CN-117272208-B - Unscented Kalman filtering state estimation method and attack method based on robust MM estimation

CN117272208BCN 117272208 BCN117272208 BCN 117272208BCN-117272208-B

Abstract

The invention discloses a unscented Kalman filtering dynamic state estimation method based on robust MM estimation, which comprises the following steps of S1, establishing a state estimation model of an electric power system, discretizing the model, initializing a state vector, a covariance matrix, a process noise covariance matrix and a measured noise covariance matrix, transmitting measured data in real time through a phasor measurement unit, S2, linearizing a system measurement function by adopting a statistical linearization method and combining data calculated by unscented Kalman filtering to establish a batch regression equation, S3, carrying out robust pre-whitening treatment on the batch regression equation established in the step S2, S4, dispersing data points in the batch regression equation obtained in the step S3 by adopting a linear transformation method, S5, estimating the state vector by using the MM estimation method for the batch regression equation, and updating the covariance matrix. The method solves the problems that the prior art cannot ensure the estimation performance and can be used for estimating the state of the nonlinear system, and the breakdown point and the estimation efficiency are low.

Inventors

ZHANG ZHENYONG
CHEN GUANGJIA
CHENG PENG
CHEN JIMING

Assignees

贵州大学
浙江大学

Dates

Publication Date: 20260505
Application Date: 20231012

Claims (8)

1. The unscented Kalman filtering dynamic state estimation method based on the robust MM estimation is characterized by comprising the following steps: S1, establishing a power system state estimation model, discretizing the model, initializing a state vector, a covariance matrix, a process noise covariance matrix and a measurement noise covariance matrix, and transmitting measurement data in real time through a phasor measurement unit; s2, linearizing a system measurement function by adopting a statistical linearization method and establishing a batch regression equation by combining data calculated by unscented Kalman filtering; S3, carrying out robust pre-whitening treatment on the batch regression equation established in the step S2; S4, dispersing data points in the batch regression equation obtained in the step S3 through a linear transformation method; S5, estimating a state vector by using a robust MM estimation method for the batch regression equation in the step S4, and updating a covariance matrix; The linear transformation method is to multiply a random number at both ends of a regression equation, wherein the random number is uniformly distributed A random number on the same.
2. The unscented kalman filter dynamic state estimation method based on robust MM estimation according to claim 1, wherein the power system state estimation model in step S1 is: Differential equation: , , , , Algebraic equation: , Wherein, the Representing the frequency of the system and, In order to be a damping coefficient, Is a constant of inertia of the system and, Is the q-axis transient open circuit time constant, Is the d-axis transient open circuit time constant, For the d-axis reactance to be, For the q-axis reactance to be, Is the transient reactance of the d-axis, For the q-axis transient reactance, Is an excitation voltage, Is a terminal voltage, Is a mechanical input torque, Is a rotor angle, For rotor angular velocity and For the active power of the terminal, Representation of The transient voltage on the axis is such that, Representing the transient voltage on the d-axis.
3. The unscented kalman filter dynamic state estimation method based on robust MM estimation according to claim 2, wherein the discretizing the model is performed by using a second-order Long Geda library method, and the discretized state space equation is: , Wherein, the Is the state vector at time k, Is the measurement vector of the data set, Is a control vector, a status vector Comprising rotor angle Angular velocity of rotor And Transient voltage on shaft And Transient voltage on shaft , Is the active power of the terminal and, Comprising exciting voltage Terminal voltage Mechanical input torque , Is the process noise at time k in the state space equation, Is the measurement noise at time k in the state space equation, The mean value is 0 and independent of each other.
4. The method for dynamic state estimation of unscented kalman filter based on robust MM estimation as claimed in claim 3, wherein the method for linearizing the system measurement function using statistical linearization method and creating the batch regression equation with the data calculated by unscented kalman filter comprises the steps of: S2-1 by using State estimation value of time Sum covariance matrix Generating The number of sigma points of the signal, , Wherein, the The state dimension is represented as a number of states, Representation matrix Is the first of (2) The number of columns in a row, Is a complex scale factor that is used to determine the desired level of the sample, And Is a free parameter that controls the sigma point distribution, The value of (2) is related to the dimension of the state vector, the higher the dimension is The smaller the value of (2) is, the range of the value is , Is 2; S2-2, weight is set For each sigma point, passing through a nonlinear function Mapping to generate a set of transformed samples to be written as By weight of And Calculate the first State prior value of time of day A priori covariance matrix , , , Wherein, the Representing the process noise covariance matrix at time k, ; S2-3 according to the first State prior value of time of day A priori covariance matrix A new sigma point is generated and, , S2-4, passing a nonlinear function on the new sigma Mapping to generate a set of transformed samples to be written as Calculating a priori measurement vectors Error covariance matrix Cross covariance matrix , , , , Wherein, the Representing the measurement noise covariance matrix at the kth time, , S2-5, calculating Kalman gain, , S2-6, updating covariance matrix ; ; S2-7, utilizing the sigma point obtained in the step S2-3 And that obtained in step S2-4 For the 2n points , Fitting by using a least square method to obtain a linear approximation function of the k moment measurement function: ; Wherein, the Representing a priori measured vectors at time k, ; S2-8, predicting error according to k moment priori of state vector And A batch regression equation is established and a batch regression equation is established, , Wherein, the Representation of And (5) a dimensional identity matrix.
5. The unscented kalman filter dynamic state estimation method based on robust MM estimation of claim 4, wherein the robust pre-whitening process is performed by: covariance matrix of calculation processing regression equation And for covariance matrix of regression equation Cholesky decomposition was performed: , Multiplying both ends of the batch regression equation by Cholesky decomposition The method comprises the following steps: , Wherein, the , , Error covariance matrix 。
6. The method for unscented kalman filter dynamic state estimation based on robust MM estimation according to claim 5, wherein the method for dispersing the data points in the batch regression equation obtained in step S3 by the linear transformation method in step S4 is as follows: Constructing a regression equation after robust pre-whitening treatment at the moment k: , multiplying both ends of the regression equation simultaneously Obtaining a regression equation after data points at the kth moment are scattered: , Wherein, the Is uniformly distributed A random number on the same.
7. The unscented kalman filter dynamic state estimation method based on robust MM estimation of claim 6, wherein the state vector estimation method is: iterating the state estimation equation using an iteration weighted least squares method, when the j+1st iteration is performed The iteration is stopped, wherein the state estimation equation is: , Wherein, the Is that In the form of a matrix of (a), Weighting function for the jth iteration In the form of a matrix of (a), ; At time k Is a matrix form of (a); And is also provided with ; , Is a robust scale estimate obtained by solving for S estimates, ; As a function of the weight, ; , Wherein the method comprises the steps of Is that In a simplified form of (a) the (c), , , 。
8. A method of attack according to the method of claim 7, characterized in that the method is: From 30 And Respectively select Sum of all And is provided with And Are all less than 15, at each moment The following attacks are injected: , Wherein, the Representing uniform distribution A random number is added to the random number, Representing the generation of a random number vector with a size of 5 rows and 1 column, wherein each element in the vector is a standard normal distributed random number which is independently and uniformly distributed.

Description

Unscented Kalman filtering state estimation method and attack method based on robust MM estimation Technical Field The invention relates to a unscented Kalman filtering state estimation method and an attack method based on robust MM estimation, belonging to the technical field of generator motion state estimation. Background In a power system, a synchronous generator is used as a power generation device and is a core component of the power system, and the real-time change of a power grid and the running state of the power system are both represented in the dynamic variable of the synchronous generator, so that the monitoring of the state variable of the synchronous generator is very important to capture the dynamic change of the power system. However, accurate monitoring and control of synchronous generators presents challenges such as generator model defects, system anomalies, network attacks, etc., and uncertainty from multiple disturbances can lead to power system breakdown, fire and other safety hazards. Therefore, in order to ensure stable operation of the generator, there is an urgent need to solve the observation and control problems caused by these uncertainty factors. Dynamic state estimation of a generator is a common method for eliminating uncertainty of a power system, and research of the dynamic state estimation is of great importance to maintaining stable operation of a power grid. In the dynamic state estimation of the generator, the traditional Kalman filtering algorithm realizes the rapid estimation of the system state through priori prediction, real-time observation and a dynamic model, but has limitations in estimating the nonlinear system state. State estimation using Extended kalman filtering (Extended KALMAN FILTER, EKF) has been proposed, which uses taylor series expansion to linearize the nonlinear system model, but jacobian is computationally expensive and diverges when the model is a strong nonlinear model. There have been studies that propose to use Unscented kalman filtering (Unscented KALMAN FILTER, UKF) for state estimation by approximating the propagation and observation of nonlinear functions using Unscented transformed sampling points, thereby providing a more accurate state estimation. However, the above methods have disadvantages in that (1) observation anomalies cannot be handled and (2) network attacks in which measured data and model parameters are tampered cannot be handled. Disclosure of Invention The invention aims to solve the technical problem of providing a camouflage attack method facing the power market and an elasticity evaluation method for resisting camouflage attack so as to overcome the defects of the prior art. The technical scheme of the invention is as follows: in a first aspect, a unscented Kalman filtering dynamic state estimation method based on robust MM estimation is provided, comprising the steps of: S1, establishing a power system state estimation model, discretizing the model, initializing a state vector, a covariance matrix, a process noise covariance matrix and a measurement noise covariance matrix, and transmitting measurement data in real time through a phasor measurement unit; s2, linearizing a system measurement function by adopting a statistical linearization method and establishing a batch regression equation by combining data calculated by unscented Kalman filtering; S3, carrying out robust pre-whitening treatment on the batch regression equation established in the step S2; S4, dispersing data points in the batch regression equation obtained in the step S3 through a linear transformation method; S5, estimating a state vector by using a robust MM estimation method for the batch regression equation in the step S4, and updating a covariance matrix. Further, in the step S1, the power system state estimation model is: Differential equation: Algebraic equation: Wherein f 0 denotes a system frequency, D is a damping coefficient, J is a system inertia constant, T 'qo is a q-axis transient open-circuit time constant, T' do is a D-axis transient open-circuit time constant, x d is a D-axis reactance, x q is a q-axis reactance, x 'd is a D-axis transient reactance, x' q is a q-axis transient reactance, E fd is an excitation voltage, V t is a terminal voltage, T m is a mechanical input torque, δ is a rotor angle, ω is a rotor angular velocity, and P t is a terminal active power, E 'q denotes a transient voltage on the q-axis, and E' d denotes a transient voltage on the D-axis. Further, the discretizing method of the model is to use a second-order Long Geda library method to discretize the model, and a state space equation after discretization is as follows: Wherein x k＝[δ,ω,e′q,e′d]T is a state vector at k time, z k＝[Pt is a measurement vector, u k＝[Tm,Efd,Vt]T is a control vector, the state vector x k includes a rotor angle δ, a rotor angular velocity ω, a transient voltage E 'd on the d-axis, and a transient voltage E' q,Pt on the q-axis, which are