CN105406471A - Bad data identification and estimation method for power grid - Google Patents

Abstract

The invention relates to a bad data identification and estimation method for a power grid. The method comprises the following steps: reading a power grid model and a plurality of measurement sections; gradually carrying out state estimation on the measurement sections; detecting suspicious parameters/measurement; carrying out synergetic identification of parameters/measurement errors on the basis of the plurality of sections and an overall error drop indicator; and carrying out parameter estimation by combination of the plurality of sections. The bad data identification and estimation method has the beneficial effects that an overall error drop indicator-based novel method is provided; influences on the method caused by measurement errors and numerical condition setting are relatively small; synergetic identification on the measurement errors and parameter errors can be efficiently and accurately achieved under the condition that a plurality of measurement errors and parameter errors simultaneously exist; and repeated iteration is not needed. Meanwhile, measurement data of a plurality of operating sections are applied to parameter estimation, so that the measurement redundancy is improved; through improvement of an algorithm, the numerical stability and the calculation efficiency are improved; and parameter error identification and estimation accuracy is finally improved.

Description

Electrical network bad data recognition and method of estimation

Technical field

The present invention relates to operation of power networks metric data technical field, especially a kind of electrical network bad data recognition and method of estimation.

Background technology

Operation of power networks metric data is the technical foundation of power grid risk assessment, failure diagnosis and scheduling decision.The regularization method of Lagrange multipliers of rising in recent years represents the highest level of current identification, and the method effectively can distinguish the source of measurement residuals, achieves bad data (measuring mistake) identification.But the method needs the diagonal element calculating Lagrange multiplier covariance matrix, and this calculating is very consuming time, cannot meet the needs of large-scale electrical power system practical application.On the other hand, deposit in case in multiple measurement mistake and parameter error, the method needs repeatedly to carry out state estimation and calculates and parameter Estimation calculating, and inefficiency, have impact on the practicality of the method.

Summary of the invention

The present invention will solve the shortcoming of above-mentioned prior art, provides a kind of precision is higher, efficiency is higher electrical network bad data recognition and method of estimation.

The present invention solves the technical scheme that its technical problem adopts: this electrical network bad data recognition and method of estimation, comprise the following steps:

1) electric network model and multiple measuring section is read in; Read in electric network model, and automatically carry out topological analysis, generate the electric network model calculated; Read in the metric data of multiple historical metrology section, for subsequent calculations simultaneously;

2) one by one state estimation is carried out to measuring section; According to the electric network model read in and metric data, section is run to each and carries out conventional sense estimation calculating; Calculate the measurement qualification rate of each section, measurement qualification rate no longer participates in parameter identification below lower than the section of set point and calculates, and measurement qualification rate participates in parameter identification higher than the section of set point and calculates;

3) suspicious parameter and measurement detect, using the global error of Correlated Case with ARMA Measurement as parameter of measurement or the index measuring suspicious degree; Get during the suspicious parameter of each detection maximum weighted measurement residuals square as threshold value, when Correlated Case with ARMA Measurement global error is less than this threshold value, think parameter or measure credible; When Correlated Case with ARMA Measurement global error is greater than this threshold value, thinks and this parameter or measure suspicious be classified to suspicious parameter/measurement collection; In the next step, only identification is carried out to the parameter that suspicious parameter/measurement is concentrated;

4) based on the parameter/measure wrong cooperative identification of multibreak and global error decline index; When carrying out identification to the parameter that suspicious parameter/measurement is concentrated, multiple measuring section is adopted to carry out combined parameters identification; Using global error decline index as parameter of measurement or the foundation measuring whether mistake, if the global error decline index of suspicious parameter/measurement is greater than 9, be then judged as wrong parameter or bad data;

5) multibreak joint parameter estimation; Multibreak is adopted to combine and parameter augmentation to be estimated is parameter state amount by weighted least-squares method, and the estimated value of each measuring section utilizing the measurement qualification rate that obtains in step 2 high and the measurement of each section, realize parameter Estimation.

The effect that the present invention is useful is: technical solution of the present invention solves the problem of current parameter identification and estimation technique inefficiency, poor accuracy, propose a kind of new method based on global error decline index, its impact arranged by error in measurement and value conditions is less, can under multiple measurement mistake and the simultaneous situation of parameter error, realize the cooperative identification measuring mistake and parameter error efficiently, accurately, without the need to iterating.The metric data of multiple operation section is used for parameter Estimation simultaneously, improves measurement redundancy, and by the improvement of algorithm, improve numerical stability and computational efficiency, the final accuracy improving parameter error Identification and estimation.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described:

As shown in the figure, this electrical network bad data recognition and method of estimation, comprise the following steps:

1) electric network model and multiple measuring section is read in; Read in electric network model, and automatically carry out topological analysis, generate the electric network model calculated; Read in the metric data of multiple historical metrology section, for subsequent calculations simultaneously;

2) one by one state estimation is carried out to measuring section; According to the electric network model read in and metric data, section is run to each and carries out conventional sense estimation calculating; Calculate the measurement qualification rate of each section, measurement qualification rate no longer participates in parameter identification below lower than the section of set point and calculates, and measurement qualification rate participates in parameter identification higher than the section of set point and calculates;

3) suspicious parameter and measurement detect, using the global error of Correlated Case with ARMA Measurement as parameter of measurement or the index measuring suspicious degree; Get during the suspicious parameter of each detection maximum weighted measurement residuals square as threshold value, when Correlated Case with ARMA Measurement global error is less than this threshold value, think parameter or measure credible; When Correlated Case with ARMA Measurement global error is greater than this threshold value, thinks and this parameter or measure suspicious be classified to suspicious parameter/measurement collection; In the next step, only identification is carried out to the parameter that suspicious parameter/measurement is concentrated;

4) based on the parameter/measure wrong cooperative identification of multibreak and global error decline index; When carrying out identification to the parameter that suspicious parameter/measurement is concentrated, multiple measuring section is adopted to carry out combined parameters identification; Using global error decline index as parameter of measurement or the foundation measuring whether mistake, if the global error decline index of suspicious parameter/measurement is greater than 9, be then judged as wrong parameter or bad data;

5) multibreak joint parameter estimation; Multibreak is adopted to combine and parameter augmentation to be estimated is parameter state amount by weighted least-squares method, and the estimated value of each measuring section utilizing the measurement qualification rate that obtains in step 2 high and the measurement of each section, realize parameter Estimation.

Parameter comprises line parameter circuit value and transformer parameter, and line parameter circuit value comprises series resistance, series reactance and shunt susceptance; Transformer parameter comprises excitatory conductance, magnetizing susceptance, series resistance, series reactance and no-load voltage ratio.

When the parameter/measure wrong cooperative identification of step 4 based on multibreak and global error decline index,

Consider measurement model:

z＝h(x,p _e)+ε(1)

Wherein, z represents measurement vector; H (x, p _e) be measurement equation; X is state vector, comprises node voltage amplitude and phase place; p _efor electrical network parameter error vector; ε is error in measurement vector;

Error in measurement is divided into two parts, namely

ε＝v _e+r(2)

Wherein v _esuspicious error in measurement vector, r is measurement residuals vector.

(2) are substituted into (1) can obtain

r＝z-h(x,p _e)-v _e(3)

By network parameter vector description be:

p _t＝p+p _e(4)

Wherein, p and p _tbe respectively supposition and real network parameter vector; p _eit is parameter error vector.

The weighted least square problem that then there is parameter error and measurement bad data is described as following optimization problem:

Minimize:L(x,p _e,v _e)＝r ^TWr(5)

Wherein, W is weight matrix, is generally taken as diagonal matrix, and its inverse matrix is for measuring covariance matrix.

Do not consider the conventional weight least-squares estimation hypothesis of bad data identification

p _e＝0(6)

v _e＝0(7)

Therefore following optimization problem can be described as:

Minimize:L(x,0,0)＝r′ ^TWr′(8)

Wherein, r '=z-h (x, 0) is measurement residuals vector.

Suppose that problem (8) converges on and separate x ⁰, at this Xie Chu, Taylor series expansion is carried out to (3), and reservation causes linear term, then have:

r＝z-h(x ⁰+Δx,p _e)-v _e

＝z-h(x ⁰,0)-H _xΔx-H _pp _e-v _e+h.o.t

≈r ⁰-H _xΔx-H _pp _e-v _e(9)

Wherein,

$H_x=\frac{\∂h(x,p_e)}{\∂x}{|}_{x=x^0,p_e=0}---\left(10\right)$

$H_p=\frac{\∂h(x,p_e)}{\∂p_e}{|}_{x=x^0,p_e=0}---\left(11\right)$

r ⁰＝z-h(x ⁰,0)(12)

For convenience of description, define

$s=\left(\begin{array}{c}{p}_e\\ v_e\end{array}\right)---\left(13\right)$

H _s＝(H _p,I)(14)

J(Δx,s)＝L(x ⁰+Δx,p _e,v _e)(15)

S represents parameter and Measurement Biases vector;

Then (9) can be rewritten as

r＝r ⁰-H _xΔx-H _ss(16)

(16) substitution (5) can be obtained Linear least square estimation problem as follows:

Minimize:J(Δx,s)＝(r ⁰-H _xΔx-H _ss) ^TW(r ⁰-H _xΔx-H _ss)(17)

The optimal solution of problem (17) is:

$s={\left(H_s^T{A}^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{A}^T{\mathrm{WAr}}^0={\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{WAr}}^0---\left(18\right)$

$\mathrm{\Δ}x={\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W(r^0-H_{s}s)---\left(19\right)$

Wherein,

$A=I-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W---\left(20\right)$

Can derive:

$\begin{array}{c}{A}^{T}WA=\[W-{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\]\[I-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\]\\ =W-2{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W+{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^T{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\\ =W-{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\\ =WA\end{array}---\left(21\right)$

Can be obtained by (19) and (20):

$r^0-H_x\mathrm{\Δ}x-H_{s}s=r^0-H_{s}s-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W(r^0-H_{s}s)=A(r^0-H_{s}s)---\left(22\right)$

Due to x ⁰be that convergence state is estimated to separate, therefore have

${\mathrm{Ar}}^0=r^0-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^T{\mathrm{Wr}}^0=r^0---\left(23\right)$

The target function that be can be derived from problem (17) by (22) and (23) is as follows:

$\begin{array}{c}J(\mathrm{\Δ}x,s)={(r^0-H_{s}s)}^T{A}^{T}WA(r^0-H_{s}s)\\ =r^{0T}{A}^T{\mathrm{WAr}}^0-2r^{0T}{A}^T{\mathrm{WAH}}_{s}s+s^T{H_s}^T{A}^T{\mathrm{WAH}}_{s}s\\ =r^{0T}{A}^T{\mathrm{WAr}}^0-r^{0T}{A}^T{\mathrm{WAH}}_s{\left(H_s^T{A}^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{A}^T{\mathrm{WAr}}^0\\ =r^{0T}{\mathrm{WAr}}^0-r^{0T}{\mathrm{WAH}}_s{\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{WAr}}^0\\ =r^{0T}{\mathrm{Wr}}^0-r^{0T}{\mathrm{WH}}_s{\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{Wr}}^0\end{array}---\left(24\right)$

Note B ^kfor kth walks bad data and the wrong parameter collection of identification, can global error be obtained by (17) as follows:

$J({\mathrm{\Δx}}^k,s^k)={(r^0-H_x{\mathrm{\Δx}}^k-H_s{s}^k)}^{T}W(r^0-H_x{\mathrm{\Δx}}^k-H_s{s}^k)---\left(25\right)$

Suppose to intend detecting suspicious measurement or parameter j, definition set

B ^k,j＝B ^k+{j}(26)

Then corresponding global error is:

J(Δx ^k,j,s ^k,j)＝(r ⁰-H _xΔx ^k,j-H _ss ^k,j) ^TW(r ⁰-H _xΔx ^k,j-H _ss ^k,j)(27)

Define global error decline index to weigh the suspicious degree of suspicious measurement or parameter j, namely

ΔJ ^k,j＝J(Δx ^k,s ^k)-J(Δx ^k,j,s ^k,j)(28)

When j corresponds to measurement or parameter, then formula (28) equal corresponding regularization residual error or regularization La Ge Lang day multiplier square, in practicality generally using be greater than 3 regularization residual error or regularization La Ge Lang day multiplier as the foundation judging bad data or parameter error, therefore generally to be greater than the global error slippage of 9 as the foundation judging bad data or parameter error.

This step is the key of this invention.By decomposing the measurement model of Power system state estimation, the weighted least square of traditional packet content sniffing mistake and parameter error can be converted into optimization problem.Then define global error decline index as parameter of measurement or the foundation measuring whether mistake, in actual application, for single operation section, exist when being greater than the global error slippage of 9, can judge have bad data or parameter error to exist.Multiple measuring section and above-mentioned global error decline index are combined, if obviously there is parameter error, then parameter error has an impact to the global error of all measuring sections, thus makes corresponding global error decline index become large.And for bad data, its global error decline index then has nothing to do with section number.Therefore, adopt multiple measuring section to carry out combined parameters identification and be conducive to correct identified parameters mistake.

When given N number of measuring section, then the measurement residuals vector of each measuring section can be described as:

$r^i=z^i-h^i(x^i,p_e)-v_e^i,\∀i\∈\{1,2...N\}---\left(30\right)$

Wherein,

I measuring section is numbered;

N measuring section number;

Z ⁱthe measurement vector of section i;

H ⁱ(x ⁱ, p _e) corresponding to the measurement equation of measuring section i;

X ⁱthe state vector of measuring section i, comprises voltage magnitude and the phase place of each node;

the bad data vector of measuring section i;

R ⁱthe residual vector of measuring section i.

Definition vector:

$r=\left[\begin{array}{c}{r}^1\\ r^2\\ .\\ .\\ .\\ r^N\end{array}\right],z=\left[\begin{array}{c}{z}^1\\ z^2\\ .\\ .\\ .\\ z^N\end{array}\right],x=\left[\begin{array}{c}{x}^1\\ x^2\\ .\\ .\\ .\\ x^N\end{array}\right],v_e=\left[\begin{array}{c}{v}_e^1\\ v_e^2\\ .\\ .\\ .\\ v_e^N\end{array}\right],h(x,p_e)=\left[\begin{array}{c}{h}^1(x^1,p_e)\\ h^2(x^2,p_e)\\ .\\ .\\ .\\ h^N(x^N,p_e)\end{array}\right]---\left(31\right)$

When there is parameter error, then parameter error has an impact to the global error of all measuring sections, thus makes corresponding global error decline index become large; And for bad data, its global error decline index then has nothing to do with section number; Adopt multiple measuring section to carry out combined parameters identified parameters mistake, when global error decline index becomes large, be judged as there is parameter error, otherwise think for bad data.Multibreak the combined parameters based on formula (30) and (31) is similar to bad data cooperative identification method to the parameter based on single section to bad data cooperative identification method.

When step 5 multibreak joint parameter estimation, be parameter state amount based on weighted least-squares method by parameter augmentation to be estimated, utilize augmented state to estimate to realize parameter Estimation;

The measurement equation of electric power system is as follows:

z _t＝h(x _t,p)+v _t

In formula:

X _tthe n of-t ties up state vector

P-k dimension intends estimated parameter vector

Z _tthe m dimension of-t measures vector

V _tthe m of-t ties up error in measurement vector

H (x _t, p)-m ties up non-linear measurement function vector, have expressed the correlation measuring true value and parameter vector and state vector;

Carry out Combined estimator to T section, then the state vector of Parameter Estimation Problem is as follows:

[x ₁,x ₂,…x _T,p] ^T

Measure vector as follows:

[z ₁,z ₂,…z _T] ^T

Parameter Estimation adopts Orthogonal Transformation Method to solve.

Although comparatively large based on multibreak joint parameter estimation method amount of calculation of ELS estimation principle, estimated accuracy is relatively high, compares and be suitable for off-line application.Because the meaning of parameter Estimation application on site is also little, the importance of contrary estimated accuracy is very high, therefore adopts multibreak joint parameter estimation method to carry out parameter Estimation.

For general state estimation problem, parameter vector p is given value, and object is the measurement vector z according to t _task for t state vector x _toptimal estimation.Because in state estimation procedure, parameter vector p is given value, thus make the estimation problem of each section full decoupled.

For Parameter Estimation Problem, parameter vector p is not re-used as given value, but joins in state estimation problem as the state vector of augmentation.Obviously, Parameter Estimation Problem adds the dimension of state vector, and the quantity measured does not change, if state estimation problem is unobservable, although or can observe, without any redundancy, then Parameter Estimation Problem is certainly unobservable.Therefore, only meet observability requirement at the measure configuration of system, and under having the condition of suitable redundancy, just likely carry out parameter Estimation.

Increase Combined estimator section number T and be conducive to the observability improving Parameter Estimation Problem, improve and measure redundancy, thus improve the precision of parameter Estimation.

Because the calculating scale of multibreak joint parameter estimation is much larger than state estimation, the sparse matrix treatment technology of orthogonal transform is the key of algorithm execution efficiency.

The present invention proposes a kind of new method based on global error decline index, not only can realize the effective Identification and estimation in single measurement mistake or parameter error situation, and can under multiple measurement mistake and the simultaneous situation of parameter error, efficiently, the cooperative identification measuring mistake and parameter error is realized accurately, process is without the need to iterating, reduce amount of calculation, improve efficiency and the accuracy of parameter identification and estimation.

In addition to the implementation, the present invention can also have other execution modes.All employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop on the protection range of application claims.

Claims (3)

1. electrical network bad data recognition and a method of estimation, is characterized in that: comprise the following steps:

1) electric network model and multiple measuring section is read in; Read in electric network model, and automatically carry out topological analysis, generate the electric network model calculated; Read in the metric data of multiple historical metrology section, for subsequent calculations simultaneously;

2) one by one state estimation is carried out to measuring section; According to the electric network model read in and metric data, section is run to each and carries out conventional sense estimation calculating; Calculate the measurement qualification rate of each section, measurement qualification rate no longer participates in parameter identification below lower than the section of set point and calculates, and measurement qualification rate participates in parameter identification higher than the section of set point and calculates;

3) suspicious parameter and measurement detect, using the global error of Correlated Case with ARMA Measurement as parameter of measurement or the index measuring suspicious degree; Get during the suspicious parameter of each detection maximum weighted measurement residuals square as threshold value, when Correlated Case with ARMA Measurement global error is less than this threshold value, think parameter or measure credible; When Correlated Case with ARMA Measurement global error is greater than this threshold value, thinks and this parameter or measure suspicious be classified to suspicious parameter/measurement collection; In the next step, only identification is carried out to the parameter that suspicious parameter/measurement is concentrated;

4) based on the parameter/measure wrong cooperative identification of multibreak and global error decline index; When carrying out identification to the parameter that suspicious parameter/measurement is concentrated, multiple measuring section is adopted to carry out combined parameters identification; Using global error decline index as parameter of measurement or the foundation measuring whether mistake, if the global error decline index of suspicious parameter/measurement is greater than 9, be then judged as wrong parameter or bad data;

5) multibreak joint parameter estimation; Multibreak is adopted to combine and parameter augmentation to be estimated is parameter state amount by weighted least-squares method, and the estimated value of each measuring section utilizing the measurement qualification rate that obtains in step 2 high and the measurement of each section, realize parameter Estimation.

2. electrical network bad data recognition according to claim 1 and method of estimation, is characterized in that: during the parameter/measure wrong cooperative identification of described step 4 based on multibreak and global error decline index, consider measurement model:

z＝h(x,p _e)+ε(1)

Wherein, z represents measurement vector; H (x, p _e) be measurement equation; X is state vector, comprises node voltage amplitude and phase place; p _efor electrical network parameter error vector; ε is error in measurement vector;

Error in measurement is divided into two parts, namely

ε＝v _e+r(2)

Wherein v _esuspicious error in measurement vector, r is measurement residuals vector.

(2) are substituted into (1) can obtain

r＝z-h(x,p _e)-v _e(3)

By network parameter vector description be:

p _t＝p+p _e(4)

Wherein, p and p _tbe respectively supposition and real network parameter vector; p _eit is parameter error vector.

The weighted least square problem that then there is parameter error and measurement bad data is described as following optimization problem:

Minimize:L(x,p _e,v _e)＝r ^TWr(5)

Wherein, W is weight matrix, is generally taken as diagonal matrix, and its inverse matrix is for measuring covariance matrix.

Do not consider the conventional weight least-squares estimation hypothesis of bad data identification

p _e＝0(6)

v _e＝0(7)

Therefore following optimization problem can be described as:

Minimize:L(x,0,0)＝r′ ^TWr′(8)

Wherein, r '=z-h (x, 0) is measurement residuals vector.

Suppose that problem (8) converges on and separate x ⁰, at this Xie Chu, Taylor series expansion is carried out to (3), and reservation causes linear term, then have:

r＝z-h(x ⁰+Δx,p _e)-v _e

＝z-h(x ⁰,0)-H _xΔx-H _pp _e-v _e+h.o.t

≈r ⁰-H _xΔx-H _pp _e-v _e(9)

Wherein,

$H_x=\frac{\∂h(x,p_e)}{\∂x}{|}_{x=x^0,p_e=0}---\left(10\right)$

$H_p=\frac{\∂h(x,p_e)}{\∂p_e}{|}_{x=x^0,p_e=0}---\left(11\right)$

r ⁰＝z-h(x ⁰,0)(12)

For convenience of description, define

$s=\left(\begin{array}{c}{p}_e\\ v_e\end{array}\right)---\left(13\right)$

H _s＝(H _p,I)(14)

J(Δx,s)＝L(x ⁰+Δx,p _e,v _e)(15)

S represents parameter and Measurement Biases vector;

Then (9) can be rewritten as

r＝r ⁰-H _xΔx-H _ss(16)

(16) substitution (5) can be obtained Linear least square estimation problem as follows:

Minimize:J(Δx,s)＝(r ⁰-H _xΔx-H _ss) ^TW(r ⁰-H _xΔx-H _ss)(17)

The optimal solution of problem (17) is:

$s={\left(H_s^T{A}^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{A}^T{\mathrm{WAr}}^0={\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{WAr}}^0---\left(18\right)$

$\mathrm{\Δ}x={\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W(r^0-H_{s}s)---\left(19\right)$

Wherein,

$A=I-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W---\left(20\right)$

Can derive:

$\begin{array}{c}{A}^{T}WA=\[W-{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\]\[I-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\]\\ =W-2{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W+{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^T{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\\ =W-{\mathrm{WH}}_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W\\ =WA\end{array}---\left(21\right)$

Can be obtained by (19) and (20):

$r^0-H_x\mathrm{\Δ}x-H_{s}s=r^0-H_{s}s-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^{T}W(r^0-H_{s}s)=A(r^0-H_{s}s)---\left(22\right)$

Due to x ⁰be that convergence state is estimated to separate, therefore have

${\mathrm{Ar}}^0=r^0-H_x{\left(H_x^T{\mathrm{WH}}_x\right)}^{-1}{H}_x^T{\mathrm{Wr}}^0=r^0---\left(23\right)$

The target function that be can be derived from problem (17) by (22) and (23) is as follows:

$\begin{array}{c}J\left(\mathrm{\Δ}x,s\right)={\left(r^0-H_{s}s\right)}^T{A}^{T}WA\left(r^0-H_{s}s\right)\\ =r^{0T}{A}^T{\mathrm{WAr}}^0-2r^{0T}{A}^T{\mathrm{WAH}}_{s}s+s^T{H_s}^T{A}^T{\mathrm{WAH}}_{s}s\\ =r^{0T}{A}^T{\mathrm{WAr}}^0-r^{0T}{A}^T{\mathrm{WAH}}_s{\left(H_s^T{A}^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{A}^T{\mathrm{WAr}}^0\\ =r^{0T}{\mathrm{WAr}}^0-r^{0T}{\mathrm{WAH}}_s{\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{WAr}}^0\\ =r^{0T}{\mathrm{Wr}}^0-r^{0T}{\mathrm{WH}}_s{\left(H_s^T{\mathrm{WAH}}_s\right)}^{-1}{H}_s^T{\mathrm{Wr}}^0\end{array}---\left(24\right)$

Note B ^kfor kth walks bad data and the wrong parameter collection of identification, can global error be obtained by (17) as follows:

J(Δx ^k,s ^k)＝(r ⁰-H _xΔx ^k-H _ss ^k) ^TW(r ⁰-H _xΔx ^k-H _ss ^k)(25)

Suppose to intend detecting suspicious measurement or parameter j, definition set

B ^k,j＝B ^k+{j}(26)

Then corresponding global error is:

J(Δx ^k,j,s ^k,j)＝(r ⁰-H _xΔx ^k,j-H _ss ^k,j) ^TW(r ⁰-H _xΔx ^k,j-H _ss ^k,j)(27)

Define global error decline index to weigh the suspicious degree of suspicious measurement or parameter j, namely

ΔJ ^k,j＝J(Δx ^k,s ^k)-J(Δx ^k,j,s ^k,j)(28)

When j corresponds to measurement or parameter, then formula (28) equal corresponding regularization residual error or regularization La Ge Lang day multiplier square, in practicality generally using be greater than 3 regularization residual error or regularization La Ge Lang day multiplier as the foundation judging bad data or parameter error, therefore generally to be greater than the global error slippage of 9 as the foundation judging bad data or parameter error.

3. electrical network bad data recognition according to claim 1 and method of estimation, it is characterized in that: during described step 5 multibreak joint parameter estimation, be parameter state amount based on weighted least-squares method by parameter augmentation to be estimated, utilize augmented state to estimate to realize parameter Estimation; The measurement equation of electric power system is as follows:

z _t＝h(x _t,p)+v _t

In formula:

X _tthe n of-t ties up state vector

P-k dimension intends estimated parameter vector

Z _tthe m dimension of-t measures vector

V _tthe m of-t ties up error in measurement vector

H (x _t, p)-m ties up non-linear measurement function vector, have expressed the correlation measuring true value and parameter vector and state vector;

Carry out Combined estimator to T section, then the state vector of Parameter Estimation Problem is as follows:

[x ₁,x ₂,…x _T,p] ^T

Measure vector as follows:

[z ₁,z ₂,…z _T] ^T

Parameter Estimation adopts Orthogonal Transformation Method to solve.