEO adaptive method is used for fine calibration.

[0191] First, the signal within the window is decomposed by ESMD to obtain 5 IMF components. The high-frequency components IMF1 and IMF2, which contain the main transient energy, are identified. The length of the window can ensure that the complete rising edge of the wavefront is included, and can effectively eliminate the interference of nearby reflected waves.

[0192] Secondly, the optimal VMD parameters are determined using the subtraction average optimization algorithm: the number of decomposition layers. Punishment factor Next, VMD secondary decomposition is performed on the high-frequency components IMF1 and IMF2 to obtain refined modal components. Finally, the improved Teager energy operator is calculated, and the step size is determined based on the system fundamental frequency of 50Hz and the sampling frequency of 20MHz. The range of values ​​is The optimal step size is selected using the kurtosis maximization criterion. The Teager energy spectrum was calculated, and the threshold coefficient was adjusted using gradient entropy. and Determine the arrival time of the wavefront: .

[0193] Similarly, the arrival times of other terminal wavefronts can be obtained: , , , Meanwhile, the calibration errors of each measurement point were calculated based on the energy spectrum kurtosis and local signal-to-noise ratio: M1 = 0.02 μs, M2 = 0.03 μs, M3 = 0.03 μs, M4 = 0.04 μs, and M5 = 0.03 μs.

[0194] Step 3: Establish a multi-terminal traveling wave positioning equation set.

[0195] Following the method in step three of Example 1, the fault location x (distance from the power source), the traveling wave velocity v, and the fault occurrence time t0 are the unknowns to be determined. Given the known coordinates of each measurement point (M1: 0km, M2: 15km, M3: 5km branch point, M4: 9km branch point, M5: 12km branch point), and combining the precise calibration arrival time and calibration error obtained in step two, a multi-terminal traveling wave positioning equation set containing five equations is established. Each equation expresses the arrival time as equal to the fault occurrence time plus the propagation distance divided by the wave velocity plus the calibration error.

[0196] Step 4: Joint Inversion

[0197] Following the method in step four of Example 1, a weighted least squares objective function is constructed. Weights are determined based on the signal-to-noise ratio (SNR) of each terminal: Terminal M1 has the highest SNR, so it is selected as the weight. The signal-to-noise ratios of terminals M2, M3, M4, and M5 are similar, so we take... .

[0198] Initial point setting: 10 initial fault location points are randomly generated within the range of [0, 15] km, and the initial wave velocity value is within [2.90 × 10⁻⁶ km]. 5 3.05×10 5 The fault location is randomly selected within the range of [-5, 5] μs, and the initial value at fault time is randomly selected within the range of [-5, 5]. An improved Levenberg-Marquardt algorithm is used for optimization, yielding the following result: Fault location: 6.79 km; Inversion wave velocity: 2.981×10 5 km / s; Fault time: 0.03 μs.

[0199] Step 5: Fault Branch Identification

[0200] Following the method in step five of Example 1, for a multi-dominated power grid, an energy spectrum correlation matrix needs to be constructed to identify faulty branches. In this example, the fault occurs on the main line (6.8km from the power source), and branch selection is not involved. If verification is required, the Frobenius norm of each candidate branch can be calculated. The norm corresponding to the main line is the smallest, so the fault is determined to be located on the main line, consistent with the preset value.

[0201] Step Six: Output Results and Accuracy Evaluation

[0202] The absolute positioning error is |6.79-6.80| = 0.01 km = 10 m. The positioning error is less than 50 meters, which meets the accuracy requirements for fault location in power distribution networks.

[0203] Following the method in step six of Example 1, the precise location of the fault point, the inverted wave velocity, and the fault time are output, and the confidence interval is given based on the bootstrap method.

[0204] Absolute positioning error: |6.79-6.80| = 0.01km = 10m, less than 50m. A non-parametric bootstrapping method (B=1000 resampling times) was used to calculate the 95% confidence interval: fault location [6.76, 6.82]km, wave velocity [2.974×10⁻¹⁰ km / s]. 5 2.988×10 5 [km / s, fault time [-0.02, 0.08]μs, positioning error radius 30m.

[0205] Final output: The fault point is located on the main line 6.79km from the power source, and the inversion wave velocity is 2.981×10⁻⁶. 5 km / s, fault occurrence time 0.03μs, positioning error 10m, 95% confidence interval [6.76, 6.82]km.

[0206] This embodiment verifies the effectiveness of the method of the present invention in a single fault scenario of a radial distribution network. The positioning error is only 10 m, which is far superior to the traditional traveling wave method. It also provides a statistically reliable error boundary and has good engineering practical value.

[0207] Example 3

[0208] A method for accurate fault location in distribution networks based on multi-terminal traveling wave wavefront calibration and wave velocity inversion, and fault branch identification in multi-branch networks, is presented in this embodiment for the multi-branch control network in Embodiment 2, assuming the fault occurs on branch 2, 1.2 km from the branch point. The specific implementation method includes:

[0209] Step 1: Wave head calibration

[0210] The arrival time of each terminal wavefront was calibrated according to the method in Example 1: , , , , .

[0211] Step 2: Calculation of energy spectrum correlation

[0212] Perform a short-time Fourier transform (window function: Hanning window, window length 256 points, overlap 128 points) on the signals before and after each terminal wavefront, and calculate the energy spectrum. ~ .

[0213] Calculate the energy spectrum correlation between any two terminals to obtain the measured energy spectrum correlation matrix:

[0214] .

[0215] Step 3: Generation of the theoretical relevance matrix

[0216] For the four candidate branches, namely the main line, branch 1, branch 2, and branch 3, calculate the theoretical correlation matrix corresponding to different fault locations.

[0217] Taking branch 2 as an example, at a distance of 1.2km from the branch point, considering the line attenuation characteristics and wave velocity inversion results ( 2.98×10 5 (km / s), calculate the theoretical correlation matrix:

[0218] .

[0219] Step 4: Branch identification

[0220] Calculate the Frobenius norm for each candidate branch:

[0221] Main line: ;

[0222] Branch 1: ;

[0223] Branch 2: ;

[0224] Branch 3: .

[0225] The Frobenius norm corresponding to branch 2 is the smallest, so the fault is determined to occur on branch 2.

[0226] Step 5: Location Results

[0227] Based on the fault branch and wave velocity inversion results determined in step 4, the precise distance between the fault point and the branch point is calculated to be 1.21 km, with a positioning error of 10 m, which is less than 50 m.

[0228] Implementation effect verification:

[0229] A complex 10kV distribution network model was built on the PSCAD / EMTDC platform, and different types of faults were set for verification. The results are shown in the table below:

[0230]

[0231] The results show that the method of the present invention can maintain high positioning accuracy under various fault types, and the positioning error of high-resistance grounding fault is less than 50m, which meets the engineering requirements of distribution network fault positioning.

[0232] Example 4

[0233] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of any one of the embodiments 1-3 of the method for accurate location of distribution network faults based on multi-terminal traveling wave head calibration and wave velocity inversion.

[0234] Example 5

[0235] A traveling wave fault location system includes: multiple traveling wave acquisition terminals for synchronously acquiring fault traveling wave signals from each node of the distribution network; a data processing center for executing the steps of the distribution network fault accurate location method based on multi-terminal traveling wave head calibration and wave velocity inversion in Embodiment 1; and a communication network for realizing data transmission between the traveling wave acquisition terminals and the data processing center.

[0236] The traveling wave acquisition terminal includes a high-frequency current transformer, a BeiDou / GPS dual-mode timing module, a high-speed A / D converter, a data storage device, and a communication module. The output of the high-frequency current transformer is connected to the input of the high-speed A / D converter. The pulse-per-second (PPS) output of the BeiDou / GPS dual-mode timing module is connected to the synchronization clock inputs of both the high-speed A / D converter and the data storage device. The data output of the high-speed A / D converter is connected to the data input of the data storage device, and the data output of the data storage device is connected to the input of the communication module. The communication module uses a 4G / 5G wireless communication module or a fiber optic Ethernet module to connect to a communication network and upload the traveling wave data. The sampling frequency of the high-frequency current transformer is not less than 10MHz, and the synchronization accuracy of the BeiDou / GPS dual-mode timing module is better than 100ns. Specifically, the BeiDou / GPS dual-mode timing module receives BeiDou and GPS satellite signals simultaneously through a BeiDou / GPS dual-mode receiver. It calculates and outputs high-precision pulse-per-second (PPS) and UTC time information. Combined with the disciplined phase-locked loop technology of the oven-controlled crystal oscillator (OCXO), the local clock is dynamically calibrated to eliminate clock drift when satellite signals are interrupted, thereby achieving a synchronization accuracy better than 100ns.

[0237] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for accurate fault location in distribution networks based on multi-terminal traveling wave front calibration and wave velocity inversion, characterized in that, The steps are as follows: Step 1: Install traveling wave acquisition terminals at multiple nodes of the distribution network, and achieve nanosecond-level synchronous sampling through Beidou / GPS dual-mode time synchronization to obtain fault traveling wave signals; Step 2: Perform optimal phase mode transformation on the acquired fault traveling wave signal to extract the optimal line mode component; perform first-order differentiation on the two optimal line mode components respectively, and take the moment when the absolute value of the first-order derivative of both is greater than the preset threshold and the product of the two is greater than 0 as the initial traveling wave wavefront coarse positioning time; take the initial traveling wave wavefront coarse positioning time as the center, use the ESMD-VMD-TEO adaptive method to perform high-precision calibration on the optimal line mode component to obtain the wavefront position of each measurement point; Step 3: Based on the relationship between the arrival time and position of the wavefront at each measurement point, establish a multi-terminal traveling wave localization equation set, with the fault location, traveling wave velocity, and fault occurrence time as variables to be determined; Step 4: Construct a weighted least squares objective function based on the multi-terminal traveling wave localization equation set, and use the Levenberg-Marquardt algorithm to jointly invert the fault location, traveling wave velocity, and fault occurrence time; Step 5: For multi-dominated power grids, construct an energy spectrum correlation matrix to identify faulty branches; Step 6: Output the precise location of the fault point, the inversion wave velocity, and the confidence interval of the positioning error.

2. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 1, characterized in that, Traveling wave acquisition terminals are installed at the power supply end, the end of the main line, and the end of each branch line of the distribution network. All traveling wave acquisition terminals are connected to the Beidou / GPS dual-mode timing system. The traveling wave acquisition terminals acquire fault transient traveling wave voltage signals or fault transient traveling wave current signals through high-frequency current transformers. The method for extracting the optimal linear modulus components is as follows: The optimal phase-mode transformation is performed on the acquired three-phase fault traveling wave current signal. The transformation matrix T of the optimal phase-mode transformation is: ； We obtain three modulus components: in, For zero modulus components, , These are the two optimal line mode components. , and These represent the fault traveling wave current signals of phases a, b, and c, respectively. The two optimal line mode components extracted: , ; For the optimal linear modulus components and The derivative sequence is obtained by taking the first derivative of each derivative. and Initial traveling wave head coarse positioning time To meet The earliest moment; among them, This is a preset threshold.

3. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 1 or 2, characterized in that, The method for obtaining the wavefront position of each measurement point by using the ESMD-VMD-TEO adaptive method to perform high-precision calibration of the optimal linear mode components is as follows: Coarsely locate the time using the initial traveling wave front. Centered on the front and back windows Optimal linear modulus components within or Pole-symmetric mode decomposition is performed on the optimal linear mode components within the window to obtain several eigenmode function components of the preliminary decomposition. The optimal decomposition parameters for variational mode decomposition, including the number of decomposition levels, are adaptively determined using a subtractive averaging optimization algorithm. and penalty factor ; Based on the optimal decomposition parameters, a second variational mode decomposition is performed on the high-frequency intrinsic mode function components obtained by pole-symmetric mode decomposition to obtain refined mode components. Based on the refined modal components, high-frequency modal components containing fault transient information are selected, and the Teager energy operator sequence is calculated; Wavefront position is determined using an adaptive dynamic threshold method. ;in, For threshold coefficient, and These are the Teager energy operator sequences. The mean and standard deviation.

4. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 3, characterized in that, The threshold coefficient is adaptively adjusted based on the signal-to-noise ratio. The implementation method is as follows: at the coarse positioning time Within the preceding and following Δt windows, calculate the adaptive difference step size i and select the optimal step size i. opt The subsequent Teager energy operator sequence ; Calculate the gradient sequence of the energy spectrum within the window. And calculate the gradient entropy. The threshold coefficient λ, reflecting the concentration of abrupt changes in the energy spectrum, is determined as follows: ; where λ min and λ max H represents the minimum value and minimum value of the threshold coefficient, respectively. min H max These are the pre-defined upper and lower bounds of the gradient entropy.

5. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 4, characterized in that, The method for calculating the Teager energy operator sequence is as follows: The Teager energy operator introduces an adaptive difference step size. According to the signal base frequency and sampling frequency Determine the adaptive difference step size The range of values ​​for: Select the optimal step size within the range of values. This maximizes the peak size of the energy spectrum; The formula for calculating the Teager energy operator sequence is: ;in, This represents the discrete sampled value at the current sampling point n in the signal sequence of the high-frequency modal components obtained after decomposition; This indicates that before the current sampling point n, i... opt Discrete sampled values ​​at each sampling point; Indicates i after the current sampling point n opt Discrete sampled values ​​at each sampling point.

6. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 5, characterized in that, The The window value range is 0.5μs ~ 5μs; The objective function of the subtraction averaging optimization algorithm is to minimize the energy entropy. ;in, For the first The energy percentage of one IMF component For the first One IMF component of energy, The total energy of the signal. Let the objective function be the subtraction average optimization algorithm; The high-frequency mode components are the first 1 to 2 intrinsic mode function components with the highest energy proportion after pole-symmetric mode decomposition and variational mode decomposition; The signal base frequency f0 is taken as the rated frequency of the power system, and the sampling frequency f s It is determined by the hardware parameters of the traveling wave acquisition terminal; The optimal step size ;in, For adaptive differential step size The corresponding Teager energy operator sequence, and These are the Teager energy operator sequences. The mean and standard deviation; The adaptive difference step size The range of values ​​is .

7. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to any one of claims 4-6, characterized in that, The multi-terminal traveling wave positioning equation set is as follows: ； Among them, t j Let be the wavefront arrival time at the j-th measurement point. t0 is the distance to the fault, v is the time of fault occurrence, and v is the traveling wave velocity. For the first Calibration error at each measurement point This represents the total number of measurement points.

8. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 7, characterized in that, The multi-terminal traveling wave positioning equations are transformed into a weighted least squares optimization problem, and the objective function is constructed as follows: ； in, These are the weighting coefficients; The objective function is solved using an improved Levenberg-Marquardt algorithm. Introducing a multi-initial-point strategy: randomly generating initial points within the feasible region. Group initial point Optimize separately, and select the objective function. The minimum solution is taken as the global optimal solution. ; The first Calibration residuals at each measurement point ;in, To the maximum calibration error, For the first Kuness at each measurement point and These are the Teager energy operator sequences. The mean and standard deviation; φ i For the optimal step size i opt The corresponding Teager energy operator sequence; For the first Signal-to-noise ratio at each measurement point; Fault Distance Coordinates of the fault location satisfy: , For the first The coordinates of the measurement points.

9. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to any one of claims 4-6 and 8, characterized in that, The method for constructing the energy spectrum correlation matrix to identify fault branches is as follows: The short-time Fourier transform is used to calculate the first... Energy spectrum of the signal near the wavefront at each measurement point The energy spectrum correlation between any two measurement points is calculated using energy spectrum, and a measured energy spectrum correlation matrix is ​​constructed based on the energy spectrum correlation. ; Calculate candidate faulty branches The theoretical energy spectrum received at the assumed fault location y. The theoretical energy spectrum correlation between measurement points is calculated using theoretical energy spectra, and a theoretical energy spectrum correlation matrix is ​​constructed. ; The problem of minimizing the determination of the exact location of the faulty branch: ;in, These represent the faulty branch and the location of the fault point, respectively. This represents the Frobenius norm.

10. The method for accurate fault location in distribution networks based on multi-terminal traveling wave head calibration and wave velocity inversion according to claim 9, characterized in that, The signal near the wavefront at the j-th measurement point is after the completion of the... Wavefront arrival time at each measurement point After calibration, the optimal linear mode component is obtained from the optimal phase mode transformation. or Extract the signal within each Δt window before and after the transient waveform; All energy spectrum correlations Constructing the correlation matrix of the measured energy spectrum The diagonal element is 1; The theoretical energy spectrum Wherein, the constant S0 is the energy spectral density of the faulted traveling wave source within the effective frequency band. The attenuation coefficient per unit length; For overhead lines, attenuation coefficient For cable lines, attenuation coefficient ,in, Indicates the frequency of the fault traveling wave signal; The theoretical energy spectrum correlation is: ; The minimization problem is solved using a two-level search strategy: outer search: traverse each candidate faulty branch l; inner search: for each candidate faulty branch l, perform a golden section search within the range from 0 to the maximum length, calculate the Frobenius norm for each position y, and record the minimum norm value and optimal position of the candidate faulty branch l; branch decision: compare the minimum norm values ​​of all candidate faulty branches, and select the faulty branch with the smallest minimum norm value. As the final faulty branch, the corresponding location is the fault point location. ; Output precise location of the fault point Traveling wave velocity When the fault occurred The steps for estimating the confidence interval of positioning error based on residual analysis are as follows: Calculate the weighted residual vector of the j-th measurement point. A nonparametric bootstrap method is used to perform B resampling cycles with replacement on n weighted residual vectors, resulting in B bootstrap samples. The perturbed wavefront arrival times are then constructed. For each bootstrap sample, the perturbed measurement time is solved inversely. ,in, For the j-th measurement point and the b-th resampling with replacement, the self-sampled sample is taken at the measurement time. As input, repeat the optimization process in step four to obtain the inversion results of group b. ;in,( () represents the precise location of the fault point retrieved in group b. For the wave velocity inverted in group b , The fault occurrence time is represented by the inversion of group b. For a given confidence level , respectively , , , Pick and Quantiles are used to obtain the confidence intervals for each component: ； ； ； ； in, This refers to the statistical term quantile; Positioning error radius Project the precise location of the fault point onto the branch mileage and output the confidence interval of the mileage value.

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