Power distribution network traveling wave head calibration method based on CEEMDAN-CPO-VMD

Abstract

The invention provides a CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method, and the method comprises the steps: collecting a current traveling wave signal in a power distribution network, and extracting a target traveling wave signal from the current traveling wave signal; carrying out primary decomposition on the target traveling wave signal by adopting CEEMDAN to obtain a plurality of intrinsic mode function components, and taking the first high-frequency intrinsic mode function component as a target intrinsic mode function component; performing secondary decomposition on the target intrinsic mode function component by using the optimized variational mode decomposition to obtain a plurality of intrinsic mode functions, the variational mode decomposition being obtained by optimizing a mode decomposition number and a penalty factor by using a crown porcupine optimization algorithm; and performing energy analysis on each intrinsic mode function to obtain an energy sequence, and extracting a moment corresponding to an energy peak value in the energy sequence as a traveling wave head moment of the current traveling wave signal. Therefore, the traveling wave head calibration precision is greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power distribution network fault diagnosis, and particularly relates to a power distribution network traveling wave front calibration method based on CEEMDAN-CPO-VMD. BACKGROUND

[0002] With the acceleration of urbanization process in China and the development of cable power supply technology, in order to beautify the city and save land resources, the power distribution network gradually changes from single overhead line to mixed power distribution line composed of overhead line and cable. At the same time, the scale of the power distribution network is continuously expanding, the number of branches is doubling, the complexity of the line topology is significantly improved, and the length of the power distribution line is relatively short, which makes the operation environment of the power distribution network increasingly complex.

[0003] The existing traveling wave front calibration method mainly relies on traditional single-stage signal decomposition and wave head detection technology. EMD (Empirical Mode Decomposition, Empirical Mode Decomposition) can decompose non-stationary signals into several intrinsic mode functions, but there is a mode aliasing problem. CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) adds multiple sets of white noise with different amplitudes to the original signal and performs ensemble averaging, which effectively suppresses the mode aliasing phenomenon, but single-stage decomposition still cannot fully analyze the fine high-frequency characteristics of the traveling wave signal, especially in the early stage of the fault, the signal amplitude is weak and the high-frequency component is easily covered by noise, resulting in insufficient wave head feature extraction. VMD (Variational Mode Decomposition, Variational Mode Decomposition) decomposes the signal into different frequency modes by solving a constrained optimization problem, and its decomposition effect is highly dependent on the mode number and penalty factor set by the user, while the traditional optimization algorithm converges slowly and is easy to fall into local optimum, often appearing mode aliasing or over-decomposition phenomenon, further reducing the wave head extraction accuracy. In the complex scenarios of the power distribution network such as high transition resistance or fault initial phase angle close to zero, the positioning error of these methods often exceeds 100 meters.

[0004] In summary, the existing technology has low traveling wave front calibration accuracy in the complex power distribution network due to insufficient signal feature extraction, strong decomposition parameter dependence, and limitations of single algorithm wave head calibration, which cannot meet the demand of high-precision fault location. SUMMARY

[0005] The present application aims to at least solve one of the above technical defects, especially the technical defect of low traveling wave front calibration accuracy in the prior art.

[0006] Firstly, this application provides a method for calibrating the traveling wave front of a distribution network based on CEEMD-CPO-VMD, the method comprising:

[0007] Acquire current traveling wave signals in the power distribution network and extract the target traveling wave signal from the current traveling wave signals;

[0008] The target traveling wave signal is decomposed once using CEEMDAN to obtain multiple intrinsic mode function components, and the first high-frequency intrinsic mode function component is taken as the target intrinsic mode function component.

[0009] The target intrinsic mode function components are decomposed twice using the optimized variational mode decomposition to obtain multiple intrinsic mode functions. The variational mode decomposition is obtained by optimizing the number of mode decompositions and the penalty factor using the hog optimization algorithm.

[0010] Energy analysis is performed on each intrinsic mode function to obtain an energy sequence. The time corresponding to the energy peak is extracted from the energy sequence and used as the wavefront time of the current traveling wave signal.

[0011] In one embodiment, the step of extracting the target traveling wave signal from the current traveling wave signal includes:

[0012] The arrival time of the first wavehead of the current traveling wave signal is estimated, and the current traveling wave signal is truncated using a time window of preset width centered on the arrival time of the first wavehead of the traveling wave to obtain the target traveling wave signal.

[0013] In one embodiment, the optimization process of variational mode decomposition includes:

[0014] The fitness function is determined, and based on the fitness function, the Crowned Porcupine optimization algorithm is used to iteratively optimize the number of mode decompositions and the penalty factor of variational mode decomposition through position updates in the exploration and development phases until the maximum number of iterations is reached, thus obtaining the optimal number of mode decompositions and penalty factor. The fitness function is used to minimize the center frequency bandwidth product corresponding to each set of mode decompositions and penalty factor.

[0015] In one embodiment, the fitness function is formulated as follows:

[0016]

[0017] in, This represents the fitness function value. Indicates the first The center frequency-bandwidth product of the eigenmode functions This represents the modal decomposition number.

[0018] In one embodiment, the formula for updating the location during the exploration phase is:

[0019]

[0020] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the location of a randomly selected individual in the population. and This represents a random number generated within the interval [0,1]. Indicates the average position of the population. Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position.

[0021] In one embodiment, the formula for position updates during the development phase is:

[0022]

[0023] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position. and This represents a random number generated within the interval [0,1]. Indicates the first The position of the individual Crowned Porcupine at the next iteration.

[0024] In one embodiment, the step of performing energy analysis on each intrinsic mode function to obtain an energy sequence includes:

[0025] The energy sequence is obtained by calculating each eigenmode function using the Teager energy operator.

[0026] Secondly, this application provides a distribution network traveling wave front calibration device based on CEEMD-CPO-VMD, the device comprising:

[0027] The target traveling wave signal extraction module is used to collect the current traveling wave signal in the distribution network and extract the target traveling wave signal from the current traveling wave signal;

[0028] The target intrinsic mode function component determination module is used to decompose the target traveling wave signal once using CEEMDAN to obtain multiple intrinsic mode function components, and to take the first high-frequency intrinsic mode function component as the target intrinsic mode function component;

[0029] The intrinsic mode function determination module is used to perform a secondary decomposition of the target intrinsic mode function components using the optimized variational mode decomposition to obtain multiple intrinsic mode functions. The variational mode decomposition is obtained by optimizing the number of mode decompositions and the penalty factor using the Crowned Porcupine optimization algorithm.

[0030] The traveling wave front time determination module is used to perform energy analysis on each intrinsic mode function, obtain an energy sequence, and extract the time corresponding to the energy peak in the energy sequence as the traveling wave front time of the current traveling wave signal.

[0031] Thirdly, this application provides a storage medium storing computer-readable instructions, which, when executed by one or more processors, cause the one or more processors to perform the steps of any of the CEEMD-CPO-VMD-based distribution network traveling wave front calibration methods described in the above embodiments.

[0032] Fourthly, this application provides a computer device, including: one or more processors, and a memory;

[0033] The memory stores computer-readable instructions, which, when executed by one or more processors, perform the steps of any of the distribution network traveling wave head calibration methods based on CEEMDAN-CPO-VMD in the above embodiments.

[0034] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0035] The CEEMD-CPO-VMD-based method for traveling wave front calibration in distribution networks provides the following steps: First, CEEMD is used to decompose the target traveling wave signal once, effectively suppressing mode aliasing and extracting the first high-frequency intrinsic mode function component, ensuring that weak high-frequency characteristics in the early stage of a fault are fully preserved. Then, variational mode decomposition optimized by the Crow Pseudo Optimization algorithm (CPO) is used to perform a second decomposition of this high-frequency component, achieving adaptive adjustment of the mode number and penalty factor, thereby avoiding over-decomposition or mode aliasing problems caused by parameter dependence in traditional VMD. Finally, by performing energy analysis on the intrinsic mode functions obtained from the second decomposition and extracting the energy peak time, the traveling wave front of the current traveling wave signal is accurately determined. This method overcomes the problems of existing technologies, such as the difficulty of single decomposition algorithms in analyzing weak high-frequency signals, strong parameter dependence, and insufficient wave front feature extraction. It significantly improves the accuracy of traveling wave front calibration, achieving high-precision fault location in complex distribution networks and meeting the actual needs of high-reliability distribution network operation and maintenance. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 A flowchart illustrating the method for calibrating the traveling wave front of a distribution network based on CEEMD, as provided in this application embodiment;

[0038] Figure 2 Example diagram of a 10kV distribution network simulation model provided in the embodiments of this application;

[0039] Figure 3 An example diagram of the α-line mode component of the M-terminal voltage traveling wave provided in the embodiments of this application;

[0040] Figure 4 Example diagram of the α-line mode component of the N-terminal voltage traveling wave provided in the embodiments of this application;

[0041] Figure 5 Example diagram of the IMF1 components after CEEMDAN decomposition provided in the embodiments of this application;

[0042] Figure 6 Example diagram of the main frequency extraction result of the M-end signal provided in the embodiments of this application;

[0043] Figure 7 Example diagram of the N-terminal signal main frequency extraction result provided in the embodiments of this application;

[0044] Figure 8 Example diagram of wavelet transform wavefront calibration results provided in the embodiments of this application;

[0045] Figure 9 This is an example diagram of the conventional dual-end positioning error variation curve provided in the embodiments of this application;

[0046] Figure 10 A schematic diagram of the structure of the distribution network traveling wave front calibration device based on CEEMD-CPO-VMD provided in the embodiments of this application;

[0047] Figure 11 This is a schematic diagram of the internal structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0048] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0049] This application provides a method for calibrating traveling wave fronts in distribution networks based on CEEMDAN-CPO-VMD. The following embodiments illustrate this method using a computer device as an example. It is understood that the computer device can be any device with data processing capabilities, including but not limited to a single server, server cluster, personal laptop, desktop computer, etc. Figure 1 As shown, the method includes:

[0050] S101: Acquires current traveling wave signals in the distribution network and extracts the target traveling wave signal from the current traveling wave signals.

[0051] Among them, the traveling current signal is an instantaneous current fluctuation signal propagating along the distribution network line, used to reflect the instantaneous information of the fault occurrence. The target traveling wave signal is a specific band signal extracted from the traveling current signal, containing high-frequency components and instantaneous change information in the early stage of the fault, used to accurately locate the traveling wave front. The distribution network consists of overhead lines and cables, with a complex line topology and a large number of branches, which makes the traveling current signal exhibit high-frequency weak amplitude and multi-mode superposition characteristics.

[0052] In practical implementation, current signals in the distribution network can be acquired in real time using a data acquisition device, and the acquired current signals are transmitted to computer equipment for processing in digital form. First, the received current signals are sampled and quantized into a discrete time series. The sampling frequency can be set according to the operating characteristics of the distribution network and the traveling wave propagation speed to ensure that high-frequency transient information in the early stages of a fault is completely captured. Then, the sampled signals are denoised using methods such as digital filters or wavelet denoising to reduce the impact of external electromagnetic interference, measurement noise, and other low-frequency load fluctuations. Next, baseline correction is performed on the signal to eliminate current zero-point drift or offset, stabilizing the signal waveform relative to zero level and improving the accuracy of subsequent feature extraction. Simultaneously, the signal is normalized to map the signal amplitude to a uniform range, ensuring that signal characteristics under different lines and acquisition conditions are comparable and preventing subsequent algorithms from being affected by amplitude differences.

[0053] After preprocessing, the target traveling wave signal is extracted from the processed current signal using digital signal processing algorithms. The processing focuses on preserving high-frequency components and instantaneous changes in the initial stage of the fault, while further suppressing low-frequency load fluctuations and residual noise interference. Extraction methods can employ frequency domain analysis, bandpass filtering, or adaptive filtering strategies to ensure effective isolation of high-frequency traveling wave characteristics. The final target traveling wave signal exhibits clear waveform abrupt changes and energy concentration characteristics, providing reliable input data for subsequent multi-level signal decomposition and wavefront localization.

[0054] The reason for acquiring the traveling wave signal of the current in the distribution network and extracting the target traveling wave signal is understandable. This is because traveling wave signals in the distribution network typically have weak amplitudes and contain high-frequency transient components in the early stages of a fault. Without targeted extraction, these high-frequency characteristics are easily masked by low-frequency load fluctuations and environmental noise, affecting the accuracy of subsequent wavefront localization. By first acquiring the raw traveling wave signal, the instantaneous current changes at the time of the fault can be fully obtained. Subsequently, extracting the target traveling wave signal preserves the high-frequency transient characteristics of the initial fault stage while suppressing low-frequency interference and noise, making the waveform changes more obvious and stable. This processing provides high-quality input signals for subsequent multi-stage signal decomposition and wavefront detection, significantly improving the accuracy of traveling wavefront calibration and enabling accurate fault localization and highly reliable fault diagnosis in complex distribution networks.

[0055] S102: The target traveling wave signal is decomposed once using CEEMDAN to obtain multiple intrinsic mode function components, and the first high-frequency intrinsic mode function component is taken as the target intrinsic mode function component.

[0056] CEEMDAN is an adaptive noise ensemble empirical mode decomposition method. By adding multiple sets of white noise with different amplitudes to the signal and performing ensemble averaging, it can decompose non-stationary signals into multiple intrinsic mode function (IMF) components while effectively suppressing mode aliasing. IMF components are several single-frequency signal components obtained after CEEMDAN decomposition. Each component has local characteristics in time and frequency. The first high-frequency IMF component mainly contains the high-frequency transient information of the signal and is a key signal reflecting the wavefront characteristics in the early stage of a fault. It is used as the target IMF component for subsequent processing.

[0057] In practical implementation, the target traveling wave signal can first be input into the CEEMDAN algorithm for decomposition. During the decomposition process, the signal generates multiple intrinsic mode function (IMF) components iteratively. In each iteration, local extrema are extracted from the residual signal of the current signal, and then an upper and lower envelope are constructed. The current IMF component is obtained by calculating the mean of the envelope and subtracting the mean from the signal. To suppress mode aliasing, white noise with adaptive amplitude adjustment is added to the signal in each iteration, generating several signals with different noise groups, which are then decomposed separately. The decomposition results are then ensemble-averaged to obtain the final IMF components for each iteration. This method ensures that each IMF component is clear and independent in frequency, reducing interference between different frequency components.

[0058] After completing all iterations, a series of intrinsic mode function (IMF) components are obtained, each with a different center frequency and local characteristics. Subsequently, frequency analysis is performed on these IMF components to calculate the instantaneous frequency of each component or to obtain its spectral characteristics through Fourier transform. Simultaneously, energy analysis is combined to calculate the average or peak energy of each component. Using frequency sorting or energy peak sorting methods, the first IMF component from the high-frequency components is selected as the target IMF component output. The selection criteria can be set to the component that satisfies the highest center frequency or the largest energy peak to ensure that it contains high-frequency transient information from the initial stage of the fault.

[0059] It is understandable that CEEMDAN is used to decompose the target traveling wave signal and extract the first high-frequency intrinsic mode function (IMF) component because the high-frequency transient components of the traveling wave signal in the early stage of a fault in the distribution network are weak. Direct single-stage processing is easily masked by low-frequency interference and noise, resulting in insufficient extraction of wavefront features. CEEMDAN decomposition decomposes the signal into multiple IMF components, making each frequency component clear and independent, and effectively suppressing mode aliasing, thus preserving high-frequency transient features. Selecting the first high-frequency IMF component as the target IMF component allows for the concentrated acquisition of key high-frequency information in the early stage of the fault, providing a high-quality input signal for subsequent secondary decomposition and wavefront extraction. This processing significantly improves the accuracy of traveling wavefront identification, ensuring accurate capture of fault wavefronts in complex distribution network environments, thereby enhancing the reliability and response speed of fault location.

[0060] S103: The target intrinsic mode function components are decomposed twice using the optimized variational mode decomposition to obtain multiple intrinsic mode functions. The variational mode decomposition is obtained by optimizing the number of mode decompositions and the penalty factor using the Crowned Porcupine optimization algorithm.

[0061] Variational mode decomposition (VMD) is a method that decomposes a signal into different frequency modes by solving a constrained optimization problem. Each intrinsic mode function (EMF) has local characteristics in time and frequency and is independent of each other, reflecting the local high-frequency and low-frequency information of the signal. The Crowned Pig Optimization Algorithm (CRPA) is an intelligent optimization method used to adaptively determine the number of modes and the penalty factor in VMD, enabling the decomposition process to converge quickly and avoid getting trapped in local optima, thereby ensuring the decomposition effect of the EMFs and the integrity of the high-frequency characteristics.

[0062] In practical implementation, the intrinsic mode function components of the target can be used as input signals and fed into a variational mode decomposition algorithm for secondary decomposition. First, feature analysis is performed on the input signal, including calculating the signal's amplitude range, instantaneous frequency distribution, and energy concentration region. Based on the analysis results, the initial number of modes and the search range for the penalty factor are set. Appropriate settings for the initial number of modes and the penalty factor help ensure that the decomposition results cover the main frequency components of the signal, while avoiding information loss or over-decomposition problems caused by too few or too many modes. Subsequently, the number of modes and the penalty factor are iteratively searched using the Crowned Pig optimization algorithm. In each iteration, the fitness function value is calculated based on the frequency center interval and energy distribution of the current decomposition results, and the parameter combination is updated to gradually approach the optimal decomposition parameters. This ensures that each intrinsic mode function is clearly independent in both the frequency and time domains, effectively preserving the signal's local high-frequency transient characteristics while reducing the risk of mode aliasing.

[0063] After obtaining the optimal parameter combination, a secondary decomposition is performed using these parameters to decompose the target intrinsic mode function components into multiple intrinsic mode functions. Each intrinsic mode function has an independent center frequency and local energy characteristics, which can accurately represent the transient changes and high-frequency characteristics of the signal in different frequency bands. After energy analysis and frequency verification of the decomposed intrinsic mode functions, the component containing the high-frequency characteristics of the initial stage of the fault can be selected as the input signal for subsequent traveling wave front extraction, thereby ensuring the integrity and reliability of the signal characteristics in subsequent processing.

[0064] It is understandable that a secondary decomposition of the target intrinsic mode function components using optimized variational mode decomposition is necessary because the high-frequency transient characteristic amplitude of the traveling wave signal in the early stage of a fault in a distribution network is relatively weak. A single decomposition can easily lead to insufficient signal characteristics or mode aliasing. Traditional VMD methods are highly dependent on the number of modes and the penalty factor; improper parameter selection may result in over-decomposition or local optima. By using the Crowned Porcupine optimization algorithm to adaptively determine the number of modes and the penalty factor for secondary decomposition, it is possible to ensure that each intrinsic mode function is clearly independent in both the frequency and time domains, fully preserving the high-frequency transient information in the target intrinsic mode function components, and avoiding mode aliasing and information loss. This processing provides high-quality signal input for subsequent traveling wave front extraction, thereby significantly improving the accuracy of traveling wave front calibration and enabling accurate identification and reliable location of the wave front in the early stage of a fault in complex distribution networks.

[0065] S104: Perform energy analysis on each intrinsic mode function to obtain an energy sequence, and extract the time corresponding to the energy peak in the energy sequence as the traveling wave head time of the current traveling wave signal.

[0066] The energy sequence is a numerical sequence calculated from the instantaneous energy of the intrinsic mode function over the entire sampling time range, used to reflect the change in signal amplitude over time. The traveling wave front moment is the time point when the current traveling wave signal undergoes a sudden change or a high energy concentration, usually corresponding to the high-frequency transient characteristics at the initial stage of a fault, and serves as a key time reference for fault location and wave front calibration.

[0067] In practical implementation, point-by-point energy calculations can be performed for each intrinsic mode function (IMF). The square of the IMF amplitude at each sampling time is taken as the instantaneous energy value, and these instantaneous energy values ​​are accumulated along the time axis or calculated using a sliding window method to obtain an energy sequence, thereby reflecting the energy distribution of the IMF throughout the entire sampling period. During the sliding window calculation, an appropriate window length and step size can be selected to smooth instantaneous fluctuations and highlight high-energy characteristics, while retaining the high-frequency transient information of the traveling wave front in the early stage of the fault.

[0068] Subsequently, peak detection processing is performed on the generated energy sequence. Local maxima locations are determined by comparing the energy values ​​of adjacent sampling points, identifying each local peak and its corresponding time point. For multiple peaks, they can be sorted and filtered according to energy magnitude, prioritizing the peak with the highest energy or earliest occurrence as the critical moment of the traveling wave front to ensure the capture of high-frequency transient characteristics in the early stages of a fault. Noise peaks with lower energy can be removed by setting energy thresholds or minimum peak spacing to avoid interference. Finally, the filtered energy peak times are determined as the traveling wave front moments of the current traveling wave signal, which can be used for subsequent fault location and wavefront calibration.

[0069] It is understandable that energy analysis is performed on each intrinsic mode function (EMF) to extract the time corresponding to the energy peak. This is because the high-frequency transient characteristic amplitude of the traveling wave signal in the distribution network is weak in the early stage of a fault. Directly judging the wavefront through the time-domain signal is easily affected by low-frequency load fluctuations and noise interference, leading to inaccurate wavefront time extraction. By calculating the energy sequence of the EMF, the high-frequency transient characteristics can be quantized into energy peaks in time, thereby effectively highlighting the key signals in the early stage of the fault. Extracting the time corresponding to the energy peak as the traveling wavefront time can accurately locate the current wavefront in the early stage of the fault, providing a reliable time reference for subsequent fault location and wavefront calibration. This processing method can significantly improve the accuracy of traveling wavefront identification, ensuring accurate capture of fault wavefronts in complex distribution network environments and achieving highly reliable fault location.

[0070] In the above embodiment, the target traveling wave signal is first decomposed using CEEMDAN to effectively suppress mode aliasing and extract the first high-frequency intrinsic mode function component, ensuring that weak high-frequency characteristics in the early stage of the fault are fully preserved. Subsequently, the high-frequency component is decomposed a second time using variational mode decomposition optimized by the Crow Pseudo Optimization algorithm (CPO), achieving adaptive adjustment of the number of modes and the penalty factor, thereby avoiding over-decomposition or mode aliasing problems caused by parameter dependence in traditional VMD. Finally, by performing energy analysis on the intrinsic mode functions obtained from the second decomposition and extracting the energy peak time, the traveling wave front of the current traveling wave signal is accurately determined. This method overcomes the problems of existing technologies, such as the difficulty of single decomposition algorithms in parsing weak high-frequency signals, strong dependence on decomposition parameters, and insufficient extraction of wave front features. It significantly improves the accuracy of traveling wave front calibration, achieves high-precision fault location in complex distribution networks, and meets the actual needs of high-reliability distribution network operation and maintenance.

[0071] In one embodiment, the step of extracting the target traveling wave signal from the current traveling wave signal includes:

[0072] The arrival time of the first wavehead of the current traveling wave signal is estimated, and the current traveling wave signal is truncated using a time window of preset width centered on the arrival time of the first wavehead of the traveling wave to obtain the target traveling wave signal.

[0073] The arrival time of the first wavefront of the traveling wave refers to the moment when the current traveling wave signal first shows a significant amplitude change or energy peak, usually corresponding to the instant the wavefront arrives at the measurement point in the early stage of a fault. The preset width time window is a time period centered on the arrival time of the first wavefront of the traveling wave and with a pre-set length, used to extract signal segments containing key transient characteristics from the current traveling wave signal.

[0074] In practical implementation, the acquired current traveling wave signal can first be preprocessed to eliminate environmental interference and measurement errors, and improve the stability and reliability of signal characteristics. Preprocessing may include noise reduction to filter out random noise and power frequency interference introduced during the acquisition process, and normalization of the signal amplitude to ensure uniformity of signal amplitude at different acquisition points, facilitating subsequent analysis and comparison. Subsequently, the preprocessed current traveling wave signal is analyzed using traveling wave characteristic prediction methods. Based on the signal amplitude change rate, instantaneous energy distribution, or frequency domain characteristics, the estimated arrival time of the first wavefront can be calculated, thereby initially determining the critical time point of the fault traveling wave.

[0075] After obtaining the estimated arrival time of the first wavefront, the start and end times of signal interception are calculated using this time as the center and according to a pre-set time window length. The time window width can be set according to the traveling wave propagation characteristics and sampling rate of the distribution network. For example, in practical applications, a window length of 0.5 milliseconds can be selected to ensure that the first wavefront and its key transient features before and after it are included. During the interception process, the time boundaries can be fine-tuned and interpolated to ensure that the target traveling wave signal is continuous and complete on the time axis, while avoiding signal feature loss due to insufficient sampling points or boundary truncation.

[0076] Subsequently, the captured target traveling wave signal can be subjected to phase mode transformation, such as using Kelvin phase mode transformation, to extract the linear mode components of the fault traveling wave signal, which can then be used as input signals for subsequent signal processing and wavefront analysis. This processing effectively highlights the high-frequency transient characteristics before and after the first wavefront, suppresses low-frequency load fluctuations and environmental noise interference, and ensures that the target traveling wave signal contains complete initial fault information, providing clear and stable input data for subsequent multi-level decomposition, energy analysis, and traveling wavefront calibration.

[0077] It is understandable that estimating the arrival time of the first wavefront in a traveling wave signal and using it as the center to extract the target traveling wave signal is necessary because the high-frequency transient characteristic amplitude of the traveling wave signal in the early stages of a distribution network fault is low. Directly processing the complete signal is easily affected by low-frequency load fluctuations and noise interference, making it difficult to accurately identify the wavefront characteristics. By estimating the arrival time of the first wavefront and using a preset-width time window centered on that time to extract the signal, key high-frequency transient information in the early stages of the fault can be retained, while redundant signals and interference are eliminated, resulting in a clear and stable target traveling wave signal. This processing method can provide high-quality input signals for subsequent multi-level decomposition and wavefront calibration, thereby significantly improving the accuracy of traveling wavefront identification and the reliability of wavefront location in the early stages of faults in complex distribution networks.

[0078] In one embodiment, the optimization process of variational mode decomposition includes:

[0079] The fitness function is determined, and based on the fitness function, the Crowned Porcupine optimization algorithm is used to iteratively optimize the number of mode decompositions and the penalty factor of variational mode decomposition through position updates in the exploration and development phases until the maximum number of iterations is reached, thus obtaining the optimal number of mode decompositions and penalty factor. The fitness function is used to minimize the center frequency bandwidth product corresponding to each set of mode decompositions and penalty factor.

[0080] The fitness function evaluates the effectiveness of different combinations of mode decomposition numbers and penalty factors in variational mode decomposition. It is defined as the magnitude of the center frequency-bandwidth product for each set of parameters. The center frequency-bandwidth product measures the frequency concentration and independence of each intrinsic mode function; a smaller value indicates a more ideal mode decomposition effect. The mode decomposition number is the number of decomposition levels set during variational mode decomposition, determining how many intrinsic mode functions the signal is decomposed into. The penalty factor is a weighting coefficient in a constrained optimization problem, used to balance signal reconstruction error and the smoothness of mode decomposition.

[0081] A fitness function is defined to evaluate the quality of the combination of variational mode decomposition parameters. The fitness function aims to minimize the center frequency-bandwidth product of the number of mode decompositions and the penalty factor for each group. The center frequency-bandwidth product measures the concentration and independence of each intrinsic mode function in terms of frequency; the smaller the value, the more ideal the decomposition effect.

[0082] First, the initial parameter combination for variational mode decomposition (VMD), namely the number of modes k and the penalty factor α, can be set to control the number of modes and the constraint strength of the signal decomposition. Then, the target signal to be analyzed is input into the VMD algorithm. Based on the current parameter combination k and α, the signal is decomposed into k intrinsic mode functions (IMFs) through iterative optimization. Each IMF represents a local oscillation mode of the signal in the time domain and has relatively concentrated and independent frequency characteristics in the frequency domain.

[0083] For each intrinsic mode function obtained from the decomposition, its spectral information is first calculated using Fourier transform, and then the center frequency of the mode is obtained by weighted averaging of the spectrum. The center frequency reflects the location of the dominant oscillation frequency of the mode. Next, the frequency bandwidth of the mode is calculated based on the standard deviation of the spectrum or based on the energy distribution to represent the degree of mode diffusion in the frequency domain. Multiplying the center frequency by the corresponding frequency bandwidth yields the center frequency-bandwidth product of the mode. The smaller the value of the center frequency-bandwidth product, the more concentrated the mode is in frequency and the more independent it is from other modes.

[0084] A certain number of candidate solutions are initialized using the Crowned Porcupine optimization algorithm. Each candidate solution corresponds to a set of mode decomposition numbers and a penalty factor, where the search range of the mode decomposition number k is 2 to 10, and the search range of the penalty factor α is 100 to 2000. The population size can be set to 30. Each candidate solution is randomly generated within the above parameter range during the initial iteration to ensure sufficient search space coverage.

[0085] During the iteration process, the position of each candidate solution in the exploration phase is first updated to allow for a broad search within the parameter space. By randomly or probabilistically adjusting the modality decomposition number and penalty factor of the candidate solutions, sufficient coverage of the entire search space is achieved to discover potentially superior parameter combinations. Subsequently, in the development phase, the candidate solutions are fine-tuned in local parameter regions. Through small-amplitude parameter perturbations and local search optimization, the center frequency-bandwidth product corresponding to each set of candidate solutions is further reduced, thereby improving the frequency concentration and independence of each intrinsic mode function in the variational mode decomposition results.

[0086] In each iteration, the fitness function is continuously calculated to evaluate the merits of each candidate solution's parameter combination. Candidate solutions are retained, updated, or replaced based on their fitness values ​​to ensure the population converges towards the optimal solution. This iterative process continues until a preset maximum number of iterations is reached, such as 50. By comprehensively considering the global search in the exploration phase and the local fine-tuning in the development phase, the parameter combination with the smallest fitness function value is finally selected from all candidate solutions; this is the optimal mode decomposition number k and penalty factor α. This approach ensures adaptive optimization of variational mode decomposition parameters, improves the accuracy of signal decomposition and the clarity of modal features, and provides high-quality input signals for subsequent traveling wavefront extraction.

[0087] It is understandable that determining the fitness function and iteratively optimizing the number of mode decompositions and the penalty factor of variational mode decomposition using the Crowned Porcupine optimization algorithm based on this function is necessary because the decomposition effect of variational mode decomposition is highly dependent on parameter selection. Inappropriate parameters can easily lead to mode aliasing or over-decomposition, reducing the accuracy of signal feature extraction. By defining a fitness function to minimize the center frequency-bandwidth product corresponding to each set of parameters, and combining global search in the exploration phase with local fine-tuning in the development phase, the optimal number of mode decompositions and the penalty factor can be adaptively found in the parameter space, ensuring that each intrinsic mode function is reasonably and independently distributed in the frequency and time domains. This approach can significantly improve the decomposition quality of the target signal by variational mode decomposition, preserve the high-frequency transient characteristics of the fault traveling wave signal, and provide a high-quality and stable input signal for subsequent traveling wave front extraction, thereby improving the accuracy of traveling wave front calibration and the reliability of initial fault front location in complex distribution networks.

[0088] In one embodiment, the fitness function is formulated as follows:

[0089]

[0090] in, This represents the fitness function value. Indicates the first The center frequency-bandwidth product of the eigenmode functions This represents the modal decomposition number.

[0091] In this embodiment, the formula sums the center-frequency bandwidth products of all intrinsic mode functions, comprehensively evaluating the frequency concentration and independence of each mode as an overall index to measure the overall quality of the current combination of mode decomposition parameters for signal decomposition. By minimizing this fitness function, each intrinsic mode function can be made as frequency-concentrated and independent as possible, thereby improving the clarity and distinguishability of the decomposition results. Using this formula for evaluation enables adaptive optimization of the number of mode decompositions and the penalty factor, significantly improving the accuracy of signal decomposition and providing high-quality, characteristic input signals for subsequent traveling wave front extraction, thus contributing to enhanced accuracy and reliability of fault detection.

[0092] In one embodiment, the formula for updating the location during the exploration phase is:

[0093]

[0094] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the location of a randomly selected individual in the population. and This represents a random number generated within the interval [0,1]. Indicates the average position of the population. Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position.

[0095] In this embodiment, the formula updates candidate solutions in the parameter space by combining random individual positions, population average positions, and the current global optimum position. This allows the solution to cover a wide search area while moving closer to potentially superior solutions during the exploration phase. The introduced random factor increases search diversity, avoids iterative optima, and guides and approximates high-quality regions by adjusting the deviation from the global optimum and average position. Using this method for position updating effectively enhances the global search capability of parameter optimization, increases the likelihood of discovering the optimal modal decomposition number and penalty factor, thereby improving the accuracy of signal decomposition and the clarity of modal features, providing high-quality input signals for subsequent traveling wave head extraction.

[0096] In one embodiment, the formula for position updates during the development phase is:

[0097]

[0098] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position. and This represents a random number generated within the interval [0,1]. Indicates the first The position of the individual Crowned Porcupine at the next iteration.

[0099] In this embodiment, the formula adjusts the position by the distance between the candidate solution and the current global optimum, causing individuals to concentrate in the optimal region during the development phase. Simultaneously, a random factor is introduced to fine-tune the local search, increasing the precision and flexibility of parameter optimization. Using this method for position updating improves the search accuracy of candidate solutions near superior solutions, accelerates convergence, and reduces local oscillations. This optimizes the selection of the mode decomposition number and penalty factor, improves the stability of signal decomposition, and enhances the frequency concentration of the intrinsic mode functions, providing a high-quality input signal for subsequent traveling wave head calibration.

[0100] In one embodiment, the step of performing energy analysis on each intrinsic mode function to obtain an energy sequence includes:

[0101] The energy sequence is obtained by calculating each eigenmode function using the Teager energy operator.

[0102] In practical implementation, intrinsic mode functions (EMFs) refer to the time-domain signal components obtained through signal decomposition methods. Each component reflects the local oscillation characteristics of the original signal in the time domain and has relatively concentrated and independent frequency characteristics in the frequency domain. The Teager energy operator is a nonlinear operator used to measure the instantaneous energy change of a signal at each sampling moment, reflecting the signal's local amplitude and frequency characteristics. The energy sequence is the sequence of energy values ​​calculated by applying the Teager energy operator to each EMF at consecutive sampling points, used to analyze the transient characteristics of the signal.

[0103] First, each intrinsic mode function (EMF) is sequentially input into the Teager energy operator calculation process. Specifically, the amplitude of the function at each sampling point and the amplitudes at adjacent points are calculated to obtain the energy value at that moment. The energy values ​​at all moments are then arranged in chronological order to form a complete energy sequence. This process can be implemented through iterative calculation or vectorized operations to ensure computational efficiency and the accuracy of the results. During the calculation process, noise interference or amplitude anomalies can be smoothed or thresholded to enhance the sensitivity and stability of the energy sequence to transient changes in the real signal.

[0104] Using the Teager energy operator to process each intrinsic mode function can highlight the transient high-frequency characteristics in the signal and accurately reflect the energy concentration at the arrival time of the first wavefront of the traveling wave. The obtained energy sequence can provide accurate time and amplitude references for subsequent wavefront detection and traveling wave signal feature extraction, which helps to improve the accuracy and reliability of traveling wavefront calibration, while reducing noise interference to signal feature recognition, and realizing high-precision analysis and processing of traveling wave signals of distribution network current.

[0105] Furthermore, the energy of each intrinsic mode function obtained through variational mode decomposition is calculated using the Teager energy operator to obtain the corresponding energy sequence. Then, the sampling time t0 corresponding to the maximum value in each energy sequence is selected, and t0 is calibrated as the arrival time of the traveling wavefront. Compared to the method of wavefront calibration using only CEEMDAN single decomposition, this method can reduce the wavefront calibration error from 100 meters to within 80 meters. Although the IMF1 obtained through CEEMDAN single decomposition has extracted the high-frequency transient features of the signal, there may still be detail aliasing. Therefore, it is necessary to further refine the IMF1 through variational mode decomposition to more accurately separate the signal according to frequency bands. In specific operation, using IMF1 as input, the optimal parameters k and α obtained by CPO optimization are used to construct the variational constraint model of VMD:

[0106]

[0107] in, This represents the impulse function, used to capture instantaneous changes in a signal; * indicates convolution operation. This represents the nth IMF (Intrinsic Mode Function) component obtained after VMD decomposition. for The corresponding center frequency. The instantaneous frequency is extracted by minimizing the time-frequency compactness error of each mode, and then multiplied by... The center frequency is constrained to minimize the sum of the time-frequency spread of all modes, while ensuring that the sum of all modes equals the input IMF1. When solving this constrained optimization problem, the Lagrange multiplier method is used to reduce mode aliasing in the final quadratic decomposition mode set.

[0108] The core characteristic of a traveling wavefront is its large instantaneous amplitude change, while the Teager energy operator has extremely high sensitivity to instantaneous changes in the signal, amplifying the energy characteristics of the wavefront. Its discrete-form calculation formula is as follows:

[0109]

[0110] In the formula, IMF VMD The amplitude at the nth sampling point; The Teager energy value at this sampling point is shown. Because the signal changes most drastically at the wavefront, the Teager energy value will exhibit a significant peak. Therefore, the energy sequence is extracted. The maximum value E in max The corresponding sampling time This refers to the "sampling point number of the wavefront arrival time"; combined with the sampling period Ts, the precise arrival time of the wavefront can be calculated:

[0111]

[0112] CEEMDAN's first decomposition involves adding multiple sets of white noise of different amplitudes to the original traveling wave signal, performing EMD decomposition on each set of noisy signals to obtain IMF components, and then ensembling the multiple IMF components to obtain a stable set of IMF components. This process effectively suppresses the mode aliasing phenomenon of traditional EMD, providing cleaner high-frequency characteristic components for subsequent second-order decomposition. After completing step five and calibrating the wavefront, the time error of the traveling wave's transmission speed v in the distribution network line multiplied by the wavefront arrival time is directly converted into distance error, and the two satisfy the following relationship:

[0113]

[0114] In the formula, The speed at which the traveling wave travels through the distribution network line is denoted as _____. Because the wavefront calibration error of this method is low, the final fault location error can be controlled within 80m.

[0115] The following is a specific application example of the distribution network traveling wave front calibration method based on CEEMDAN-CPO-VMD.

[0116] PSCAD was used for simulation verification, and a simulation environment was built for example. Figure 2The classic distribution network model shown is set to a voltage level of 220kV, and considering the frequency-dependent attenuation characteristics of the line, a distributed parameter model is used for the line. It is assumed that at a certain moment, a single-phase ground fault occurs on phase A of the line at point F, 80km from the measurement point M, with a transition resistance of 10Ω, an initial phase angle of 90°, and a sampling frequency of 10MHz.

[0117] The acquired traveling current signal undergoes data preprocessing and primary decomposition. The arrival times of the first wavefront at measurement points M and N are calibrated. Using this calibration time as the center, a time window of 0.5 ms is used to capture the first wavefront signal, followed by phase-mode transformation to extract the linear mode component x. m and x n And then db50 white noise was added to it to simulate the noise under real working conditions, and the results are as follows. Figure 3 and Figure 4 As shown. The CEEMDAN algorithm is used to process the linear mode signal x. m and x n Modal decomposition was performed to extract the highest frequency component (IMF1), and an FFT was applied to IMF1. The frequency corresponding to the maximum energy value in the frequency domain was selected as the dominant frequency of the traveling wave signal, providing input for subsequent secondary decomposition. The results are as follows: Figure 5 As shown.

[0118] According to the set parameter range and rules, the Crowned Porcupine optimization algorithm was executed to optimize the parameters of Variational Mode Decomposition (VMD). First, the population parameters were initialized, with a population size of 30 and a maximum number of iterations of 50. The fitness function aimed to minimize the center frequency-bandwidth product of each mode after VMD decomposition. After 50 iterations and convergence, the optimal parameter combination k*=5 and α*=850 was obtained. Subsequently, the optimal parameters were used to perform a secondary VMD decomposition on the IMF1 extracted by CEEMDAN, obtaining five intrinsic mode functions (IMFVMD1~IMFVMD5). Then, the Teager energy operator was used to calculate the energy sequence of each IMFVMD, and the time corresponding to the maximum value of the energy sequence was extracted. Figure 6 and Figure 7 It can be seen that the arrival time t of the wavefront at the M end is obtained respectively. M =276.3μs, arrival time t of the N-end wavefront N =404.1μs, and the calculated time difference Δt =127.8μs.

[0119] To further verify the advantages of the method presented in this chapter, a comparative analysis was adopted. Existing wavelet-based traveling wave localization methods were selected as a control group. The db6 wavelet was used to process the M and N-end detection waveforms under the same fault conditions, and the arrival time of the first wave head was extracted. Figure 8 As shown. By Figure 8It can be seen that, after wavelet transform calibration, the time for the first wavehead of the traveling wave to reach the detection point M is t. m =277.8μs, the time to reach detection point N is t n =405.7μs. Traditional wavelet-based two-end positioning methods are affected by wave velocity selection and two-end time synchronization errors. Assuming the wave velocity varies from 298.5 to 300 m / μs, and incorporating a time synchronization error of -3 to 3 μs in the calculation, the final results show the impact of wave velocity and time synchronization error on positioning error. Figure 9 As shown. By Figure 9 It can be seen that when the wave velocity is 298.5 m / μs and the time synchronization error is 3 μs, the maximum positioning error reaches 1358 m, while when the wave velocity is 300 m / μs and the time synchronization error is -3 μs, the minimum positioning error is 365.7 m, both of which are much higher than the positioning accuracy of the method proposed in this chapter. Based on the above comparative analysis, it can be seen that the algorithm in this chapter can effectively reduce the positioning error caused by the difficulty of wavefront calibration and wave velocity selection, while avoiding the influence of dual-end time synchronization error on the positioning results, improving the dual-end positioning accuracy, and finally the positioning error is only 114 m.

[0120] To further verify the adaptability of the method presented in this chapter under different fault scenarios, simulation verification was conducted considering application scenarios with different fault distances and fault types. The method presented in this chapter was used to analyze the signals at both ends of the measurement point and locate the fault, and the results were compared with the actual set fault distances to calculate the location error. Different fault points F1~F5 were set in the distribution network model, where the distance between F1 and the M end is d1=50km, F2 and the M end is d2=80km, F3 and the M end is d3=115km, F4 and the M end is d4=135km, and F5 and the M end is d5=155km. The fault transition resistance was set to 10Ω for all faults, and the initial phase angle of the fault was set to 90° for all faults. The fault location was performed using the method presented in this chapter, and the error was calculated. The results are shown in the table below.

[0121]

[0122] To further pinpoint the fault location, fault points F1, F3, and F5 were selected for analysis. At these three fault points, A-phase ground fault (AG), AB-phase inter-fault (AB), AB-phase inter-ground fault (ABG), and three-phase ground fault (ABCG) were generated, respectively. The fault transition resistance was set to 10Ω for all faults, and the initial phase angle was set to 90°. The method described in this chapter was used for fault location, and the location error was calculated. The results are shown in the table below. Simulation results show that this patented method can effectively eliminate the location error caused by wave velocity selection, while avoiding the influence of time synchronization errors in double-ended traveling wave location, thus improving the location accuracy of double-ended traveling wave in distribution networks. Accurate location can be achieved under various fault conditions, including different fault locations, different fault types, different transition resistances, and different initial phase angles, with the location error generally controlled within ±100m.

[0123]

[0124] The following describes the distribution network traveling wave front calibration device based on CEEMD-CPO-VMD provided in the embodiments of this application. The distribution network traveling wave front calibration device based on CEEMD-CPO-VMD described below can be referred to in correspondence with the distribution network traveling wave front calibration method based on CEEMD-CPO-VMD described above. Figure 10 As shown, this application provides a distribution network traveling wave front calibration device based on CEEMD-CPO-VMD, the device comprising:

[0125] The target traveling wave signal extraction module 201 is used to collect the current traveling wave signal in the power distribution network and extract the target traveling wave signal from the current traveling wave signal.

[0126] The target intrinsic mode function component determination module 202 is used to decompose the target traveling wave signal once using CEEMDAN to obtain multiple intrinsic mode function components, and to take the first high-frequency intrinsic mode function component as the target intrinsic mode function component;

[0127] The intrinsic mode function determination module 203 is used to perform a secondary decomposition of the target intrinsic mode function components using the optimized variational mode decomposition to obtain multiple intrinsic mode functions. The variational mode decomposition is obtained by optimizing the number of mode decompositions and the penalty factor using the Crowned Porcupine optimization algorithm.

[0128] The traveling wave head time determination module 204 is used to perform energy analysis on each intrinsic mode function, obtain an energy sequence, and extract the time corresponding to the energy peak in the energy sequence as the traveling wave head time of the current traveling wave signal.

[0129] In one embodiment, the target traveling wave signal extraction module 201 includes:

[0130] The target traveling wave signal extraction unit is used to estimate the arrival time of the first wave head in the current traveling wave signal, and to extract the current traveling wave signal using a time window of preset width centered on the arrival time of the first wave head, so as to obtain the target traveling wave signal.

[0131] In one embodiment, the intrinsic mode function determination module 203 includes:

[0132] The variational mode decomposition optimization unit is used to determine the fitness function. Based on the fitness function, the Crowned Porcupine optimization algorithm is used to iteratively optimize the number of mode decompositions and the penalty factor of the variational mode decomposition through position updates in the exploration and development phases until the maximum number of iterations is reached, and the optimal number of mode decompositions and penalty factor are obtained. The fitness function is used to minimize the center frequency-bandwidth product corresponding to each set of mode decompositions and penalty factor.

[0133] In one embodiment, the fitness function is formulated as follows:

[0134]

[0135] in, This represents the fitness function value. Indicates the first The center frequency-bandwidth product of the eigenmode functions This represents the modal decomposition number.

[0136] In one embodiment, the formula for updating the location during the exploration phase is:

[0137]

[0138] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the location of a randomly selected individual in the population. and This represents a random number generated within the interval [0,1]. Indicates the average position of the population. Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position.

[0139] In one embodiment, the formula for position updates during the development phase is:

[0140]

[0141] in, Indicates the first The position of the individual crowned porcupine at the next iteration. This indicates the current globally optimal position. and This represents a random number generated within the interval [0,1]. Indicates the first The position of the individual Crowned Porcupine at the next iteration.

[0142] In one embodiment, the traveling wave head timing determination module 204 includes:

[0143] The energy sequence determination unit is used to calculate the energy sequence for each intrinsic mode function using the Teager energy operator.

[0144] 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 traveling wavefront calibration method based on CEEMDAN-CPO-VMD as described in any of the above embodiments.

[0145] 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 traveling wave head calibration method based on CEEMDAN-CPO-VMD as described in any of the above embodiments.

[0146] Indicatively, such as Figure 11 As shown, Figure 11 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 1 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 CEEMD-CPO-VMD-based distribution network traveling wavefront calibration method of any of the above embodiments.

[0147] 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.

[0148] Those skilled in the art will understand that Figure 11The 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.

[0149] 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.

[0150] 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.

[0151] 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 traveling wave front calibration method based on CEEMDAN-CPO-VMD, characterized in that, The method comprises: Collecting a current traveling wave signal in a power distribution network, and extracting a target traveling wave signal from the current traveling wave signal; Performing primary decomposition on the target traveling wave signal by using CEEMDAN to obtain a plurality of intrinsic mode function components, and taking a first high-frequency intrinsic mode function component as a target intrinsic mode function component; Performing secondary decomposition on the target intrinsic mode function component by using an optimized variational mode decomposition to obtain a plurality of intrinsic mode functions, the variational mode decomposition being obtained by optimizing a mode decomposition number and a penalty factor by using a Gao-Hogei optimization algorithm; Performing energy analysis on each intrinsic mode function to obtain an energy sequence, and extracting a time corresponding to an energy peak value in the energy sequence as a traveling wave front time of the current traveling wave signal.

2. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 1, characterized in that, The step of extracting a target traveling wave signal from the current traveling wave signal comprises: Estimating a traveling wave front arrival time in the current traveling wave signal, and taking the traveling wave front arrival time as a center to intercept the current traveling wave signal by using a time window with a preset width to obtain the target traveling wave signal.

3. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 1, characterized in that, The optimization process of the variational mode decomposition comprises: Determining a fitness function, and based on the fitness function, performing iterative optimization on a mode decomposition number and a penalty factor of the variational mode decomposition by using the Gao-Hogei optimization algorithm through position updates in an exploration stage and a development stage until a maximum iteration number is reached to obtain an optimal mode decomposition number and penalty factor, wherein the fitness function is used to minimize a center frequency bandwidth product corresponding to each group of mode decomposition number and penalty factor.

4. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 3, characterized in that, The formula of the fitness function is: wherein denotes a fitness function value, denotes the center frequency-band product of the th eigenmode function, denotes the number of mode decompositions.

5. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 3, characterized in that, The formula of the position update in the exploration stage is: wherein, represents the position of the crown-hyena individual at the th iteration, represents a randomly selected population individual position, and represents a random number generated in the interval [0, 1], represents the population average position, represents the position of the crown-hyena individual at the th iteration, represents the current global optimum position.

6. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 3, characterized in that, The formula of the position update in the development stage is: wherein, denotes the position of the th iteration of the th iteration of the th iteration of the denotes a random number generated in the interval [0, 1], denotes the position of the th iteration of the 7. The CEEMDAN-CPO-VMD-based power distribution network traveling wave front calibration method according to claim 1, characterized in that, The step of performing energy analysis on each intrinsic mode function to obtain an energy sequence comprises: Calculating each intrinsic mode function by using a Teager energy operator to obtain the energy sequence.

8. A power distribution network wave head calibration device based on CEEMDAN-CPO-VMD, characterized in that, The device comprises: A target traveling wave signal extraction module configured to collect a current traveling wave signal in a power distribution network, and extract a target traveling wave signal from the current traveling wave signal; A target intrinsic mode function component determination module configured to perform primary decomposition on the target traveling wave signal by using CEEMDAN to obtain a plurality of intrinsic mode function components, and take a first high-frequency intrinsic mode function component as a target intrinsic mode function component; An intrinsic mode function determination module configured to perform secondary decomposition on the target intrinsic mode function component by using an optimized variational mode decomposition to obtain a plurality of intrinsic mode functions, the variational mode decomposition being obtained by optimizing a mode decomposition number and a penalty factor by using a Gao-Hogei optimization algorithm; A traveling wave front time determination module configured to perform energy analysis on each intrinsic mode function to obtain an energy sequence, and extract a time corresponding to an energy peak value in the energy sequence as a traveling wave front time of the current traveling wave signal.

9. A storage medium characterized by: The storage medium has computer readable instructions stored therein, and the computer readable instructions, when executed by one or more processors, cause the one or more processors to perform the steps of the power distribution network traveling wave front calibration method based on CEEMDAN-CPO-VMD as claimed in any one of claims 1 to 7.

10. A computer device, comprising: Comprise: One or more processors, and a memory; The memory has computer readable instructions stored therein, and the computer readable instructions, when executed by the one or more processors, perform the steps of the power distribution network traveling wave front calibration method based on CEEMDAN-CPO-VMD as claimed in any one of claims 1 to 7.

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