CN106950446A - The abnormal quick detection of power network based on PCA and localization method - Google Patents

Abstract

A fast detection and location method for power grid anomalies based on principal component analysis method, which reduces the dimension of the random matrix of the power grid, extracts the principal components, judges the power grid anomalies according to the strength of the principal components, and performs abnormal location according to the location information of the anomalies. The invention utilizes the principal component analysis method to realize abnormal detection and abnormal location of the power grid, provides information support for subsequent processing and removal, and has obvious advantages in processing large-scale data.

Description

Fast detection and location method of power grid anomalies based on principal component analysis

technical field

The invention relates to the technical field of grid anomaly detection, in particular to a method for quickly detecting and locating grid anomalies based on principal component analysis.

Background technique

At present, the neural network, expert system and other algorithms used in power grid anomaly detection have defects such as insufficient robustness and limited power grid structure. The scale is getting bigger and bigger, and the shortcomings of these algorithms are more obvious.

Contents of the invention

The present invention provides a fast detection and positioning method for power grid anomalies based on principal component analysis, which uses principal component analysis to realize power grid anomaly detection and abnormal positioning, provides information support for subsequent processing and removal, and has obvious advantages when processing large-scale data. Advantage.

In order to achieve the above object, the present invention provides a method for rapid detection and location of power grid abnormalities based on principal component analysis, which includes the following steps:

Step S1, performing dimensionality reduction on the random matrix of the power grid, and extracting principal components;

Step S2, judging the abnormality of the power grid according to the strength of the principal components;

Step S3, perform abnormal location according to the location information of the abnormal point.

In the step S1, the method for extracting principal components specifically includes:

Step S1.1, using _n three _- phase current samples x _{i =} ( _xi1 , x _i2 ,...,x _ip )', forming an n×p dimensional sample matrix X=(x _ij ) _n×p ;

Step S1.2, carry out standardized processing: i=1,2,...,n, j=1,2,...,p, get standardized matrix Among them, var is the variance;

Step S1.3, calculating the sample correlation coefficient matrix of the normalization matrix Z

Step S1.4, calculating the eigenvalue λ ₁ ≥λ ₂ ≥...≥λ _p of the sample correlation coefficient matrix R;

Step S1.5, calculating principal components Y _i =u _i 'X, i=1, 2,...,p, or Y=UX;

Among them, the orthogonal matrix is the characteristic unit eigenvector.

In the step S2, when the value of the first principal component changes by more than 5%, it is determined that an abnormality has occurred.

In the step S3, the method for abnormal location specifically includes:

Step S3.1, selecting the first M principal components for matrix reconstruction to generate an orthogonal matrix U;

Step S3.2, selecting the first N sampling points with the largest coefficient absolute value in the orthogonal matrix U;

Step S3.3, determining the positions of the N sampling points in the distribution network, and completing abnormal location.

In the step S3, N≤M.

The invention utilizes the principal component analysis method to realize abnormal detection and abnormal location of the power grid, provides information support for subsequent processing and removal, and has obvious advantages in processing large-scale data.

Description of drawings

Figure 1 is a conceptual diagram of principal component analysis data.

Figure 2 is the effect diagram of the principal component algorithm.

Fig. 3 is a flow chart of a fast detection and location method for power grid abnormality based on principal component analysis method provided by the present invention.

Figure 4 is a schematic diagram of circuit PSCAD simulation.

FIG. 5 is a system model diagram of FIG. 4 .

Fig. 6 is the short circuit fault module in Fig. 5 .

Fig. 7 is the harmonic injection module in Fig. 5 .

detailed description

A preferred embodiment of the present invention will be specifically described below with reference to FIGS. 1 to 7 .

Principal Component Analysis (PCA) is a statistical method to study how to transform multi-indicator problems into fewer comprehensive indicators, that is, "dimensionality reduction". It transforms the problem of high-dimensional space into low-dimensional space, making the processing problem simple and intuitive. The transformed comprehensive indicators are not correlated with each other, but can cover most of the information in the original high-dimensional data. Principal component analysis is regarded as the most important multivariate statistical method, and it is widely used in various aspects such as social economy, enterprise management, geological exploration, and biomedicine. It is often used in comprehensive evaluation, data compression and noise reduction, signal processing, pattern recognition and other fields.

Figure 1 is a set of data in a two-dimensional space. The purpose of principal component analysis is to find out the general direction of the axis of the principal component through calculation, as shown in Figure 2. There is the same algorithm for high-dimensional data, the so-called main axis, which is defined as the largest variance of the projection of all data on this axis.

make is a positive definite matrix and is a given phasor, then for any non-zero vector have:

And the maximum value is reached when x=cB ^-1 d, where c is any non-zero constant.

make is a positive definite matrix, and its eigenvalues satisfy λ ₁ ≥λ ₂ ≥…≥λ _p ≥0, and the corresponding unit vectors are e ₁ , e ₂ ,…,e _p , then

and

The above shows that for all points x whose distance to the origin is unit length, λ ₁ and λ _p are the maximum and minimum values of the quadratic form x'Bx respectively. When x is chosen such that it is perpendicular to the first chosen eigenvector, the other eigenvalues of B also correspond to the corresponding maxima.

Let X=(X ₁ ,X ₂ ,...X _P )' be a p-dimensional random vector, and its i-th principal component can be expressed as Y _i =u _i 'X, i=1,2,...,p, where u _i is the ith column vector of the orthogonal matrix U, and satisfies the following conditions:

Y ₁ is the linear combination of X ₁ , X ₂ ,...X _P with the largest variance;

Y _k is the _one with the _{largest variance} among linear combinations of X ₁ , X ₂ , .

It has the following three properties:

Property 1. Let Σ be the covariance matrix of the random vector X=(X ₁ ,X ₂ ,…X _P )', and its eigenvalue-eigenvector pair Where λ ₁ ≥λ ₂ ≥...≥λ _p ≥0, then the i-th principal component is: Y _i ＝e _i 'X＝e _r1 X ₁ +e _r2 X ₂ +...+e _rp X _p , i=1 ,2,...,p, and variance var(Y _i )=e _i 'Σe _i =λ _i , covariance cov(Y _l ,Y _k )=e _l 'Σe _k =0;

Property 2. Let the random vector X=(X ₁ ,X ₂ ,…X _P )’ have a covariance matrix Σ, and its eigenvalue-eigenvector pairs (λ ₁ ,e ₁ ),(λ ₂ ,e ₂ ),… ,(λ _p ,e _p ), where λ ₁ ≥λ ₂ ≥…≥λ _p ≥0, Y _k is the principal component, then

In principal component analysis, the contribution rate of the kth principal component is defined as The cumulative variance contribution rate of the first k principal components is defined as

Property 3. If Y _i = e _i 'X, i = 1, 2, ..., p is the principal component obtained from the covariance matrix Σ, then is the correlation coefficient between component Y _k and variable Xi _, also known as the loading of Xi in _{Y k .}

As shown in Figure 3, the present invention provides a fast detection and location method for grid abnormalities based on principal component analysis, including the following steps:

Step S1, performing dimensionality reduction on the random matrix of the power grid, and extracting principal components;

Step S2, judging the abnormality of the power grid according to the strength of the principal components;

Step S3, perform abnormal location according to the location information of the abnormal point.

In the step S1, the method for extracting principal components specifically includes:

Step S1.1, using _n three _- phase current samples x _{i =} ( _xi1 , x _i2 ,...,x _ip )', forming an n×p dimensional sample matrix X=(x _ij ) _n×p ;

Step S1.2, carry out standardized processing: i=1,2,...,n, j=1,2,...,p, get standardized matrix Among them, var is the variance;

Step S1.3, calculating the sample correlation coefficient matrix of the normalization matrix Z

Step S1.4, calculating the eigenvalue λ ₁ ≥λ ₂ ≥...≥λ _p of the sample correlation coefficient matrix R;

Step S1.5, calculating principal components Y _i =u _i 'X, i=1, 2,...,p, or Y=UX;

Among them, the orthogonal matrix is the characteristic unit eigenvector.

In one embodiment of the present invention, the available function [coeff, score, latent]=pca(X) in the matlab software can be used to carry out principal component analysis, wherein X is an input n×p dimensional sample matrix, and coeff is a coeff Variance matrix, score is the linear expression of the variable x in the principal components, latent is the characteristic root of coeff, arranged in descending order, this function has been automatically standardized.

In the step S2, when the value of the first principal component changes by more than 5%, it is determined that an abnormality has occurred.

In the step S3, when an abnormality occurs, the main feature of the standardized matrix is the abnormal component, so according to the position of the abnormal component in the distribution network, the monitoring and positioning of the abnormality in the distribution network can be realized.

The methods for abnormal location specifically include:

Step S3.1. Select the first M (in this example, M is 10) principal components for matrix reconstruction to generate an orthogonal matrix U;

Step S3.2, select the first N (in this example, N is 8) sampling points with the largest coefficient absolute value in the orthogonal matrix U, where N≤M;

Step S3.3, determining the positions of the N sampling points in the distribution network, and completing abnormal location.

In a specific embodiment of the present invention, in combination with the actual situation of my country's distribution network, a PSCAD circuit diagram as shown in Figure 4 is built, and the specific system model is shown in Figure 5, which simulates short-circuit anomalies and harmonic anomalies, and completes data analysis. Acquisition, wherein, the short-circuit fault module is shown in Figure 6, and the harmonic injection module is shown in Figure 7.

The following table selects the results of principal component analysis for a total of 13 random matrices from the 5 time intervals before the detection of the anomaly to the 8 time intervals after the detection. Take M=10, N=10, the first column in the table is the cumulative variance contribution rate of the first M principal components, and the last 10 columns in the table are the N PMU observation points with the largest absolute value of the coefficient. It can be seen that the principal component increases significantly after the anomaly occurs, that is, the anomaly is detected. This shows that exception occurrence is a transient process. The selected observation points before anomaly detection are relatively random, while the selected PMU observation points after anomaly detection are relatively locked. These locked points are anchor points. The above examples illustrate the effectiveness of this algorithm in the application of power system anomaly detection and location.

Short circuit 1 line 183 abnormal

Short circuit 2 line 54 abnormal

Interpretation of principal components 1 2 3 4 5 6 7 8 9 10 0.142 169 197 168 209 231 130 211 119 98 202 0.143 211 236 98 119 197 209 122 90 169 202 0.143 202 211 119 98 213 155 29 117 231 130 0.143 211 159 103 98 236 213 233 87 231 130 0.143 103 202 211 97 214 198 148 130 170 156 0.143 236 63 103 133 130 213 149 87 198 190 0.144 236 63 103 198 149 98 133 106 30 136 0.145 57 149 87 44 236 50 198 63 159 213 0.151 56 198 63 57 50 202 133 44 42 147 0.160 63 57 50 30 56 55 198 159 59 214 0.169 63 57 55 51 56 44 30 45 53 50 0.177 63 57 50 56 45 214 51 30 53 60 0.186 63 57 56 30 45 50 51 44 39 53

Harmonic 1, 2 line 201 is abnormal

The above case analysis shows that the use of principal component analysis can clearly realize abnormal detection, locate abnormalities, lock the location of abnormalities, and provide information support for subsequent processing and removal. Principal component analysis has obvious advantages when dealing with large-scale data by using the idea of dimensionality reduction.

Although the content of the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description should not be considered as limiting the present invention. Various modifications and alterations to the present invention will become apparent to those skilled in the art upon reading the foregoing disclosure. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims (5)

1. A method for abnormal fast detection and location of power grid based on principal component analysis, characterized in that it comprises the following steps: Step S1, performing dimensionality reduction on the random matrix of the power grid, and extracting principal components; Step S2, judging the abnormality of the power grid according to the strength of the principal components; Step S3, perform abnormal location according to the location information of the abnormal point. 2. The abnormal fast detection and location method of power grid based on principal component analysis method as claimed in claim 1, characterized in that, in the described step S1, the method for extracting principal components specifically comprises: Step S1.1, using _n three _- phase current samples x _{i =} ( _xi1 , x _i2 ,...,x _ip )', forming an n×p dimensional sample matrix X=(x _ij ) _n×p ; Step S1.2, carry out standardized processing: get normalized matrix Among them, var is the variance; Step S1.3, calculating the sample correlation coefficient matrix of the normalization matrix Z Step S1.4, calculating the eigenvalue λ ₁ ≥λ ₂ ≥...≥λ _p of the sample correlation coefficient matrix R; Step S1.5, calculating principal components Y _i =u _i 'X, i=1, 2,...,p, or Y=UX; Among them, the orthogonal matrix is the characteristic unit eigenvector. 3. The method for rapidly detecting and locating abnormalities in power grids based on principal component analysis as claimed in claim 1, wherein in said step S2, when the numerical value of the first principal component changes by more than 5%, it is determined to be abnormal occur. 4. The abnormal fast detection and location method of power grid based on principal component analysis method as claimed in claim 1, characterized in that, in the described step S3, the method for abnormal location specifically includes: Step S3.1, selecting the first M principal components for matrix reconstruction to generate an orthogonal matrix U; Step S3.2, selecting the first N sampling points with the largest coefficient absolute value in the orthogonal matrix U; Step S3.3, determining the positions of the N sampling points in the distribution network, and completing abnormal location. 5. The method for rapidly detecting and locating abnormality of power grid based on principal component analysis method according to claim 1, characterized in that, in said step S3, N≤M.