Low-voltage distribution network topology identification method based on weighted mahalanobis distance and granularity clustering

Abstract

The application relates to a low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granularity clustering, which comprises the following steps: collecting the voltage sequence of each user's electric meter box under each block as a sample point; using an improved weighted Mahalanobis distance to calculate the weighted Mahalanobis distance between each voltage meter sequence; calculating the density between the sample points according to the weighted Mahalanobis distance between two voltage meter sequences; for each sample point, constantly obtaining the sample point closest to the current sample point and having increased density, clustering, determining the clustering center, and discriminating the block to which the user belongs according to the clustering result. Compared with the prior art, the application is simple to realize, only needs to measure the voltage data of the smart electric meter, does not need to increase additional measuring equipment in the system, and the calculation result of the weighted Mahalanobis distance is more relevant and can better reflect the similarity relationship between the data.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of low-voltage power distribution network topology identification, in particular to a low-voltage power distribution network topology identification method based on weighted Mahalanobis distance and granularity clustering. BACKGROUND

[0002] With the continuous development of society, human beings have increasingly high requirements for power supply. As one of the most important energy infrastructure in modern society, the power distribution network is also the "last mile" to ensure high-quality power supply for users, so its stable and safe operation has an extremely important influence on ensuring reliable power supply for users. Due to the random wiring of users, the affiliation of the users to the transformer area is ambiguous;

[0003] Most of the existing low-voltage power distribution network topology identification methods directly cluster and identify according to voltage, power and current data. For example, the invention disclosed in the publication No. CN116231637A discloses a low-voltage power distribution network topology identification method based on big data analysis, which comprises the following steps: step 1, time clock synchronization of all devices under the low-voltage transformer area; step 2, configuration of the transformer area low-voltage concentrator profile, task and scheme; step 3, according to the similarity of the voltage curves of each node of the same phase, the clustering algorithm is used to cluster and analyze the reduced voltage time series data, and the topology relationship of each device is preliminarily judged; step 4, the regression coefficient of each phase device is calculated by using the law of conservation of energy, and the meter table not belonging to the branch unit is identified; step 5, the regression coefficient of the selected meter table belonging to other phase is calculated, the coefficient is compared, and the affiliation of the selected meter table is determined, and finally the topology of the entire transformer area is sorted out. The present application can effectively sort out the topology relationship of the transformer area by using the big data analysis algorithm to process the low-voltage transformer area voltage and active power data.

[0004] The above-mentioned scheme needs to obtain various basic data, and the data clustering analysis process directly calculates the similarity according to the basic data, so the clustering result will have errors, and therefore there is an urgent need for a low-voltage power distribution network topology identification method which is simple to implement, high in accuracy, and can monitor and update the affiliation of the users to the transformer area. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art and provide a low-voltage power distribution network topology identification method which is simple to implement, high in accuracy, and can monitor and update the affiliation of the users to the transformer area.

[0006] The purpose of the present application can be achieved by the following technical scheme:

[0007] A low-voltage power distribution network topology identification method based on weighted Mahalanobis distance and granularity clustering, comprising the following steps:

[0008] Collecting the voltage sequence of the meter box of each user under each transformer area as a sample point;

[0009] The improved weighted Mahalanobis distance is used to calculate the weighted Mahalanobis distance between each voltage meter sequence;

[0010] The density between sample points is calculated according to the weighted Mahalanobis distance between two voltage meter sequences, for each sample point, the sample point with the closest distance and the increased density is obtained, clustering is performed, the cluster center is determined, and the area to which the user belongs is determined according to the clustering result.

[0011] Further, the calculation expression of the weighted Mahalanobis distance is:

[0012]

[0013] In the formula, dist P (x, y) is the weighted Mahalanobis distance between sample point x and sample point y, S is the overall covariance matrix of the sample, * is the matrix multiplication operation, P is the characteristic weighted matrix, and N is the total sample number of characteristics.

[0014] Further, the acquisition process of the characteristic weighted matrix P includes:

[0015] The Mahalanobis distances of different users in the same area and the Mahalanobis distances between users in different areas are calculated to form a Mahalanobis distance matrix.

[0016] The Relief-F algorithm is used to obtain the sample feature weight according to the Mahalanobis distance matrix to construct the characteristic weighted matrix P.

[0017] Further, the calculation expression of the density between sample points is:

[0018]

[0019] In the formula, ρ j is the density of sample point j and i, d ij is the weighted Mahalanobis distance between sample point i and j, and d c is the truncation distance.

[0020] Further, the clustering is performed by using the improved DPC algorithm.

[0021] Further, the clustering process specifically includes the following steps:

[0022] An arbitrary sample point j is taken, and the initial density of the sample point is obtained.

[0023] Traverse other sample points, calculate the density of other sample points and sample point j, select sample point i closest to sample point j and having a density greater than the initial density, construct sample point i set to perform sample clustering, calculate the minimum distance between sample point i set and sample point j as the center offset distance; if there is no sample point having a density greater than the initial density, the maximum distance between sample point j and the rest of sample points is taken as the center offset distance of sample point j;

[0024] Select the point with the maximum center offset distance as the clustering center point.

[0025] Further, the calculation expression of the center offset distance of the sample point j is:

[0026]

[0027] In the formula, δ j is the center offset distance of the sample point j, d ij is the distance between the sample point i and the sample point j.

[0028] Further, the user meter box incoming line voltage effective value under each transformer area is used to construct the voltage sequence set of each transformer area in the collected sample point data.

[0029] Further, the transformer area is a transformer area in a low-voltage power distribution network.

[0030] Further, according to the clustering result, the judgment of the transformer area to which the user belongs is obtained, so that the identification of the low-voltage power distribution network topology is realized.

[0031] Compared with the prior art, the present application has the following advantages:

[0032] (1) The Mahalanobis distance corrects the problem of inconsistent and related dimensions in the Euclidean distance, and the calculation result is more relevant and can better reflect the similarity relationship between data.

[0033] (2) Only the voltage data measured by the smart meter needs to be analyzed, without the need to install additional measuring equipment, and the economy is good.

[0034] (3) The present application has less calculation amount, the principle is easy to understand, and has strong real-time performance, and has high practical research value. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 It is a flowchart of a low-voltage power distribution network topology identification method based on weighted Mahalanobis distance and granularity clustering provided in the embodiments of the present application;

[0036] Figure 2 It is a flowchart of a KNN algorithm-based neighborhood relationship calculation provided in the embodiments of the present application;

[0037] Figure 3 A result diagram obtained by clustering on a spiral data set provided in an embodiment of the present application;

[0038] Figure 4 A clustering center decision diagram based on a DPC algorithm provided in an embodiment of the present application;

[0039] Figure 5 A clustering center decision diagram based on a DPC algorithm when the number of samples is unbalanced provided in an embodiment of the present application;

[0040] Figure 6 A topological structure diagram containing multiple low-voltage distribution areas provided in an embodiment of the present application. DETAILED DESCRIPTION

[0041] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0042] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0043] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0044] Embodiment 1

[0045] As shown in the drawings, the present embodiment provides a low-voltage power distribution network topology identification method based on weighted Mahalanobis distance and granularity clustering, including the following steps: Figure 1 S1: Collect the voltage sequence of each user's meter box under each area as a sample point;

[0046] S2: Calculate the weighted Mahalanobis distance between each voltage meter sequence by using the improved weighted Mahalanobis distance;

[0047]

[0048] ​S3: Calculate the density between sample points according to the weighted Mahalanobis distance between two voltage table sequences, for each sample point, constantly obtain the sample point closest to the current sample point and with increased density, cluster, and determine the cluster center, and according to the clustering result, determine the district to which the user belongs.

[0049] The clustering process specifically includes the following steps:

[0050] Take any sample point j, obtain the initial density of the sample point;

[0051] Traverse other sample points, calculate the density of other sample points and sample point j, select sample point i closest to sample point j and with density greater than the initial density, construct sample point i set for sample clustering, calculate the minimum distance between sample point i set and sample point j as the center offset distance; if there is no sample point with density greater than the initial density, the maximum distance of sample point j and the rest of the sample points is taken as the center offset distance of sample point j;

[0052] Select the point with the maximum center offset distance as the cluster center point.

[0053] The following provides a specific implementation process of the above scheme, including the following steps:

[0054] Step 1: Accurate low-voltage power distribution network topology is the basis for fault location, electricity stealing identification and power flow calculation, and is also the prerequisite for stable operation of power grid economy. Due to the random wiring of users, the membership relationship of the user belonging to the district is fuzzy, and the present application is to identify the user and the district to which the user belongs. The Mahalanobis distance is used to calculate the electrical distance between user voltages, and the size of the electrical distance is used to determine whether there is strong correlation between the two, and then to determine the district to which the user belongs.

[0055] Step 2, the present application uses the voltage collected under the district and the voltage sequence of the user's electric meter box to calculate the distance matrix, and analyzes the matrix to realize the identification of the relationship between the user and the transformer. The collection of all voltages under the district S = { {S1} {S2} {S3}}.

[0056] Among them, S1 represents the set of user voltage sequences under district 1, S1 = {U 11 , U 12 …U 1n}, wherein U 11 represents the effective value of the incoming line voltage of the electric meter box of user 1 under district 1; U 12 represents the effective value of the incoming line voltage of the electric meter box of user 2 under district 1; U 1n represents the effective value of the incoming line voltage of the electric meter box of user n under district 1.

[0057] S2 represents the set of the incoming line voltage of the electric meter box of the users under the transformer area 2, S2={U 21 、 22 …U 2n} wherein U 21 represents the effective value of the incoming line voltage of the electric meter box of the user 1 under the transformer area 2; U 22 represents the effective value of the incoming line voltage of the electric meter box of the user 2 under the transformer area 2; and so on, U 2n represents the effective value of the incoming line voltage of the electric meter box of the user n under the transformer area 2.

[0058] S3 represents the set of the incoming line voltage of the electric meter box of the users under the transformer area 3, S3={U 31 、 32 …U 3n} wherein U 31 represents the effective value of the incoming line voltage of the electric meter box of the user 1 under the transformer area 3; U 32 represents the effective value of the incoming line voltage of the electric meter box of the user 2 under the transformer area 3; and so on, U 3n represents the effective value of the incoming line voltage of the electric meter box of the user n under the transformer area 3.

[0059] Step 3, the judgment method of the user and the transformer area to which the user belongs, the relationship between the user and the transformer area is calculated and judged by using Mahalanobis distance. The method comprises the following steps.

[0060] Step 3.1, Mahalanobis distance is derived from the probability density function of multivariate normal distribution, wherein n is the dimension of the feature vector x, μ and ∑ respectively represent the mean vector and n*n covariance matrix, and the square Mahalanobis distance of the vector x is defined as:

[0061] d 2 (x)=(x-μ) t ∑ -1 (x-μ)

[0062] Step 3.2, here ∑ is symmetric positive definite, when there are enough samples, it is a non-singular variance matrix, and the improvement of the Mahalanobis distance in the application is based on the LDt decomposition proposed by Bierman in 1977. Wherein L is a lower triangular matrix, the main diagonal elements are 1, and D is a diagonal positive definite matrix.

[0063] Step 3.3, with the improvement of step 3.2, the formula of the Mahalanobis distance is changed to the following formula:

[0064] d 2 =(x-μ) t (LDL t ) -1 (x-μ)

[0065] =(L -1 (x-μ)) t D -1 (L-1 (x-μ)

[0066] When ω is substituted for L -1 (x-μ), the above equation can be written as:

[0067]

[0068] L is a lower diagonal matrix, with 1 in the diagonal, so the previous system is solved by forward substitution:

[0069]

[0070] Step 3.4, using the modified Mahalanobis distance to calculate

[0071] Step 3.4.1, the modified Mahalanobis distance is calculated according to the above equation, first factorization, and then use the equation d 2 formula to calculate. For each round of distance calculation, there is a threshold G to determine whether to proceed to the next step of calculation or interrupt the calculation, the threshold G is the minimum value between G k and d min 2 , as shown below.

[0072] Step 3.4.2, G = Min(G k , d min 2 ). Where G is an empirical constant, representing the maximum Mahalanobis distance between vector x and C k , when the eigenvalue can be divided into C k classes, there is the following equation:

[0073] G k = {max(d m 2 (x, C k )) | x e C k}

[0074] Step 3.5, process the data, calculate the "Mahalanobis distance", which can be seen as a modification of the Euclidean distance, which modifies the problem of inconsistent and related dimensions in the Euclidean distance. The Mahalanobis distance between data points x and y:

[0075]

[0076] Where ∑ -1 is the covariance matrix of the multi-dimensional random variable, if the covariance matrix is a unit vector, then each dimension is independent and identically distributed, and the Mahalanobis distance becomes the Euclidean distance. Calculate the Mahalanobis distance between different users in the same area and the Mahalanobis distance between different area users to form a Mahalanobis distance matrix, and then analyze it.

[0077] Step 3.6, the application proposes a weighted Mahalanobis distance based on the Relief-F algorithm, and the feature weight matrix P is constructed according to the Relief-F algorithm:

[0078]

[0079] The above matrix P is a diagonal matrix, and the value in the P matrix is the weight corresponding to the feature, and N is the total sample number of the feature. The Relief-F algorithm expands the use range of the Relief algorithm, and can realize feature processing of multi-class samples, and the feature weight calculation formula is as follows:

[0080]

[0081] Where t is the sample sampling number, c is the number of nearest neighbor samples, P(y) is the probability belonging to y, M j is the nearest neighbor sample set, N j is the sample set of different categories from y, diff(A,x,M j ) is the difference of the sample in feature A.

[0082] Step 3.7, the weighted Mahalanobis distance calculation formula of the sample and the class center is:

[0083]

[0084] In the formula, S is the total covariance matrix of the sample, * is the product operation of the matrix, the membership function a(i) based on the weighted Mahalanobis distance determines the importance measure index of the sample point to the belonging class center, and the calculated a(i) is small, then the sample is given greater membership value. The membership function based on the weighted Mahalanobis distance is expressed as follows:

[0085]

[0086] Where R=maxdist P i (x,y) represents the radius of clustering, and y is the center of the clustering sample.

[0087] Step 3.8, the weighted Mahalanobis distance between the user voltage curves is calculated.

[0088] Table 1

[0089] Table No. 1 4 5 6 7 8 1 0.000 2.121 2.044 2.098 2.235 1.991 4 2.321 0.000 1.009 2.401 1.102 0.425 5 2.124 1.109 0.000 1.965 0.635 2.133 6 2.198 2.261 1.515 0.000 2.063 2.499 7 2.015 1.302 0.435 2.063 0.000 1.901 8 1.961 0.215 2.023 2.288 1.981 0.000

[0090] Table 1 is the result of calculation by using the weighted Mahalanobis distance, which is the Mahalanobis distance between different user voltages in the transformer district 1. It can be seen that the minimum distance between the users in the transformer district 1 is 2.499.

[0091] Step 3.9, calculating neighborhood relation based on KNN algorithm, using KNN algorithm to select k samples with minimum weighted Mahalanobis distance as the neighborhood set of each sample.

[0092] Step 4.1, as shown in the formula, calculating sample density based on improved DPC algorithm. DPC algorithm is an algorithm that can automatically calculate clustering center and realize clustering of features with arbitrary distribution. The algorithm realizes clustering process as follows: Figure 2

[0093] Step 4.1.1, calculating the density ρ j of sample point.

[0094]

[0095] where d ij is the weighted Mahalanobis distance between sample points i and j, and d c is the truncation distance.

[0096] Step 4.1.2, randomly selecting a sample point j, and according to the following formula, finding the nearest neighborhood sample point i with density greater than the above formula.

[0097]

[0098] where δ j is the minimum distance between sample point j and samples with density higher than ρ j , also called center offset distance. If the density is less than ρ j , the minimum distance is the maximum distance between the sample point and other points, and i is the sample number with density higher than ρ j .

[0099] Step 4.2, selecting the clustering center of the sample. Density peak clustering algorithm considers that the point with large center offset distance is the clustering center point, that is, the clustering center density should be relatively large, and should be far away from the point with larger density.

[0100]

[0101] In the above formula, ρ = [ρ1, …, ρ i , …, ρ m ] and δ = [δ1, …, δ i , …, δ m ] are density vector and distance vector respectively, and m is the number of samples. is the inner product of vectors, and γ represents the clustering center. The larger the value is, the more it indicates the clustering center.

[0102] ​Step 4.3, complete DPC clustering, output clustering results, that is, the set of users contained in each area {C T1 , C T2 , …, C Ti}, wherein C Tl (l = 1, 2…i) is the clustering result of the area l, and i is the total number of areas.

[0103] Step 5, according to the previous calculation, we can know the weighted Mahalanobis distance of the users in a certain area, and the density and clustering center of the sample are calculated according to the density peak value clustering algorithm to output the clustering result. Thus, the discrimination of the user belonging to the area is completed.

[0104] Figure 3 is the result obtained by clustering on the spiral data set, and three clustering centers are obtained, which are consistent with the true structure, and the output clustering centers are 95, 198 and 301.

[0105] Figure 4 is the clustering center decision diagram based on the DPC algorithm, and the abnormal points with larger γ values are taken as the clustering centers. As shown in the figure, the γ values of three sample points are obviously larger than those of other sample points, and the γ values of other sample points are all close to 2 and are connected closely, and there is no abnormal value such as breakage between them. Therefore, it can be judged that there are three clustering centers, that is, three areas.

[0106] Figure 5 is the clustering center decision diagram based on the DPC algorithm when the number of samples is unbalanced, and the abnormal points with larger γ values are taken as the clustering centers. As shown in the figure, it contains two sample centers, that is, two areas, which is contrary to the true situation.

[0107] Figure 6 is the topological structure provided by the application containing a plurality of low-voltage power distribution areas. In the figure, users 4-18 are single-phase loads. In order to avoid the graph being messy, the graph is simplified, and a single-line graph is used to represent.

[0108] The connection relationship between the user and the area is finally determined, and the automatic identification of the power grid topology is realized.

[0109] The above describes the preferred embodiments of the application in detail. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment on the basis of the prior art according to the concept of the application shall be within the protection scope determined by the claims.

Claims

1. A method for topology identification of low-voltage distribution networks based on weighted Mahalanobis distance and granular clustering, characterized in that, Includes the following steps: Collect the voltage sequence of the meter box of each user under each transformer area as a sample point; The weighted Mahalanobis distance between each voltmeter sequence is calculated using an improved weighted Mahalanobis distance method. The density between sample points is calculated based on the weighted Mahalanobis distance between two voltmeter sequences. For each sample point, the nearest sample point with increasing density is continuously acquired, clustered, and the cluster center is determined. The user's transformer area is then identified based on the clustering results. The expression for calculating the density between the sample points is: In the formula, Let the density of sample points j and i be... d ij d is the weighted Mahalanobis distance between sample points i and j. c It is the cutoff distance; The weighted Mahalanobis distance is calculated as follows: In the formula, For sample points and sample points The weighted Mahalanobis distance between them Let be the population covariance matrix of the sample, and * denote the matrix multiplication operation. This is the feature weighting matrix, where N is the total number of samples for each feature. The clustering process specifically includes the following steps: Take any sample point j and obtain the initial density of that sample point; Traverse other sample points, calculate the density of other sample points and sample point j, select sample point i that is closest to sample point j and has a density greater than the initial density, construct sample point i set for sample clustering, calculate the minimum distance between sample point i set and sample point j as the center offset distance; if there is no sample point with a density greater than the initial density, then take the maximum distance between sample point j and the other sample points as the center offset distance of sample point j. The point with the largest center offset distance is selected as the cluster center.

2. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, The feature weighting matrix The acquisition process includes: Calculate the Mahalanobis distance between different users in the same transformer area and the Mahalanobis distance between users in different transformer areas to form a Mahalanobis distance matrix. Using the Relief-F algorithm, the feature weighting matrix P is constructed by obtaining the sample feature weights based on the Mahalanobis distance matrix.

3. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, The clustering is performed using an improved DPC algorithm.

4. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, The expression for calculating the center offset distance of sample point j is: In the formula, The center offset distance of sample point j. Let be the distance between sample point i and sample point j.

5. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, In the collected sample point data, the voltage sequence set of each transformer substation is constructed based on the effective value of the incoming line voltage of the user meter box under each transformer substation.

6. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, The transformer substation refers to a transformer substation in a low-voltage distribution network.

7. The low-voltage distribution network topology identification method based on weighted Mahalanobis distance and granular clustering according to claim 1, characterized in that, Based on the clustering results, the user's distribution area is identified, thereby realizing the identification of the low-voltage distribution network topology.

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