Robust synchrophasor measurement estimation method and terminal
By using a Kalman filter model and Taylor series expansion, combined with residual functions and loss functions, the accuracy problem of synchronous phasor measurement under multi-harmonic/interharmonic interference and frequency shift was solved, and high-precision synchronous phasor estimation was achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- MAINTENANCE BRANCH OF STATE GRID FUJIAN ELECTRIC POWER
- Filing Date
- 2021-09-22
- Publication Date
- 2026-05-12
AI Technical Summary
Existing synchronous phasor measurement techniques are insufficient in accuracy and response speed when faced with multi-harmonic/interharmonic interference and frequency shifts, resulting in a significant increase in phasor estimation errors.
A Kalman filter model combined with Taylor series expansion is used to establish a Kalman filter model for state variables. By processing Kalman gain and integrating residual functions, a second Kalman filter observation equation is constructed, and a loss function is introduced to improve the robustness of the prediction expression.
It improves the accuracy and dynamic characteristics of synchronous phasor measurement, reduces interference from bad data, and enables effective tracking and accurate measurement of dynamic changes in signals.
Smart Images
Figure CN113886760B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power equipment, and in particular to a robust synchronous phasor measurement estimation method and terminal. Background Technology
[0002] Currently, most research on synchronous phasor measurement technology focuses on power transmission networks. To differentiate between the accuracy and response speed requirements of phasor measurements, the most classic algorithm is the Discrete Fourier Transform (DFT). This algorithm has the advantages of clear principles, simple implementation, and low computational cost, making it a long-standing favorite among researchers. However, the classic DFT algorithm can only effectively filter out harmonic interference, failing to address interharmonics. Furthermore, leakage errors occur when the system frequency shifts due to asynchronous sampling. To improve the performance of the DFT algorithm, researchers have implemented various improvements, such as adaptive sampling to track the system frequency, signal windowing, sampling point interpolation, and frequency offset error compensation. While these improvements have enhanced the accuracy of synchronous phasor measurements to some extent, there is still room for improvement in multiharmonic / interharmonic suppression.
[0003] To improve the synchronization of phasor measurements, algorithms based on linear Kalman filtering or nonlinear extended Kalman filtering (EKF) principles have been used to improve the real-time performance of phasor estimation. These algorithms can quickly and efficiently calculate the phasor value at the current moment using a recursive approach. However, improvements are needed in handling multi-harmonic / interharmonic interference and responding quickly to sudden changes in phasor parameters. Many publications have proposed a phasor algorithm based on Taylor series Fourier transform. This algorithm effectively tracks the dynamic process of the signal by approximating the fundamental frequency signal using a Taylor series. However, it assumes that the measured signal contains only the fundamental frequency component and that the signal frequency is known. When the measured signal exhibits a large frequency shift or contains a large number of harmonic and interharmonic components, the established signal model does not match the actual signal, leading to a significant increase in phasor estimation error. Summary of the Invention
[0004] The technical problem to be solved by the present invention is: a robust synchronous phasor measurement estimation method and terminal to improve the accuracy of synchronous phasor measurement.
[0005] To solve the above problems, the present invention adopts the following solution:
[0006] A robust synchronous phasor measurement estimation method includes the following steps:
[0007] S1. Establish a Kalman filter model for the state variables of the signal to be measured;
[0008] S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model;
[0009] S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function;
[0010] S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation.
[0011] S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable;
[0012] S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
[0013] To solve the above problems, another solution adopted by the present invention is as follows:
[0014] A robust synchronous phasor measurement estimation terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it performs the following steps:
[0015] S1. Establish a Kalman filter model for the state variables of the signal to be measured;
[0016] S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model;
[0017] S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function;
[0018] S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation.
[0019] S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable;
[0020] S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
[0021] In summary, the beneficial effects of this invention are as follows: It provides a robust synchronous phasor measurement estimation method and terminal. Based on the establishment of a Kalman filter model of the signal to be measured, a second Kalman filter observation equation is constructed by combining the residual function and introducing a loss function to greatly improve the robustness of the prediction expression. This makes the measurement estimation process unaffected by bad data, improves the accuracy of the measurement estimation, and has good dynamic characteristics. Attached Figure Description
[0022] Figure 1 This is a schematic diagram illustrating the steps of a robust synchronous phasor measurement estimation method according to an embodiment of the present invention;
[0023] Figure 2 This is a system block diagram of a robust synchronous phasor measurement estimation terminal according to an embodiment of the present invention.
[0024] Label Explanation:
[0025] 1. A robust synchronous phasor measurement estimation terminal; 2. Memory; 3. Processor. Detailed Implementation
[0026] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.
[0027] Please refer to Figure 1 A robust synchronous phasor measurement estimation method includes the following steps:
[0028] S1. Establish a Kalman filter model for the state variables of the signal to be measured;
[0029] S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model;
[0030] S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function;
[0031] S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation.
[0032] S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable;
[0033] S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
[0034] As can be seen from the above description, the beneficial effects of the present invention are as follows: It provides a robust synchronous phasor measurement estimation method. Based on the establishment of the Kalman filter model of the signal to be measured, it constructs a second Kalman filter observation equation by combining the residual function and introduces a loss function to greatly improve the robustness of the prediction expression, so that the estimation process is not affected by bad data, improves the accuracy of measurement estimation, and has good dynamic characteristics.
[0035] Further, step S1 specifically includes:
[0036] S11. Establish the sinusoidal signal expression for the signal to be measured, wherein the sinusoidal signal expression is:
[0037]
[0038] Where ω represents the signal rotation angular frequency, and t represents the time variable. X represents the initial phase angle of the signal. m Represents the signal amplitude;
[0039] S12. Perform a Taylor expansion on the dynamic phasor of the sinusoidal signal expression to obtain a Taylor expansion that includes the derivatives of the dynamic phasor. The Taylor expansion is as follows:
[0040]
[0041] Where K represents the order, p K (t0) represents the dynamic phasor. The Kth derivative of the dynamic phasor is represented by t, which represents the time variable, and τ represents the time difference.
[0042] S13. Based on the Taylor expansion, obtain the recursive formulas in matrix form for the derivatives of the dynamic phasor and the time-domain signal expression of the dynamic phasor at the current moment. The recursive formulas are as follows:
[0043] p K (t)=Φ K (τ)P K (t0);
[0044] Among them, 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) ;
[0045] The first state transition matrix is:
[0046]
[0047] The time-domain signal expression is:
[0048] S K (t)=Re{h T P K (t)e j2πft};
[0049] Among them, h T Represents [10……0] T That is, take the vector value corresponding to the fundamental frequency phasor;
[0050] S14. Calculate the discrete state-space equation of the state variable based on the recursive formula and the time-domain signal expression. The expression of the discrete state-space equation is:
[0051] X(n) = AX(n-1);
[0052] Where X(n) represents the state variables, A represents the second state transition matrix, and A∈R 2M(K+1)×2M(K+1) ;
[0053] The expression for the state variable is:
[0054] X(n)=[x 1K (n), x 2K (n), ..., x mK (n)] T ∈R 2M(K+1)×1 ;
[0055] Where, m∈[0,1,2……], x mK The expression for (n) is:
[0056]
[0057] Where, r 1K (n) and These represent the rotation vector and its conjugate vector of the state variable, respectively.
[0058] The expression for the second state transition matrix is:
[0059]
[0060] Among them, Ω mK The expression for (τ) is:
[0061]
[0062] Among them, Ψ mK (τ) and These represent their complex conjugate vectors, respectively;
[0063] S15. Establish the Kalman filter model based on the discrete state-space equation.
[0064] As can be seen from the above description, by performing Taylor series approximation on the signal under test, the dynamic change process of the phasor of the signal under test can be effectively tracked, and on this basis, a recursive transformation is performed to establish a Kalman filter model for synchronous phasor measurement.
[0065] Furthermore, step S14 also includes:
[0066] Add state noise to the discrete state-space equations;
[0067] The expression for the discrete state-space equation after adding the aforementioned state noise is:
[0068] X(n) = AX(n-1) + Γv(n);
[0069] Where, Γ=[H 1K H 2K , ...H mK ] T ∈R 2M(K+1)×1 v(n) represents the state noise.
[0070] The state noise is zero when the discrete state-space equation represents the non-fundamental frequency components.
[0071] As can be seen from the above description, adding state noise to the discrete state-space equations effectively reduces the error of the Kalman filter model, making the model more consistent with the actual signal and avoiding the transformation of the recursive process into a deterministic prediction problem.
[0072] Furthermore, after step S6, the method further includes:
[0073] S7. Substitute the estimated value expression into the Taylor expansion to calculate the estimated value of the fundamental frequency phasor at a preset time.
[0074] As can be seen from the above description, the estimation expression calculates the estimated values of some parameters of the signal under test, such as amplitude and frequency, so as to complete the measurement estimation more accurately.
[0075] Furthermore, the Kalman gain processing of the state variable prediction function specifically involves:
[0076] Establish the covariance prediction function for the state variables;
[0077] The Kalman gain coefficients of the Kalman filter model are updated according to the covariance prediction function;
[0078] The state variable prediction function is updated using the updated Kalman gain coefficients.
[0079] As can be seen from the above description, updating the Kalman gain coefficient through the covariance prediction function further updates the state variable prediction function, making the entire prediction system in an optimal state and reducing the measurement prediction error.
[0080] Please refer to Figure 2 A robust synchronous phasor measurement estimation terminal 1 includes a memory 2, a processor 3, and a computer program stored in the memory 2 and executable on the processor 3. When the processor 3 executes the program, it performs the following steps:
[0081] S1. Establish a Kalman filter model for the state variables of the signal to be measured;
[0082] S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model;
[0083] S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function;
[0084] S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation.
[0085] S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable;
[0086] S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
[0087] As can be seen from the above description, the beneficial effects of the present invention are as follows: It provides a robust synchronous phasor measurement estimation terminal, which, based on the establishment of a Kalman filter model of the signal to be measured, constructs a second Kalman filter observation equation by combining the residual function and introduces a loss function, thereby greatly improving the robustness of the estimated value expression, so that the estimation process is not affected by bad data and has good dynamic characteristics.
[0088] Further, step S1 specifically includes:
[0089] S11. Establish the sinusoidal signal expression for the signal to be measured, wherein the sinusoidal signal expression is:
[0090]
[0091] Where ω represents the signal rotation angular frequency, and t represents the time variable. X represents the initial phase angle of the signal. m Represents the signal amplitude;
[0092] S12. Perform a Taylor expansion on the dynamic phasor of the sinusoidal signal expression to obtain a Taylor expansion that includes the derivatives of the dynamic phasor. The Taylor expansion is as follows:
[0093]
[0094] Where K represents the order, P K (t0) represents the dynamic phasor. The Kth derivative of the dynamic phasor is represented by t, which represents the time variable, and τ represents the time difference.
[0095] S13. Based on the Taylor expansion, obtain the recursive formulas in matrix form for the derivatives of the dynamic phasor and the time-domain signal expression of the dynamic phasor at the current moment. The recursive formulas are as follows:
[0096] P K (t)=Φ K (τ)P K (t0);
[0097] Among them, 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) ;
[0098] The first state transition matrix is:
[0099]
[0100] The time-domain signal expression is:
[0101] S K (t)=Re{h T P K (t)e j2πft};
[0102] Among them, h T Represents [10……0] T That is, take the vector value corresponding to the fundamental frequency phasor;
[0103] S14. Calculate the discrete state-space equation of the state variable based on the recursive formula and the time-domain signal expression. The expression of the discrete state-space equation is:
[0104] X(n) = AX(n-1);
[0105] Where X(n) represents the state variables, A represents the second state transition matrix, and A∈R 2M(K+1)×2M(K+1) ;
[0106] The expression for the state variable is:
[0107] X(n)=[x 1K (n), x 2K (n), ..., x mK (n)] T ∈R 2M(K+1)×1 ;
[0108] Where, m∈[0,1,2……], x mK The expression for (n) is:
[0109]
[0110] Where, r 1K (n) and These represent the rotation vector and its conjugate vector of the state variable, respectively.
[0111] The expression for the second state transition matrix is:
[0112]
[0113] Among them, Ω mK The expression for (τ) is:
[0114]
[0115] Among them, Ψ mK (τ) and These represent the rotation transition matrix and its complex conjugate vector, respectively.
[0116] S15. Establish the Kalman filter model based on the discrete state-space equation.
[0117] As can be seen from the above description, by performing Taylor series approximation on the signal under test, the dynamic change process of the phasor of the signal under test can be effectively tracked, and on this basis, a recursive transformation is performed to establish a Kalman filter model for synchronous phasor measurement.
[0118] Furthermore, step S14 also includes:
[0119] Add state noise to the discrete state-space equations;
[0120] The expression for the discrete state-space equation after adding the aforementioned state noise is:
[0121] X(n) = AX(n-1) + Γv(n);
[0122] Where, Γ=[H 1K H 2K , ...H mK ] T ∈R 2M(K+1)×1 v(n) represents the state noise.
[0123] The state noise is zero when the discrete state-space equation represents the non-fundamental frequency components.
[0124] As can be seen from the above description, adding state noise to the discrete state-space equations effectively reduces the error of the Kalman filter model, making the model more consistent with the actual signal and avoiding the transformation of the recursive process into a deterministic prediction problem.
[0125] Furthermore, after step S6, the method further includes:
[0126] S7. Substitute the estimated value expression into the Taylor expansion to calculate the estimated value of the fundamental frequency phasor at a preset time.
[0127] As can be seen from the above description, the estimation expression calculates the estimated values of some parameters of the signal under test, such as amplitude and frequency, so as to complete the measurement estimation more accurately.
[0128] Furthermore, the Kalman gain processing of the state variable prediction function specifically involves:
[0129] Establish the covariance prediction function for the state variables;
[0130] The Kalman gain coefficients of the Kalman filter model are updated according to the covariance prediction function;
[0131] The state variable prediction function is updated using the updated Kalman gain coefficients.
[0132] As can be seen from the above description, updating the Kalman gain coefficient through the covariance prediction function further updates the state variable prediction function, making the entire prediction system in an optimal state and reducing the measurement prediction error.
[0133] Please refer to Figure 1 Embodiment 1 of the present invention is as follows:
[0134] A robust synchronous phasor measurement estimation method, such as Figure 1 As shown, it includes the following steps:
[0135] S1. Establish a Kalman filter model for the state variables of the signal to be measured;
[0136] In this embodiment, the specific process of model establishment is as follows:
[0137] S11. Establish the sinusoidal signal expression for the signal to be measured. The sinusoidal signal expression is as follows:
[0138]
[0139] Where ω represents the signal rotation angular frequency, and t represents the time variable. X represents the initial phase angle of the signal. m Represents the signal amplitude;
[0140] S12. Perform a Taylor expansion on the dynamic phasor of the sinusoidal signal expression to obtain the Taylor expansion containing the derivatives of the dynamic phasor. The Taylor expansion is:
[0141]
[0142] Where K represents the order, P K (t0) represents the dynamic phasor. τ represents the Kth derivative of the dynamic phasor, t represents the time variable, and τ represents the time difference.
[0143] S13. Based on the Taylor expansion, the recursive formulas for the derivatives of the dynamic phasor in matrix form and the time-domain signal expression of the dynamic phasor at the current moment are obtained. The recursive formulas are:
[0144] P K (t)=Φ K (τ)P K (t0);
[0145] Among them, 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) ;
[0146] The first state transition matrix is:
[0147]
[0148] The time-domain signal expression is:
[0149] S K (t)=Re{h T P K (t)e j2πf 1 t};
[0150] Among them, h T Represents [10……0] T That is, take the vector value corresponding to the fundamental frequency phasor, where f1 represents the frequency;
[0151] S14. Calculate the discrete state-space equation of the state variables based on the recursive formula and the time-domain signal expression. The expression of the discrete state-space equation is:
[0152] X(n) = AX(n-1) + Γv(n);
[0153] Where, Γ=[H 1K H 2K , ...H mK ] T ∈R 2M(K+1)×1 v(n) represents the state noise. X(n) represents the state variables, and A represents the second state transition matrix, A∈R 2M(K+1)×2M(K+1) Furthermore, the state noise is zero when the discrete state-space equations represent non-fundamental frequency components.
[0154] The expression for the state variable is:
[0155] X(n)=[x 1K (n), x 2K (n), ..., x mK (n)] T ∈R 2M(K+1)×1 ;
[0156] Where, m∈[0,1,2……], x mK The expression for (n) is:
[0157]
[0158] Where, r 1K (n) and These represent the rotation vector and its conjugate vector of the state variable, respectively;
[0159] The expression for the second state transition matrix is:
[0160]
[0161] Among them, Ω mK The expression for (τ) is:
[0162]
[0163] Among them, Ψ mK (τ) and These represent the rotation transition matrix and its complex conjugate vector, respectively.
[0164] S15. Establish a Kalman filter model based on the discrete state-space equation.
[0165] S2. Derive the first Kalman filter observation equation for the state variables based on the Kalman filter model. The expression for the first Kalman filter observation equation is:
[0166] S mK (n)=Re{Λ T X(n)}=ΘX(n)+ω(n);
[0167] Among them, Λ T =[δ1 T ……δ m T ], δ m T =[1,0,0,0,0,0] T Θ=[θ1 T， θ2 T ……θ mK T ], θ mK T =[0.5, 0 1×K , 0.5, 0 1×K ] T ω(n) represents measurement noise.
[0168] S3. Establish the state variable prediction function for the state variables, and perform Kalman gain processing on the state variable prediction function;
[0169] In this embodiment, it mainly includes two processes: prediction of state variables such as dynamic phasors and their derivatives, and prediction of the covariance matrix during the prediction process.
[0170] First, the expression for the state variable prediction function is:
[0171]
[0172] The expression for the covariance prediction function is:
[0173] P - (n)=AP(n-1)A T +ΓΓ T σ 2 v ;
[0174] in, P represents the predicted value of the state variable at time n. - (n) represents the prediction function of the covariance matrix of the error in the recursive process, σ 2 v The variance of the noise in the spatial state model.
[0175] Then, the Kalman gain coefficients of the Kalman filter model are updated according to the covariance prediction function;
[0176] The updated expression for the Kalman gain coefficient is:
[0177] K(n)=P - (n)Θ T (ΘP - (n)Θ T +σ 2 ω ) -1 ;
[0178] Finally, the state variable prediction function and the covariance matrix prediction function are updated using the updated Kalman gain coefficients;
[0179] The updated expression for the state variable prediction function is:
[0180]
[0181] The updated expression for the covariance prediction function is:
[0182] P(n)=(IK(n)Θ T )P - (n);
[0183] Where K(n) represents the Kalman gain coefficient, I represents the identity matrix, and σ 2 ω The variance of the noise during the measurement process is represented by s(n), and the measurement value at time n is represented by s(n). P(n) represents the updated value of the state variable at time n, and P(n) represents the updated value of the covariance matrix prediction function.
[0184] S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation.
[0185] Specifically, the expression for the residual function is:
[0186]
[0187] The expression for linear regression integration is:
[0188]
[0189] The above equation can be rewritten as the expression for the second Kalman filter observation equation:
[0190] L(n) = M(n)X(n) + η(n);
[0191] in
[0192]
[0193]
[0194]
[0195] Redefine the residual as:
[0196] ε(n) = M(n)X(n) - L(n);
[0197] S5. Establish the loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable;
[0198] Specifically, the expression for the loss function is:
[0199]
[0200] Where δ represents the standard deviation of ε.
[0201] Therefore, the objective function of the loss function is defined as:
[0202] J(X(n))=Σρ(ε);
[0203] It is evident that the loss function is a quadratic function when the error value is small, but becomes a linear function when the error value is large. The derivative expression obtained by taking its derivative is:
[0204]
[0205] Substituting this into the second Kalman filter observation equation, we get:
[0206]
[0207] S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression;
[0208] The estimated value expression is:
[0209]
[0210] Where, matrix E = [I K+1 0 K+1 0 (K+1)×2M(+-1)(K+1) ] is used to extract the fundamental frequency phasor and its derivatives.
[0211] S7. Substitute the estimated value expression into the Taylor expansion to calculate the estimated value of the fundamental frequency phasor at the preset time.
[0212] In this embodiment, the amplitude and phase of the fundamental frequency phasor at the reference point in the Taylor expansion, as well as its first derivative, frequency, and rate of change of frequency, can be calculated using the above formula.
[0213] For example:
[0214] A c =a=2|p|,
[0215] a' = 2Re{p'e -jb},b'=2Im(p'e -jb ) / a0;
[0216] f c =f+b' / 2π,a"=Re{p"e -jb}+2a×b' 2 ;
[0217] ROCOF c =b" / 2π={Im(p"e -jb )-a'×b'} / 2πa;
[0218] Among them, A c , f c and ROCOF c These represent the amplitude, phase, frequency, and rate of change of the calculated fundamental frequency phasor, respectively; p is the fundamental frequency signal phasor; a and b are the symbols for the first derivative.
[0219] Please refer to Figure 2 Embodiment two of the present invention is as follows:
[0220] A robust synchronous phasor measurement estimation terminal 1, such as Figure 2 As shown, it includes a memory 2, a processor 3, and a computer program stored in the memory 2 and capable of running on the processor 3. When the processor 3 executes the program, it implements a robust synchronous phasor measurement estimation method according to Embodiment 1.
[0221] In summary, this invention discloses a robust synchronous phasor measurement estimation method and terminal. It utilizes Taylor series expansion to grasp the dynamic interconnected changes of the signal under test, introduces state noise, and constructs a more accurate Kalman filter model. During state variable prediction and covariance matrix prediction, Kalman coefficient gain is applied to update the predicted system state. A second Kalman filter observation equation is constructed using the residual function, and a loss function with good robustness is introduced to significantly improve the robustness of the predicted expression. This ensures that the measurement estimation process is not affected by poor data, improves the accuracy of the measurement estimation, and exhibits good dynamic characteristics.
[0222] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.
Claims
1. A robust synchronous phasor measurement estimation method, characterized in that, Includes the following steps: S1. Establish a Kalman filter model for the state variables of the signal to be measured; S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model; S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function; S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation. Specifically, The expression for the residual function is: ； Where n represents time n, and e(n) represents the residual function; The expression for linear regression integration is: ； in, Represents measurement noise; The above equation can be rewritten as the expression for the second Kalman filter observation equation: L(n) = M(n)X(n) + η(n); in Redefine the residual as: ε(n) = M(n)X(n) - L(n); Where ε(n) represents the residual at time n; S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable; Specifically, the expression for the loss function is: ； Where δ represents the standard deviation of ε; Therefore, the objective function of the loss function is defined as: J(X(n))=Σρ(ε); Where J(X(n)) represents the objective function of the loss function, and ρ(ε) represents the loss function; The derivative expression obtained by taking its derivative is: ； Substituting this into the second Kalman filter observation equation, we get: ； S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
2. The robust synchronous phasor measurement estimation method according to claim 1, characterized in that, Step S1 specifically involves: S11. Establish the sinusoidal signal expression for the signal to be measured, wherein the sinusoidal signal expression is: ； Where ω represents the signal rotation angular frequency, t represents the time variable, and x(t) represents a sinusoidal signal with time variable t. X represents the initial phase angle of the signal. m Represents the signal amplitude; S12. Perform a Taylor expansion on the dynamic phasor of the sinusoidal signal expression to obtain a Taylor expansion that includes the derivatives of the dynamic phasor. The Taylor expansion is as follows: ； Where K represents the order, (t0) represents the dynamic phasor. (t) represents the Kth derivative of the dynamic phasor, t represents the time variable, and τ represents the time difference; S13. Based on the Taylor expansion, obtain the recursive formulas in matrix form for the derivatives of the dynamic phasor and the time-domain signal expression of the dynamic phasor at the current moment. The recursive formulas are as follows: P K (t)=Φ K (τ)P K (t0); Among them, 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 }; Among them, S K (t) represents the time-domain signal, h T Represents [10……0] T That is, take the vector value corresponding to the fundamental frequency phasor; S14. Calculate the discrete state-space equation of the state variable based on the recursive formula and the time-domain signal expression. The expression of the discrete state-space equation is: X(n) = AX(n-1); Where X(n) represents the state variables, and A represents the second state transition matrix, A R 2M(K+1)×2M(K+1) ; The expression for the state variable is: X(n)=[x 1K (n),x 2K (n),……x mK (n)] T R 2M(K+1)×1 ; Where, m [0, 1, 2...], x mK The expression for (n) is: ； Where, r 1K (n) and These represent the rotation vector and its conjugate vector of the state variable, respectively. The expression for the second state transition matrix is: ； in, The expression is: ； Among them, Ψ mK (τ) and These represent their complex conjugate vectors, respectively; S15. Establish the Kalman filter model based on the discrete state-space equation.
3. The robust synchronous phasor measurement estimation method according to claim 2, characterized in that, Step S14 further includes: Add state noise to the discrete state-space equations; The expression for the discrete state-space equation after adding the aforementioned state noise is: X(n) = AX(n-1) + Γv(n); Where, 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 the non-fundamental frequency components.
4. The robust synchronous phasor measurement estimation method according to claim 2, characterized in that, Following step S6, the following is also included: S7. Substitute the estimated value expression into the Taylor expansion to calculate the estimated value of the fundamental frequency phasor at a preset time.
5. The robust synchronous phasor measurement estimation method according to claim 2, characterized in that, The specific steps of performing Kalman gain processing on the state variable prediction function are as follows: Establish the covariance prediction function for the state variables; The Kalman gain coefficients of the Kalman filter model are updated according to the covariance prediction function; The state variable prediction function is updated using the updated Kalman gain coefficients.
6. A robust synchronous phasor measurement estimation terminal, characterized in that, Includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, performs the following steps: S1. Establish a Kalman filter model for the state variables of the signal to be measured; S2. Derive the first Kalman filter observation equation for the state variable based on the Kalman filter model; S3. Establish the state variable prediction function for the state variable, and perform Kalman gain processing on the state variable prediction function; S4. Establish the residual function of the state variable prediction function after Kalman gain processing, and integrate the residual function and the first Kalman filter observation equation by linear regression to obtain the second Kalman filter observation equation. Specifically, The expression for the residual function is: ； Where n represents time n, and e(n) represents the residual function; The expression for linear regression integration is: ； in, Represents measurement noise; The above equation can be rewritten as the expression for the second Kalman filter observation equation: L(n) = M(n)X(n) + η(n); in Redefine the residual as: ε(n) = M(n)X(n) - L(n); Where ε(n) represents the residual at time n; S5. Establish a loss function, substitute the loss function into the second Kalman filter observation equation, and obtain the iterative expression of the state variable; Specifically, the expression for the loss function is: ； Where δ represents the standard deviation of ε; Therefore, the objective function of the loss function is defined as: J(X(n))=Σρ(ε); Where J(X(n)) represents the objective function of the loss function, and ρ(ε) represents the loss function; The derivative expression obtained by taking its derivative is: ； Substituting this into the second Kalman filter observation equation, we get: ； S6. Extract the estimated value expression of the fundamental frequency phasor from the iterative expression.
7. A robust synchronous phasor measurement estimation terminal according to claim 6, characterized in that, Step S1 specifically involves: S11. Establish the sinusoidal signal expression for the signal to be measured, wherein the sinusoidal signal expression is: ； Where ω represents the signal rotation angular frequency, t represents the time variable, and x(t) represents a sinusoidal signal with time variable t. X represents the initial phase angle of the signal. m Represents the signal amplitude; S12. Perform a Taylor expansion on the dynamic phasor of the sinusoidal signal expression to obtain a Taylor expansion that includes the derivatives of the dynamic phasor. The Taylor expansion is as follows: ； Where K represents the order, (t0) represents the dynamic phasor. (t) represents the Kth derivative of the dynamic phasor, t represents the time variable, and τ represents the time difference; S13. Based on the Taylor expansion, obtain the recursive formulas in matrix form for the derivatives of the dynamic phasor and the time-domain signal expression of the dynamic phasor at the current moment. The recursive formulas are as follows: P K (t)=Φ K (τ)P K (t0); Among them, 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 }; Among them, S K (t) represents the time-domain signal, h T Represents [10……0] T That is, take the vector value corresponding to the fundamental frequency phasor; S14. Calculate the discrete state-space equation of the state variable based on the recursive formula and the time-domain signal expression. The expression of the discrete state-space equation is: X(n) = AX(n-1); Where X(n) represents the state variables, and A represents the second state transition matrix, A R 2M(K+1)×2M(K+1) ; The expression for the state variable is: X(n)=[x 1K (n),x 2K (n),……x mK (n)] T R 2M(K+1)×1 ; Where, m [0, 1, 2...], x mK The expression for (n) is: ； Where, r 1K (n) and These represent the rotation vector and its conjugate vector of the state variable, respectively. The expression for the second state transition matrix is: ； in, The expression is: ； Among them, Ψ mK (τ) and These represent the rotation transition matrix and its complex conjugate vector, respectively. S15. Establish the Kalman filter model based on the discrete state-space equation.
8. A robust synchronous phasor measurement estimation terminal according to claim 7, characterized in that, Step S14 further includes: Add state noise to the discrete state-space equations; The expression for the discrete state-space equation after adding the aforementioned state noise is: X(n) = AX(n-1) + Γv(n); Where, 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 the non-fundamental frequency components.
9. A robust synchronous phasor measurement estimation terminal according to claim 7, characterized in that, Following step S6, the following is also included: S7. Substitute the estimated value expression into the Taylor expansion to calculate the estimated value of the fundamental frequency phasor at a preset time.
10. A robust synchronous phasor measurement estimation terminal according to claim 7, characterized in that, The specific steps of performing Kalman gain processing on the state variable prediction function are as follows: Establish the covariance prediction function for the state variables; The Kalman gain coefficients of the Kalman filter model are updated according to the covariance prediction function; The state variable prediction function is updated using the updated Kalman gain coefficients.