Power distribution network state parameter joint estimation method based on double extended Kalman filtering

Abstract

The invention discloses a power distribution network state parameter joint estimation method based on double extended Kalman filter, relates to the technical field of power grid state prediction, and effectively avoids the influence of parameter variation on a state estimation result and the influence of state deviation on the parameter estimation result by introducing the double extended Kalman filter. For the situation that state data and parameter data in a power distribution network are inaccurate and have mutual influence, prior estimation and posterior estimation of two processes are set to interact to construct a state-parameter iterative estimation model, and the model converts a traditional state and parameter segmentation model into a unified estimation model. The state estimation model and the parameter estimation model of the power distribution network are jointly solved to solve the problem that the estimation precision is limited due to the fact that the models are mutually independent in a traditional method. Therefore, the real-time and accurate estimation of the operation state and parameters of the power distribution network is realized, the observability of the power distribution network is more comprehensively improved, and powerful data support is provided for fault diagnosis and operation optimization.

Description

Technical Field

[0001] The present application relates to the technical field of power grid state prediction, and in particular to a method for joint estimation of distribution network state parameters based on dual extended Kalman filtering. Background Art

[0002] With the gradual integration of distributed generation, electric vehicles, and new loads into distribution networks, the operational state of distribution networks has become increasingly complex, and their dynamic characteristics have also increased. Furthermore, due to the complex and volatile environment in which distribution networks operate, the parameters of their equipment have also become dynamic. These state and parameter changes pose new requirements and challenges for the real-time observation and operation and maintenance of distribution networks. Therefore, overcoming the state uncertainty brought about by the influx of distributed resources, improving the estimation accuracy of distribution network operating states and real-time parameters, and thus ensuring the effectiveness and stability of observations, is a key challenge for the development of distribution systems.

[0003] State estimation and parameter estimation techniques are fundamental approaches to effectively observing distribution network states and parameters. Their fundamental concept involves collecting information through the use of various sensors, metering equipment, and network communication technologies installed in the distribution network, and then utilizing data analysis, regression, and other methods to calculate and correct the network's operating status and system parameters in real time. The models for state and parameter estimation are essentially nonlinear data regression problems. State estimation requires recovering the system's true state from measurements containing errors. The goal of parameter estimation is to infer the system's parameter values ​​from measured electrical quantities.

[0004] Most existing research focuses solely on solving state and parameter estimation models independently, without considering the interplay between them. When solving for states, system parameters influence the final calculation results, while when solving for parameters, the accuracy of state data also influences the effectiveness of parameter estimation. This results in insufficient consideration of the interdependence between parameter and state estimation, limiting the accuracy and practicality of estimation models. Summary of the Invention

[0005] In order to solve the above technical problems, this application proposes the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a method for jointly estimating distribution network state parameters based on a double extended Kalman filter, comprising:

[0007] Obtain variable data through the initial topology and line parameters of the distribution network, wherein the variable data includes: state variables, parameter variables and measurement variables;

[0008] Establishing state equations, parameter equations and measurement equations respectively according to the variable data;

[0009] Using a double extended Kalman filter in combination with the state equation, parameter equation and measurement equation, respectively, determine a priori estimates of the state and its covariance and a priori estimates of the parameters and their covariance;

[0010] Determining the state Kalman gain, the state posterior estimate and its covariance, the parameter Kalman gain and the parameter posterior estimate and its covariance in sequence according to the obtained state prior estimate and its covariance and the parameter prior estimate and its covariance;

[0011] The final posterior estimation result is solved again as the prior estimation value, and the state error limit and parameter error limit are set at the same time. If the difference between two adjacent estimation results is less than the set limit at the same time, it is considered that the parameter and state have reached the optimal estimation value at the same time.

[0012] In a possible implementation, obtaining variable data through the initial topology and line parameters of the distribution network includes:

[0013] The voltage amplitude and voltage phase angle of each node in the distribution network are selected as state variables, and a model of the state variables is established:

[0014] s k ={u k ,θ k}

[0015] ={[U 1,k ,...,U i,k ,...,U n,k ],[θ 1,k ,...,θ i,k ,...,θ n,k ]}

[0016] Where: u k is the node voltage amplitude vector of the system, i=1,…,n is the node number of the distribution network, U i,k represents the voltage amplitude of the i-th node at the k-th moment, θ k is the node phase angle vector of the system, θ i,k represents the phase angle of the i-th node at the k-th moment;

[0017] The conductance and susceptance of the lines in the distribution network are selected as parameter variables, and a model of parameter variables is established:

[0018] w k ={g k ,b k}

[0019] ={[g 12,k ,...,g ij,k ,...,g n-1n,k ],[b12,k ,...,b ij,k ,...,b n-1n,k ]}

[0020] Where: g k is the conductivity parameter vector of the system at time k, g ij,k represents the conductance parameter of branch ij; b k is the susceptance parameter vector of the system at time k, b ij,k represents the conductance parameter of branch ij;

[0021] All voltage amplitudes, partial voltage phase angles, node injection power, branch power, and branch current in the distribution network are selected as measured electrical quantities, and the model of the measured variables is established as follows:

[0022]

[0023] in: and represents the observed values ​​of voltage amplitude and phase angle, and represents the observed value of active and reactive power injected by the node, and represents the power flowing through the branch, Indicates the current flowing through the branch.

[0024] In one possible implementation, establishing a state equation, a parameter equation, and a measurement equation based on the variable data includes:

[0025] The quadratic exponential smoothing method is used to establish the transfer equation that describes the changes of state variables and parameter variables in time series:

[0026]

[0027] in: Represents the estimated value of the data sequence at time k. When s is the state, s is x, and when s is the parameter, s is w. and represents the forecast value of the sequence at time k and k+1; a k is the horizontal component, b k is the tilt component; α k and β k is the smoothing parameter;

[0028] For the node voltage amplitude and voltage phase angle in the measurement variables, the measurement equation is established:

[0029]

[0030] in: represents the voltage observation of node i at time k, represents the voltage observation of node i at time k;

[0031] For the injected active power of node i and reactive power The relationship between its observation value and state value is:

[0032]

[0033] in: represents the active power observed at node i; represents the reactive power observed at node i; θ ij,k =θ i,k -θ j,k represents the phase difference between nodes ij; G ij,k and B ij,k are the real and imaginary parts of the element of the node admittance matrix at position ij respectively;

[0034] For the branch current flowing from node i to node j, the relationship between its state value and observation value is as follows:

[0035]

[0036] Where: g ij,k and b ij,k is the conductance and susceptance of branch ij;

[0037] For the branch power flowing from node i to node j and reactive power The relationship between its state value and observation value is as follows:

[0038]

[0039] When estimating the parameters of the line, the independent variables in the measurement equation are converted from states to parameters, and the G in the node admittance matrix is ij,k and B ij,k for:

[0040]

[0041] Among them, G ii,k and B ii,k represents the self-conductance and self-susceptance, j∈r(i) represents all nodes connected to i;

[0042] Convert the node injection power measurement equation into an equation about parameter variables:

[0043]

[0044] For the branch current measurement equation, the square of the current is linearly related to the parameter variable, so the current measurement equation is:

[0045]

[0046] In one possible implementation, the method of using a double extended Kalman filter in combination with the state equation, the parameter equation, and the measurement equation to respectively determine a priori state estimates and their covariances and a priori parameter estimates and their covariances includes:

[0047] Establishing the state-parameter-measurement observation equation of nonlinear relationship:

[0048]

[0049] Where: s is the system state variable, F is the state equation; w is the system parameter variable, R is the parameter equation; z is the system measurement variable, H is the measurement equation; v, n, e are the errors of these three types of variables respectively; F, R, H are linear or nonlinear equations;

[0050] Combine two Kalman filters, the state Kalman filter estimates the system state, and the parameter Kalman filter estimates the model parameters. The two Kalman filters use the same observation equation;

[0051] In each control cycle, the two Kalman filters perform one operation each. The state Kalman filter uses the estimated value of the parameter Kalman filter in the previous cycle when operating, and the parameter filter uses the estimated value of the state filter in the previous cycle when operating. The observation equation is linearized by combining the two Kalman filters.

[0052] In one possible implementation, linearizing the observation equation by combining two Kalman filters includes:

[0053] The state prediction step uses the state variables estimated a posteriori at time k-1 Predict the prior estimate state at time k, the prior estimate of the state variable:

[0054]

[0055] Among them, F sk represents the state transfer matrix, h sk Indicates the state of external items, F sk and h sk for:

[0056] F sk =α sk (1+β sk )I

[0057]

[0058] Where I is the identity matrix;

[0059] After obtaining the prior estimate of the state variables, the prior state error covariance matrix To update:

[0060]

[0061] in is the state posterior estimation error covariance at time k-1; V sk is the state process noise covariance matrix;

[0062] The linearized equation established in the parameter prediction link:

[0063]

[0064] R wk =α wk (1+β wk )I

[0065]

[0066] in, is the prior estimate of the parameter at time k; is the posterior estimate of the parameter at time k-1; R wk and d wk is the parameter transfer matrix and parameter external terms;

[0067] Then the prior parameter error covariance is updated:

[0068]

[0069] in, is the prior error covariance of the parameter at time k; is the posterior error covariance at time k-1; N wk is the covariance matrix of the parameter process noise;

[0070] First, linearize the observation equation of the state filter and convert the nonlinear observation equation into the prior estimate of the state Perform Taylor expansion at , and ignore quadratic and above terms to obtain the linearized model of the observation equation of state:

[0071]

[0072] Among them, H zs,k is the linearization matrix of the measurement function for the state variable. When the measurement variable and the state variable are in a linear relationship, H zs,kThe corresponding elements are its coefficient matrix; when the relationship between the measured variable and the state variable is nonlinear, the corresponding linearization matrix is ​​its Jacobian matrix;

[0073] The nonlinear measurement equation is linearized to obtain the linearized measurement matrix H zs,k , substitute the admittance parameters of each branch into the prior estimated values ​​of the parameters at time k Each voltage amplitude and phase angle is substituted into the state prior estimation value at time k

[0074] In one possible implementation, H zs,k The specific elements are shown below:

[0075] H uu,k , H uθ,k , H θu,k and H θθ,k The coefficient matrix between the voltage amplitude and phase angle measurement variables and the state variables is:

[0076]

[0077] and The Jacobian matrix of the injected active power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, is as follows:

[0078]

[0079] and The Jacobian matrix of the injected reactive power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, is as follows:

[0080]

[0081] and is the Jacobian matrix of the branch active power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows:

[0082]

[0083] and is the Jacobian matrix of the branch reactive power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows:

[0084]

[0085] H iu,k and H iθ,kis the Jacobian matrix of the branch current measurement variables to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows:

[0086]

[0087] In one possible implementation, determining the state Kalman gain and the state posterior estimate includes:

[0088] By the H zs,k Determine the state Kalman gain, including:

[0089]

[0090] Among them, K sk is the state Kalman gain, R sk is the noise covariance matrix of the state observation;

[0091] After obtaining the state Kalman gain, calculate the posterior estimate of the state and its corresponding error covariance matrix:

[0092]

[0093] in, Represents the posterior estimate of the state quantity, P sk represents the posterior error covariance matrix of the state variables;

[0094] Then, the voltage amplitude and phase angle estimated by the a posteriori state are taken as fixed values ​​to solve the a posteriori estimate of the parameter variables.

[0095] In one possible implementation, when calculating the parameter Kalman gain, the state quantity in the measurement equation is assumed to be the state posterior estimate At this time, the state is a known value, and the measurement equation is transformed into a linear equation about the parameter variable w. The linearized parameter measurement equation is as follows:

[0096]

[0097] Among them, H zw,k is the linear coefficient matrix of the measurement function with respect to the parameter variables;

[0098] The specific forms of each sub-matrix are as follows:

[0099] and is the linear coefficient of the injected active power measurement variable to the branch admittance:

[0100]

[0101] Among them, [H <P i,k ,g ij,k>] A simplified representation of the matrix, where each element is P i,k and g ij,k The corresponding position elements between the two matrices are represented as follows:

[0102]

[0103] and is the linear coefficient of injected reactive power measurement variable to branch admittance:

[0104]

[0105] and is the linear coefficient of the branch admittance of the active power measurement variable flowing through the branch:

[0106]

[0107] and is the linear coefficient of the reactive power measurement variable flowing through the branch to the branch admittance:

[0108]

[0109] H ig,k and H ib,k is the linear coefficient of the branch current measurement variable to the branch admittance:

[0110]

[0111] In the above matrix, each voltage amplitude and phase angle is substituted into the state posterior estimate at time k

[0112] In one possible implementation, determining the parameter Kalman gain and the parameter posterior estimate and their covariance includes:

[0113] Determine the Kalman gain formula for calculating parameter variables:

[0114]

[0115] Among them, K wk is the Kalman gain of the parameter variable; is the prior error covariance of the parameter at time k; N wk is the noise covariance matrix of the parameter observations;

[0116] After obtaining the parameter Kalman gain, calculate the k-time posterior parameter estimate and its corresponding error covariance matrix as follows:

[0117]

[0118] in, is the posterior estimate of the parameter variable, P wk is the posterior error covariance matrix of the parameter variables.

[0119] In one possible implementation, the final posterior estimation result is again solved as the prior estimation value, and a state error limit and a parameter error limit are set. If the difference between two adjacent estimation results is less than the set limit at the same time, it is considered that the parameter and state have reached the optimal estimation value at the same time, including:

[0120] Assume that the state error limit is δ sk , the parameter error limit is δ wk , then when the state and parameters to be solved satisfy the following conditions at the same time:

[0121]

[0122] in, and They represent the prior estimate and the posterior estimate of the state variable calculated by the measurement equation in the iterative process; and Represents the prior estimate and posterior estimate of the parameter variable between two iterations; Mean() represents the average value of each variable;

[0123] If the average value of the difference between the two variables is not less than the state error limit and the parameter error limit at the same time, then the estimation result is considered not optimal. At this time, the posterior estimate replaces the prior estimate and the next iteration is continued until the limit requirements are met.

[0124] In the embodiment of the present application, by introducing a dual extended Kalman filter, the influence of parameter changes on the state estimation results and the influence of state deviation on the parameter estimation results are effectively avoided. A state-parameter iterative estimation model is constructed through the interaction of the prior estimates of the two lines. The model transforms the traditional state and parameter segmentation model into a unified estimation model. The state estimation model and parameter estimation model of the distribution network are jointly solved to solve the problem of limited estimation accuracy caused by the independence of the models in the traditional method. Thereby, real-time and accurate estimation of the operating state and parameters of the distribution network is achieved, the observability of the distribution network is improved more comprehensively, and strong data support is provided for fault diagnosis and operation optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 A schematic flow chart of a method for joint estimation of distribution network state parameters based on dual extended Kalman filtering is provided in an embodiment of the present application. DETAILED DESCRIPTION

[0126] The present invention will be described below with reference to the accompanying drawings and specific implementation methods.

[0127] See also Figure 1 The method for jointly estimating distribution network state parameters based on dual extended Kalman filtering provided in this embodiment includes:

[0128] S101, obtaining variable data through the initial topology and line parameters of the distribution network, wherein the variable data includes: state variables, parameter variables and measurement variables.

[0129] The voltage amplitude and voltage phase angle of each node in the distribution system are selected as state variables. When all state variables are known, the system is considered observable. The state variables of this model are as follows:

[0130]

[0131] Among them, u k is the node voltage amplitude vector of the system. Assuming that the distribution network nodes are numbered as i=1,…,n, then U i,k represents the voltage amplitude of the i-th node at the k-th moment, θ k is the node phase angle vector of the system, θ i,k represents the phase angle of the i-th node at the k-th moment.

[0132] Parameter variables refer to the distribution network structural parameters. Assuming that the distribution network topology is known, the parameters to be estimated are the impedance or admittance of the line. Accurate acquisition of these parameters will affect the distribution network state estimation. At the same time, accurate state estimation results will also improve the distribution network parameter identification accuracy. The parameter variables established in this model are as follows:

[0133]

[0134] Among them, g k is the conductivity parameter vector of the system at time k, and g ij,k represents the conductance parameter of branch ij; b k is the susceptance parameter vector of the system at time k, and b ij,k Represents the conductance parameter of branch ij.

[0135] Measured variables refer to the electrical quantities measured by various data acquisition devices in the distribution network, typically including all voltage amplitudes, some voltage phase angles, node injection power, branch power, branch current, etc. The measurement matrix is ​​shown below:

[0136]

[0137] in, and represents the observed values ​​of voltage amplitude and phase angle, and represents the observed value of active and reactive power injected by the node, and represents the power flowing through the branch, Indicates the current flowing through the branch.

[0138] S102, establishing a state equation, a parameter equation and a measurement equation respectively according to the variable data.

[0139] The transfer equations for states and parameters are used to describe how they change over time. In a time series, the physical characteristics of the states and parameters can be ignored, retaining only their mathematical characteristics. Therefore, the same type of equation can be used to construct the transfer equations. The quadratic exponential smoothing method is often used to construct the transfer equations. This method takes into account the trend of the data, and its basic equation is:

[0140]

[0141] in, Represents the estimated value of the data sequence at time k. When s is the state, s is x, and when s is the parameter, s is w. and represents the forecast value of the sequence at time k and k+1; a k is the horizontal component, b k is the tilt component; α k and β k is the smoothing parameter.

[0142] A measurement equation generally refers to the relationship between a measurement variable and a state variable. This study adds parameter variables to the model, so the relationship between these three variables is the relationship between the measurement variable, the state variable, and the parameter variable.

[0143] Taking a node i in the system as an example, the related measurement equation is given. First, for the node voltage amplitude and voltage phase angle, the measurement equation is established as follows:

[0144]

[0145] in, represents the voltage observation of node i at time k; represents the observed voltage at node i at time k. It should be noted that while voltage amplitude measurement equipment is installed at virtually every node in a distribution network, not every node has the capability to measure voltage phase angle. Even if the phase angle is partially known, the established measurement equations are redundant based on other collected electrical quantities, so the phase angle can still be estimated.

[0146] For the injected active power of node i and reactive power The relationship between its observation value and state value is:

[0147]

[0148] in, represents the active power observed at node i; Represents the reactive power observed at node i. ij,k =θ i,k -θ j,k represents the phase difference between nodes ij; G ij,k and B ij,k are the real and imaginary parts of the element at position ij of the node admittance matrix, respectively.

[0149] For the branch current flowing from node i to node j, the relationship between its state value and observation value is as follows:

[0150]

[0151] Among them, g ij,k and b ij,k are the conductance and susceptance of branch ij.

[0152] For the branch power flowing from node i to node j and reactive power The relationship between its state value and observation value is as follows:

[0153]

[0154] When estimating the parameters of a line, the essence is to convert the independent variables in the measurement equation from states to parameters. ij,k and B ij,k for:

[0155]

[0156] Among them, G ii,k and B ii,k represents the self-conductance and self-susceptance, j∈r(i) represents all nodes connected to i

[0157] The node injection power measurement equation can be transformed into an equation about parameter variables as follows

[0158]

[0159] It can be found that this equation is a linear equation with respect to the parameter. For the branch current measurement equation, the square of the current is linearly related to the parameter variable, so the current measurement equation can be written as:

[0160]

[0161] The power equation of each branch is itself a linear equation about parameter variables, so there is no need to modify it.

[0162] S103 , using a double extended Kalman filter in combination with the state equation, parameter equation and measurement equation to respectively determine a priori state estimates and their covariances and a priori parameter estimates and their covariances.

[0163] The dual extended Kalman filter (EKF) consists of two EKFs: a state-based EKF (EKFx) and a parameter-based EKF (EKFw). Each EKF has two parts: a prediction part and an update part. The dual EKF operates sequentially, using two EKFs at each iteration to simultaneously estimate parameters and states.

[0164] Assume that the state-parameter-measurement space expression containing nonlinear relationships is:

[0165]

[0166] Among them, s is the system state variable, F is the state transfer equation; w is the system parameter variable, R is the parameter transfer equation; z is the system measurement variable, H is the measurement equation; v, n, e are the errors of these three types of variables respectively; F, R, H are linear or nonlinear equations.

[0167] For the distribution network state-parameter joint estimation model, the state equation or parameter equation established by the quadratic exponential smoothing method is easy to linearize, and the parameter measurement equation itself is a linear equation, but the state measurement equation is a nonlinear equation, so it needs to be linearized during calculation.

[0168] The basic idea of ​​the DEKF is to combine two EKFs: the state EKF estimates the system state, and the parametric EKF estimates the model parameters, using the same observation equation. In each control cycle, each filter performs an operation: the state filter uses the parameter filter's estimate from the previous cycle, and the parameter filter uses the state filter's estimate from the previous cycle. This may seem like a simple series connection of the state and parameter filters, but the combination of the two filters changes the linearization process of the parameter filter's observation equation, requiring a cyclic derivative form similar to recursive learning for linearization.

[0169] The state prediction step is to use the state variables estimated a posteriori at time k-1 Predict the prior estimate state at time k, use the quadratic exponential smoothing equation established in the previous section as the state transfer equation, and linearize it to obtain the prior estimate of the state variable as follows:

[0170]

[0171] Among them, F sk represents the state transfer matrix, h sk Indicates the state of external use, F sk and h sk for:

[0172]

[0173] Where I is the identity matrix.

[0174] After obtaining the prior estimate of the state variables, the prior state error covariance matrix To update:

[0175]

[0176] in is the state posterior estimation error covariance at time k-1; V sk is the state process noise covariance matrix.

[0177] Since both the parameter transfer equation and the state transfer equation are two-parameter exponential smoothing models, the parameter prediction process is basically the same as the state prediction process, and the established linearization equations are the same, as follows:

[0178]

[0179] in, is the prior estimate of the parameter at time k; is the posterior estimate of the parameter at time k-1; R wk and d wk is the parameter transfer matrix and the parameter external term.

[0180] Then the prior parameter error covariance is updated as follows:

[0181]

[0182] in, is the prior error covariance of the parameter at time k; is the posterior error covariance at time k-1; N wk is the covariance matrix of the parametric process noise.

[0183] First, linearize the observation equation of the state filter. The core idea of ​​the EKF algorithm is to linearize the nonlinear observation equation in the state prior estimate. Perform Taylor expansion at , and ignore quadratic and above terms, and obtain the linearized model of the observation equation of state, as follows:

[0184]

[0185] Among them, H zs,k is the linearization matrix of the measurement function for this state variable. When the measurement variable and the state variable are in a linear relationship, H zs,k The corresponding elements are its coefficient matrix. When the relationship between the measured variable and the state variable is nonlinear, the corresponding linearization matrix is ​​its Jacobian matrix. zs,k The specific elements are as follows:

[0186] H uu,k , H uθ,k , H θu,k and H θθ,k is the coefficient matrix between the voltage amplitude and phase angle measurement variables and the state variables, which can be expressed as:

[0187]

[0188] and is the Jacobian matrix of the injected active power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0189]

[0190] and is the Jacobian matrix of the reactive power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0191]

[0192] and is the Jacobian matrix of the branch active power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0193]

[0194] and is the Jacobian matrix of the branch reactive power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0195]

[0196] H iu,k and H iθ,k is the Jacobian matrix of the branch current measurement variables with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0197]

[0198] At this point, the nonlinear measurement equation has been linearized, and the linearized measurement matrix H is obtained. zs,k .

[0199] S104, determining the state Kalman gain, the state posterior estimate and its covariance, the parameter Kalman gain and the parameter posterior estimate and its covariance in sequence according to the acquired state prior estimate and its covariance and the parameter prior estimate and its covariance.

[0200] In the above Jacobian matrix equation, the admittance parameters of each branch are substituted into the prior estimated values ​​of the parameters at time k. Each voltage amplitude and phase angle is substituted into the state prior estimation value at time k Based on the above information, the state Kalman gain can be calculated as follows:

[0201]

[0202] Among them, K sk is the state estimation Kalman gain, R sk is the noise covariance matrix of the state observation.

[0203] After obtaining the state Kalman gain, calculate the posterior estimate of the state and its corresponding error covariance matrix, as shown in the formula:

[0204]

[0205] in, Represents the posterior estimate of the state quantity, P sk represents the a posteriori error covariance matrix of the state variables. Next, the a posteriori state estimated voltage amplitude and phase angle are used as fixed values ​​to solve the a posteriori estimates of the parameter variables.

[0206] When calculating the parameter Kalman gain, assume that the state quantity in the measurement equation is the state posterior estimate At this point, the state is a known value, so the measurement equation is transformed into a linear equation about the parameter variable w. The linearized parameter measurement equation is as follows:

[0207]

[0208] Among them, H zw,k is the linear coefficient matrix of the measurement function with respect to the parameter variable; according to equations (13)-(15), the specific forms of each submatrix are as follows.

[0209] and is the linear coefficient of the injected active power measurement variable to the branch admittance, as shown below

[0210]

[0211] Among them, [H <P i,k ,g ij,k >] A simplified representation of the matrix, where each element is P i,k and g ij,k The corresponding position elements between the two matrices are represented as follows:

[0212]

[0213] Subsequent matrices all use this simplified expression.

[0214] and is the linear coefficient of injected reactive power measurement variable to branch admittance, as shown below:

[0215]

[0216] and is the linear coefficient of the branch active power measurement variable to the branch admittance, as follows:

[0217]

[0218] and The linear coefficient of the reactive power measurement variable flowing through the branch to the branch admittance is as follows:

[0219]

[0220] H ig,k and H ib,k is the linear coefficient of the branch current measurement variable to the branch admittance, as shown below:

[0221]

[0222] At this point, the linear measurement matrix of each measurement variable to the parameter variable is obtained. In the above matrix, each voltage amplitude and phase angle is substituted into the state posterior estimation value at time k

[0223] Afterwards, the Kalman gain of the parameter variable can be calculated as follows:

[0224]

[0225] Among them, K wk is the Kalman gain of the parameter variable; is the prior error covariance of the parameter at time k; N wk is the noise covariance matrix of the parameter observations.

[0226] After obtaining the parameter Kalman gain and parameter filter observation equation, the posterior parameter estimate at time k and its corresponding error covariance matrix can be calculated as follows:

[0227]

[0228] in, is the posterior estimate of the parameter variable; P wk is the posterior error covariance matrix of the parameter variables.

[0229] S105, the final posterior estimation result is solved again as the prior estimation value, and the state error limit and parameter error limit are set at the same time. If the difference between two adjacent estimation results is less than the set limit at the same time, it is considered that the parameter and state have reached the optimal estimation value at the same time.

[0230] Through the above calculation steps, we can obtain a posteriori estimates of the distribution network parameters and operating status. However, this result cannot be simply used as the final state or parameter, as its accuracy and rationality must be verified. Therefore, using the concept of rolling iteration, the obtained posteriori estimate results are again used as the prior estimate value to solve, while setting state error limits and parameter error limits. If the difference between two consecutive estimation results is less than the limit, it can be considered that the parameter and state have reached the optimal estimate.

[0231] Assume that the state error limit is δ sk , the parameter error limit is δ wk , then when the state and parameters to be solved satisfy the following conditions at the same time:

[0232]

[0233] in, and They represent the prior and posterior estimates of the state variables calculated by the measurement equation during the iteration process; and Represents the prior and posterior estimates of the parameter variables between two iterations. Mean() calculates the average of the variables. If the average of the difference between the two variables is not less than both the state error limit and the parameter error limit, the estimate is considered suboptimal. In this case, the posterior estimate replaces the prior estimate, and the next iteration continues until the limits are met.

[0234] In the embodiments of the present application, "at least one" refers to one or more, and "more" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.

[0235] The above description is merely a specific embodiment of the present application. Any person skilled in the art may easily conceive of variations or substitutions within the technical scope disclosed in this application, and such variations or substitutions shall be within the scope of protection of this application. The scope of protection of this application shall be subject to the scope of protection of the claims.

Claims

1. A method for joint estimation of distribution network state parameters based on double extended Kalman filtering, characterized in that: include: Obtain variable data through the initial topology and line parameters of the distribution network, wherein the variable data includes: state variables, parameter variables and measurement variables; Establishing state equations, parameter equations and measurement equations respectively according to the variable data; Using a double extended Kalman filter in combination with the state equation, parameter equation and measurement equation, respectively, determine a priori estimates of the state and its covariance and a priori estimates of the parameters and their covariance; Determining the state Kalman gain, the state posterior estimate and its covariance, the parameter Kalman gain and the parameter posterior estimate and its covariance in sequence according to the obtained state prior estimate and its covariance and the parameter prior estimate and its covariance; The final posterior estimation result is solved again as the prior estimation value, and the state error limit and parameter error limit are set at the same time. If the difference between two adjacent estimation results is less than the set limit at the same time, it is considered that the parameter and state have reached the optimal estimation value at the same time.

2. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 1, characterized in that: The variable data is obtained through the initial topology and line parameters of the distribution network, including: The voltage amplitude and voltage phase angle of each node in the distribution network are selected as state variables, and a model of the state variables is established: s k ={u k ,i k } ={[U 1,k ,...,U i,k ,...,U n,k ],[θ 1,k ,...,θ i,k ,...,θ n,k ]} Where: u k is the node voltage amplitude vector of the system, i=1,…,n is the node number of the distribution network, U i,k represents the voltage amplitude of the i-th node at the k-th moment, θ k is the node phase angle vector of the system, θ i,k represents the phase angle of the i-th node at the k-th moment; The conductance and susceptance of the lines in the distribution network are selected as parameter variables, and a model of parameter variables is established: w k ={g k ,b k } ={[g 12,k ,...,g ij,k ,...,g n-1n,k ],[b 12,k ,...,b ij,k ,...,b n-1n,k ]} Where: g k is the conductivity parameter vector of the system at time k, g ij,k represents the conductance parameter of branch ij; b k is the susceptance parameter vector of the system at time k, b ij,k represents the conductance parameter of branch ij; All voltage amplitudes, partial voltage phase angles, node injection power, branch power, and branch current in the distribution network are selected as measured electrical quantities, and a model of the measured variables is established: in: and represents the observed values ​​of voltage amplitude and phase angle, and represents the observed value of active and reactive power injected by the node, and represents the power flowing through the branch, Indicates the current flowing through the branch.

3. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 2, characterized in that: Establishing state equations, parameter equations and measurement equations respectively according to the variable data, including: The quadratic exponential smoothing method is used to establish the transfer equation that describes the changes of state variables and parameter variables in time series: in: Represents the estimated value of the data sequence at time k. When s is the state, s is x, and when s is the parameter, s is w. and represents the forecast value of the sequence at time k and k+1; a k is the horizontal component, b k is the tilt component; α k and β k is the smoothing parameter; For the node voltage amplitude and voltage phase angle in the measurement variables, the measurement equation is established: in: represents the voltage observation of node i at time k, represents the voltage observation of node i at time k; For the injected active power of node i and reactive power The relationship between its observation value and state value is: in: represents the active power observed at node i; represents the reactive power observed at node i; θ ij,k =θ i,k -θ j,k represents the phase difference between nodes ij; G ij,k and B ij,k are the real and imaginary parts of the element of the node admittance matrix at position ij respectively; For the branch current flowing from node i to node j, the relationship between its state value and observation value is as follows: Where: g ij,k and b ij,k is the conductance and susceptance of branch ij; For the branch power flowing from node i to node j and reactive power The relationship between its state value and observation value is as follows: When estimating the parameters of the line, the independent variables in the measurement equation are converted from states to parameters, and the G in the node admittance matrix is ij,k and B ij,k for: Among them, G ii,k and B ii,k represents the self-conductance and self-susceptance, j∈r(i) represents all nodes connected to i; Convert the node injection power measurement equation into an equation about parameter variables: For the branch current measurement equation, the square of the current is linearly related to the parameter variable, so the current measurement equation is:

4. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 1, characterized in that: The method of using a double extended Kalman filter in combination with the state equation, the parameter equation and the measurement equation to respectively determine the state prior estimate and its covariance and the parameter prior estimate and its covariance includes: Establishing the state-parameter-measurement observation equation of nonlinear relationship: Where: s is the system state variable, F is the state equation; w is the system parameter variable, R is the parameter equation; z is the system measurement variable, H is the measurement equation; v, n, e are the errors of these three types of variables respectively; F, R, H are linear or nonlinear equations; Combine two Kalman filters, the state Kalman filter estimates the system state, and the parameter Kalman filter estimates the model parameters. The two Kalman filters use the same observation equation; In each control cycle, the two Kalman filters perform one operation each. The state Kalman filter uses the estimated value of the parameter Kalman filter in the previous cycle when operating, and the parameter filter uses the estimated value of the state filter in the previous cycle when operating. The observation equation is linearized by combining the two Kalman filters.

5. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 4, characterized in that: The linearization of the observation equation by combining two Kalman filters includes: The state prediction step uses the state variables estimated a posteriori at time k-1 The prior estimate of the state at time k is predicted. The prior estimate of the state variable is as follows: Among them, F sk represents the state transfer matrix, h sk Indicates the state of external items, F sk and h sk for: F sk =a sk (1+b sk )I Where I is the identity matrix; After obtaining the prior estimate of the state variables, the prior state error covariance matrix To update: in is the state posterior estimation error covariance at time k-1; V sk is the state process noise covariance matrix; The linearized equation established in the parameter prediction link: R wk =a wk (1+b wk )I in, is the prior estimate of the parameter at time k; is the posterior estimate of the parameter at time k-1; R wk and d wk is the parameter transfer matrix and parameter external terms; Then the prior parameter error covariance is updated: in, is the prior error covariance of the parameter at time k; is the posterior error covariance at time k-1; N wk is the covariance matrix of the parameter process noise; First, linearize the observation equation of the state filter and convert the nonlinear observation equation into the prior estimate of the state Perform Taylor expansion at , and ignore quadratic and above terms to obtain the linearized model of the observation equation of state: Among them, H zs,k is the linearization matrix of the measurement function for the state variable. When the measurement variable and the state variable are in a linear relationship, H zs,k The corresponding elements are its coefficient matrix; when the relationship between the measured variable and the state variable is nonlinear, the corresponding linearization matrix is ​​its Jacobian matrix; The nonlinear measurement equation is linearized to obtain the linearized measurement matrix H zs,k , substitute the admittance parameters of each branch into the prior estimated values ​​of the parameters at time k Each voltage amplitude and phase angle is substituted into the state prior estimation value at time k 6. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 5, characterized in that: H zs,k The specific elements are shown below: H uu,k , H uθ,k , H θu,k and H θθ,k is the coefficient matrix between the voltage amplitude and phase angle measurement variables and the state variables, expressed as: and The Jacobian matrix of the injected active power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, is as follows: and The Jacobian matrix of the injected reactive power measurement variable with respect to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables, is as follows: and is the Jacobian matrix of the branch active power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows: and is the Jacobian matrix of the branch reactive power measurement variable to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows: H iu,k and H iθ,k is the Jacobian matrix of the branch current measurement variables to the voltage amplitude and phase angle, where the elements are the partial derivatives between the corresponding variables as follows:

7. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 5, characterized in that: Determine the state Kalman gain and state posterior estimate, including: By the H zs,k Determine the state Kalman gain: Among them, K sk is the state Kalman gain, R sk is the noise covariance matrix of the state observation; After obtaining the state Kalman gain, calculate the posterior estimate of the state and its corresponding error covariance matrix: in, Represents the posterior estimate of the state quantity, P sk represents the posterior error covariance matrix of the state variables; Then, the voltage amplitude and phase angle estimated by the a posteriori state are taken as fixed values ​​to solve the a posteriori estimate of the parameter variables.

8. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 7, characterized in that: When calculating the parameter Kalman gain, assume that the state quantity in the measurement equation is the state posterior estimate At this time, the state is a known value, and the measurement equation is transformed into a linear equation about the parameter variable w. The linearized parameter measurement equation is: Among them, H zw,k is the linear coefficient matrix of the measurement function with respect to the parameter variables; The specific forms of each sub-matrix are as follows: and is the linear coefficient of the injected active power measurement variable to the branch admittance, as shown below: Among them, [H <P i,k ,g ij,k >] A simplified representation of the matrix, where each element is P i,k and g ij,k The corresponding position elements between the two matrices are represented as follows: and is the linear coefficient of injected reactive power measurement variable to branch admittance: and is the linear coefficient of the branch admittance of the active power measurement variable flowing through the branch: and is the linear coefficient of the reactive power measurement variable flowing through the branch to the branch admittance: H ig,k and H ib,k is the linear coefficient of the branch current measurement variable to the branch admittance: In the above matrix, each voltage amplitude and phase angle is substituted into the state posterior estimate at time k 9. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 8, characterized in that: Determine the parameter Kalman gains and the parameter posterior estimates and their covariances, including: Determine the Kalman gain formula for calculating parameter variables: Among them, K wk is the Kalman gain of the parameter variable; is the prior error covariance of the parameter at time k; N wk is the noise covariance matrix of the parameter observations; After obtaining the parameter Kalman gain, calculate the k-time posterior parameter estimate and its corresponding error covariance matrix: in, is the posterior estimate of the parameter variable, P wk is the posterior error covariance matrix of the parameter variables.

10. The method for joint estimation of distribution network state parameters based on double extended Kalman filtering according to claim 1, characterized in that: The final posterior estimation result is used as the prior estimation value to solve again, and the state error limit and parameter error limit are set at the same time. If the difference between two adjacent estimation results is less than the set limit at the same time, it is considered that the parameter and state have reached the optimal estimation value at the same time, including: Assume that the state error limit is δ sk , the parameter error limit is δ wk , then when the state and parameters to be solved satisfy the following conditions at the same time: in, and They represent the prior estimate and the posterior estimate of the state variable calculated by the measurement equation in the iterative process; and Represents the prior estimate and posterior estimate of the parameter variable between two iterations; Mean() represents the average value of each variable; If the average value of the difference between the two variables is not less than the state error limit and the parameter error limit at the same time, then the estimation result is considered not optimal. At this time, the posterior estimate replaces the prior estimate and the next iteration is continued until the limit requirements are met.

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