Joint estimation method for state parameters of distribution network based on double extended kalman filter

Abstract

The application discloses a power distribution network state parameter joint estimation method based on double extended Kalman filtering, relates to the power grid state prediction technical field, and effectively avoids the influence of parameter variation on state estimation results and the influence of state deviation on parameter estimation results by introducing a double extended Kalman filter. For the case that state data and parameter data in the power distribution network are inaccurate and interact with each other, two processes of priori estimation and posteriori estimation are set up to interactively construct a state-parameter iterative estimation model, which 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 accuracy is limited due to the mutual independence of models in the traditional method. Thus, 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 strong 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 power distribution network state parameter joint estimation method based on double extended Kalman filtering. BACKGROUND

[0002] With the gradual access of distributed power generation, electric vehicles, new loads and other devices to the power distribution network, the operation state of the power distribution network is more complex, and its dynamic characteristics are also increased. In addition, due to the complex and changeable environment in which the power distribution network operates, the device parameters in the power distribution network also become dynamic. The changes in state and parameters pose new requirements and challenges to real-time observation and operation maintenance of the power distribution network. Therefore, how to overcome the state uncertainty brought by the influx of distributed resources, improve the estimation accuracy of the operation state and real-time parameters of the power distribution network, and thus ensure the effectiveness and stability of the observation, is a key challenge for the development of the power distribution system.

[0003] State estimation technology and parameter estimation technology are basic ways to realize effective observation of the state and parameters of the power distribution network. The basic idea of both is to collect information by using various sensors, metering devices and network communication technology installed in the power distribution network, and to realize real-time calculation and correction of the operation state and system parameters of the power distribution network by using data analysis and regression calculation methods. The solution model of state estimation and parameter estimation is essentially a nonlinear data regression problem. State estimation needs to recover the true state of the system from the measurements containing errors. The purpose of parameter estimation is to back-calculate the system parameter values from the measured electrical quantities.

[0004] Existing researches mostly only focus on the independent solution of state estimation model and parameter estimation model, but do not consider the mutual influence relationship between them. When solving the state, the parameters of the system will affect the final calculation result, and when solving the parameters, whether the state data is accurate will also affect the estimation effect of the parameters. This leads to the fact that the mutual dependence of parameter and state estimation is not fully considered, which to some extent limits the accuracy and practicability of the estimation model. SUMMARY

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

[0006] In a first aspect, the present application provides a power distribution network state parameter joint estimation method based on double extended Kalman filtering, comprising:

[0007] Obtaining variable data from the initial topology and line parameters of the power distribution network, wherein the variable data includes state variables, parameter variables and measurement variables;

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

[0009] The state prior estimation and its covariance and the parameter prior estimation and its covariance are determined by using a double extended Kalman filter in combination with the state equation, the parameter equation and the measurement equation respectively;

[0010] The state Kalman gain, the state posterior estimation and its covariance, the parameter Kalman gain and the parameter posterior estimation and its covariance are sequentially determined according to the obtained state prior estimation and its covariance and the parameter prior estimation and its covariance;

[0011] The finally obtained posterior estimation result is taken as a prior estimation value again for solving, and the state error limit value and the parameter error limit value are set, and if the difference between the estimation results of two adjacent times is less than the set limit value at the same time, it is considered that the parameter and the state reach the optimal estimation value at the same time.

[0012] In a possible implementation manner, the variable data is obtained by using the initial topology of the power distribution network and the line parameters, and the variable data includes:

[0013] The voltage amplitude and the voltage phase angle of each node in the power distribution network are selected as the 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] Wherein, u k is a node voltage amplitude vector of the system, i = 1, …, n is a node number of the power distribution network, U i,k denotes a voltage amplitude of the i th node at the k th moment, θ k is a node phase angle vector of the system, and θ i,k denotes a phase angle of the i th node at the k th moment.

[0017] The conductance and the susceptance of the line in the power distribution network are selected as the parameter variables, and a model of the 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] wherein: g k is the conductance 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, part of 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 measurement variable is established as follows:

[0022]

[0023] wherein: and represent the observation values of voltage amplitude and phase angle, and represent the observation values of node injection active and reactive power, and represent the power flowing through the branch, represent the current flowing through the branch.

[0024] In a possible implementation manner, the state equation, the parameter equation and the measurement equation are respectively established according to the variable data, including:

[0025] A quadratic exponential smoothing method is adopted to establish a transition equation describing the change of state variables and parameter variables in time series:

[0026]

[0027] wherein: represents the estimation value of the data sequence at k, when s is a state, s is x, and when s is a parameter, s is w, and represent the prediction values of the sequence at k and k+1; a k is a horizontal component, b k is a tilt component; α k and β k are smoothing parameters;

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

[0029]

[0030] wherein: V (i) k denotes the voltage observation of node i at time k, V (i) k denotes the voltage observation of node i at time k;

[0031] P (i) denotes the injected active power of node i and reactive power Q (i) of node i The relationship between its observation and state value is:

[0032]

[0033] wherein: V (i) denotes the active observation of node i Q (i) denotes the reactive observation of node i; θ ij,k = θ i,k - θ j,k denotes the phase difference between nodes ij; G ij,k and B ij,k are the real part and imaginary part of the admittance matrix at the ij position element of the node, respectively;

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

[0035]

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

[0037] For the branch power flowing out of node i to node j, the relationship between its state value and observation value is as follows: and reactive power Q (i) of node i

[0038] When estimating the parameters of the line, the independent variables in the measurement equation are converted from the state to the parameter, and the G ij,k and B ij,k in the node admittance matrix are:

[0039]

[0040]

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

[0042] The node injection power measurement equation is converted into an equation about the parameter variable:

[0043]

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

[0045]

[0046] In a possible implementation, the state prior estimation and covariance thereof and the parameter prior estimation and covariance thereof are respectively determined by using the double extended Kalman filter in combination with the state equation, the parameter equation and the measurement equation, comprising:

[0047] The state-parameter-measurement observation equation of nonlinear relationship is established:

[0048]

[0049] Wherein: 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 errors of the three types of variables respectively; F, R, H are linear or nonlinear equations;

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

[0051] In each control period, the two Kalman filters each perform an operation, the state Kalman filter uses the estimated value of the parameter Kalman filter in the last period when operating, the parameter filter uses the estimated value of the state filter in the last period when operating, and the observation equation is linearized through the combination of the two Kalman filters.

[0052] In a possible implementation, the observation equation is linearized through the combination of the two Kalman filters, comprising:

[0053] The state prediction link uses the state variable of the posterior estimation at k-1 time The prior estimation state at k time is predicted, and the prior estimation of the state variable is:

[0054]

[0055] Wherein, F sk represents the state transition matrix, h sk represents the state external term, F sk and h sk are:

[0056] F sk =α sk (1+β sk )I

[0057]

[0058] where I is the identity matrix;

[0059] After obtaining the prior estimate of state variable, the prior state error covariance matrix is updated as:

[0060]

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

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

[0063]

[0064] R wk = a wk (1 + b wk )I

[0065]

[0066] where is the prior estimate of parameter at time k; is the posterior estimate of parameter at time k-1; R wk and d wk are the parameter transition matrix and the parameter exogenous term;

[0067] The prior parameter error covariance is then updated as:

[0068]

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

[0070] The observation equation of state filter is first linearized. The nonlinear observation equation is Taylor expanded at the prior estimate of state and the quadratic and higher order terms are ignored, obtaining the linearized model of the observation equation of state:

[0071]

[0072] where H zs,k is the linearization matrix of the measurement function with respect to the state variable. When the measurement variable and the state variable are linearly related, H zs,kThe corresponding element is 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 linearization of the nonlinear measurement equation is completed, and the linearized measurement matrix H is obtained zs,k The admittance parameters of each branch are all substituted into the parameter prior estimation value at time k Each voltage amplitude and phase angle is substituted into the state prior estimation value at time k

[0074] In a possible implementation, H zs,k The specific elements in the matrix are as follows:

[0075] H uu,k , H uθ,k , H θu,k and H θθ,k are the coefficient matrices between the voltage amplitude and phase angle measurement variables and the state variables, and are as follows:

[0076]

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

[0078]

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

[0080]

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

[0082]

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

[0084]

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

[0086]

[0087] In a possible implementation, the state Kalman gain and the state posterior estimate are determined, comprising:

[0088] The H zs,k The state Kalman gain is determined, comprising:

[0089]

[0090] wherein 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, the posterior estimate of the state and its corresponding error covariance matrix are calculated:

[0092]

[0093] wherein represents the posterior estimate of the state variable, P sk represents the posterior error covariance matrix of the state variable;

[0094] Then, the voltage amplitude and phase angle of the posterior state estimate are taken as fixed values, and the posterior estimate of the parameter variable is solved.

[0095] In a possible implementation, when the parameter Kalman gain is calculated, the state variable in the measurement equation is taken as the state posterior estimate At this time, the state is a known value, and the measurement equation is converted into a linear equation about the parameter variable w. The linearized parameter measurement equation is as follows:

[0096]

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

[0098] The specific forms of the submatrices are as follows:

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

[0100]

[0101] wherein [H i,k , g ij,kA simplified representation of a matrix in which each element is P i,k and g ij,k The corresponding position elements between P

[0102]

[0103] and is the linear coefficient of the branch admittance to the active power measurement variable flowing through the branch:

[0104]

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

[0106]

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

[0108]

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

[0110]

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

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

[0113] Determining the Kalman gain formula for calculating the parameter variable:

[0114]

[0115] where 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 observation;

[0116] After obtaining the parameter Kalman gain, the posterior parameter estimation at time k and its corresponding error covariance matrix are calculated as follows:

[0117]

[0118] wherein, is the posteriori estimation of the parameter variable, P wk is the posteriori error covariance matrix of the parameter variable.

[0119] In a possible implementation, the final obtained posteriori estimation result is solved again as a priori estimation value, and a state error limit value and a parameter error limit value are set, and if the difference between the estimation results of two adjacent times is less than the set limit value at the same time, it is considered that the parameter and the state reach the optimal estimation value at the same time, comprising:

[0120] Let the state error limit value be δ sk , and the parameter error limit value be δ wk , and when the solved state and parameter satisfy the following conditions at the same time:

[0121]

[0122] wherein, and respectively represent the priori estimation and the posteriori estimation of the state variable calculated through the measurement equation in the iteration process; and represent the priori estimation and the posteriori estimation of the parameter variable between two iterations; Mean() represents the average of each variable;

[0123] If the average of the difference between the two variables is not less than the state error limit value and the parameter error limit value at the same time, it is considered that the estimation result is not optimal, and at this time, the posteriori estimation value is replaced by the priori estimation value, and the next iteration is continued until the limit value requirement is met.

[0124] In the embodiments of the present application, by introducing the double extended Kalman filter, the influence of parameter variation on the state estimation result and the influence of state deviation on the parameter estimation result are effectively avoided. The state-parameter iterative estimation model is constructed by the priori estimation of the two lines, which converts the traditional state and parameter segmentation model into a unified estimation model. The state estimation model and the parameter estimation model of the distribution network are jointly solved to solve the problem that the estimation accuracy is limited due to the independence of the models in the traditional method. Thus, the real-time and accurate estimation of the operation state and the parameter of the distribution network is realized, and the observability of the distribution network is more comprehensively improved, thereby providing strong data support for fault diagnosis and operation optimization. BRIEF DESCRIPTION OF DRAWINGS

[0125] Figure 1 is a flowchart of a distribution network state parameter joint estimation method based on double extended Kalman filtering provided by the embodiments of the present application. DETAILED DESCRIPTION

[0126] The scheme is described below in combination with the accompanying drawings and specific embodiments.

[0127] Referring to Figure 1 The power distribution network state parameter joint estimation method based on double extended Kalman filtering provided by the embodiment includes:

[0128] S101, obtain variable data through the initial topology and line parameters of the power 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 power distribution system are selected as the state variables. When all the state variables are known, the system is considered observable. The state variables of the model are as follows:

[0130]

[0131] Among them, u k is the node voltage amplitude vector of the system, assuming that the node number of the power distribution network is 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, and θ i,k represents the phase angle of the i-th node at the k-th moment.

[0132] The parameter variable refers to the structure parameter of the power distribution network. Assuming that the topology of the power distribution network is known, the parameters to be estimated are the impedance or admittance of the line at this time. The accurate acquisition of these parameters will affect the state estimation of the power distribution network, and at the same time, the accurate state estimation result will also improve the parameter identification accuracy of the power distribution network. The parameter variables established by the model are as follows:

[0133]

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

[0135] The measurement variable refers to the electrical quantity value measured by various data acquisition devices in the power distribution network, which usually includes all voltage amplitudes, part of voltage phase angles, node injected power, branch power, branch current, etc. The measurement matrix is as follows:

[0136]

[0137] Among them, and represent the observed values of the voltage amplitude and phase angle, and denote the observed value of active and reactive power injected at node, and denote the power flowing through branch, denote the current flowing through branch.

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

[0139] The transfer equation of state and parameter is used to describe the change mode of them in time series, in which the physical characteristics of state and parameter can be ignored, and only the mathematical characteristics are reserved. Therefore, the same type of equation can be used for the construction of the transfer equation. The quadratic exponential smoothing method is usually used to establish the transfer equation, which considers the trend of data, and its basic equation is:

[0140]

[0141] wherein, denote the estimated value of data sequence at k, when s is state, s is x, and when s is parameter, s is w, and denote the predicted value of sequence at k and k+1; a k is the horizontal component, b k is the tilt component; α k and β k are smoothing parameters.

[0142] The measurement equation generally refers to the relationship between the measurement variables, state variables. In this study, parameter variables are added to the model, so the relationship between the measurement variables, state variables and parameter variables.

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

[0144]

[0145] wherein, denote the voltage observation of node i at k; denote the voltage observation of node i at k. It should be noted that in the distribution network, measurement equipment for voltage amplitude is installed at almost every node, but not every node measurement equipment has the function of measuring voltage phase angle. But even if part of the phase angle is known, the measurement equation established according to the other electrical quantities collected is redundant, so the phase angle state can still be estimated.

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

[0147]

[0148] where, represents the active observation of node i; represents the reactive observation of 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 part and imaginary part of the nodal admittance matrix at the ij position element, respectively.

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

[0150]

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

[0152] For the active power and reactive power flowing out of node i to node j, the relationship between its state value and observation value is as follows:

[0153]

[0154] When estimating the parameters of the line, the essence is to convert the independent variables in the measurement equation from the state to the parameter. The G ij,k and B ij,k in the nodal admittance matrix are:

[0155]

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

[0157] The nodal injection power measurement equation can be converted into an equation about the parameter variable, as follows

[0158]

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

[0160]

[0161] As for the power equation of each branch, it is itself a linear equation with respect to the parameter variable, thus no modification is needed.

[0162] S103, respectively determine the state prior estimation and its covariance and the parameter prior estimation and its covariance by using the double extended Kalman filter in combination with the state equation, the parameter equation and the measurement equation.

[0163] The double extended Kalman filter comprises two extended Kalman filters: a state-based extended Kalman filter (EKFx) and a parameter-based extended Kalman filter (EKFw), each of which has two parts: a prediction part and an update part. The double extended Kalman filter works in a sequential manner to achieve simultaneous estimation of parameters and states by using the two extended Kalman filters at each iteration.

[0164] Suppose that the state-parameter-measurement space expression containing a nonlinear relationship is as follows:

[0165]

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

[0167] For the power grid state-parameter joint estimation model, the state equation or the parameter equation established by the quadratic exponential smoothing method is easy to linearize, and the parameter measurement equation is itself a linear equation, but the state measurement equation is a nonlinear equation, thus linearization is needed when calculating.

[0168] The basic idea of DEKF is to combine two EKF together, the state EKF estimates the system state, the parameter EKF estimates the model parameters, and they use the same observation equation. In each control period, the two filters each perform an operation, the state filter uses the estimated value of the parameter filter in the last period when operating, and the parameter filter uses the estimated value of the state filter in the last period when operating, which looks like a simple series connection of the state filter and the parameter filter, but the combination of the two filters changes the linearization process of the observation equation of the parameter filter, which must be linearized using a form similar to recursive learning.

[0169] The state prediction link uses the state variable of the posterior estimation at time k-1 The prior estimation state at time k is predicted, the quadratic exponential smoothing equation established in the last section is used as the state transition equation, and linearization is performed, and the prior estimation of the state variable can be obtained, as follows:

[0170]

[0171] where F sk is the state transition matrix, h sk is the state function, F sk and h sk are:

[0172]

[0173] where I is the identity matrix.

[0174] After obtaining the prior state estimate, the prior state error covariance matrix is updated as:

[0175]

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

[0177] Since the parameter transition equation and the state transition equation are both two-parameter exponential smoothing models, the parameter prediction link is basically the same as the state prediction, and the linearized equations are the same, as follows:

[0178]

[0179] where is the parameter prior estimate at time k; is the parameter posterior estimate at time k-1; R wk and d wk are the parameter transition matrix and the parameter function.

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

[0181]

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

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

[0184]

[0185] where H zs,k is the linearization matrix of the measurement function with respect to the state variables. When the measurement variables are linear with respect to the state variables, H zs,k is the coefficient matrix of the measurement function. When the measurement variables are nonlinear with respect to the state variables, H zs,k is the Jacobian matrix of the measurement function. The specific elements of H

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

[0187]

[0188] and are the Jacobian matrices of the injected real power measurement variables with respect to the voltage magnitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0189]

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

[0191]

[0192] and are the Jacobian matrices of the branch real power measurement variables with respect to the voltage magnitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0193]

[0194] and are the Jacobian matrices of the branch reactive power measurement variables with respect to the voltage magnitude 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 are the Jacobian matrices of the branch current measurement variables with respect to the voltage magnitude and phase angle, where the elements are the partial derivatives between the corresponding variables, as follows:

[0197]

[0198] Thus, the non-linear measurement equation is linearized to obtain the linearized measurement matrix H zs,k .

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

[0200] In the equation of the above Jacobian matrix, the admittance parameters of each branch are substituted into the parameter prior estimate value at time k Each voltage amplitude and phase angle is substituted into the state prior estimate value at time k Through the above information, the state Kalman gain can be calculated according to the following formula:

[0201]

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

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

[0204]

[0205] wherein, represents the posterior estimate of the state variable, P sk represents the posterior error covariance matrix of the state variable. Next, the voltage amplitude and phase angle of the posterior state estimate are taken as fixed values to solve the posterior estimate of the parameter variable.

[0206] In calculating the parameter Kalman gain, the state variable in the measurement equation is the state posterior estimate At this time, the state is a known value, so the measurement equation is converted into a linear equation about the parameter variable w. The linearized parameter measurement equation is as follows:

[0207]

[0208] wherein, H zw,k is the linear coefficient matrix of the measurement function for the parameter variable; according to the formula (13)-(15), the specific form of each sub-matrix is as follows.

[0209] and The linear coefficients of the branch admittance with respect to the active power injection measurement variables are given by

[0210]

[0211] where [H i,k , g ij,k ] is a simplified representation of the matrix, where each element is the corresponding position element between P i,k and g ij,k , and the matrix is represented as follows:

[0212]

[0213] The subsequent matrices are all expressed in this simplified form.

[0214] and The linear coefficients of the branch admittance with respect to the reactive power injection measurement variables are given by

[0215]

[0216] and The linear coefficients of the branch admittance with respect to the active power flow measurement variables are given by

[0217]

[0218] and The linear coefficients of the branch admittance with respect to the reactive power flow measurement variables are given by

[0219]

[0220] H ig,k and H ib,k The linear coefficients of the branch admittance with respect to the current flow measurement variables are given by

[0221]

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

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

[0224]

[0225] where 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 observation.

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

[0227]

[0228] wherein, is the posterior estimation of the parameter variable; P wk is the posterior error covariance matrix of the parameter variable.

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

[0230] Through the above calculation links, the posterior estimation of the distribution network network parameter and the running state can be obtained, but this result cannot be simply taken as the final state or parameter to be solved, because the accuracy and rationality need to be verified. For this purpose, the obtained posterior estimation result is solved again as a prior estimation value, and the state error limit value and the parameter error limit value are set. If the difference between the adjacent two estimation results is less than the limit value at the same time, it can be considered that the parameter and the state reach the optimal estimation value at the same time.

[0231] Let the state error limit value be δ sk , and the parameter error limit value be δ wk , then when the solved state and parameter satisfy the following conditions at the same time:

[0232]

[0233] wherein, and respectively represent the prior estimation and the posterior estimation of the state variable calculated through the measurement equation in the iteration process; and represent the prior estimation and the posterior estimation of the parameter variable between two iterations. Mean() represents the average value of each variable. If the average value of the difference between two variables is not less than the state error limit value and the parameter error limit value at the same time, it is considered that the estimation result is not optimal, and the posterior estimation value is replaced by the prior estimation value at this time, and the next iteration is continued until the limit value requirement is met.

[0234] In the embodiments of the present application, "at least one" refers to one or more, and "multiple" refers to two or two or more. The "and / or" describes the association relationship of the associated objects, which means that there can be three kinds of relationships, for example, A and / or B, which can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Wherein A, B can be singular or plural. The character " / " generally represents that the associated objects before and after are in an "or" relationship. "At least one of the following" and the like means any combination of these items, including any combination of single or multiple items. For example, at least one of a, b and c can represent: a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, c can be single or multiple.

[0235] The above is only a specific embodiment of the present application, and any skilled person in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. The protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A joint estimation method of power distribution network state parameters based on double extended Kalman filter, characterized in that, The method comprises: obtaining variable data through an initial topology and line parameters of the power distribution network, wherein the variable data comprises state variables, parameter variables and measurement variables; the obtaining variable data through an initial topology and line parameters of the power distribution network comprises: selecting voltage amplitude and voltage phase angle of each node in the power distribution network as the state variables, and establishing a model of the state variables: wherein: is a vector of voltage magnitudes of the nodes of the system, i = 1,..., n is a vector of node numbers of the distribution network, denotes the voltage magnitude of the i th node at the k th time instant, is a vector of phase angles of the nodes of the system, denotes the phase angle of the i th node at the k th time instant; selecting conductance and susceptance of the line in the power distribution network as the parameter variables, and establishing a model of the parameter variables: wherein: is the conductance parameter vector of the system at time k t, denotes the conductance parameter of branch ij i; is the susceptance parameter vector of the system at time k t, denotes the susceptance parameter of branch ij i; selecting all voltage amplitudes, part of voltage phase angles, node injected power, branch power and branch current in the line in the power distribution network as the measured electrical quantities, and establishing a model of the measurement variables: wherein: and Vobsdenotes the observed voltage magnitude and phase angle, and PQobsdenotes the observed node injection active and reactive power, and Pbranchdenotes the power flowing through a branch, Ibranchdenotes the current flowing through a branch; establishing state equations, parameter equations and measurement equations according to the variable data; determining state prior estimates and their covariances and parameter prior estimates and their covariances by using double extended Kalman filters in combination with the state equations, the parameter equations and the measurement equations; the determining state prior estimates and their covariances and parameter prior estimates and their covariances by using double extended Kalman filters in combination with the state equations, the parameter equations and the measurement equations comprises: establishing a state-parameter-measurement observation equation of a nonlinear relationship: where: s is a system state variable, F is a state equation; w is a system parameter variable, R is a parameter equation; z is a system measurement variable, H is a measurement equation; v n e are errors of these three types of variables, respectively; F R H is a linear or nonlinear equation;​​​​ combining the two Kalman filters, a state Kalman filter estimates system states, and a parameter Kalman filter estimates model parameters, and the two Kalman filters use the same observation equation; in each control cycle, the two Kalman filters each perform an operation, the state Kalman filter uses the estimated value of the parameter Kalman filter in the last cycle when performing the operation, the parameter Kalman filter uses the estimated value of the state Kalman filter in the last cycle when performing the operation, and the observation equation is linearized through the combination of the two Kalman filters; determining state Kalman gains, state posterior estimates and their covariances, parameter Kalman gains and parameter posterior estimates and their covariances in sequence according to the obtained state prior estimates and their covariances and parameter prior estimates and their covariances; the finally obtained posterior estimate results are used as prior estimate values again for solving, and a state error limit value and a parameter error limit value are set, and if the difference between the estimation results of two adjacent times is less than the set limit value at the same time, it is considered that the parameter and the state reach the optimal estimation value at the same time.

2. The power distribution network state parameter joint estimation method based on double extended Kalman filtering according to claim 1, characterized in that, the establishing state equations, parameter equations and measurement equations according to the variable data comprises: establishing a transition equation describing the change of the state variables and the parameter variables in the time sequence by using a quadratic exponential smoothing method: where: represents the estimated value of the data sequence at k when s is the state, s is x when s is the parameter, s is w , and represent the predicted value of the sequence at k and k +1 time instant; is the horizontal component, is the tilt component; α k and β k is the smoothing parameter; for the node voltage amplitude and the voltage phase angle in the measurement variables, a measurement equation is established: wherein: represents a node i at k a voltage observation at the time instant represents a node i at k a voltage observation at the time instant For a node i injected active power and reactive power whose observed values are related to the state values by wherein: represents the active observation at node i ; represents the reactive observation at node i ; represents the phase difference between nodes ij ; G ij,k and B ij,k are the real and imaginary parts of the admittance matrix at ij position elements, respectively. For a node i The branch current flowing out of the node j The state value of which has the following relationship with the observed value: wherein: and are the conductance and susceptance of the branch ij ​ For a node i The active power j and the reactive power of the branches flowing to the node whose state values are related to the observation values as follows: When estimating the parameters of the line, the independent variables in the measurement equation are transformed from states to parameters, and the node admittance matrix in the state-space formulation is transformed from G ij,k and B ij,k is: wherein G ii,k and B ii,k denotes the self conductance and the self susceptance, j∈r(i) denotes all nodes connected to i the node. the node injected power measurement equation is converted into an equation about the parameter variables: for the measurement equation of the branch current, the square of the current has a linear relationship with the parameter variables, and thus the measurement equation of the current is: 。 3. The dual extended Kalman filter based joint state parameter estimation method for power distribution network according to claim 1, characterized in that, the linearization of the observation equation through the combination of the two Kalman filters comprises: The state prediction block uses k the state variable of the a posteriori estimate at time -1 prediction k The prior estimate of the state at time -1 is given by the state variable wherein F sk denotes a state transition matrix, h sk denotes a state out term, F sk and h sk is: wherein I is the identity matrix; After obtaining the prior estimate of the state variable, the prior state error covariance matrix is updated: wherein is k the state posterior estimation error covariance at time -1; V sk is the state process noise covariance matrix; a linear equation established by a parameter prediction link: wherein is k the parameter prior estimate at time is k the parameter posterior estimate at time R wk and d wk is the parameter transition matrix and is the parameter offset term. then the prior parameter error covariance is updated: wherein is the prior error covariance at time k is the posterior error covariance at time k N wk is the covariance matrix of the process noise of the parameters​​ First, the observation equation of the state Kalman filter is linearized. The nonlinear observation equation is Taylor expanded at the prior estimate of the state and the second and higher order terms are ignored to obtain a linearized model of the observation equation of the state: wherein, is a linearization matrix of the measurement function with respect to the state variable, when the measurement variable and the state variable are in a linear relationship, corresponding elements are its coefficient matrix; when the measurement variable and the state variable are in a nonlinear relationship, the corresponding linearization matrix is its Jacobian matrix; The measurement equation of nonlinearity is linearized to obtain the linearized measurement matrix The admittance parameters of each branch are substituted into k The parameter prior estimate value at time The voltage amplitude and phase angle are substituted into k The state prior estimate value at time ; The specific elements are shown as follows: , , and is a coefficient matrix between the voltage magnitude and phase angle measurement variables and the state variables, denoted as: and Jv = ∂v / ∂x = ∂v / ∂P inj, where the elements of the Jacobian matrix are partial derivatives between corresponding variables as follows: and Jv = ∂v / ∂x where x is the vector of reactive power injection measurement variables, and the elements of Jv are the partial derivatives between corresponding variables as follows: and Jv = ∂V / ∂x where x is the vector of branch active power measurement variables and V is the vector of voltage magnitude and phase angle variables. The elements of Jv are the partial derivatives between corresponding variables as follows: and Jv = ∂V / ∂(V, θ) = [∂V / ∂V ∂V / ∂θ] = [1 0] is the Jacobian matrix of the voltage magnitude and phase angle with respect to the branch reactive power measurement variables, where the elements are the partial derivatives between the corresponding variables as follows: and Jv = ∂v / ∂x = ∂v / ∂x1 ∂v / ∂x2... ∂v / ∂xn is the Jacobian matrix of the voltage magnitude and phase angle with respect to the branch current measurement variables, where the elements are the partial derivatives between the corresponding variables as follows: 。 4. The power distribution network state parameter joint estimation method based on double extended Kalman filter of claim 3, characterized in that, the determining state Kalman gains and state posterior estimates comprises: by the determine the state Kalman gain: wherein, is the state Kalman gain, is the state observation noise covariance matrix; after the state Kalman gains are obtained, the posterior estimates of the state and their corresponding error covariance matrices are calculated: wherein represents a posteriori estimate of the state variable, represents a posteriori error covariance matrix of the state variable; Then the voltage amplitude and phase angle of the posterior state estimation are taken as fixed values to solve the posterior estimation of the parameter variable.

5. The dual extended Kalman filter based joint state parameter estimation method for power distribution network according to claim 4, characterized in that, In computing the parameter Kalman gain, assume the state quantities in the measurement equation are the state posterior estimates , at which point the state is known, the measurement equation is transformed into a linear equation in the parameter variables w , the linearized parameter measurement equation: wherein is the linear coefficient matrix of the measurement function with respect to the parameter variables; The specific form of each sub-matrix is as follows: and The linear coefficient of the branch admittance to the injected active power measurement variable is as follows: wherein A simplified representation of a matrix in which each element is and The corresponding position elements between and are represented by the matrix as follows: and Linear coefficient of the branch admittance to the injected reactive power measurement variable: and linear coefficient of the branch flow through the active power measurement variable on the branch admittance: and Linear coefficient of the branch flow over the reactive power measurement variable to the branch admittance: and Linear coefficient of the branch current flow variable to the branch admittance: In the above matrix, each voltage amplitude and phase angle is substituted as k State posterior estimate at time instant .

6. The dual extended Kalman filter based joint state parameter estimation method for power distribution network according to claim 5, characterized in that, The parameter Kalman gain and the posterior estimation of the parameter and its covariance are determined, including: The formula for calculating the Kalman gain of the parameter variable is determined: in, Kalman gain for parameter variables; For parameters in k The prior error covariance at time t; The noise covariance matrix of the parameter observations; After obtaining the parameter Kalman gain, the posterior parameter estimation at time k and the corresponding error covariance matrix are calculated: wherein is the posterior estimate of the parameter variable, is the posterior error covariance matrix of the parameter variable.

7. The dual extended Kalman filter based joint state parameter estimation method for power distribution network according to claim 1, characterized in that, The finally obtained posterior estimation result is taken as the prior estimation value again to solve, and the state error limit value and the parameter error limit value are set, if the difference between the estimation results of two adjacent times is less than the set limit value at the same time, it is considered that the parameter and the state reach the optimal estimation value at the same time, including: Let the state error limit be delta sk and the parameter error limit be delta wk then when the state and parameter solved simultaneously satisfy the following conditions: wherein and denote the prior and posterior estimates of the state variables calculated by the measurement equation during the iteration process; and denote the prior and posterior estimates of the parameter variables between two iterations; Mean() denotes the average of each variable; If the average value of the difference between the two variables is not less than the state error limit value and the parameter error limit value at the same time, it is considered that the estimation result is not optimal, at this time, the posterior estimation value is replaced by the prior estimation value, and the next iteration is continued until the limit value requirement is met.

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