Electric power system bad data identification method and system based on random matrix and spectral clustering

Abstract

The invention discloses an electric power system bad data identification method and system based on a random matrix and spectral clustering, and the method comprises the steps: obtaining a corresponding measurement error based on the obtained measurement data of an electric power system, and constructing a corresponding first measurement matrix based on the measurement error; constructing a corresponding first Hermitian matrix based on the first measurement matrix; extracting a feature vector and an estimated feature value of the first Hermitian matrix by using a random matrix theory, and obtaining a residual feature quantity based on the feature vector and the estimated feature value; and performing spectral clustering analysis on the residual characteristic quantity, and identifying bad data of the power system. According to the method, the influence of measurement errors on bad data identification accuracy can be reduced, and the accuracy of state estimation of the power system is further improved.

Description

Technical Field

[0001] The present application relates to the technical field of power system situation awareness, and in particular to a method and system for identifying bad data in a power system based on random matrices and spectral clustering. Background Art

[0002] Power system state estimation plays an important role in power system operation (such as optimal power flow, stability analysis and economic dispatch). During the process of information collection and transmission, measurement data is often affected by measuring instrument noise, communication noise and random fluctuations, and thus has the problem of bad data, which in turn affects the accuracy of power system state estimation.

[0003] The existing technology generally uses the weighted least squares method to identify bad data in the power system. Its core strategy is to use the deviation between the output of the least squares estimator and the measured data as the evaluation basis, and then identify and eliminate bad data through hypothesis testing. However, in actual power systems, the error between the measured value and the true value (i.e., measurement error) is often unknown. Therefore, this method is essentially limited to only considering the impact of the residual on the state estimation result, but fails to directly involve the potential impact of the measurement error itself on the state estimation, affecting the effect of bad data identification, and then affecting the accuracy of power system state estimation.

[0004] Application Contents

[0005] The present application provides a method and system for identifying bad data in a power system based on random matrix and spectral clustering, so as to reduce the influence of measurement error on the accuracy of bad data identification, thereby improving the accuracy of power system state estimation.

[0006] In a first aspect, the present application provides a method for identifying bad data in a power system, comprising:

[0007] Obtaining a corresponding measurement error based on the acquired power system measurement data, and constructing a corresponding first measurement matrix based on the measurement error;

[0008] constructing a corresponding first Hermitian matrix based on the first measurement matrix;

[0009] Extracting eigenvectors and estimated eigenvalues ​​of the first Hermitian matrix using random matrix theory, and obtaining residual feature quantities based on the eigenvectors and the estimated eigenvalues;

[0010] A spectral clustering analysis is performed on the residual feature quantity to identify bad data of the power system.

[0011] The embodiment of the present application obtains the corresponding measurement error based on the acquired power system measurement data, and constructs the corresponding first measurement matrix based on the measurement error, so as to facilitate the subsequent conversion into the corresponding Hermitian matrix and extract the eigenvalues ​​related to the measurement error; constructs the corresponding first Hermitian matrix based on the first measurement matrix, and extracts the eigenvalues ​​from the first Hermitian matrix, so as to mine the residual feature quantities related to the measurement error in the multi-section measurement data, so as to facilitate the subsequent accurate identification of bad data; and by performing bad parameter identification on the residual feature quantities related to the measurement error, the influence of the measurement error on the accuracy of bad data identification can be reduced, thereby improving the accuracy of power system state estimation.

[0012] Furthermore, the obtaining of the corresponding measurement error based on the acquired power system measurement data and constructing the corresponding first measurement matrix based on the measurement error are specifically as follows:

[0013] Obtain the measurement data of the power system during operation within the sampling period through the SCADA system;

[0014] Calculating a measurement error corresponding to the measurement data, and normalizing the measurement error to obtain a measurement vector;

[0015] Based on the measurement vector within a sampling period, a corresponding first measurement matrix is ​​constructed.

[0016] In this way, by constructing the corresponding first measurement matrix from the perspective of the measurement error, it is convenient to extract the eigenvalues ​​related to the measurement error after subsequent conversion into the corresponding Hermitian matrix.

[0017] Furthermore, the constructing of a corresponding first Hermitian matrix based on the first measurement matrix is ​​specifically:

[0018] Obtaining a conjugate transposed matrix corresponding to the first measurement matrix;

[0019] A first Hermitian matrix corresponding to the first measurement matrix is ​​constructed based on the first measurement matrix and the conjugate transposed matrix.

[0020] In this way, by converting the first measurement matrix into a first Hermitian matrix, it is convenient to bridge the covariance matrix and the measurement matrix, and it is convenient to extract the eigenvalues ​​related to the measurement error.

[0021] Furthermore, the formula for constructing the first Hermitian matrix corresponding to the first measurement matrix is ​​specifically:

[0022]

[0023] Where D Z is the first Hermitian matrix, Z is the first measurement matrix, and Z His the conjugate transposed matrix of the first measurement matrix.

[0024] In this way, by converting the first measurement matrix into a first Hermitian matrix, it is convenient to bridge the covariance matrix and the measurement matrix, and it is convenient to extract the eigenvalues ​​related to the measurement error.

[0025] Furthermore, the random matrix theory is used to extract the eigenvector and estimated eigenvalue of the first Hermitian matrix, and based on the eigenvector and the estimated eigenvalue, the residual feature quantity is obtained, specifically:

[0026] Based on the first Hermitian matrix, obtaining a covariance matrix corresponding to the first measurement matrix;

[0027] extracting the estimated eigenvalues ​​in the first Hermitian matrix and the covariance matrix respectively;

[0028] reconstructing a second Hermitian matrix based on the eigenvectors and the estimated eigenvalues, and restoring a second measurement matrix based on the second Hermitian matrix;

[0029] The residual feature quantity is extracted from the second measurement matrix.

[0030] In this way, by bridging the covariance matrix and the first measurement matrix through the first Hermitian matrix, the eigenvalues ​​of the first measurement matrix can be obtained according to the eigenvalues ​​of the covariance matrix, and by restoring the second measurement matrix, the residual feature quantities related to the measurement errors in the multi-section measurement data can be mined, which facilitates the subsequent accurate identification of bad data.

[0031] Furthermore, the formula for extracting the estimated eigenvalue is specifically:

[0032]

[0033] In the formula, ξ i is the i-th eigenvalue λ in the partial matrix of the covariance matrix i The corresponding ith estimated eigenvalue, h E (λ i ) is the real part of the Stieltjes transform of the partial matrix in the covariance matrix, ρ E (λ i ) is the result of the inverse Stieltjes transform of the partial matrix in the covariance matrix, q=T / N, T is the number of columns in the measurement matrix, and N is the number of rows in the measurement matrix.

[0034] In this way, by bridging the covariance matrix and the first measurement matrix through the first Hermitian matrix, the eigenvalues ​​of the first measurement matrix can be obtained according to the eigenvalues ​​of the covariance matrix, and by restoring the second measurement matrix, the residual feature quantities related to the measurement errors in the multi-section measurement data can be mined, which facilitates the subsequent accurate identification of bad data.

[0035] Furthermore, the residual feature quantity is subjected to spectral clustering analysis to identify bad data of the power system, specifically:

[0036] Establishing a similarity matrix based on the similarity between any two of the residual feature quantities, and constructing a corresponding diagonal matrix based on the similarity matrix;

[0037] Based on the diagonal matrix and the similarity matrix, a Laplace matrix is ​​obtained;

[0038] Extracting the minimum eigenvalue in the Laplace matrix, and forming a characteristic matrix based on the eigenvector corresponding to the minimum eigenvalue;

[0039] By performing K-means clustering on the feature matrix, bad data of the power system is identified.

[0040] In this way, by establishing a similarity matrix based on the similarity between any two of the residual feature quantities, and then obtaining a diagonal matrix and a Laplace matrix, and using the eigenvalues ​​of the Laplace matrix to capture the intrinsic correlation between the features, bad data can be identified more accurately with higher robustness and precision.

[0041] Furthermore, the objective function of the spectral clustering analysis is specifically:

[0042]

[0043] In the formula, A i is the subgraph of spectral clustering, m is the number of subgraphs, is the cutting weight, is a matrix consisting of m indicator vectors as column vectors.

[0044] In this way, by establishing a similarity matrix based on the similarity between any two of the residual feature quantities, and then obtaining a diagonal matrix and a Laplace matrix, and using the eigenvalues ​​of the Laplace matrix to capture the intrinsic correlation between the features, bad data can be identified more accurately with higher robustness and precision.

[0045] In a second aspect, the present application provides a bad data identification system for a power system, comprising: a first building module, a second building module, an extraction module and an identification module;

[0046] The first constructing module is used to obtain a corresponding measurement error based on the acquired power system measurement data, and construct a corresponding first measurement matrix based on the measurement error;

[0047] The second construction module is used to construct a corresponding first Hermitian matrix based on the first measurement matrix;

[0048] The extraction module is used to extract the eigenvectors and estimated eigenvalues ​​of the first Hermitian matrix by using random matrix theory, and obtain residual feature quantities based on the eigenvectors and the estimated eigenvalues;

[0049] The identification module is used to perform spectral clustering analysis on the residual feature quantity to identify bad data of the power system.

[0050] The embodiment of the present application obtains the corresponding measurement error based on the acquired power system measurement data, and constructs the corresponding first measurement matrix based on the measurement error, so as to facilitate the subsequent conversion into the corresponding Hermitian matrix and extract the eigenvalues ​​related to the measurement error; constructs the corresponding first Hermitian matrix based on the first measurement matrix, and extracts the eigenvalues ​​from the first Hermitian matrix, so as to mine the residual feature quantities related to the measurement error in the multi-section measurement data, so as to facilitate the subsequent accurate identification of bad data; and by performing bad parameter identification on the residual feature quantities related to the measurement error, the influence of the measurement error on the accuracy of bad data identification can be reduced, thereby improving the accuracy of power system state estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flowchart of an embodiment of a method for identifying bad data in a power system provided by the present application;

[0052] Figure 2 is a flow chart of estimated feature value extraction provided by the applicant;

[0053] Figure 3 It is a result diagram of bad data identification of voltage amplitude measurement at a time section of IEEE30 node 100 according to the present invention;

[0054] Figure 4 This is a comparison chart of the bad data identification accuracy between the present invention and the traditional method;

[0055] Figure 5 It is a structural schematic diagram of an embodiment of a power system bad data identification system provided by the present application. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0057] It should be understood that the step numbers used in this article are only for the convenience of description and are not intended to limit the order in which the steps are executed.

[0058] It should be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an" and "the" are intended to include plural forms unless the context clearly indicates otherwise.

[0059] The terms “include” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0060] The term "and / or" means and includes any and all possible combinations of one or more of the associated listed items.

[0061] Random Matrix Theory (RMT) is a mathematical tool that uses the principles of statistical mechanics to simulate and study the interactions of complex systems in multiple mathematical fields. It can aggregate completely random measurement errors into matrix form and study high-dimensional data characteristics such as the eigenvalues ​​of their covariance matrices, which helps to extract the deterministic characteristics of measurement errors, thereby making up for the problem that traditional bad data identification methods fail to consider measurement errors.

[0062] Spectral clustering (SC) is a clustering method based on graph theory. Its core idea is to regard data points as nodes in the graph, and the similarity or distance between nodes as the weight of the edge, so as to construct a weighted undirected graph. Then, the spectral clustering algorithm divides the graph into two or more optimal subgraphs by optimizing a certain objective function, so that the data points within the subgraphs are as similar as possible, and the data points between the subgraphs are as different as possible, so as to achieve the purpose of clustering. In this application, an undirected weighted graph composed of measurement sampling samples of a time section can be divided into multiple subgraphs to achieve clustering of bad data and normal data.

[0063] Power system state estimation is crucial in optimal power flow, stability analysis, economic dispatch and other operations. Measurement data often contains bad data due to instrument noise, communication noise and random fluctuations, which in turn affects the accuracy of power system state estimation. At present, the weighted least squares method is commonly used to identify bad data, using the deviation between the output of the least squares estimator and the measurement data as the evaluation basis, and then using hypothesis testing to identify and eliminate bad data. However, since the actual measurement error is unknown, this method can only evaluate the impact of residuals on state estimation, and does not directly consider the potential impact of measurement errors on state estimation, which limits the identification effect of bad data and the accuracy of power system state estimation.

[0064] Embodiment 1

[0065] Please refer to Figure 1 , Figure 1 It is a flowchart of an embodiment of a method for identifying bad data in a power system provided by the present application, including steps S11 to S14;

[0066] Step S11, obtaining a corresponding measurement error based on the acquired power system measurement data, and constructing a corresponding first measurement matrix based on the measurement error;

[0067] It can be understood that, firstly, the SCADA system can be deployed in various locations in the power system to obtain measurement data during the operation of the power system within a sampling time period; wherein the measurement data includes but is not limited to the voltage amplitude of different nodes in the power system, the active and reactive power injected by the nodes, and the power flow at the input and output of the branch.

[0068] It should be noted that the SCADA (Supervisory Control and Data Acquisition) system collects measurement data through a variety of measurement devices distributed throughout the power grid, such as voltage transformers, current transformers, power meters, and intelligent electronic devices. On the one hand, the measurement data can be obtained directly through the SCADA system, and on the other hand, the measurement data can also be obtained in advance through the SCADA system and transmitted to data acquisition units such as remote terminal units (RTUs) and intelligent electronic devices (IEDs), and then uploaded to the control center in real time through communication protocols and networks. After preliminary quality inspection and processing, it is stored in the database of the SCADA system, and the measurement data is subsequently obtained from the database. Among them, the sampling frequency of the SCADA system is usually determined according to the specific needs of the power grid, which can range from several times per second to once every few seconds.

[0069] Secondly, it is necessary to calculate the measurement error corresponding to the measurement data, the measurement error includes variance and deviation, and normalize the measurement error to obtain a measurement vector; wherein the normalization formula is:

[0070]

[0071] In the formula, z i is the measurement vector, σ i is the standard deviation of the measurement error, z i is the measurement error, b i is the variance of the measurement error, is the weight coefficient of the i-th measurement data in the least squares method.

[0072] Finally, based on the measurement vector in the sampling time period, a corresponding first measurement matrix is ​​constructed. For example, a sampling window is divided from the current moment forward by T (N < T) moments to form a measurement matrix of N × T (N < T) dimensions. in In the formula, is the normalized measurement vector at the current moment, N is the number of rows in the measurement matrix (the number of sampled measurement data), each row in the matrix represents a measurement data sampled by the SCADA system, and T is the number of columns in the measurement matrix (the number of continuous samples in the sampling time period).

[0073] It should be noted that, assuming that the true value matrix corresponding to the measurement matrix Z is, where H = [h(x) k-N+1 ,h(x) k-N+2 ,……,h(x) k-1 ,h(x) k ], we can also get the measurement matrix Z = H + G, where G is a normalized Gaussian matrix, each element of which is independent and identically distributed, with zero mean and unit variance.

[0074] In this way, by constructing the corresponding first measurement matrix from the perspective of the measurement error, it is convenient to extract the eigenvalues ​​related to the measurement error after subsequent conversion into the corresponding Hermitian matrix.

[0075] Step S12: constructing a corresponding first Hermitian matrix based on the first measurement matrix;

[0076] It can be understood that after constructing the first measurement matrix corresponding to the measurement error, it can be converted into the corresponding first Hermitian matrix. Specifically, the conjugate transposed matrix Z corresponding to the first measurement matrix Z is obtained. H ; and place the first measurement matrix Z in the upper right corner, and the conjugate transposed matrix Z H Place it in the lower left corner to perform matrix block construction to construct the first Hermitian matrix D corresponding to the first measurement matrix Z , where the first Hermitian matrix D Z The construction formula is as follows:

[0077]

[0078] Where D Z is the first Hermitian matrix, Z is the first measurement matrix, Z H is the conjugate transposed matrix of the first measurement matrix.

[0079] It should be noted that a Hermitian matrix refers to a self-conjugate matrix. A matrix A is a Hermitian matrix if and only if A = A H , where A H represents the conjugate transpose of A. The Hermitian matrix has two properties: (1) The absolute value of the eigenvalue of a Hermitian matrix is ​​equal to its corresponding singular value. (2) If λ is an eigenvalue of a Hermitian matrix, then its opposite -λ must be another eigenvalue. The singular value is related to the singular value decomposition (SVD) of the matrix, which describes the degree of "stretching" of the matrix in different directions. For an m×n matrix A, its singular value is A T The square root of the eigenvalue of A. The purpose of constructing the Hermitian matrix is ​​to use its properties to obtain the first Hermitian matrix D from the first measurement matrix Z The covariance matrix F Z The first Hermitian matrix D of the first measurement matrix is ​​restored from the eigenvalues ​​of Z The characteristic value of .

[0080] In this way, by converting the first measurement matrix into a first Hermitian matrix, it is convenient to bridge the covariance matrix and the measurement matrix, and it is convenient to extract the eigenvalues ​​related to the measurement error.

[0081] Step S13, extracting the eigenvector and estimated eigenvalue of the first Hermitian matrix by using random matrix theory, and obtaining residual feature quantities based on the eigenvector and the estimated eigenvalue;

[0082] It is understandable that after obtaining the first Hermitian matrix, the corresponding eigenvalues ​​can be extracted by random matrix theory. Specifically, first, based on the first Hermitian matrix D Z , and obtain the covariance matrix F corresponding to the first measurement matrix Z ,in,

[0083] It should be noted that since the first Hermitian matrix D Z The absolute value of the eigenvalue in is equal to its corresponding singular value, so the first Hermitian matrix D Z The singular values ​​of Z T D Z =F Z The square of the eigenvalues, so the first Hermitian matrix D Zand the covariance matrix F Z The relationship between the eigenvalues ​​of is: In the formula, and Denote the first Hermitian matrix D Z and the covariance matrix F Z The eigenvalues ​​of and the covariance matrix F Z and ZZ H The eigenvalues ​​of are reversibly related, that is: Therefore, based on this feature, the covariance matrix F can be extracted separately Z and the first Hermitian matrix D Z The estimated eigenvalue ξ Fi and Di .

[0084] It should be noted that the Hermitian matrix and covariance matrix corresponding to the true value matrix can also be constructed. By constructing the Hermitian matrix and covariance matrix corresponding to the true value matrix, the corresponding eigenvalues ​​can be extracted, and the relationship between the measurement matrix and the true value matrix can be established to facilitate the subsequent extraction of the eigenvalues ​​of the corresponding measurement matrix. H and the covariance matrix F H They are: Its Hermitian matrix D H The eigenvalue λ DH , covariance matrix F H The eigenvalue of and HH H The eigenvalue of for:

[0085] Secondly, by the first Hermitian matrix D Z Perform eigenvalue decomposition to obtain eigenvectors, and extract the estimated eigenvalues ​​in the covariance matrix; ZZ can be used H Estimated HH H The eigenvalue of Thus, the actual value of the measurement value is further estimated, thereby extracting the residual feature quantity of the measurement matrix. Specifically, E = ZZ H and C=HH H To express the measurement matrix Z = H + G as a covariance matrix, that is:

[0086] E=(H+G)(H+G) H

[0087] =C+GG H +HG H +GH H

[0088] =C+B;

[0089] Let c i 、v li and v ri denote the i-th eigenvalue, left eigenvector, and right eigenvector of C respectively. Let λ i 、u li and u ri denote the i-th eigenvalue, left eigenvector, and right eigenvector of E, respectively. Let ξ i is the same as λ in E i The corresponding i-th estimated eigenvalue. The estimated objective function is:

[0090] Where Γ(E) is the estimate of C by E. Since Γ(E) and C are both symmetric matrices, the l of Γ(E)-C is 2 The norm is equal to the trace of its square, since the trace of the matrix C (equal to the sum of its eigenvalues) can be approximated.

[0091] Assuming that Γ(E) and E have the same eigenvector, the formula is:

[0092] Among them, λ in E i The corresponding i-th estimated eigenvalue ξ i The calculation formula is:

[0093] In the formula, (·) represents the inner product between two vectors, indicates (v lj ·u li ) 2 expectations, The calculation formula is:

[0094]

[0095] in, λ i and c i It can be obtained by eigenvalue decomposition of matrix E and matrix C respectively, h E (λ i ) is the Stieltjes transformation g in random matrix theory E The real part of (s), that is: ρ E (λ i ) is the Stieltjes inverse transform in random matrix theory: Here, η is a small integer close to zero, and Im[·] represents the imaginary part.

[0096] It should be noted that one of the most common pre-solutions of the covariance matrix E is: E(s)=(sI N -E) -1 ;in is a complex variable, is the identity matrix. Therefore, the Stieltjes transform can be defined as: where Tr(·) is the trace of E. N represents the number of rows of E, and λ i is the i-th eigenvalue of E.

[0097] Therefore, combined with λ in E i The corresponding i-th estimated eigenvalue ξ i The calculation formula is the same as (v lj ·u li ) 2 The expected estimated eigenvalue of Γ(E) is:

[0098]

[0099] In the formula, ξ i is the i-th eigenvalue λ in the partial matrix of the covariance matrix i The corresponding ith estimated eigenvalue, h E (λ i ) is the real part of the Stieltjes transform of the partial matrix in the covariance matrix, ρ E (λ i ) is the result of the inverse Stieltjes transform of the partial matrix in the covariance matrix.

[0100] According to the principle of matrix eigenvalue decomposition and the principle of rotation invariance (that is, the eigenvalues ​​before and after estimation share the same eigenvector), the second Hermitian matrix Γ (D Z ),in, Among them, Di 、u lDi and u rDi Respectively represent D Z The estimated value of the i-th eigenvalue and the corresponding first Hermitian matrix D Z The left and right eigenvectors are extracted by the above-mentioned extraction method, which will not be repeated here, and are based on the second Hermitian matrix Γ(D Z )Select Γ(D Z ) The first to N rows and the N+1 to N+T columns restore the second measurement matrix Γ(Z). Then, the residual feature r is extracted from the second measurement matrix to restore the second measurement matrix Γ(Z). i :r i =|z i -γ(z i )|, where γ(zi ) is the i-th estimator measurement, z i is the ith estimator.

[0101] It should be noted that the measured variables can be divided into sets of appropriate size according to their physical meaning. For example, assuming that a set of measured data is obtained for the cross section at the current moment, the measured data includes: voltage amplitude, node injected active power, node injected reactive power, then the measured data is divided into three groups to construct three sets of measurement matrices, and their Hermitian matrices and covariance matrices are constructed respectively, and the corresponding feature quantities are further extracted respectively, and finally the feature quantities are combined in the order of voltage amplitude, node injected active power, and node injected reactive power. In this way, the size of the required calculation matrix can be greatly reduced without significantly reducing the effect of the extracted features, thereby improving the calculation efficiency.

[0102] To understand the method of estimating eigenvalue extraction, please refer to Figure 2 , Figure 2 is a flowchart of estimated eigenvalue extraction provided by the applicant; first, a measurement matrix Z is constructed based on the measurement error of the measurement data, and the measurement matrix Z is converted into the first Hermitian matrix D Z ; Secondly, get the first Hermitian matrix D Z The corresponding left and right eigenvectors, and the first Hermitian matrix D Z Convert to covariance matrix F Z , and measure the matrix Z = H + G expressed as a covariance matrix, and get the matrix E = ZZ H , using random matrix theory to extract the estimated eigenvalues ​​in the matrix E, and further obtain the second Hermitian matrix Γ(D Z ) corresponding to the estimated eigenvalue; then based on the first Hermitian matrix D Z The corresponding left and right eigenvectors and the second Hermitian matrix Γ(D Z ) corresponding to the estimated eigenvalues ​​to reconstruct the second Hermitian matrix Γ(D Z ), and further restore the second measurement matrix Γ(Z), and then the residual feature r can be extracted from the second measurement matrix Γ(Z) i , for use in subsequent spectral clustering analysis.

[0103] In this way, by bridging the covariance matrix and the first measurement matrix through the first Hermitian matrix, the eigenvalues ​​of the first measurement matrix can be obtained according to the eigenvalues ​​of the covariance matrix, and by restoring the second measurement matrix, the residual feature quantities related to the measurement errors in the multi-section measurement data can be mined, which facilitates the subsequent accurate identification of bad data.

[0104] Step S14: performing spectral clustering analysis on the residual feature quantity to identify bad data of the power system.

[0105] It can be understood that after obtaining the residual feature, the residual feature can be input into spectral clustering to identify bad data. Specifically, first, the similarity ω between any two residual feature is calculated. ij , and establish a similarity matrix W based on the similarity, where In the formula, ω ij is the similarity between any two residual feature quantities, r i and r j are the i-th and j-th residual feature quantities, δ i is the scaling function δ i =d(r i ,r K ), where d(·) represents the Euclidean distance function, r K Represents the data with connectivity K with i; then construct the corresponding diagonal matrix D based on the similarity matrix d ; Among them, the diagonal matrix D d The formula is: D d =diag(d i ),i=1,2,…,n, where

[0106] Secondly, based on the diagonal matrix D d and the similarity matrix W, we get the Laplace matrix L, where L = D d -W, where L is a symmetric positive semidefinite matrix with eigenvalue λ i , the eigenvalues ​​are arranged as follows: 0 = λ 1 ≤λ 2 ≤...≤λ n .

[0107] Next, extract the minimum eigenvalue in the Laplace matrix, and form a characteristic matrix based on the eigenvector corresponding to the minimum eigenvalue; define the indicator vector h j , where h j =[h 1j h 2j ...h nj ] T , make is a matrix composed of m indicator vectors as column vectors, whose column vectors are mutually orthogonal, that is, H T H=I. It can be proved that for subgraph A i , whose cut corresponds to For m subgraphs, we can get:

[0108]

[0109] In the formula, Ai is the subgraph of spectral clustering, m is the number of subgraphs, is the cutting weight, is a matrix L consisting of m indicator vectors as column vectors.

[0110] And the spectral clustering objective function is converted to: According to the Rayleigh quotient property, the minimum value of the spectral clustering objective function is equal to the sum of the first m smallest eigenvalues ​​of the matrix L.

[0111] Finally, by performing K-means clustering on the matrix F consisting of the eigenvectors corresponding to the minimum eigenvalue of the matrix L, cluster C is obtained. 1 and C 2 , where C 1 Contains normal data, C 2 Contains bad data, thereby identifying bad data in the power system.

[0112] In this way, by establishing a similarity matrix based on the similarity between any two of the residual feature quantities, and then obtaining a diagonal matrix and a Laplace matrix, and using the eigenvalues ​​of the Laplace matrix to capture the intrinsic correlation between the features, bad data can be identified more accurately with higher robustness and precision.

[0113] The embodiment of the present application obtains the corresponding measurement error based on the acquired power system measurement data, and constructs the corresponding first measurement matrix based on the measurement error, so as to facilitate the subsequent conversion into the corresponding Hermitian matrix and extract the eigenvalues ​​related to the measurement error; constructs the corresponding first Hermitian matrix based on the first measurement matrix, and extracts the eigenvalues ​​from the first Hermitian matrix, so as to mine the residual feature quantities related to the measurement error in the multi-section measurement data, so as to facilitate the subsequent accurate identification of bad data; and by performing bad parameter identification on the residual feature quantities related to the measurement error, the influence of the measurement error on the accuracy of bad data identification can be reduced, thereby improving the accuracy of power system state estimation.

[0114] The present invention uses the IEEE 30 node system to simulate and verify the above method to prove the beneficial effect of the present invention in bad data identification. The method can be implemented and run in MATLAB 2022b. The result of the bad data identification of the voltage amplitude measurement at the time section of the IEEE 30 node 100 is shown in the figure below. Figure 3 The IEEE30 node measurement data includes 30 nodes, 41 branches, node voltage amplitude, node injected active and reactive power, and branch input and output power flow, a total of 254 measurement points. The MATPOWER software is used to calculate the power flow of the IEEE30 node as the true value of its measurement point, and a deviation b is added to the true value. i~U(-0.03,0.03) Gaussian measurement error, where the variance of power flow and injected power measurement is 5% of the original value, and the variance of voltage amplitude measurement is 1% of the original value, as the measurement vector. Then the size of the measurement vector is 254×1, and 1.2*254≈305 measurement time sections are selected to construct a measurement matrix with a dimension of 254×305. The bad data is set on the latest time section, and the bad data of 1%, 3%, and 5% of the measurement points are randomly set, and the measurement error is 10%, 5%, and 3% of the original measurement. The method proposed in the present invention is compared with the bad data identification method based on standardized residual (NR) and the method for bad data identification based on density clustering algorithm (DBSCAN) to compare the identification accuracy of 500 Monte Carlo experiments. The results are shown in Table 1:

[0115] Table 1 Comparison of experimental results of bad recognition accuracy of different methods

[0116]

[0117] It can be seen from the table that when the bad data ratio (i.e., the penetration rate of bad data to the quantity measurement) is the same, the method of the present invention (i.e., the RMT-SC method in the figure) has the best recognition accuracy for bad data of different degrees compared with the other two methods. The comparison of the bad data recognition accuracy between the present invention and the traditional method is shown in the figure. Figure 4 As shown. This means that its recognition sensitivity is high, and it can maintain a high recognition accuracy rate when the bad data is small; when the bad data deviation is the same, the method of the present invention (i.e., the RMT-SC method in the figure) also maintains the best recognition accuracy rate when facing bad data with different penetration rates, and can maintain a recognition accuracy rate of more than 90% when there is 5% bad data penetration in the system measurement, which means that the bad data recognition method of the present invention (i.e., the RMT-SC method in the figure) has good robustness for bad data with high penetration and interactive effects.

[0118] Embodiment 2

[0119] Please refer to Figure 5 , Figure 5 It is a structural schematic diagram of an embodiment of a bad data identification system for a power system provided by the present application, comprising a first construction module 01, a second construction module 02, an extraction module 03 and an identification module 04;

[0120] The first construction module 01 is used to obtain a corresponding measurement error based on the acquired power system measurement data, and to construct a corresponding first measurement matrix based on the measurement error;

[0121] The second construction module 02 is used to construct a corresponding first Hermitian matrix based on the first measurement matrix;

[0122] The extraction module 03 is used to extract the eigenvector and estimated eigenvalue of the first Hermitian matrix by using random matrix theory, and obtain the residual feature quantity based on the eigenvector and the estimated eigenvalue;

[0123] The identification module 04 is used to perform spectral clustering analysis on the residual feature quantity to identify bad data of the power system.

[0124] The embodiment of the present application obtains the corresponding measurement error based on the acquired power system measurement data, and constructs the corresponding first measurement matrix based on the measurement error, so as to facilitate the subsequent conversion into the corresponding Hermitian matrix and extract the eigenvalues ​​related to the measurement error; constructs the corresponding first Hermitian matrix based on the first measurement matrix, and extracts the eigenvalues ​​from the first Hermitian matrix, so as to mine the residual feature quantities related to the measurement error in the multi-section measurement data, so as to facilitate the subsequent accurate identification of bad data; and by performing bad parameter identification on the residual feature quantities related to the measurement error, the influence of the measurement error on the accuracy of bad data identification can be reduced, thereby improving the accuracy of power system state estimation.

[0125] The information interaction, execution process, etc. between the modules in the above-mentioned device are based on the same concept as the embodiment of the method for identifying bad data in the power system of the first aspect of the present invention. For specific contents, please refer to the description in the first embodiment of the method of the present invention, and will not be repeated here.

[0126] The device embodiments described above are merely illustrative, wherein the modules described as separate components may or may not be physically separated, i.e., may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the method of this embodiment.

[0127] The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the scope of protection of the present application. It is particularly pointed out that for those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of protection of the present application.

Claims

1. A method for identifying bad data in a power system, characterized in that: include: Obtaining a corresponding measurement error based on the acquired power system measurement data, and constructing a corresponding first measurement matrix based on the measurement error; constructing a corresponding first Hermitian matrix based on the first measurement matrix; Extracting eigenvectors and estimated eigenvalues ​​of the first Hermitian matrix using random matrix theory, and obtaining residual feature quantities based on the eigenvectors and the estimated eigenvalues; A spectral clustering analysis is performed on the residual feature quantity to identify bad data of the power system.

2. The method for identifying bad data in a power system according to claim 1, characterized in that: The method of obtaining a corresponding measurement error based on the acquired power system measurement data and constructing a corresponding first measurement matrix based on the measurement error is specifically as follows: Obtain the measurement data of the power system during operation within the sampling period through the SCADA system; Calculating a measurement error corresponding to the measurement data, and normalizing the measurement error to obtain a measurement vector; Based on the measurement vector within a sampling period, a corresponding first measurement matrix is ​​constructed.

3. The method for identifying bad data in a power system according to claim 1, characterized in that: The constructing of the corresponding first Hermitian matrix based on the first measurement matrix is ​​specifically: Obtaining a conjugate transposed matrix corresponding to the first measurement matrix; A first Hermitian matrix corresponding to the first measurement matrix is ​​constructed based on the first measurement matrix and the conjugate transposed matrix.

4. The method for identifying bad data in a power system according to claim 3, characterized in that: The formula for constructing the first Hermitian matrix corresponding to the first measurement matrix is ​​specifically: Where D Z is the first Hermitian matrix, Z is the first measurement matrix, and Z H is the conjugate transposed matrix of the first measurement matrix.

5. The method for identifying bad data in a power system according to claim 1, characterized in that: The method of extracting the eigenvector and estimated eigenvalue of the first Hermitian matrix by using random matrix theory, and obtaining the residual feature quantity based on the eigenvector and the estimated eigenvalue, is specifically: Based on the first Hermitian matrix, obtaining a covariance matrix corresponding to the first measurement matrix; extracting the estimated eigenvalues ​​in the first Hermitian matrix and the covariance matrix respectively; reconstructing a second Hermitian matrix based on the eigenvectors and the estimated eigenvalues, and restoring a second measurement matrix based on the second Hermitian matrix; The residual feature quantity is extracted from the second measurement matrix.

6. The method for identifying bad data in a power system according to claim 5, characterized in that: The formula for extracting the estimated eigenvalue is specifically: In the formula, ξ i is the i-th eigenvalue λ in the partial matrix of the covariance matrix i The corresponding ith estimated eigenvalue, h E (λ i ) is the real part of the Stieltjes transform of the partial matrix in the covariance matrix, ρ E (λ i ) is the result of the inverse Stieltjes transform of the partial matrix in the covariance matrix, q=T / N, T is the number of columns in the measurement matrix, and N is the number of rows in the measurement matrix.

7. The method for identifying bad data in a power system according to claim 1, characterized in that: The spectral clustering analysis is performed on the residual feature quantity to identify bad data of the power system, specifically: Establishing a similarity matrix based on the similarity between any two of the residual feature quantities, and constructing a corresponding diagonal matrix based on the similarity matrix; Based on the diagonal matrix and the similarity matrix, a Laplace matrix is ​​obtained; Extracting the minimum eigenvalue in the Laplace matrix, and forming a characteristic matrix based on the eigenvector corresponding to the minimum eigenvalue; By performing K-means clustering on the feature matrix, bad data of the power system is identified.

8. The method for identifying bad data in a power system according to claim 7, characterized in that: The objective function of the spectral clustering analysis is specifically: In the formula, A i is the subgraph of spectral clustering, m is the number of subgraphs, is the cutting weight, is a matrix consisting of m indicator vectors as column vectors.

9. A bad data identification system for a power system, characterized in that: include: A first building module, a second building module, an extraction module and a recognition module; The first constructing module is used to obtain a corresponding measurement error based on the acquired power system measurement data, and construct a corresponding first measurement matrix based on the measurement error; The second construction module is used to construct a corresponding first Hermitian matrix based on the first measurement matrix; The extraction module is used to extract the eigenvectors and estimated eigenvalues ​​of the first Hermitian matrix by using random matrix theory, and obtain residual feature quantities based on the eigenvectors and the estimated eigenvalues; The identification module is used to perform spectral clustering analysis on the residual feature quantity to identify bad data of the power system.

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