CN1738143A - Power network topology error identification method based on mixed state estimation - Google Patents

Abstract

The invention relates to electrical network topological error identification method based on mixed evaluation, belonging to the network topological error identification technique of evaluating the condition of electrical system. Said method comprises: detection: checking the correspondence between each branch switch telemetry and branch current measurement, attaining relative suspected switch integration when they are not corresponding; evaluation and identification: using the topological structure corresponded to the suspected switch integration to form a possible correct topological structure integration, utilizing mixed evaluation method to find a network topological structure which can make the remote measurement and telemetry total information be damaged least, as a correct topological from said possible topological structure integration; correcting the switch telemetry: correcting the fault telemetry according to said correct topological structure. The invention can integrated take regard of network topological information of remote measurement and telemetry, to improve the accuracy of topological error identification.

Description

Based on the power network topology error identification method that blendes together state estimation

Technical field

The invention belongs to network topology misidentification (the network topology error identification) technical field in the Power system state estimation (state estimation).

Background technology

EMS (Energy management system is abbreviated as EMS) is based on the dispatch automated system of the modern power systems of computer, its task be to electric power system gather in real time, monitor, analyze, optimization and control decision.Power system state estimation is basis and the core link of EMS, and its utilizes the real-time measurement information gather from electric power system, and debug information estimates complete, the believable electric power system real-time status of making peace, and guarantees the correctness of EMS control decision.

The real-time measurement information that EMS gathers comprises remote measurement and remote signalling two parts, and remote measurement is meant the analog quantity (as: trend, voltage, electric current etc.) of being gathered, and remote signalling is meant the 0-1 digital quantity of being gathered (as: folding condition of switch etc.).The error message that state estimation need be got rid of mainly comprises remote measurement mistake, topological mistake and parameter error three classes, wherein gets rid of the wrong process of topology and is called the network topology misidentification.

Because the switch remote signalling of being gathered mistake occurs through regular meeting; and the disconnecting link state also is difficult to gather complete, causes the network topology mistake thus, can cause state estimation disperse or the result unavailable; be a difficult problem during state estimation is used, also be the focus of Power system state estimation research always.

Up to now, propose many power network topology error identification methods, mainly can be divided into regular method and numerical method two big classes.

The basic principle of rule method is to set up the Expert Rules storehouse, and whether remote signalling by the sense switch place and remote measurement amount corresponding infers correcting errors of topology.Because logic-based is inferred, so this method is simply quick.But because large scale electric network is very complicated and it is frequent to change, be difficult to set up complete and general rule base, the topological mistake of some complexity also is difficult to be described with simple rule, and its effect is restricted.

The basic principle of numerical method is to think that topological mistake can make the state estimation result big residual error occur, therefore at the state estimation result, has designed various identification criterions based on residual error, and topological mistake is carried out identification and correction.This class methods identification accuracy rate is generally higher, but amount of calculation is bigger.

The combination of the practical normally above-mentioned two kinds of methods of power network topology error identification method.One piece of document having delivered (Yu Erkeng work, Power system state estimation, hydraulic and electric engineering publishing house,, 209-212 page or leaf in 1985) has provided a kind of network configuration search discrimination method, and it mainly may further comprise the steps:

Step 1, detection: relatively whether each branch switch remote signalling and branch road trend remote measurement amount be corresponding, if not corresponding, be suspicious remote signalling then, and obtain corresponding suspicious switch set;

Step 2, estimation: the testing result of utilizing step 1, determine possible correct several network topology structures of suspicious switch set correspondence, select a kind of topological structure wherein, this topological structure is carried out state estimation, and calculate the target function value that state estimation is separated

Wherein, Be separate (node voltage is separated) of state estimation, subscript a represents analog quantity:

Step 3, identification: utilize

The result carry out the misidentification of this topological structure, if:

$J\left({\hat{X}}_a\right)<{\mathrm{\&epsiv;}}_J---\left(1\right)$

Then this topological structure is correct, the ε in the formula (1) _JIt is the threshold values of topology error identification; If:

$J\left({\hat{X}}_a\right)<{\mathrm{\&epsiv;}}_J---\left(2\right)$

Show that then topological mistake still exists, select a possible correct topological structure again else, repeating step two and step 3 are estimated and identification, till finding a correct topological structure or several possible topological structure all to be finished, change step 4 over to by identification; If several possible topological structures all this identification still can not satisfy formula (1), then this topology error identification failure;

The correction of step 4, switch remote signalling:, the remote signalling of mistake is revised according to the correct topological structure that picks out in the step 3.

Said method is the combination of regular method and numerical method.Wherein, step 1 is a kind of regular method, can determine possible network topology structure fast, dwindles the hunting zone of follow-up numerical method, improves computational efficiency; Step 2 and three is key links of this method, is a kind of numerical method, is used for determining correct network topology structure.

For many years, the document of research electric power topology error identification method is a lot, but above-mentioned basic step and principal character do not change always, mainly are made up of detection, estimation, identification and four steps of correction.Up to now, in the state estimation step of all topology error identification methods, only utilize remote measurement to do state estimation, fail to take into account the topology information that switch remote signalling amount itself is contained, thereby increased the randomness of remote signalling correction, reduced the accuracy rate of topology error identification.

With the widest weighted least-squares of application surface (WLS) method for estimating state is example, finds the solution the target function value that state estimation is separated

Its Mathematical Modeling of finding the solution is:

$\underset{X_a}{\min }J\left(X_a\right)={[Z_a-H_a\left(X_a\right)]}^T{B}^{-1}[Z_a-H_a\left(X_a\right)]---\left(3\right)$

In the following formula, J is the target function value of state estimation, X _aBe node voltage vector to be estimated, Z _aBe remote measurement vector, H _a(X _a) being the non-linear measurement function of remote measurement, the transposition of subscript T representing matrix, B are the covariance matrixs of telemetry errors.Order Be separating of state estimation formula (3),

It promptly is the target function value that state estimation is separated.As long as one group of quantity of state X to be estimated is arranged _a, just can obtain the calculated value H of one group of remote measurement amount _a(X _a), given remote measurement value Z _aWith its calculated value H _a(X _a) difference be called residual error, promptly the residual error vector is defined as r _a=Z _a-H _a(X _a).Obviously the WLS state estimation promptly is to make the minimized nonlinear optimal problem of remote measurement residual error weighted sum, and it is found the solution is a kind of mature technology.In the Mathematical Modeling that this is found the solution, only considered the contribution of remote measurement, and ignored the amount of information that contains in remote signalling the state estimation target function, reduced the accuracy rate of topology error identification.

Present inventor Sun Hong is refined etc., at " the informatics principle of electric power system minimum information loss state estimation " (Proceedings of the CSEE, 2005, the 25th volume, the 6th phase, 11-16 page or leaf) a kind of more general power system method for estimating state, that is: minimum information loss (MIL have been proposed, Minimum Information Loss) method for estimating state, its substance is described as follows:

The Mathematical Modeling that the MIL method for estimating state is found the solution as state estimation with following information loss minimum:

$\underset{X_a}{\min }{I}_{\mathrm{loss}}\left(X_a\right)---\left(4\right)$

In the formula, I _LossThe overall information loss amount of remote measurement in the expression state estimation procedure.

Suppose the unknown of remote measurement prior information, and the telemetry errors Normal Distribution, then the overall information loss amount in the formula (4) is:

$I_{\mathrm{loss}}\left(X_a\right)=\frac{1}{2}{[Z_a-H_a\left(X_a\right)]}^T{B}^{-1}[Z_a-H_a\left(X_a\right)]---\left(5\right)$

At this moment, MIL state estimation formula (4) is separated together with WLS state estimation formula (3), and the information loss in the formula (5) is the information loss of remote measurement in the state estimation procedure, does not still take into account the loss of remote signalling information.

Summary of the invention

The objective of the invention is to propose a kind of based on the power network topology error identification method that blendes together state estimation (HSE) for overcoming the weak point of prior art.This method is unified Modeling on information space with remote measurement (analog quantity) and remote signalling (0-1 amount), under the optimization aim of minimum information loss (MIL), electric power system remote measurement and remote signalling are implemented to blend together state estimation (HSE), can take all factors into consideration the network topological information that contains in remote measurement and the remote signalling, improve the accuracy rate of topology error identification.

The present invention propose based on the network topology misidentification method that blendes together state estimation (HSE), may further comprise the steps:

Step 1, detection: relatively whether each branch switch remote signalling and branch road trend remote measurement amount be corresponding, if not corresponding, be suspicious remote signalling then, and obtain corresponding suspicious switch set;

Step 2, estimation and identification: form the correct topological structure set of possibility by the topological structure of suspicious switch set correspondence, utilization blendes together state estimation (HSE) method, from the correct topological structure set of this possibility, find a kind of network topology structure of remote measurement and remote signalling overall information loss minimum that makes as correct topological structure;

The correction of step 3, switch remote signalling:, the remote signalling of mistake is revised according to the correct topological structure that picks out in the step 2.

The Mathematical Modeling that blendes together state estimation (HSE) method in the above-mentioned steps two is:

$\underset{(X_a,X_d)}{\min }{I}_{\mathrm{losss}}(X_a,X_d)=I_{a,\mathrm{loss}}(X_a,X_d)+I_{d,\mathrm{loss}}\left(X_d\right)---\left(6\right)$

In the following formula, subscript a and d represent analog quantity and 0-1 amount, X respectively _aAnd X _dBe respectively node voltage vector and on off state vector, I _{A, loss}(X _a, X _d) and I _{D, loss}(X _d) be respectively the information loss amount of remote measurement and remote signalling in the state estimation procedure, calculating formula is respectively:

$I_{a,\mathrm{loss}}(X_a,X_d)=\frac{1}{2}{[Z_a-H_a(X_a,X_d)]}^T{B}^{-1}[Z_a-H_a(X_a,X_d)]---\left(7\right)$

$I_{d,\mathrm{loss}}\left(X_d\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{dk}}-A_k^T{X}_d)}^2\&CenterDot;\ln \left(\frac{p_k}{1-p_k}\right)---\left(8\right)$

In the formula (8), K is the number of switch remote signalling; z _DkRepresent k remote signalling value; A _k ^TX _dBe the measurement function of k remote signalling amount, A _kBe the incidence vector between k remote signalling and the switch, when k remote signalling collection is X _dDuring j on off state, A _kIn j element be 1, other element is 0; p _kIt is the accuracy of k remote signalling; X _dIn each element and z _DkValue be 0 or 1, represent that respectively switch is for leaving or closing.

Principle of the present invention

Power system state estimation belongs to the point estimation that classical statistics is inferred one of three kinds of citation forms, it is an information decision process judging the electric power system time of day according to the real time data that observes, estimated result should approach the best estimate of the real-time time of day of electric power system most, according to minimum information loss (MIL) State Estimation Theory, should make that the total information loss that measures is minimum, except the information loss that should comprise remote measurement, also should comprise the information loss of remote signalling.

But remote measurement and remote signalling belong to data of different nature, and the former is an analog quantity, and the latter is the 0-1 amount, is difficult to directly set up comprehensive estimation model.The present invention projects to both on the information loss space, has adopted unified measure information, has satisfied mathematical additive property, has realized the state estimation that blendes together of remote measurement (continuous quantity) and remote signalling (0-1 amount), is the Mathematical Modeling shown in the formula (6).

The present invention has scientifically quantized the information loss of remote measurement (continuous quantity) and remote signalling (0-1 amount), on the basis of the information loss calculating formula (5) of existing remote measurement, by the expansion switch state, draw formula (7), and draw the information loss calculating formula (8) of remote signalling through derivation.

In order to illustrate principle, below the information loss calculating formula (8) of remote signalling is simply derived.

Electric power system K dimension remote signalling vector can be considered to the memoryless multiple source symmetry of a binary system correlated channels model, as shown in Figure 1.

In Fig. 1, the input and output vector of channel is respectively V _d=[v _D1, v _D2..., v _DK] ^T, Z _d=[z _D1, z _D2..., z _DK] ^T, input V _dExpression on off state true value, output Z _dExpression switch remote signalling value subscript d represents remote signalling, and 0,1 represents that respectively switch is for leaving and close, P _EiRepresent e _iThe probability that takes place, and have $\stackrel{U}{\mathrm{\&Sigma;}}{p}_{e_i}=1$ U＝2 ^K。Wherein, e _i(i=1 ..., U) the information source set that expresses possibility output error takes place, concrete implication is explained as follows.

Structure information source S set={ v _D1, v _D2..., v _DKPower set:

E＝{φ，{v _d1}，{v _d2}，…，{v _dK}，{v _d1，v _d2}，

{v _d1，v _d3}，…，{v _d1，v _d2，…，v _dK}}

Then each element is expressed as e corresponding to the information source combination that output error may take place among the power set E _iFor example: e ₃={ v _D2Have only the output error of the 2nd information source component correspondence in K information source of expression, other outputs are correctly.

Then the forward direction transition probability matrix Q of channel is following symmetrical matrix:

The channel model Q that following formula provides is equivalent to following probability-distribution function: P _Cd(V _d, Z _d)

$=\underset{i=1}{\overset{U}{\mathrm{\&Pi;}}}{p_{e_i}}^{\underset{k=1,v_{\mathrm{dk}}\&Element;e_i}{\overset{k}{\mathrm{\&Pi;}}}{(z_{\mathrm{dk}}-v_{\mathrm{dk}})}^2\underset{k=1,v_{\mathrm{dk}}\&Element;e_i}{\overset{k}{\mathrm{\&Pi;}}}[1-{(z_{\mathrm{dk}}-v_{\mathrm{dk}})}^2]}---\left(10\right)$

In the following formula, P _CdBe the probability-distribution function of channel, subscript C represents channel, z _DkAnd v _DkAll be the 0-1 amount, v _Dk∈ e _iWith $v_{\mathrm{dk}}\&NotElement;e_i$ Represent whether k information source is present in the set e that makes mistakes _iIn.Still with e _i={ v _D2Be example, this moment v _D2∈ e ₃, and ${\mathrm{<figure-callout\; id="1"\; label="v\; d"\; filenames="A20051009298400122.png"\; state="\{\{state\}\}">v</figure-callout>}}_d\&NotElement;e_3.$

According to information theory, to the channel model of higher-dimension discrete random variable, if known channel is output as Z _d, what obtained is V about the information source value _dChannel information loss amount calculating formula can be:

$I_{d.\mathrm{loss}}(V_d;Z_d)=\ln \frac{P_{\mathrm{Cd}}(Z_d,Z_d)}{P_{\mathrm{Cd}}(V_d,Z_d)}---\left(11\right)$

Can get by following formula, from switch remote signalling value Z _dJudge that the on off state true value is V _dInformation loss be:

$I_{d,\mathrm{loss}}=(V_d;Z_d)=\ln p_{e_1}-\underset{i=1}{\overset{U}{\mathrm{\&Sigma;}}}\{\underset{k=1,v_{\mathrm{dk}}\&Element;e_i}{\overset{k}{\mathrm{\&Pi;}}}{(z_{\mathrm{dk}}-v_{\mathrm{dk}})}^2\underset{k=1,v_{\mathrm{dk}}\&Element;e_i}{\overset{k}{\mathrm{\&Pi;}}}{[1-(z_{\mathrm{dk}}-v_{\mathrm{dk}})}^2\&CenterDot;]\&CenterDot;\ln p_{e_i}\}---\left(12\right)$

For the ease of calculating, usually K remote signalling channel of supposition is separate, then the channel model decoupling zero of Fig. 1 be by K the memoryless single information source symmetric channel of independent binary system forms also use channel model, Fig. 2 to provide this and with the channel model of k remote signalling in the channel, wherein p _kThe accuracy of representing k remote signalling.

By formula (12), the information loss calculating formula of remote signalling is reduced to:

$I_{d,\mathrm{loss}}(V_d;Z_d)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{dk}}-v_{\mathrm{dk}})}^2\ln \left(\frac{p_k}{1-p_k}\right)---\left(13\right)$

A _kRepresent the incidence vector between the 7th remote signalling and the switch, when k remote signalling collection is X _dDuring j on off state, A _kIn j element be 1, other element is 0, then has $v_{\mathrm{dk}}=A_k^T{X}_d,$ Formula (13) can be expressed as:

$I_{d,\mathrm{losss}}\left(X_d\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{dk}}-A_k^T{X}_d)}^2\&CenterDot;\ln \left(\frac{p_k}{1-p_k}\right)---\left(14\right)$

Formula (14) is formula (8), and the derivation of equation is finished.

Technical characterstic of the present invention and effect

Topology error identification method of the present invention is a kind of based on the topology error identification method that blendes together state estimation (HSE, Hybrid stateestimation).The innovative point of this method mainly is to have proposed a kind of new method for estimating state, i.e. HSE method, and it is applied to the core procedure of topology error identification, i.e. step 2 (estimating and identification).The HSE method has not only been taken into account the network topological information that contains in the remote signalling, and quantity of state that will be to be estimated expands, and not only comprises node voltage vector X in the quantity of state _a, also comprised on off state vector X _dTherefore, blend together state estimation formula (6), can solve simultaneously by finding the solution With Correct network topology structure is

Obviously, this new method for estimating state blendes together remote measurement (analog quantity) and remote signalling (0-1 amount) together, estimate the node voltage (analog quantity) and the on off state (0-1 amount) of electric power system synchronously, so the present invention is referred to as to blend together state estimation (HSE) method.

Method and existing methods that the present invention adopts are significantly distinguished: (1) is in core procedure of the present invention (being step 2), adopted and blended together state estimation (HSE) method and replace existing method for estimating state to carry out topology wrong estimation and identification, taken all factors into consideration the network topological information that contains in remote measurement and the remote signalling, the information of utilizing is more abundant, can improve the accuracy rate of topology error identification.(2) blend together state estimation (HSE) method and can estimate the node voltage of electric power system and correct network topology structure synchronously, therefore, step 3 (estimation) and step 4 (identification) that method of the present invention will have now in the topology error identification method integrate, and are step 2 of the present invention.

Description of drawings

The memoryless multiple source symmetry of the binary system correlated channels model that Fig. 1 adopts for remote signalling among the present invention.

Fig. 2 is k memoryless single information source symmetric channel model of binary system that remote signalling is adopted among the present invention.

Fig. 3 is the performing step block diagram based on the power network topology error identification method that blendes together state estimation of the present invention.

The little example system schematic that Fig. 4 proposes for the present invention based on the power network topology error identification method that blendes together state estimation.

Embodiment

The power network topology error identification method based on blending together state estimation that the present invention proposes reaches embodiment in conjunction with the accompanying drawings

Be described in detail as follows:

Method of the present invention may further comprise the steps as shown in Figure 3:

Step 1, detection: relatively whether each branch switch remote signalling and branch road trend remote measurement amount be corresponding, if not corresponding, be suspicious remote signalling then, and obtain corresponding suspicious switch set.

A kind of specific embodiment of above-mentioned steps is as follows:

The remote signalling that utilizes EMS to gather, folding condition according to switch, at first carry out a power network topology analysis (a kind of network analysis technique of maturation), in order to determine that each bar branch road (comprising: branch roads such as transmission line, transformer, generator, load) whether be in the state of putting into operation in the electrical network.Then, relatively whether the state that puts into operation of each branch road is corresponding with its trend remote measurement amount, if not corresponding, then is judged to be suspicious branch road, and the primitive rule of judgement mainly contains two: (1) is not if branch road puts into operation, and the branch road trend is non-vanishing, then is suspicious branch road; (2) if branch road puts into operation, and the branch road trend is zero, then is suspicious branch road.At last, search for, find the suspicious switch remote signalling that makes on this branch road, obtain suspicious switch set along suspicious branch road.

For the ease of understanding, below provide the implementation process that a little example of principle illustrates this step, the example mini system is as shown in Figure 4.LN represents circuit among the figure, and CB1, CB2 represent two end switch of circuit, and switch is filled expression switch remote signalling closure.Its switch remote signalling vector is Z _d=[z _CB1, z _CB2] ^T=[1,0] ^T, 0,1 represent that respectively switch is for leaving and close, the meritorious trend remote measurement z at circuit two ends _P1, z _P2Be marked on the arrow top at circuit two ends, the direction of the direction indication trend of arrow, then the remote measurement vector is Z _a=[z _P1, z _P2] ^T=[0.30,0.28] ^TBecause circuit remote signalling z _CB2For opening, by the power network topology analysis, can determine that this circuit is in the state of not putting into operation, and the remote measurement of circuit trend is non-vanishing, therefore, this circuit is suspicious branch road, z _CB1And z _CB2Be suspicious switch remote signalling, CB1 and CB2 form suspicious switch collection.

Step 2, estimation and identification: form the correct topological structure set of possibility by the topological structure of suspicious switch set correspondence, utilization blendes together state estimation (HSE) method, from the correct topological structure set of this possibility, find a kind of network topology structure of remote measurement and remote signalling overall information loss minimum that makes as correct topological structure.

In above-mentioned steps, need find the solution by blending together the state estimation Mathematical Modeling shown in the formula (6), this Mathematical Modeling belongs to typical mixed integer programming problem, and multiple solution can be arranged, so the embodiment of above-mentioned steps can have multiple.The present invention proposes a kind of specific embodiment of above-mentioned steps, be subdivided into following 3 sub-steps:

1) the determined suspicious switch collection of step 1 is carried out permutation and combination, determine the topological structure set that possibility is correct $\left\{X_d^m\right|m=1,...,M\},$ M is the correct total number of topological structure of possible, and subscript m represents m the topological structure that possibility is correct.

2) m is from 1 to M, the topological structure set that scanning may be correct $\left\{X_d^m\right|m=1,...,M\},$ Therefrom determine a kind of topological structure X _d ^mOrder $X_d=X_d^m,$ Blend together state estimation, ask overall information loss amount (information loss that comprises remote measurement and remote signalling).At this moment since network topology structure determined, also be $X_d=X_d^m$ Given, therefore, the HSE Mathematical Modeling that is provided by formula (6) deteriorates to:

$\underset{X_a}{\min }{i}_{\mathrm{loss}}(X_a,X_d^m)=\frac{1}{2}{[Z_a-H_a(X_a,X_d^m)]}^T{B}^{-1}[Z_a-H_a(X_a,X_d^m)]---\left(15\right)$

Because X _d ^mGiven, be constant.Therefore the solution of the solution of the state estimation shown in the formula (15) and conventional WLS state estimation formula (3) is identical, belongs to mature technology, does not repeat them here.If the estimation of formula (15) is separated try to achieve, be expressed as X _a ^mWith quantity of state X _a ^mAnd X _d ^mSubstitution formula (6), (7), (8) can get overall information loss amount I at this moment _Loss(X _a ^m, X _d ^m) calculating formula of (comprising remote measurement and remote signalling) is:

$I_{\mathrm{losss}}(X_a^m,X_d^m)=\frac{1}{2}{[Z_a-H_a(X_a^m,X_d^m)]}^T{B}^{-1}[Z_a-H_a(X_a^m,X_d^m)]+\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{dk}}-A_k^T{X}_d^m)}^2\&CenterDot;\ln \left(\frac{p_k}{1-p_k}\right)---\left(16\right)$

4) topological structure set that may be correct $\left\{X_d^m\right|m=1,...,M\}$ In compare, find overall information loss amount I _Loss(X _a ^m, X _d ^m) minimum network topology state separates

Be the correct network topology structure that finally picks out.

The implementation process of this step is described at the little example of principle shown in Figure 4 equally.For the purpose of simplifying the description, ignore the line power loss, then the state variable of analog quantity is X _a=[x ₁], x wherein ₁The meritorious trend of table circuit.The state variable of 0-1 amount is X _d=[x ₂, x ₃] ^T, x wherein ₂, x ₃The on off state of representing CB1 and CB2 respectively.Remote measurement Z _aThe measurement function be H _a(X _a, X _d)=[x ₁x ₂x ₃, x ₁x ₂x ₃] ^TParameter setting: $B=\left[\begin{array}{cc}0.01& 0\\ 0& 0.01\end{array}\right],$ Two switch remote signalling z _CB1And z _B2Accuracy all be made as P _k=0.999.The determined suspicious switch collection of step 1 is carried out permutation and combination, determine the correct topological structure set of possibility as table 1, the total number M of topological structure=4 that may be correct, the m in the table is a sequence number.The topological structure set that table 1 possibility is correct

m	x 2	x 3
			1 2 3 4	0 0 1 1	0 1 0 1

Possible correct topological structure set shown in the scan table 1 blendes together state estimation and finds the solution, and with above-mentioned given data substitution formula (6), (7) and formula (8), the Mathematical Modeling that gets HSE is:

$\begin{array}{c}\underset{(x_1,x_2,x_3)}{\min }{I}_{\mathrm{loss}}(x_1,x_2,x_3)=50{(z_{P1}-x_1\&CenterDot;x_2\&CenterDot;x_3)}^2+50(z_{P2}-x_1\&CenterDot;x_2\&CenterDot;x_3)2^{}\\ +6.907{(z_{\mathrm{CB}1}-x_2)}^2+6.907{(z_{\mathrm{CB}2}-x_3)}^2\end{array}$

By formula (15) and (16), can see Table 2 corresponding to the separating and the overall information loss amount of the HSE of table 1.By table 2, can find the network topology state of overall information loss amount minimum to separate to be: x ₂=1 and x ₃=1, this is the correct network topology structure that finally picks out.

Table 2 is separated and the overall information loss amount corresponding to the HSE's of table 1

m	x 1	x 2	x 3	I loss
					1 2 3 4	0 0 0 0.29	0 0 1 1	0 1 0 1	15.327 22.234 8.420 6.917

The correction of step 3, switch remote signalling:, the remote signalling of mistake is revised according to the correct topological structure that picks out in the step 2.

The implementation process of this step is described at the little example of principle shown in Figure 4 equally.Having picked out correct network topology structure by step 2 is x ₂=1 and x ₃=1, mistake has appearred in the remote signalling of CB2 as can be known, promptly the remote signalling state of CB2 is revised: close by opening to change into.

Claims (2)

1, a kind ofly it is characterized in that based on the power network topology error identification method that blendes together state estimation this method may further comprise the steps:

Step 1, detection: relatively whether each branch switch remote signalling and branch road trend remote measurement amount be corresponding, if not corresponding, be suspicious remote signalling then, and obtain corresponding suspicious switch set;

Step 2, estimation and identification: form the correct topological structure set of possibility by the topological structure of suspicious switch set correspondence, utilization blendes together method for estimating state, from the correct topological structure set of this possibility, find a kind of network topology structure of remote measurement and remote signalling overall information loss minimum that makes as correct topological structure;

The correction of step 3, switch remote signalling:, the remote signalling of mistake is revised according to the correct topological structure that picks out in the step 2.

The Mathematical Modeling that blendes together method for estimating state in the above-mentioned steps two is:

$\underset{(X_a,X_d)}{\min }{I}_{\mathrm{loss}}(X_a,X_d)=I_{a,\mathrm{loss}}(X_a,X_d)+I_{d,\mathrm{loss}}\left(X_d\right)$

In the following formula, subscript a and d represent analog quantity and 0-1 amount, X respectively _aAnd X _dBe respectively node voltage vector and on off state vector, I _{A, loss}(X _a, X _d) and I _{D, loss}(X _d) be respectively the information loss amount of remote measurement and remote signalling in the state estimation procedure, calculating formula is respectively:

$I_{a,\mathrm{loss}}(X_a,X_d)=\frac{1}{2}{[Z_a-H_a(X_a,X_d)]}^T{B}^{-1}[Z_a-H_a(X_a,X_d)]$

$I_{d,\mathrm{loss}}\left(X_d\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{dk}}-A_k^T{X}_d)}^2\&CenterDot;\ln \left(\frac{p_k}{1-p_k}\right)$

In the formula, K is the number of switch remote signalling; z _DkRepresent k remote signalling value; A _k ^TX _dBe the measurement function of k remote signalling amount, A _kBe the incidence vector between k remote signalling and the switch, when k remote signalling collection is X _dDuring j on off state, A _kIn j element be 1, other element is 0; p _kIt is the accuracy of k remote signalling; x _d, in each element and z _DkValue be 0 or 1, represent that respectively switch is for leaving or closing.

2, power network topology error identification method as claimed in claim 1 is characterized in that, described step 2 specifically comprises:

1) the determined suspicious switch collection of step 1 is carried out permutation and combination, determine the topological structure set that possibility is correct $\left\{X_d^m\right|m=1,\&CenterDot;\&CenterDot;\&CenterDot;,M\}$ , M is the correct total number of topological structure of possible, subscript m represents m the topological structure that possibility is correct;

2) m is from 1 to M, the topological structure set that scanning may be correct $\left\{X_d^m\right|m=1,\&CenterDot;\&CenterDot;\&CenterDot;,M\}$ , therefrom determine a kind of topological structure X _d ^mOrder $X_d=X_d^m$ , blend together state estimation, ask the overall information loss amount:

$\underset{X_a}{\min }{I}_{\mathrm{loss}}(X_a,X_d^m)=\frac{1}{2}{[Z_a-H_a(X_a,X_d^m)]}^T{B}^{-1}[Z_a-H_a(X_a,X_d^m)]$

X in the formula _d ^mBe given constant, the estimation in the formula is separated and is X _a ^m, can comprise the overall information loss amount I of remote measurement and remote signalling _Loss(X _a ^m, X _d ^m) calculating formula be:

$I_{\mathrm{loss}}(X_a^m,X_d^m)=\frac{1}{2}{[Z_a-H_a(X_a^m,X_d^m)]}^T{B}^{-1}[Z_a-H_a(X_a^m,X_d^m)]+\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{(z_{\mathrm{ak}}-A_k^T{X}_d^m)}^2\&CenterDot;\ln \left(\frac{p_k}{1-p_k}\right)$

3) gather at topological structure that may be correct $\left\{X_d^m\right|m=1,\&CenterDot;\&CenterDot;\&CenterDot;,M\}$ In compare, find overall information loss amount I _Loss(X _a ^m, X _d ^m) minimum network topology state separates

Be the correct network topology structure that finally picks out.

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