Power distribution network fault section positioning method based on improved dynamic time bending algorithm

Abstract

The invention discloses a power distribution network fault section positioning method based on an improved dynamic time bending algorithm. The method comprises the following steps: step 1, collecting transient zero-sequence voltage of a power distribution network model bus; step 2, collecting transient zero-sequence current data at two ends of each section by using a VMD algorithm; 3, forming time sequences corresponding to the two ends of each section; step 4, solving the distance by using an improved dynamic time warping (VDDTW) algorithm, and standardizing the VDDTW distance; and 5, setting a threshold value, and comparing the size of the standardized VDDTW distance to realize the judgment of a fault section.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power systems, more particularly to a power distribution network fault section positioning method based on an improved dynamic time warping algorithm. BACKGROUND

[0002] In recent years, the continuous deterioration of global climate and environment has promoted the low-carbon transformation in the energy field. As the main link of fossil energy consumption, the transformation of the power system into a new low-carbon power system has become an inevitable trend. The power supply reliability of the power distribution network, which directly faces users, largely determines the power supply quality at the user side, and therefore has attracted widespread attention. In order to achieve rapid isolation of the fault section and timely recovery of the non-fault section, thereby improving the power supply reliability and the power supply quality, the fault section positioning technology of the power distribution network has become one of the core problems in the research of the power distribution system.

[0003] In the operation of the power distribution network, the rapid positioning and isolation of the fault section are important links to ensure the power supply reliability. According to statistics, the occurrence rate of single-phase grounding faults in a small current grounding system accounts for about 80% of all faults. When a single-phase grounding fault occurs in such a system, the three-phase voltage remains symmetrical, and the fault current is small. In order to reduce the economic losses caused by power outages, the system is usually allowed to continue operating for 1-2 hours in a faulty state in existing projects. However, if the fault arc is not extinguished in time, the long-term existence will pose a serious threat to the system operation: on the one hand, transient grounding faults may evolve into permanent grounding faults; on the other hand, single-phase grounding faults may further develop into more serious fault forms such as two-phase grounding short circuits, and even may cause personal injury and major economic losses. Therefore, how to achieve rapid detection, accurate positioning and timely isolation of faults in a small current grounding system has become a key problem that needs to be solved. SUMMARY

[0004] The purpose of the present method is to provide a power distribution network fault section positioning method based on an improved dynamic time warping algorithm, in order to solve the technical problems of low positioning efficiency and low accuracy.

[0005] To achieve the above purpose, the present application comprises the following steps:

[0006] Step 1: Collect the transient zero sequence voltage of the bus of the power distribution network. If it exceeds the setting value, start the fault positioning process.

[0007] Step 2: Collect the transient zero sequence current signals of each section at both ends for 10 ms before and after the fault, and use the VMD algorithm to adaptively decompose the zero sequence high-frequency components.

[0008] Step 3: Form the respective time series corresponding to the two ends of the section.

[0009] Step 4, solve the distance with modified dynamic time warping algorithm (VDDTW), and normalize the VDDTW distance.

[0010] Step 5, compare the normalized VDDTW distance. Set threshold D set , if the distance is greater than D set , determine it as a fault section; otherwise, it is a healthy section.

[0011] The application is also characterized in that, in step 2, the VMD algorithm process is as follows:

[0012] a. Construction of the variational problem

[0013] The original signal f(t) is decomposed into K intrinsic modal components, and the sum of the broadband of the K IMFs is minimized and the sum of the K IMFs is equal to f(t), and the variational model with the constraint condition is as follows:

[0014]

[0015] In the formula, u k (t) = {u1, u2,..., u k} represents the set of all modal components, ω k = {ω1, ω2,..., ω k} represents the center frequency of each IMF component, δ(t) represents the unit impulse function, and "*" is the convolution calculation.

[0016] b. Solution of the variational problem

[0017] The Lagrange quadratic penalty factor α and the Lagrange multiplier λ are introduced to convert the variational problem into a non-constrained variational form, and the obtained augmented Lagrange function is as follows:

[0018]

[0019] The minimization problem is converted into the saddle point problem of the augmented Lagrange function, and the alternating direction multiplier method is used to solve the parameters by multiple iterations, and each modal component is updated by the following formula:

[0020]

[0021] In the formula, ω k = ω k+1 , and the Fourier transform of the above formula can obtain the mathematical expression in the frequency domain:

[0022]

[0023] ​The center frequency of each IMF is obtained in the same way and Lagrange multiplier The updating expression in the frequency domain is shown as follows:

[0024]

[0025] Let the parameters be The initial values of n are all 0, and the parameters u k ,ω k ,λ are iteratively updated until the convergence condition shown below is satisfied, and the iteration is stopped.

[0026]

[0027] In step 3, the time series corresponding to each end of the section are formed as shown below:

[0028] Suppose there are two sequences X = {x1, x2,..., x i ,...,x m} and Y = {y1, y2,..., y j ,...,y n}, and the distance matrix is W m×n , as shown below:

[0029]

[0030] In the above formula, W ij represents the Euclidean distance between the ith element of sequence X and the jth element of sequence Y, that is:

[0031]

[0032] The set of bending paths between the sequences is defined as Q = {q1, q2,..., q s ,...,q k}, which is a continuous set composed of the mutual mapping of sequences X and Y in W, where q s =(i,j) = W ij , represents the sth element of the bending path, and k represents the total number of elements on the path. The following constraints are set for the bending path Q:

[0033] 1) Boundary condition: the first and last ends of the bending path should be aligned, that is, q1 = (1, 1), q k =(m,n).

[0034] 2) Continuity: the two elements before and after the bending path must be adjacent, that is, given q s =(i,j) and its adjacent element q s-1 =(i',j'), it must satisfy i-i'≤1, j-j'≤1.

[0035] 3) Monotonicity: Given q s = (i,j) and its adjacent element q s-1 = (i',j'), must satisfy i-i' >= 0.

[0036] Obviously, there are many bending path numbers that meet the constraint condition, but there will always be an optimal bending path, which has the minimum That is:

[0037]

[0038] According to the idea of dynamic programming, a cumulative distance matrix is constructed, and the constraint is expressed as:

[0039]

[0040] In the formula, i=1,2,…,m, j=1,2,…,n. D(m,n) is the minimum distance value of the DTW algorithm to measure the distance between time series X and Y.

[0041] In step 4, the improved dynamic time warping algorithm process is as follows:

[0042] The original distance matrix W m×n The element defined in the two time series corresponding elements of the Euclidean distance is modified to the product of the Euclidean distance of the two time series corresponding elements and the square of the Euclidean distance of the corresponding first derivative sequence. The improved W ij As follows:

[0043]

[0044] In the formula, D(x i ) and D(y i ) represent the first derivative sequence as follows:

[0045]

[0046] The VDDTW algorithm adds the trend information of the original time series, and through comparison and verification, a standardized distance method suitable for the VDDTW algorithm is proposed, as follows:

[0047]

[0048] Compared with the prior art, the present application has the following beneficial effects: effectively improve the efficiency and accuracy of single-phase ground fault section positioning. BRIEF DESCRIPTION OF DRAWINGS

[0049] The description is attached Figure 1 is the flow chart of the method section positioning of the present application; DETAILED DESCRIPTION

[0050] The technical solutions in the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application.

[0051] Step 1, collect the transient zero sequence voltage of the bus of the power distribution network, and if the transient zero sequence voltage exceeds the setting value, start the fault location process.

[0052] Step 2, collect the transient zero sequence current signals of each section at both ends within 10 ms before and after the fault, and decompose the zero sequence high-frequency component adaptively by using the VMD algorithm.

[0053] In step 2, the VMD algorithm process is as follows:

[0054] a. Construction of the variational problem

[0055] The original signal f(t) is decomposed into K intrinsic modal components, and the sum of the K IMFs is minimized and the sum of the K IMFs is equal to f(t), and the variational model with the constraint condition is shown in the following formula:

[0056]

[0057] In the formula, u k (t)={u1,u2,···,u k} represents the set of all modal components, ω k ={ω1,ω2,···,ω k} represents the center frequency of each IMF component, δ(t) represents the unit impulse function, and “*” is the convolution calculation.

[0058] b. Solution of the variational problem

[0059] The Lagrange quadratic penalty factor α and the Lagrange multiplier λ are introduced to convert the variational problem into a non-constrained variational form, and the obtained augmented Lagrange function is shown in the following formula:

[0060]

[0061] The minimization problem is converted into the saddle point problem of the augmented Lagrange function, and the alternating direction multiplier method is used to solve the parameters by iteration, and each modal component is updated by the following formula:

[0062]

[0063] In the formula, ω k =ω k+1 , and the Fourier transform of the above formula can obtain The mathematical expression in the frequency domain is:

[0064]

[0065] The center frequency of each IMF is obtained in the same way and the Lagrange multiplier The update expression in the frequency domain is as follows:

[0066]

[0067] Let the parameters be The initial values of n are all 0, and the parameters u k ,ω k ,λ are iteratively updated until the convergence condition shown below is met, and the iteration is stopped.

[0068]

[0069] Step 3, form the respective time series corresponding to the two ends of the section.

[0070] In step 3, there are two corresponding time series, X = {x1, x2, …, x i ,…,x m} and Y = {y1, y2, …, y j ,…,y n}, which form a distance matrix W m×n , as shown below:

[0071]

[0072] In the above formula, W ij represents the Euclidean distance between the ith element of sequence X and the jth element of sequence Y, that is:

[0073]

[0074] The set of bending paths between the sequences is defined as Q = {q1, q2, …, q s ,,q k}, which is a continuous set composed of the mutual mapping of sequences X and Y in W, where q s =(i,j)=W ij , represents the sth element of the bending path, and k represents the total number of elements on the path. The following constraints are set for the bending path Q:

[0075] 1) Boundary condition: the first and last ends of the bending path should be aligned, that is, q1 = (1, 1), q k =(m,n).

[0076] 2) Continuity: the two elements before and after the bending path must be adjacent, that is, given q s= (i, j) and its adjacent elements q s-1 = (i', j') must satisfy i - i' < 1, j - j' < 1.

[0077] 3) Monotonicity: Given q s = (i, j) and its adjacent elements q s-1 = (i', j') must satisfy i - i' > 0.

[0078] It is obvious that there are many bending path numbers that meet the constraint conditions, but there will always be an optimal bending path with the smallest That is:

[0079]

[0080] According to the idea of dynamic programming, a cumulative distance matrix is constructed, and its constraint is expressed as:

[0081]

[0082] In the formula, i = 1, 2, …, m, j = 1, 2, …, n. D(m, n) is the DTW algorithm to measure the minimum distance value between time series X and Y.

[0083] Step 4, use the improved dynamic time warping algorithm (VDDTW) to solve the distance, and standardize the VDDTW distance.

[0084] In step 4, the improved dynamic time warping algorithm (VDDTW) is as follows:

[0085] The original distance matrix W m×n The Euclidean distance between the corresponding elements of the two time series defined by the elements in the matrix is modified to the product of the Euclidean distance between the corresponding elements of the two time series and the square of the Euclidean distance between the corresponding elements of the first derivative sequence. The improved W ij is as follows:

[0086]

[0087] In the formula, D(x i ) and D(y i ) represent the first derivative sequence as follows:

[0088]

[0089] The VDDTW algorithm adds the trend information of the original time series. Through comparison and verification, this paper proposes a standardized distance method suitable for VDDTW algorithm, as follows:

[0090]

[0091] Step 5, compare the normalized VDDTW distance size. Set a threshold D set , if the distance is greater than D set , then determine it as a fault section; otherwise, as a healthy section.

Claims

1. A method for locating fault sections in a distribution network based on an improved dynamic time-warping algorithm, characterized in that, Includes the following steps: Step 1: Collect the transient zero-sequence voltage of the distribution network bus. If it exceeds the set value, start the fault location process. Step 2: Collect transient zero-sequence current signals at both ends of each segment 10ms before and after the fault, and use the VMD algorithm to adaptively decompose the zero-sequence high-frequency components. Step 3: Form the time series corresponding to each end of the segment. Step 4: Solve for the distance using the improved Dynamic Time Warping (VDDTW) algorithm and normalize the VDDTW distance. Step 5: Compare the standardized VDDTW distances. Set the threshold D. set The distance is greater than D set If it is a faulty section, then it is determined to be a healthy section; otherwise, it is a healthy section.

2. In the method for locating fault sections in a distribution network based on an improved dynamic time-warping algorithm according to claim 1, step 2, the VMD algorithm flow is as follows: a. Construction of variational problems The original signal f(t) is decomposed into K intrinsic mode components, satisfying the condition that the sum of the bandwidths of the K IMF components is minimum and the sum of the K IMF components equals f(t). Its variational model with constraints is shown below: In the formula, u k (t)={u1,u2,…,u k } represents the set of all modal components, ω k ={ω1,ω2,…,ω k } represents the center frequency of each IMF component, δ(t) represents the unit impulse function, and "*" represents convolution calculation. b. Solving variational problems By introducing the Lagrange quadratic penalty factor α and the Lagrange multiplication operator λ, the variational problem is transformed into an unconstrained variational form, and the resulting augmented Lagrangian function is shown in the following equation: The minimization problem is transformed into a saddle point problem of the augmented Lagrangian function. Using the alternating direction multiplier method, the parameters are... Multiple iterations are performed to solve for each modal component. Update using the following formula: In the formula ω k =ω k+1 Performing a Fourier transform on the above equation yields... Mathematical expression in the frequency domain: The center frequencies of each IMF were obtained using the same method. and Lagrange multiplication operators The update expression in the frequency domain is as follows: Set parameters The initial value of n is 0, and the parameter u is updated iteratively. k ,ω k The iteration continues until the convergence condition shown in the following equation is met, at which point the iteration stops.

3. In the method for locating fault sections in a distribution network based on an improved dynamic time warping algorithm according to claim 1, in step 3, the time series corresponding to both ends of the section are as follows: Suppose we have two sequences X = {x1, x2, ..., x...} i ,,x m } and Y = {y1, y2, ..., y j ,,y n }, which constitutes the distance matrix W m×n As shown below: In the above formula, W ij Let represent the Euclidean distance between the i-th element of sequence X and the j-th element of sequence Y, i.e.: The set of curved paths between sequences is defined as Q = {q1, q2, ..., q}. s ,…,q k } is a continuous set consisting of the mutual mappings of sequences X and Y in W, where q s =(i,j)=W ij Let represent the s-th element of the curved path, and k represent the total number of elements on the path. The following constraints are applied to the curved path Q: 1) Boundary conditions: The beginning and end of the curved path should be aligned, i.e., q1 = (1,1), q k = (m, n). 2) Continuity: The two elements before and after a curved path must be adjacent, i.e., given q s = (i,j) and its adjacent elements q s-1 = (i', j'), which must satisfy i-i'≤1 and j-j'≤1. 3) Monotonicity: Given q s = (i,j) and its adjacent elements q s-1 = (i', j'), which must satisfy i - i' ≥ 0. Clearly, there are many curved paths that satisfy the constraints, but there will always be an optimal curved path that has the minimum... Right now: Based on the idea of ​​dynamic programming, a cumulative distance matrix is ​​constructed, and its constraints are expressed as: In the formula, i = 1, 2, ..., m, j = 1, 2, ..., n. D(m, n) is the minimum distance value between time series X and Y measured by the DTW algorithm.

4. In the method for locating fault sections in a distribution network based on an improved dynamic time-warping algorithm according to claim 1, the improved dynamic time-warping algorithm in step 4 is as follows: The original distance matrix W m×n The Euclidean distance between corresponding elements of two time series defined in the middle element definition is modified to be the product of the Euclidean distance between corresponding elements of the two time series and the square of the Euclidean distance of their corresponding first derivative sequences. The improved W ij as follows: In the formula, D(x) i ) and D(y i The sequence of first derivatives, represented by ), is shown below: The VDDTW algorithm incorporates the trend information of the original time series. Through comparative verification, this paper proposes a standardized distance method suitable for the VDDTW algorithm, as shown below:

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