CN102738794A - Seidel-type recursion bayesian method and application thereof to state estimation - Google Patents

Abstract

The invention discloses a Seidel-type recursion bayesian method and application thereof to the state estimation. According to the invention, the recursive estimation calculation of posterior probabilities of different modes is implemented by extracting characteristic quantities of different modes; and in the recursive calculation, the Seidel-type recursion bayesian method utilizes the posterior probabilities just obtained in the recursion to replace prior probabilities to implement the calculation of the posterior probabilities. The method can be used for rapidly and accurately carrying out mode identification and has strong robustness for noise. A power grid topology error identification method or a transformation tapping point position estimation method on the basis of the Seidel-type recursion bayesian method can be used for rapidly and accurately obtaining a correct power grid operation mode or a correct transformer tapping point position, so that the qualified rate of the state estimation can be greatly improved and the practicality of an integral energy management system is further promoted.

Description

A kind of Saden that formula recursion bayes method and the application in state estimation thereof

Technical field

The present invention relates to a kind of Saden that formula recursion bayes method and the application in Power system state estimation thereof, belong to power system analysis and control field.

Background technology

Along with the development of intelligent grid, to EMS (Energy Management System, EMS) reliability of analysis decision and required precision are increasingly high, the further practicability of EMS becomes the focus that people pay close attention to.(State Estimation SE) is basis and the core of EMS, for the advanced applied software in the EMS system provides the real time data source to Power system state estimation.The factor that influences the state estimation qualification rate comprises bad data, topological mistake and parameter error.At present, the research of academia and the identification of engineering bound pair bad data and application are more relatively, and be then less to the research and the application of topology error identification and parameter Estimation.And the accuracy of the correctness of topological structure and parameter (particularly load tap changer position) is the key factor of Guarantee Status computed reliability and precision.Therefore, how to guarantee that the accuracy of correctness and the network parameter (particularly load tap changer position) of topological structure becomes the prerequisite of EMS application software reliability services such as state estimation, stability analysis, safety check.

Existing topology error identification method mainly comprises residual error method, the augmented state estimation technique, regular method, minimum information loss method, new breath figure method, shifts trend method etc.The standardized residual that surpasses threshold value that the residual error method obtains state estimation is owing to the relevant topology mistake, but bad data also can cause standardized residual to be crossed the border, and when topology is wrong when coexisting with bad data, the identification capability of residual error method is limited.The augmented state estimation technique with the voltage amplitude value difference at the trend of suspicious branch road, branch road two ends and phase angle difference as the augmented state variable; Estimate simultaneously with the voltage magnitude and the phase angle of other computing nodes; But the part that this method needs measures the redundancy height, and is prone to produce the numerical value instability problem.The rule method is come identification topology mistake through setting up cover logic rules, can handle some simple topological mistakes, but when the mode of connection more complicated of electrical network, and the formulation of rule that is adapted to various operational modes is cumbersome.The minimum information loss method is converted into a mixed integer programming problem with the topology error identification problem, is that topology error identification provides new thinking from information-theoretical angle, but the modeling more complicated of this method, and the difficulty of application is bigger.New breath figure method is the wrong and simultaneous situation of bad data of identification topology fast, but the identification when taking place simultaneously for the topological mistake of branch road and a plurality of bad data also has difficulties.Can effectively pick out branch road topology mistake and the simultaneous situation of a plurality of bad data though shift the trend method, the precondition of this method is that a last time section state results estimated is right-on, supposes too harsh.For precision and the qualification rate that improves state estimation, the topology error identification method of research practicability becomes the task of top priority.

The accuracy of parameter also is the key factor of Guarantee Status computed reliability and precision.In all parameters, because transformer voltage ratio occurs with quadratic term in the calculating of reactive power flow, its error is the most remarkable to state estimation result's influence, therefore, estimates that accurately the load tap changer position is the important prerequisite that realizes reliable state estimation.Up to now, the method for estimation to the load tap changer position mainly comprises the augmented state estimation technique, residual error method, tap position Tracking Estimation method and perturbation method etc.The augmented state estimation technique as the augmented state variable, is estimated transformer voltage ratio with node voltage amplitude and phase angle jointly.This method is simple, but it is higher to require to measure redundancy, and is prone to the numerical value instability problem.The residual error method utilizes the sensitivity relation between residual error and ratio error to estimate the tram of tap, but receives the influence that residual error is polluted and residual error is flooded easily.Tap Tracking Estimation method is regarded tap joint position as a Markov Chain over time; Utilizing markovian state transition probability to carry out tap joint position estimates; This method has certain robustness to measurement noise; But the precision that tap position is estimated depends on state transition probability; And currently also do not have reliable method to confirm rational state transition probability, and test shows that this method only can obtain the estimation of tap joint position as a rule with little probability, its result's confidence level still can not be satisfactory.The perturbation ratio juris is that suspicious transformer is all carried out one time state estimation under all tap joint position, and the pairing tap joint position of least residual promptly is considered to correct tap joint position.Because the existence of measurement noise and receive residual error to pollute the influence of flooding with residual error, when the tap joint position error hour, perturbation method possibly obtain the estimation of mistake.In recent years scholar's research has been arranged and utilized the PMU data to carry out the method for estimation of tap joint position, but needed transformer branch road two ends all will have PMU to measure., measure under the less situation of layouting at current PMU, research to obtain correct load tap changer position accurately and rapidly, has important and practical meanings based on the method for estimation of RTU data for this reason.

Integrate consideration, topology error identification is in possible power network topology pattern, to find unique correct topological mode; And the load tap changer location estimation is from a plurality of definite tap joint position, to select a correct position.From the angle of statistical learning, topology error identification and load tap changer location estimation all belong to the category of pattern recognition.So-called pattern recognition is characteristic or attribute according to research object, and through constructing certain system, utilization certain analysis method is judged the classification of sample, and system should make the result of sample classification identification meet the fact as much as possible.At present, pattern recognition theory and technology successfully apply to a plurality of fields such as industry, agricultural, biology, scientific research, and this field is also in continuous expansion.A very important link in the pattern recognition is feature extraction and feature selecting; Its role is to extract and select to lie in fixing, essence and important characteristic or attribute in the sample data; Thereby produce the pattern that to represent a certain special object; Get final product the learning of structure system on this basis, and accomplish Classification and Identification.To different objects and different purpose, can select different mode identification methods.In these methods, Bayesian Estimation (grader) combines prior information and sample information, can fine sample be discerned, thereby is a kind of outstanding mode identification method, has obtained increasingly extensive application.

When utilization Bayesian Estimation when carrying out topology error identification and load tap changer location estimation, choose suitable feature or attribute is most important.Because it is under different patterns, to obtain state estimation residual error difference that a kind of topological structure of electric is different from the characteristic feature of another kind of topological structure of electric, so can the state estimation residual error under the different topological structure of electric be carried out the characteristic quantity of topology error identification as the utilization Bayesian Estimation; Equally; The difference of load tap changer position and the characteristic feature of another tap joint position are that the state estimation residual error that under different tap joint position, obtains is different, therefore can be with the state estimation residual error under the different tap joint position as using Bayesian Estimation carry out the characteristic quantity of load tap changer location estimation.In Bayesian Estimation, the preferred features amount when becoming power network topology misidentification and load tap changer location estimation by the formed likelihood function of residual error.In order to increase ornamental, when carrying out power network topology misidentification or load tap changer location estimation, can introduce pseudo-the measurement and virtual measurement with Bayesian Estimation, they constitute the measurement vector together with actual measurements.Move a plurality of state estimation by measuring vector with different topological structure of electric or load tap changer position, can obtain the residual error under different topological structure of electric or the different load tap changers position, and then can obtain corresponding likelihood function numerical value.Owing to contain noise inevitably in the metric data; Therefore the corresponding likelihood function numerical value of topological structure of electric or correct load tap changer position can not become to reflect topological structure of electric and correct tap joint position strictly according to the facts, and the result of single Bayesian Estimation is always not reliable.

In order to eliminate the influence of measurement noise, can adopt the recursion Bayesian Estimation to estimated result.In each step of recursion Bayesian Estimation; All need to obtain the residual error under different topological structure of electric or the load tap changer position in a plurality of state estimation of operation under different topological structure of electric or the load tap changer position, and then obtain likelihood function numerical value according to measuring vector; In different recursion steps, substantial amount is measured constant, and pseudo-measurement is all different with virtual measurement.In the recursion, the different topological structure of electric that last recursion is obtained or the posterior probability of different load tap changers position can realize that as the prior probability of this recursion the recursion of posterior probability is calculated.Suppose according to Bayes; Initial distribution does not influence final posterior probability values; So can all topological structure of electric when recursion first or the posterior probability of load tap changer position be set to even distribution; Calculate through recursion, correct topological structure of electric or the pairing posterior probability in load tap changer position can progressively level off to 1, and the posterior probability of other topological structure of electric or load tap changer position then can progressively level off to 0.Thus, can obtain correct topological structure of electric or load tap changer position.

Based on above thought; The foreign scholar has proposed the power network topology misidentification method based on the recursion Bayesian Estimation; Domestic scholars has then proposed the load tap changer location estimation method based on the recursion Bayesian Estimation, can estimate correct topological structure of electric or correct load tap changer position.But in these methods; In ought recursion last time all be on once recursion obtain different topological structure of electric or load tap changer position posterior probability as prior probability; And the posterior probability that in recursion last time, has obtained is not used in this recursion, and they are up to just used in the recursion next time, and theory analysis all shows with test; Adopt the recursion Bayesian Estimation of this mode to calculate, its efficient and robustness all can not be satisfactory.Adopt more rational recursion Bayesian Estimation method; To estimate the tram of correct topological structure of electric or load tap changer fast, accurately, robust; For the precision and the qualification rate that improve state estimation, thereby promote the practicability of whole EMS system to have great importance.

Summary of the invention

It is high to the purpose of this invention is to provide a kind of computational efficiency, and noise is had the Saden that formula recursion bayes method of very strong robustness.

To achieve these goals, technical scheme of the present invention is: a kind of Saden that formula recursion bayes method is provided, and wherein, you formula recursion Bayesian Estimation method carry out this Saden according to the following steps:

Step (1) initialization

Make the initial probability of all patterns to be identified all equate, even p is (η ₁| ε ⁽⁰⁾)=p (η ₂| ε ⁽⁰⁾)=L=p (η _N| ε ⁽⁰⁾)=1/N, wherein η _iBe i pattern, ε ⁽⁰⁾Be the initial characteristics amount, p (η _i| ε ⁽⁰⁾) be η _iInitial probability, N is the total number of pattern; Recursion counter k=1 is set;

Step (2) recursion is calculated to obtain correct pattern

Step (2.1) judges that the maximum of the posterior probability that all patterns are corresponding whether less than threshold value, promptly judges max{p (η _i| ε ^(k-1)Whether }＜threshold sets up (threshold is a threshold value), is then to change step (2.2); Otherwise change step (3);

Step (2.2) is extracted and is obtained the pairing characteristic quantity of all patterns;

Step (2.3) utilizes following formula to calculate the posterior probability of all patterns;

$\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})=\frac{p\left(e_i^{\left(k\right)}\right|{\mathrm{\&eta;}}_i)p\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{(k-1)})}{\underset{j<i}{\mathrm{\&Sigma;}}p\left(e_j^{\left(k\right)}\right|{\mathrm{\&eta;}}_j)\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})+\underset{j\&GreaterEqual;i}{\mathrm{\&Sigma;}}p\left(e_j^{\left(k\right)}\right|{\mathrm{\&eta;}}_j)p\left({\mathrm{\&eta;}}_j\right|{\mathrm{\&epsiv;}}^{(k-1)})}$

Wherein,

Be the pairing characteristic quantity of all N pattern, i.e. residual error vector;

Pattern η when being the k time recursion _iPosterior probability, p (η _i| ε ^(k-1)) be prior probability;

Be pattern η in the k time recursion _iThe conditional probability of corresponding residual error, i.e. likelihood function numerical value;

Step (2.4) is utilized following formula that the posterior probability of all patterns is carried out normalization and is calculated;

$p\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})=\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})/{\mathrm{\&Sigma;}}_{j=1}^N\hat{p}\left({\mathrm{\&eta;}}_j\right|{\mathrm{\&epsiv;}}^{\left(k\right)})$

Wherein, p (η _i| ε ^(k)) pattern η when being the k time recursion _iThe normalization posterior probability values.

Step (2.5) makes k=k+1, changes step (2.1);

The maximum pattern of step (3) posterior probability is correct pattern.

More than be the calculation procedure of your formula recursion bayes method of Saden, this method has general adaptability for the pattern recognition that all contain uncertain measurement amount.Compare with basic recursion bayes method, your formula recursion bayes method of Saden has in time used the posterior probability of the pattern that has just obtained in each step of recursion, and research shows that the recognition efficiency of such recursion mode is higher, and robustness is better.

Another object of the present invention is to provide the application of Saden that formula recursion bayes method in state estimation, when carrying out power network topology misidentification or load tap changer location estimation with your formula recursion bayes method of Saden, its concrete calculation procedure is following:

Step (1) initialization

Form all possible power network topology pattern or all possible load tap changer position; Make the initial probability of all power network topology patterns to be identified or all tap joint position of transformer all equate; Even

wherein is the initial probability of i power network topology pattern or load tap changer position, N is the total number of power network topology pattern or load tap changer position; Recursion counter k=1 is set;

Step (2) recursion is calculated to obtain correct power network topology pattern or load tap changer position

Step (2.1) judges that whether the maximum of the pairing posterior probability of all power network topology patterns or load tap changer position is less than threshold value; Judging promptly whether

(threshold is a threshold value) sets up, is then to change step (2.2); Otherwise change step (3);

Step (2.2) input actual measurements, virtual measurement and pseudo-the measurement, these measurement amounts form measurement equation and do

z＝h(x)+τ

Wherein, z ∈ R ^mBe the measurement vector, comprise that node injects meritorious measurement, node injects idle measurement, the meritorious measurement of branch road, the idle measurement of branch road and node voltage and measures; These measurement amounts are generally got substantial amount and are measured, if substantial amount is measured disappearance, then replace with pseudo-the measurement, and the superpose random number of 10% normal distribution of the result that pseudo-measurement is employed in last state estimation is come pattern; In measuring vector, should add 0 simultaneously and inject virtual measurement; X ∈ R ⁿIt is the state variable that comprises node voltage amplitude and phase angle; H (x) is the Nonlinear Mapping of state vector to the measurement vector; τ～N (0, R) be error in measurement;

Be the error in measurement variance matrix.

According to above measurement equation; Carry out iteration through following update equation; Up to the state estimation convergence, can obtain state vector estimated value

x _k+1＝x _k+G(x _k)H ^T(x _k)R ^-1(z-h(x _k))

Wherein,

Be Jacobian matrix, G (x _k)=(H ^T(x _k) R ^-1H (x _k)) ^-1

According to following formula, the independent respectively residual error vector

that calculates under all power network topology patterns or the load tap changer position

$e_i^{\left(k\right)}=z-h\left(\hat{x}\right)$

According to following formula, the independent respectively error variance Matrix C of calculating under all power network topology patterns or the load tap changer position _{F, i}(i=1,2, L, N)

$C_{f,i}^{-1}=\mathrm{diag}({\mathrm{\&sigma;}}_v^2,{\mathrm{\&sigma;}}_{p_i}^2,{\mathrm{\&sigma;}}_{q_i}^2,{\mathrm{\&sigma;}}_{p_b}^2,{\mathrm{\&sigma;}}_{q_b}^2)$

C _{F, i}(i=1,2, L, in N)

From [H ^TR ^-1H] ^-1The respective items of diagonal element obtains, C _{F, i}(i=1,2, L, in N)

Each item can be from matrix H [H ^TR ^-1H] ^-1H ^TThe respective items of diagonal element obtains.

When carrying out the power network topology misidentification, more than the state estimation of being carried out be the whole network state estimation; And when carrying out the load tap changer location estimation, the state estimation of more than carrying out be the transformer branch road and near the local state of branch road estimate.

Step (2.3) utilizes following formula to calculate all topological structure of electric or the pairing posterior probability of tap joint position;

${\hat{p}}_i^{\left(k\right)}=\frac{\exp (-{\left(e_i^{\left(k\right)}\right)}^T{C}_{f,i}{e}_i^{\left(k\right)}/2)p_i^{(k-1)}}{\underset{j<i}{\mathrm{\&Sigma;}}\exp (-{\left(e_j^{\left(k\right)}\right)}^T{C}_{f,j}{e}_j^{\left(k\right)}/2){\hat{p}}_j^{\left(k\right)}+\underset{j\&GreaterEqual;i}{\mathrm{\&Sigma;}}\exp (-{\left(e_j^{\left(k\right)}\right)}^T{C}_{f,j}{e}_j^{\left(k\right)}/2)p_j^{(k-1)}}$

Wherein, be the pairing characteristic quantity of pattern i, i.e. residual error vector when being the k time recursion;

posterior probability of pattern i when being the k time recursion, is prior probability; is the conditional probability of the corresponding residual error of pattern i in the k time recursion, i.e. likelihood function numerical value;

Step (2.4) is utilized following formula that the posterior probability of all patterns is carried out normalization and is calculated;

$p_i^{\left(k\right)}={\hat{p}}_i^{\left(k\right)}/{\mathrm{\&Sigma;}}_{j=1}^N{\hat{p}}_j^{\left(k\right)}$

Wherein, the normalization posterior probability values of pattern i during

the k time recursion.

Step (2.5) makes k=k+1, changes step (2.1);

The maximum pattern of step (3) posterior probability is correct power network topology pattern or load tap changer position.

The Saden that formula recursion bayes method that the present invention proposes belongs to a kind of new mode identification method.Compare with existing recursion bayes method, your computational efficiency of formula recursion bayes method of Saden is high, and noise is had very strong robustness.Your formula recursion bayes method of Saden has in electric power system widely to be used, and can obtain correct topological structure of electric or correct load tap changer position accurately and fast based on your formula recursion bayes method of Saden.

Description of drawings

The sketch map of your formula recursion Bayes mode identification method of Fig. 1 Saden;

Fig. 2 is based on the power network topology misidentification method or the load tap changer location estimation method sketch map of your formula recursion bayes method of Saden;

The winding diagram of Fig. 3 test macro;

Fig. 4 noise is 1% o'clock topological mode recognition result based on basic recursion bayes method;

Fig. 5 noise is 1% o'clock topological mode recognition result based on your formula recursion bayes method of Saden;

Fig. 6 noise is 6% o'clock topological mode recognition result based on basic recursion bayes method;

Fig. 7 noise is 6% o'clock topological mode recognition result based on your formula recursion bayes method of Saden;

Fig. 8 noise is 10% o'clock topological mode recognition result based on basic recursion bayes method;

Fig. 9 noise is 10% o'clock topological mode recognition result based on your formula recursion bayes method of Saden;

Embodiment

For the technology contents, the structural feature that specify your formula recursion bayes method of Saden that the present invention proposes and the application in state estimation thereof, be described further below in conjunction with execution mode and conjunction with figs..

Fig. 7 is the sketch map of your formula recursion Bayes mode identification method of Saden; When carrying out power network topology misidentification or load tap changer location estimation with your formula recursion bayes method of Saden, sketch map is as shown in Figure 2.

The present invention utilizes the anglist, and (U.K.Generic Distribution System, the power distribution network of two 11kV UKGDS) test the validity based on the topology error identification method of Saden that formula recursion Bayesian Estimation method with distribution system.This system comprises two networks, and two networks connect through normal open switch, and wherein network 1 comprises 26 computing nodes, 25 branch roads, 13 loads and a generator, and network 2 comprises 13 computing nodes, 13 branch roads and 8 loads.Network parameter, load parameter and generator parameter can obtain on the http://monaco.eee.strath.ac.uk/ukgds/ of website.The winding diagram of this network is as shown in Figure 3.

Because the load that wasted power is little is little to state estimation result's influence, losing big load then has bigger influence to the state estimation result, therefore, thinks that change has taken place the operation of power networks pattern when loss is loaded greatly; In addition, branch breaking that is determined by protective device action or closure also are considered to the operation of power networks pattern change have taken place.Through analysis, network shown in Figure 31 there is operation of power networks pattern possible in 5, as shown in table 1.

Table 1 network 1 possible 5 in topological mode

In this example, pattern 1 is correct topological mode, gets threshold value threshold=0.9.The topological operational mode that your the formula recursion bayes method of Saden that below adopts basic recursion bayes method and the present invention to propose respectively comes estimation network 1 is with the estimated result of two kinds of methods of examination contrast when the measurement noise in various degree.

1) estimated result during 1% noise

When measuring noise when being 1%, when adopting basic recursion bayes method, the change curve of the posterior probability of all topological mode is as shown in Figure 4.Visible by Fig. 4, through 100 recursion, the posterior probability of correct topological mode 1 reaches 0.9, and basic recursion bayes method has obtained correct estimated result.But the recursion number of times of the needs of basic recursion bayes method is many.

At this moment, when adopting your the formula recursion bayes method of Saden of this paper invention, the change curve of the posterior probability of all topological mode is as shown in Figure 5.Visible by Fig. 5, through 66 recursion, the posterior probability of correct topological mode 1 reaches 0.9, and you have obtained correct estimated result by formula recursion bayes method equally Saden, and its efficient is apparently higher than basic recursion bayes method.

2) estimated result during 6% noise

When the measurement noise increases to 6%; Adopt the change curve of posterior probability of all topological mode that basic recursion bayes method obtains as shown in Figure 6; It is thus clear that, along with the increase of measurement noise, the mis-behave of basic recursion bayes method a lot; Be that basic recursion bayes method needs recursion just can identify correct topological operational mode many times, its recursion efficient descends greatly.

At this moment, when adopting your the formula recursion bayes method of Saden of this paper invention, the change curve of the posterior probability of all topological mode is as shown in Figure 7.Visible by Fig. 7; Though measurement noise has increased; But your performance of formula recursion bayes method of Saden is unaffected basically, and promptly the recursion number of times of Saden that formula recursion bayes method needs is far smaller than basic recursion bayes method, and the former has good recursion efficient and stronger robustness.

3) estimated result during 10% noise

When measuring noise when continuing to increase to 10%, adopt the change curve of posterior probability of all topological mode that basic recursion bayes method obtains as shown in Figure 8, visible, this moment, basic recursion bayes method can't identify correct topological mode,

At this moment, when adopting your the formula recursion bayes method of Saden of this paper invention, the change curve of the posterior probability of all topological mode is as shown in Figure 9.Visible by Fig. 9, this moment, your formula recursion bayes method of Saden can identify correct topological mode, and its recognition efficiency is not affected, and had shown very strong robustness.

Can find out by above estimated result, the efficient of your formula recursion bayes method of the Saden that the present invention proposes far above with basic recursion bayes method, and measurement noise had very strong robustness, the latter's robustness is then very poor.

Above disclosedly be merely preferred embodiment of the present invention, can not limit the present invention's interest field certainly with this, the equivalent variations of therefore doing according to claim of the present invention still belongs to the scope that the present invention is contained.

Claims (2)

1. your formula recursion bayes method of a Saden, it is characterized in that: you carry out this Saden by formula recursion bayes method according to the following steps:

Step (1) initialization

Make the initial probability of all patterns to be identified all equate, even p is (η ₁| ε ⁽⁰⁾)=p (η ₂| ε ⁽⁰⁾)=L=p (η _N| ε ⁽⁰⁾)=1/N, wherein η _iBe i pattern, ε ⁽⁰⁾Be the initial characteristics amount, p (η _i| ε ⁽⁰⁾) be η _iInitial probability, N is the total number of pattern; Recursion counter k=1 is set;

Step (2) recursion is calculated to obtain correct pattern

Step (2.1) judges that the maximum of the posterior probability that all patterns are corresponding whether less than threshold value, promptly judges max{p (η _i| ε ^(k-1)Whether }＜threshold sets up, and being then changes step (2.2); Otherwise change step (3);

Step (2.2) is extracted and is obtained the pairing characteristic quantity of all patterns;

Step (2.3) utilizes following formula to calculate the posterior probability of all patterns;

$\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})=\frac{p\left(e_i^{\left(k\right)}\right|{\mathrm{\&eta;}}_i)p\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{(k-1)})}{\underset{j<i}{\mathrm{\&Sigma;}}p\left(e_j^{\left(k\right)}\right|{\mathrm{\&eta;}}_j)\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})+\underset{j\&GreaterEqual;i}{\mathrm{\&Sigma;}}p\left(e_j^{\left(k\right)}\right|{\mathrm{\&eta;}}_j)p\left({\mathrm{\&eta;}}_j\right|{\mathrm{\&epsiv;}}^{(k-1)})}$

Wherein,

Be the pairing characteristic quantity of all N pattern, i.e. residual error vector;

Pattern η when being the k time recursion _iPosterior probability, p (η _i| ε ^(k-1)) be prior probability;

Be pattern η in the k time recursion _iThe conditional probability of corresponding residual error, i.e. likelihood function numerical value;

Step (2.4) is utilized following formula that the posterior probability of all patterns is carried out normalization and is calculated;

$p\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})=\hat{p}\left({\mathrm{\&eta;}}_i\right|{\mathrm{\&epsiv;}}^{\left(k\right)})/{\mathrm{\&Sigma;}}_{j=1}^N\hat{p}\left({\mathrm{\&eta;}}_j\right|{\mathrm{\&epsiv;}}^{\left(k\right)})$

Wherein, p (η _i| ε ^(k)) pattern η when being the k time recursion _iThe normalization posterior probability values;

Step (2.5) makes k=k+1, changes step (2.1);

The maximum pattern of step (3) posterior probability is correct pattern, and algorithm finishes.

2. the application of a Saden that formula recursion bayes method as claimed in claim 1 in state estimation; It is characterized in that: when carrying out power network topology misidentification or load tap changer location estimation with your formula recursion bayes method of Saden, its concrete calculation procedure is following:

Step (1) initialization

Form all possible power network topology pattern or all possible load tap changer position; Make the initial probability of all power network topology patterns to be identified or all tap joint position of transformer all equate; Even

wherein

is the initial probability of i power network topology pattern or load tap changer position, N is the total number of power network topology pattern or load tap changer position; Recursion counter k=1 is set;

Step (2) recursion is calculated to obtain correct power network topology pattern or load tap changer position

Step (2.1) judges that whether the maximum of the pairing posterior probability of all power network topology patterns or load tap changer position is less than threshold value; Whether promptly judge

and set up, be then to change step (2.2); Otherwise change step (3);

Step (2.2) input actual measurements, virtual measurement and pseudo-the measurement, these measurement amounts form measurement equation and do

z＝h(x)+τ

Wherein, z ∈ R ^mBe the measurement vector, comprise that node injects meritorious measurement, node injects idle measurement, the meritorious measurement of branch road, the idle measurement of branch road and node voltage and measures; These measurement amounts are generally got substantial amount and are measured, if substantial amount is measured disappearance, then replace with pseudo-the measurement, and the superpose random number of 10% normal distribution of the result that pseudo-measurement is employed in last state estimation is come pattern; In measuring vector, should add 0 simultaneously and inject virtual measurement; X ∈ R ⁿIt is the state variable that comprises node voltage amplitude and phase angle; H (x) is the Nonlinear Mapping of state vector to the measurement vector; τ～N (0, R) be error in measurement;

Be the error in measurement variance matrix;

According to above measurement equation; Carry out iteration through following update equation; Up to the state estimation convergence, can obtain state vector estimated value

x _k+1＝x _k+G(x _k)H ^T(x _k)R ^-1(z-h(x _k))

Wherein,

Be Jacobian matrix, G (x _k)=(H ^T(x _k) R ^-1H (x _k)) ^-1

According to following formula, the independent respectively residual error vector that calculates under all power network topology patterns or the load tap changer position

And error variance Matrix C _{F, i}(i=1,2, L, N)

$e_i^{\left(k\right)}=z-h\left(\hat{x}\right)$

According to following formula, the independent respectively error variance Matrix C of calculating under all power network topology patterns or the load tap changer position _{F, i}(i=1,2, L, N)

$C_{f,i}^{-1}=\mathrm{diag}({\mathrm{\&sigma;}}_v^2,{\mathrm{\&sigma;}}_{p_i}^2,{\mathrm{\&sigma;}}_{q_i}^2,{\mathrm{\&sigma;}}_{p_b}^2,{\mathrm{\&sigma;}}_{q_b}^2)$

C _{F, i}(i=1,2, L, in N)

From [H ^TR ^-1H] ^-1The respective items of diagonal element obtains, C _{F, i}(i=1,2, L, in N)

Each item can be from matrix H [H ^TR ^-1H] ^-1H ^TThe respective items of diagonal element obtains;

When carrying out the power network topology misidentification, more than the state estimation of being carried out be the whole network state estimation; And when carrying out the load tap changer location estimation, the state estimation of more than carrying out be the transformer branch road and near the local state of branch road estimate;

Step (2.3) utilizes following formula to calculate all topological structure of electric or the pairing posterior probability of tap joint position;

${\hat{p}}_i^{\left(k\right)}=\frac{\exp (-{\left(e_i^{\left(k\right)}\right)}^T{C}_{f,i}{e}_i^{\left(k\right)}/2)p_i^{(k-1)}}{\underset{j<i}{\mathrm{\&Sigma;}}\exp (-{\left(e_j^{\left(k\right)}\right)}^T{C}_{f,j}{e}_j^{\left(k\right)}/2){\hat{p}}_j^{\left(k\right)}+\underset{j\&GreaterEqual;i}{\mathrm{\&Sigma;}}\exp (-{\left(e_j^{\left(k\right)}\right)}^T{C}_{f,j}{e}_j^{\left(k\right)}/2)p_j^{(k-1)}}$

Wherein,

be the pairing characteristic quantity of pattern i, i.e. residual error vector when being the k time recursion; posterior probability of pattern i when being the k time recursion, is prior probability; is the conditional probability of the corresponding residual error of pattern i in the k time recursion, i.e. likelihood function numerical value;

Step (2.4) is utilized following formula that the posterior probability of all patterns is carried out normalization and is calculated;

$p_i^{\left(k\right)}={\hat{p}}_i^{\left(k\right)}/{\mathrm{\&Sigma;}}_{j=1}^N{\hat{p}}_j^{\left(k\right)}$

Wherein, the normalization posterior probability values of pattern i during

the k time recursion;

Step (2.5) makes k=k+1, changes step (2.1);

The maximum pattern of step (3) posterior probability is correct power network topology pattern or load tap changer position, and algorithm finishes.

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