Power distribution network state estimation fusion strategy based on maximum correlation entropy criterion

Abstract

According to the power distribution network state estimation fusion strategy based on the maximum correlation entropy criterion, compared with a basic weighted least square estimation method, the maximum correlation entropy criterion is adopted, and an objective function is established; applying a state estimator based on the maximum correlation entropy criterion to the state estimation of the power distribution network according to the maximum correlation entropy criterion in combination with an adjustable Parzen window; on the basis of a traditional measurement system, a phasor measurement system is fully utilized, a hybrid estimation structure is adopted, results obtained through estimation of two kinds of measurement data are subjected to fusion processing, and therefore an optimal estimation value is obtained; an algorithm based on a maximum correlation entropy criterion and a fusion structure are combined to be used for state estimation of the power distribution network, and simulation analysis is carried out on an improved IEEE33 node power distribution network system. According to the power distribution network state estimation method based on the maximum correlation entropy criterion, a mixed two-stage evaluation system structure is utilized at the same time, and high-quality phasor measurement is fully utilized on the premise that state estimation measurement data which is widely used is guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of distribution network state estimation, and in particular to a distribution network state estimation fusion strategy based on a maximum correlation entropy criterion. Background Art

[0002] In recent years, with the large-scale access of distributed power sources and various new loads to the distribution network, the operation of the distribution network has become increasingly complex, which in turn affects the stable operation of the distribution network and increases the difficulty of real-time state monitoring and situation awareness of the distribution network. As a key link in the distribution management system, distribution network state estimation processes raw data to provide reliable data support for real-time state monitoring, scheduling and various advanced applications of the distribution system. State estimation is based on the collected data and a certain state estimation algorithm to reliably estimate the actual operation status of the system. Most of the measurement data for state estimation are remote terminal unit RTU measurement data provided by the data acquisition and supervisory control (SCADA) system. The data is not real-time, lacks time stamps, and has low data accuracy and few types. It mainly includes node injection power, branch power and node voltage amplitude.

[0003] At present, the high-precision measurement data provided by the wide area measurement system (WAMS) based on the phasor measurement unit (PMU) has high real-time performance, a time scale like GPS, and low data transmission delay and high accuracy. It can also directly measure various types of measurement data such as node voltage and branch current phasor, which has opened up a new direction for the development of state estimation. However, in a short period of time, it is not very likely that PMU technology will completely replace the traditional SCADA system, so the two measurement technologies will still coexist. In the face of different measurement data collected by the two measurement systems, the traditional weighted least squares method (WLS) still needs to add additional identification procedures in terms of the robustness of the state estimation model, which increases the computational complexity. Therefore, it is particularly important to seek a method for distribution network state estimation that can effectively process mixed measurement data. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a distribution network state estimation fusion strategy based on the maximum related entropy criterion which has certain robustness and can effectively improve the state estimation accuracy.

[0005] The present invention is implemented by the following technical solution: a distribution network state estimation fusion strategy based on the maximum correlation entropy criterion, comprising the following steps:

[0006] S1. Compared with the basic weighted least squares estimation method, the maximum relevant entropy criterion is adopted to establish the objective function;

[0007] S2, according to the maximum correlation entropy criterion combined with the adjustable Parzen window, the state estimator based on the maximum correlation entropy criterion is used in the distribution network state estimation;

[0008] S3. Make full use of the phasor measurement system on the basis of the traditional measurement system, adopt a hybrid estimation structure, and fuse the results of the two measurement data estimates to obtain the optimal estimation value;

[0009] S4, combining the algorithm based on the maximum correlation entropy criterion with the fusion structure, and applying it to the distribution network state estimation, and performing simulation analysis on the improved IEEE33-node distribution network system. In step S1, when the correlation entropy criterion is applied to the state estimation, the appropriate correlation entropy function is defined as shown in formula (6):

[0010]

[0011] in, is the measurement vector z and the corresponding estimated measurement vector The related entropy function of ; Σ is the summation symbol; i represents the number of measurements; m represents the total number of measurement sample data; is the Gaussian kernel of each measurement value i, and its calculation formula can also be written as in It is used to determine the width of the Parzen window of the ith measurement, and e represents an exponential function. In step S2, when the state estimation is performed according to the maximum correlation entropy criterion, the objective function is iteratively solved to obtain the equation shown in formula (8):

[0012]

[0013] In formula (8), H is the m×n order measurement Jacobian matrix; W is the measurement weight matrix, in h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T is the transposed matrix of the m×n-order measurement Jacobian matrix; Δx is the change in the state quantity during the iteration; And Δz is the change of the measured quantity during the iteration process.

[0014] Formula (8) is solved by Cholesky decomposition, forward or backward iteration, and orthogonal method. Therefore, the corresponding information matrix of the state estimator based on the maximum correlation entropy criterion can be defined as shown in formula (9):

[0015] G M =H T WH (9)

[0016] In formula (9), H is the m×n order measurement Jacobian matrix; G M represents the information matrix; W is the measurement weight matrix, in h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T m×n is the transposed matrix of the Jacobian matrix of the order measure.

[0017] Standard Deviation The Parzen window width is defined and is directly related to the selectivity of the objective function in the maximum correlation entropy criterion. w The estimation process is initialized with the value so that the Parzen window is large enough to include all the estimated residuals. Therefore, the strategy for adjusting the Parzen window width in each interaction k follows formula (10):

[0018]

[0019] In formula (10), represents the i-th standard deviation of the k-th interaction, Ω ii 、r、 max, ||, i, and m represent the residual covariance matrix, residual vector, square root sign, maximum value sign, absolute value sign, number of measurements, and total number of measurement sample data, respectively; S k-1 is the set of measurements identified as outliers in the previous iteration, and the set S is initialized to S (0) =Φ.

[0020] In step S3, in the actual application of state estimation, two types of sensors are considered, namely SCADA and PMU measurements, and their corresponding estimates are respectively and Indicates that the estimated error covariance matrix is ​​P s and P p , assuming that the data channels of SCADA and PMU are independent and the error covariance matrix of state estimation is available, the simplified fusion formula can be expressed as formula (16):

[0021]

[0022] In formula (16), is the best estimate; P s and P p are the estimation error covariance matrices respectively; and are the state estimates.

[0023] In step S4, the algorithm based on the maximum correlation entropy criterion and the fusion structure are combined for distribution network state estimation. By analyzing the equation obtained by solving its objective function, it is interpreted as a measurement model similar to a linearized version, as shown in formula (17):

[0024]

[0025] In formula (17), and x represent the m-dimensional and n-dimensional measurement vectors and state variable vectors respectively; H, W, E represent the measurement Jacobian matrix, measurement weight matrix and expected symbol respectively; ε is the m-dimensional measurement error, which is generally a matrix with mean and known error covariance A Gaussian random variable of

[0026] The estimated value based on the maximum correlation entropy criterion It can be given by formula (18):

[0027]

[0028] In formula (18), z and Represent the m-dimensional and n-dimensional quantity measurement vector and state variable vector respectively; H, G M denote the transposed matrix and information matrix of the measurement Jacobian matrix respectively; h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the ith measurement vector.

[0029] The estimation error is further calculated based on the estimated value, and the estimation error covariance matrix based on the maximum correlation entropy criterion is derived. On the other hand, the extension to the maximum correlation entropy criterion estimator and Therefore, the optimal solution is as follows:

[0030]

[0031] In formula (19), is the best estimate; P M,s and P M,p are the estimation error covariance matrices respectively; and are the state estimates.

[0032] The fusion formula is simplified to better adapt to large network systems and rewritten as formula (20):

[0033]

[0034] In formula (20), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates, respectively;

[0035] Further transformed into formula (21):

[0036]

[0037] In formula (21), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates.

[0038] In step S4, in order to verify the effectiveness of the estimation fusion structure of the present invention, a comparison is made between the centralized state estimation and the fusion state estimation results based on the basic weighted least squares method, and six estimation indices are used to analyze the simulation results.

[0039] The present invention has the following advantages: A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion of the present invention:

[0040] 1. By performing state estimation on traditional SCADA measurement data and PMU phase measurement data, it is shown that high-precision PMU data will affect the state estimation results to a certain extent. Applying it together with traditional SCADA measurement data in distribution network state estimation can effectively improve the accuracy of state estimation;

[0041] 2. An estimation fusion structure is used to estimate different measurement data respectively, and the estimated values ​​generated are fused. When compared with the results of traditional centralized state estimation, the results show that the estimation fusion system proposed in the present invention has the same estimation performance as the centralized state estimation, which further proves that the proposed strategy is effective and feasible.

[0042] 3) The present invention proposes an estimation fusion structure, based on which the maximum correlation entropy criterion and the basic weighted least squares estimation method are combined to conduct simulation tests on the system network, and the node voltage amplitude and phase angle are estimated based on the true value of the power flow. The results show that the present invention has a certain degree of robustness compared with the basic weighted least squares estimation method, verifying the effectiveness and reliability of the proposed strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings are part of the present invention and are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but do not constitute an improper limitation of the present invention. Obviously, the accompanying drawings described below are only some embodiments. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0044] In the attached picture:

[0045] Figure 1 The improved IEEE 33-node power distribution network diagram of the present invention;

[0046] Figure 2 The node voltage amplitude state estimation value distribution of the present invention is Figure 1 ;

[0047] Figure 3 The node voltage phase angle state estimation value distribution of the present invention is Figure 1 ;

[0048] Figure 4 The node voltage amplitude state estimation value distribution of the present invention is Figure 2 ;

[0049] Figure 5 The node voltage phase angle state estimation value distribution of the present invention is Figure 2 .

[0050] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0052] In the description of the present invention, it should be noted that the directions or positional relationships indicated by terms such as “upper”, “lower”, “front”, “back”, “left”, “right”, “vertical”, “inside” and “outside” are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as a limitation on the present invention.

[0053] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0054] In view of the differences in measurement data acquisition and measurement data composition among the coexisting measurement technologies in the distribution network state estimation, the present invention proposes a distribution network state estimation method based on the maximum correlation entropy criterion, and uses a hybrid two-stage evaluation system architecture to make full use of high-quality phasor measurements while ensuring widely used state estimation measurement data. Based on the maximum correlation entropy criterion (MCC) combined with an adjustable Parzen window, the MCC-based state estimator and the estimation fusion structure are jointly applied to the distribution network state estimation to estimate the voltage amplitude and phase angle of the system node. Compared with the traditional basic weighted least squares estimation method, it has certain robustness and can effectively improve the accuracy of state estimation.

[0055] like Figures 1 to 5 A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion is shown. S1. First, compared with the basic weighted least squares estimation method, which has shortcomings in enhancing the robustness of the state estimation model, the maximum correlation entropy criterion is adopted to establish the objective function;

[0056] S2. Further, based on the maximum correlation entropy criterion and the adjustable Parzen window, the MCC-based state estimator is used in the distribution network state estimation; S3. Secondly, on the basis of the traditional measurement system, the phasor measurement system is fully utilized, and a hybrid estimation structure is adopted to fuse the results of the two measurement data estimates respectively, so as to obtain the optimal estimate value; S4. Finally, the algorithm based on the maximum correlation entropy criterion is combined with the fusion structure and used in the distribution network state estimation, and simulation analysis is carried out on the improved IEEE33-node distribution network system.

[0057] In step S1, the weighted least squares estimation method is a mathematical optimization technique, which designs weights based on the least squares method and can easily obtain unknown data by minimizing the sum of squares of errors. The basic weighted least squares estimation method is currently the most widely used method in state estimation.

[0058] The basic principle of weighted least squares estimation is as follows:

[0059] Under the conditions of given measurement information, line parameters and network connections, the nonlinear measurement equation for state estimation is shown in formula (1):

[0060] z=h(x)+v (1)

[0061] In formula (1), z and x represent the m-dimensional and n-dimensional measurement vector and state variable vector respectively; h(x) represents the nonlinear measurement function of the system; v is the m-dimensional measurement error, which is generally a matrix with a mean and a known error covariance matrix is a Gaussian random variable.

[0062] The basic weighted least squares estimation method takes the weighted sum of squares of the difference between the measured estimate and the measured value as the objective function, and uses the Gauss-Newton method to iteratively solve the system's iterative equations as shown in formula (2):

[0063]

[0064] In formula (2), H T (x (t) )、h(x (t) ) are the transposed matrix of the Jacobian matrix of the m×n-order measurement vector generated in the t-th iteration and the nonlinear measurement function in the t-th iteration; W is the measurement weight matrix, W = R -1 ; z is the m-dimensional measurement vector; x (t) 、x (t+1) , Δx (t) are the state quantities obtained at the t-th and t+1-th iterations and the changes in the state quantities during the iteration process; G -1 (x (t) ) is the error covariance matrix generated during the t-th iteration.

[0065] The information matrix is ​​defined as shown in formula (3):

[0066] G(x)=H T (x)WH(x) (3)

[0067] In formula (3), H(x) and H T (x) are the m×n order measurement Jacobian matrix and its transposed matrix; W is the measurement weight matrix; G(x) is the information matrix.

[0068] The estimation effect of state estimation can be expressed by the information matrix, and its error covariance matrix can be expressed as formula (4):

[0069] P=G -1 (x)=(H T (x)WH(x)) -1 (4)

[0070] In formula (4), P, G -1 (x) represents the error covariance matrix; H(x), H T (x) are the m×n order measurement Jacobian matrix and its transposed matrix; W is the measurement weight matrix.

[0071] Maximum Correlation Entropy Criterion State Estimator:

[0072] The concept of correlation entropy can be interpreted as a measure of the similarity of two random variables X and Y in a region of their joint space, as shown in formula (5):

[0073] V(X,Y)=E[k σ (X,Y)]=∫k σ (x,y)dF X,Y (x,y) (5)

[0074] In formula (5), X and Y represent two random variables, V(X,Y) represents the correlation entropy, E represents the expectation, and k σ is a Mercer kernel that satisfies the reproducible kernel Hilbert space, and its kernel width is controlled by the parameter σ. ∫ represents the integral symbol, F X,Y (x, y) represents the joint distribution function of X and Y. Generally, the kernel function used in correlation entropy is the Gaussian kernel function.

[0075] When the correlation entropy criterion is applied to state estimation, the appropriate correlation entropy function is defined as shown in formula (6):

[0076]

[0077] In formula (6), is the measurement vector z and the corresponding estimated measurement vector The related entropy function of ; Σ is the summation symbol; i represents the number of measurements; m represents the total number of measurement sample data; is the Gaussian kernel of each measurement value i, and its calculation formula can be written as in Used to determine the width of the Parzen window for the i-th measurement, and e represents an exponential function.

[0078] In step S1, the maximum correlation entropy criterion aims to find the value that makes the measurement vector z and the corresponding estimated measurement vector The state estimation vector that maximizes the similarity between Thus, the following objective function is established, as shown in formula (7):

[0079]

[0080] In formula (7), R -1 is the weight factor; e represents the exponential function; z i and They represent the i-th measurement vector and the corresponding estimated measurement vector respectively; σ, ∑, max, J, i, and m represent the standard deviation, summation sign, maximum value sign, objective function sign, number of measurements, and the total number of measurement sample data respectively.

[0081] In step S2, when the state estimation is performed according to the maximum relevant entropy criterion, the objective function is iteratively solved to obtain the equation shown in formula (8):

[0082]

[0083] In formula (8), H is the m×n order measurement Jacobian matrix; W is the measurement weight matrix, in h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T is the transposed matrix of the m×n-order measurement Jacobian matrix; Δx is the change in the state quantity during the iteration; And Δz is the change of the measured quantity during the iteration process.

[0084] Formula (8) can be solved by Cholesky decomposition, forward or backward iteration, or orthogonal method.

[0085] Therefore, the corresponding information matrix of the state estimator based on the maximum correlation entropy criterion can be defined as shown in formula (9):

[0086] G M =H T WH (9)

[0087] In formula (9), H is the m×n order measurement Jacobian matrix; G M represents the information matrix; W is the measurement weight matrix, in hi (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T is the transposed matrix of the m×n measurement Jacobian matrix.

[0088] Considering the similarities between the solution methods applicable to the basic weighted least squares and the maximum relevant entropy criterion based estimator, it is reasonable to introduce algorithmic changes in the existing basic weighted least squares estimator to convert it into the maximum relevant entropy criterion based estimator, which can be done while maintaining the traditional structure.

[0089] In step S2, the standard deviation The Parzen window width is defined and is directly related to the selectivity of the objective function in the maximum correlation entropy criterion, as it adjusts the influence of each measurement on the final estimated solution. By adjusting this parameter during the interaction of the estimation process, the harmful effects of gross errors can be automatically eliminated. This is achieved because the Parzen window width imposes restrictions on the set of measurements that effectively influence the final estimate.

[0090] Using high σ w The estimation process is initialized with a value σ, so that the Parzen window is large enough to include all the estimation residuals. Therefore, at this stage, the estimates produced by the maximum correlation entropy criterion and the basic weighted least squares estimation method are the same, since there is no restriction on the measurements used. In the iterative process, σ can be reduced according to established rules, which are usually defined as a function of the residual values. w The purpose of this is to significantly reduce the impact of coarse measurements on the estimation process. This mechanism is equivalent to assigning different standards to individual measurements depending on the size of their corresponding residuals.

[0091] Therefore, the strategy for adjusting the Parzen window width in each interaction k follows formula (10):

[0092]

[0093] In formula (10), represents the i-th standard deviation of the k-th interaction, Ω ii 、r、 max, ||, i, and m represent the residual covariance matrix, residual vector, square root sign, maximum value sign, absolute value sign, number of measurements, and total number of measurement sample data, respectively; S k-1 is the set of measurements identified as outliers in the previous iteration, and the set S is initialized to S (0)=Φ.

[0094] σ w The choice of update rule may have some impact on the convergence speed of the maximum relevant entropy criterion. A more conservative rule may lead to more iterations, although it does not necessarily reduce the ability to capture bad data. The strategy adopted by formula (10) can achieve a good compromise between convergence speed and robustness against bad data.

[0095] As a type of filtering, state estimation mainly uses redundant measurement information to further improve the accuracy of data in the measurement system, process bad data, and further reliably estimate the real operating state of the system.

[0096] In step S3, the traditional measurement system mainly refers to the Supervisory Control and Data Acquisition (SCADA) system, which can provide remote terminal unit RTU data, usually including node injection power, branch power and node voltage amplitude, with low data accuracy, no time stamp and long data transmission time.

[0097] The measurement system based on the phasor measurement unit (PMU) constitutes a phasor measurement system, which can not only provide high-precision measurement data, but also directly measure the node voltage and branch current phasors. It can measure a variety of data types with high accuracy and time stamp.

[0098] Hybrid estimation structure For the two estimation modules in the first stage, each type of measurement is processed separately, and the resulting estimation results are merged in the second stage through the estimation fusion method. Multi-sensor data fusion theory is a relatively new research and development field related to aerospace, which involves processes or environments detected by different types of sensors and aims to combine data generated by different categories of sensors.

[0099] Generally speaking, estimation fusion aims to integrate data collected by different types of sensors in the best way, with the ultimate goal of improving the quality of the estimation process, while also taking into account the characteristics of each data acquisition technology. In technical terms, this is equivalent to minimizing the variance of the estimation error. Consider a set of N s Different types of sensors, represents the estimation vector obtained by the i-th sensor. In addition, it is assumed that the estimation errors generated by them can be correlated with each other, so that the corresponding covariance matrix is ​​shown in formula (11):

[0100]

[0101] In formula (11), P is N s ×N s dimensional error covariance matrix; is the corresponding error covariance submatrix; N sIndicates the total number of sensors of different types.

[0102] Its best estimate A single estimate It can be realized by the linear combination of , as shown in formula (12):

[0103]

[0104] In formula (12), is the best estimate; By a single The estimated value set composed of T By a single A set of weighted matrices composed of; is the transposed matrix of the weight matrix; N s Indicates the total number of sensors of different types.

[0105] Minimizing the estimation error variance is the key to this optimization problem. By solving the following optimization problem, we can further obtain As shown in formula (13):

[0106]

[0107] In formula (13), x, Ψ T ,Ψ, I, E, min, ∑, i, N s They respectively represent the state quantity, the transposed matrix of the weighted matrix, the weighted matrix, the state estimate, the unit matrix, the expected symbol, the minimum value symbol, the summation symbol, the number of sensors, and the total number of sensors of different types.

[0108] In current practical applications, if only two types of sensors are considered, that is, N s =2, we can get formula (14):

[0109]

[0110] In formula (14), is the best estimate; is a single estimate; is the transposed matrix of the weight matrix.

[0111] For the special case of only two types of sensors, the optimal estimation result can be written as formula (15):

[0112]

[0113] In formula (15), is the best estimate; P 11 , P 12 , P21 , P 22 is the error covariance submatrix; is a single estimate.

[0114] In step S3, in the actual application of state estimation, only two types of sensors are considered, namely SCADA and PMU measurements, and their corresponding estimates are respectively and Indicates that the estimated error covariance matrix is ​​P s and P p Assuming that the data channels of SCADA and PMU are independent and the error covariance matrix of state estimation is available, the simplified fusion formula can be expressed as formula (16):

[0115]

[0116] In formula (16), is the best estimate; P s and P p are the estimation error covariance matrices respectively; and are the state estimates.

[0117] In step S4, the algorithm based on the maximum correlation entropy criterion and the fusion structure are combined for distribution network state estimation. By analyzing the equation obtained by solving its objective function, it can be interpreted as a measurement model similar to a linearized version, as shown in formula (17):

[0118]

[0119] In formula (17), and x represent the m-dimensional and n-dimensional measurement vectors and state variable vectors respectively; H, W, E represent the measurement Jacobian matrix, measurement weight matrix and expected symbol respectively; ε is the m-dimensional measurement error, which is generally a matrix with mean and known error covariance is a Gaussian random variable.

[0120] Therefore, the estimated value based on the maximum correlation entropy criterion is It can be given by formula (18):

[0121]

[0122] In formula (18), z and Represent the m-dimensional and n-dimensional quantity measurement vector and state variable vector respectively; H, G M denote the transposed matrix and information matrix of the measurement Jacobian matrix respectively; h i(x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the ith measurement vector.

[0123] The estimation error is further calculated based on the estimated value, and the estimation error covariance matrix based on the maximum correlation entropy criterion is derived. On the other hand, the extension to the maximum correlation entropy criterion estimator and Therefore, the optimal solution is as follows:

[0124]

[0125] In formula (19), is the best estimate; P M,s and P M,p are the estimation error covariance matrices respectively; and are the state estimates.

[0126] The fusion formula can be further simplified to better adapt to large network systems. The equation can be rewritten as formula (20):

[0127]

[0128] In formula (20), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates.

[0129] Further transformed into formula (21):

[0130]

[0131] In formula (21), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates.

[0132] Equation (21) represents the basic state estimation fusion formula for hybrid state estimation based on the maximum correlation entropy criterion method. This form is obviously preferred because it does not require matrix inversion and can be solved by sparse triangular decomposition and substitution using sparse technology.

[0133] In step S4, an estimation fusion structure is adopted, combined with the maximum correlation entropy criterion and basic weighted least squares estimation, and simulation analysis is performed on the improved IEEE 33-node system. Under the configuration of the measurement device and the existing measurement data set, it is observable to meet the requirements of traditional SCADA and PMU measurement devices. The maximum correlation entropy criterion is adopted to simulate and analyze the state estimation results of the traditional SCADA measurement system and the PMU measurement system. At the same time, in order to verify the effectiveness of the estimation fusion structure of the present invention, on the basis of the basic weighted least squares method, the centralized state estimation and the fused state estimation results are compared, and the simulation results are analyzed using six estimation indicators. Finally, simulation tests of the traditional basic weighted least squares estimation method and the maximum correlation entropy criterion method of the present invention are respectively carried out on the estimation fusion structure to further verify the effectiveness and reliability of the method based on the maximum correlation entropy criterion combined with the estimation fusion structure.

[0134] The technical effects of the present invention will be further illustrated by examples below:

[0135] The improved IEEE 33-node power distribution system is used for simulation analysis. On the basis of the true value of the power flow, the corresponding error that obeys the Gaussian distribution is added to further obtain the required measurement data, among which the SCADA measurement superposition error has a mean of 0 and a standard deviation of 0.02; and the configured PMU device has a voltage amplitude and phase angle superposition error mean of 0 and a standard deviation of 0.005 / 0.002. Under the requirement of observability of SCADA and PMU devices, the maximum correlation entropy criterion is used to simulate and analyze the state estimation results of the traditional SCADA measurement system and the PMU measurement system respectively. At the same time, in order to verify the effectiveness of the estimation fusion structure of the present invention, on the basis of the basic weighted least squares method, the centralized state estimation and the fused state estimation results are compared, and the simulation results are analyzed using six estimation indicators. Finally, based on the estimation fusion structure, simulation tests are carried out with the traditional weighted least squares method and the maximum correlation entropy criterion method of the present invention to further verify the effectiveness and reliability of the method combining the maximum correlation entropy criterion with the estimation fusion system.

[0136] The improved IEEE 33 node is simulated and analyzed, and its topology structure is shown in the figure below: Figure 1 As shown. Traditional SCADA systems usually obtain inaccurate results for state estimation, which cannot accurately reflect the actual operating status of the system. The successful application of high-precision PMU measurement data has brought new development directions to state estimation to some extent. Based on the simulation analysis of the maximum correlation entropy criterion method, the power flow results are taken as the true value, and the node voltage amplitude and phase angle absolute error are used as comparison indicators. Figure 2 and Figure 3 ,pass Figure 2 and Figure 3It can be concluded that the results of state estimation using traditional SCADA measurement data have larger errors than those using PMU data. In general, the error curve obtained using PMU measurement data is relatively stable, with the maximum absolute error of voltage amplitude being 0.0131% and the average error being 0.0026%. The maximum absolute error of voltage phase angle in PMU measurement results reaches 0.1190 rad, and the average error is 0.0536 rad. The state estimation results containing PMU measurement data are superior to SCADA measurement estimation results in terms of absolute error and average error of node voltage amplitude and phase angle, proving that high-precision PMU measurement data can bring better state estimation results.

[0137] The state estimation architecture proposed in the present invention mainly regards the measurement systems as different sensors and estimates and fuses the collected data. In order to further verify that the estimation fusion structure proposed in the present invention has the same results as the traditional centralized state estimation, the state estimation of the two methods is simulated and tested based on the widely used basic weighted least squares estimation method. The specific index analysis is listed in Table 1, where e v.max is the maximum voltage estimation error; e angle.max is the maximum phase angle estimation error; e v.min is the minimum voltage estimation error; e angle.min is the minimum phase angle estimation error; e v.mean is the average voltage estimation error; e angle.mean is the average phase angle estimation error.

[0138] Table 1 Error evaluation of simulation results

[0139]

[0140] It can be seen from Table 1 that in a network with a more complex topology, the estimation fusion structure adopted by the present invention has the same effect as the centralized state estimation, and the performance of the estimator has not changed much, which verifies the effectiveness of the estimation fusion system proposed in the present invention.

[0141] Furthermore, the maximum correlation entropy criterion algorithm is combined with the estimation fusion system to perform state estimation calculations based on the SCADA and PMU measurement systems, and then fuse their respective estimated values. Taking the power flow results as the true value, the node voltage amplitude and phase angle distribution are obtained by comparison with the weighted least squares estimation method. The results are as follows: Figure 4 and Figure 5 shown.

[0142] Depend on Figure 4 and Figure 5It can be seen that the state estimation method proposed in the present invention can estimate the node voltage amplitude and phase angle more accurately. In a network with a more complex topology, based on the estimation fusion structure, both methods can meet the requirements of fast response characteristics, and can estimate the operating state of the system within the range of accuracy, further verifying the reliability of the method of the present invention.

[0143] In the description provided herein, a large number of specific details are described. However, it is understood that embodiments of the present invention can be practiced without these specific details. In some instances, well-known methods, structures and techniques are not shown in detail so as not to obscure the understanding of this description.

[0144] In addition, those skilled in the art will understand that, although some embodiments described herein include certain features included in other embodiments but not other features, the combination of features of different embodiments also means being within the scope of protection of the present invention and forming different embodiments. For example, in the above embodiments, those skilled in the art can use them in combination according to the known technical solutions and the technical problems to be solved by this application. The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this patent can make some changes or modify the equivalent embodiments of equivalent changes by using the technical content suggested above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still belongs to the scope of the solution of the present invention.

Claims

1. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion, characterized by: The steps include: S1. Compared with the basic weighted least squares estimation method, the maximum relevant entropy criterion is adopted to establish the objective function; S2, according to the maximum correlation entropy criterion combined with the adjustable Parzen window, the state estimator based on the maximum correlation entropy criterion is used in the distribution network state estimation; S3. Make full use of the phasor measurement system on the basis of the traditional measurement system, adopt a hybrid estimation structure, and fuse the results of the two measurement data estimates to obtain the optimal estimation value; S4. The algorithm based on the maximum correlation entropy criterion and the fusion structure are combined and used in distribution network state estimation. Simulation analysis is carried out on the improved IEEE33-node distribution network system.

2. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 1, characterized in that: In step S1, when the correlation entropy criterion is applied to state estimation, an appropriate correlation entropy function is defined as shown in formula (6): in, is the measurement vector z and the corresponding estimated measurement vector The related entropy function of ; Σ is the summation symbol; i Indicates the number of measurements; m Indicates the total number of measurement sample data; Each measurement value i The Gaussian kernel of in To determine the i The width of the Parzen window for each measurement. e represents an exponential function.

3. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 1, characterized in that: In step S2, when the state estimation is performed according to the maximum relevant entropy criterion, the objective function is iteratively solved to obtain the equation shown in formula (8): In formula (8), H is the m×n order measurement Jacobian matrix; W is the measurement weight matrix, in h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T is the transposed matrix of the m×n-order measurement Jacobian matrix; Δx is the change in the state quantity during the iteration; And Δz is the change of the measured quantity during the iteration process.

4. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 3, characterized in that: Formula (8) is solved by Cholesky decomposition, forward or backward iteration, and orthogonal method. Therefore, the corresponding information matrix of the state estimator based on the maximum correlation entropy criterion can be defined as shown in formula (9): G M =H T WH (9) In formula (9), H is the m×n order measurement Jacobian matrix; G M represents the information matrix; W is the measurement weight matrix, in h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the i-th measurement vector, I is a constant matrix, H T m×n is the transposed matrix of the Jacobian matrix of the order measure.

5. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 3 or 4, characterized in that: Standard Deviation i w The Parzen window width is defined and is directly related to the selectivity of the objective function in the maximum correlation entropy criterion. w The estimation process is initialized with the value so that the Parzen window is large enough to include all the estimated residuals. Therefore, the strategy for adjusting the Parzen window width in each interaction k follows formula (10): In formula (10), represents the i-th standard deviation of the k-th interaction, Ω ii 、r、 max, ||, i, and m represent the residual covariance matrix, residual vector, square root sign, maximum value sign, absolute value sign, number of measurements, and total number of measurement sample data, respectively; S k-1 is the set of measurements identified as outliers in the previous iteration, and the set S is initialized to S (0) =Φ.

6. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 1, characterized in that: In step S3, in the actual application of state estimation, two types of sensors are considered, namely SCADA and PMU measurements, and their corresponding estimates are respectively and Indicates that the estimated error covariance matrix is ​​P s and P p , assuming that the data channels of SCADA and PMU are independent and the error covariance matrix of state estimation is available, the simplified fusion formula can be expressed as formula (16): In formula (16), is the best estimate; P s and P p are the estimation error covariance matrices respectively; and are the state estimates.

7. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 1, characterized in that: In step S4, the algorithm based on the maximum correlation entropy criterion and the fusion structure are combined for distribution network state estimation. By analyzing the equation obtained by solving its objective function, it is interpreted as a measurement model similar to a linearized version, as shown in formula (17): In formula (17), and x represent the m-dimensional and n-dimensional measurement vectors and state variable vectors, respectively; H, W, and E represent the measurement Jacobian matrix, the measurement weight matrix, and the expected symbol, respectively; ε is the m-dimensional measurement error, which is generally a matrix with mean and known error covariance A Gaussian random variable of The estimated value based on the maximum correlation entropy criterion It can be given by formula (18): In formula (18), z and Represent the m-dimensional and n-dimensional quantity measurement vector and state variable vector respectively; H, G M denote the transposed matrix and information matrix of the measurement Jacobian matrix respectively; h i (x) is the nonlinear measurement function of the system in the i-th iteration process, R -1 is the weight factor; e represents the exponential function, σ represents the standard deviation, z i is the ith measurement vector.

8. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 7, characterized in that: The estimation error is further calculated based on the estimated value, and the estimation error covariance matrix based on the maximum correlation entropy criterion is derived. On the other hand, the extension to the maximum correlation entropy criterion estimator and Therefore, the optimal solution is as follows: In formula (19), is the best estimate; P M,s and P M,p are the estimation error covariance matrices respectively; and are the state estimates.

9. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 8, characterized in that: The fusion formula is simplified to better adapt to large network systems and rewritten as formula (20): In formula (20), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates, respectively; Further transformed into formula (21): In formula (21), is the best estimate; G M,s and G M,p are the gain matrices respectively; and are the state estimates.

10. A distribution network state estimation fusion strategy based on the maximum correlation entropy criterion as claimed in claim 1, characterized in that: In step S4, in order to verify the effectiveness of the estimation fusion structure of the present invention, a comparison is made between the centralized state estimation and the fusion state estimation results based on the basic weighted least squares method, and six estimation indices are used to analyze the simulation results.

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