Medium voltage cable earth fault location method based on anti-resonance frequency

Abstract

This application discloses a method for locating grounding faults in medium-voltage cables based on anti-resonance frequency, comprising: acquiring the instantaneous three-phase voltage at the cable's head end, obtaining the zero-mode voltage transient component through phase-mode transformation, acquiring the amplitude spectrum and constructing the reciprocal spectrum through Fourier transform, converting the anti-resonance depression in the original spectrum into detectable peak values, and extracting the observed anti-resonance peak frequency sequence. The boundary of the frequency domain transfer function at the head end of the modal domain is decoupled, eliminating interference from fault resistance and modal coupling, constructing a zero-mode frequency domain response model, and calculating the theoretical anti-resonance peak frequency sequence. Candidate fault locations are screened using a preset tolerance, and dynamic programming is used to complete the ordered matching of peak sequences and calculate scores. The location with the highest score is selected as the estimated fault distance. This invention does not require two-end communication and time-domain wavefront identification, exhibits strong robustness to high-resistance, complex boundary, arc, and various grounding faults, has high single-end online positioning accuracy, and is easy to deploy in engineering, effectively improving the efficiency and reliability of medium-voltage cable grounding fault location.

Description

Technical Field

[0001] This application relates to the field of power system fault detection, and more specifically, to a method for locating grounding faults in medium-voltage cables based on anti-resonance frequencies. Background Technology

[0002] After a grounding fault occurs in a medium-voltage distribution cable, quickly and accurately determining the fault location is a crucial technical step in shortening power outage time, reducing inspection workload, and supporting rapid restoration of the distribution network. Compared to offline detection methods, online location methods do not require line shutdown and are more suitable for actual distribution network operation scenarios.

[0003] Existing online cable fault location technologies mainly include traveling wave method, impedance method, and data-driven method. Among them, traveling wave method is widely studied due to its high location accuracy and low dependence on the power frequency operating state of the line. The double-ended traveling wave method usually uses the time difference of the fault traveling wave arriving at the two ends of the line for distance measurement, but it requires two-end communication, precise clock synchronization, and high system configuration; the single-ended traveling wave method is relatively simple to implement in engineering, but it depends on the accurate identification of the arrival time of the reflected wavefront at the fault point.

[0004] In actual fault scenarios of medium-voltage distribution cables, factors such as fault resistance, grounding method, branch structure, and line length can significantly alter transient waveforms. When the fault resistance is high or the fault boundary is complex, the amplitude of the reflected wavefront weakens and its shape is distorted, making wavefront identification difficult. When the line is short, the initial wave and the reflected wave are prone to overlap in the time domain, further reducing the reliability of ranging based on the arrival time.

[0005] To reduce reliance on time-domain wavefront identification, existing technologies utilize the inherent frequencies in transient fault signals for location. These methods extract the inherent frequencies from the modal voltage or current spectrum measured at one end and calculate the fault distance by combining wave velocity and boundary reflection coefficient. Swift first established the relationship between fault distance and inherent frequency in 1979, and since then, methods based on inherent frequency have been applied in HVDC systems. However, in high-voltage transmission lines, the fault resistance is usually much smaller than the wave impedance, and can be approximated as a low-resistance fault; therefore, the inherent frequency is relatively less affected by changes in fault resistance. In distribution cable lines, fault resistance cannot be ignored, especially under high-resistance fault conditions, where the reflection coefficient at the fault point changes with the fault resistance, causing the inherent frequency to no longer be determined solely by the fault distance, leading to decreased location accuracy or even failure. On the other hand, in grounding faults of three-phase AC cables, unbalanced fault boundaries can cause recoupling between modes, resulting in the spectrum of one observed mode simultaneously containing frequency components of other modes, forming mode aliasing and affecting the location results. Therefore, existing technologies still lack a frequency domain feature extraction and localization method that does not rely on accurate identification of time-domain wavefronts, is insensitive to changes in fault resistance and grounding fault type, and can achieve online localization of medium-voltage cable grounding faults using single-end measurements.

[0006] To overcome the above problems, this invention provides a single-end online location method for medium-voltage cable grounding faults based on anti-resonance frequency. By measuring the three-phase instantaneous voltage at the beginning of the line, the zero-mode transient voltage is extracted and a voltage spectrum reciprocal spectrum is constructed. The local dips of the anti-resonance frequency in the original spectrum are converted into detectable peaks. Then, combined with the theoretical anti-resonance peak frequency sequence corresponding to the candidate fault location, the fault distance is determined by an ordered peak sequence matching method, thereby realizing online location of medium-voltage cable grounding faults that relies solely on measurements at the beginning of the line. Summary of the Invention

[0007] To address the aforementioned issues, this application provides a medium-voltage cable grounding fault location method based on anti-resonance frequency. This method aims to solve problems such as the reliance of existing single-ended traveling wave location methods on time-domain wavefront identification and the instability of location results caused by the susceptibility of natural frequency location methods to fault resistance and mode aliasing.

[0008] This invention provides a method for locating grounding faults in medium-voltage cables based on anti-resonance frequency, comprising: The three-phase instantaneous voltage signals at the beginning of the medium-voltage cable line under test are collected, and the three-phase instantaneous voltage signals are subjected to phase mode transformation to obtain the zero-mode voltage transient component. A Fourier transform is performed on the transient component of the zero-mode voltage to obtain the zero-mode voltage amplitude spectrum, and a reciprocal spectrum is constructed on the amplitude spectrum to convert the anti-resonance depression in the amplitude spectrum into the peak value in the reciprocal spectrum. Peak detection is performed in the reciprocal spectrum to obtain the observed anti-resonance peak frequency sequence; boundary decoupling is performed on the frequency domain transfer function of the cable head in the modal domain to eliminate fault resistance and modal coupling interference, and a zero-mode frequency domain response model is obtained; the theoretical anti-resonance peak frequency sequence is calculated based on the zero-mode frequency domain response model. If the frequency difference between the theoretical anti-resonance peak frequency sequence and the observed anti-resonance peak frequency sequence corresponding to the candidate fault location is less than the preset tolerance, then ordered matching is performed and the matching score is calculated. The candidate fault location with the highest matching score is selected as the fault distance estimate to achieve fault localization.

[0009] In one alternative implementation, the expression for the reciprocal spectrum is:

[0010] In the formula, For the reciprocal spectrum, The amplitude spectrum of the zero-mode voltage signal. A tiny positive number introduced to prevent the denominator from being zero.

[0011] In one optional implementation, peak detection is performed on the reciprocal spectrum to obtain an observed anti-resonance peak frequency sequence, specifically including: Under the constraints of peak height threshold, minimum peak spacing and frequency band range, the observed peak sequence is extracted from the reciprocal spectrum through local peak search.

[0012] In one optional implementation, the modal domain transfer function at the cable head end considers the multipath propagation of the fault transient traveling wave in the cable, and its expression is:

[0013] in,

[0014] In the formula, For the first-end frequency domain transfer function, This is the transmission coefficient matrix. Here is the reflection coefficient matrix. , and These are the propagation factors for the section from the beginning to the fault point, the section from the fault point to the end, and the entire line for one round trip, respectively. It is a natural constant. Let be the cable propagation constant. This indicates the relative location of the fault.

[0015] In one optional implementation, the frequency domain transfer function at the cable head end in the modal domain is decoupled at the boundary to eliminate fault resistance and modal coupling interference, thereby obtaining a zero-mode frequency domain response model, specifically including: By introducing a fault resistance matrix to characterize the fault boundary, it is derived that the reflection coefficient matrix and transmission matrix at the fault point satisfy a matrix relationship in the modal domain:

[0016] In the formula, This is the transmission coefficient matrix. Here is the reflection coefficient matrix. It is the identity matrix; Based on this matrix relationship, the frequency domain transfer function at the cable head end is simplified, and the fault resistance and modal coupling terms are eliminated, yielding the zero-mode anti-resonance condition:

[0017] In the formula, The cable propagation constant in the zero-mode condition. and These represent the total length of the cable line and the relative location of the fault, respectively. Based on the zero-mode anti-resonance condition and combined with the phase expression of the cable propagation constant under high-frequency conditions, the zero-mode frequency domain response model is obtained, and the expression is:

[0018] In the formula, The candidate fault location is At that time, the theoretical frequency domain response of the cable head end in zero mode, Angular frequency, The imaginary unit, The phase propagation constant of the cable in zero mode is given. This refers to the total length of the cable line.

[0019] In one optional implementation, both the observed anti-resonance peak frequency sequence and the theoretical anti-resonance peak frequency sequence are ordered sequences, and the candidate fault location is determined by traversing the entire length of the cable with a preset search step size.

[0020] In one optional implementation, after determining that the frequency difference between the theoretical anti-resonance peak frequency sequence and the observed anti-resonance peak frequency sequence corresponding to the candidate fault location meets the preset tolerance condition, a dynamic programming algorithm is used to perform ordered matching of the observed anti-resonance peak frequency sequence and the theoretical anti-resonance peak frequency sequence of the candidate fault location to achieve global optimal alignment.

[0021] In one alternative implementation, the ordered matching must satisfy frequency order constraints and allow for limited peak offsets and peak omissions.

[0022] In one alternative implementation, the expression for the matching score is:

[0023] In the formula, Let be the objective function. Candidate positions Next, the The theoretical anti-resonance peak frequency and the first The observed anti-resonance peak frequencies form a set of matched peaks. Candidate fault location Next, the The theoretical anti-resonance peak frequency and the first The degree of matching between the observed anti-resonance peak frequencies and These are the penalty coefficients for the unmatched theoretical peak and the unmatched observed peak, respectively. and These represent the number of unmatched theoretical peaks and the number of unmatched observed peaks, respectively.

[0024] This application has at least the following advantages or beneficial effects: (1) This application uses the anti-resonance frequency as the fault location feature. By extracting the transient signal of the zero-mode voltage at the first end and constructing the reciprocal spectrum to highlight the anti-resonance peak, it does not need to rely on the time-domain traveling wave front identification. It effectively solves the problem of difficult wave front identification and unreliable location under high-resistance faults, short lines, and complex boundary conditions. At the same time, it is compatible with various fault forms such as single-phase grounding, two-phase grounding, three-phase asymmetrical grounding, and arc grounding, and has a wider range of applications.

[0025] (2) This application constructs a theoretical anti-resonance peak frequency sequence based on the first-end frequency domain transfer function and uses ordered peak sequence matching to realize the fault distance calculation, so that the anti-resonance frequency is determined only by the fault location and propagation constant, which significantly reduces the influence of fault resistance, fault type and mode mixing on the location result, and still has strong robustness under complex fault boundaries.

[0026] (3) This application only uses single-end voltage measurement and zero-mode signal processing, without the need for double-end communication and clock synchronization, and is not affected by branch load. The engineering deployment is simpler and online fault location can be realized. At the same time, the positioning accuracy is higher through precise peak frequency matching and global optimal alignment. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A flowchart of the medium-voltage cable grounding fault location method based on anti-resonance frequency provided by the present invention; Figure 2 This is a schematic diagram illustrating the multipath propagation of the fault transient traveling wave in the cable according to the present invention; Figure 3 This is a waveform diagram of the voltage signal of the first-terminal fault phase in Embodiment 1 of the present invention; Figure 4 This is a waveform diagram of the zero-mode voltage signal in Embodiment 1 of the present invention; Figure 5 This is the reciprocal spectrum of the zero-mode voltage in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the matching score results in Embodiment 1 of the present invention; Figure 7 The diagram shows the zero-mode voltage reciprocal spectrum and matching score results for the fault location result at 900 meters in Embodiment 2 of the present invention. Figure 8This is a schematic diagram of the zero-mode voltage reciprocal spectrum and matching score results for the fault location result of 2700 meters in Embodiment 2 of the present invention. Figure 9 The diagram shows the zero-mode voltage reciprocal spectrum and matching score results for the fault location result at 4500 meters in Embodiment 2 of the present invention. Figure 10 This is a schematic diagram of the zero-mode voltage reciprocal spectrum and matching score results for the fault location result of 6300 meters in Embodiment 2 of the present invention. Figure 11 The diagram shows the zero-mode voltage reciprocal spectrum and matching score results for the fault location result of 8100 meters in Embodiment 2 of the present invention. Figure 12 This is the reciprocal spectrum of the zero-mode voltage in Embodiment 3 of the present invention; Figure 13 This is a schematic diagram of the location results at a distance of 7km under different fault resistances in Embodiment 3 of the present invention; Figure 14 This is a diagram showing the relationship between the actual fault location and the estimated fault location in Embodiment 3 of the present invention; Figure 15 This is a relative error distribution diagram of different grounding fault types and fault resistances in Embodiment 3 of the present invention; Figure 16 This is a waveform diagram of the voltage signal of the first-terminal fault phase in Embodiment 4 of the present invention; Figure 17 This is a waveform diagram of the zero-mode voltage signal in Embodiment 4 of the present invention; Figure 18 This is the reciprocal spectrum of the zero-mode voltage of the arc fault at 6km in Embodiment 4 of the present invention; Figure 19 This is a schematic diagram of the arc fault location result at 6km in Embodiment 4 of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] Please refer to Figure 1 This invention provides a method for locating grounding faults in medium-voltage cables based on anti-resonance frequency, comprising the following steps: S1. Collect the three-phase instantaneous voltage signal at the beginning of the medium-voltage cable line to be tested, and perform phase-mode transformation on the three-phase instantaneous voltage signal to obtain the zero-mode voltage transient component; Specifically, a voltage acquisition device is installed at the beginning of the medium-voltage cable line under test. The three-phase instantaneous voltage is acquired at a set sampling frequency and sampling window. The acquired three-phase voltage is then subjected to phase-mode transformation to obtain the zero-mode voltage. The phase domain voltage and current satisfy the following relationship with the mode domain voltage and current: (1) In the formula, and These are the phase domain voltage vector and the phase domain current vector, respectively. and These are the modal domain voltage vector and the modal domain current vector, respectively. The phase mode transformation matrix; The sampling frequency and sampling window are set according to the line length, transient frequency band and equipment capabilities.

[0031] S2. Perform a Fourier transform on the transient component of the zero-mode voltage to obtain the zero-mode voltage amplitude spectrum, and construct a reciprocal spectrum for the amplitude spectrum to convert the anti-resonance depression in the amplitude spectrum into the peak value in the reciprocal spectrum. Since the anti-resonance frequency usually appears as a local dip in the original amplitude spectrum, to enhance its detectability, the reciprocal of the amplitude spectrum is taken. The expression for the reciprocal spectrum is: (2) In the formula, For the reciprocal spectrum, The amplitude spectrum of the zero-mode voltage signal. A tiny positive number introduced to prevent the denominator from being zero.

[0032] S3. Peak detection is performed in the reciprocal spectrum to obtain the observed anti-resonance peak frequency sequence; boundary decoupling is performed on the frequency domain transfer function of the cable head in the modal domain to eliminate fault resistance and modal coupling interference, and a zero-mode frequency domain response model is obtained. The theoretical anti-resonance peak frequency sequence is calculated based on the zero-mode frequency domain response model. Among them, under the conditions of satisfying the peak height threshold, minimum peak spacing constraints and frequency band range constraints, the observed peak sequence is extracted from the reciprocal spectrum through local peak search; After a fault occurs, the high-frequency transient traveling wave excited at the fault point propagates, reflects, and transmits between the fault point, the beginning of the line, and the end of the line. The traveling wave components along different propagation paths superimpose at the measurement point at the beginning of the line. When components at certain frequencies cancel each other out, a local minimum appears in the amplitude-frequency response at the beginning of the line. The frequency corresponding to this local minimum is the anti-resonance frequency. Unlike the poles of the transfer function corresponding to the natural frequency, the anti-resonance frequency corresponds to the zeros of the transfer function.

[0033] The frequency domain transfer function of the cable head can be defined as follows: (3) In the formula, For the first-end transient response, The initial traveling wave generated on one side at the fault point.

[0034] The transient response at the beginning can be considered as the superposition of the components corresponding to a unit traveling wave along multiple propagation paths. For example... Figure 2 The diagram illustrates the multipath propagation of a fault transient traveling wave in a cable. For a positive unit initial traveling wave, the response at its starting end can be summarized into three basic components, denoted as follows: , and For a negative unit initial traveling wave, it first propagates between the fault point and the end point, and after multiple reflections, returns to the beginning point through the fault point. This initial propagation path is denoted as... Therefore, the subsequent response formed at the head end can be further expressed as: , and In summary, the transient response measured at the first end is... , , , , and It consists of six components.

[0035] in, The response component formed by the direct propagation of the positive unit initial traveling wave excited at the fault point to the head end; The response component is formed when the positive unit initial traveling wave arrives at the head end, undergoes multiple round-trip reflections between the head end and the fault point, and then arrives at the head end again. The response component formed by the positive unit initial traveling wave arriving at the beginning, undergoing multiple round-trip reflections between the beginning and the fault point, then passing through the fault point into the interval between the fault point and the end, and undergoing multiple round-trip reflections in this interval before returning to the beginning. The preceding path component, representing the initial negative unit traveling wave that undergoes multiple round-trip reflections between the fault point and the end point before passing through the fault point and continuing to propagate towards the beginning, can be further correlated with... , and Cascades to form complex propagation paths.

[0036] Furthermore, define the propagation factor: (4) In the formula, , and These are the propagation factors for the section from the beginning to the fault point, the section from the fault point to the end, and the entire line for one round trip, respectively. Let be the cable propagation constant. This indicates the relative location of the fault.

[0037] Since transformers exhibit high impedance under high-frequency conditions, the voltage reflection coefficient at both ends of the cable can be approximated as 1. Its value is determined by the cable's characteristic impedance and fault resistance. Therefore: (5) In the formula, The reflection coefficient at the fault location, and These are the cable characteristic impedance and fault resistance, respectively. The transmission coefficient at the fault point; The frequency domain transfer function at the cable head end can also be expressed as: (6) Furthermore, substituting the formulas for each response component, the frequency domain transfer function at the cable head end can be written in rational fractional form with respect to the propagation factor and the reflection and projection characteristics at the fault point: (7) Furthermore, the frequency domain transfer function at the cable head end in the modal domain is decoupled at the boundary to eliminate fault resistance and modal coupling interference, resulting in a zero-mode frequency domain response model, specifically including: By introducing a fault resistance matrix to characterize the fault boundary, and by deriving equation (5), the reflection coefficient matrix and transmission matrix at the fault point in the modal domain satisfy the following matrix relationship: (8) In the formula, This is the transmission coefficient matrix. Here is the reflection coefficient matrix. It is the identity matrix; Based on this matrix relationship, the frequency domain transfer function at the cable head end is simplified, and the fault resistance and modal coupling terms are eliminated, yielding the zero-mode anti-resonance condition: (9) In the formula, The cable propagation constant in the zero-mode condition. and These represent the total length of the cable line and the relative location of the fault, respectively. Based on the zero-mode anti-resonance condition and combined with the phase expression of the propagation constant under high-frequency conditions, the zero-mode frequency domain response model is obtained, and the expression is: (10) In the formula, The candidate fault location is At that time, the theoretical frequency domain response of the cable head end in zero mode, Angular frequency, The imaginary unit, The phase propagation constant of the cable in zero mode is given. This refers to the total length of the cable line.

[0038] It should be explained that existing location studies based on natural frequencies typically assume that the fault resistance is zero during a single-phase ground fault, meaning that the reflection coefficient at the fault point satisfies... However, in actual faults, the fault resistance is not necessarily zero, and the pole condition... , and Both may produce observable solutions, thus relating the natural frequency to the fault location. The correspondence between them is no longer unique. Therefore, when the ideal assumption that "the fault resistance is zero" does not hold, the accuracy of traditional location methods based on natural frequency will be significantly affected.

[0039] In addition to changes in fault resistance, the extraction of natural frequencies is also affected by mode aliasing. Actual three-phase cable lines are multi-conductor transmission lines, typically requiring phase-mode transformation to the modal domain for analysis. However, under unbalanced fault conditions, the boundary conditions at the fault point may still cause the reflection and transmission matrices to be off-diagonal, leading to mode re-coupling and making it difficult to extract natural frequencies stably.

[0040] If the fault is a balanced fault, both the reflection coefficient matrix and the transmission coefficient matrix are diagonal matrices. In this case, the modes are decoupled from each other. Under the condition that the fault resistance is small and the modes can be clearly identified, the fault location can be estimated using the natural frequency of the corresponding mode. However, when an unbalanced fault such as a single-phase ground fault occurs, the fault boundary will cause the modes to recouple, and the reflection coefficient matrix will no longer be a diagonal matrix, thus causing the voltage spectrum of a certain observed mode to contain the frequency components of multiple propagation modes simultaneously. But no matter how the fault type or fault resistance changes, the transmission coefficient matrix and the reflection coefficient matrix at the fault point always satisfy formula (8).

[0041] Therefore, for a single modal component, the anti-resonance condition still originates from the constraint that the numerator of the corresponding transfer function is zero. Thus, the anti-resonance condition for the zero mode can be written as: (11) The anti-resonance condition no longer explicitly includes the reflection coefficient matrix and transmission coefficient matrix at the fault point; their values ​​are mainly determined by the fault location. and zero-mode propagation constant The anti-resonance frequency is jointly determined by the fault resistance and is independent of changes in the fault resistance. On the other hand, since this condition does not explicitly depend on the mode coupling matrix, the anti-resonance frequency exhibits stronger robustness against mode aliasing compared to the natural frequency. Therefore, the anti-resonance frequency is more suitable as a stable location characterization quantity in fault location. Further combining this with the phase expression of the propagation constant under high-frequency conditions, the relationship between the anti-resonance frequency and the fault location can be obtained. The relationship between them is as follows: (12) In the formula, It is the anti-resonance frequency. For harmonic order, This refers to the propagation speed of the modal voltage traveling wave in the cable; It can be seen that a clear analytical mapping relationship can be established between the anti-resonance frequency and the fault location. Therefore, this invention uses the anti-resonance frequency as a characterization of the fault location.

[0042] S4. If the frequency difference between the theoretical anti-resonance peak frequency sequence and the observed anti-resonance peak frequency sequence corresponding to the candidate fault location is less than the preset tolerance, then perform ordered matching and calculate the matching score. The observed anti-resonance peak frequency sequence and the theoretical anti-resonance peak frequency sequence are both ordered sequences. The candidate fault location is determined by traversing the entire length of the cable according to a preset search step size. The ordered matching must meet the frequency order constraint and allow limited peak position shift and peak leakage.

[0043] Furthermore, in some embodiments, different methods can be used to traverse and search to determine candidate fault locations; For example, in some embodiments, when the target positioning accuracy is at the meter level, a coarse search can be performed first, followed by a fine search near the peak of the matching score, in order to reduce the amount of computation.

[0044] For each candidate fault location, the observed peak frequency sequence is compared with the theoretical peak frequency sequence. If the frequency difference between a theoretical peak frequency and an observed peak frequency is less than a preset tolerance... At that time, it is assumed that a matching relationship can be established between the two. To avoid cross-pairing, missed peaks, or suboptimal results caused by simple greedy matching, this invention uses an ordered sequence matching method to calculate the matching score: (13) In the formula, Let be the objective function. Candidate positions Next, the The theoretical anti-resonance peak frequency and the first The observed anti-resonance peak frequencies form a set of matched peaks. Candidate fault location Next, the The theoretical anti-resonance peak frequency and the first The degree of matching between the observed anti-resonance peak frequencies and These are the penalty coefficients for the unmatched theoretical peak and the unmatched observed peak, respectively. and These represent the number of unmatched theoretical peaks and the number of unmatched observed peaks, respectively.

[0045] Since both the observed and theoretical peak frequency sequences are ordered sequences, sequence matching not only needs to satisfy frequency order constraints but also needs to achieve globally optimal alignment while allowing for finite peak position shifts and missing peaks. Therefore, this paper employs a dynamic programming algorithm to solve for the optimal peak matching result at each candidate position, avoiding cross-pairing and suboptimal global alignment that may result from local greedy matching.

[0046] S5. Select the candidate fault location with the highest matching score as the fault distance estimate to achieve fault location.

[0047] Among them, the fault distance estimate : (14) To systematically evaluate the fault location performance of this invention, a distribution network model was established in PSCAD / EMTDC. The system neutral point was grounded via a small resistor, and both ends of the line were connected via transformers. The total cable length was 9 km, and the branch loads were connected to feeder F4 at points 2 km and 6 km from the beginning of the line, respectively. Transient three-phase voltage signals of the fault were collected at the beginning of the line, and the simulation output data was imported into MATLAB for subsequent frequency domain analysis and fault location calculation. The sampling rate was 10 MHz, and the time window was 4 ms.

[0048] The following simulation cases are implemented: Example 1: Typical single-phase grounding fault case; Example 2: Cases with different fault locations; Example 3: Cases with different fault boundaries; Example 4: Arc grounding fault case.

[0049] Example 1: To verify the positioning principle and explain the positioning process of this invention, the relative location of the fault was selected. Fault resistor A typical single-phase grounding fault condition is analyzed.

[0050] like Figure 3 , Figure 4 The diagram shows the waveforms of the faulty phase and the zero-mode voltage signal at the cable's head end. Figure 5 , Figure 6The figure shows the reciprocal spectrum and matching score function of the zero-mode voltage signal under this typical operating condition. It can be seen that the reciprocal spectrum contains significant peaks with equal spacing, corresponding to the anti-resonance frequency, indicating that the fault is located at a relatively fixed position. Fault resistor Under typical single-phase ground fault conditions, the spectrum can form a clear and identifiable anti-resonance characteristic.

[0051] Among them, with Figure 5 Taking the spacing between a group of adjacent peaks as an example, the combined wave velocity is approximately Based on the analytical relationships, the fault location was calculated as follows:

[0052] This result is consistent with the analytical relationship described above, indicating that the anti-resonance frequency can serve as an effective frequency domain feature characterizing the fault location. Based on this, and combining local normalization and minimum peak spacing constraints, the observed peak frequency sequence is extracted from the reciprocal spectrum and matched. Figure 6 As can be seen, the matching score function achieves a significant maximum value near the actual fault location, indicating that the matching method based on the observed peak frequency sequence and the theoretical peak frequency sequence can effectively distinguish the fault location, thereby achieving accurate location.

[0053] Example 2: To analyze the positioning accuracy across the entire line and examine the applicability of this invention to short and medium-length lines, single-phase grounding faults were set at 900m, 2700m, 4500m, 6300m, and 8100m, and the fault resistance was uniformly measured. The inverse spectrum and matching score results corresponding to the fault location are shown in the following diagrams: Figure 7 , 8 As shown in 9, 10, and 11.

[0054] Simulation results show that the present invention maintains high positioning accuracy at all test locations. When the fault point is close to the beginning of the line, although some background noise appears in the reciprocal spectrum, S(x) still forms a significant peak near the actual fault location, indicating that the positioning method based on anti-resonance peak sequence matching has good positioning capability across the entire length of the long cable.

[0055] To further verify the applicability of the proposed method in short-to-medium length line scenarios, this paper conducts supplementary verification on feeder lines F1, F2, and F3 with lengths of 1 km, 2 km, and 4 km, respectively, under the same fault parameter settings. The specific results are shown in Table 1. Table 1 shows the positioning results in the short-line scenario.

[0056] The results show that the proposed method can achieve accurate location across the entire length of medium- and short-length power lines and is applicable to fault scenarios at both the near and far ends of the cable. In summary, shortening the total line length does not disrupt the correspondence between anti-resonance characteristics and fault location. The location method based on anti-resonance peak sequence matching is applicable not only to conventional length distribution cables but also to fault location in medium- and short-length power lines.

[0057] Example 3: To verify the robustness of this invention to fault boundaries, a single-phase ground fault was set 7km from the cable's starting point, with the fault resistance... Set to respectively The analysis is conducted from two aspects: fault resistance and fault type.

[0058] Depend on Figure 12 It is evident that as the fault resistance changes, the spectral amplitude and peak intensity change to some extent, but the position of the anti-resonance peak remains basically stable. This indicates that changes in fault resistance primarily affect the energy distribution of the transient signal, while having a relatively small impact on the frequency position corresponding to the anti-resonance peak sequence. Figure 13 Furthermore, it can be seen that the matching score curves under different fault resistances all reach their maximum values ​​near the actual fault location, indicating that the change in fault resistance has little impact on the final location result.

[0059] Figure 14 The correspondence between the actual and estimated fault locations of feeder F4 under different fault locations and fault resistance conditions is presented. It can be seen that the location results under each operating condition are distributed across... The proximity further demonstrates that the proposed method has strong robustness to changes in fault resistance.

[0060] Furthermore, to further verify the applicability of the established anti-resonance location relationship under different grounding fault types, such as... Figure 15 Simulation analyses were performed on single-phase ground faults (AG), two-phase ground faults (BC-G), and three-phase asymmetrical ground faults (ABC-G), respectively. Simulation results show that the relative error is controlled within 0.4% under all operating conditions, and the location results are concentrated near the actual fault location, indicating that the proposed method has strong robustness to changes in ground fault type.

[0061] Example 4: To verify the applicability of this invention under nonlinear, time-varying fault boundary conditions, a single-phase grounding arc fault was set up 6.0 km from the starting point. The traveling waves of the fault phase voltage and zero-mode voltage at the measuring point at the starting point are as follows: Figure 16 and 17 As shown.

[0062] Simulation results are as follows Figure 18 , 19As shown, it can be seen that although arc faults introduce more complex spectral disturbances, the present invention can still form obvious peaks at the actual fault location, indicating that the present invention also has good localization capability for arc grounding faults.

[0063] Overall, in the above implementation cases, when a branch-type power distribution cable model is established in PSCAD / EMTDC with a sampling rate of 10MHz and a time window of 4ms, the positioning error can be controlled within 5m under different fault locations, short lines, different fault resistances, different grounding forms, and arc grounding conditions.

[0064] The above provides a detailed description of the medium-voltage cable grounding fault location method based on anti-resonance frequency provided in this application. Specific examples have been used to illustrate the principle and implementation of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this application. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for locating grounding faults in medium-voltage cables based on anti-resonance frequency, characterized in that, include: The three-phase instantaneous voltage signals at the beginning of the medium-voltage cable line under test are collected, and the three-phase instantaneous voltage signals are subjected to phase mode transformation to obtain the zero-mode voltage transient component. A Fourier transform is performed on the transient component of the zero-mode voltage to obtain the zero-mode voltage amplitude spectrum, and a reciprocal spectrum is constructed on the amplitude spectrum to convert the anti-resonance depression in the amplitude spectrum into the peak value in the reciprocal spectrum. Peak detection is performed in the reciprocal spectrum to obtain the observed anti-resonance peak frequency sequence; boundary decoupling is performed on the frequency domain transfer function of the cable head in the modal domain to eliminate fault resistance and modal coupling interference, and a zero-mode frequency domain response model is obtained; the theoretical anti-resonance peak frequency sequence is calculated based on the zero-mode frequency domain response model. If the frequency difference between the theoretical anti-resonance peak frequency sequence and the observed anti-resonance peak frequency sequence corresponding to the candidate fault location is less than the preset tolerance, then ordered matching is performed and the matching score is calculated. The candidate fault location with the highest matching score is selected as the fault distance estimate to achieve fault localization.

2. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, The expression for the reciprocal spectrum is: In the formula, For the reciprocal spectrum, The zero-mode voltage amplitude spectrum, A tiny positive number introduced to prevent the denominator from being zero.

3. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, Peak detection is performed on the reciprocal spectrum to obtain the observed anti-resonance peak frequency sequence, specifically including: Under the constraints of peak height threshold, minimum peak spacing and frequency band range, the observed peak sequence is extracted from the reciprocal spectrum through local peak search.

4. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, The frequency domain transfer function at the cable head end in the modal domain, considering the multipath propagation of the fault transient traveling wave in the cable, is expressed as follows: in, In the formula, For the first-end frequency domain transfer function, This is the transmission coefficient matrix. Here is the reflection coefficient matrix. , and These are the propagation factors for the section from the beginning to the fault point, the section from the fault point to the end, and the entire line for one round trip, respectively. It is a natural constant. Let be the cable propagation constant. This indicates the relative location of the fault.

5. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, By decoupling the frequency domain transfer function at the cable head end in the modal domain and eliminating fault resistance and modal coupling interference, a zero-mode frequency domain response model is obtained, which specifically includes: By introducing a fault resistance matrix to characterize the fault boundary, it is derived that the reflection coefficient matrix and transmission matrix at the fault point satisfy a matrix relationship in the modal domain: In the formula, This is the transmission coefficient matrix. Here is the reflection coefficient matrix. It is the identity matrix; Based on this matrix relationship, the frequency domain transfer function at the cable head end is simplified, and the fault resistance and modal coupling terms are eliminated, yielding the zero-mode anti-resonance condition: In the formula, The cable propagation constant in the zero-mode condition. and These represent the total length of the cable line and the relative location of the fault, respectively. Based on the zero-mode anti-resonance condition and combined with the phase expression of the cable propagation constant under high-frequency conditions, the zero-mode frequency domain response model is obtained, and the expression is: In the formula, The candidate fault location is At that time, the theoretical frequency domain response of the cable head end in zero mode, Angular frequency, The imaginary unit, The phase propagation constant of the cable in zero mode is given. This refers to the total length of the cable line.

6. The method for locating grounding faults in medium-voltage cables based on anti-resonance frequency according to claim 1, characterized in that, Both the observed anti-resonance peak frequency sequence and the theoretical anti-resonance peak frequency sequence are ordered sequences, and the candidate fault location is determined by traversing the entire length of the cable with a preset search step size.

7. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, After determining that the frequency difference between the theoretical anti-resonance peak frequency sequence and the observed anti-resonance peak frequency sequence corresponding to the candidate fault location meets the preset tolerance condition, a dynamic programming algorithm is used to perform ordered matching of the observed anti-resonance peak frequency sequence and the theoretical anti-resonance peak frequency sequence of the candidate fault location to achieve global optimal alignment.

8. The method for locating grounding faults in medium-voltage cables based on anti-resonance frequency according to claim 7, characterized in that, The ordered matching must satisfy frequency order constraints and allow for limited peak position shifts and peak omissions.

9. The method for locating medium-voltage cable grounding faults based on anti-resonance frequency according to claim 1, characterized in that, The expression for the matching score is: In the formula, Let be the objective function. Candidate positions Next, the The theoretical anti-resonance peak frequency and the first The observed anti-resonance peak frequencies form a set of matched peaks. Candidate fault location Next, the The theoretical anti-resonance peak frequency and the first The degree of matching between the observed anti-resonance peak frequencies and These are the penalty coefficients for the unmatched theoretical peak and the unmatched observed peak, respectively. and These represent the number of unmatched theoretical peaks and the number of unmatched observed peaks, respectively.

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