Distributed power distribution network fusion estimation method

Abstract

The invention relates to a distributed power distribution network fusion estimation method. The method comprises the following steps: S1, establishing a power distribution network system model; s2, obtaining predicted values and a predicted information matrix of the node i and a neighbor node j thereof; s3, setting an iteration initial step and a filtering estimation value when t times of fixed point iteration is carried out on the ith node; s4, Cholesky decomposition is carried out; s5, calculating a consensus weighted item of the node i, and obtaining an optimal estimation value of a current state by using a fixed point iteration method of a maximum correlation entropy extension information filter; and S6, comparing the current state estimation value with the estimation value of the previous iteration step, if the current state estimation value is smaller than a threshold value, taking the current state estimation value as the state estimation value of the next iteration, and calculating the state estimation error covariance, otherwise, updating the number of iterations, and returning to S5. Compared with the prior art, the method has the advantages of improving the precision of the filter adopted by the power distribution network state estimation method and the like.

Description

Technical Field

[0001] The present invention relates to the field of distribution network state estimation under non-Gaussian noise interference, and in particular to a distributed distribution network fusion estimation method. Background Art

[0002] First, most of the current distribution network state estimation algorithms use the Gaussian kernel function, which is more likely to produce singular phenomena. Secondly, since the Kalman filter has numerical instability when inverting the matrix, it will affect the stability of the distribution network. Finally, the existing maximum relevant entropy Kalman filter based on the consensus strategy does not consider the consensus problem of measuring high-order statistical characteristics with consensus differences, and the differences in network communication and data heterogeneity between nodes and data processing speed may lead to inconsistency in state estimation, thereby affecting the accuracy of the filter. Summary of the invention

[0003] The purpose of the present invention is to provide a distributed distribution network fusion estimation method in order to improve the accuracy of the filter used in the distribution network state estimation method and improve the stability of the distribution network state estimation.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A distributed distribution network fusion estimation method, the method comprising the following steps:

[0006] S1. Establish a distribution network system model, which includes an observation vector and a state vector, and obtain an initial state estimation value and an initial estimation information matrix;

[0007] S2, obtain the predicted value and prediction information matrix of node i and its neighbor node j through the Student's t-core maximum correlation entropy extended information filter with consensus weighted terms;

[0008] S3, set the initial iteration step t = 1, let in It represents the filter estimate of the ith node when performing t fixed point iterations;

[0009] S4, through the state prediction error covariance of node i and Perform Cholesky decomposition to obtain and

[0010] S5. Calculate the consensus weighted item of node i The fixed point iteration method of the maximum correlation entropy extended information filter is used to obtain the optimal estimate of the current state;

[0011] S6. Compare the current state estimate with the estimate of the previous iteration step. If it is less than the threshold, use the current state estimate as the state estimate for the next iteration and calculate the state estimate error covariance. Otherwise, update the number of iterations and return to S5.

[0012] Furthermore, the observation vector and the state vector are:

[0013] x k =f(x k-1 )+w k,k-1

[0014] z k =h(x k )+v k

[0015] Among them, x k : The m-dimensional state vector at time k. The amplitude and phase angle of the node voltage are usually selected as the node state quantity, that is, x k =[V k ,θ k ] T , f(·): nonlinear state transfer function, z k : n-dimensional observation vector at time k.

[0016] Furthermore, the optimal estimated value of the current state is:

[0017]

[0018] Furthermore, in the optimal estimated value of the current state,

[0019]

[0020] Furthermore, if the current state estimate is compared with the estimate of the previous iteration step and is less than the threshold, then:

[0021]

[0022] Here, ζ represents the threshold value.

[0023] Furthermore, the current state estimation value is used as the state estimation value of the next iteration:

[0024] make

[0025] Furthermore, the consensus weighted term for:

[0026]

[0027] in, is the state prediction error covariance of node j, Represents a weighted term.

[0028] Furthermore, the consensus weighted term middle,

[0029]

[0030] Furthermore, the calculated state estimation error covariance is:

[0031]

[0032] Furthermore, in the state estimation error covariance,

[0033]

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The single node data collected by SCADA and PMU are combined into multiple local data sets by using a distributed fusion algorithm, and then the state estimation of the distribution network is realized by using a consensus strategy. In order to improve the accuracy of state estimation, this work point proposes a distributed filtering algorithm based on a high-order measurement method of consensus difference by introducing a high-order measurement method of consensus difference. First, since the Student's t kernel function has a relatively slow attenuation rate to zero for large errors when the degree of freedom is low, a new Student's t kernel maximum correlation entropy criterion containing a consensus weighted term is defined, and the corresponding consensus loss function is to use the consensus error containing the consensus weighted term as the input of the kernel function, and the new information loss function is to use the observation information as the input of the kernel function; secondly, a distributed filtering algorithm is designed based on this new maximum correlation entropy criterion, and then covariance cross-fusion is performed on multiple local data sets; the method of the present invention has a high state estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is the number set of node i and its neighboring nodes of the present invention;

[0037] Figure 2 is the MAE of voltage amplitude;

[0038] Figure 3 is the MAE of the voltage phase angle. DETAILED DESCRIPTION

[0039] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0040] The present invention proposes a distributed distribution network fusion estimation method, which includes the following steps:

[0041] S1. Establish a distribution network system model, which includes an observation vector and a state vector, and obtain an initial state estimation value and an initial estimation information matrix;

[0042] S2, obtain the predicted value and prediction information matrix of node i and its neighbor node j through the Student's t-core maximum correlation entropy extended information filter with consensus weighted terms;

[0043] S3, set the initial iteration step t = 1, let in It represents the filter estimate of the ith node when performing t fixed point iterations;

[0044] S4, through the state prediction error covariance of node i and Perform Cholesky decomposition to obtain and

[0045] S5. Calculate the consensus weighted item of node i The fixed point iteration method of the maximum correlation entropy extended information filter is used to obtain the optimal estimate of the current state;

[0046] S6. Compare the current state estimate with the estimate of the previous iteration step. If it is less than the threshold, use the current state estimate as the state estimate for the next iteration and calculate the state estimate error covariance. Otherwise, update the number of iterations and return to S5.

[0047] The present invention uses a distributed fusion algorithm to combine the single node data collected by SCADA and PMU into multiple local data sets, and then uses the consensus strategy to realize the state estimation of the distribution network. In order to improve the accuracy of state estimation, this work point proposes a distributed filtering algorithm based on the high-order measurement method of consensus difference by introducing a high-order measurement method of consensus difference. First, since the Student's t kernel function has a relatively slow attenuation and zeroing speed for large errors when the degree of freedom is low, a new Student's t kernel maximum correlation entropy criterion containing consensus weighted terms is defined, and its corresponding consensus loss function is to use the consensus error containing consensus weighted terms as the input term of the kernel function, and the new information loss function is to use the observation information as the input term of the kernel function; secondly, a distributed filtering algorithm is designed based on this new maximum correlation entropy criterion, and then covariance cross fusion is performed on multiple local data sets; finally, considering the numerical stability of the matrix when inverting, a distributed fusion algorithm based on the Student's t kernel maximum correlation entropy extended information filter with consensus weighted terms is proposed with the information filter as the basic algorithm, and the proposed algorithm is verified by simulation to have high state estimation accuracy.

[0048] The derivation process of the present invention is:

[0049] Distribution network model

[0050] For the distribution network system model described in (1) and (2), it is assumed that is the estimated value of the state at time k-1, is the estimated information matrix at time k-1.

[0051] x k =f(x k-1 )+w k,k-1 , (1)

[0052] z k =h(x k )+v k , (2)

[0053] Where:

[0054] x k : The m-dimensional state vector at time k. The amplitude and phase angle of the node voltage are usually selected as the node state quantity, that is, x k =[V k ,θ k ] T ;

[0055] f(·): nonlinear state transfer function, the process of state change caused by load change. When the power system tends to steady state, its linearized state transfer matrix is ​​usually the unit matrix;

[0056] z k : n-dimensional observation vector at time k, the SCADA device collects analog quantities, and the observation data z k Including voltage amplitude, injection power and line power. The power system is equipped with SCADA equipment to observe data. k It can be divided into two situations:

[0057] One is to equip the entire network with expensive PMU devices. Since the PMU devices collect digital quantities, including voltage amplitude, voltage phase angle, node injection power, etc., the observed quantity z k =[V i ,θ i ] T However, due to economic reasons, it is difficult to configure PMU devices in the entire network, so I will not go into details.

[0058] Another case is that some PMU devices are equipped or no PMU devices are configured, and the observed quantity is

[0059] z k =[P ij ,Q ij P i ,Q i ,V i ] T , (3)

[0060] Where:

[0061] P ij : The active power of branch ij, that is, P ij =(V i ) 2 g ij -V i V j g ij cosθ ij -V i V j b ij sinθ ij ;

[0062] Q ij : Reactive power of branch ij, i.e. Q ij =-(V i ) 2 b ij -V i V j g ij sinθ ij +V i V j b ij cosθ ij ;P i: The injected active power of node i, that is Q i : The injected reactive power of node i, that is n i : The set of nodes connected to node i;

[0063] V i : The voltage amplitude of node i, that is, V i =V i .

[0064] G ij is the element corresponding to the node admittance matrix, g ij represents the conductance between nodes i and j, b ij represents the susceptance between nodes i and j, θ ij Represents the difference between the phase angle of node i and the phase angle of node j.

[0065] h(·): nonlinear observation function, which describes the nonlinear relationship between power and voltage. In order to obtain the state value, h(x k ) is linearized, similar to Newton power flow calculation, and h(x k ) is Taylor expanded, that is,

[0066] h(x k )=h(x0)+H(x0)(x k -x0), (4)

[0067] Where:

[0068] H(x0): The Jacobian matrix of the linear relationship between the observation value and the state value, that is,

[0069]

[0070] Specifically,

[0071]

[0072] w k,k-1 :The process noise of the system and the variance is Q k,k-1 Gaussian distribution of

[0073] v k :The observation noise of the system and the variance is R k and Student's t distribution with degrees of freedom df, that is:

[0074] w k,k-1 ~N(0,Q k,k-1 ). (7)

[0075] v k ~St(0,Rk ,df).(8)II. Student's t kernel maximum correlation entropy extended information filter with consensus weighting term

[0076] The state prediction value and state prediction error covariance of node i are given by the following formula:

[0077]

[0078]

[0079] Where:

[0080]

[0081] The state prediction value and state prediction error covariance matrix of neighbor node j are given by the following formula:

[0082]

[0083]

[0084] Where:

[0085]

[0086] For the power system mathematical model equations (1) and (2), we can get

[0087]

[0088] Where:

[0089]

[0090] Through The Cholesky decomposition of Right now

[0091]

[0092]

[0093] Multiply both sides of equation (15) by have to

[0094]

[0095]

[0096]

[0097] Defining Innovation Error yes The lth element of L = n(i)m + n is The dimension of n(i) represents the number of node i and its neighboring nodes, such as Figure 1 shown. yes The lth element of yes The l-th row element of .

[0098] Define consensus error with consensus weights N i represents the number of neighbor nodes of node i, is the consensus weighted term. Where:

[0099]

[0100]

[0101]

[0102] The innovation error and consensus error As the input of Student's t kernel function, the following loss function based on MC criterion is established:

[0103]

[0104] Consensus Error yes The lth element of The estimated values ​​of neighboring nodes have been weighted and summed. Contains only status information corresponding items, so The dimension of is m. If the corresponding item of observation information is not included, the loss function can be further written as

[0105]

[0106] The optimal estimate of can be obtained by solving the maximum value of equation (26), that is,

[0107]

[0108] right Ask about The derivative of and make it zero, that is

[0109]

[0110] After simplification,

[0111]

[0112] The optimal solution can be obtained as

[0113]

[0114] because and contain So the optimal solution (30) is a The fixed point equation of , further simplified, is

[0115]

[0116] Where:

[0117]

[0118]

[0119]

[0120]

[0121] Formula (31) can be further expressed as

[0122]

[0123] Where:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] Formula (36) can be further written into the general form of distributed filter,

[0130]

[0131] By cross-fusion of covariances in equation (42), we can obtain the solution closest to the optimal estimate of the system, namely:

[0132]

[0133] Regarding how to use the Student's t-kernel maximum correlation entropy extended information filter with consensus weighted terms to improve the reliability of distribution network state estimation and the consensus effect of the distributed non-Gaussian filtering algorithm, the algorithm can be summarized as follows.

[0134] Step 1: Select an appropriate kernel bandwidth σ and a small positive number ξ, and set the initial state estimate of the i-th node and the initial estimated information matrix

[0135] Step 2: Use equations (9), (10) and (12), (13) to respectively calculate the predicted value and predicted information matrix of node i and its neighbor node j.

[0136] Step 3: Set the initial iteration step t = 1, and let in Represents the filter estimate of the ith node when performing t fixed point iterations.

[0137] Step 4: By and the observation noise covariance Perform Cholesky decomposition to obtain the square root matrix Sum square root matrix

[0138] Step 5: Calculate the consensus weighted term of node i through formula (22) And use the fixed point iteration method to obtain the optimal state estimate,

[0139]

[0140] Where:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] Step 6: Compare the estimated value of the current iteration step with the estimated value of the previous iteration step.

[0152]

[0153] If (55) holds, then And execute step 7. Otherwise, t→t-1 and return to step 5.

[0154] Step 7: The state estimation error covariance is,

[0155]

[0156] Where:

[0157]

[0158] III. In the distribution network system, due to various reasons, such as the time lag caused by network data congestion during node data transmission, various network attacks, and various communication noises, the information received by the SCADA and PMU devices may be different. Therefore, the consensus algorithm cannot make each node reach a complete consensus, but can only make the estimated values ​​of all sensor nodes tend to be consistent. By analyzing the parameters of the consensus algorithm, the consensus effect can be better.

[0159] Assume that both SCADA and PMU devices have the same observation information, the variance between each observation device is R, and before the filter is updated, ensure that the estimated values ​​of all sensors reach the same value. When updating, the filter estimate achieves complete consensus. According to (49), the variance between the estimated values ​​at the next moment is calculated as

[0160]

[0161] _When the filtering algorithm converges, is a fixed value. Under ideal conditions,

[0162]

[0163] The variance between the estimates at the next moment is,

[0164]

[0165] As can be seen from (60), since full consensus is related to the consensus difference term, full consensus can be approached by reducing the consensus difference between nodes.

[0166] From (53), we can see that if we want to reach a complete consensus, we need to satisfy

[0167]

[0168] From (61), we can see that the consensus weighted term The design of needs to consider the relationship between nodes to a certain extent. Medium weighted items The design must meet and The choice makes (23) The trace or determinant of is the smallest. Therefore, in the case of non-Gaussian distributed filtering, the consensus effect needs to consider the consensus diagonal matrix with consensus difference terms to achieve ideal consensus

[0169] In the distribution network system affected by non-Gaussian noise, based on the distributed non-Gaussian filtering algorithm, this technical solution fully considers the consensus differences between nodes. First, a new Student's t kernel maximum correlation entropy criterion with consensus weighted terms is defined, and the corresponding consensus loss function and innovation loss function are used as input items of the Student's t kernel function respectively. Secondly, the distributed filtering algorithm is designed according to this new maximum correlation entropy criterion, and then the covariance cross-fusion of each node is performed.

[0170] The distribution network node data is obtained by using the Matpower software package, and the Matlab software is used as the simulation experiment platform. For the non-Gaussian distribution network system, the numerical simulation results show that the distributed maximum correlation entropy extended information filter with consensus weighted terms (DTMCEIF-IW-CWT) algorithm proposed in this paper has better accuracy. When the distribution network is estimated, the kernel bandwidth σ should not be too small. Choosing a suitable kernel bandwidth can make the DTMCEIF-IW-CWT algorithm perform better in the case of non-Gaussian noise.

[0171] For this experiment, all results are based on the average of 100 independent runs of the Monte Carlo experiment, using 100 samples in each run to evaluate the mean absolute error (MAE) of the state. Assume that the system noise follows the following non-Gaussian distribution,

[0172] w k,k-1 :N(0,0.01),(62)

[0173]

[0174] By comparing the Student's t-core maximum correlation entropy extended information filter (TMCEIF), the Student's t-core maximum correlation entropy extended information filter based on local sequential fusion (TMCEIF-LSFF), the distributed Student'st core maximum correlation entropy extended information filter (DTMCEIF), the distributed Student's t-core maximum correlation entropy extended information filter based on correlation entropy consensus (DTMCEIF-W-MCC) algorithm and the DTMCEIF-IW-CWT algorithm proposed in this paper, it is verified that the proposed algorithm has good accuracy, such as Figure 2 The MAE of the voltage amplitude and Figure 3 The voltage phase angle is shown in MAE.

[0175] Table 1 MAE comparison of voltage amplitude and phase angle of various algorithms

[0176]

[0177] As can be seen from Table 1, for non-Gaussian distribution network systems, since the TMCEIF-LSFF algorithm directly transmits the observation data of each node to the fusion center in the distribution network state estimation, compared with the DTMCEIF algorithm, the interference is less, so the accuracy is slightly higher than the DTMCEIF algorithm. However, in order to reduce the computational load of the distribution network system and improve the stability of the distribution network, it is necessary to improve the DTMCEIF algorithm. It can be seen that the DTMCEIF-IW-CWT algorithm has good accuracy. Compared with the TMCEIF algorithm, the voltage amplitude accuracy of the DTMCEIF-IW-CWT algorithm is improved by 36.870%, and the voltage phase angle accuracy is improved by 55.233%. Compared with the DTMCEIF-W-MCC algorithm, the voltage amplitude accuracy of the DTMCEIF-IW-CWT algorithm is improved by 13.000%, and the voltage phase angle accuracy is improved by 24.071%.

[0178] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A distributed distribution network fusion estimation method, characterized in that: The method comprises the following steps: S1. Establish a distribution network system model, which includes an observation vector and a state vector, and obtain an initial state estimation value and an initial estimation information matrix; S2, obtain the predicted value and prediction information matrix of node i and its neighbor node j through the Student's t-core maximum correlation entropy extended information filter with consensus weighted terms; S3, set the initial iteration step t = 1, let in It represents the filter estimate of the ith node when performing t fixed point iterations; S4. Through and the observation noise covariance Perform Cholesky decomposition to obtain the square root matrix Sum square root matrix S5. Calculate the consensus weighted item of node i The fixed point iteration method of the maximum correlation entropy extended information filter is used to obtain the optimal estimate of the current state; S6. Compare the current state estimate with the estimate of the previous iteration step. If it is less than the threshold, use the current state estimate as the state estimate for the next iteration and calculate the state estimate error covariance. Otherwise, update the number of iterations and return to S5.

2. A distributed distribution network fusion estimation method according to claim 1, characterized in that: The observation vector and state vector are: x k =f(x k-1 )+w k,k-1 z k =h(x k )+v k Among them, x k : The m-dimensional state vector at time k. The amplitude and phase angle of the node voltage are usually selected as the node state quantity, that is, x k =[V k ,θ k ] T , f(·): nonlinear state transfer function, z k : n-dimensional observation vector at time k.

3. A distributed distribution network fusion estimation method according to claim 1, characterized in that: The optimal estimated value of the current state is: in, The kernel function input representing the consensus error, represents the consensus gain, represents the consensus observation, represents the consensus covariance quantity, represents the consensus weighted term.

4. A distributed distribution network fusion estimation method according to claim 3, characterized in that: In the optimal estimated value of the current state, the parameters are: in, The predicted information of the state new information is all reliable, represents the observed covariance product, The kernel function input quantity representing the state quantity innovation error, represents the covariance value of the observed innovation, represents the consensus error.

5. A distributed distribution network fusion estimation method according to claim 4, characterized in that: Compare the current state estimate with the estimate of the previous iteration step. If it is less than the threshold, then: Here, ζ represents the threshold value.

6. A distributed distribution network fusion estimation method according to claim 5, characterized in that: The current state estimate is used as the state estimate for the next iteration: make 7. A distributed distribution network fusion estimation method according to claim 1, characterized in that: The consensus weighted term for: in, is the state prediction error covariance of node j, represents the weighted term, Represents the diagonal matrix of weighted terms.

8. A distributed distribution network fusion estimation method according to claim 7, characterized in that: The consensus weighted term In , the weighted term is:

9. A distributed distribution network fusion estimation method according to claim 8, characterized in that: The calculated state estimation error covariance is:

10. A distributed distribution network fusion estimation method according to claim 9, characterized in that: In the state estimation error covariance, in, represents the decomposition value of the observation error covariance, represents the observation matrix.

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