A method for decoupling and fault ranging of multi-modal resonant signals

Abstract

The application provides a multi-modal resonant signal decoupling separation and fault ranging method, comprising the following steps: building an electromagnetic transient simulation model of a to-be-observed line; constructing a mapping database of time difference and wave velocity; obtaining a multi-modal resonant frequency spectrum database under a non-fault condition; determining a fault line section and a preliminary position based on the mapping database and a time difference method; setting a simulation fault near the preliminary position, obtaining a resonant frequency spectrum database of the fault line section through frequency domain simulation; converting a fault traveling wave signal to a frequency domain to obtain a measured frequency spectrum; reconstructing and separating the measured frequency spectrum by using an orthogonal matching pursuit algorithm to obtain a fault line frequency spectrum; and determining a fault position by calculating a correlation coefficient of the fault line frequency spectrum and the resonant frequency spectrum database through weight weighting. The application eliminates a detection blind area of a short-distance cable under a long-distance overhead line background, and improves the reliability of mixed line fault ranging.

Description

Technical Field

[0001] This invention relates to the technical field of transmission line transient signal analysis and fault location, and in particular to a method for decoupling and separating multimode resonant signals and fault location. Background Technology

[0002] In current power distribution networks and new energy distribution systems such as wind power and photovoltaics, transmission lines are typically a mix of overhead lines and buried cables, and are prone to faults such as grounding, short circuits, and lightning strikes. Therefore, quickly and accurately determining the distance and location of faults is crucial for the operation and maintenance of power supply systems. Traveling wave analysis based on high-frequency fault signals is a widely used technique for fault location and positioning. However, the propagation speed of traveling wave signals varies significantly in different transmission media and is frequency-dependent. Therefore, the random variation in wave speed makes the traditional time-difference method difficult to apply in this scenario. Spectrum analysis methods require using different resonant frequency differences to estimate fault distance, but in mixed transmission line media, different line segments will form multiple resonant frequencies, exhibiting multi-mode aliasing, making the frequency difference method unsuitable for direct application.

[0003] Currently, there is a lack of a decoupling and separation method for fault resonant frequencies in hybrid transmission line media, which would allow the resonant signals of different transmission line segments to be directly correlated with the line length, thus enabling the estimation and location of fault distances.

[0004] Patent application number 202410904520.9 discloses a fault location method and system based on line carrier. The method includes deploying carrier signal monitoring devices according to a set of installation points; acquiring and preprocessing carrier signals; performing short-time Fourier transform on the preprocessed signals to obtain the time spectrum; calculating the statistical characteristics of the time spectrum; extracting the instantaneous frequency features of the preprocessed signals; constructing a time-frequency domain feature vector; based on the time-frequency domain feature vector, calling a pre-configured CNN model to identify the fault type and perform preliminary fault location; calling a pre-constructed adaptive weighted fusion location model to calculate the fused fault location result; performing time delay jitter compensation and fault confidence interval calculation on the fused fault location result; and outputting the final fault detection result. This invention establishes an optimized installation point layout scheme, which can obtain more and more effective information. Through lightweight CNN and GAT interactive loop training, they mutually reinforce each other, continuously improving the accuracy of fault identification and fault location. However, the aforementioned patent still cannot solve the problem of resonant signal coupling between different lines in fault signal analysis of multiple transmission media. Summary of the Invention

[0005] To address the technical problems of overlapping and feature annihilation of traveling wave spectra caused by multiple reflections in overhead-cable hybrid lines, this invention proposes a method for decoupling and separating multi-mode resonant signals and for fault location. This method can solve the problem of resonant signal coupling between different lines in fault signal analysis under various transmission media. This invention utilizes a pre-constructed full-topology simulation fingerprint library and employs signal sparse decomposition technology to extract and reconstruct the masked weak cable resonant features from complex measured hybrid waveforms. Based on the separated pure spectral features, the fault distance of each segment is calculated independently, effectively eliminating the detection blind zone of short-distance cables in the context of long-distance overhead lines, and significantly improving the reliability of fault location in hybrid lines.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows: a method for decoupling and separating multimodal resonant signals and for fault location, comprising the following steps:

[0007] Step 1: Based on the topology of the hybrid line and the transmission line parameters of different line segments, build an electromagnetic transient simulation circuit model of the line to be observed.

[0008] Step 2: Construct a mapping database between time difference and wave speed in the electromagnetic transient simulation circuit model;

[0009] Step 3: Construct the impulse response transfer function of the single-mode resonance spectrum under non-fault conditions to obtain the multi-mode resonance spectrum database under non-fault conditions;

[0010] Step 4: When a fault occurs, acquire the fault traveling wave signal;

[0011] Step 5: Based on the mapping database and time difference method obtained in Step 2, determine the faulty line segment and preliminary location;

[0012] Step 6: Set up a simulated fault near the initial location within the faulty line segment, and obtain the resonant frequency spectrum database of the faulty line segment through frequency domain simulation;

[0013] Step 7: Convert the acquired fault traveling wave signal to the frequency domain to obtain the measured spectrum; use the orthogonal matching pursuit algorithm to reconstruct and separate the measured spectrum to obtain the fault line spectrum of the measured signal;

[0014] Step 8: Construct weights based on the frequency difference between the measured fault line spectrum and the resonance spectrum database of the fault line segment. Calculate the correlation coefficient between the measured fault line spectrum and the resonance spectrum database using these weights. Determine the fault location based on the correlation coefficient.

[0015] Preferably, the method for constructing the time difference-wave velocity mapping database is as follows: In a hybrid line with multiple transmission line media of total line length L, fault sensors are installed at the beginning and end of the line, respectively, at time... ,Location A fault occurs at the fault point; a fault traveling wave is generated at the fault point, propagating to both ends, and the time when it reaches the fault sensor at the first end is... The time of arrival at the end fault sensor is According to the traveling wave principle, the wave velocities at the beginning and end of the wave are as follows: The time difference between the arrival time of the first-end fault sensor and the last-end fault sensor. The circuit between the fault sensors is divided into N segments according to distance, resulting in N-1 simulated fault points. At each of the N-1 simulated fault points, a square wave impulse signal is injected to establish the traveling wave velocity. Time difference with double-ended traveling wave The analytical correspondence; N-1 sets of traveling wave velocities are established through N-1 simulations. Time difference with double-ended traveling wave The mapping database.

[0016] Preferably, the arrival time is based on the arrival time wavefronts of the first-end fault sensor and the last-end fault sensor. Obtain the time difference of the two-end traveling wave The equivalent wave speed is obtained by looking up a table in the mapping database. Calculate the initial location of the fault:

[0017] ;

[0018] Based on the initial location of the fault The faulty line segment was determined by the span and topology information of the line.

[0019] Preferably, in the electromagnetic transient simulation circuit model, a sinusoidal signal source is connected to one side of the line, and a voltage or current signal is output from the other side. The boundary resistance of the line segment is set as the characteristic impedance of the transmission lines on both sides, and the length of the line segments on both sides is greater than or equal to 10 times the length of the target line segment in the middle. Frequency domain simulation is performed within a finite frequency range to obtain the resonant spectrum of a single mode under non-fault conditions. The impulse response transfer function of different line segments i is obtained. When there are N line segments, construct a multimode resonance spectrum database under non-fault conditions. Where i is the line segment number;

[0020] Based on the identified faulty line segment and preliminary location, a short-circuit fault is set up to simulate a low-resistance short-circuit fault at the preliminary location of the fault. Nearby detailed mesh simulation of fault location In frequency domain simulation, the location of the fault is obtained. Transfer function to the first or last fault sensor Establish a resonant spectrum database for line segments. .

[0021] Preferably, when a fault occurs, the traveling wave current signal collected by the fault sensor at the beginning or end of the line is selected; the traveling wave current signal is then converted to the frequency domain to obtain the corresponding measured spectrum. or The resonance spectrum database H under non-fault conditions r Resonance spectrum database H under fault conditions f A simulated transfer function matrix is ​​formed by combining the data to establish a sparse representation model of the measured spectrum. Using the orthogonal matching pursuit algorithm, through iterative processes of normalized correlation calculation, spectrum template selection, least squares estimation, and residual update, the estimated sparse coefficient vector is obtained. Based on the dictionary columns corresponding to the non-zero elements in the estimated sparse coefficient vector, the measured spectrum is reconstructed and separated to obtain the spectrum-separated resonant spectrum of the non-faulty line. and the spectrum of the faulty line This completes spectral separation based on sparse decomposition.

[0022] Preferably, the resonant spectrum database under non-fault conditions is used. Resonance spectrum database under fault conditions Combined to form the simulation transfer function matrix: Each column of the simulation transfer function matrix H represents a spectrum template corresponding to a candidate line segment or candidate fault location.

[0023] Based on the measured spectrum under mixed line fault conditions, which is formed by the superposition of resonant components from non-faulty and faulty line segments to create a multi-mode resonant spectrum, a sparse representation model is established: ;in, Let be the sparse coefficient vector to be determined, y represent the measured spectrum, and e be the error term between the measured spectrum and the simulated spectrum; the sparse coefficient vector It is used to characterize the contribution of each candidate spectral template to the measured spectrum y. When a certain spectral template matches the measured spectrum well, its corresponding coefficient is large; otherwise, its corresponding coefficient is close to zero.

[0024] The sparse coefficient vector is obtained by solving the sparse representation model using the orthogonal matching pursuit algorithm. Based on the sparse coefficient vector The index positions and amplitudes of the non-zero elements are used to reconstruct and separate the measured spectrum into the resonant spectral components of each segment of the non-faulty line and the spectrum of the faulty line segment. .

[0025] Preferably, the sparse coefficient vector is obtained by solving the sparse representation model using the orthogonal matching pursuit algorithm. The method is as follows: Initialize the initial residual vector as follows: In the k-th iteration, calculate the current residual. With each spectrum template in the simulation transfer function matrix H Normalized correlation between them: Select normalized correlation The largest spectral template is added to the current spectral template matching index set, and then added to the updated spectral template matching index set. k+1 The corresponding simulation transfer function matrix To obtain an estimate of the current sparse coefficient vector, perform least squares estimation. Based on the estimated value of the sparse coefficient vector Update the residual vector for the (k+1)th iteration: Repeated normalized correlation calculation—spectral template selection—least square estimation—residual vector update, until the updated residual vector is less than a preset threshold or reaches a preset maximum number of iterations, to obtain the estimated value as a sparse coefficient vector. .

[0026] Calculate the spectrum of the isolated faulty line Resonance spectrum database under fault conditions The correlation coefficient Cor(i) is: ,in, This represents the spectrum of the faulty line based on the measured data. With resonance spectrum database The simulated spectrum corresponding to the i-th candidate position The dot product of the vectors between them Indicates the spectrum of the faulty line The energy norm, Represents the simulated spectrum The 2-norm, Let be the weight of the i-th line;

[0027] The location coordinates corresponding to the maximum value of the search correlation coefficient Cor(i) are taken as the fault location.

[0028] Preferably, the weight of the i-th line is: ;in, It is the width factor; To simulate frequency difference, This represents the measured frequency difference.

[0029] Preferably, the topology of the hybrid line includes: branch routing, line length, and line type topology information; transmission line parameters include overhead line tower structure, cable type, cable cross-sectional structure, and cable medium; the electromagnetic transient simulation circuit model includes various types of transmission lines and loads of the line to be observed.

[0030] Extracting the main resonant frequency peak from the spectrum of the faulty line of the measured signal. The measured frequency difference is obtained by calculating the interval between the peak points of the resonant frequency. ;

[0031] For the resonance spectrum database under fault conditions Each transfer function in The simulated frequency difference is obtained by calculating the interval between the peak points of the resonant frequency: ,in, , These represent the frequencies corresponding to the resonant peak values ​​of the i-th and (i-1)-th lines, respectively.

[0032] Width coefficient ,parameter .

[0033] Compared with existing technologies, the beneficial effects of this invention are as follows: By using pre-simulation, a fingerprint database of the time-domain pulse arrival time difference ∆t and equivalent wave velocity at different simulated fault locations is established, realizing the segmented decoupling of wave velocities in different transmission line media, solving the wave velocity identification problem in multiple transmission media, eliminating the positioning error introduced by the traditional average wave velocity method, and enabling fault interval identification and coarse location coordinate positioning. This invention introduces pre-simulated multi-mode fault resonance spectrum "dictionary" data and, based on the sparse vector decomposition method, completes the decoupling and separation of signal spectra of faulty and non-faulty lines, solving the problem of spectral feature aliasing caused by impedance mismatch in mixed lines, and effectively identifying weak cable resonance signals masked by strong signals. The sparse decomposition algorithm used in this invention can achieve blind source separation of signals without prior knowledge of the fault location, achieving fine-grained fault location positioning and possessing strong anti-noise interference capabilities. Attached Figure Description

[0034] 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.

[0035] Figure 1 This is a flowchart of the present invention.

[0036] Figure 2 This is a schematic diagram of the hybrid circuit of the multi-transmission line medium of the present invention.

[0037] Figure 3 For the present invention A graph mapping the fingerprint database.

[0038] Figure 4 The following are the resonant spectrum diagrams of each segment under non-fault conditions of the present invention, wherein (a) is Figure 2 The resonant spectrum of section 1 of the overhead line, (b) is Figure 2 The resonant spectrum of the buried cable section, (c) is Figure 2 The resonant spectrum of two sections of the overhead line.

[0039] Figure 5 This is a time-domain waveform diagram of the fault traveling wave at the first and last sensor positions of the present invention.

[0040] Figure 6 The fault traveling wave spectrum at the first and last sensor positions of the present invention is shown in (a), which is a multimode resonance spectrum at the first sensor position and (b) is a multimode resonance spectrum at the last sensor position. Detailed Implementation

[0041] 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.

[0042] Example 1

[0043] like Figure 1 As shown, a method for decoupling and separating multimodal resonant signals and for fault location includes the following specific implementation steps:

[0044] Step 1: Based on the topology of the hybrid line and the transmission line parameters of different line segments, build an electromagnetic transient simulation circuit model of the line to be observed.

[0045] Obtain the topology and transmission line parameters of the multi-transmission-medium hybrid line, including: branch routing, line length, line type topology information, overhead line tower structure, cable type, cable cross-sectional structure, and cable medium transmission line parameter information. In the Electromagnetic Transient Simulation (EMTP) software, input the transmission line parameters based on the topology information, select the transmission line model in the software, and build an electromagnetic transient simulation circuit model of the line under study. This model should include all types of transmission lines and loads of the line to be observed.

[0046] Step 2: Construct a mapping database of time difference and wave speed in the electromagnetic transient simulation circuit model.

[0047] Distributed sensors (voltage or current sensors) already installed in the power grid are selected, and a mapping database between time difference and wave velocity is constructed in the electromagnetic transient simulation circuit model. A hybrid line with multiple transmission line media, such as... Figure 2 As shown, the total length of the line is L, and fault sensors are installed at both ends of the line, including the beginning and end. At time [time missing], [fault sensors are detected]. ,Location A fault occurs at the fault point. A fault traveling wave is generated at the fault point, propagating in both directions, and arriving at the first sensor at the following time: The time of arrival at the end sensor is According to the traveling wave principle, the wave velocities at the beginning and end of the wave can be obtained as follows:

[0048] ; (1)

[0049] (2)

[0050] The lines between distributed sensors are divided into N segments according to distance, resulting in N-1 simulated fault locations. . This represents the time difference between the arrival times at the head and tail sensors. In the simulation environment, at these N-1 simulated fault points, a square wave impact signal is injected. Based on formulas (1) and (2), the traveling wave velocity can be established respectively. Time difference with double-ended traveling wave The analytical correspondence is established. Through N-1 simulations, N-1 sets of traveling wave velocities are established. Time difference with double-ended traveling wave The mapping database.

[0051] Step 3: Construct a transfer function database of single-mode resonance spectra under non-fault conditions.

[0052] For different segments of the hybrid circuit, frequency sweep simulation is performed sequentially at the junctions of each segment in the electromagnetic transient simulation circuit model to obtain the transfer function database of the single-mode resonant spectrum of each segment. A sinusoidal signal source is connected to one side of the circuit, and a voltage or current signal is output from the other side within a finite frequency range. Frequency domain simulation was performed within the specified range. The boundary resistance of the line segment was set as the characteristic impedance of the transmission lines on both sides. The lengths of the line segments on both sides were greater than or equal to 10 times the length of the target line segment in the middle to eliminate reflected waves at the line boundaries and ensure that the frequency domain simulation obtained under non-fault conditions yielded a single-mode resonant spectrum. The impulse response transfer function of different line segments i was obtained. When there are N line segments, a multimode resonance spectrum database under non-fault conditions is constructed. , where i is the line segment number.

[0053] Step 4: When a fault occurs, collect the fault traveling wave signal.

[0054] When a fault occurs, a fault traveling wave signal is collected. Taking a current sensor as an example, when a fault occurs, the sensor current data from both sides of the fault, namely the beginning and end, are selected. .

[0055] Step 5: Based on the mapping database and time difference method obtained in Step 2, determine the faulty line segment and preliminary location.

[0056] Time of arrival wavefront based on two sensors To obtain the time difference between the two The equivalent wave velocity is obtained by looking up a table in the mapping database in step two. The preliminary location of the fault is obtained based on the following formula (3):

[0057] ; (3)

[0058] Based on the initial location of the fault The faulty line segment is determined by the line's span and topology information. The accurate faulty line segment can be corrected by subsequent frequency domain algorithms.

[0059] Step 6: Set up a simulated fault near the initial location within the faulty line segment, and obtain the resonant frequency spectrum database of the faulty line segment through frequency domain simulation.

[0060] Based on the faulty line segment and preliminary fault location obtained in step four, a short-circuit fault is set, and the fault impedance is set to a low impedance value. Simulating a low-impedance short-circuit fault reduces echo reflection interference from the opposite side, at the location Detailed meshing of the surrounding area to simulate fault location Simulation was performed in the frequency domain, similar to step three, to obtain the fault location. Transfer function to one of the first and last sensors (i.e., from position) (Transfer function from the sensor location to the line segment) to establish a resonant spectrum database for the line segment. .

[0061] Step 7: Convert the fault traveling wave signal acquired in Step 4 to the frequency domain to obtain the measured spectrum; use the Orthogonal Matching Pursuit (OMP) algorithm to reconstruct and separate the measured spectrum to obtain the fault line spectrum of the measured signal.

[0062] The time-domain fault traveling wave current signal acquired by the first-end or last-end sensor or Perform a Fourier transform to obtain the corresponding measured spectrum. or The method transforms reflection, catadioptric reflection, and mode aliasing phenomena, which are difficult to distinguish directly in the time domain, into the frequency domain for decoupling and feature extraction. By using the orthogonal matching pursuit (OMP) algorithm, the resonant spectrum caused by different line segments and faulty lines is separated and decoupled, which greatly reduces the difficulty of frequency domain analysis and thus greatly improves the accuracy of fault location.

[0063] The sensor current data at the beginning and end or The measured spectrum was obtained by converting to the frequency domain. or The measured spectrum was calculated using the OMP algorithm. or Respectively with resonance spectrum database Resonance Spectrum Database The normalized correlation is calculated to determine which spectrum in the resonance spectrum database is most correlated with the measured spectrum. If the fault occurs in a cable segment, the spectrum representing the "cable fault" will be selected, and its corresponding normalized correlation will be high, while the normalized correlation of non-faulty segments will be close to 0. Using the orthogonal matching pursuit algorithm, through the iterative process of normalized correlation calculation, spectrum template selection, least squares estimation, and residual update, the sparse coefficient vector estimate is obtained. Based on the dictionary columns corresponding to the non-zero elements in the sparse coefficient vector estimate, the measured spectrum is reconstructed and separated. By extracting the columns corresponding to the non-zero correlation coefficients, spectrum separation is achieved.

[0064] The transfer function database under non-fault conditions and the resonance spectrum database under fault conditions are combined to form the simulation transfer function matrix:

[0065] ; (4)

[0066] Each column of the simulation transfer function matrix H represents a spectral template corresponding to a candidate line segment or candidate fault location. Since the measured spectrum under mixed line fault conditions is typically a multi-mode resonant spectrum formed by the superposition of resonant components from both non-faulty and faulty line segments, the following sparse representation model can be established:

[0067] ; (5)

[0068] Where y represents the measured signal spectrum data, i.e., the measured spectrum, and its value is the measured spectrum. or H is the simulation transfer function matrix obtained through steps three and six, and its specific analytical expression is as described in formula (4); Let be the sparse coefficient vector to be determined, and e be the error term between the measured spectrum and the simulated spectrum.

[0069] The sparse coefficient vector The coefficient y is used to characterize the contribution of each candidate spectral template to the measured mixed spectrum. When a spectral template matches the measured spectrum well, its coefficient is large; otherwise, its coefficient is close to zero. The measured spectrum y is usually formed by the superposition of a few resonant components from non-faulty line segments and resonant components from faulty line segments.

[0070] To solve for the sparse coefficient vector, the orthogonal matching pursuit algorithm is used to solve the above sparse representation model. First, the initial residual vector is initialized as follows:

[0071] (6)

[0072] The spectral template matching index set is initialized to an empty set; then, correlation quantization is performed, and in the k-th iteration, the current residual vector is calculated. With each spectrum template in the simulation transfer function matrix H Normalized correlation between them:

[0073] ; (7)

[0074] Normalized correlation Used to characterize the explanatory power of the i-th spectral template for the current residual vector, normalizing the correlation. The larger the value, the better the simulation spectrum of the i-th simulation and the current residual vector of the k-th iteration. The more similar the data, the more likely it is to be selected into the current spectral template matching index set. This is based on normalized correlation. The least squares method is used to estimate the spectral template index with the highest normalized correlation in the k-th iteration. That is, the current residual vector Best matching index:

[0075] ; (8)

[0076] Furthermore, define It is a set of spectrum template matching indices selected from the previous k iterations and corresponding to the measured signal spectrum data. Each newly added index corresponds to the spectrum template with the highest matching degree with the current residual vector in the current iteration. The spectrum matching index set is used to record the column index of the currently selected spectrum template in the simulation transfer function matrix.

[0077] Then, the index of the selected spectral template with the highest normalized correlation is... Add to the set of spectral template matching indices updated for the current frequency:

[0078] ; (9)

[0079] Then, least squares estimation is performed on the corresponding submatrix of the updated spectrum template matching index set to obtain the current sparse coefficient vector estimate, and the residual vector is updated. By repeating the above process, the sparse decomposition of the measured spectrum is gradually completed.

[0080] Match the index set according to the updated spectrum template. Extract the corresponding columns from the simulation transfer function matrix H to form a submatrix. Then, least squares estimation is performed on the said submatrix to obtain the current estimate of the sparse coefficient vector:

[0081] ; (10)

[0082] Where z is the coefficient vector to be calculated corresponding to the currently selected spectral template set. The analytical solution to the above formula is:

[0083] ; (11)

[0084] in, Given the current set of selected spectrum templates, this represents the optimal contribution weight estimate of each spectrum template to the measured spectrum y. This represents the transfer function matrix corresponding to the current spectrum matching index set. The sparse coefficient vector estimate represents the set of contribution weights that minimizes the fitting error between the measured spectrum y and the linear combination of the spectrum templates, given the current set of selected spectrum templates.

[0085] Furthermore, the residual vector for the (k+1)th iteration is updated based on the sparse coefficient vector estimate:

[0086] ;(12)

[0087] Repeat the iterative process of "normalized correlation calculation - spectral template selection - least squares estimation - residual update" until the updated residual vector is less than a preset threshold. That is, satisfying

[0088] ; (13)

[0089] Alternatively, the number of indices in the spectrum matching index set reaches the preset maximum number of iterations N, thus obtaining the final sparse coefficient vector. .

[0090] The obtained sparse coefficient vector estimate This is used to characterize the contribution of each candidate spectral template to the measured mixed spectrum. Based on the index positions and amplitudes of the non-zero elements in the obtained sparse coefficient vector estimates, the measured spectrum y can be reconstructed and separated into the resonant spectral components of each segment of the non-faulty line. The resonant spectrum components of the faulty line segment ,and

[0091] (14)

[0092] The obtained fault segment resonant spectrum signal It can be used for subsequent precise positioning steps.

[0093] Based on the above steps, the measured spectrum is reconstructed and separated into: the overhead line spectrum and the cable spectrum of the non-faulty line. and the spectrum of the faulty line This completes spectral separation based on sparse decomposition.

[0094] Before performing the Orthogonal Matching Pursuit (OMP) algorithm, the spectrum of the faulty line of the measured signal was analyzed. Extract the spectrum corresponding to the peak value of the main resonant frequency. Calculate the interval between its resonant frequency peaks: .

[0095] Step 8: Construct a weight vector based on the frequency difference between the fault line spectrum of the measured signal and the resonant spectrum database. Use the weight vector to calculate the correlation coefficient of the transfer function of the fault line spectrum of the measured signal and the resonant spectrum database. Determine the fault location based on the correlation coefficient.

[0096] For the resonance spectrum database under fault conditions Each transfer function in Extract the frequency corresponding to its main resonant frequency peak. And calculate the interval between its resonant frequency peaks: ,in, , Let represent the frequencies corresponding to the i-th and (i-1)-th resonant peaks, respectively. Construct a weight vector. The i-th weight is defined as a Gaussian kernel function:

[0097] ; (15)

[0098] in, It is the width factor, used to tolerate wave velocity errors between the measured and simulated signals. , If the simulation frequency difference With respect to measured frequency difference If they are very close, then the weights are... To maintain the contribution of this data; if the deviation is large, the weighting... This will suppress the contribution of the data.

[0099] Calculate the spectrum of the faulty line separated in formula (8) according to the following formula. With the resonance spectrum database in step six The correlation coefficient Cor(i) is:

[0100] ; (16)

[0101] in, Database representing measured fault data spectrum and resonance spectrum The spectrum corresponding to the i-th candidate position The dot product of the vectors between them Represents measured data The energy norm, Represents the simulated spectrum The 2-norm (energy norm), divided by the denominator. and The energy norm is used to normalize different spectral amplitudes.

[0102] Finally, the index corresponding to the maximum value of the search relevance coefficient Cor(i) is further defined as follows:

[0103] (17)

[0104] The coordinates of the fault location are then represented as:

[0105] (18)

[0106] Where x(Index) is the position coordinate corresponding to the index Index in the line.

[0107] Example 2

[0108] like Figure 1 As shown, a method for decoupling and separating multimodal resonant signals and for fault location includes the following steps:

[0109] Step 1: Construct an electromagnetic transient circuit model of the circuit to be observed.

[0110] This example uses a multi-transmission medium line consisting of a 2km overhead line, a 4km cable line, and a 1km overhead line as an example. Electromagnetic transient simulation circuit models of the line under study are built using the electromagnetic transient simulation software EMTP-RV and PSCAD-V5. To ensure the effectiveness of algorithm verification, fault data and localization algorithms are verified in different simulation environments. Faults are simulated in EMTP-RV, and a simulation mapping database is established in PSCAD-V5. The topology of the hybrid line is as follows: Figure 2 As shown, a grounding fault occurred at a point 3 km along the cable.

[0111] Step 2: Construct a mapping database of traveling wave velocities.

[0112] Select the distributed sensors already installed in two lines, and in the PSCAD-V5 simulation model, perform the following steps according to the method in step two of Example 1. Figure 2 The circuit constructs a mapping database of traveling wave velocities to determine the time difference between the signals received by the dual-end sensors. and equivalent wave velocity One-to-one correspondence, such as Figure 3 As shown. (Through) Figure 3 The time difference on the horizontal axis can be seen directly. and equivalent wave velocity .

[0113] Step 3: Construct a multimodal resonance spectrum database under non-fault conditions.

[0114] In the PSCAD-V5 simulation model, following the method in step three of Example 1, frequency sweep simulation was performed on the intersection of each line segment to obtain the resonance spectrum diagram of each segment under non-fault conditions, as shown below. Figure 4 As shown, the resonant spectrum feature values ​​of each segment under non-fault conditions are extracted to construct a multi-mode resonant spectrum database under non-fault conditions. The specific resonant spectrum data are as follows:

[0115] The overhead line segment of the spectrum database on the left,

[0116] ;

[0117] Left side of the spectrum database cable segment,

[0118] ;

[0119] The overhead line segment of the spectrum database on the right,

[0120] ;

[0121] Right side spectrum database cable segment,

[0122] .

[0123] Step 4: When a fault occurs, measure and record the fault signal.

[0124] In the EMTP-RV simulation model, a ground fault is simulated at a 3km section of the cable. Sensors on both sides of the fault are selected to record fault data, and the fault voltage waveform is as follows. Figure 5 As shown. (Through) Figure 5 It can be seen that the fault location cannot be directly calculated based on the two-end time difference fault location method.

[0125] Step 5: Based on fingerprint data and time difference method, determine the fault section and preliminary location.

[0126] The time difference between the two is obtained using the fault data obtained in step four. The average wave speed on both sides is obtained by querying the mapping database. , Substituting into formula (3), we get:

[0127] ;

[0128] Subtracting the 2000 meters of the overhead line section from the 4999 meters, we can conclude that the fault is located near the 2000 meters of the cable section minus the 2999 meters of the overhead line section.

[0129] Step 6: Obtain the resonant frequency spectrum at the fault distance.

[0130] Based on the faulty line segment and location obtained in step four, a simulated fault is set according to the fault type, and the fault impedance is set to a low impedance value. ),exist Detailed meshing of the surrounding area to simulate fault location We obtained a database of resonance spectra under fault conditions.

[0131] Step 7: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full Figure 5 The fault signal in the image is subjected to Fourier transform to obtain the resonance spectrum of the data from the first and last sensors, as shown in the figure. Figure 6 As shown, a sparse optimization objective function is established, and the orthogonal matching pursuit (OMP) algorithm is used to solve for the sparse coefficient vector of the measured mixed spectrum vector in the resonant spectrum database. Based on the distribution of the coefficient vector, the measured spectrum is reconstructed and separated into: the overhead line spectrum of non-faulty lines and the cable spectrum.

[0132] The multimode resonance spectrum of the faulty line on the left is as follows:

[0133] ;

[0134] Querying the multimode resonance spectrum database obtained in step three under non-fault conditions, it can be divided into the spectrum of normal overhead line sections:

[0135] ;

[0136] Spectrum segment where the fault is located:

[0137] Fault location is performed using the frequency difference method, where the frequency difference is calculated from the spectrum of the faulty segment. Wave velocity is selected from the pure cable dielectric wave velocity. According to the distance of the fault Difference in spectrum with adjacent resonances The analytical relationship between them ,in It is the propagation speed of the traveling wave in the medium; the calculated fault location is at a distance from the left end of the cable segment. Place.

[0138] Similarly, the multimode resonance spectrum of the faulty line on the right is:

[0139] ;

[0140] Querying the multimode resonance spectrum database obtained in step three under non-fault conditions, it can be divided into the spectrum of normal overhead line sections:

[0141] ;

[0142] Spectrum segment where the fault is located:

[0143] ;

[0144] Similarly, the frequency difference method is used for fault location, where the frequency difference is calculated from the spectrum of the faulty segment. Wave velocity is selected from the pure cable dielectric wave velocity. The calculated location of the fault is at a distance from the right end of the cable segment. Place.

[0145] Based on the technical path established in the implementation plan, the fault is first preliminarily located using the time-domain method in step five to determine the specific line segment where the fault occurred. This coarse time-domain measurement result provides the necessary prerequisites for decoupling multimode resonant signals in subsequent frequency-domain analysis, effectively reducing the complexity of frequency-domain processing and making the separation process of multimode signals simpler and more feasible. On this basis, frequency-domain calculation methods are further used to achieve accurate fault location.

[0146] The present invention provides a novel solution for locating faults in hybrid power transmission lines under mixed transmission media conditions. By pre-establishing a fingerprint database of time difference and equivalent wave velocity, the equivalent wave velocity can be accurately estimated. The present invention combines time-domain and frequency-domain joint analysis, and based on the resonant frequency fingerprint spectrum database of non-faulty sections, it uses the orthogonal matched pursuit method to complete the decoupling and separation of multi-mode resonant signals, thereby achieving accurate calculation of fault distance in the frequency domain.

[0147] 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 decoupling and separating multimodal resonant signals and for fault location, characterized in that, The steps include: Step 1: Based on the topology of the hybrid line and the transmission line parameters of different line segments, build an electromagnetic transient simulation circuit model of the line to be observed. Step 2: Construct a mapping database between time difference and wave speed in the electromagnetic transient simulation circuit model; Step 3: Construct the impulse response transfer function of the single-mode resonance spectrum under non-fault conditions to obtain the multi-mode resonance spectrum database under non-fault conditions; Step 4: When a fault occurs, acquire the fault traveling wave signal; Step 5: Based on the mapping database and time difference method obtained in Step 2, determine the faulty line segment and preliminary location; Step 6: Set up a simulated fault near the initial location within the faulty line segment, and obtain the resonant frequency spectrum database of the faulty line segment through frequency domain simulation; Step 7: Convert the acquired fault traveling wave signal to the frequency domain to obtain the measured spectrum; use the orthogonal matching pursuit algorithm to reconstruct and separate the measured spectrum to obtain the fault line spectrum of the measured spectrum; Step 8: Construct weights based on the frequency difference between the measured fault line spectrum and the resonant spectrum database of the fault line segment. Calculate the correlation coefficient between the measured fault line spectrum and the resonant spectrum database using these weights. Determine the fault location based on the correlation coefficient.

2. The method for decoupling and separating multi-mode resonant signals and fault location according to claim 1, characterized in that, The method for constructing the time difference-wave velocity mapping database is as follows: In a hybrid transmission line with multiple transmission line media of total length L, fault sensors are installed at the beginning and end of the line, respectively, at time... ,Location A fault occurs at the fault point; a fault traveling wave is generated at the fault point, propagating to both ends, and the time when it reaches the fault sensor at the first end is... The time of arrival at the end fault sensor is According to the traveling wave principle, the wave velocities at the beginning and end of the wave are as follows: The time difference between the arrival time of the first-end fault sensor and the last-end fault sensor. The circuit between the fault sensors is divided into N segments according to distance, resulting in N-1 simulated fault points. At each of the N-1 simulated fault points, a square wave impulse signal is injected to establish the traveling wave velocity. Time difference with double-ended traveling wave The analytical correspondence; N-1 sets of traveling wave velocities are established through N-1 simulations. Time difference with double-ended traveling wave The mapping database.

3. The method for decoupling and separating multimodal resonant signals and fault location according to claim 2, characterized in that, Arrival time of wavefront based on the arrival time of the head-end fault sensor and the tail-end fault sensor Obtain the time difference of the two-end traveling wave The equivalent wave speed is obtained by looking up a table in the mapping database. Calculate the initial location of the fault: ； Based on the initial location of the fault The faulty line segment was determined by the span and topology information of the line.

4. The method for decoupling and separating multimode resonant signals and fault location according to any one of claims 1-3, characterized in that, In the electromagnetic transient simulation circuit model, a sinusoidal signal source is connected to one side of the line, and a voltage or current signal is output from the other side. The boundary resistance of the line segment is set as the characteristic impedance of the transmission lines on both sides, and the length of the line segments on both sides is greater than or equal to 10 times the length of the target line segment in the middle. Frequency domain simulation is performed within a finite frequency range to obtain the resonant spectrum of a single mode under non-fault conditions. The impulse response transfer function of different line segments i is obtained. When there are N line segments, construct a multimode resonance spectrum database under non-fault conditions. Where i is the line segment number; Based on the identified faulty line segment and preliminary location, a short-circuit fault is set up to simulate a low-resistance short-circuit fault at the preliminary location of the fault. Nearby detailed mesh simulation of fault location In frequency domain simulation, the location of the fault is obtained. Transfer function to the first or last fault sensor Establish a resonant spectrum database for line segments. .

5. The method for decoupling and separating multimodal resonant signals and fault location according to claim 4, characterized in that, When a fault occurs, the traveling wave current signal collected by the fault sensor at the beginning or end of the line is selected; the traveling wave current signal is then converted to the frequency domain to obtain the corresponding measured spectrum. or ; The resonance spectrum database H under non-fault conditions r Resonance spectrum database H under fault conditions f The simulated transfer function matrix is ​​combined to establish a sparse representation model of the measured spectrum; using the orthogonal matching pursuit algorithm, the estimated value of the sparse coefficient vector is obtained through the iterative process of normalized correlation calculation, spectrum template selection, least squares estimation and residual update. Based on the dictionary entries corresponding to the non-zero elements in the sparse coefficient vector estimate, the measured spectrum is reconstructed and separated to obtain the resonant spectrum of the non-faulty line after spectrum separation. and the spectrum of the faulty line This completes spectral separation based on sparse decomposition.

6. The method for decoupling and separating multimodal resonant signals and fault location according to claim 5, characterized in that, Resonance spectrum database under non-fault conditions Resonance spectrum database under fault conditions Combined to form the simulation transfer function matrix: Each column of the simulation transfer function matrix H represents a spectrum template corresponding to a candidate line segment or candidate fault location. Based on the measured spectrum under mixed line fault conditions, which is formed by the superposition of resonant components from non-faulty and faulty line segments to create a multi-mode resonant spectrum, a sparse representation model is established: ;in, Let be the sparse coefficient vector to be determined, y represent the measured spectrum, and e be the error term between the measured spectrum and the simulated spectrum; The sparse coefficient vector is obtained by solving the sparse representation model using the orthogonal matching pursuit algorithm. Based on the sparse coefficient vector The index positions and amplitudes of the non-zero elements are used to reconstruct and separate the measured spectrum into the resonant spectra of each segment of the non-faulty line. and spectrum of faulty line segment .

7. The method for decoupling and separating multimodal resonant signals and fault location according to claim 6, characterized in that, The orthogonal matching pursuit algorithm is used to solve the sparse representation model to obtain the sparse coefficient vector. The method is as follows: Initialize the initial residual vector as follows: In the k-th iteration, calculate the current residual. With each spectrum template in the simulation transfer function matrix H Normalized correlation between them: Select normalized correlation The largest spectral template is added to the current spectral template matching index set, and least squares estimation is performed on the simulation transfer function matrix corresponding to the current spectral template matching index set to obtain the estimated value of the current sparse coefficient vector: ;in, Match the index set to the updated spectrum template. Match the simulation transfer function matrix corresponding to the index set for the updated spectral template; based on the estimated values ​​of the sparse coefficient vector... Update the residual vector for the (k+1)th iteration: Repeated normalized correlation calculation—spectral template selection—least square estimation—residual vector update, until the updated residual vector is less than a preset threshold or reaches a preset maximum number of iterations, the obtained estimate is a sparse coefficient vector. .

8. The method for decoupling and separating multimodal resonant signals and for fault location according to claim 6 or 7, characterized in that, Calculate the spectrum of the isolated faulty line Resonance spectrum database under fault conditions The correlation coefficient Cor(i) is: ,in, This represents the spectrum of the faulty line based on the measured data. With resonance spectrum database The simulated spectrum corresponding to the i-th candidate position The dot product of the vectors between them Indicates the spectrum of the faulty line The energy norm, Represents the simulated spectrum The 2-norm, Let be the weight of the i-th line; The location coordinates corresponding to the maximum value of the search correlation coefficient Cor(i) are taken as the fault location.

9. The method for decoupling and separating multimodal resonant signals and for fault location according to claim 8, characterized in that, The weight of the i-th line: ;in, It is the width factor; To simulate frequency difference, This represents the measured frequency difference.

10. The method for decoupling and separating multimodal resonant signals and fault location according to claim 9, characterized in that, The topology of the hybrid line includes: branch routing, line length, and line type topology information; transmission line parameters include overhead line tower structure, cable type, cable cross-sectional structure, and cable medium; the electromagnetic transient simulation circuit model includes various types of transmission lines and loads of the line to be observed. Extracting the main resonant frequency peak from the spectrum of the faulty line of the measured signal. The measured frequency difference is obtained by calculating the interval between the peak points of the resonant frequency. ; For the resonance spectrum database under fault conditions Each transfer function in The simulated frequency difference is obtained by calculating the interval between the peak points of the resonant frequency: ,in, , These represent the frequencies corresponding to the resonant peak values ​​of the i-th and (i-1)-th lines, respectively. Width coefficient ,parameter .

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