CN-113886760-B - Robust synchronous phasor measurement estimation method and terminal

CN113886760BCN 113886760 BCN113886760 BCN 113886760BCN-113886760-B

Abstract

The invention discloses an robust synchronous phasor measurement estimation method and a terminal, which are characterized in that a Kalman filtering model of a state variable of a signal to be measured is established; the method comprises the steps of obtaining a first Kalman filtering observation equation of a state variable according to a Kalman filtering model, establishing a state variable prediction function of the state variable, carrying out Kalman gain processing on the state variable prediction function, further establishing a residual function of the state variable prediction function after Kalman gain processing, carrying out linear regression integration on the residual function and the first Kalman filtering observation equation, obtaining a second Kalman filtering observation equation, establishing a loss function, substituting the loss function into the second Kalman filtering observation equation to obtain an iterative expression of the state variable, and finally extracting a predicted value expression of fundamental frequency phasors from the iterative expression. According to the invention, a loss function is introduced into a Kalman filtering observation equation, so that the robust capacity is improved, the estimation process is not interfered by bad data, and the Kalman filtering observation equation has good dynamic characteristics.

Inventors

XU XINJING
YU SHUXIAN
ZHU QI
HUANG XUCHAO
CHEN KAIBAO
Chen Taomin
JIANG HONGXIANG
ZHAO GUOSHENG

Assignees

国网福建省电力有限公司检修分公司

Dates

Publication Date: 20260512
Application Date: 20210922

Claims (10)

1. The robust synchronous phasor measurement estimation method is characterized by comprising the following steps of: S1, establishing a Kalman filtering model of a state variable of a signal to be detected; S2, deducing a first Kalman filtering observation equation of the state variable according to the Kalman filtering model; S3, establishing a state variable prediction function of the state variable, and carrying out Kalman gain processing on the state variable prediction function; S4, establishing a residual function of the state variable prediction function after Kalman gain processing, carrying out linear regression integration on the residual function and the first Kalman filtering observation equation to obtain a second Kalman filtering observation equation, The residual function is expressed as: ; Wherein n represents the time n and e (n) represents the residual function; The expression of linear regression integration is: ; Wherein, the Representing measurement noise; the expression written above as the second Kalman filter observation equation is: L(n)=M(n)X(n)+η(n); Wherein the method comprises the steps of Redefining the residual is: ε(n)=M(n)X(n)-L(n); wherein ε (n) represents the residual error at time n; S5, establishing a loss function, substituting the loss function into the second Kalman filtering observation equation, and obtaining an iterative expression of the state variable; specifically, the expression of the loss function is: ; Wherein δ represents the standard deviation of ε; The objective function defining the loss function is then: J(X(n))=Σρ(ε); Wherein J (X (n)) represents an objective function of the loss function, ρ (epsilon) represents the loss function; The derivative expression derived from it is: ; Then substituting a second Kalman filtering observation equation to obtain: ; s6, extracting a predicted value expression of the fundamental frequency phasor from the iterative expression.
2. The robust synchrophasor measurement estimation method according to claim 1, wherein the step S1 specifically includes: S11, establishing a sine signal expression of the signal to be detected, wherein the sine signal expression is as follows: ; where ω represents the signal rotation angular frequency, t represents the time variable, x (t) represents the sinusoidal signal of the time variable t, Representing the initial phase angle of the signal, and X m represents the amplitude of the signal; S12, carrying out Taylor expansion on the dynamic phasors of the sinusoidal signal expression to obtain a Taylor expansion comprising each derivative of the dynamic phasors, wherein the Taylor expansion is as follows: ; Wherein K represents the order number, (T 0 ) represents the dynamic phasor, (T) represents the K-th derivative of the dynamic phasor, t represents the time variable, τ represents the time difference; S13, according to the Taylor expansion, a recursive formula of each derivative of the dynamic phasor in a matrix form and a time domain signal expression of the dynamic phasor at the current moment are obtained, wherein the recursive formula is as follows: P K (t)=Φ K (τ)P K (t 0 ); Wherein P K (t) represents the column phasor composed of the dynamic phasor and its derivatives, Φ K (τ) is the first state transition matrix, Φ K (τ) R (K+1)×(K+1) ; The first state transition matrix is: ; the time domain signal expression is: S K (t)=Re{h T P K (t)e j2πft }; Wherein S K (t) represents a time domain signal, h T represents [ 10..once., 0] T , namely, taking a vector value corresponding to the fundamental frequency phasor; S14, calculating a discrete state space equation of the state variable according to the recursion formula and the time domain signal expression, wherein the expression of the discrete state space equation is as follows: X(n)=AX(n-1); Wherein X (n) represents a state variable, A represents a second state transition matrix, A R 2M(K+1)×2M(K+1) ; The expression of the state variable is: X(n)=[x 1K (n),x 2K (n),……x mK (n)] T R 2M(K+1)×1 ; Wherein m is [0,1,2. ], X mK (n) has the expression: ; Wherein r 1K (n) and A rotation vector and a conjugate vector respectively representing the state variables; The expression of the second state transition matrix is: ; Wherein, the The expression of (2) is: ; wherein, ψ mK (τ) and Respectively representing and complex conjugate vectors thereof; S15, establishing the Kalman filtering model according to the discrete state space equation.
3. The robust synchrophasor measurement estimation method according to claim 2, wherein the step S14 further comprises: adding state noise in the discrete state space equation; the expression of the discrete state space equation after adding the state noise is: X(n)=AX(n-1)+Γv(n); Wherein Γ= [ H ] 1K ,H 2K ,……H mK ] T R 2M(K+1)×1 , v (n) represents the state noise, H mK = [ H, ] T =[1,0 1×K ,1 1×K ,0] T ; The state noise is zero when the discrete state space equation represents a non-fundamental component.
4. The robust synchrophasor measurement estimation method according to claim 2, wherein after the step S6, further comprises: s7, substituting the pre-estimated value expression into the Taylor expansion, and calculating the pre-estimated value of the fundamental frequency phasor at the preset moment.
5. The robust synchrophasor measurement estimation method according to claim 2, wherein the performing kalman gain processing on the state variable prediction function is specifically: establishing a covariance prediction function of the state variable; updating a Kalman gain coefficient of the Kalman filtering model according to the covariance prediction function; and updating the state variable prediction function through the updated Kalman gain coefficient.
6. A robust synchrophasor measurement estimation terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the following steps when executing the program: S1, establishing a Kalman filtering model of a state variable of a signal to be detected; S2, deducing a first Kalman filtering observation equation of the state variable according to the Kalman filtering model; S3, establishing a state variable prediction function of the state variable, and carrying out Kalman gain processing on the state variable prediction function; S4, establishing a residual function of the state variable prediction function after Kalman gain processing, carrying out linear regression integration on the residual function and the first Kalman filtering observation equation to obtain a second Kalman filtering observation equation, The residual function is expressed as: ; Wherein n represents the time n and e (n) represents the residual function; The expression of linear regression integration is: ; Wherein, the Representing measurement noise; the expression written above as the second Kalman filter observation equation is: L(n)=M(n)X(n)+η(n); Wherein the method comprises the steps of Redefining the residual is: ε(n)=M(n)X(n)-L(n); wherein ε (n) represents the residual error at time n; S5, establishing a loss function, substituting the loss function into the second Kalman filtering observation equation, and obtaining an iterative expression of the state variable; specifically, the expression of the loss function is: ; Wherein δ represents the standard deviation of ε; The objective function defining the loss function is then: J(X(n))=Σρ(ε); Wherein J (X (n)) represents an objective function of the loss function, ρ (epsilon) represents the loss function; The derivative expression derived from it is: ; Then substituting a second Kalman filtering observation equation to obtain: ; s6, extracting a predicted value expression of the fundamental frequency phasor from the iterative expression.
7. The robust synchrophasor measurement estimation terminal according to claim 6, wherein the step S1 specifically comprises: S11, establishing a sine signal expression of the signal to be detected, wherein the sine signal expression is as follows: ; where ω represents the signal rotation angular frequency, t represents the time variable, x (t) represents the sinusoidal signal of the time variable t, Representing the initial phase angle of the signal, and X m represents the amplitude of the signal; S12, carrying out Taylor expansion on the dynamic phasors of the sinusoidal signal expression to obtain a Taylor expansion comprising each derivative of the dynamic phasors, wherein the Taylor expansion is as follows: ; Wherein K represents the order number, (T 0 ) represents the dynamic phasor, (T) represents the K-th derivative of the dynamic phasor, t represents the time variable, τ represents the time difference; S13, according to the Taylor expansion, a recursive formula of each derivative of the dynamic phasor in a matrix form and a time domain signal expression of the dynamic phasor at the current moment are obtained, wherein the recursive formula is as follows: P K (t)=Φ K (τ)P K (t 0 ); Wherein P K (t) represents the column phasor composed of the dynamic phasor and its derivatives, Φ K (τ) is the first state transition matrix, Φ K (τ) R (K+1)×(K+1) ; The first state transition matrix is: ; the time domain signal expression is: S K (t)=Re{h T P K (t)e j2πft }; Wherein S K (t) represents a time domain signal, h T represents [ 10..once., 0] T , namely, taking a vector value corresponding to the fundamental frequency phasor; S14, calculating a discrete state space equation of the state variable according to the recursion formula and the time domain signal expression, wherein the expression of the discrete state space equation is as follows: X(n)=AX(n-1); Wherein X (n) represents a state variable, A represents a second state transition matrix, A R 2M(K+1)×2M(K+1) ; The expression of the state variable is: X(n)=[x 1K (n),x 2K (n),……x mK (n)] T R 2M(K+1)×1 ; Wherein m is [0,1,2. ], X mK (n) has the expression: ; Wherein r 1K (n) and A rotation vector and a conjugate vector respectively representing the state variables; The expression of the second state transition matrix is: ; Wherein, the The expression of (2) is: ; wherein, ψ mK (τ) and Respectively representing the rotation transfer matrix and complex conjugate vectors thereof; S15, establishing the Kalman filtering model according to the discrete state space equation.
8. The robust synchrophasor measurement estimation terminal according to claim 7, wherein said step S14 further comprises: adding state noise in the discrete state space equation; the expression of the discrete state space equation after adding the state noise is: X(n)=AX(n-1)+Γv(n); Wherein Γ= [ H ] 1K ,H 2K ,……H mK ] T R 2M(K+1)×1 , v (n) represents the state noise, H mK = [ H, ] T =[1,0 1×K ,1 1×K ,0] T ; The state noise is zero when the discrete state space equation represents a non-fundamental component.
9. The robust synchrophasor measurement estimation terminal according to claim 7, further comprising, after said step S6: s7, substituting the pre-estimated value expression into the Taylor expansion, and calculating the pre-estimated value of the fundamental frequency phasor at the preset moment.
10. The robust synchrophasor measurement estimation terminal according to claim 7, wherein the performing kalman gain processing on the state variable prediction function is specifically: establishing a covariance prediction function of the state variable; updating a Kalman gain coefficient of the Kalman filtering model according to the covariance prediction function; and updating the state variable prediction function through the updated Kalman gain coefficient.

Description

Robust synchronous phasor measurement estimation method and terminal Technical Field The invention relates to the field of power equipment, in particular to an robust synchronous phasor measurement estimation method and a terminal. Background Along with the present, synchronous phasor measurement technology is mainly researched by a power transmission network, and is most classical as a discrete fourier transform (DiscreteFourierTransform, DFT) algorithm for distinguishing the requirements of accuracy and response speed of phasor measurement. The algorithm has the advantages of clear principle, simple realization and small calculation amount, and is favored by researchers for a long time. However, the classical DFT algorithm can only effectively filter out harmonic interference, cannot function for inter-harmonics, and can generate leakage errors due to asynchronous sampling when the system frequency is shifted. In order to improve the performance of the DFT algorithm, researchers have made various improvements, such as adaptive sampling of the frequency of the tracking system, windowing of the signal, interpolation of sampling points, and compensation of frequency offset error, and although the measurement accuracy of the synchrophasor is improved to some extent, there is still room for improvement in terms of multi-harmonic/inter-harmonic suppression. In order to improve the synchronicity of synchrophasor measurement, an algorithm based on the principle of linear kalman filter or nonlinear extended kalman filter (ExtendedKalmanfilter, EKF) is used to improve the real-time performance of phasor estimation, and the algorithm can rapidly and efficiently calculate the phasor value at the current moment based on a recursive manner, but has to be improved in the aspects of coping with multi-harmonic/inter-harmonic interference, rapid response of phasor parameter mutation and the like. Several documents propose a phasor algorithm based on taylor series fourier transform, and the algorithm realizes effective tracking of a signal dynamic process by performing taylor series approximation on a fundamental frequency signal. However, if the measured signal only contains a fundamental frequency component and the frequency of the signal is known, and if the measured signal has a large frequency offset or contains a large number of harmonic components and inter-harmonic components, the established signal model does not match the actual signal, which will cause a significant increase in the phasor estimation error. Disclosure of Invention The invention aims to solve the technical problem of improving the accuracy of synchronous phasor measurement by using an robust synchronous phasor measurement estimation method and a terminal. In order to solve the problems, the invention adopts the following scheme: the robust synchronous phasor measurement estimation method comprises the following steps: S1, establishing a Kalman filtering model of a state variable of a signal to be detected; S2, deducing a first Kalman filtering observation equation of the state variable according to the Kalman filtering model; S3, establishing a state variable prediction function of the state variable, and carrying out Kalman gain processing on the state variable prediction function; s4, establishing a residual function of the state variable prediction function after Kalman gain processing, and performing linear regression integration on the residual function and the first Kalman filtering observation equation to obtain a second Kalman filtering observation equation; S5, establishing a loss function, substituting the loss function into the second Kalman filtering observation equation, and obtaining an iterative expression of the state variable; s6, extracting a predicted value expression of the fundamental frequency phasor from the iterative expression. In order to solve the above problems, another scheme adopted by the invention is as follows: An robust synchrophasor measurement estimation terminal comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the following steps when executing the program: S1, establishing a Kalman filtering model of a state variable of a signal to be detected; S2, deducing a first Kalman filtering observation equation of the state variable according to the Kalman filtering model; S3, establishing a state variable prediction function of the state variable, and carrying out Kalman gain processing on the state variable prediction function; s4, establishing a residual function of the state variable prediction function after Kalman gain processing, and performing linear regression integration on the residual function and the first Kalman filtering observation equation to obtain a second Kalman filtering observation equation; S5, establishing a loss function, substituting the loss function into the second Kalman filtering observation equation, an