Medium and low voltage distribution network fault on-line detection method based on cross wavelet coherence analysis

Abstract

The invention relates to the technical field of electric power operation and maintenance, and particularly discloses a middle and low voltage distribution network fault online detection method based on cross wavelet coherence analysis, which comprises the following steps: carrying out cross wavelet coherence analysis on zero-sequence current of all lines, finding out a common high-energy frequency band, and selecting the line current with the highest energy as a detection object; monitoring the selected current sequence by using a sliding window method, and dividing the current sequence into small time periods for detection; analyzing the current waveform in each time window through a fractal theory, calculating the fractal dimension of the current waveform, and constructing a multi-scale fractal dimension feature vector; and using a Dirichlet process Gaussian mixture model to perform clustering analysis on the feature vectors so as to accurately identify faults. According to the medium and low voltage power distribution network fault online detection method based on cross wavelet coherence analysis, the optimal frequency band / scale can be determined in a self-adaptive mode, rapid fault detection is achieved in a short time window, and therefore the efficiency and accuracy of fault detection are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electric power operation and maintenance, and in particular to an online fault detection method for medium and low voltage distribution networks based on cross wavelet coherence analysis. Background Art

[0002] During the operation of medium and low voltage distribution networks, they often face the challenge of single-phase grounding faults, which have complex patterns and evolution characteristics such as instantaneous and weak. Since the initial fault resistance is usually high and the fault current is weak, traditional protection methods based on power frequency quantities often have difficulty in effectively detecting these faults, resulting in untimely fault handling of medium and low voltage distribution networks, which in turn causes serious power outage losses and electrocution deaths.

[0003] Existing fault detection methods are mostly based on single feature quantities or local fault features, which have the following main problems:

[0004] First, the sensitivity and reliability of fault detection are not high, especially in the detection of weak fault currents, which can easily lead to missed or misjudgment;

[0005] Secondly, it is difficult to extract fault features, which makes it difficult to fully reflect the time domain characteristics of fault signals, affecting the accuracy of fault identification;

[0006] Thirdly, the threshold selection has poor flexibility and often needs to be set based on experience, which makes it difficult to adapt to different fault conditions;

[0007] In addition, the real-time requirement is high, and the existing detection methods are difficult to meet the demand for rapid response in terms of processing speed;

[0008] Finally, since the distribution lines are short and do not transpose, the fault waveform appears as a series of aliased time-varying traveling waves. The distribution of fault characteristics under different line structures and fault conditions varies greatly, making it difficult to effectively extract signal scale / frequency band characteristics.

[0009] In response to the above problems, those skilled in the art have been seeking a method that can improve the sensitivity and reliability of fault detection, has good adaptability, does not require a preset fixed threshold, and can achieve real-time detection.

[0010] In view of this, the present invention proposes an online fault detection method for medium and low voltage distribution networks based on cross wavelet coherence analysis, which is used to adaptively determine the optimal frequency band / scale and realize rapid fault detection within a shorter time window, thereby significantly improving the efficiency and accuracy of fault detection. Summary of the invention

[0011] An object of the present invention is to provide an online fault detection method for medium and low voltage distribution networks based on cross wavelet coherence analysis. By adopting technical means such as fractal theory, Dirichlet process Gaussian mixture model and sliding window method, the optimal frequency band / scale can be adaptively determined, and rapid fault detection can be achieved within a shorter time window, thereby significantly improving the efficiency and accuracy of fault detection.

[0012] To achieve the above objectives, the present invention provides a method for online detection of faults in medium and low voltage distribution networks based on cross wavelet coherence analysis, comprising:

[0013] S10: Obtain the zero-sequence currents of all lines, perform cross-wavelet coherence analysis on each line, and determine the frequency band with the largest content in the zero-sequence current signal of each line as the best frequency band / scale for subsequent transformation based on the time-frequency region with the stronger cross-wavelet power spectrum density, and select the zero-sequence current of the line with the largest energy as the sequence to be detected in the fault detection method;

[0014] S20: Based on the real-time requirement, the sliding window method is used to perform sliding detection on the sequence to be detected, and the waveform sequence is divided into shorter time windows;

[0015] S30: Extract the time domain features of the sequence in the sliding window based on fractal theory, use the box counting method to calculate the minimum number of boxes covering the waveform texture, change the size of the box covering the waveform to estimate the fractal dimension, calculate the fractal dimension of the waveform at different scales, and construct the multi-scale fractal dimension vector of zero-sequence current;

[0016] S40: A clustering method based on the Dirichlet process Gaussian mixture model is used to perform fault detection on the extracted feature vectors to achieve accurate fault identification.

[0017] Optionally, the S10 includes:

[0018] S101: Obtain zero-sequence current of all lines within the time range of 1ms before and 15ms after startup; the sampling rate is f s =1MHz, sampling interval t s =1μs, record the start time as t0;

[0019] S102: Take the line zero-sequence current i1ms before and 5ms after the start time 0m (j), m is the line number, j is the sampling number; calculate the energy E of the zero-sequence current of line m m , the calculation formula is

[0020] (1);

[0021] Where N is the total number of sampling points and M is the total number of lines. mThe largest line x is used as the reference line;

[0022] (2);

[0023] S103: Taking line x as the reference line, cross wavelet transform is performed with zero-sequence currents of other lines to obtain cross wavelet power spectrum density; the calculation process is:

[0024] For the zero-sequence current signals of the two lines and , its cross wavelet transform and cross wavelet power spectrum density are expressed by equation (3) and equation (4);

[0025] (3);

[0026] (4);

[0027] In the formula, is the cross wavelet transform, is the cross wavelet power spectral density, The larger it is, the greater the coherence of the two signals. , The zero-sequence current signal , The wavelet transform of is defined by equation (5); * represents complex conjugate;

[0028] (5);

[0029] Where, ψ is the mother wavelet; a (a>0) is the scale operator; b is the shift operator; * represents the complex conjugate;

[0030] The complex wavelet function - Morlet wavelet is selected as the mother wavelet function, and its mathematical expression is

[0031] (6);

[0032] The calculation results of the cross wavelet power spectrum density are normalized; the normalized cross wavelet power spectrum density is actually the "significance level" in the statistical sense; the time-frequency point set B whose cross wavelet power spectrum density satisfies equation (7) is defined as the "high correlation time-frequency space" of line m and reference line x;

[0033] (7);

[0034] Where σ x , σ m are the zero-sequence current standard deviations of line x and line m respectively;

[0035] S104: Select the overlapping area of ​​the "high correlation time-frequency space" of the cross wavelet transform results of all lines and the reference line; define the set with the highest frequency peak in the time-frequency set as the best time-frequency window; when the overlapping area contains only one time-frequency set, define the time-frequency set as the selected best time-frequency window; when the overlapping area contains multiple disconnected time-frequency sets, calculate the peak , extract the smaller value as the optimal scale coefficient; since the cross wavelet transform is a continuous wavelet transform based on the complex wavelet function, the scale coefficients j obtained are all in decimal form; select the smallest integer j0 in the range of scale coefficient j as the scale coefficient used for subsequent fractal dimension extraction features.

[0036] Optionally, in step S103, .

[0037] Optionally, step S20 is specifically as follows:

[0038] S201: Based on the real-time requirement, the sequence to be detected is subjected to sliding detection using the sliding window method, and the sequence to be detected is divided into shorter time windows. The sliding window W is defined as , represents the jth sliding window, and s is the data time step in the sliding window;

[0039] S202: Perform DP-GMM detection on the data in the sliding window W and calculate the The probability that the data belongs to "fault" or "normal" is determined, so as to adaptively determine whether there is a fault in the window.

[0040] Optionally, in step S201, the data time step length in the sliding window is .

[0041] Optionally, in step S202,

[0042] A detection result marked as 0 indicates that the sample data is normal data, and a detection result marked as 1 indicates that the sample data is fault data.

[0043] Optionally, step S30 includes:

[0044] The time domain signal of length N is divided into n components, and the gray value of the signal at time x is f(x); at this time, the signal is regarded as a two-dimensional object, with the horizontal axis being time and the vertical axis being the gray value; the signal is composed of n grids, and a small square box with a unit length of 1 is superimposed on each grid. In the i-th grid, the m-th box contains the minimum gray value in the grid, and the l-th box contains the maximum gray value in the grid. Then the number of boxes covering this grid is:

[0045] (12);

[0046] The number of boxes that cover the entire signal is:

[0047] (13);

[0048] The fractal dimension can be calculated:

[0049] (14);

[0050] By changing the size of the box, a set of , then Perform the least squares fitting, and the slope of the straight line is ;

[0051] A multi-scale fractal dimension calculation method is used to display signal characteristics at different scales. For a time domain signal with a length of N, the scale factor is , divide the signal into several time series , , ..., , and then calculate the mean value of each segmentation subset;

[0052] (15);

[0053] In the formula, is a new time series; is the scale factor; ; ;

[0054] Finally, calculate the multiscale fractal dimension:

[0055] (16);

[0056] Where: D is the multi-scale fractal dimension, is the number of morphological decompositions;

[0057] Calculate the zero-sequence current waveform sequence at different scales ( ), construct the multi-scale fractal dimension vector of zero-sequence current, denoted as , .

[0058] Optionally, step S40 includes:

[0059] S401: Initialization; Input Dataset , clustering penalty parameter ; Initialization parameters , , cluster center , initialize the clustering index ;

[0060] S402: Circular calculation until convergence; for each data point , calculate the Euclidean distance from the data point to the cluster center:

[0061] (20);

[0062] if , Otherwise, let ; Then, according to , generate point set ; For each point set ,calculate ;

[0063] S403: Output point set and the number of clusters ;

[0064] DP-GMM only needs to set one penalty parameter Output point set in real time and the number of clusters ;

[0065] Each type of point set calculated by DP-GMM is attributed to a Gaussian sub-distribution, and then the mean and covariance are incrementally calculated using the Welford formula to update the parameters of GMM online; the specific calculation formula is:

[0066] (twenty one);

[0067] (twenty two);

[0068] Where: They represent the data points, mean and covariance at time t respectively, and the approximate solution of GMM parameters is obtained online;

[0069] Based on the above steps S401-S402, Perform DP-GMM model clustering; after DP-GMM model clustering, divide the samples into two Gaussian sub-models: "fault" and "normal".

[0070] The beneficial effect of the present invention is to provide a method for online detection of medium and low voltage distribution network faults based on cross wavelet coherence analysis:

[0071] ① Improved fault detection accuracy: The frequency bands with relatively large contents in the zero-sequence current signals of each line are determined through cross-wavelet coherence analysis, and the zero-sequence current of a line with the largest energy is selected as the sequence to be detected, which effectively reduces noise and harmonic interference and improves the accuracy of fault detection.

[0072] ② Adaptive optimal frequency band / scale selection: Cross wavelet transform can adaptively determine the optimal frequency band / scale for zero-sequence current signal analysis of distribution lines according to the characteristics of zero-sequence current traveling waves of distribution lines, thus enhancing the flexibility and adaptability of the detection method.

[0073] ③ Real-time: The sliding window method is used to perform real-time sliding detection on the detection sequence, and the time domain features are extracted based on fractal theory to achieve rapid response and real-time monitoring of faults.

[0074] ④ Multi-scale feature extraction: By calculating the fractal dimensions at different scales and constructing the multi-scale fractal dimension vector of zero-sequence current, it can fully reflect the complexity and randomness of the signal and provide rich feature information for fault detection.

[0075] ⑤ Unsupervised learning clustering method: Using the clustering method based on the Dirichlet process Gaussian mixture model (DP-GMM), there is no need to pre-set the number of clustering categories. It can adaptively identify fault data and solve the problems of difficult threshold setting and low parameter estimation efficiency in traditional methods.

[0076] ⑥ Accurate fault identification: The DP-GMM clustering method can accurately classify sample data into two categories: "fault" and "normal". Experimental verification shows that the probability density distribution of fault data and normal data is quite different, which is conducive to accurate fault identification.

[0077] ⑦ Improve monitoring efficiency: This method can effectively improve the monitoring efficiency of medium and low voltage distribution networks, detect and locate faults in a timely manner, and ensure the stable operation of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in this embodiment or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0079] Figure 1 It is a flow chart of a method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis provided by an embodiment of the present invention;

[0080] Figure 2 It is a double logarithmic slope fitting graph provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0081] In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, the technical scheme in this embodiment will be clearly and completely described below in conjunction with the drawings in this embodiment. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] This embodiment provides an online detection method for medium and low voltage distribution network faults based on cross wavelet coherence analysis, which is suitable for application scenarios of detecting medium and low voltage distribution network faults and can improve the efficiency of power grid operation monitoring. The online detection method for medium and low voltage distribution network faults based on cross wavelet coherence analysis is executed by a monitoring device and implemented by software and / or hardware.

[0083] Figure 1 This is a flow chart of the online fault detection method for medium and low voltage distribution networks based on cross wavelet coherence analysis provided in the first embodiment.

[0084] See also Figure 1 The online detection method for medium and low voltage distribution network faults based on cross wavelet coherence analysis comprises the following steps:

[0085] S10: Obtain the zero-sequence currents of all lines, perform cross-wavelet coherence analysis on each line, and determine the frequency band with the largest content in the zero-sequence current signal of each line as the best frequency band / scale for subsequent transformation based on the time-frequency region with the stronger cross-wavelet power spectrum density, and select the zero-sequence current of the line with the largest energy as the sequence to be detected in the fault detection method;

[0086] The fault signal of distribution network contains strong background noise and harmonic interference components. Therefore, cross wavelet coherence analysis is used to obtain the optimal frequency band / scale of fault characteristics to reduce noise interference and enhance fault characteristics.

[0087] The cross wavelet transform is based on the wavelet analysis theory. By analyzing two energy-limited non-stationary signals in the time-frequency domain, the time-frequency correlation characteristics between the two signals can be determined. If the cross wavelet coherence of a certain frequency band of the two signals is large, it means that the content of the frequency band component in both signals is large. Since noise is random and uncorrelated, the cross wavelet transform can effectively shield the influence of noise and provide a powerful analysis tool for the selection of the optimal frequency band / scale in the detection of grounding faults in distribution networks.

[0088] The cross wavelet transform is used to determine the time-frequency region where the cross wavelet power spectrum density of the zero-sequence current traveling wave of the distribution line is relatively strong, thereby realizing the selection of the adaptive optimal frequency band / scale. The specific implementation steps are as follows:

[0089] S101: Signal acquisition. Obtain the zero-sequence current of all lines within the time range of 1ms before and 15ms after startup. The sampling rate is f s =1MHz, sampling interval t s =1μs. Record the start time as t0.

[0090] S102: Reference line selection. Take the line zero-sequence current i 1ms before the start time and 5ms after the start time 0m (j), m is the line number, j is the sampling number. Calculate the energy E of the zero-sequence current of line m m , the calculation formula is

[0091] (1)

[0092] Where N is the total number of sampling points and M is the total number of lines. m The largest line x is used as the reference line.

[0093] (2)

[0094] S103: Cross-wavelet coherence analysis of line zero-sequence current. Take line x as the reference line and perform cross-wavelet transform with zero-sequence currents of other lines to obtain cross-wavelet power spectrum density. The calculation process is:

[0095] For the zero-sequence current signals of the two lines and , its cross wavelet transform and cross wavelet power spectrum density are expressed by equation (3) and equation (4).

[0096] (3)

[0097] (4)

[0098] In the formula, is the cross wavelet transform, is the cross wavelet power spectral density, The larger it is, the greater the coherence of the two signals. , They are zero-sequence current signals , The wavelet transform of is defined by equation (5); * represents complex conjugate.

[0099] (5)

[0100] Where ψ is the mother wavelet; a (a>0) is the scaling operator; b is the shift operator; * represents the complex conjugate.

[0101] The most commonly used complex wavelet function, Morlet wavelet, is selected as the mother wavelet function. It has good time-frequency localization characteristics, and its mathematical expression is:

[0102] (6)

[0103] In order to unify the selection criteria in all cases, the calculation results of the cross-wavelet power spectrum density are normalized. The normalized cross-wavelet power spectrum density is actually the "significance level" in a statistical sense. The time-frequency point set B whose cross-wavelet power spectrum density satisfies equation (7) is defined as the "high correlation time-frequency space" of line m and reference line x.

[0104] (7)

[0105] Where σ x , σ m are the zero-sequence current standard deviations of line x and line m respectively. The ideal effect of optimal frequency band / scale selection can be obtained.

[0106] S104: Optimal frequency band / scale determination rule. Select the overlapping area of ​​the "high correlation time-frequency space" of the cross-wavelet transform results of all lines and the reference line. Define the set with the highest frequency peak in the time-frequency set as the optimal time-frequency window. When the overlapping area contains only one time-frequency set, define the time-frequency set as the selected optimal time-frequency window (the most common case); when the overlapping area contains multiple disconnected time-frequency sets, calculate the peak , extract the smaller value as the optimal scale coefficient. Since the cross wavelet transform is a continuous wavelet transform based on the complex wavelet function, the scale coefficients j obtained are all in decimal form. The smallest integer j0 in the scale coefficient j range is selected as the scale coefficient used for subsequent fractal dimension extraction features.

[0107] S20: Based on the real-time requirement, the sliding window method is used to perform sliding detection on the sequence to be detected, and the waveform sequence is divided into shorter time windows;

[0108] S201: Based on the real-time requirement, the sequence to be detected is subjected to sliding detection using the sliding window method. The sequence to be detected is divided into shorter time windows, and the sliding window W is defined as , represents the jth sliding window, s is the data time step in the sliding window, and the present invention selects .

[0109] S202: Perform DP-GMM detection on the data in the sliding window W and calculate the The probability that the data belongs to "fault" or "normal" is determined, so as to adaptively judge whether there is a fault in the window. The detection result marked as 0 indicates that the sample data is normal data, and the detection result marked as 1 indicates that the sample data is fault data.

[0110] S30: Extract the time domain features of the sequence in the sliding window based on fractal theory, use the box counting method to calculate the minimum number of boxes covering the waveform texture, change the size of the box covering the waveform to estimate the fractal dimension, calculate the fractal dimension of the waveform at different scales, and construct the multi-scale fractal dimension vector of zero-sequence current;

[0111] In view of the complexity of the fault signal, the present invention adopts fractal dimension (FD) to evaluate. Fractal dimension was originally used to characterize the geometric pattern generated by the abstract recursive process called fractal process, which has the advantage of simple calculation. The methods for estimating fractal dimension are: box counting dimension, correlation dimension and information dimension. The fractal dimension method is essentially an approximate sequence related to a decreasing ratio, which is a geometric factor of a simple graph that forms an approximate value. The present invention adopts box counting dimension to estimate the fractal dimension.

[0112] Gangepain and Roques-Carms proposed the fractal dimension based on box counting in 1986, which is measured by calculating the minimum number of boxes covering the image surface. Therefore, the fractal dimension is estimated by calculating the minimum number of boxes covering the waveform, and the differential box dimension is used to extract the time domain features of the signal.

[0113] Divide the time domain signal of length N into n components, and the gray value of the signal at time x is f(x). At this time, the signal is regarded as a two-dimensional object, with the horizontal axis being time and the vertical axis being the gray value. The signal is composed of n grids. Assume that there are small square boxes with a unit length of 1 (the unit length can be customized) superimposed on each grid. In the i-th grid, the m-th box contains the minimum gray value in the grid, and the l-th box contains the maximum gray value in the grid. Then the number of boxes covering this grid is:

[0114] (12)

[0115] The number of boxes that cover the entire signal is:

[0116] (13)

[0117] The fractal dimension can be calculated:

[0118] (14)

[0119] By changing the size of the box, a set of , then Perform the least squares fitting, and the slope of the straight line is Attached Figure 2 Based on the slope calculated for boxes of different sizes, a double logarithmic graph was obtained by least square fitting, and the slope of the fitting line was the estimated fractal dimension.

[0120] Single-scale fractal dimension is not enough to characterize the complexity and randomness of the signal. In order to solve this defect in signal characterization, a multi-scale fractal dimension calculation method is used. Multi-scale analysis can display signal characteristics at different scales. For a time domain signal with a length of N, the scale factor is , the signal can be divided into several time series , , ..., , and then calculate the mean of each split subset.

[0121] (15)

[0122] In the formula, is a new time series; is the scale factor; ; .

[0123] Finally, calculate the multiscale fractal dimension:

[0124] (16)

[0125] Where: D is the multi-scale fractal dimension, is the number of morphological decompositions.

[0126] Calculate the zero-sequence current waveform sequence at different scales ( ), construct the multi-scale fractal dimension vector of zero-sequence current, denoted as , .

[0127] The fractal dimension vector obtained from the zero-sequence current waveform after the above characteristics are enhanced , to detect the fault. Since the detection method based on the threshold has poor flexibility, the fault judgment threshold is difficult to set. For this reason, an unsupervised learning clustering method based on a mixed Gaussian model is considered to detect the fault. However, the traditional clustering method based on the mixed Gaussian model requires the number of clustering categories to be set in advance, resulting in false detection of normal sequences. Therefore, the present invention proposes a fault adaptive detection method based on the Dirichlet process Gaussian mixture model, which overcomes the limitations of the traditional clustering method and realizes adaptive detection of faults.

[0128] S40: A clustering method based on the Dirichlet process Gaussian mixture model is used to perform fault detection on the extracted feature vectors to achieve accurate fault identification.

[0129] Aiming at the problem that the threshold of the fault detection method based on threshold is difficult to set, a clustering method based on mixed Gaussian model is considered to detect faults, and the problem of low parameter estimation efficiency of the clustering method of Gaussian mixture model is improved. A clustering method based on Dirichlet process Gaussian mixture model is proposed to perform fault detection on the fractal dimension data in the sliding window W, and calculate the probability of the fractal dimension data at different time scales in the window belonging to "fault" and "normal", so as to adaptively judge whether there is a fault in the window.

[0130] Gaussian Mixture Model (GMM) is a clustering method based on probability model. GMM assumes that the input samples obey The parameters of the Gaussian distribution are unknown, and the samples that obey the same distribution are clustered into one category. GMM can be seen as A linear combination of Gaussian distributions, that is

[0131] (17)

[0132] Where: Represents the state quantity; Indicates the number of GMM neutron distributions; represents the mixing coefficient (i.e., weight) and satisfies and ; represents a Gaussian distribution, and Represents the mean and covariance of the kth sub-model. For the GMM model of the above sFD sequence, it is defined as two categories: normal and fault, that is, .

[0133] GMM usually uses the Expectation Maximization (EM) algorithm to fit k mixed Gaussian distributions. However, the EM algorithm needs to use all data points in each iteration, which has low computational efficiency. Therefore, the present invention improves the problem of low efficiency of GMM parameter estimation.

[0134] For the parameter estimation problem of GMM, in addition to the above-mentioned EM algorithm, the Dirichlet Process (DP), an important method in non-parametric Bayesian statistics, can also be used. In the parameter estimation process, DP can well solve the problem of low computational efficiency caused by the EM algorithm's repeated use of all data points. The value does not need to be specified in advance and can change adaptively with the data.

[0135] DP-GMM consists of basic probability distribution and aggregation parameters composition, As it approaches infinity, G approaches DP-GMM is represented as

[0136] (18)

[0137] for Gaussian sub-models with

[0138] (19)

[0139] In the formula, It represents the sum of the probabilities of the discrete distribution G in the kth Gaussian submodel; Dir represents the Dirichlet distribution.

[0140] The specific implementation steps of the DP-GMM online clustering algorithm are as follows:

[0141] S401: Initialization. Input Dataset , clustering penalty parameter ; Initialization parameters , , cluster center , initialize the clustering index .

[0142] S402: Calculate repeatedly until convergence. For each data point , calculate the Euclidean distance from the data point to the cluster center:

[0143] (20)

[0144] if , Otherwise, let Then, according to , generate point set For each point set ,calculate .

[0145] S403: Output point set and the number of clusters .

[0146] DP-GMM only needs to set one penalty parameter Output point set in real time and the number of clusters , which solves the problem that GMM needs to pre-specify the number of clusters.

[0147] Furthermore, each type of point set calculated by DP-GMM is attributed to a Gaussian sub-distribution, and then the mean and covariance are incrementally calculated using the Welford formula to update the parameters of the GMM online. The specific calculation formula is:

[0148] (twenty one)

[0149] (twenty two)

[0150] Where: Respectively represent the data point, mean and covariance at time t. This method can be used to obtain the approximate solution of GMM parameters online with high computational efficiency.

[0151] Based on the above method, Perform DP-GMM model clustering. After DP-GMM model clustering, the samples are divided into two Gaussian sub-models: "fault" and "normal". Experimental verification shows that the probability density distribution of fault data and normal data is very different, and the Gaussian sub-model with a large difference in mean and variance can accurately identify the fault data in the sample.

[0152] In summary, the online detection method for medium and low voltage distribution network faults based on cross wavelet coherence analysis provided in this embodiment has the following beneficial effects:

[0153] ① Improved fault detection accuracy: The frequency bands with relatively large contents in the zero-sequence current signals of each line are determined through cross-wavelet coherence analysis, and the zero-sequence current of a line with the largest energy is selected as the sequence to be detected, which effectively reduces noise and harmonic interference and improves the accuracy of fault detection.

[0154] ② Adaptive optimal frequency band / scale selection: Cross wavelet transform can adaptively determine the optimal frequency band / scale for zero-sequence current signal analysis of distribution lines according to the characteristics of zero-sequence current traveling waves of distribution lines, thus enhancing the flexibility and adaptability of the detection method.

[0155] ③ Real-time: The sliding window method is used to perform real-time sliding detection on the detection sequence, and the time domain features are extracted based on fractal theory to achieve rapid response and real-time monitoring of faults.

[0156] ④ Multi-scale feature extraction: By calculating the fractal dimensions at different scales and constructing the multi-scale fractal dimension vector of zero-sequence current, it can fully reflect the complexity and randomness of the signal and provide rich feature information for fault detection.

[0157] ⑤ Unsupervised learning clustering method: Using the clustering method based on the Dirichlet process Gaussian mixture model (DP-GMM), there is no need to pre-set the number of clustering categories. It can adaptively identify fault data and solve the problems of difficult threshold setting and low parameter estimation efficiency in traditional methods.

[0158] ⑥ Accurate fault identification: The DP-GMM clustering method can accurately classify sample data into two categories: "fault" and "normal". Experimental verification shows that the probability density distribution of fault data and normal data is quite different, which is conducive to accurate fault identification.

[0159] ⑦ Improve monitoring efficiency: This method can effectively improve the monitoring efficiency of medium and low voltage distribution networks, detect and locate faults in a timely manner, and ensure the stable operation of the power grid.

[0160] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis, characterized in that: include: S10: Obtain the zero-sequence currents of all lines, perform cross-wavelet coherence analysis on each line, and determine the frequency band with the largest content in the zero-sequence current signal of each line as the best frequency band / scale for subsequent transformation based on the time-frequency region with the stronger cross-wavelet power spectrum density, and select the zero-sequence current of the line with the largest energy as the sequence to be detected in the fault detection method; S20: Based on the real-time requirement, the sliding window method is used to perform sliding detection on the sequence to be detected, and the waveform sequence is divided into shorter time windows; S30: Extract the time domain features of the sequence in the sliding window based on fractal theory, use the box counting method to calculate the minimum number of boxes covering the waveform texture, change the size of the box covering the waveform to estimate the fractal dimension, calculate the fractal dimension of the waveform at different scales, and construct the multi-scale fractal dimension vector of zero-sequence current; S40: A clustering method based on the Dirichlet process Gaussian mixture model is used to perform fault detection on the extracted feature vectors to achieve accurate fault identification.

2. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 1 is characterized in that: The S10 includes: S101: Obtain zero-sequence current of all lines within the time range of 1ms before and 15ms after startup; the sampling rate is f s =1MHz, sampling interval t s =1μs, record the start time as t0; S102: Take the line zero-sequence current i1ms before and 5ms after the start time 0m (j), m is the line number, j is the sampling number; calculate the energy E of the zero-sequence current of line m m , the calculation formula is （1）； Where N is the total number of sampling points and M is the total number of lines. m The largest line x is used as the reference line; （2）； S103: Taking line x as the reference line, cross wavelet transform is performed with zero-sequence currents of other lines to obtain cross wavelet power spectrum density; the calculation process is: For the zero-sequence current signals of the two lines and , its cross wavelet transform and cross wavelet power spectrum density are expressed by equation (3) and equation (4); （3）； （4）； In the formula, is the cross wavelet transform, is the cross wavelet power spectral density, The larger it is, the greater the coherence of the two signals. , They are zero-sequence current signals , The wavelet transform of is defined by equation (5); * represents complex conjugate; （5）； Where, ψ is the mother wavelet; a (a>0) is the scale operator; b is the shift operator; * represents the complex conjugate; The complex wavelet function - Morlet wavelet is selected as the mother wavelet function, and its mathematical expression is （6）； The cross wavelet power spectrum density calculation results are normalized; the normalized cross wavelet power spectrum density is actually the "significance level" in the statistical sense; the time-frequency point set B whose cross wavelet power spectrum density satisfies equation (7) is defined as the "high correlation time-frequency space" of line m and reference line x; （7）； Where σ x , σ m are the zero-sequence current standard deviations of line x and line m respectively; S104: Select the overlapping area of ​​the "high correlation time-frequency space" of the cross wavelet transform results of all lines and the reference line; define the set with the highest frequency peak in the time-frequency set as the best time-frequency window; when the overlapping area contains only one time-frequency set, define the time-frequency set as the selected best time-frequency window; when the overlapping area contains multiple disconnected time-frequency sets, calculate the peak , extract the smaller value as the optimal scale coefficient; since the cross wavelet transform is a continuous wavelet transform based on the complex wavelet function, the scale coefficients j obtained are all in decimal form; select the smallest integer j0 in the range of scale coefficient j as the scale coefficient used for subsequent fractal dimension extraction features.

3. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 2 is characterized in that: In step S103, .

4. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 2 is characterized in that: Step S20 is specifically as follows: S201: Based on the real-time requirement, the sequence to be detected is subjected to sliding detection using the sliding window method, and the sequence to be detected is divided into shorter time windows. The sliding window W is defined as , represents the jth sliding window, and s is the data time step in the sliding window; S202: Perform DP-GMM detection on the data in the sliding window W and calculate the The probability that the data belongs to "fault" or "normal" is determined, so as to adaptively determine whether there is a fault in the window.

5. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 4 is characterized in that: In step S201, the data time step length in the sliding window is .

6. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 4 is characterized in that: In step S202, A detection result marked as 0 indicates that the sample data is normal data, and a detection result marked as 1 indicates that the sample data is fault data.

7. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 4 is characterized in that: Step S30 includes: The time domain signal of length N is divided into n components, and the gray value of the signal at time x is f(x); at this time, the signal is regarded as a two-dimensional object, with the horizontal axis being time and the vertical axis being the gray value; the signal is composed of n grids, and a small square box with a unit length of 1 is superimposed on each grid. In the i-th grid, the m-th box contains the minimum gray value in the grid, and the l-th box contains the maximum gray value in the grid. Then the number of boxes covering this grid is: （12）； The number of boxes that cover the entire signal is: （13）； The fractal dimension can be calculated: （14）； By changing the size of the box, a set of , then Perform the least squares fitting, and the slope of the straight line is ; A multi-scale fractal dimension calculation method is used to display signal characteristics at different scales. For a time domain signal with a length of N, the scale factor is , divide the signal into several time series , , ..., , and then calculate the mean value of each segmentation subset; （15）； In the formula, is a new time series; is the scale factor; ; ; Finally, calculate the multiscale fractal dimension: （16）； Where: D is the multi-scale fractal dimension, is the number of morphological decompositions; Calculate the zero-sequence current waveform sequence at different scales ( ), construct the multi-scale fractal dimension vector of zero-sequence current, denoted as , .

8. The method for online fault detection in medium and low voltage distribution networks based on cross wavelet coherence analysis according to claim 7 is characterized in that: Step S40 includes: S401: Initialization; Input Dataset , clustering penalty parameter ; Initialization parameters , , cluster center , initialize the clustering index ; S402: Circular calculation until convergence; for each data point , calculate the Euclidean distance from the data point to the cluster center: （20）； if , Otherwise, let ; Then, according to , generate point set ; For each point set ,calculate ; S403: Output point set and the number of clusters ; DP-GMM only needs to set one penalty parameter Output point set in real time and the number of clusters ; Each type of point set calculated by DP-GMM is attributed to a Gaussian sub-distribution, and then the mean and covariance are incrementally calculated using the Welford formula to update the parameters of GMM online; the specific calculation formula is: （21）； （22）； Where: They represent the data points, mean and covariance at time t respectively, and the approximate solution of GMM parameters is obtained online; Based on the above steps S401-S402, Perform DP-GMM model clustering; after DP-GMM model clustering, the samples are divided into two Gaussian sub-models: "fault" and "normal".

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