Distribution network traveling wave fault identification method based on symplectic geometric mode decomposition

Abstract

The invention discloses a distribution network traveling wave fault identification method based on symplectic geometric mode decomposition. The method comprises the following steps: step 1, sampling a distribution network traveling wave fault current signal; step 2, carrying out two-end symmetric point continuation on the initial signal by adopting a self-adaptive waveform matching endpoint continuation method; 3, using a symplectic geometric mode decomposition method to decompose a distribution network traveling wave initial current signal; step 4, effective components of the continuation components obtained in the step 3 are determined by calculating Pearson's correlation coefficients between construction components, and similar initial components in the effective components are reconstructed by constructing a Pearson's correlation coefficient matrix, so that final symplectic geometric components are obtained; and 5, demodulating the optimized symplectic geometric component by using a frequency weighted energy operator to obtain a time-energy spectrum diagram of the symplectic geometric component, and finally identifying a fault. In combination with ASGMD-FWEO, the method shows excellent performance in the aspects of adaptive preferential selection, interference resistance, noise resistance and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of traveling wave fault identification, and in particular to a distribution network traveling wave fault identification method based on symplectic geometric mode decomposition. Background Art

[0002] The demand for power resources is growing, and users have higher and higher requirements for power quality. However, problems such as complex distribution network lines and aging equipment are becoming more and more serious, and line failures are very likely to occur. In order to deal with line failures in a timely manner and ensure efficient, safe and stable operation of the distribution network, it is urgent to solve the problem of distribution network fault location.

[0003] When a single-phase grounding fault is detected in the system, the distribution network with backward intelligence still uses the method of pulling the switch one by one to determine the fault line, and then dispatches relevant professional and technical personnel to the site to patrol along the fault line. The fault search takes several hours, which is not conducive to emergency repair and rapid power restoration, and it is difficult to meet the requirements of grid automation and intelligence. It can be seen that the exploration of distribution network fault accurate positioning and insulation hidden danger monitoring methods has high research value and practical value.

[0004] Symplectic Geometry Mode Decomposition (SGMD) is a method for processing non-stationary and nonlinear signals based on symplectic geometry and protecting the geometric structure of the phase space. However, on the one hand, the traditional SGMD cannot directly analyze signals of different types and contents because of the non-adaptive cutoff conditions during iterative decomposition operations. The number of SGC components generated will also require artificial setting of the periodic similarity threshold depending on the cutoff conditions, which has great uncertainty. When the number is large, the components will contain more noise, and when the number is small, the key information in the original signal may be lost. On the other hand, as a quasi-empirical mode decomposition method, traditional SGMD also has phenomena such as endpoint effects and mode aliasing. Therefore, it is necessary to add adaptive extension endpoints and calculate the Pearson correlation coefficient to reconstruct the effective components in the decomposition process, which can perfectly avoid the above shortcomings.

[0005] Traditional Hilbert transform has a strong ability to extract impulse signals, but it is easily interfered by external factors and produces endpoint effects, demodulating negative frequencies. Traditional TEO can better overcome the above shortcomings of Hilbert and is widely used, but it also has obvious shortcomings, that is, it can only process single-component signals. If mixed with a large amount of background noise, its application will be greatly limited. Therefore, a new energy operator is used to detect signal mutation points, namely the frequency weighted energy operator (FWEO). Summary of the invention

[0006] Purpose of the invention: The present invention provides a distribution network traveling wave fault identification method based on symplectic geometric mode decomposition, which combines ASGMD-FWEO to show its excellent performance in adaptive optimization, anti-interference and anti-noise.

[0007] Technical solution: The present invention discloses a method for identifying traveling wave faults in a distribution network based on symplectic geometric modal decomposition, comprising the following steps:

[0008] Step 1: sampling the distribution network traveling wave fault current signal;

[0009] Step 2: The initial signal is extended by using an adaptive waveform matching endpoint extension method to perform symmetrical point extension at both ends;

[0010] Step 3: Decompose the initial signal of the distribution network traveling wave by using the symplectic geometric mode decomposition method;

[0011] Step 4: Determine the effective components by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and reconstruct the similar initial components in the effective components by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components;

[0012] Step 5: Use the frequency-weighted energy operator to demodulate the selected symplectic geometric components to obtain their time-energy spectrum and finally identify the fault.

[0013] Furthermore, in step 1, a suitable sampling frequency f is selected s , collect the original traveling wave fault current signal to be diagnosed, and obtain the form of x=x1, x2, ..., x n A one-dimensional time series of , where n is the length of the signal.

[0014] Furthermore, in step 2, the initial signal is extended to two symmetrical points at both ends using an adaptive waveform matching endpoint extension method, which specifically includes the following steps:

[0015] Step 21, let the original signal be x(t), determine the two adjacent extreme value points at the leftmost end of x(t), let them be the maximum value point and the minimum value point, respectively, record them as P0 and P1, and the waveform from the starting point to P1 is recorded as w0, and its length is l;

[0016] Step 22: Set E max is the maximum point set of x(t), with E max -Every maximum point P in {P0} i As a reference point, calculate the waveforms w0 and w of the same length i The matching degree M(w0,w i ,P i ); let M(w0,w i0 ,P i0)=min{M(w0,w i ,P i ),i=1,2,…};

[0017] Step 23, if M(w0,w i0 ,P i0 )<α·l, where α is a constant, then take w i0 The left side contains a sub-wave with a maximum and a minimum, which serves as the extension of the left end of the original x(t). Otherwise, the average of the two adjacent maximum points on the left end of the original signal is taken as the maximum of the left endpoint, and the average of the two adjacent minimum points on the left end of the signal is taken as the minimum of the left endpoint, and the extension is completed.

[0018] Furthermore, in step 3, decomposing the distribution network traveling wave initial current signal using the symplectic geometric mode decomposition method specifically includes the following steps:

[0019] Step 31: Based on Takens embedding theorem, x = x1, x2, ..., x n The one-dimensional time series of is reconstructed into a trajectory matrix X containing a multi-dimensional signal:

[0020]

[0021] Where d represents the embedding dimension, τ is 1, represents the delay time, and m = n-(d-1)τ;

[0022] Step 32: Construct a Hamilton matrix based on the trajectory matrix X obtained in step 31. Where the covariance matrix A = X T X;

[0023] Step 33: Construct the Householder matrix and H is an orthogonal symplectic matrix; then we get

[0024]

[0025] Step 34: Transform X by diagonal average transformation i Convert to a time series Y of length n i =y1,y2,…y n (i=1, 2, ..., d), thus we get d time series of length n, that is, d initial components, whose sum is a one-dimensional time series x=x1, x2, ..., x n .

[0026] Further, in step 34, X is transformed by diagonal average transformation. i Convert to a time series Y of length n i =y1,y2,…y n(i=1, 2, ..., d) is specifically:

[0027] For an element x in the matrix X ij (1≤i≤m, 1≤j≤d), let d * =min(m,d),m * =max(m, d), m=n-(d-1)τ, and then the time series Y is calculated by the following formula i The element y k (k=1,2,…,n) to calculate

[0028] If m<d, let x ij * =x ij , otherwise let x ij * =x ji .

[0029] Further, in step 4, the effective components are determined by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and the similar initial components in the effective components are reconstructed by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components. Specifically, the steps include:

[0030] Step 41, distinguishing the effective component from the noise component by calculating the Pearson correlation coefficient;

[0031] Step 42: construct a Pearson correlation coefficient matrix and reconstruct similar components in the effective components by superposition, so as to obtain the final symplectic geometric components.

[0032] Furthermore, in step 41, the effective component and the noise component are distinguished by calculating the Pearson correlation coefficient: the first f (f = 1, 2, ..., d) initial components Y i =y1,y2,…y n (i=1,2,…,d) add to get d groups of structural components Then calculate the sum of the two adjacent first f terms and N f The Pearson correlation coefficient is: When the Pearson coefficient grows to a certain value and remains basically unchanged, the first k value corresponding to this value is considered to be the dividing point between the effective component and the noise component. Then the component after the kth initial component is the noise component and should be separated from the d group of initial components.

[0033] Furthermore, in step 42, by constructing a Pearson correlation coefficient matrix, similar components in the effective components are superimposed and reconstructed to obtain the final symplectic geometric components. Specifically, the k effective components remaining after removing the noise components are reconstructed by constructing a Pearson correlation coefficient matrix. Finally, p symplectic geometric components are obtained.

[0034] Furthermore, in step 5, the frequency-weighted energy operator is used to demodulate the preferred symplectic geometric component to obtain its time-energy spectrum, and the fault is finally identified as follows: The frequency-weighted energy operator is defined as:

[0035] E[x(t)]=|x′(t)+jH[x′(t)] 2 = x′ 2 (t)+H[x′(t)] 2 , where x(t) represents the initial signal and H[·] represents the Hilbert transform. The initial signal x(t) should be a harmonic signal, and its form should be x(t) = Acos(wt+φ), then x′(t) = -Awsin(wt+φ), H[x′(t)] = Awcos(wt+φ), and substituting it into the frequency-weighted energy operator, we can get E[x(t)] = A 2 w 2 , its discrete form is:

[0036]

[0037] After processing the fault component, the fault can be accurately identified by analyzing the obtained time-energy spectrum.

[0038] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention adopts the adaptive waveform matching extension method to extend the symmetrical points at both ends, so as to effectively suppress the endpoint effect of the traditional empirical mode decomposition; on the basis of the SGMD algorithm, the Pearson correlation coefficient is introduced in the link of component reorganization, so as to realize the adaptive reconstruction of the symplectic geometric components; in addition, by applying the energy peak detection algorithm of the frequency-weighted energy operator, the transient impact is strengthened, the fault characteristic signal is secondary enhanced, and the traveling wave fault signal is accurately identified, and the fault, frequency and its multiple frequency components can be clearly seen in the FWEO energy spectrum, with a large amplitude and not affected by interference frequency and noise. The algorithm combined with ASGMD-FWEO shows its excellent performance in adaptive optimization, anti-interference and anti-noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0040] Figure 2 It is a schematic diagram of the decomposition process of the initial signal by the ASGMD of the present invention. DETAILED DESCRIPTION

[0041] like Figure 1 and Figure 2 As shown, a distribution network traveling wave fault identification method based on symplectic geometric mode decomposition includes the following steps:

[0042] Step 1: sampling the distribution network traveling wave fault current signal;

[0043] Step 2: The initial signal is extended by using an adaptive waveform matching endpoint extension method to perform symmetrical point extension at both ends;

[0044] Step 3: Decompose the distribution network traveling wave initial current signal using the symplectic geometry mode decomposition method;

[0045] Step 4: Determine the effective components by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and reconstruct the similar initial components in the effective components by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components;

[0046] Step 5: Use the frequency-weighted energy operator to demodulate the selected symplectic geometric components to obtain their time-energy spectrum and finally identify the fault.

[0047] In step 1, select a suitable sampling frequency f s , collect the original traveling wave fault current signal to be diagnosed, and obtain the form of x=x1, x2, ..., x n A one-dimensional time series of , where n is the length of the signal.

[0048] In step 2, the initial signal is extended to two symmetrical points at both ends using an adaptive waveform matching endpoint extension method, which specifically includes the following steps:

[0049] Step 21, let the original signal be x(t), determine the two adjacent extreme value points at the leftmost end of x(t), let them be the maximum value point and the minimum value point, respectively, record them as P0 and P1, and the waveform from the starting point to P1 is recorded as w0, and its length is l;

[0050] Step 22: Set E max is the maximum point set of x(t), with E max -Every maximum point P in {P0} i As a reference point, calculate the waveforms w0 and w of the same length i The matching degree M(w0,w i ,P i ); let M(w0,w i0 ,P i0 )=min{M(w0,w i ,P i),i=1,2,…};

[0051] Step 23, if M(w0,w i0 ,P i0 )<α·l, where α is a constant, then take w i0 The left side contains a sub-wave with a maximum and a minimum, which serves as the extension of the left end of the original x(t). Otherwise, the average of the two adjacent maximum points on the left end of the original signal is taken as the maximum of the left endpoint, and the average of the two adjacent minimum points on the left end of the signal is taken as the minimum of the left endpoint, and the extension is completed.

[0052] In step 3, decomposing the distribution network traveling wave initial current signal using the symplectic geometric mode decomposition method specifically includes the following steps:

[0053] Step 31: Based on Takens embedding theorem, x = x1, x2, ..., x n The one-dimensional time series of is reconstructed into a trajectory matrix X containing a multi-dimensional signal:

[0054]

[0055] Where d represents the embedding dimension, τ is 1, represents the delay time, and m = n-(d-1)τ;

[0056] Step 32: Construct a Hamilton matrix based on the trajectory matrix X obtained in step 31. Where the covariance matrix A = X T X;

[0057] Step 33: Construct the Householder matrix and H is an orthogonal symplectic matrix; then we get

[0058]

[0059] Step 34: Transform X by diagonal average transformation i Convert to a time series Y of length n i =y1,y2,…y n (i=1, 2, ..., d), thus obtaining d time series of length n, i.e., d initial components, the sum of which is a one-dimensional time series x=x1, x2, ..., x n .

[0060] In step 34, X is transformed by diagonal average transformation. i Convert to a time series Y of length n i =y1,y2,…y n (i=1, 2, ..., d) is specifically:

[0061] For an element x in the matrix X ij (1≤i≤m, 1≤j≤d), let d * =min(m,d),m * =max(m, d), m=n-(d-1)τ, and then the time series Y is calculated by the following formula i The element y k (k=1,2,…,n) to calculate

[0062] If m<d, let x ij * =x ij , otherwise let x ij * =x ji .

[0063] In step 4, the effective components are determined by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and the similar initial components in the effective components are reconstructed by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components. Specifically, the steps include:

[0064] Step 41, distinguishing the effective component from the noise component by calculating the Pearson correlation coefficient;

[0065] Step 42: construct a Pearson correlation coefficient matrix and reconstruct similar components in the effective components by superposition, so as to obtain the final symplectic geometric components.

[0066] In step 41, the effective component and the noise component are distinguished by calculating the Pearson correlation coefficient. Specifically, the first f (f = 1, 2, ..., d) initial components Y i =y1,y2,…y n (i=1,2,…,d) add to get d groups of structural components Then calculate the sum of the two adjacent first f terms and N f The Pearson correlation coefficient is: When the Pearson coefficient grows to a certain value and remains basically unchanged, the first k value corresponding to this value is considered to be the dividing point between the effective component and the noise component. Then the component after the kth initial component is the noise component and should be separated from the d group of initial components.

[0067] In step 42, by constructing a Pearson correlation coefficient matrix, similar components in the effective components are superimposed and reconstructed to obtain the final symplectic geometric components. Specifically, the k effective components remaining after removing the noise components are reconstructed by constructing a Pearson correlation coefficient matrix. Finally, p symplectic geometric components are obtained.

[0068] In step 5, the frequency-weighted energy operator is used to demodulate the preferred symplectic geometric component to obtain its time-energy spectrum, and the fault is finally identified as follows: The frequency-weighted energy operator is defined as:

[0069] E[x(t)]=|x′(t)+jH[x′(t)] 2 = x′ 2 (t)+H[x′(t)] 2 , where x(t) represents the initial signal and H[·] represents the Hilbert transform. The initial signal x(t) should be a harmonic signal, and its form should be x(t) = Acos(wt+φ), then x′(t) = -Awsin(wt+φ), H[x′(t)] = Awcos(wt+φ), and substituting it into the frequency-weighted energy operator, we can get E[x(t)] = A 2 w 2 , its discrete form is:

[0070]

[0071] After processing the fault component, the fault can be accurately identified by analyzing the obtained time-energy spectrum.

[0072] The non-negative frequency-weighted energy operator FWEO, like TEO, estimates the instantaneous energy of the signal x(t), but FWEO can ensure that there will be no meaningless negative energy and is more robust than TEO.

Claims

1. A distribution network traveling wave fault identification method based on symplectic geometric mode decomposition, characterized in that: The steps include: Step 1: sampling the distribution network traveling wave fault current signal; Step 2: The initial signal is extended by using an adaptive waveform matching endpoint extension method to perform symmetrical point extension at both ends; Step 3: Decompose the distribution network traveling wave initial current signal using the symplectic geometry mode decomposition method; Step 4: Determine the effective components by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and reconstruct the similar initial components in the effective components by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components; Step 5: Use the frequency-weighted energy operator to demodulate the selected symplectic geometric components to obtain their time-energy spectrum and finally identify the fault.

2. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 1, characterized in that: In step 1, select a suitable sampling frequency f s , collect the original traveling wave fault current signal to be diagnosed, and obtain the form of x=x1, x2, ..., x n A one-dimensional time series of , where n is the length of the signal.

3. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 1, characterized in that: In step 2, the initial signal is extended to two symmetrical points at both ends using an adaptive waveform matching endpoint extension method, which specifically includes the following steps: Step 21, let the original signal be x(t), determine the two adjacent extreme value points at the leftmost end of x(t), let them be the maximum value point and the minimum value point, respectively, record them as P0 and P1, and the waveform from the starting point to P1 is recorded as w0, and its length is l; Step 22: Set E max is the maximum point set of x(t), with E max -Every maximum point P in {P0} i As a reference point, calculate the waveforms w0 and w of the same length i The matching degree M(w0,w i ,P i ); let M(w0,w i0 ,P i0 )=min{M(w0,w i ,P i ),i=1,2,…}; Step 23, if M(w0,w i0 ,P i0 )<α·l, where α is a constant, then take w i0 The left side contains a sub-wave with a maximum and a minimum, which serves as the extension of the left end of the original x(t). Otherwise, the average of the two adjacent maximum points on the left end of the original signal is taken as the maximum of the left endpoint, and the average of the two adjacent minimum points on the left end of the signal is taken as the minimum of the left endpoint, and the extension is completed.

4. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 1, characterized in that: In step 3, decomposing the distribution network traveling wave initial current signal using the symplectic geometric mode decomposition method specifically includes the following steps: Step 31: Based on Takens embedding theorem, x = x1, x2, ..., x n The one-dimensional time series of is reconstructed into a trajectory matrix X containing multidimensional signals: Where d represents the embedding dimension, τ is 1, represents the delay time, and m = n-(d-1)τ; Step 32: Construct a Hamilton matrix based on the trajectory matrix X obtained in step 31. Where the covariance matrix A = X T X; Step 33: Construct the Householder matrix And H is an orthogonal symplectic matrix; then we get the formula: Step 34: Transform X by diagonal average transformation i Convert to a time series Y of length n i =y1,y2,…y n (i=1, 2, ..., d), thus obtaining d time series of length n, i.e., d initial components, the sum of which is a one-dimensional time series x=x1, x2, ..., x n .

5. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 4, characterized in that: In step 34, X is transformed by diagonal average transformation. i Convert to a time series Y of length n i =y1,y2,…y n (i=1, 2, ..., d) is specifically: For an element x in the matrix X ij (1≤i≤m, 1≤j≤d), let d * =min(m,d),m * =max(m, d), m=n-(d-1)τ, and then the time series Y is calculated by the following formula i The element y k (k=1,2,…,n) to calculate If m < d, then let x ij * =x ij , otherwise let x ij * =x ji .

6. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 1, characterized in that: In step 4, the effective components are determined by calculating the Pearson correlation coefficient between the construction components for the extended components obtained in step 3, and the similar initial components in the effective components are reconstructed by constructing a Pearson correlation coefficient matrix, so as to obtain the final symplectic geometric components. Specifically, the steps include: Step 41, distinguishing the effective component from the noise component by calculating the Pearson correlation coefficient; Step 42: construct a Pearson correlation coefficient matrix and reconstruct similar components in the effective components by superposition, so as to obtain the final symplectic geometric components.

7. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 6, characterized in that: In step 41, the effective component and the noise component are distinguished by calculating the Pearson correlation coefficient. Specifically, the first f (f = 1, 2, ..., d) initial components Y i =y1,y2,…y n (i=1,2,…,d) add to get d groups of structural components Then calculate the sum of the two adjacent first f terms and N f The Pearson correlation coefficient is: When the Pearson coefficient grows to a certain value and remains basically unchanged, the first k value corresponding to this value is considered to be the dividing point between the effective component and the noise component. Then the component after the kth initial component is the noise component and should be separated from the d group of initial components.

8. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 6, characterized in that: In step 42, by constructing a Pearson correlation coefficient matrix, similar components in the effective components are superimposed and reconstructed to obtain the final symplectic geometric components. Specifically, the k effective components remaining after removing the noise components are reconstructed by constructing a Pearson correlation coefficient matrix. Finally, p symplectic geometric components are obtained.

9. The method for identifying traveling wave faults in a distribution network based on symplectic geometric mode decomposition according to claim 1, characterized in that: In step 5, the frequency-weighted energy operator is used to demodulate the preferred symplectic geometric component to obtain its time-energy spectrum, and the fault is finally identified as follows: The frequency-weighted energy operator is defined as: E[x(t)]=|x′(t)+jH[x′(t)] 2 = x′ 2 (t)+H[x′(t)] 2 , where x(t) represents the initial signal, H[·] represents the Hilbert transform, and the initial signal x(t) should be a harmonic signal, and its form should be x(t) = Acos(wt+φ), then x′(t) = -Awsin(wt+φ), H[x′(t)] = Awcos(wt+φ), and substituting it into the frequency-weighted energy operator, we can get E[x(t)] = A 2 w 2 , its discrete form is: After processing the fault component, the fault can be accurately identified by analyzing the obtained time-energy spectrum.

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