Power distribution network fault identification method based on CEEMDAN-SSA

Abstract

The invention provides a CEEMDAN-SSA-based power distribution network fault identification method, and the method comprises the steps: receiving a traveling wave signal of a power distribution network, and carrying out the preprocessing of the traveling wave signal; decomposing the preprocessed traveling wave signal by adopting CEEMDAN to obtain an intrinsic mode function component set, and selecting a high-frequency intrinsic mode function component from the intrinsic mode function component set; performing noise reduction on the high-frequency intrinsic mode function component by using singular spectrum analysis to obtain a pure fault feature signal; analyzing and reconstructing the frequency spectrum characteristics of the pure fault characteristic signal by using fast Fourier transform, and calculating the average frequency spectrum content of the low-frequency-band signal and the amplitude ratio of the high-frequency-band signal according to the frequency spectrum characteristics; and generating a fault identification result of the power distribution network by taking the average frequency spectrum content of the low-frequency-band signal as a main criterion and taking the amplitude proportion of the high-frequency-band signal as an auxiliary criterion according to the fault traveling wave transmission characteristics. Therefore, high-precision power distribution network fault identification can be realized in a complex working condition and a high-noise environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power distribution network fault identification, and particularly relates to a power distribution network fault identification method based on CEEMDAN-SSA. BACKGROUND

[0002] With the increasing penetration of distributed power sources in power distribution networks, the system operating environment is becoming increasingly complex, and the requirements for power supply reliability and stability are significantly increasing. Realizing rapid and accurate identification of faults is a key link to ensure the safe operation of power grids. If the fault state cannot be identified in time, it may lead to misoperation or refusal of protection devices, causing serious economic losses and social impact.

[0003] At present, the commonly used fault identification methods for power distribution networks include transient characteristic analysis method, signal injection method, impedance analysis method, and identification method based on traveling wave characteristics. Among them, the traveling wave characteristic method analyzes the voltage or current traveling wave signals caused by faults to extract transient characteristic quantities to realize fault positioning. However, with the multi-power and complex fault mode of power distribution networks, the characteristics of traveling wave signals are non-stationary and high-noise, and traditional signal analysis methods have limitations in feature extraction. Although methods such as wavelet transform have time-frequency localization advantages, their analysis performance depends on the prior selection of basis functions and decomposition scales, and they lack adaptive ability, making it difficult to accurately capture the key features of complex transient signals.

[0004] Therefore, the existing methods are difficult to achieve high-precision identification of power distribution network faults under complex conditions and strong noise environment, and there is a problem of inaccurate fault identification. SUMMARY

[0005] The purpose of the present application is to at least solve one of the above technical defects, in particular, the technical defect that the existing method is difficult to achieve high-precision identification of power distribution network faults under complex conditions and strong noise environment.

[0006] In a first aspect, the present application provides a power distribution network fault identification method based on CEEMDAN-SSA, the method comprising:

[0007] Receiving a traveling wave signal of a power distribution network and pre-processing the traveling wave signal;

[0008] Decomposing the pre-processed traveling wave signal using CEEMDAN to obtain a set of intrinsic mode function components, and selecting a high-frequency intrinsic mode function component from the set of intrinsic mode function components;

[0009] Using singular spectrum analysis to denoise the high-frequency intrinsic mode function component to obtain a pure fault characteristic signal;

[0010] The frequency spectrum characteristics of the pure fault characteristic signal are analyzed by using fast Fourier transform, and according to the frequency spectrum characteristics, the average frequency spectrum content of the low-frequency signal and the amplitude ratio of the high-frequency signal are calculated.

[0011] According to the fault traveling wave transmission characteristics, the average frequency spectrum content of the low-frequency signal is taken as the main criterion, and the amplitude ratio of the high-frequency signal is taken as the auxiliary criterion to generate the fault identification result of the distribution network.

[0012] In one embodiment, the step of decomposing the preprocessed traveling wave signal by CEEMDAN to obtain the intrinsic mode function component set comprises:

[0013] The original white noise is added to the preprocessed traveling wave signal to obtain the disturbance signal of the first stage, and the intrinsic mode function component of the traveling wave signal of the first stage and the residual of the first stage are obtained by empirical mode decomposition according to the disturbance signal of the first stage.

[0014] In each stage starting from the second stage, the disturbance signal of the current stage is constructed according to the residual of the previous stage and the noise intrinsic mode function component obtained by empirical mode decomposition of the original white noise of the previous stage, and the traveling wave signal intrinsic mode function component of the current stage is obtained according to the disturbance signal of the current stage, until the residual of the current stage meets the preset iteration termination condition, and the traveling wave signal intrinsic mode function component of each stage is taken as the intrinsic mode function component set.

[0015] In one embodiment, the disturbance signal formula in each stage starting from the second stage is:

[0016]

[0017] Wherein, represents the value of the first disturbance signal at time t in the first stage, represents the value of the residual at time t in the first stage, represents the noise intensity coefficient of the first stage, represents the value of the noise intrinsic mode function component at time t of the first stage obtained by empirical mode decomposition on the original white noise sequence, represents the total number of disturbance signals.

[0018] In one embodiment, the step of denoising the high-frequency intrinsic mode function component by singular spectrum analysis to obtain the pure fault characteristic signal comprises:​​​​​​​​​

[0019] The trajectory matrix of the high-frequency intrinsic mode function components is constructed, and multiple singular values ​​of the trajectory matrix are obtained through singular spectrum analysis;

[0020] The joint index function is determined. The joint index function is composed of the weighted difference spectrum and the modified cumulative energy ratio. The weighted difference spectrum is used to reflect the local jumps of the singular value sequence, the modified cumulative energy ratio is used to measure the overall energy contribution of the signal, and the joint index function is used to integrate the local jump and the overall energy information.

[0021] Based on each singular value, the optimal reconstruction order is determined by finding the maximum point of the joint index function;

[0022] Based on the optimal reconstruction order, the reconstruction matrix of the traveling wave signal is constructed to obtain the pure fault characteristic signal.

[0023] In one embodiment, the formula for the joint index function is:

[0024]

[0025]

[0026]

[0027] in, This represents the value of the joint index function. Indicates the first Weighted difference spectrum of singular values Indicates the preceding The corrected cumulative energy ratio of each singular value Indicates the order of candidate reconstruction. Indicates the first Weighted difference spectrum of singular values Indicates the first A singular value, Indicates the ( ) singular values, The index representing the singular value. Indicates all The maximum value, This represents the total number of singular values.

[0028] In one embodiment, the step of calculating the average spectral content of the low-frequency band signal and the amplitude ratio of the high-frequency band signal based on spectral characteristics includes:

[0029] Based on the spectral characteristics, the amplitude points in the low-frequency band are determined, and the average amplitude points in the low-frequency band are amplified to obtain the average spectral content of the low-frequency band signal.

[0030] According to the spectral feature, the high-frequency band amplitude point and the maximum amplitude are determined, the high-frequency band amplitude points are averaged and amplified to obtain a high-frequency band signal average spectral content, and a ratio of the high-frequency band signal average spectral content to the maximum amplitude is taken as a high-frequency band signal amplitude proportion.

[0031] In one embodiment, according to the fault traveling wave transmission feature, the step of generating the fault identification result of the power distribution network includes taking the low-frequency band signal average spectral content as a main criterion and taking the high-frequency band signal amplitude proportion as an auxiliary criterion.

[0032] According to the fault traveling wave transmission feature, after the low-frequency band signal average spectral content is greater than or equal to a first preset threshold value, it is preliminarily determined that the power distribution network has a fault, and if the high-frequency band signal amplitude proportion is less than or equal to a second preset threshold value, noise interference is excluded, and the fault identification result of the power distribution network is finally determined.

[0033] In a second aspect, the present application provides a CEEMDAN-SSA-based power distribution network fault identification device, which comprises:

[0034] A traveling wave signal receiving module is configured to receive a traveling wave signal of a power distribution network and pre-process the traveling wave signal.

[0035] A high-frequency intrinsic mode function component selecting module is configured to decompose the pre-processed traveling wave signal by using CEEMDAN to obtain an intrinsic mode function component set and select a high-frequency intrinsic mode function component from the intrinsic mode function component set.

[0036] A pure fault feature signal determining module is configured to denoise the high-frequency intrinsic mode function component by using singular spectrum analysis to obtain a pure fault feature signal.

[0037] A spectral feature reconstructing module is configured to analyze and reconstruct the spectral feature of the pure fault feature signal by using fast Fourier transform, and calculate a low-frequency band signal average spectral content and a high-frequency band signal amplitude proportion according to the spectral feature.

[0038] A fault identification result generating module is configured to generate a fault identification result of the power distribution network according to the fault traveling wave transmission feature, taking the low-frequency band signal average spectral content as a main criterion and taking the high-frequency band signal amplitude proportion as an auxiliary criterion.

[0039] In a third aspect, the present application provides a storage medium, which stores computer readable instructions. When the computer readable instructions are executed by one or more processors, the one or more processors perform the steps of the CEEMDAN-SSA-based power distribution network fault identification method in any of the above embodiments.

[0040] In a fourth aspect, the present application provides a computer device, which comprises one or more processors and a memory.

[0041] The computer readable instructions are stored in the memory and are executed by one or more processors to perform the steps of the power distribution network fault identification method based on CEEMDAN-SSA as described in any of the above embodiments.

[0042] From the above technical solutions, the embodiments of the present application have the following advantages:

[0043] The power distribution network fault identification method based on CEEMDAN-SSA provided by the present application first uses CEEMDAN to adaptively decompose the preprocessed traveling wave signal, which can decompose the non-stationary and complex spectrum traveling wave signal into multiple intrinsic mode function components, extract high-frequency components, effectively retain fault transient characteristics, and capture key fault information even in a complex power distribution network environment with multiple power sources and multiple branches. Then, the singular spectrum analysis is used to denoise the high-frequency modal components, which can significantly suppress system noise and interference, so as to obtain pure fault characteristic signals in a strong noise environment and improve the accuracy and robustness of feature extraction. Further, the frequency spectrum characteristics of the pure signals are analyzed by fast Fourier transform, and the criterion of average spectrum content in the low-frequency band and amplitude ratio in the high-frequency band is combined to realize accurate identification of fault type and location. The method retains key signal characteristics under complex conditions through adaptive decomposition, and overcomes strong noise interference through noise reduction and spectrum criterion combination, so as to realize high-precision and reliable power distribution network fault identification in complex conditions and high-noise environment, and significantly improve the safety and stability of system operation. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0045] Figure 1 The flowchart of the power distribution network fault identification method based on CEEMDAN-SSA provided by the embodiments of the present application is shown in the figure.

[0046] Figure 2 The example diagram of the line simulation model provided by the embodiments of the present application is shown in the figure.

[0047] Figure 3 The example diagram of the waveform after adding noise provided by the embodiments of the present application is shown in the figure.

[0048] Figure 4 The example diagram of the waveform after denoising provided by the embodiments of the present application is shown in the figure.

[0049] Figure 5 A structural schematic diagram of a power distribution network fault identification device based on CEEMDAN-SSA is provided for the embodiments of the present application.

[0050] Figure 6 An internal structural schematic diagram of a computer device is provided for the embodiments of the present application. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0052] The present application provides a power distribution network fault identification method based on CEEMDAN-SSA. The following embodiments take the application of the method in a computer device as an example for illustration. It can be understood that the computer device can be various devices with data processing functions, which can be but are not limited to a single server, a server cluster, a personal notebook computer, a desktop computer, etc. As shown in the figure, the method comprises: Figure 1

[0053] S101: receiving a traveling wave signal of a power distribution network and pre-processing the traveling wave signal.

[0054] The traveling wave signal of the power distribution network refers to a transient signal generated by current or voltage change and propagated along the line when a fault or disturbance occurs in the power distribution line. The signal contains rich transient information that can represent fault type, occurrence location and propagation characteristics. Pre-processing refers to operations such as data standardization, filtering, removing outliers and time synchronization on the received traveling wave signal to ensure that the signal characteristics can be accurately captured and utilized in subsequent analysis. The received traveling wave signal can include single-phase or multi-phase voltage and current signals, and the sampling frequency and time resolution should meet the accurate recording requirements of fault transient characteristics. Through the explicit description of the definition and preprocessing of the traveling wave signal, the usability and reliability of the signal in the complex power distribution network environment can be ensured.

[0055] ​In the implementation process, the received traveling wave signal can first be removed of high-frequency noise and power grid interference through a digital filtering method, ensuring that the fault characteristics in the signal are not covered by external interference. At the same time, the signal can be amplitude normalized and sample point corrected to eliminate the influence of measurement errors and sensor deviations on subsequent feature analysis. In addition, the multi-channel signal can be time-aligned to ensure that the traveling wave signals of each phase or each measuring point are analyzed under a unified time reference, thereby ensuring accurate extraction of fault propagation characteristics. Through the above processing, the quality of the signal is improved, and the fault information can be more reliably reflected under complex working conditions.

[0056] The preprocessed traveling wave signal can be further subjected to noise evaluation and abnormal data correction to exclude sudden abnormalities or missing data during transmission. A smoothing filter or adaptive threshold algorithm can be used to correct signal amplitude fluctuations, ensuring that subsequent feature decomposition and spectral analysis can be based on clean and continuous signals. This processing method ensures that the transient characteristics in the signal are clear and available, even in a multi-source, multi-branch, and high-noise environment, and the key fault information can be retained to provide a reliable basis for subsequent fault identification.

[0057] By preprocessing the received traveling wave signal, noise and interference in the signal can be effectively removed, and the influence of measurement errors and abnormal data on subsequent analysis can be eliminated, thereby ensuring the integrity and accuracy of the fault characteristics. Preprocessing can also achieve signal amplitude normalization, time alignment, and continuity correction, so that signals from different channels or measuring points can be analyzed under a unified time reference, ensuring that transient characteristics are clear and available under complex working conditions. Through the above processing, subsequent feature extraction and fault identification can be based on high-quality, clean signals, thereby improving the accuracy and robustness of power distribution network fault identification, especially in high-noise and complex network environments, and still reliably reflecting fault information to ensure the safety and stability of power grid operation.

[0058] S102: decompose the preprocessed traveling wave signal using CEEMDAN to obtain a set of intrinsic mode function components, and select a high-frequency intrinsic mode function component from the set of intrinsic mode function components.

[0059] CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) is an adaptive noise-assisted method for fully integrated empirical mode decomposition. It decomposes non-stationary signals with complex spectra into several intrinsic mode function (EMF) components. Each EMF component reflects the local oscillation characteristics of the signal within a specific frequency range. The EMF component set refers to the collection of EMFs obtained through CEEMDAN decomposition, which includes high-frequency, low-frequency, and mid-frequency components of the signal. High-frequency EMF components are those with higher frequencies that primarily reflect transient changes and fault characteristics of the signal.

[0060] In practical implementation, the preprocessed traveling wave signal can be adaptively decomposed using the fully integrated empirical mode decomposition method CEEMDAN. By introducing adaptive white noise of different amplitudes into the signal and iteratively decomposing it, the non-stationary, spectrally complex traveling wave signal can be decomposed into several intrinsic mode function components, each reflecting the local oscillation characteristics of the signal within a specific frequency range. This decomposition allows transient fault characteristics to be fully preserved in the high-frequency components, while separating low-frequency components from slowly changing trends, providing a structured signal basis for subsequent feature analysis.

[0061] During the decomposition process, mean processing and residual correction can be applied to each iteration result to ensure the stability of the intrinsic mode function (IMF) components in terms of frequency and amplitude. Subsequently, based on the frequency characteristics or spectral energy distribution of the components, high-frequency IMF components can be selected from the set of IMF components obtained from the decomposition as the main objects for subsequent fault characteristic analysis. High-frequency components typically contain abrupt information about the instantaneous change in fault occurrence and can reflect key characteristics of fault type and location, which is particularly important for distribution network environments with multiple power sources, multiple branches, and complex topologies.

[0062] By decomposing the preprocessed traveling wave signal using CEEMDAN, the non-stationary, spectrally complex signal can be broken down into multiple intrinsic mode function (EMF) components, thus distinguishing different frequency components within the structured signal. By selecting high-frequency EMF components from the component set, transient fault characteristics can be preserved, while low-frequency interference and redundant information are removed, ensuring that key signal features are clearly reflected even under complex operating conditions and high-noise environments. This processing method improves the accuracy and robustness of subsequent feature extraction and fault identification, ensuring that transient fault information is effectively captured, providing a reliable basis for accurately determining fault type and location, thereby enhancing the reliability and stability of distribution network fault identification.

[0063] S103: Use singular spectrum analysis to reduce noise in high-frequency intrinsic mode function components to obtain a clean fault characteristic signal.

[0064] Singular Spectrum Analysis (SSA) is a method that constructs the trajectory matrix of a signal and uses singular value decomposition to denoise the signal, distinguishing noise in the high-frequency intrinsic mode function components from the true signal features. A clean fault feature signal refers to a high-quality signal that, after singular spectral analysis denoising, retains the transient characteristics of the fault while removing noise interference, and is used for subsequent feature extraction and fault identification.

[0065] In practical implementation, the high-frequency intrinsic mode function components can first be constructed into a trajectory matrix with a certain time delay. This allows the temporal structure and local features of the signal to be fully unfolded in the matrix, with each row or column reflecting the local variation trend of the signal within a continuous time window. Subsequently, singular value decomposition (SVD) is performed on the trajectory matrix, decomposing it into several singular values ​​and their corresponding singular vectors. Each singular value reflects the energy level of that component in the signal. By analyzing the amplitude and energy proportion of the singular values, singular values ​​with higher energy that represent the main signal features and their corresponding vectors can be selected, while singular values ​​with lower energy that are mainly noise can be removed, thereby achieving preliminary noise reduction of the signal.

[0066] When reconstructing the selected singular vectors, the vectors can be merged according to the original matrix arrangement. Simultaneously, smoothing is applied to any amplitude anomalies or abrupt changes to maintain the continuity and integrity of the transient characteristics of the reconstructed signal. During reconstruction, amplitude normalization or standardization can be performed based on the actual sampling frequency and signal amplitude range to ensure that the reconstructed signal matches the original signal on the amplitude scale. The resulting pure fault characteristic signal retains the high-frequency transient characteristics of the traveling wave signal while effectively suppressing noise and interference. This allows the signal to clearly reflect fault information even in complex power distribution networks, multi-power sources, multi-branch environments, and high-noise environments, providing a high-quality and reliable analytical foundation for subsequent fault type identification and location.

[0067] By employing singular spectral analysis to denoise the high-frequency intrinsic mode function components, fault transient features and noise interference in the signal can be effectively separated, and redundant information caused by amplitude fluctuations or random interference can be eliminated, thus obtaining a pure fault feature signal. This processing method can significantly improve the signal-to-noise ratio and feature clarity of the signal, enabling the high-frequency transient information in the traveling wave signal to be accurately preserved even under complex operating conditions and strong noise environments. This provides a reliable foundation for subsequent fault feature extraction and identification, thereby improving the accuracy, robustness, and stability of distribution network fault identification.

[0068] S104: Utilize Fast Fourier Transform to analyze and reconstruct the spectral characteristics of the pure fault feature signal, and calculate the average spectral content of the low-frequency band signal and the amplitude ratio of the high-frequency band signal based on the spectral characteristics.

[0069] The Fast Fourier Transform (FFT) is a mathematical transformation method that converts a time-domain signal into a frequency-domain signal, used to analyze the frequency components and amplitude distribution of a signal. Reconstructing a clean fault characteristic signal refers to a high-quality signal that retains the transient characteristics of the fault and removes noise interference after the aforementioned singular spectrum analysis and noise reduction processing. Spectral characteristics refer to the amplitude information corresponding to each frequency of the signal in the frequency domain, reflecting the energy distribution of different frequency components in the signal. The average spectral content of the low-frequency band signal refers to the average amplitude of the spectrum within a preset low-frequency range, used to reflect the slow changing trend of the signal. The amplitude proportion of the high-frequency band signal refers to the proportion of the amplitude of the spectrum within a preset high-frequency range to the total amplitude, used to characterize the strength of the signal's transient characteristics.

[0070] In the specific implementation process, the reconstructed clean fault characteristic signal can first be stored on a computer in the form of a discrete time series, and then subjected to a Fast Fourier Transform (FFT) to completely convert the time-domain signal into a frequency-domain signal. This yields the frequency amplitude and phase information corresponding to each sampling point, making the energy distribution of the signal clearly visible in the frequency domain. After obtaining the spectrum, it can be divided into low-frequency and high-frequency bands according to a pre-set frequency threshold. The low-frequency band is typically used to reflect the slow change trend of the signal, while the high-frequency band is used to reflect transient change characteristics. For the low-frequency band, the amplitudes of all frequency points can be summed and divided by the number of frequency points to calculate the average spectral content of the low-frequency band signal, thereby quantifying the energy distribution of the signal in the low-frequency band. For the high-frequency band, the amplitudes of each frequency point can be accumulated and divided by the sum of the amplitudes of the entire spectrum to obtain the proportion of the high-frequency band signal amplitude, reflecting the proportion of transient characteristics in the total signal energy.

[0071] During the calculation process, the spectral amplitude sequence can be smoothed to remove local fluctuations caused by sampling errors or discretization, ensuring that the calculated results of low-frequency average values ​​and high-frequency proportions are more stable and reliable. Simultaneously, by combining the relationship between spectral amplitude and corresponding frequency, abnormal peaks can be corrected or filtered out to avoid the impact of transient noise on feature quantization. Through these processes, the clean fault characteristic signal in the time domain is refined and analyzed in the frequency domain. Its low-frequency trends and high-frequency transient characteristics can be accurately quantified, providing directly usable numerical indicators for subsequent fault identification. This enables reliable extraction and characterization of fault information under complex operating conditions and high-noise environments, thereby improving the accuracy, robustness, and stability of distribution network fault identification.

[0072] By performing a Fast Fourier Transform (FFT) on the reconstructed clean fault characteristic signal, the time-domain signal can be converted into a frequency-domain signal, thus clearly reflecting the amplitude distribution of the signal at different frequencies. Calculating the average spectral content of the low-frequency band signal can quantify the slow changing trend of the signal, while calculating the amplitude proportion of the high-frequency band signal can quantify the strength of transient change characteristics, thereby accurately distinguishing fault transient information from the overall energy distribution. This processing method enables clear quantification of low-frequency and high-frequency characteristics in the frequency domain, providing a reliable basis for subsequent fault feature extraction and identification, and enabling accurate identification of fault characteristics in complex operating conditions and high-noise environments, thereby improving the accuracy, robustness, and stability of distribution network fault identification.

[0073] S105: Based on the fault traveling wave transmission characteristics, the average spectral content of low-frequency band signals is used as the main criterion, and the amplitude ratio of high-frequency band signals is used as the auxiliary criterion to generate the fault identification results of the distribution network.

[0074] Among them, the fault traveling wave transmission characteristics refer to the time-domain and frequency-domain characteristics of the transient voltage or current waveform propagating along the distribution line when a fault occurs. It reflects key information such as the fault type, location, and severity. The fault identification result refers to the output result that determines the fault type, location, and related status information of the distribution network based on the low-frequency average spectral content and the proportion of high-frequency amplitude. It can be used for subsequent protection control and operation decisions.

[0075] In practical implementation, the average spectral content of low-frequency signals can be used as the primary criterion. First, this characteristic value is precisely calculated on a computer and compared with a pre-established threshold range or empirical judgment range to determine the fault type reflected by the signal and the degree of line impact. During the comparison, the judgment threshold can be adjusted by considering the distribution network line length, number of branches, power supply type, and historical fault data to make the low-frequency judgment results more consistent with actual operating conditions. After the initial judgment, the proportion of high-frequency signal amplitude is used as an auxiliary criterion to correct and optimize the low-frequency judgment results, fully utilizing the sensitivity of transient characteristics to supplement the explanation of rapid changes during fault occurrence. When processing the high-frequency amplitude proportion, amplitude anomalies or local peaks can be smoothed or weighted to reduce the impact of noise interference on the judgment results. Subsequently, the low-frequency judgment results and high-frequency correction results are comprehensively analyzed. The final fault identification output, including fault type, fault location, fault severity, and related status information, can be generated through weighted averaging, logical rules, or model mapping. Throughout the process, the continuity and rationality of the judgment results can be verified to ensure that the generated fault identification results are accurate and stable in complex power distribution network structures, multi-branch, multi-power supply and strong noise environments, providing reliable data and analysis basis for subsequent protection control, fault isolation and operation decision-making.

[0076] By using the average spectral content of low-frequency signals as the primary criterion, the overall trend of fault signals can be accurately reflected, thereby determining the fault type and the extent of line impact. Simultaneously, using the amplitude proportion of high-frequency signals as an auxiliary criterion allows for the quantification of the strength of transient change characteristics, supplementing and verifying the transient fault information. This processing method organically combines low-frequency overall characteristics with high-frequency transient characteristics, enabling the fault traveling wave characteristics to be fully captured and quantified under complex operating conditions and high-noise environments. This results in accurate and reliable distribution network fault identification results, improving the accuracy, robustness, and stability of fault type judgment and fault location.

[0077] In the above embodiments, firstly, CEEMDAN is used to adaptively decompose the preprocessed traveling wave signal, which decomposes the non-stationary, spectrally complex traveling wave signal into multiple intrinsic mode function components, extracting high-frequency components and effectively preserving transient fault characteristics. This allows for the capture of key fault information even in complex distribution network environments with multiple power sources and branches. Subsequently, singular spectrum analysis is used to denoise the high-frequency mode components, significantly suppressing system noise and interference, thereby obtaining a clean fault feature signal in a high-noise environment and improving the accuracy and robustness of feature extraction. Furthermore, the spectral characteristics of the clean signal are analyzed using Fast Fourier Transform, and combined with the criteria of low-frequency average spectral content and high-frequency amplitude ratio, accurate identification of the fault type and location is achieved. This method preserves key signal characteristics under complex operating conditions through adaptive decomposition and overcomes strong noise interference by combining denoising and spectral criteria, thus achieving high-precision and reliable distribution network fault identification in complex operating conditions and high-noise environments, significantly improving the safety and stability of system operation.

[0078] In one embodiment, the step of decomposing the preprocessed traveling wave signal using CEEMDAN to obtain the intrinsic mode function component set includes:

[0079] Original white noise is added to the preprocessed traveling wave signal to obtain the first stage of the perturbation signal. Based on the first stage of the perturbation signal, the eigenmode function components of the first stage of the traveling wave signal are obtained through empirical mode decomposition, and the residual of the first stage is also obtained.

[0080] Starting from the second stage, in each stage, the disturbance signal of the current stage is constructed based on the residual of the previous stage and the noise intrinsic mode function components obtained by empirical mode decomposition of the original white noise of the previous stage. Based on the disturbance signal of the current stage, the intrinsic mode function components of the traveling wave signal of the current stage are obtained. This process continues until the residual of the current stage meets the preset iteration termination condition. The intrinsic mode function components of the traveling wave signal of each stage are then used as the intrinsic mode function component set.

[0081] In this system, the original white noise refers to a random signal with an amplitude following a Gaussian distribution and a mean of zero. It is used to introduce perturbations during signal decomposition to improve the stability and adaptability of empirical mode decomposition. The perturbation signal is the signal formed by adding white noise to the traveling wave signal, used to enhance the ability to distinguish different modes during decomposition. The residual refers to the portion of the signal not explained by the intrinsic mode function components during decomposition, used for perturbation construction in subsequent iterations. The preset iteration termination condition means that the decomposition process stops when the amplitude or energy of the residual falls below a set threshold, ensuring the integrity and validity of the decomposition results.

[0082] In the specific implementation process, the preprocessed traveling wave signal can first be stored in a computer as a discrete-time series, and an original white noise sequence of the same length as the signal can be generated. Then, the white noise is directly superimposed onto the preprocessed traveling wave signal according to its amplitude to form the first-stage perturbation signal, thereby enhancing the signal's adaptability in empirical mode decomposition and reducing mode aliasing. Next, empirical mode decomposition is performed on the first-stage perturbation signal, decomposing the signal into multiple intrinsic mode function components. Each component reflects the oscillation characteristics of different frequency components. Simultaneously, the residual after the first-stage decomposition is extracted, which contains low-energy components or non-intrinsic feature information that have not yet been decomposed.

[0083] For the second stage and subsequent stages, the residual obtained from the previous stage can be used as the base signal, while the noise intrinsic mode function components obtained from the previous stage decomposition are used to reconstruct the perturbation signal for the current stage. This perturbation signal combines residual information and noise characteristics, enabling the signal to maintain sensitivity to high-frequency transient characteristics and low-frequency trends in the new iteration stage. By performing empirical mode decomposition again on the perturbation signal of the current stage, the intrinsic mode function components of the traveling wave signal for the current stage can be obtained, and the residuals can be updated for the next stage iteration.

[0084] This iterative process is repeated until the amplitude or energy of the residual meets the preset termination condition, ensuring the sufficiency and effectiveness of the decomposition. After each stage of decomposition, the obtained intrinsic mode function components of the traveling wave signal are summarized in the order of the stages to form a complete set of intrinsic mode function components. Through this stage-by-stage perturbation and iterative decomposition method, the mode aliasing problem in the decomposition process can be effectively suppressed, making each intrinsic mode function component purer in frequency and energy, and fully preserving the high-frequency transient characteristics and low-frequency trend information of the traveling wave signal, providing a high-quality and reliable input foundation for subsequent signal analysis, feature extraction, and distribution network fault identification.

[0085] By adding original white noise to the preprocessed traveling wave signal to form the first-stage perturbation signal, a moderate perturbation can be introduced into the empirical mode decomposition process, making the different intrinsic mode function components of the signal easier to distinguish and reducing mode aliasing. The second and subsequent stages use the residuals from the previous stage and the noisy intrinsic mode function components obtained from the previous stage to construct the perturbation signal, instead of using the original white noise. This avoids additional interference introduced by noise accumulation while maintaining the adaptive separation capability for high-frequency transient characteristics and low-frequency trends. By decomposing the perturbation signal at each stage, extracting the intrinsic mode function components of the traveling wave signal, and updating the residuals, key feature information in the signal is gradually separated until the residuals meet the preset iteration termination condition. The intrinsic mode function components obtained at each stage are sequentially summarized to form a complete intrinsic mode function component set, thereby obtaining a decomposition result with clear frequency characteristics and complete transient features. This processing method can effectively extract traveling wave signal features under complex operating conditions and high noise environments, improve the identifiability of fault transient information, and provide a reliable foundation for subsequent fault feature analysis and accurate identification, thereby improving the accuracy, stability and robustness of distribution network fault identification.

[0086] In one embodiment, the perturbation signal formula for each stage starting from the second stage is:

[0087]

[0088] in, Indicates the first Phase 1 A disturbance signal in time The value of , Indicates the ( Stage residuals in time The value of , Indicates the ( Noise intensity coefficient during the ) stage This indicates the original white noise sequence. After performing empirical mode decomposition, the obtained () The noise intrinsic mode function components during the ) stage in time The value of , This indicates the total number of disturbance signals.

[0089] In this embodiment, the formula forms the disturbance signal of the current stage by weighted superposition of the residual from the previous stage and the noise intrinsic mode function components obtained from the noise decomposition of the previous stage. This ensures that the signal decomposition in each stage retains the undecomposed low-frequency information while introducing appropriate disturbances to enhance mode separation capability. This method of constructing disturbance signals stage by stage avoids the additional interference caused by directly superimposing the original white noise in subsequent stages, while maintaining sensitivity to high-frequency transient characteristics and low-frequency trends, resulting in purer intrinsic mode function components and clearer frequency characteristics. The disturbance signal formed through multi-stage iteration gradually approximates the characteristics of the real signal, effectively reducing mode aliasing and improving the extraction accuracy of traveling wave signal characteristics in complex operating conditions and high-noise environments. This provides a reliable foundation for subsequent fault feature analysis and distribution network fault identification, thereby significantly improving the accuracy, stability, and robustness of fault identification.

[0090] It should be noted that Fully Integrated Empirical Mode Decomposition (CEEMDAN) is an improved adaptive noise-assisted signal decomposition method. Its core idea is to adaptively add specific white noise components to the signal residuals during the extraction of each order of Intrinsic Mode Function (IMF) components, and perform multiple integrated calculations to suppress mode aliasing. Unlike the Ensemble Empirical Mode Decomposition (EEMD) method, which adds noise all at once for complete decomposition, CEEMDAN gradually extracts physically meaningful mode components by injecting white noise in stages. Its decomposition steps are as follows: First, the first-order IMF components of the noisy signal are extracted and integrated for averaging. Then, white noise components are adaptively added to each order of residuals, and subsequent IMF components are iteratively calculated until the original signal is decomposed into several IMF components and the final residual.

[0091] Add to the original signal S(t) Multiplying Gaussian white noise by a factor of 1, I perturbation signals are generated using the following formula:

[0092]

[0093] For each disturbance signal X i (t) Perform complete EMD decomposition and extract the first-order IMF of each signal, denoted as IMF1. i (t), the ensemble average of the I first-order IMFs is used to obtain the first-order IMF of CEEMDAN, as shown in the formula:

[0094]

[0095] Calculate the residual r1(t) of the first stage, which is the difference between the original signal and the first-order IMF:

[0096]

[0097] Starting from the second order, the original white noise is no longer used. Instead, an adaptive noise is constructed based on the IMF of the white noise, and the white noise w is adjusted accordingly. i (t) Perform EMD decomposition and extract its first-order IMF, denoted as E1(w i (t)); with the first stage residual r i Based on (t), add times E1(w) i (t) is used as adaptive noise to construct the set of perturbation signals for the second stage:

[0098]

[0099] For each X i 2(t) is decomposed into EMD, and only its first-order IMF is extracted (this IMF corresponds to the second-order IMF of the entire decomposition process); the ensemble average of the above IMFs is calculated to obtain the second-order IMF of CEEMDAN:

[0100]

[0101] Calculate the residual r of the first stage i (t), which is the difference between the original signal and the first-order IMF:

[0102]

[0103] When the residual r at a certain stage k When condition (t) is met, IMF can no longer be extracted through EMD, and the iteration terminates. At this point, the original signal can be accurately reconstructed from all extracted IMFs and the final residual, as shown in the formula:

[0104]

[0105] In one embodiment, the step of using singular spectrum analysis to denoise the high-frequency intrinsic mode function components to obtain a clean fault characteristic signal includes:

[0106] The trajectory matrix of the high-frequency intrinsic mode function components is constructed, and multiple singular values ​​of the trajectory matrix are obtained through singular spectrum analysis;

[0107] The joint index function is determined. The joint index function is composed of the weighted difference spectrum and the modified cumulative energy ratio. The weighted difference spectrum is used to reflect the local jumps of the singular value sequence, the modified cumulative energy ratio is used to measure the overall energy contribution of the signal, and the joint index function is used to integrate the local jump and the overall energy information.

[0108] Based on each singular value, the optimal reconstruction order is determined by finding the maximum point of the joint index function;

[0109] Based on the optimal reconstruction order, the reconstruction matrix of the traveling wave signal is constructed to obtain the pure fault characteristic signal.

[0110] The trajectory matrix is ​​a matrix constructed by embedding high-frequency intrinsic mode function components using a certain delay method. It is used to preserve the signal's temporal structure and facilitate singular spectrum analysis. The joint index function is a criterion combining the weighted difference spectrum and the modified cumulative energy ratio. The weighted difference spectrum reflects the local jump characteristics of the singular value sequence, while the modified cumulative energy ratio measures the overall energy contribution of the signal. The joint index function integrates local transient changes and global energy information to help determine the optimal reconstruction order. The optimal reconstruction order refers to the number of singular values ​​selected under the joint index function analysis that best restores the main features of the signal. The reconstruction matrix is ​​a matrix formed by recombinating the signal patterns corresponding to the selected singular values ​​according to the optimal reconstruction order, used to recover the main features of the signal.

[0111] In practical implementation, the high-frequency intrinsic mode function components can first be arranged in time sequence to construct a trajectory matrix using a sliding window and delay embedding method. This ensures that the matrix's row and column structure fully preserves the signal's temporal characteristics and local variation patterns. Subsequently, this trajectory matrix is ​​input into a singular spectrum analysis program, where singular value decomposition (SVD) is performed on the computer to obtain each singular value and its corresponding energy contribution, reflecting the signal's oscillation intensity and characteristic distribution under different modes. Based on the obtained singular value sequence, a weighted difference spectrum can be calculated on the computer. By measuring the amplitude of local jumps in the singular value sequence, transient change characteristics in the signal can be identified. Simultaneously, a corrected cumulative energy ratio is calculated to evaluate the overall energy distribution and cumulative contribution of the signal. Combining the weighted difference spectrum and the corrected cumulative energy ratio forms a joint index function, enabling the computer to comprehensively consider local feature changes and overall energy information, providing a basis for determining the optimal reconstruction order.

[0112] In the analysis of the joint index function, the optimal reconstruction order can be determined by finding the maximum point of the function, i.e., selecting the set of singular values ​​that can retain the high-frequency transient information and main energy characteristics to the greatest extent. On a computer, based on the determined optimal reconstruction order, corresponding components are selected from the singular values ​​and their corresponding signal modes, and a reconstruction matrix is ​​constructed by weighted combination. The reconstruction matrix can completely recover the selected high-frequency characteristic signal while suppressing noise and irrelevant interference. Finally, the signal extracted from the reconstruction matrix is ​​the pure fault characteristic signal. This signal retains the key characteristics of the fault traveling wave in both the time and frequency domains, providing high-quality and reliable input data for subsequent spectrum analysis, feature extraction, and distribution network fault identification, and ensuring the accuracy and stability of fault identification under complex operating conditions and strong noise environments.

[0113] By constructing the trajectory matrix of the high-frequency intrinsic mode function components and performing singular spectrum analysis, the energy distribution of the signal under different oscillation modes can be clearly separated, effectively distinguishing high-frequency transient characteristics from low-frequency trends. Using a joint index function to synthesize the weighted differential spectrum and corrected cumulative energy ratio, both local jumps and overall energy contributions of the singular value sequence can be reflected, thus scientifically determining the reconstruction order corresponding to the main characteristics of the signal. Determining the optimal reconstruction order based on the maximum point of the joint index function and constructing a reconstruction matrix to reconstruct the signal preserves high-frequency transient information while effectively suppressing noise and irrelevant interference, resulting in a pure fault characteristic signal. This processing method can completely extract fault features from traveling wave signals, significantly improving the accuracy of signal analysis under complex operating conditions and high-noise environments. It provides a reliable, stable, and high-precision foundation for subsequent frequency domain analysis and distribution network fault identification, ensuring clear and identifiable fault features and improving the accuracy and robustness of fault identification.

[0114] In one embodiment, the formula for the joint index function is:

[0115]

[0116]

[0117]

[0118] in, This represents the value of the joint index function. Indicates the first Weighted difference spectrum of singular values Indicates the preceding The corrected cumulative energy ratio of each singular value Indicates the order of candidate reconstruction. Indicates the first Weighted difference spectrum of singular values Indicates the first A singular value, Indicates the ( ) singular values, The index representing the singular value. Indicates all The maximum value, This represents the total number of singular values.

[0119] In this embodiment, a comprehensive index is formed by combining the local variation characteristics of singular values ​​with the cumulative energy characteristics to evaluate the contribution of the main components of the signal at different reconstruction orders. The weighted differential spectrum reflects the local jumps in the singular value sequence, enabling the calculation to sensitively capture the energy changes of transient abrupt changes in the signal. The corrected cumulative energy ratio measures the contribution of the first few singular values ​​to the overall energy, ensuring that the signal reconstruction retains high-energy components without over-relying on a single local jump. The optimal reconstruction order is determined by the maximum point of the joint index function, which can effectively eliminate noise and low-energy interference while maintaining the key characteristics of the signal. This processing method can extract a clean signal with clear frequency characteristics and complete transient features, improving the identification accuracy of key features of traveling wave signals in complex operating conditions and strong noise environments. This provides a reliable foundation for subsequent fault feature analysis and distribution network fault identification, thereby significantly enhancing the accuracy, stability, and robustness of fault identification.

[0120] It's important to note that the core principle of Singular Spectrum Analysis (SSA) is based on signal decomposition and reconstruction. This is achieved by constructing a trajectory matrix through embedding dimensions and utilizing Singular Value Decomposition (SVD). In signal denoising, the singular values ​​obtained from SVD typically exhibit a decaying distribution: the first few singular values ​​correspond to the main structure of the original signal, while the subsequent large number of small-amplitude singular values ​​primarily reflect noise components. Therefore, the key to effective denoising lies in accurately distinguishing between effective signal components and noise components. Commonly used methods include the cumulative variance contribution rate threshold method and the singular value difference spectrum curvature extremum judgment. By selecting effective components to reconstruct the signal and removing the dominant noise components, signal denoising and the extraction of useful information can be achieved.

[0121] Embedding and Singular Value Decomposition (SVD) Stages: Initially, the window length (L) is defined, and then the one-dimensional time series is transformed into an L×K-dimensional trajectory matrix X. L×K :

[0122]

[0123] N is the total length or total number of points of the original one-dimensional time series. K = N - L + 1 is the number of columns in the trajectory matrix. Singular value decomposition of the trajectory matrix yields:

[0124]

[0125]

[0126] Where: d = rank(X), each matrix X is a matrix with rank 1, U j Let U be the j-th column vector, and V be the vector of the same order. j Let σ be the j-th column vector of V.i Let i be the i-th singular value.

[0127] Reconstruction Phase: Signal-to-noise separation is achieved by identifying the boundaries within the singular value spectrum. The first r singular values ​​are retained to construct the reconstruction matrix, while the remaining singular values ​​are set to zero. The determination of the reconstruction order is considered a key factor affecting denoising performance. Traditional methods, such as Singular Value Difference Spectrum (SVDS), determine the signal-to-noise separation boundary by finding the largest abrupt change point in the singular value sequence. While this method effectively identifies the steep descent characteristics of singular values, it is easily affected by subsequent small fluctuations, often leading to over-denoising and signal waveform distortion. On the other hand, methods based on cumulative energy ratio rely on empirical threshold settings and lack adaptability under different signal-to-noise ratio conditions, often resulting in insufficient denoising due to inappropriate reconstruction order selection.

[0128] To address the aforementioned limitations, a boundary determination method combining singular value difference spectrum and modified cumulative energy ratio is adopted: the weighted singular value difference spectrum is combined with the modified cumulative energy ratio to optimize the reconstruction order. Traditional SVDS methods assign equal weights to all singular value differences, failing to adequately consider prior knowledge of signal component distributions. Here, ordinal-related weighting factors are used to construct the weighted difference spectrum.

[0129]

[0130] To address the issue of the traditional cumulative energy ratio changing gradually at boundary points, a differential enhancement mechanism is introduced to calculate the cumulative energy ratio E. r :

[0131]

[0132] By leveraging the complementarity between local mutation characteristics and global energy distribution, a function J(r) is constructed:

[0133]

[0134] The reconstruction order r is determined by finding the maximum point of this joint index. n :

[0135]

[0136] Based on the determined optimal reconstruction order r n Keep the first r n Constructing a reconstructed matrix from singular value components:

[0137]

[0138] In one embodiment, the step of calculating the average spectral content of the low-frequency band signal and the amplitude ratio of the high-frequency band signal based on spectral characteristics includes:

[0139] Based on the spectral characteristics, the amplitude points in the low-frequency band are determined, and the average amplitude points in the low-frequency band are amplified to obtain the average spectral content of the low-frequency band signal.

[0140] Based on the spectral characteristics, the amplitude points and maximum amplitude of the high-frequency band are determined. The average amplitude points of the high-frequency band are then amplified to obtain the average spectral content of the high-frequency band signal. The ratio of the average spectral content of the high-frequency band signal to the maximum amplitude is taken as the amplitude proportion of the high-frequency band signal.

[0141] In this context, low-frequency amplitude points refer to the amplitude data points located in the low-frequency range within the reconstructed fault characteristic signal spectrum, reflecting the low-frequency energy distribution of the signal. High-frequency amplitude points refer to the amplitude data points located in the high-frequency range within the spectrum, reflecting the intensity of the signal's high-frequency transient characteristics. The maximum amplitude value refers to the largest amplitude value among the high-frequency amplitude points, representing the peak energy of the high-frequency transient signal.

[0142] In the specific implementation process, the Fast Fourier Transform (FFT) spectrum of the pure fault characteristic signal can first be calculated on a computer to obtain complete frequency distribution information. By analyzing the spectrum data, all amplitude points in the low-frequency range can be identified. These amplitude points can reflect the steady-state of the signal and the low-frequency energy distribution. A numerical average of these low-frequency amplitude points is then calculated on the computer to obtain a mean signal reflecting the overall low-frequency energy level. This mean signal is then amplified according to a preset amplification factor to enhance its discriminative role in subsequent fault identification, making the low-frequency energy characteristics more obvious and easier to quantify.

[0143] Subsequently, the amplitude points in the high-frequency range of the spectrum can be further analyzed on a computer, and the maximum amplitude within this range can be identified. The average spectral content of the high-frequency signal can be obtained by numerically averaging the high-frequency amplitude points, and then amplified to highlight the high-frequency transient characteristics. Simultaneously, the ratio of the average spectral content of the high-frequency signal to the maximum amplitude within this range is calculated to obtain the amplitude proportion of the high-frequency signal. This indicator can quantify the concentration and peak contribution of high-frequency transient energy, making the transient change characteristics more clearly comparable numerically.

[0144] By averaging and amplifying the amplitude points in the low-frequency band, the overall energy level of the signal in the low-frequency range can be quantified, making steady-state characteristics and low-frequency trends more apparent, which helps reflect the overall energy distribution of fault signals in the distribution network. Averaging and amplifying the amplitude points in the high-frequency band, while simultaneously calculating the amplitude proportion based on the highest high-frequency amplitude, can effectively capture the intensity and concentration of transient changes in the signal, thus highlighting the high-frequency transient characteristics of the fault traveling wave. By simultaneously considering the average energy in the low-frequency band and the amplitude proportion in the high-frequency band, multi-dimensional analysis of the signal can be performed on a computer, comprehensively quantifying steady-state information and transient characteristics. This processing method enhances the ability to identify key fault characteristics under complex operating conditions and high-noise environments, improves the accuracy and reliability of distribution network fault identification, and provides stable and clear signal evidence for subsequent frequency domain analysis and fault determination, thereby significantly improving the accuracy and robustness of fault identification.

[0145] It should be noted that,

[0146] In the formula, This represents the average spectral content within the frequency interval [i, j], and its value is determined by the amplitude within that interval. The mean is obtained by amplifying it with an amplification factor M, which is defined as 10000.

[0147]

[0148] In the formula, This indicates the amplitude percentage of a frequency segment. This indicates the maximum amplitude value in the signal.

[0149] In one embodiment, the step of generating fault identification results for a distribution network based on the fault traveling wave transmission characteristics, using the average spectral content of low-frequency signals as the primary criterion and the amplitude ratio of high-frequency signals as an auxiliary criterion, includes:

[0150] Based on the characteristics of fault traveling wave transmission, when the average spectral content of the low-frequency band signal is greater than or equal to the first preset threshold, a fault is initially determined in the distribution network. If the amplitude ratio of the high-frequency band signal is less than or equal to the second preset threshold, noise interference is eliminated, and the fault identification result of the distribution network is finally determined.

[0151] The first preset threshold is a reference value used to determine whether the low-frequency energy is sufficient to characterize the existence of a fault, and the second preset threshold is a reference value used to eliminate the influence of noise or interference on fault determination.

[0152] In the specific implementation process, the purified fault characteristic signal after frequency domain analysis can be acquired on a computer first, and then analyzed based on the fault traveling wave transmission characteristics. The so-called fault traveling wave transmission characteristics refer to the specific frequency and amplitude distribution patterns exhibited by the voltage or current traveling waves generated when a fault occurs in the distribution network as they propagate through the transmission lines. Low-frequency signals mainly reflect the overall energy generated by the fault and the steady-state response of the line, while high-frequency signals mainly reflect the transient energy fluctuations and spikes of the fault. The computer can first calculate the average spectral content of the signal in the low-frequency band and compare this value with a pre-set first threshold to determine whether the overall energy in the low-frequency band reaches the reference level required for fault determination. When the calculation result shows that the average spectral content of the low-frequency band signal is greater than or equal to the first preset threshold, the computer will preliminarily determine that a fault may exist in the distribution network and mark the signal as an object to be further analyzed, so as to perform fine processing of the high-frequency transient characteristics.

[0153] Subsequently, the computer calculates the proportion of high-frequency signal amplitude. This proportion is obtained by averaging the high-frequency amplitude points and comparing it with the maximum amplitude within that range, reflecting the concentration of transient signal energy. The computer compares this proportion with a pre-set second threshold. When the proportion is less than or equal to the second threshold, it indicates that the high-frequency portion is not significantly affected by noise or external interference. The computer eliminates false positives and confirms the initial assessment of the low-frequency band as a genuine fault. Finally, after integrating the low-frequency average energy and high-frequency transient characteristics, the computer generates the final fault identification result for the distribution network, providing reliable signal input for power grid operation monitoring and fault handling.

[0154] The reason for processing the fault using the average spectral content of low-frequency signals and the proportion of high-frequency signal amplitude is understandable. This is based on the physical characteristics of traveling wave transmission in fault systems, specifically, the simultaneous generation of low-frequency steady-state energy and high-frequency transient energy in the traveling wave signal due to a distribution network fault. First, by determining whether the average spectral content of the low-frequency signal reaches a preset threshold, the occurrence of a fault can be preliminarily confirmed, ensuring that the overall energy level meets the fault assessment criteria. Then, using the proportion of high-frequency signal amplitude for auxiliary assessment, the abnormality of high-frequency transients in the signal can be effectively distinguished from genuine fault characteristics or anomalies caused by noise or external interference, thus eliminating false positives. This dual-criteria processing method enables high-precision fault identification in the distribution network, ensuring both the sensitivity of fault detection and enhanced robustness against noise interference, thereby obtaining accurate and reliable final fault identification results. This provides a stable and reliable signal basis for power grid operation monitoring and fault handling.

[0155] It should be noted that, taking advantage of the relatively small attenuation of low-frequency components (10~100 kHz) in the fault traveling wave during transmission, the frequency amplitude content of the signal in this frequency band is selected as the discrimination criterion to achieve low-frequency feature identification of the sampled signal, i.e., satisfying:

[0156]

[0157] Where μ represents the threshold value of low-frequency amplitude content, which is 4. If the low-frequency feature meets this condition, the amplitude proportion of high-frequency components (1~5 MHz) is further introduced as an auxiliary criterion. Since high-frequency components attenuate faster during propagation and their amplitude proportion is lower, the following discrimination condition is set:

[0158]

[0159] Here, ψ is the threshold for the proportion of high-frequency amplitude, which is set to 2.

[0160] To facilitate understanding of the scheme in this application, specific examples are provided below.

[0161] A 10 kV distribution system simulation model was constructed based on the PSCAD platform for fault simulation analysis and to acquire traveling wave data. To verify the effectiveness of the proposed CEEMDAN-SSA-based distribution network fault identification method, a model was established as follows: Figure 2 The 10 kV line simulation model shown has traveling wave acquisition devices with a sampling frequency of 10 MHz configured at both ends M and N.

[0162] To verify the noise resistance of the proposed method, three white noises of different intensities were superimposed on the original sampled signal, with signal-to-noise ratios (SNR) set to 10 dB, 20 dB and 30 dB, respectively. Figure 3 Corresponding to the sampled signal after adding noise, Figure 4 This is the noise-reduced signal obtained by the CEEMDAN-SSA method. Figure 3 , Figure 4 The experimental results under different noise levels show that the CEEMDAN-SSA algorithm can effectively overcome strong white noise interference and highlight key traveling wave features while denoising.

[0163] To meet the detection requirements of various faults in the distribution network, a typical fault point (point D2) in the simulation network model was selected for multi-scenario analysis. The experimental configuration included the following test conditions: under fault conditions with initial phases of 30°, 60°, and 90°, single-phase ground faults (AG) with fault transition resistances of 300Ω, 1000Ω, and 3000Ω, and AB-phase combined ground faults (ABG) with resistances of 200Ω and 500Ω were set, respectively. The fault settings of the simulation model are shown in the table below:

[0164]

[0165] The fault identification results under different operating conditions are shown in the table below:

[0166]

[0167] Comprehensive analysis shows that this method exhibits good robustness under various complex operating conditions, including multiple fault modes, multi-phase conditions, and high-resistivity grounding faults. It can effectively extract traveling wave characteristics and achieve accurate identification of different grounding faults.

[0168] To verify the method's adaptability to different fault locations, we Figure 2 Faults under various operating conditions were set at points D3 and D9 for verification. The fault identification results for different fault locations are shown in the table below:

[0169]

[0170] Fault identification results for different fault locations:

[0171]

[0172] Therefore, it can be seen that the distribution network fault identification method based on CEEMDAN-SSA has good adaptability under complex power grid structures. It can achieve accurate fault identification for different fault locations and under different fault conditions, demonstrating the effectiveness and robustness of the method.

[0173] The following describes the CEEMDAN-SSA-based distribution network fault identification device provided in the embodiments of this application. The CEEMDAN-SSA-based distribution network fault identification device described below can be referred to in correspondence with the CEEMDAN-SSA-based distribution network fault identification method described above. Figure 5 As shown, this application provides a distribution network fault identification device based on CEEMDAN-SSA, the device comprising:

[0174] The traveling wave signal receiving module 201 is used to receive the traveling wave signal from the power distribution network and to preprocess the traveling wave signal.

[0175] The high-frequency intrinsic mode function component selection module 202 is used to decompose the preprocessed traveling wave signal using CEEMDAN to obtain the intrinsic mode function component set, and select high-frequency intrinsic mode function components from the intrinsic mode function component set;

[0176] The pure fault feature signal determination module 203 is used to reduce noise in the high-frequency intrinsic mode function components by using singular spectrum analysis to obtain a pure fault feature signal.

[0177] The spectrum feature reconstruction module 204 is used to reconstruct the spectrum features of the clean fault feature signal using fast Fourier transform analysis, and to calculate the average spectrum content of the low-frequency band signal and the amplitude ratio of the high-frequency band signal based on the spectrum features.

[0178] The fault identification result generation module 205 is used to generate fault identification results for the distribution network based on the fault traveling wave transmission characteristics, with the average spectral content of the low-frequency band signal as the main criterion and the amplitude ratio of the high-frequency band signal as the auxiliary criterion.

[0179] In one embodiment, the high-frequency intrinsic mode function component selection module 202 includes:

[0180] The first traveling wave signal decomposition unit is used to add original white noise to the preprocessed traveling wave signal to obtain the first stage disturbance signal, and based on the first stage disturbance signal, obtain the eigenmode function components of the first stage traveling wave signal through empirical mode decomposition, and obtain the first stage residual.

[0181] The second traveling wave signal decomposition unit is used to construct the disturbance signal of the current stage in each stage starting from the second stage, based on the residual of the previous stage and the noise intrinsic mode function components obtained by empirical mode decomposition of the original white noise of the previous stage. Based on the disturbance signal of the current stage, the intrinsic mode function components of the traveling wave signal of the current stage are obtained until the residual of the current stage meets the preset iteration termination condition. The intrinsic mode function components of the traveling wave signal of each stage are used as the intrinsic mode function component set.

[0182] In one embodiment, the perturbation signal formula for each stage starting from the second stage is:

[0183]

[0184] in, Indicates the first Phase 1 A disturbance signal in time The value of , Indicates the ( Stage residuals in time The value of , Indicates the ( Noise intensity coefficient during the ) stage This indicates the original white noise sequence. After performing empirical mode decomposition, the obtained () The noise intrinsic mode function components during the ) stage in time The value of , This indicates the total number of disturbance signals.

[0185] In one embodiment, the clean fault characteristic signal determination module 203 includes:

[0186] The singular value determination unit is used to construct the trajectory matrix of the high-frequency intrinsic mode function components and obtain multiple singular values ​​of the trajectory matrix through singular spectrum analysis.

[0187] The joint index function determination unit is used to determine the joint index function, which is composed of a weighted difference spectrum and a modified cumulative energy ratio. The weighted difference spectrum is used to reflect the local jumps of the singular value sequence, the modified cumulative energy ratio is used to measure the overall energy contribution of the signal, and the joint index function is used to integrate the local jumps and the overall energy information.

[0188] The optimal reconstruction order determination unit is used to determine the optimal reconstruction order based on each singular value by finding the maximum point of the joint index function.

[0189] The pure fault characteristic signal determination unit is used to construct the reconstruction matrix of the traveling wave signal based on the optimal reconstruction order, thereby obtaining the pure fault characteristic signal.

[0190] In one embodiment, the formula for the joint index function is:

[0191]

[0192]

[0193]

[0194] in, This represents the value of the joint index function. Indicates the first Weighted difference spectrum of singular values Indicates the preceding The corrected cumulative energy ratio of each singular value Indicates the order of candidate reconstruction. Indicates the first Weighted difference spectrum of singular values Indicates the first A singular value, Indicates the ( ) singular values, The index representing the singular value. Indicates all The maximum value, This represents the total number of singular values.

[0195] In one embodiment, the spectrum feature reconstruction module 204 includes:

[0196] The low-frequency band signal average spectral content calculation unit is used to determine the low-frequency band amplitude points based on the spectral characteristics, and then amplify the average value of the low-frequency band amplitude points to obtain the low-frequency band signal average spectral content.

[0197] The high-frequency band signal amplitude ratio calculation unit is used to determine the high-frequency band amplitude points and maximum amplitude based on the spectral characteristics, and then amplify the average amplitude points of the high-frequency band to obtain the average spectral content of the high-frequency band signal. The ratio of the average spectral content of the high-frequency band signal to the maximum amplitude is used as the high-frequency band signal amplitude ratio.

[0198] In one embodiment, the fault identification result generation module 205 includes:

[0199] The fault identification result generation unit is used to preliminarily determine that there is a fault in the distribution network when the average spectral content of the low-frequency band signal is greater than or equal to the first preset threshold, based on the fault traveling wave transmission characteristics. If the amplitude ratio of the high-frequency band signal is less than or equal to the second preset threshold, noise interference is eliminated, and the fault identification result of the distribution network is finally determined.

[0200] In one embodiment, this application also provides a storage medium storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the distribution network fault identification method based on CEEMDAN-SSA as described in any of the above embodiments.

[0201] In one embodiment, this application also provides a computer device storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the distribution network fault identification method based on CEEMDAN-SSA as described in any of the above embodiments.

[0202] Indicatively, such as Figure 6 As shown, Figure 6 This is a schematic diagram of the internal structure of a computer device 300 provided in an embodiment of this application. The computer device 300 can be provided as a server. (Refer to...) Figure 6 The computer device 300 includes a processing component 302, which further includes one or more processors, and memory resources represented by memory 301 for storing instructions, such as application programs, that can be executed by the processing component 302. The application programs stored in memory 301 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 302 is configured to execute instructions to perform the CEEMDAN-SSA-based distribution network fault identification method of any of the above embodiments.

[0203] The computer device 300 may also include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input / output (I / O) interface 305. The computer device 300 may operate on an operating system stored in memory 301, such as Windows Server™, Mac OS X™, Unix™, Linux™, Free BSD™, or similar.

[0204] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0205] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. In this document, "a," "an," "the," "the," and "its" may also include plural forms unless the context clearly indicates otherwise. "Multiple" refers to at least two, such as 2, 3, 5, or 8, etc. "And / or" includes any and all combinations of the related listed items.

[0206] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0207] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A power distribution network fault identification method based on CEEMDAN-SSA, characterized in that, The method comprises: receiving a traveling wave signal of the power distribution network, and preprocessing the traveling wave signal; using CEEMDAN to decompose the preprocessed traveling wave signal to obtain an intrinsic mode function component set, and selecting a high-frequency intrinsic mode function component from the intrinsic mode function component set; using singular spectrum analysis to denoise the high-frequency intrinsic mode function component to obtain a pure fault characteristic signal; using fast Fourier transform analysis to reconstruct the frequency spectrum characteristics of the pure fault characteristic signal, and calculating the low-frequency signal average spectrum content and the high-frequency signal amplitude proportion according to the frequency spectrum characteristics; according to the fault traveling wave transmission characteristics, taking the low-frequency signal average spectrum content as the main criterion and the high-frequency signal amplitude proportion as the auxiliary criterion, to generate a fault identification result of the power distribution network.

2. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 1, characterized in that, The step of using CEEMDAN to decompose the preprocessed traveling wave signal to obtain an intrinsic mode function component set comprises: adding original white noise to the preprocessed traveling wave signal to obtain a first-stage disturbance signal, and obtaining a first-stage traveling wave signal intrinsic mode function component and a first-stage residual through empirical mode decomposition according to the first-stage disturbance signal; in each stage starting from the second stage, constructing a current-stage disturbance signal according to the residual of the previous stage and the noise intrinsic mode function component obtained through empirical mode decomposition of the original white noise of the previous stage, and obtaining a current-stage traveling wave signal intrinsic mode function component according to the current-stage disturbance signal, until the residual of the current stage meets a preset iteration termination condition, and taking the traveling wave signal intrinsic mode function component of each stage as the intrinsic mode function component set.

3. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 2, characterized in that, The disturbance signal formula in each stage starting from the second stage is: wherein, denotes the value of the (i)th disturbance signal at time in the (j)th stage, denotes the value of the (i)th disturbance signal at time denotes the value of the (i)th residual signal at time in the (j)th stage, denotes the value of the (i)th noise intensity coefficient in the (j)th stage, denotes the value of the (i)th noise intrinsic mode function component at time in the (j)th stage after empirical mode decomposition of the original white noise sequence denotes the value of the (i)th noise intrinsic mode function component at time denotes the total number of disturbance signals.​​​​ 4. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 1, characterized in that, The step of using singular spectrum analysis to denoise the high-frequency intrinsic mode function component to obtain a pure fault characteristic signal comprises: constructing a trajectory matrix of the high-frequency intrinsic mode function component, and obtaining a plurality of singular values of the trajectory matrix through singular spectrum analysis; determining a joint index function, the joint index function being composed of a weighted differential spectrum and a modified cumulative energy ratio, the weighted differential spectrum being used to reflect local jumps of the singular value sequence, the modified cumulative energy ratio being used to measure the overall energy contribution of the signal, and the joint index function being used to comprehensively consider local jumps and overall energy information; determining an optimal reconstruction order by finding a maximum point of the joint index function according to each singular value; constructing a reconstruction matrix of the traveling wave signal according to the optimal reconstruction order to obtain the pure fault characteristic signal.

5. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 4, characterized in that, The formula of the joint index function is: wherein, denotes the joint index function value, denotes the weighted difference spectrum value of the th singular value, denotes the modified cumulative energy ratio of the first singular values, denotes the candidate reconstruction order, denotes the weighted difference spectrum value of the th singular value, denotes the th singular value, denotes the th singular value, denotes the index of the singular value, denotes the maximum of all , and denotes the total number of singular values.

6. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 1, characterized in that, The step of calculating the low-frequency signal average spectrum content and the high-frequency signal amplitude proportion according to the frequency spectrum characteristics comprises: determining a low-frequency amplitude point according to the frequency spectrum characteristics, amplifying the average value of the low-frequency amplitude point to obtain the low-frequency signal average spectrum content; and According to the frequency spectrum feature, a high-frequency amplitude point and a maximum amplitude are determined, the high-frequency amplitude point is averaged and amplified to obtain a high-frequency signal average spectrum content, and a ratio of the high-frequency signal average spectrum content to the maximum amplitude is taken as a high-frequency signal amplitude proportion.

7. The CEEMDAN-SSA-based power distribution network fault identification method according to claim 1, characterized in that, The step of generating the fault identification result of the power distribution network according to the fault traveling wave transmission feature, taking the low-frequency signal average spectrum content as the main criterion and the high-frequency signal amplitude proportion as the auxiliary criterion, includes: According to the fault traveling wave transmission feature, when the low-frequency signal average spectrum content is greater than or equal to a first preset threshold, it is preliminarily determined that the power distribution network has a fault, and if the high-frequency signal amplitude proportion is less than or equal to a second preset threshold, noise interference is excluded, and the fault identification result of the power distribution network is finally determined.

8. A power distribution network fault identification device based on CEEMDAN-SSA, characterized in that, The device includes: A traveling wave signal receiving module for receiving a traveling wave signal of the power distribution network and pre-processing the traveling wave signal; A high-frequency intrinsic mode function component selecting module for decomposing the pre-processed traveling wave signal by CEEMDAN to obtain an intrinsic mode function component set and selecting a high-frequency intrinsic mode function component from the intrinsic mode function component set; A pure fault feature signal determining module for denoising the high-frequency intrinsic mode function component by singular spectrum analysis to obtain a pure fault feature signal; A frequency spectrum feature reconstructing module for analyzing and reconstructing the frequency spectrum feature of the pure fault feature signal by fast Fourier transform, and calculating a low-frequency signal average spectrum content and a high-frequency signal amplitude proportion according to the frequency spectrum feature; A fault identification result generating module for generating the fault identification result of the power distribution network according to the fault traveling wave transmission feature, taking the low-frequency signal average spectrum content as the main criterion and the high-frequency signal amplitude proportion as the auxiliary criterion.

9. A storage medium characterized by: The storage medium has computer readable instructions stored therein, and the computer readable instructions are executed by one or more processors to cause the one or more processors to perform the steps of the CEEMDAN-SSA-based power distribution network fault identification method according to any one of claims 1 to 7.

10. A computer device, comprising: It includes: One or more processors and a memory; The memory has computer readable instructions stored therein, and the computer readable instructions are executed by the one or more processors to perform the steps of the CEEMDAN-SSA-based power distribution network fault identification method according to any one of claims 1 to 7.

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