CN113505852B - Low-voltage user phase identification method based on principal component analysis and EM distance - Google Patents
Low-voltage user phase identification method based on principal component analysis and EM distance Download PDFInfo
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Abstract
The low-voltage user phase identification method based on principal component analysis and EM distance comprises the following steps: collecting three-phase voltage and low-voltage user voltage of a gateway meter; carrying out Newton interpolation treatment on the missing data in the low-voltage user voltage; mapping the high-dimensional data into a low-dimensional space by utilizing principal component analysis, forming a matrix by all low-voltage user voltages, and removing the mean value of all features in the matrix to obtain a covariance matrix C; calculating the eigenvalue and eigenvector of the matrix C; calculating to obtain a principal component PC according to the eigenvalue and the eigenvector 1 、PC 2 Clustering is carried out to obtain the curves of the clustered users in each phase; calculating a clustering median according to the curve; and classifying and analyzing the cluster median and the EM distance of each phase voltage of the gateway table to obtain an identification result. The method has higher accuracy of identifying the phase, has obvious distinction degree when judging the phase compared with the traditional similarity algorithm, and solves the problem that the existing intelligent ammeter has low accuracy and selectivity of identifying the phase of the low-voltage user.
Description
Technical Field
The application relates to the technical field of smart grids, in particular to a low-voltage user phase identification method based on principal component analysis and EM distance.
Background
Single-phase electricity is mostly adopted by low-voltage users in a power distribution network, and three-phase voltage can be changed from a balanced state to an unbalanced state along with the increase, maintenance, recovery, reconfiguration and change of a user consumption mode. The unbalanced load can generate the problems of poor electric energy quality, increased power loss, shortened service life of the transformer and the like. The user phase can be accurately identified, part of the user phases can be adjusted, three-phase load balance is achieved as far as possible, distribution line loss and low-voltage power supply line power consumption are reduced, power quality is improved, and distribution transformer service life is prolonged.
Traditional phase identification is achieved by manually or actively injecting signals, both of which are costly, labor intensive, time consuming and prone to error. False phase identification can lead to errors in topology detection, state estimation, and fault location detection. At present, the electric power company upgrades the manual reading analog instrument in the distribution network to the intelligent instrument, thereby improving the observability and controllability of the distribution network. However, most of the existing intelligent electric meters only have the functions of collecting voltage and electric quantity, if only voltage is utilized, the accuracy of a judging result is difficult to guarantee, and the existing intelligent electric meters are low in identification accuracy and selectivity to low-voltage users.
Disclosure of Invention
The application provides a low-voltage user identification method based on principal component analysis and EM distance, which aims to solve the problem that the existing intelligent ammeter is low in identification accuracy and selectivity of the low-voltage user.
Earth Mover's Distance is the bulldozer Distance, EMD for short, also called Wasserstein Distance, used to represent the degree of similarity of the two distributions.
The application provides a low-voltage user phase identification method based on principal component analysis and EM distance, which comprises the following steps:
collecting three-phase voltage and low-voltage user voltage of a gateway meter;
carrying out Newton interpolation treatment on the missing data in the low-voltage user voltage to obtain high-dimensional data;
mapping the high-dimensional data into a low-dimensional space by utilizing principal component analysis, forming a matrix by all low-voltage user voltages, and removing the mean value of all features in the matrix to obtain a covariance matrix C;
calculating the eigenvalue and eigenvector of the matrix C;
calculating to obtain a principal component PC according to the characteristic value and the characteristic vector 1 、PC 2 Clustering is carried out to obtain the curves of the clustered users in each phase;
calculating a clustering median according to the curve;
and classifying and analyzing the clustering median and the EM distance of each phase voltage of the gateway table to obtain an identification result.
Optionally, the step of obtaining the high-voltage data includes:
let the sample contain n points { (x) 1 ，(x 1 )),…,(x n ，f(x n ) (x) is the missing point i ，f(x i ) Then the interpolation polynomial f (x) i ) The method comprises the following steps:
wherein f (x) i ) And calculating missing data according to the function value obtained by Newton interpolation and the interpolation polynomial.
Optionally, the step of mapping the high-dimensional data to a low-dimensional space by using principal component analysis, forming a matrix from all low-voltage user voltages, and removing the mean value of all features in the matrix to obtain a covariance matrix C includes:
mapping high-dimensional data into low-dimensional space by principal component analysis, and providing discrete time domain signal X containing M samples { X } 1 ,X 2 ,...,X M Each sample has N features, i.eFeatures x j All have respective characteristic values;
removing the mean value of all the features, solving the mean value of the same feature of all the samples, and subtracting the mean value from the self feature to obtain a covariance matrix C;
wherein, the mean formula is as follows:
the covariance matrix C is expressed as follows:
optionally, the step of calculating the eigenvalues and eigenvectors of the matrix C includes:
calculating covariance according to a covariance solving formula, wherein the diagonal of the matrix C is variance, and the non-diagonal is each covariance; the covariance solving formula is as follows:
calculating the eigenvalue and the corresponding eigenvector of the matrix C, wherein the calculation formula is as follows:
Cμ＝λμ。
optionally, calculating to obtain a principal component PC according to the characteristic value and the characteristic vector 1 、PC 2 And clustering, wherein the step of obtaining the clustered curves of the users in each phase comprises the following steps:
arranging the characteristic values from large to small to obtain { lambda } 1 ,λ 2 ,...,λ N Corresponding eigenvector is { μ } 1 ,μ 2 ,...,μ N Maximum eigenvalue λ 1 Corresponding feature vector mu 1 The 1 st main component is denoted as PC 1 The method comprises the steps of carrying out a first treatment on the surface of the Eigenvalue lambda 2 Corresponding feature vector mu 2 The 2 nd main component is denoted as PC 2 PC is connected with 1 With PC (personal computer) 2 As main information characterizing X, PC was used 1 With PC (personal computer) 2 And clustering different phase users to obtain curves of the users of each phase.
Optionally, the step of classifying and analyzing the cluster median and the EM distance of each phase voltage of the gateway table to obtain the identification result includes:
calculating the EM distance by combining the clustering median value obtained by calculating the average value of all the curves after clustering with the voltage of each phase of the gateway;
and carrying out classification analysis and correlation comparison on the EM distance to obtain attribution and recognition results of each cluster category.
Alternatively, the EM distance is calculated by:
in p 1 ，p 2 For two probability distributions, pi (p 1 ,p 2 ) Is p 1 And p is as follows 2 Combining the obtained joint distribution sets; the joint distribution of samples x and y is denoted by γ; the distance between samples is represented by the distance expectation value of the samples under the condition that the inter-sample distance is equal to the distance between samples and the joint distribution gamma is calculated, wherein the distance expectation value of the samples is represented as E (x,y):γ [||x-y||]。
The low-voltage user phase identification method based on principal component analysis and EM distance comprises the following steps: collecting three-phase voltage and low-voltage user voltage of a gateway meter; carrying out Newton interpolation treatment on the missing data in the low-voltage user voltage to obtain high-dimensional data; mapping the high-dimensional data into a low-dimensional space by utilizing principal component analysis, forming a matrix by all low-voltage user voltages, and removing the mean value of all features in the matrix to obtain a covariance matrix C; calculating the eigenvalue and eigenvector of the matrix C;calculating to obtain a principal component PC according to the characteristic value and the characteristic vector 1 、PC 2 Clustering is carried out to obtain the curves of the clustered users in each phase; calculating a clustering median according to the curve; and classifying and analyzing the clustering median and the EM distance of each phase voltage of the gateway table to obtain an identification result.
The beneficial effects of this application are: the method has the advantages that the main components of the low-voltage user voltage are firstly extracted by utilizing the main component analysis to cluster, then the clustering median value and the EM distance between each phase of voltage at the gateway are calculated to carry out phase attribution, actual measurement data prove that the method has higher accuracy of identifying the phase, and compared with the traditional similarity algorithm, the method has obvious distinction degree when judging the phase, and the problem that the existing intelligent ammeter has low accuracy and selectivity of identifying the low-voltage user phase is solved.
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In order to more clearly illustrate the technical solutions of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a flowchart of a method for identifying a low-voltage user based on principal component analysis and EM distance according to an embodiment of the present application;
FIG. 2 is a graph showing the comparison of the difference values before and after the data preprocessing in example 1 of the present application;
FIG. 3 is a graph of a low-voltage user voltage curve cluster in PCA spatial clustering point cluster in embodiment 1 of the present application;
FIG. 4 is a graph of clustering results of low voltage user voltage curve clusters in example 1 of the present application;
fig. 5 is a three-phase voltage diagram of the gate voltage ABC in example 1 of the present application.
Detailed Description
Reference will now be made in detail to the embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The embodiments described in the examples below do not represent all embodiments consistent with the present application. Merely as examples of systems and methods consistent with some aspects of the present application as detailed in the claims.
Referring to fig. 1, a flowchart of a low-voltage user phase identification method based on principal component analysis and EM distance is provided in an embodiment of the present application.
The embodiment of the application provides a low-voltage user phase identification method based on principal component analysis and EM distance, which comprises the following steps:
1. collecting three-phase voltage and low-voltage user voltage of gateway meter
2. Newton method difference value is adopted for missing data
When collecting the low-voltage user voltage curve, the data is incomplete possibly caused by the abnormality of the measuring device, interpolation processing is needed to be carried out on the data, and the sample is set to contain n points { (x) 1 ,f(x 1 )),…,(x n ,f(x n ) (x) is the missing point i ,f(x i ) Then the interpolation polynomial f (x) i ) Can be written in the following form:
in the formula (1), f (xi) is a function value obtained by newton interpolation.
3. The low-voltage user voltage forms a matrix, all the characteristics are averaged, and a covariance matrix C is obtained
Mapping high-dimensional data into low-dimensional space by principal component analysis, and providing discrete time domain signal X containing M samples { X } 1 ,X 2 ,...,X M Each sample is characterized by N, i.eFeatures x j Each having a respective characteristic value.
And removing the mean value of all the features, averaging the same feature of all the samples, and subtracting the mean value from the self feature.
Solving a covariance matrix C, wherein the expression form of the covariance matrix is as follows:
4. PC for calculating all low voltage user voltages 1 、PC 2 Clustering is carried out
And C, calculating the characteristic value and the corresponding characteristic vector.
Cμ＝λμ (4)
The eigenvalues are arranged from large to small to obtain { lambda } 1 ,λ 2 ,...,λ N Corresponding feature vector { mu } 1 ,μ 2 ,...,μ N Maximum eigenvalue λ 1 Corresponding feature vector mu 1 The 1 st principal component is denoted as PC 1 The method comprises the steps of carrying out a first treatment on the surface of the Eigenvalue lambda 2 Corresponding feature vector mu 2 The 2 nd principal component, designated PC 2 And so on. PC in general 1 And PC (personal computer) 2 Contains more than 90% of information of the sample, so that the PC can be used for 1 With PC (personal computer) 2 Two principal components are used as main information for representing X, and PC is utilized 1 With PC (personal computer) 2 Clustering of different phase users can be achieved.
5. Calculating the median value of the clustered user voltages of each phase
6. Calculating Wasserstein distance between clustering median value and gateway each phase voltage for classification
And calculating an average value of the clustered curves, and comparing the average value with each phase of the gateway to obtain the attribution of each clustered result category. Wasserstein (EM) distance is defined as follows:
in p 1 ，p 2 For two probability distributions, pi (p 1 ,p 2 ) Is p 1 And p is as follows 2 The resulting set of joint distributions is combined. Gamma table for joint distribution of samples x and yShown. The distance between samples is represented by the distance expectation value of the samples under the condition that the inter-sample distance is equal to the distance between samples and the joint distribution gamma is calculated, wherein the distance expectation value of the samples is represented as E (x,y):γ [||x-y||]The lower bound of the expected value is p in all possible joint distribution 1 And p is as follows 2 Is a Wasserstein distance of (C). Simply put, we simply put the probability distribution p 1 To probability distribution p 2 Minimum energy consumed.
In practical application, the clustering median value of various curve clusters is calculated, and the class can be accurately distinguished by comparing the clustering median value with the Wasserstein distance of the three-phase voltage, and the clustering result and the class can be finally identified because the clustering median value of various clusters and other phase distances have large homogeneous difference.
7. Outputting the identification result
In practical application, if user phases are to be identified, data are required to be clustered, and in order to fully reflect the similarity among the phases and give consideration to the algorithm operation efficiency, feature dimension reduction re-clustering is performed by using principal component analysis (Principal Component Analysis, PCA), and clustering median and gateway voltage Wasserstein distance are calculated to identify the clustering result phase category.
The following describes a low-voltage user phase identification method based on principal component analysis and EM distance provided by the present application in combination with specific measured data.
Example 1: and the three-phase voltage of the gateway in a certain region of Yunnan and the measured data of 70 low-voltage user voltages below the gateway are used.
The specific steps are as shown in fig. 1:
firstly, the missing data is subjected to interpolation treatment by adopting a Newton method, and a 24-point low-voltage user voltage curve before and after interpolation is shown in fig. 2.
Secondly, PCA clustering is carried out on 70 low-voltage user voltages, contribution degree and contribution rate of each component are calculated, the first component contribution rate is 77.26%, the second component contribution rate is 14.94%, and PC is carried out 1 With PC (personal computer) 2 The total contribution ratio of (2) is 92.2%, more than 90%, PC 1 With PC (personal computer) 2 The primary data contains most of information, so the first two principal components are selected for clustering, 70 low-voltage user voltage curve clusters are clustered in PCA space, the result of which is shown in FIG. 3, and 70 low-voltage user voltage curve clusters are clustered in PCA spaceThe clustering result of the voltage curve clusters of the voltage users is shown in fig. 4, and the three-phase voltages of the gate voltage ABC are shown in fig. 5.
And finally, calculating a median value for each clustering result according to a formula (5), and calculating a Wasserstein distance with each phase voltage of the gateway. The distance between the median value of class I curve cluster clustering and the phase A voltage Wasserstein is minimum, and the minimum distance is 0.206; the distance between the clustering median of the class II curve cluster and the phase B voltage Wasserstein is minimum, and the distance is 0.149; the distance between the median value of class III curve cluster clustering and the C-phase voltage Wasserstein is the smallest, the smallest distance is 0.197, and the distances between the median value of various clusters and other phases are relatively large.
According to the method, the principal component analysis is utilized to extract the low-voltage user voltage principal components for clustering, then the clustering median value is calculated to be attributed to the distance between each phase voltage EM of the gateway, actual measurement data prove that the method is higher in phase identification accuracy, and compared with the Pearson correlation coefficient, kendall correlation coefficient and Spearman correlation coefficient three correlation analysis algorithms, compared with the traditional similarity algorithm, the method has obvious distinction degree when judging the phase, and the problem that the existing intelligent ammeter is low in phase identification accuracy and selectivity of the low-voltage user is solved.
The foregoing detailed description of the embodiments is merely illustrative of the general principles of the present application and should not be taken in any way as limiting the scope of the invention. Any other embodiments developed in accordance with the present application without inventive effort are within the scope of the present application for those skilled in the art.
Claims (1)
1. A low-voltage user phase identification method based on principal component analysis and EM distance, comprising the steps of:
collecting three-phase voltage and low-voltage user voltage of a gateway meter;
carrying out Newton interpolation treatment on the missing data in the low-voltage user voltage to obtain high-dimensional data;
let the sample contain n points { (x) 1 ，(x 1 )),…,(x n ，f(x n ) (x) is the missing point i ，f(x i ) Then the interpolation polynomial f (x) i ) The method comprises the following steps:
wherein f (x) i ) The function value obtained by Newton interpolation is used for calculating missing data according to the interpolation polynomial;
mapping the high-dimensional data into a low-dimensional space by utilizing principal component analysis, forming a matrix by all low-voltage user voltages, and removing the mean value of all features in the matrix to obtain a covariance matrix C;
mapping high-dimensional data into low-dimensional space by principal component analysis, and providing discrete time domain signal X containing M samples { X } 1 ,X 2 ,...,X M Each sample has N features, i.eFeatures x j All have respective characteristic values;
removing the mean value of all the features, solving the mean value of the same feature of all the samples, and subtracting the mean value from the self feature to obtain a covariance matrix C;
wherein, the mean formula is as follows:
the covariance matrix C is expressed as follows:
calculating the eigenvalue and eigenvector of the matrix C;
calculating covariance according to a covariance solving formula, wherein the diagonal of the matrix C is variance, and the non-diagonal is each covariance; the covariance solving formula is as follows:
calculating the eigenvalue and the corresponding eigenvector of the matrix C, wherein the calculation formula is as follows:
Cμ＝λμ；
calculating to obtain a principal component PC according to the characteristic value and the characteristic vector 1 、PC 2 Clustering is carried out to obtain the curves of the clustered users in each phase;
arranging the characteristic values from large to small to obtain { lambda } 1 ,λ 2 ,...,λ N Corresponding eigenvector is { μ } 1 ,μ 2 ,...,μ N Maximum eigenvalue λ 1 Corresponding feature vector mu 1 The 1 st main component is denoted as PC 1 The method comprises the steps of carrying out a first treatment on the surface of the Eigenvalue lambda 2 Corresponding feature vector mu 2 The 2 nd main component is denoted as PC 2 PC is connected with 1 With PC (personal computer) 2 As main information characterizing X, PC was used 1 With PC (personal computer) 2 Clustering different phase users to obtain curves of the users in each phase;
calculating a clustering median according to the curve;
classifying and analyzing the clustering median and the EM distance of each phase voltage of the gateway table to obtain an identification result;
calculating the EM distance by combining the clustering median value obtained by calculating the average value of all the curves after clustering with the voltage of each phase of the gateway;
the EM distance is calculated by the following formula:
in p 1 ，p 2 For two probability distributions, pi (p 1 ,p 2 ) Is p 1 And p is as follows 2 Combining the obtained joint distribution sets; the joint distribution of samples x and y is denoted by γ; the distance between samples is represented by the distance expectation value of the samples under the condition that the inter-sample distance is equal to the distance between samples and the joint distribution gamma is calculated, wherein the distance expectation value of the samples is represented as E (x,y)～γ [||x-y||]；
And carrying out classification analysis and correlation comparison on the EM distance to obtain attribution and recognition results of each cluster category.
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