CN103593566B - The power system comprehensive state method of estimation of mixing quadratic programming form - Google Patents

Abstract

The present invention discloses a kind of power system comprehensive state method of estimation of mixing quadratic programming form, may comprise steps of：Form network model, calculate node admittance matrix and branch node incidence matrix；Enter line translation to measuring vector state vector, obtain middle measurement vector intermediateness vector；Based on the middle measurement equation for measuring vector intermediateness vector, forming exact linearization method；Based on the linearisation measurement equation being previously obtained, the power system comprehensive state for proposing mixing quadratic programming form estimates model, then solved using CPLEX softwares, obtain the estimated value of intermediateness vector, recognize bad data, Topology Error and parameter error in the process simultaneously；And inverse transformation is carried out to the intermediateness vector for obtaining, obtain the estimated value of the voltage magnitude and phase angle of all nodes.The method has accurately and reliably, the high advantage of solution efficiency.

Description

The power system comprehensive state method of estimation of mixing quadratic programming form

Technical field

The invention belongs to dispatching automation of electric power systems field, and in particular to a kind of mixing quadratic programming form（mixed- Integer quadratic programming, MIQP）Power system comprehensive state method of estimation.

Background technology

Power system state estimation is the requisite basic software system of grid dispatching center, is electric power netting safe running Ensure.Power system state estimation needs the switch provided according to telemetry, remote signalling and disconnecting link state and network parameter to estimate Obtain an optimum state vector（That is state variable）, to realize perceiving the comprehensive, real-time and accurate of electrical network.

For various reasons, in telemetry, remote signalling data and network parameter always contains bad data, and existing state estimation Method often assumes that topological sum parameter is correct while state vector estimation is carried out, and carries bad data recognition function；? There is the synchronous research for carrying out bad data and topology error identification or synchronously carrying out bad data and parameter error identification.External Person propose can and meanwhile carry out bad data recognition, topology error identification and parameter error identification comprehensive state method of estimation, But its computational efficiency is relatively low, still there is no practical value.Therefore, up to the present, still lack efficient power system synthesis shape State estimates implementation method.

Content of the invention

It is contemplated that at least solving one of technical problem present in prior art.

For this purpose, it is an object of the invention to propose a kind of accurately and reliably, the high mixing quadratic programming form of solution efficiency Power system comprehensive state method of estimation.

To achieve these goals, mix the power system synthesis shape of quadratic programming form according to an embodiment of the invention State method of estimation, may comprise steps of：A. network model, calculate node admittance matrix and branch road-node association square are formed Battle array；B. enter line translation to measuring vector state vector, obtain middle measurement vector intermediateness vector；C. intermediate quantity is based on Vector intermediateness vector is surveyed, the measurement equation of exact linearization method is formed；D. the linearisation measurement side for being obtained based on step C Journey, the power system comprehensive state for proposing mixing quadratic programming form estimate model, are then solved using CPLEX softwares, are obtained The estimated value of intermediateness vector, recognizes bad data, Topology Error and parameter error in the process simultaneously；And E. steps The intermediateness vector that D is obtained carries out inverse transformation, obtains the estimated value of the voltage magnitude and phase angle of all nodes.

The power system comprehensive state method of estimation of mixing quadratic programming form according to embodiments of the present invention, at least has Advantages below：1）This model only needs to solve mixing quadratic programming problem, theoretically can ensure that and obtains globally optimal solution；2） While state vector estimation is carried out, bad data recognition, parameter error identification and topology error identification can be carried out；3）Available Business software CPLEX is solved, and solution efficiency is high, is suitable for application on site.

In addition, the power system comprehensive state method of estimation of mixing quadratic programming form according to embodiments of the present invention may be used also With with following additional technical feature：

In one embodiment of the invention, step A is specifically included：By all of circuit and transformator etc. in network Imitate as π type branch road ij, note y_s=1/(r_ij+jx_ij)=g_s+jb_sFor the series connection susceptance of π type branch road ij, r_ij+jx_ijFor π type branch road ij's Series impedances, b_cFor the ground connection susceptance of π type branch road ij, wherein, if π type branch roads ij is transformer branch, b_c=0 and k is reason Think the no-load voltage ratio of transformator, if π type branch roads ij is common line, k=1, a plurality of branch road in parallel are equivalent to a branch road；Wait In circuit after effect, g is remembered_ij=g_s/ k, b_ij=b_s/ k, g_si=(1-k)g_s/k², b_si=(1-k)b_s/k²+b_c/ 2, g_sj=(k-1)g_s/ k, b_sj=(k-1)b_s/k+b_c/2；Calculate node admittance matrix Y=G+jB, G and B are respectively the real part of bus admittance matrix and imaginary part, Then branch road-node incidence matrix A={ a are calculated_ij(1≤i≤b, 1≤j≤N-1), wherein a_ijIt is defined as：

In one embodiment of the invention, step B is specifically included：Choosing intermediateness vector isWherein, total numbers of the N for all nodes in network, b For the number of all branch roads in network, l is branch number, l_iAnd l_jFor the two ends node number of branch road l,WithIt is node respectively l_iAnd l_jVoltage magnitude,WithIt is node l respectively_iAnd l_jPhase angle,For phase angle difference,Contribution of all of b bars branch road to middle state vector X is represented, Also all of b bar branch road contribution to middle state vector X, X ∈ R are represented^N+2bFor intermediateness vector；And choose The middle vector that measures is y ∈ R^m, including node voltage amplitude square, branch road is active, branch road is idle, injection is active, Injection is idle, branch current magnitudes square, wherein, total numbers of the m for measurement, when with intermediateness vector X During expression, node voltage amplitude square isv_iFor the voltage of node i, the branch road from node i to node j has Work(isBranch road from node i to node j is idle to beThe injection of node i is active to beSection The injection of point i is idle to beG_ij+jB_ijCorresponding element in for bus admittance matrix, branch road Current amplitude square isWherein, I_ijElectric current width for π type branch road ij Value, A=(g_si+g_ij)²+(b_si+b_ij)²,D=-g_sib_ij+b_sig_ij.

In one embodiment of the invention, step C is specifically included：If J is ∈ R^m×(N+2b)For Jacobian matrix, its In, square corresponding Jacobian matrix element that node voltage amplitude is measured is Branch power measures corresponding Jacobian matrix element It is right that injecting power is measured The Jacobian matrix element that answers is Branch current magnitudes measure a square corresponding Jacobian matrix element beAnd the centre after the conversion obtained according to step B Vector intermediateness vector is measured, the measurement equation for obtaining exact linearization method is：Y=JX+ τ, wherein, τ ∈ R^mFor error in measurement Vector, J ∈ R^m×(N+2b)For constant Jacobian matrix.

In one embodiment of the invention, step D is specifically included：D1. the uncertainty of measurement is considered, will Exact linearization method measurement equation y=JX+ τ in step C are rewritten as inequality Wherein, y_iAnd J_iI-th component of respectively y and J,Respectively in order to weigh measure uncertainty the upper bound and lower bound, M For arbitrarily fully big scalar, b_iFor measurement y_iCorresponding 0/1 binary variable；For suspicious branch parameters, equally copy with The probabilistic processing method of upper metric data obtains the indeterminacy section of suspicious parameter, and the state of suspicious switch/disconnecting link is adopted Linear inequalityTo represent, wherein,b_k Corresponding 0/1 binary variable of switch/disconnecting link for this, M are a fully big number, b if switch/disconnecting link is closed_k=0, if opening Pass/disconnecting link opens then b_k=1；D2. the power system comprehensive state for proposing mixing quadratic programming form estimates that model is as follows：And D3. is solved using CPLEX softwares, obtains centre The estimated value of state vector and the numerical value of binary variable, if certain metric data or the corresponding binary variable of network parameter The estimated value of bi is 0, then which is normal metric data or correct network parameter, is otherwise bad data value or the network of mistake Parameter, if the corresponding binary variable b of certain switch/disconnecting link_kEstimated value be 0, then its actual topology status for closure, otherwise For opening, bad data, parameter error and Topology Error is picked out accordingly.

In one embodiment of the invention, step E specifically includes following steps：In described Between state vector X estimated valueAccording toInverse transformation is carried out, is obtained All node voltage amplitudes and the estimated values theta of all branch road two ends phase angle difference_2b∈R^2b, i.e.,And using all branch road two ends phase angle difference Estimated values theta_2bConstruction Min J (θ)=(θ_2b-A₂θ)^TW_θ(θ_2b-A₂Linear weighted function least square problem θ), wherein W_θFor weight matrix, Value be unit matrix, A₂=[A^TA^T]^T, branch road-node incidence matrix that A is obtained for step A, θ ∈ R^N-1It is except reference mode The phase angle of outer all nodes, wherein optimal solution should meet conditionObtainA is substituted into A₂, and solve Obtain θ=(A^TA)^-1A^Tθ_b, wherein,

The additional aspect and advantage of the present invention will be set forth in part in the description, and partly will become from the following description Obtain substantially, or recognized by the practice of the present invention.

Description of the drawings

The above-mentioned and/or additional aspect and advantage of the present invention will become from the description with reference to accompanying drawings below to embodiment Substantially and easy to understand, wherein：

Flow processs of the Fig. 1 for the power system comprehensive state method of estimation of the mixing quadratic programming form of the embodiment of the present invention Figure；

Schematic diagrams of the Fig. 2 for π type branch roads；

Schematic diagrams of the Fig. 3 for π type branch road equivalent circuits；And

Fig. 4 is that MIQP calculates the time-consuming graph of a relation with system scale.

Specific embodiment

Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings, wherein from start to finish Same or similar label represents same or similar element or the element with same or like function.Below with reference to attached The embodiment of figure description is exemplary, it is intended to for explaining the present invention, and be not considered as limiting the invention.

It is well known that only when network topology, parameter and metric data are all correct, state estimation is only possible to obtain correctly As a result.Therefore while the estimation of POWER SYSTEM STATE vector is carried out, it is necessary to while carry out bad data recognition, Topology Error distinguishing Know and parameter estimation, i.e., comprehensive state estimates the only way which must be passed for being state estimation.Moreover, comprehensive state estimate should also have compared with High computational efficiency is ensureing application on site.For this purpose, it is contemplated that the mixing that proposition is a kind of accurately and reliably, computational efficiency is higher The power system comprehensive state method of estimation of quadratic programming form.

The present invention relates to a kind of comprehensive state method of estimation of the mixing quadratic programming form that can apply to power system (a mixed integer quadratic programming, MIQP), the model carry out state vector estimate while, Bad data recognition, topology error identification and parameter estimation can synchronously be carried out；The model belongs to quadratic programming problem simultaneously, from number Can ensure to obtain globally optimal solution on learning.As shown in figure 1, the method may comprise steps of：

（1）Network model

Three-winding transformer in network is equivalent to three two-winding transformers, then all of branch road and transformation in network Device can be represented with unified π type branch roads, as shown in Figure 1.In Fig. 1, y_s=1/(r_ij+jx_ij)=g_s+jb_sSeries connection for branch road ij Susceptance；r_ij+jx_ijFor series impedances；b_cFor the ground connection susceptance of branch road, for transformer branch, b_c=0；K is ideal transformer No-load voltage ratio, for ordinary branch, k=1.

The equivalent circuit of the π type branch roads of Fig. 1 is as shown in Figure 2.In Fig. 2, g_ij=g_s/k；b_ij=b_s/k；g_si=(1-k)g_s/k²； b_si=(1-k)b_s/k²+b_c/2；g_sj=(k-1)g_s/k；b_sj=(k-1)b_s/k+b_c/2.

Then bus admittance matrix Y=G+jB is formed using network model and parameter, G and B is respectively bus admittance matrix Real part and imaginary part.

（2）Line translation is entered to state vector and measurement vector

Choosing intermediateness vector is

Wherein, N is the total number of all nodes in network；B is number (a plurality of branch road in parallel of all branch roads in network It is equivalent to a branch road)；L is branch number, l_iAnd l_jFor the two ends node number of branch road l,WithIt is node l respectively_iAnd l_j's Voltage magnitude,WithIt is the phase angle of node li and lj respectively,For phase angle difference；Represent Contribution of all of b bars branch road to state vector X,Also all of b bar branch road is represented to state vector X Contribution；X∈R^N+2bFor new state vector.

It is y ∈ R to measure vector in the middle of choosing^m, the measurement type which includes has：Node voltage amplitude square, branch road has Work(, branch road are idle, injection is active, injection is idle, branch current magnitudes square；Total numbers of the m for measurement.

Measure vector to be expressed with intermediateness vector X in the middle of then.

A) voltage magnitude measure square

Wherein, v_iVoltage for node i.

B) from node i to the active and idle measurement of the branch road of node j

Wherein, P_ijAnd Q_ijRespectively node i flow to node j branch road active and idle.

C) injection of node i is active and injection is idle

Wherein, P_iAnd Q_iThe injection of respectively node i is active and injects idle, G_ij+jB_ijRight in for bus admittance matrix Answer element.

D) branch current magnitudes measure square

Wherein, I_ijCurrent amplitude for branch road ij；A=(g_si+g_ij)²+(b_si+b_ij)²；

D=-g_sib_ij+b_sig_ij.

（3）Obtain the measurement equation of exact linearization method

According to measurement vector intermediateness vector in the middle of choosing above, you can obtain the measurement equation of exact linearization method For：

y=JX+σ （7）

Wherein, y ∈ R^mFor measuring vector, including node voltage amplitude square, branch road is active, branch road is idle, be injected with Work(, inject idle, branch current magnitudes square；X∈R^N+2bFor state vector；σ～N (0, R) is error in measurement vector, whereinWhereinFor τ_iVariance；J∈R^m×(N+2b)For constant Jacobian matrix, the element of its various pieces Expression formula as follows.

A) square corresponding Jacobian matrix element that voltage magnitude is measured

For voltage magnitude measure square, its corresponding Jacobian matrix element is

B) branch power measures corresponding Jacobian matrix element

For branch power is measured, its corresponding Jacobian matrix element is

C) injecting power measures corresponding Jacobian matrix element

For injecting power is measured, its corresponding Jacobian matrix element is

D) square corresponding Jacobian matrix element that branch current magnitudes are measured

For branch current magnitudes measure square, its corresponding Jacobian matrix element is

（4）The comprehensive state of mixing quadratic programming form is estimated（MIQP）Model

Consider the uncertainty of measurement, formula（7）Rewritable for following inequality

Wherein, y_iAnd J_iRespectively formula（7）I-th component of middle y and J；Respectively do not know in order to weigh to measure The upper bound of degree and lower bound;M is arbitrarily fully big scalar;b_iFor measurement y_iCorresponding 0/1 binary variable；For normal measurement b_i=0, for bad data, b_i=1.

For suspicious branch parameters, formula can be equally copied（7）Obtain the indeterminacy section of its parameter.

Using formula（7）In state vector when, the state of suspicious switch/disconnecting link can use following linear inequality to represent

Wherein,b_kSwitch/disconnecting link corresponding 0/1 for this Binary variable；M is a fully big number；If switch/disconnecting link is closed, b_k=0；If switch/disconnecting link is opened, b_k=1.

The comprehensive state of mixing quadratic programming form proposed by the present invention is estimated（MIQP）Model is as follows

Model（10）It is a typical mixing quadratic programming problem, can be solved with business software CPLEX.Solved Afterwards, you can pick out bad data, parameter error and Topology Error.

(5) inverse transformation obtains end-state vector

Obtain the estimated value of XAfterwards, the voltage complex phase amount of all nodes be able to can be obtained further with inverse transformation, specifically Method is to calculate first

In formula：Voltage magnitude v on the right of equal sign_iTake fromL represents branch road, l_iAnd l_jTwo end node of branch road is represented,With Node l is represented respectively_iAnd l_jVoltage magnitude,WithNode l is represented respectively_iAnd l_jVoltage phase angle,Represent branch road l two The phase angle difference at end；In formula (11), the symbol of arccos should be consistent with the symbol of arcsin.

So far, the estimated value of all node voltage amplitudes obtained, but the phase angle of all nodes or unknown, show So can be estimated using the phase angle difference at all branch road two ends.

OrderObviously, can lead to Cross formula（11）Obtain θ_2b.Following with θ_2bEstimate the phase angle for obtaining all nodes.

Make A={ a_ij(1≤i≤b, 1≤j≤N-1) represent depression of order branch road-node incidence matrix（Reference mode institute is not included Row）, it is clear that A ∈ R^b×(N-1), its each element is defined as follows

Make θ=[θ₂,…,θ_N]^TRepresent the phase angle (node 1 being set as reference mode) of all nodes, then θ_2bRelation with θ is

θ_2b=A₂θ （12）

Wherein, A₂=[A^TA^T]^T, A₂Matrix for 2b × (N-1).

Because θ_2bIt is to be derived by by the state estimation result of first stage, so can be by θ_2bIt is considered as containing noisy Measurement.And θ is value to be estimated, then formula（12）The following measurement equation with regard to θ can be rewritten as

θ_2b=A₂θ+τ （13）

Following linear weighted function least square problem can be then constructed, θ is estimated

Min J(θ)=(θ_2b-A₂θ)^TW_θ(θ_2b-A₂θ) （14）

Wherein, W_θFor weight matrix, without loss of generality, W is can use_θFor unit matrix.Work as formula（14）Optimal value is obtained, must be full Foot

Bring A into A₂, can obtain

A^TAθ=A^Tθ_b（16）

Wherein,For b n dimensional vector ns, Obviously can be by θ_2bObtain θ_b.

By formula（16）The estimated value that θ can be obtained is θ=(A^TA)^-1A^Tθ_b.

So far, the estimated value of the voltage magnitude and phase angle of all nodes has been obtained.

The comprehensive state of the mixing quadratic programming form for being applied to power system proposed by the present invention is estimated（MIQP）Method At least there is advantages below：1）This model only needs to solve mixing quadratic programming problem, theoretically can ensure that and obtains the overall situation Optimal solution；2）While state vector estimation is carried out, bad data recognition, parameter error identification and Topology Error can be carried out and distinguished Know；3）Available business software CPLEX is solved, and solution efficiency is high, is suitable for application on site.

In order that those skilled in the art more fully understand the present invention, applicant is using the ieee standard system test present invention The comprehensive state of the mixing quadratic programming form of proposition is estimated（MIQP）Performance.Test adopts ieee standard system, in order to survey The Robustness least squares of examination MIQP and computational efficiency.

1) robustness

In IEEE-300 systems, branch road 1-5 impedances are reduced into original 1/10（Then node 1 is changed into leverage points）, with When 4 concordance bad datas and 10 Topology Errors are set.Then estimated using MIQP proposed by the present invention, model Solved using CPLEX.Result of the test shows：Even if in the case where there is leverage points bad data, MIQP also can be correct Identify all bad datas, parameter error and Topology Error；And conventional weighted least-squares method, Weighted least absolute value etc. Method then gives the estimated result of mistake.

2) computational efficiency

This trifle carries out efficiency test, is repeatedly tested in different ieee standard systems respectively, and average computation takes As shown in table 1.Calculate the relation of time-consuming and system scale as shown in figure 4, in the diagram, abscissa represents system interstitial content, indulge Coordinate is represented to calculate and is taken.From the calculating of table 1 and Fig. 4, MIQP time-consuming approximate with system scale be directly proportional, thus MIQP is fitted Should be in the application on site of large scale system.

The computational efficiency test of table 1MIQP

In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show The description of example " or " some examples " etc. means specific features, structure, material or the spy described with reference to the embodiment or example Point is contained at least one embodiment or example of the present invention.In this manual, to the schematic representation of above-mentioned term not Identical embodiment or example must be directed to.And, the specific features of description, structure, material or feature can be with office Combined in one or more embodiments or example in an appropriate manner.Additionally, those skilled in the art can be by this specification Described in different embodiments or example be combined and combine.

Although embodiments of the invention have been shown and described above, it is to be understood that above-described embodiment is example Property, it is impossible to limitation of the present invention is interpreted as, one of ordinary skill in the art within the scope of the invention can be to above-mentioned Embodiment is changed, changes, replacing and modification.

Claims (1)

1. a kind of mixing quadratic programming form power system comprehensive state method of estimation, it is characterised in that comprise the following steps：

A. network model, calculate node admittance matrix and branch road-node incidence matrix are formed；

B. enter line translation to measuring vector state vector, obtain middle measurement vector intermediateness vector；

C. based on the middle measurement equation for measuring vector intermediateness vector, forming exact linearization method；

D. the linearisation measurement equation for being obtained based on step C, the power system comprehensive state for proposing mixing quadratic programming form are estimated Meter model, is then solved using CPLEX softwares, obtains the estimated value of intermediateness vector, is recognized simultaneously in the process bad Data, Topology Error and parameter error；And

The estimated value of the intermediateness vector that E. step D is obtained carries out inverse transformation, obtains the voltage magnitude and phase angle of all nodes Estimated value,

Wherein, step A is specifically included：

All of circuit and transformator in network are equivalent to π type branch road ij, y is remembered_s=1/ (r_ij+jx_ij)=g_s+jb_sFor π types The series admittance of road ij, r_ij+jx_ijFor the series impedances of π type branch road ij, b_cFor the ground connection susceptance of π type branch road ij, wherein, if π Type branch road ij is transformer branch, then b_c=0 and k is the no-load voltage ratio of ideal transformer, if π type branch roads ij is common line, k= 1, a plurality of branch road in parallel is equivalent to a branch road；

In circuit after equivalent, g is remembered_ij=g_s/ k, b_ij=b_s/ k, g_si=(1-k) g_s/k², b_si=(1-k) b_s/k²+b_c/ 2, g_sj =(k-1) g_s/ k, b_sj=(k-1) b_s/k+b_c/2；

Calculate node admittance matrix Y=G+jB, G and B be respectively bus admittance matrix real part and imaginary part, then calculate branch road- Node incidence matrix A={ a_ijWherein, 1≤i≤b, 1≤j≤N-1, wherein a_ijIt is defined as：

Step B is specifically included：

Choosing intermediateness vector isWherein, 1≤l≤b, wherein, N For the total number of all nodes in network, b is the number of all branch roads in network, and l is branch number, l_iAnd l_jFor branch road l two End segment period,WithIt is node l respectively_iAnd l_jVoltage magnitude,WithIt is node l respectively_iAnd l_jPhase angle, For phase angle difference,Contribution of all of b bars branch road to middle state vector X is represented,Also represent all Contribution of the b bars branch road to middle state vector X, X ∈ R^N+2bFor intermediateness vector；And

It is y ∈ R to measure vector in the middle of choosing^m, including node voltage amplitude square, branch road is active, branch road is idle, injection Active, inject idle, branch current magnitudes square, wherein, m is the total number for measuring vector, when being sweared with intermediateness X is when representing for amount, and node voltage amplitude square isv_iFor the voltage of node i, propping up from node i to node j Road is active to beBranch road from node i to node j is idle to beThe injection of node i is active to beNode The injection of i is idle to beG_ij+jB_ijCorresponding element in for bus admittance matrix, branch road electricity Stream amplitude square isWherein, I_ijFor the current amplitude of π type branch road ij, A=(g_si+g_ij)²+(b_si+b_ij)²,D=-g_sib_ij+b_sig_ij,

Step C is specifically included：

If J is ∈ R^m×(N+2b)For Jacobian matrix, wherein, square corresponding Jacobian matrix element that node voltage amplitude is measured isBranch power measures corresponding Jacobian matrix element Injecting power measures corresponding Jacobian matrix element Branch current magnitudes are measured Square corresponding Jacobian matrix element isAnd

According to the middle measurement vector intermediateness vector after the conversion that step B is obtained, the measurement side of exact linearization method is obtained Cheng Wei：Y=JX+ τ, wherein, τ ∈ R^mFor error in measurement vector, J ∈ R^m×(N+2b)For constant Jacobian matrix,

Step D is specifically included：

D1. the uncertainty for measuring vector is considered, the exact linearization method measurement equation y=JX+ τ in step C is rewritten For inequalityWherein, y_iAnd J_iI-th component of respectively y and J,Point It is not to weigh the upper bound and lower bound for measuring uncertainty, M is arbitrarily fully big scalar, b_iFor measuring vector y_iCorresponding 0/1 Binary variable；For suspicious branch parameters, the probabilistic processing method of above metric data is equally copied to obtain suspicious The indeterminacy section of parameter；The state of suspicious switch/disconnecting link adopts linear inequalityTo represent, its In,b_kCorresponding 0/1 binary variable of switch/disconnecting link for this, M is a fully big number, b if switch/disconnecting link is closed_k=0, b if switch/disconnecting link is opened_k=1；

D2. the power system comprehensive state for proposing mixing quadratic programming form estimates that model is as follows：

$Min\underset{alliandk}{\Σ}{b}_i$

$\begin{array}{cc}s.t.& \left\{\begin{array}{c}{y}_i-t_i^{-}-{\mathrm{Mb}}_i\≤J_{i}X\≤y_i+t_i^{+}+{\mathrm{Mb}}_i,i=1,2,...,m_s\\ \left\{\begin{array}{c}-{\mathrm{Mb}}_k\≤V_{2i}-V_{2j}\≤{\mathrm{Mb}}_k\\ -{\mathrm{Mb}}_k\≤V_{ij}^s\≤{\mathrm{Mb}}_k\\ -{\mathrm{Mb}}_k\≤V_{ij}^c-V_{2i}\≤{\mathrm{Mb}}_k,L_{ij}foralllinks\end{array}\right.\\ b_i,b_k=0or1\end{array}\right.\end{array};$

D3. solved using CPLEX softwares, obtained the estimated value of intermediateness vector and the numerical value of binary variable, if Certain metric data or the corresponding binary variable b of network parameter_iEstimated value be 0, then which is normal metric data or correct Network parameter, be otherwise bad data value or the network parameter of mistake, if the corresponding binary variable b of certain switch/disconnecting link_k Estimated value be 0, then its actual topology status for closure, otherwise be open, pick out bad data, parameter error accordingly and open up Flutter mistake,

Step E is specifically included：

Estimated value using the intermediateness vector XAccording toCarry out inverse Conversion, obtains the estimated values theta of all node voltage amplitudes and all branch road two ends phase angle difference_2b∈R^2b, i.e., Wherein, 1≤l≤b；And

Estimated values theta using all branch road two ends phase angle difference_2bConstruction Min J (θ)=(θ_2b-A₂θ)^TW_θ(θ_2b-A₂Line θ) Property weighted least-squares problem, wherein W_θFor weight matrix, value is unit matrix, A₂=[A^TA^T]^T, A obtained for step A The branch road for arriving-node incidence matrix, θ ∈ R^N-1It is the phase angle of all nodes in addition to reference mode, wherein optimal solution should meet ConditionObtainA is substituted into A₂, and solve and obtain θ=(A^TA)^-1A^Tθ_b, wherein,Wherein, 1≤l≤b.