CN105699804A - Big data fault detection and positioning method for power distribution network - Google Patents

Abstract

The invention provides a big data fault detection and positioning method for a power distribution network, and belongs to the field of intelligent power grids. The method comprises the steps: receiving voltage sampling data of the power distribution network through employing PMUs (Phasor Measurement Units); carrying out the preprocessing of voltages received by all PMUs, and constructing a receiving matrix; obtaining an unbiased estimated value of a receiving data covariance matrix through employing a random matrix theory; carrying out the eigenvalue decomposition of the covariance matrix, and obtaining a corresponding principal component; calculating a linear regression coefficient through employing PCA (Principal Component Analysis); comparing a relative approximation error and a threshold value, and achieving the fault detection and positioning of the power distribution network. The method provided by the invention solves a problem that the conventional covariance matrix estimation is biased under the measurement of a plurality of PMUs, and can achieve the real-time fault detection and positioning of the power distribution network.

Description

The big data fault detection of a kind of power distribution network and localization method

Technical field

The invention belongs to intelligent grid field, be specifically related to the big data fault detection of a kind of power distribution network and localization method。

Background technology

Power distribution network is the network powered to end user, is to the key link of customer power supply in power system generating, transmission of electricity, distribution, electricity consumption。Power distribution network is in the end of power system, and Regional Distribution is wide, electrical network scale is big, device category is many, network connection is various, the method for operation is changeable etc. makes its running state analysis have certain difficulty and complexity。In smart electric grid system, along with synchronous measuring apparatus (PhasorMeasurementUnit, PMU) widely uses, the real-time processing problem of operation of power networks data attracts wide attention。

Monitoring, monitoring and the control of application synchronous measuring apparatus data analysis electrical network have been achieved with remarkable break-throughs。The voltage phasor of Lyapunov index is utilized to monitor the stability of Short-term Voltage Stability, utilize discrete Fourier transform can realize the detection of adaptive technique transmission line failure and the location of PMU, additionally, application phasor angular surveying and system topology can realize distribution network failure detection。

From the angle of research, the subject matter that the large-scale deployment of synchro measure phasor brings is to receive the increase of data matrix dimension, and namely PMU number and sampling number tend to infinitely great with constant proportionality coefficient simultaneously。Detecting with localization method at the existing distribution network failure based on spatial coherence, its committed step is to calculate the unbiased esti-mator of the covariance matrix receiving data。Traditional method calculating covariance matrix is based on this thought of maximum likelihood, using the sample covariance matrix unbiased estimator as true covariance matrix, but, the applicable elements of these computational methods is that PMU number is less, and sample number is far longer than PMU number。When above-mentioned traditional covariance matrix computational methods based on maximal possibility estimation being applied directly to the PMU measurement apparatus of large scale deployment, will appear from bigger estimated bias, causing that corresponding algorithm performance is decreased obviously。

In addition, the large-scale use of synchronous phasor measurement unit also will clearly result in the increase receiving data volume, add the difficulty of analytical data spatial coherence, from mathematical angle analysis, when power distribution network breaks down, necessarily cause that data space dependency changes, therefore, when PMU number is more, explores and reduce the dimension receiving data, promote the effectiveness of analytical data spatial coherence, be have another problem to be solved。

Random Matrices Theory is to study when the dimension of matrix and sample number tend to infinite simultaneously, the precise Estimation Method of covariance matrix, eigen vector effective mathematical tool of distribution character etc.。Method proposed by the invention is fully being analyzed on the basis of Random Matrices Theory, work out and measure, suitable in many PMU, the unbiased esti-mator method that lower voltage receives the covariance matrix of data, disease says that principal component analysis is applied in distribution network voltage fault detection and location, with the real-time of boosting algorithm and effectiveness。

Summary of the invention

The invention provides the big data fault detection of a kind of power distribution network and localization method。For solving when PMU number is more, receive data covariance matrix and estimate inaccurate, the problem that data dimension increases limit algorithm practicality, is difficult to distribution network failure is carried out real-time diagnosis and location。

The scheme that the present invention takes is to comprise the steps of:

(1) lay PMU according to power distribution network topological structure, form the big data measurement unit of power distribution network；

(2) measurement apparatus in applying step (1) receives distribution network voltage data；

(3) voltage data received is carried out pretreatment；

(4) pretreated data configuration data receiver matrix is applied；

(5) application Random Matrices Theory calculates the unbiased esti-mator of the covariance matrix of data receiver matrix；

(6) unbiased esti-mator of covariance matrix is carried out Eigenvalues Decomposition, extract corresponding main constituent；

(7) application principal component analysis calculates linear regression coeffficient；

(8) application linear regression coeffficient calculates relative error of approximation；

(9) size of relative error of approximation and threshold value is contrasted, it is achieved distribution network failure detection and location。

The process of data preprocessing that receives described in said method is mainly the average calculating the voltage data received, and deducts average based on this from reception data；

Step of the present invention (4) structure data receiver matrix, its specific configuration method is the row that each PMU data received constitute receiving matrix, the sampled data in each moment constitutes the row of receiving matrix, assume that PMU number is N, N road PMU data is carried out M sampling, i-th (i=0 ..., N) the voltage sample data that receive of individual PMU are expressed asWherein subscript T is the transposition of matrix, then receiving data matrix is Y_M×N:=[y⁽¹⁾,.y⁽²⁾,..,y^(N-1),y^(N)]。

Step of the present invention (5) application Random Matrices Theory calculates the unbiased esti-mator of the covariance matrix receiving voltage data matrix, and its detailed process is in OAS estimates, obtains estimation function by weighing low deviation and low varianceDefine as follows:

$\begin{array}{cc}\underset{p}{\min }& E\left\{\right||\widetilde{\mathrm{\Σ}}-R_Y|{|}_F^2\}\end{array}$

Wherein: E is mathematic expectaion, and

$\widetilde{\mathrm{\Σ}}=(1-p){\tilde{R}}_Y+p\tilde{U}$

WhereinSample covariance matrix, p is contraction factor, is used for reducing mean square error, generally value between 0 and 1, shrink target U definition as follows:

$\tilde{U}=\frac{Tr\left({\tilde{R}}_Y\right)}{N}I$

In formula, Tr is matrix trace, and I is that N ties up unit matrix, it is assumed that be independent same distribution between each sample, then

$p_p=\frac{(1-\frac{2}{N})Tr\left(R_Y^2\right)+{\mathrm{Tr}}^2\left(R_Y\right)}{(M+1-\frac{2}{N})Tr\left(R_Y^2\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left(R_Y\right)}$

R_YFor true covariance matrix, in actual applications, the true covariance matrix R of direct solution_YIt is infeasible, estimates above formula is iterated by OAS, obtain approximate covariance matrixR is used first during iteration_YAn original hypothesis value,p₀The arbitrary value between 0 to 1 can be taken, by continuous iteration, the covariance matrix tried to achieve is modified afterwards, until iteration convergence:

$p_{i+1}=\frac{(1-\frac{2}{N})Tr\left({\widetilde{\mathrm{\Σ}}}_i{\tilde{R}}_Y\right)+{\mathrm{Tr}}^2\left({\widetilde{\mathrm{\Σ}}}_i\right)}{(M+1-\frac{2}{N})Tr\left({\widetilde{\mathrm{\Σ}}}_i{\tilde{R}}_Y\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left({\widetilde{\mathrm{\Σ}}}_i\right)}$

${\widetilde{\mathrm{\Σ}}}_{i+1}=(1-p_{i+1}){\tilde{R}}_Y+p_{i+1}\tilde{U}$

When above formula is restrained, it is possible to obtain p_OAS

$p_{OAS}=min\{\frac{(1-\frac{2}{N})Tr\left({\tilde{R}}_Y^2\right)+{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{(M+1-\frac{2}{N})\[Tr\left({\tilde{R}}_Y^2\right)-\frac{{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{N}\]},1\}$

Utilize the p obtained_OASThe unbiased esti-mator of the covariance matrix finally estimatedFor

${\hat{R}}_Y=(1-p_{OAS}){\tilde{R}}_Y+p_{OAS}\tilde{U}.$

Extracting main constituent in step of the present invention (6), its process is the unbiased esti-mator to covariance matrixCarry out Eigenvalues Decomposition

$\frac{1}{M}{\hat{R}}_Y{\mathrm{\α}}_j=l_j{\mathrm{\α}}_j,j=1,2,...,N$

WhereinFor covariance matrix unbiased esti-matorN number of eigenvalue,For the N number of characteristic vector corresponding with eigenvalue；

WillN number of eigenvalue carry out descending, its characteristic of correspondence vector sorts with eigenvalue；τ is set to variance threshold values, utilizes accumulative variance contribution ratio to select and be just met forFront L characteristic vector, structure L tie up main constituent PCm。

Calculating linear regression coeffficient in step of the present invention (7), its method is by matrix Y_M×NTie up main constituent subspace at L to project, obtain matrix YY

YY=Y PCm

$Y_B:=\[y_b^1,y_b^2,...,y_b^S\]\∈R^{M\×S}$

Wherein S < L, y_bMeet

$cos\mathrm{\&theta;}=(y_b^i\&CenterDot;y_b^j)/\left(\right|y_b^i|\&CenterDot;|y_b^j\left|\right)\&ap;0,i,j=1,2,...,S$

Utilize Y_BRepresent yⁱ, wherein yⁱ∈Y_M×NAndThen linear regression coeffficient vⁱMeet

$y^i\&ap;\underset{j=1}{\overset{m}{\&Sigma;}}{v}_j^i\&CenterDot;y_b^j=Y_B\&CenterDot;v^i$

Linear regression coeffficient v can be obtained furtherⁱ

$v^i={\left(Y_B^T{Y}_B\right)}^{-1}{Y}_B^T{y}^i$

Wherein subscript-1 is inverse of a matrix。

Step of the present invention (8) calculates relative proximity like error, its method assume that detection-phase is similar to n-th (n=1,2 ..., N-S) individual PMU in the data of t is

$\tilde{x}{\left(t\right)}^n:=\widetilde{Y_B}\left(t\right)\&CenterDot;v^i$

In formulaFor at the calculated Y of t_B, obtain approximateVirtual voltage sampled data z (t) with tⁿDo difference, obtain absolute error of approximation

$\hat{e}{\left(t\right)}^n=\tilde{x}{\left(t\right)}^n-z{\left(t\right)}^n$

Owing to, in power system, the amplitude of variation of fault generation variations per hour is not as big, soBeing very little, this causes can not judging whether fault occurs exactly, for avoiding this problem, therefore willDivided by training stage correspondence PMU'sMeansigma methods er_s ⁿ, it is possible to the error of approximation data of fault moment are amplified, accomplishes relative error of approximation r (t)ⁿ

$r{\left(t\right)}^n=\frac{\hat{e}{\left(t\right)}^n}{{{\mathrm{er}}_s}^n}\&times;100\%$

Realizing distribution network failure detection and location in step of the present invention (9), its method is the PMU data by history accident, it is determined that a threshold value η, when

|r(t)ⁿ|≥η

Time, can determine that fault occurs, t is fault time, namely characterizes the detection to fault, and n is fault PMU, characterizes the location to fault。

The invention have the advantage that

(1) institute of the present invention extracting method have studied the computational methods of multiple covariance matrix unbiased esti-mator in Random Matrices Theory, by relative analysis, OAS reconstructing method is incorporated into the big Data processing of power distribution network, overcome the problem that tradition sample covariance matrix computational methods estimated bias is bigger, improve the suitability of respective algorithms；

(2) institute of the present invention extracting method is obtaining on the basis receiving data covariance matrix unbiased estimator, application principal component analysis reduces the dimension receiving data, improves the effectiveness of distribution network voltage spatial Correlation Analysis and the calculating effectiveness of respective algorithms；

(3) standard that relative error of approximation is changed by institute of the present invention extracting method as evaluation distribution network voltage spatial coherence, determine, by the relation of relatively relative error of approximation with threshold value, the moment and position whether distribution network failure occur and occurs, it may be achieved the detection in real time of voltage failure with position。

Accompanying drawing explanation

Fig. 1 is distribution network voltage data measurement unit schematic diagram of the present invention；

Fig. 2 is the flow chart of the present invention；

Fig. 3 is IEEE39 node system figure；

Fig. 4 is that eigenvalue contribution is than selecting result figure；

Fig. 5 is distribution network voltage failure detection result figure；

Fig. 6 is distribution network voltage fault location result figure。

Detailed description of the invention

Comprise the following steps:

(1): lay PMU according to power distribution network topological structure, the big data measurement unit of power distribution network is formed；

Laying PMU according to power distribution network topological structure, the measurement apparatus formed is as it is shown in figure 1, be characterized in that the uniform cloth of PMU is placed on whole power distribution network；

(2): the measurement apparatus in applying step (1) receives distribution network voltage data；

PMU device is laid in required detection region, it is used for receiving respectively the PMU data of regional, the initial data obtained is transported in local phase data concentrator, afterwards each local data is concentrated the data summarization of device, it is transported to company data concentrator, and stores；

(3): carry out pretreatment to receiving data；

Calculate the average v of the voltage data u received, from reception data, deduct average based on this, it is thus achieved that pretreated voltage data y=u-v；

(4): apply pretreated data configuration data receiver matrix；

The data that each PMU receives constitute the row of receiving matrix, and the sampled data in each moment constitutes the row of receiving matrix, it is assumed that PMU number is N, N road PMU data is carried out M sampling, i-th (i=0 ..., N) the voltage sample data that receive of individual PMU are expressed asWherein subscript T is the transposition of matrix, then receiving data matrix is Y_M×N:=[y⁽¹⁾,.y⁽²⁾,..,y^(N-1),y^(N)]；

(5): application Random Matrices Theory calculates the unbiased esti-mator of the covariance matrix of data receiver matrix；

In OAS estimates, obtain estimation function by weighing low deviation and low varianceDefine as follows:

$\begin{array}{cc}\underset{p}{\min }& E\left\{\right||\widetilde{\mathrm{\&Sigma;}}-R_Y|{|}_F^2\}\end{array}$

Wherein: E is mathematic expectaion, and

$\widetilde{\mathrm{\&Sigma;}}=(1-p){\tilde{R}}_Y+p\tilde{U}$

WhereinFor Y_M×NSample covariance matrix, p is contraction factor, is used for reducing mean square error, generally value between 0 and 1。Shrink target U definition as follows:

$\tilde{U}=\frac{Tr\left({\tilde{R}}_Y\right)}{N}I$

In formula, Tr is matrix trace, and I is that N ties up unit matrix, it is assumed that be independent same distribution between each sample, then

$p_p=\frac{(1-\frac{2}{N})Tr\left(R_Y^2\right)+{\mathrm{Tr}}^2\left(R_Y\right)}{(M+1-\frac{2}{N})Tr\left(R_Y^2\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left(R_Y\right)}$

R_YFor true covariance matrix, in actual applications, the true covariance matrix R of direct solution_YIt is infeasible, estimates above formula is iterated by OAS, obtain approximate covariance matrixR is used first during iteration_YAn original hypothesis value,p₀The arbitrary value between 0 to 1 can be taken, by continuous iteration, the covariance matrix tried to achieve is modified afterwards, until iteration convergence:

$p_{i+1}=\frac{(1-\frac{2}{N})Tr\left({\widetilde{\mathrm{\&Sigma;}}}_i{\tilde{R}}_Y\right)+{\mathrm{Tr}}^2\left({\widetilde{\mathrm{\&Sigma;}}}_i\right)}{(M+1-\frac{2}{N})Tr\left({\widetilde{\mathrm{\&Sigma;}}}_i{\tilde{R}}_Y\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left({\widetilde{\mathrm{\&Sigma;}}}_i\right)}$

${\widetilde{\mathrm{\&Sigma;}}}_{i+1}=(1-p_{i+1}){\tilde{R}}_Y+p_{i+1}\tilde{U}$

When above formula is restrained, it is possible to obtain p_OAS

$p_{OAS}=min\{\frac{(1-\frac{2}{N})Tr\left({\tilde{R}}_Y^2\right)+{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{(M+1-\frac{2}{N})\&lsqb;Tr\left({\tilde{R}}_Y^2\right)-\frac{{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{N}\&rsqb;},1\}$

Utilize the p obtained_OASThe unbiased esti-mator of the covariance matrix finally estimatedFor

${\hat{R}}_Y=(1-p_{OAS}){\tilde{R}}_Y+p_{OAS}\tilde{U}$

(6): covariance matrix is carried out Eigenvalues Decomposition, corresponding main constituent is extracted；

Unbiased esti-mator to covariance matrixCarry out Eigenvalues Decomposition

$\frac{1}{M}{\hat{R}}_Y{\mathrm{\&alpha;}}_j=l_j{\mathrm{\&alpha;}}_j,j=1,2,...,N$

WhereinFor covariance matrix unbiased esti-matorN number of eigenvalue,For the N number of characteristic vector corresponding with eigenvalue；

WillN number of eigenvalue carry out descending, its characteristic of correspondence vector sorts with eigenvalue；τ is set to variance threshold values, utilizes accumulative variance contribution ratio to select and be just met forFront L characteristic vector, structure L tie up main constituent PCm；

(7): application principal component analysis calculates linear regression coeffficient；

By matrix Y_M×NTie up main constituent subspace at L to project, obtain matrix YY

YY=Y PCm

$Y_B:=\&lsqb;y_b^1,y_b^2,...,y_b^S\&rsqb;\&Element;R^{M\&times;S}$

Wherein S < L, y_bMeet

$cos\mathrm{\&theta;}=(y_b^i\&CenterDot;y_b^j)/\left(\right|y_b^i|\&CenterDot;|y_b^j\left|\right)\&ap;0,i,j=1,2,...,S$

Utilize Y_BRepresent yⁱ, wherein yⁱ∈Y_M×NAndThen linear regression coeffficient vⁱMeet

$y^i\&ap;\underset{j=1}{\overset{m}{\&Sigma;}}{v}_j^i\&CenterDot;y_b^j=Y_B\&CenterDot;v^i$

Linear regression coeffficient v can be obtained furtherⁱ

$v^i={\left(Y_B^T{Y}_B\right)}^{-1}{Y}_B^T{y}^i$

Wherein subscript-1 is inverse of a matrix；

(8): application linear regression coeffficient calculates relative error of approximation；

Assume detection-phase approximate n-th (n=1,2 ..., N-S) individual PMU in the data of t is

$\tilde{x}{\left(t\right)}^n:=\widetilde{Y_B}\left(t\right)\&CenterDot;v^i$

In formulaFor at the calculated Y of t_B, obtain approximateVirtual voltage sampled data z (t) with tⁿDo difference, obtain absolute error of approximation

$\hat{e}{\left(t\right)}^n=\tilde{x}{\left(t\right)}^n-z{\left(t\right)}^n$

Owing to, in power system, the amplitude of variation of fault generation variations per hour is not as big, soBeing very little, this causes can not judging whether fault occurs exactly。For avoiding this problem, therefore willDivided by training stage correspondence PMU'sMeansigma methods er_s ⁿ, it is possible to the error of approximation data of fault moment are amplified, accomplishes relative error of approximation r (t)ⁿ

$r{\left(t\right)}^n=\frac{\hat{e}{\left(t\right)}^n}{{{\mathrm{er}}_s}^n}\&times;100\%$

(9): contrast the size of relative error of approximation and threshold value, it is achieved distribution network failure detection and location,

PMU data by history accident, it is determined that a threshold value η, when

|r(t)ⁿ|≥η

Time, can determine that fault occurs, t is fault time, namely characterizes the detection to fault, and n is fault PMU, characterizes the location to fault。

Performance below by the big data fault diagnosis of the power distribution network that some analysis of experimental data are proposed by the invention with localization method。The simulation software that emulation experiment 1 and emulation experiment 2 adopt is MATLAB software。

Emulation experiment: the effectiveness of this experiment contribution ratio and institute's extracting method in order to analyze eigenvalue, experimentation adopts the voltage data that IEEE39 nodal analysis method produces formed and receive data matrix, play node system figure as shown in Figure 3, this model being assumed, the 9th PMU and the 30th PMU is abort situation, time of failure is respectively the 235th sampled point and the 274th sampled point, the simulation result of eigenvalue contribution coin ratio is as shown in Figure 4, distribution network voltage fault detection and location result is respectively as shown in Figure 5 and Figure 6, analysis chart 4 is known, when the data matrix of application 39 dimension carries out fault detect with fault location, optional characteristic vector corresponding to 10 dominant eigenvalues is as main constituent, analysis chart 5 is known, proposed method is significantly greater than other sampled points in the sampled point label respectively 235 relative error of approximation with 274, namely the real-time detection of voltage failure is achieved；Analysis chart 6 is it can be seen that when the 9th PMU and the 30th PMU, the relative error of approximation that institute's extracting method calculates, apparently higher than other PMU, can realize being accurately positioned voltage failure。

Claims (7)

1. the big data fault detection of power distribution network and localization method, it is characterised in that comprise the steps of:

(1) lay PMU according to power distribution network topological structure, form the big data measurement unit of power distribution network；

(2) measurement apparatus in applying step (1) receives distribution network voltage data；

(3) voltage data received is carried out pretreatment；

(4) pretreated data configuration data receiver matrix is applied；

(5) application Random Matrices Theory calculates the unbiased esti-mator of the covariance matrix of data receiver matrix；

(6) unbiased esti-mator of covariance matrix is carried out Eigenvalues Decomposition, extract corresponding main constituent；

(7) application principal component analysis calculates linear regression coeffficient；

(8) application linear regression coeffficient calculates relative error of approximation；

(9) size of relative error of approximation and threshold value is contrasted, it is achieved distribution network failure detection and location。

2. a kind of big data fault of power distribution network detects and localization method according to claim 1, it is characterized in that: the specific configuration method of step (4) structure data receiver matrix is the row that each PMU data received constitute receiving matrix, the sampled data in each moment constitutes the row of receiving matrix, assume that PMU number is N, N road PMU data is carried out M sampling, i-th (i=0 ..., N) the voltage sample data that receive of individual PMU are expressed asWherein subscript T is the transposition of matrix, then receive data matrix and be $Y_{M\&times;N}:=\&lsqb;y^{\left(1\right)},.y^{\left(2\right)},\mathrm{..},y^{(N-1)},y^{\left(N\right)}\&rsqb;.$

3. a kind of big data fault of power distribution network detects and localization method according to claim 1, it is characterised in that: the detailed process of step (5) is in OAS estimates, obtains estimation function by weighing low deviation and low varianceDefine as follows:

$\begin{array}{cc}\underset{p}{min}& E\left\{\right||\widetilde{\&Sigma;}-R_Y|{|}_F^2\}\end{array}$

Wherein: E is mathematic expectaion, and

$\widetilde{\&Sigma;}=(1-p){\tilde{R}}_Y+p\tilde{U}$

WhereinFor Y_M×NSample covariance matrix, p is contraction factor, is used for reducing mean square error, generally value between 0 and 1。Shrink target U definition as follows:

$\tilde{U}=\frac{Tr\left({\tilde{R}}_Y\right)}{N}I$

In formula, Tr is matrix trace, and I is that N ties up unit matrix, it is assumed that be independent same distribution between each sample, then

$p_p=\frac{(1-\frac{2}{N})Tr\left(R_Y^2\right)+{\mathrm{Tr}}^2\left(R_Y\right)}{(M+1-\frac{2}{N})Tr\left(R_Y^2\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left(R_Y\right)}$

R_YFor true covariance matrix, in actual applications, the true covariance matrix R of direct solution_YIt is infeasible, estimates above formula is iterated by OAS, obtain approximate covariance matrixR is used first during iteration_YAn original hypothesis value,p₀The arbitrary value between 0 to 1 can be taken, by continuous iteration, the covariance matrix tried to achieve is modified afterwards, until iteration convergence:

$p_{i+1}=\frac{(1-\frac{2}{N})Tr\left({\widetilde{\&Sigma;}}_i{\tilde{R}}_Y\right)+{\mathrm{Tr}}^2\left({\widetilde{\&Sigma;}}_i\right)}{(M+1-\frac{2}{N})Tr\left({\widetilde{\&Sigma;}}_i{\tilde{R}}_Y\right)+(1-\frac{M}{N}){\mathrm{Tr}}^2\left({\widetilde{\&Sigma;}}_i\right)}$

${\widetilde{\&Sigma;}}_{i+1}=(1-p_{i+1}){\tilde{R}}_Y+p_{i+1}\tilde{U}$

When above formula is restrained, it is possible to obtain p_OAS

$p_{OAS}=min\{\frac{(1-\frac{2}{N})Tr\left({\tilde{R}}_Y^2\right)+{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{(M+1-\frac{2}{N})\&lsqb;Tr\left({\tilde{R}}_Y^2\right)-\frac{{\mathrm{Tr}}^2\left({\tilde{R}}_Y\right)}{N}\&rsqb;},1\}$

Utilize the p obtained_OASThe unbiased esti-mator of the covariance matrix finally estimatedFor:

${\hat{R}}_Y=(1-p_{OAS}){\tilde{R}}_Y+p_{OAS}\tilde{U}.$

4. according to the big data fault detection of claim 1 power distribution network and localization method, it is characterised in that: the process extracting main constituent in described step (6) is the unbiased esti-mator to covariance matrixCarry out Eigenvalues Decomposition:

$\frac{1}{M}{\hat{R}}_Y{\mathrm{\&alpha;}}_j=l_j{\mathrm{\&alpha;}}_j,j=1,2,\mathrm{...},N$

WhereinFor covariance matrix unbiased esti-matorN number of eigenvalue,For the N number of characteristic vector corresponding with eigenvalue；

WillN number of eigenvalue carry out descending, its characteristic of correspondence vector sorts with eigenvalue；τ is set to variance threshold values, utilizes accumulative variance contribution ratio to select and be just met forFront L characteristic vector, structure L tie up main constituent PCm；。

5. a kind of big data fault of power distribution network detects and localization method according to claim 1, it is characterised in that: the method calculating linear regression coeffficient in described step (7) is by matrix Y_M×NTie up main constituent subspace at L to project, obtain matrix YY:

YY=Y PCm

$Y_B:=\&lsqb;y_b^1,y_b^2,...,y_b^S\&rsqb;\&Element;R^{M\&times;S}$

Wherein S < L, y_bMeet:

$cos\mathrm{\&theta;}=(y_b^i\&CenterDot;y_b^j)/\left(\right|y_b^i|\&CenterDot;|y_b^j\left|\right)\&ap;0,i,j=1,2,...,S$

Utilize Y_BRepresent yⁱ, wherein yⁱ∈Y_M×NAndThen linear regression coeffficient vⁱMeet:

$y^i\&ap;\underset{j=1}{\overset{m}{\&Sigma;}}{v}_j^i\&CenterDot;y_b^j=Y_B\&CenterDot;v^i$

Linear regression coeffficient v can be obtained furtherⁱ:

$v^i={\left(Y_B^T{Y}_B\right)}^{-1}{Y}_B^T{y}^i$

Wherein subscript-1 is inverse of a matrix。

6. a kind of big data fault of power distribution network detects and localization method according to claim 1, it is characterized in that: in described step (8), calculating relative proximity assumes that, like the method for error, the n-th (n=1 that detection-phase is approximate, 2 ..., N-S) individual PMU in the data of t is

$\tilde{x}{\left(t\right)}^n:=\widetilde{Y_B}\left(t\right)\&CenterDot;v^i$

In formulaFor at the calculated Y of t_B, obtain approximateVirtual voltage sampled data z (t) with tⁿDo difference, obtain absolute error of approximation

$\hat{e}{\left(t\right)}^n=\tilde{x}{\left(t\right)}^n-z{\left(t\right)}^n$

WillDivided by training stage correspondence PMU'sMeansigma methodsThe error of approximation data of fault moment can be amplified, accomplish relative error of approximation r (t)ⁿ

$r{\left(t\right)}^n=\frac{\hat{e}{\left(t\right)}^n}{{{\mathrm{er}}_s}^n}\&times;100\%.$

7. a kind of big data fault of power distribution network detects and localization method according to claim 1, it is characterised in that: realizing distribution network failure detection in described step (9) is the PMU data by history accident with the method positioned, it is determined that a threshold value η, when

|r(t)ⁿ|≥η

Time, can determine that fault occurs, t is fault time, namely characterizes the detection to fault, and n is fault PMU, characterizes the location to fault。