Synchronous generator dynamic state estimation method based on kernel adaptive maximum correlation entropy CKF

Abstract

The invention discloses a synchronous generator dynamic state estimation method based on kernel adaptive maximum correlation entropy CKF, which is used for coping with generator dynamic state estimation under the condition of non-Gaussian noise or abnormal value, and comprises the following steps: firstly, in the dynamic state estimation process of a generator, calculating the dynamic state of the generator; discretizing a four-order continuous model of the synchronous generator into a discrete state space model, and estimating a one-step predicted value and a state error covariance of a state quantity in a state prediction step; thirdly, introducing a kernel adaptive maximum correlation entropy criterion to dynamically adjust kernel parameters in the filtering process; an MCC criterion with a kernel adaptation strategy is applied to the synchronous generator discrete model. Then, iteratively adjusting a state error covariance matrix through iteration CKF based on L-M, and calculating a state estimation value and a state error covariance of the kth step; finally, in the measurement updating stage of the synchronous generator, the process noise covariance and the measurement noise covariance are updated in a self-adaptive iteration mode based on the innovation residual error between the state quantity and the estimator.

Description

Technical Field

[0001] The invention relates to the field of synchronous generator state monitoring, and in particular to a synchronous generator dynamic state estimation method based on kernel adaptive maximum correlated entropy CKF. Background Art

[0002] The dynamic state estimation of synchronous generators plays a vital role in the safe and stable operation of power systems. DSE technology abandons the shortcomings of static state estimation technology that assumes that the power system is in a static state, and provides a new method for real-time monitoring of the power system state. The Kalman filter method is widely used in communication, navigation, and power fields because of its advantages of easy programming and real-time update and processing of the system. The traditional KF is a filtering method proposed for linear systems and is not suitable for highly nonlinear systems such as synchronous generators. Therefore, many scholars at home and abroad have proposed various variants based on Kalman filtering, such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Cubic Kalman Filter (CKF). However, these filtering methods all assume that the filtering noise is known and basically unchanged, but in practical applications, power systems usually face non-Gaussian noise or innovative outliers. In recent years, in order to solve the adverse effects of non-Gaussian noise and outliers on filtering accuracy, many scholars have begun to try to introduce the Maximum Correntropy Criterion (MCC) into the dynamic state estimation of synchronous generators.

[0003] The generalized maximum correlation entropy UKF was proposed to deal with emergencies such as non-Gaussian noise and load mutation in power systems. G. Wang, B. Cui et al. proposed a robust cubature Kalman filter based on maximum correlation entropy to deal with non-Gaussian noise. Other scholars have proposed a maximum correlation entropy square root cubature Kalman filter based on a new cost function to ensure that the processing of heavy-tailed noise may produce and numerical problems. However, these filtering algorithms do not consider the sensitivity of the maximum correlation entropy criterion to the kernel bandwidth parameter. At the same time, they also do not consider the time-varying characteristics of the noise covariance and the estimation error covariance, which further reduces the filtering performance. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention proposes a dynamic state estimation method for a synchronous generator based on kernel adaptive maximum correlated entropy (CKF). According to the fourth-order model of the synchronous generator, the kernel adaptive MCC criterion is adopted to dynamically track the operating state quantity of the synchronous generator to cope with non-Gaussian noise and outlier interference.

[0005] The method of the present invention is as follows: first, in the process of dynamic state estimation of the generator, the fourth-order continuous model of the synchronous generator is discretized into a discrete state space model, and the one-step prediction value of the state quantity and the state error covariance are estimated in the state prediction step. Next, the kernel adaptive maximum correlation entropy criterion is introduced to dynamically adjust the kernel parameters of the filtering process. The MCC criterion with the kernel adaptive strategy is applied to the synchronous generator discrete model. Then, through the LM-based iterative CKF, the state error covariance matrix is ​​iteratively adjusted to calculate the state estimation value and state error covariance of the kth step. Finally, in the measurement update phase of the synchronous generator, the process noise covariance and the measurement noise covariance are adaptively iteratively updated based on the new information residual between the state quantity and the estimation quantity.

[0006] Specifically, the first aspect of the present invention provides a method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF, comprising the following steps:

[0007] (1) Establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide it into k steps, and select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated;

[0008] (2) In the measurement update phase of the synchronous generator, the kernel adaptive maximum correlation entropy criterion is introduced, and the kernel parameters are dynamically adjusted based on the kernel adaptive strategy of the kernel adaptive maximum correlation entropy criterion; the matrix form of the synchronous generator state estimation discrete model is generated based on the adjusted kernel function, and the state error covariance and measurement noise covariance are iteratively updated;

[0009] (3) In the measurement update phase of the synchronous generator, the state error covariance matrix is ​​iteratively adjusted, the Kalman gain is calculated, the state quantity is iteratively cycled and a specific threshold is set to limit the number of iterations, and the state prediction value and state error covariance of the time step k are calculated through the iterative CKF based on the LM principle;

[0010] (4) In the measurement update phase of the synchronous generator, the process noise covariance and the measurement noise covariance are adaptively iteratively updated based on the new information residual between the state quantity and the estimated quantity and used for the next prediction.

[0011] Based on the above, in step (1), the fourth-order continuous model of the synchronous generator is established as follows:

[0012] For synchronous generators, consider the fourth-order continuous differential equation in the local dq coordinate system:

[0013]

[0014] Where δ is the rotor angle in radians of the generator, ω is the unit rotor speed, ω0=2πf0 is the angular frequency rating, H and K D are the inertia constant and damping coefficient respectively, and the parameter T m and T e are mechanical torque and electrical gap torque respectively, E fd is the internal field voltage, variable e′ d and e′ q are the transient voltages along the local d and q axes, respectively, and the parameter T d ′0 and T q ′0 is the open circuit time constant along the d and q axis directions respectively; x d and x q are the synchronous reactances along the d-axis and q-axis respectively; x′ d and x′ q are the transient reactances related to the d-axis and q-axis respectively; i d and i q are the stator currents in the d-axis and q-axis directions respectively;

[0015] The method of discretizing the fourth-order continuous model of synchronous generator into a discrete state space model is:

[0016] Formula (1) can be simplified as follows:

[0017]

[0018] Among them, c represents the continuous time model, x represents the d and e′ q The state variables composed of c and v c represents process noise and measurement noise, and their covariances are Q k and R k , f c (·) represents the nonlinear state transfer function, h c (·) is the measurement function, u is the input variable, and y is the output variable;

[0019] u=[T m E fd i R i I ] T (3)

[0020] y=[δ ω e R e I ] T (4)

[0021] Discretize a continuous-time model into discrete form:

[0022]

[0023] Where k represents the instantaneous moment of kΔt, Δt represents the sampling interval, and w k and v k They are respectively k and R k process noise and measurement noise;

[0024] The discrete state transfer function is obtained using the improved Euler method:

[0025]

[0026] Measurement function h c (·) is represented as:

[0027] y k =h c (x k ,u k )+v k (9)

[0028] The method for estimating the one-step state prediction value and state error covariance of the state quantity is:

[0029] Setting up the state matrix And the corresponding estimated covariance matrix 2n volume points are generated:

[0030] χ i,k-1 =x k-1 +ξ i S k-1 i=1,2,…,2n (10)

[0031] Among them, S k-1 Indicates P k-1 Perform Cholesky decomposition, χ i,k-1 is the newly generated volume point, ξ i represents the i-th column of the identity matrix with dimension n×n;

[0032] The volume point is calculated through the state transfer function to obtain the state prediction value and state error covariance:

[0033]

[0034]

[0035] In the formula, represents the transformed cubic point, is the state prediction value, P kk-1 is the corresponding state error covariance, and the superscript T represents the matrix transpose operation.

[0036] Based on the above, in step (2), the kernel adaptive strategy of the kernel adaptive maximum correlation entropy criterion is introduced as follows:

[0037] The maximum correlation entropy is a criterion for describing the correlation between two random variables. For any two random variables M and N, the maximum correlation entropy is defined as follows:

[0038] V(M,N)=E[κ(M,N)]=∫κ(m,n)F MN (m,n)dmdn (14)

[0039] Among them, F MN (m,n) is the joint distribution function of M and N, E[·] represents the expected distribution function;

[0040] The Gaussian kernel function is used as the kernel function of the maximum correlation entropy, that is,

[0041]

[0042] Where, σ is the kernel width;

[0043] Due to the unknown nature of the joint distribution function, the mean of the Gaussian kernel function is used to obtain the relevant entropy estimation result:

[0044]

[0045] Based on the pseudo-Huber weight function, the kernel width is adaptively updated:

[0046]

[0047] in, is the residual, ρ is the adjustment factor;

[0048] The matrix form of the synchronous generator state estimation discrete model is generated based on the adjusted kernel function, and the method of iteratively updating the state error covariance and measurement noise covariance is:

[0049]

[0050] in,

[0051] definition

[0052] Multiply both sides of formula (18) by M k -1 have to:

[0053] A=Bx k +ε k

[0054] in, εk =A-Bx k

[0055] According to the Gaussian kernel function, G σ (e)

[0056] κ p =diag{G σ (e1),G σ (e2),…,G σ (e m )} (20)

[0057] κ r =diag{G σ (e m+1 ),G σ (e m+2 ),…,G σ (e n )} (twenty one)

[0058] In the formula, m represents the number of measurements, n = 2m;

[0059] The state error covariance and the measurement noise covariance R k Updated to:

[0060]

[0061] Based on the above, the state error covariance matrix is ​​iteratively adjusted through iterative CKF based on the LM principle:

[0062]

[0063] Where j represents the number of iterations, the damping parameter μ is used to correct the state error covariance matrix, and then the corrected covariance matrix is ​​used for iterative observation update

[0064] Generate a set of volume points based on the prediction step:

[0065]

[0066] After measuring the function, the volume point propagation is:

[0067] Z i,kk-1 =h(χ i,kk-1 ,u k ) i=1,2,…,2n (26)

[0068] Compute the quantity measure means and interaction covariances:

[0069]

[0070] Calculate the Kalman filter gain and state prediction value:

[0071]

[0072]

[0073] When the state quantity satisfies Then the iteration stops, where The state prediction value and state error covariance of the kth step are output as follows:

[0074]

[0075] Based on the above, a sliding window adaptive update Q is designed based on the residual between the quantity measurement and the estimation quantity. k and R k :

[0076]

[0077] Where m is the window length, e i is the residual between the state quantity and the estimated value;

[0078] Then, update the process noise covariance and measurement noise covariance:

[0079]

[0080] A second aspect of the present invention provides a synchronous generator dynamic state estimation system based on kernel adaptive maximum correlation entropy CKF, comprising:

[0081] The first processing module is configured to: establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide k steps, select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated;

[0082] The second processing module is configured to: introduce a kernel adaptive maximum correlation entropy criterion in the measurement update phase of the synchronous generator, dynamically adjust the kernel parameters based on the kernel adaptive strategy of the introduced kernel adaptive maximum correlation entropy criterion; generate a matrix form of a discrete model of the synchronous generator state estimation based on the adjusted kernel function, and then iteratively update the state error covariance and the measurement noise covariance;

[0083] The third processing module is configured to: in the measurement update phase of the synchronous generator, iteratively adjust the state error covariance matrix, calculate the Kalman gain, iteratively cycle the state quantity and set a specific threshold, limit the number of iterations, and calculate the state prediction value and state error covariance of the time k step through iterative CKF based on the LM principle;

[0084] The fourth processing module is configured to: in the measurement update phase of the synchronous generator, adaptively and iteratively update the process noise covariance and the measurement noise covariance based on the innovation residual between the state quantity and the estimation quantity and use them for the next prediction.

[0085] A third aspect of the present invention provides an electronic device, comprising:

[0086] at least one processor, and a memory coupled to the at least one processor;

[0087] The memory stores a computer program, and the computer program can be executed by the at least one processor to implement the synchronous generator dynamic state estimation method based on kernel adaptive maximum correlation entropy CKF as described.

[0088] A fourth aspect of the present invention provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed, the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlated entropy CKF as described above can be implemented.

[0089] A fifth aspect of the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF as described above.

[0090] Compared with the existing synchronous generator dynamic state estimation method, the present invention has the following advantages and technical effects:

[0091] (1) The adaptive updating method of kernel width proposed by the present invention based on pseudo-Huber weight function overcomes the sensitivity of filtering accuracy to kernel width parameter.

[0092] (2) The iterative CKF based on the LM principle in the present invention iteratively adjusts the error covariance matrix, thereby improving the calculation efficiency and filtering accuracy.

[0093] (3) The present invention takes into account the time-varying characteristics of the noise covariance and the estimation error covariance, and adaptively updates the noise covariance and the estimation error covariance, thereby further enhancing the accuracy and robustness of the filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 The figure is a flow chart of the method of the present invention.

[0095] Figure 2 It is the dynamic state estimation result of δ under non-Gaussian noise.

[0096] Figure 3 It is the dynamic state estimation result of ω under non-Gaussian noise.

[0097] Figure 4 e′ is the non-Gaussian noise q Dynamic state estimation results.

[0098] Figure 5 e′ is the non-Gaussian noise d Dynamic state estimation results.

[0099] Figure 6 It is the dynamic state estimation result of δ under outlier disturbance.

[0100] Figure 7 This is the dynamic state estimation result of ω under abnormal value disturbance.

[0101] Figure 8 is e′ under outlier disturbance q Dynamic state estimation results.

[0102] Fig. 9 is e′ under outlier disturbance d Dynamic state estimation results. DETAILED DESCRIPTION

[0103] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0104] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device comprising a series of steps or units is not limited to the listed steps or units, but may include steps or units that are not listed.

[0105] To facilitate understanding of the technical solutions provided by the present application, the technical terms involved in the embodiments of the present application are explained below.

[0106] Example 1

[0107] This embodiment provides a method for estimating the dynamic state of a synchronous generator based on kernel adaptive maximum correlation entropy CKF. Figure 1 As shown, it includes the following steps:

[0108] (1) Establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide it into k steps, and select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated.

[0109] In step (1), the fourth-order continuous model of the synchronous generator is established as:

[0110] For synchronous generators, consider the fourth-order continuous differential equation in the local dq coordinate system:

[0111]

[0112] Where δ is the rotor angle in radians of the generator, ω is the unit rotor speed, ω0=2πf0 is the angular frequency rating, H and K D are the inertia constant and damping coefficient respectively, and the parameter T m and T e are mechanical torque and electrical gap torque respectively, E fd is the internal field voltage, variable e′ d and e′ q are the transient voltages along the local d and q axes, respectively, and the parameter T d ′0 and T q ′0 is the open circuit time constant along the d and q axis directions respectively; x d and x q are the synchronous reactances along the d-axis and q-axis respectively; x′ d and x′ q are the transient reactances related to the d-axis and q-axis respectively; i d and i q are the stator currents in the d-axis and q-axis directions respectively.

[0113] The method of discretizing the fourth-order continuous model of synchronous generator into a discrete state space model is:

[0114] Simplify formula (1) to:

[0115]

[0116] Among them, c represents the continuous time model, x represents the d and e′ q The state variables composed of c and v c represents process noise and measurement noise, and their covariances are Q k and R k, f c (·) represents the nonlinear state transfer function, h c (·) is the measurement function, u is the input variable, and y is the output variable;

[0117] u=[T m E fd i R i I ] T (3)

[0118] y=[δ ω e R e I ] T (4)

[0119] Discretize a continuous-time model into discrete form:

[0120]

[0121] Where k represents the instantaneous moment of kΔt, Δt represents the sampling interval, and w k and v k They are respectively k and R k process noise and measurement noise.

[0122] The discrete state transfer function is obtained using the improved Euler method:

[0123]

[0124] Measurement function h c (·) is represented as:

[0125] y k =h c (x k ,u k )+v k (9).

[0126] The method for estimating the one-step state prediction value and state error covariance of the state quantity is:

[0127] Setting up the state matrix And the corresponding estimated covariance matrix 2n volume points are generated:

[0128] χ i,k-1 =x k-1 +ξ i S k-1 i=1,2,…,2n (10)

[0129] Among them, S k-1 Indicates P k-1Perform Cholesky decomposition, χ i,k-1 is the newly generated volume point, ξ i represents the i-th column of the identity matrix with dimension n×n;

[0130] The volume point is calculated through the state transfer function to obtain the state prediction value and state error covariance:

[0131]

[0132] In the formula, represents the transformed cubic point, is the state prediction value, P kk-1 is the corresponding state error covariance, and the superscript T represents the matrix transpose operation.

[0133] (2) In the measurement update stage of the synchronous generator, the kernel adaptive maximum correlation entropy criterion is introduced, and the kernel parameters are dynamically adjusted based on the kernel adaptive strategy based on the introduced kernel adaptive maximum correlation entropy criterion; the matrix form of the synchronous generator state estimation discrete model is generated based on the adjusted kernel function, and then the state error covariance and measurement noise covariance are iteratively updated.

[0134] In step (2), the kernel adaptive strategy of the kernel adaptive maximum correlation entropy criterion introduced is:

[0135] The maximum correlation entropy is a criterion for describing the correlation between two random variables. For any two random variables M and N, the maximum correlation entropy is defined as follows:

[0136] V(M,N)=E[κ(M,N)]=∫κ(m,n)F MN (m,n)dmdn (14)

[0137] Among them, F MN (m,n) is the joint distribution function of M and N, E[·] represents the expected distribution function;

[0138] The Gaussian kernel function is used as the kernel function of the maximum correlation entropy, that is,

[0139]

[0140] Where, σ is the kernel width;

[0141] Due to the unknown nature of the joint distribution function, the mean of the Gaussian kernel function is used to obtain the relevant entropy estimation result:

[0142]

[0143] Based on the pseudo-Huber weight function, the kernel width is adaptively updated:

[0144]

[0145] in, is the residual, and ρ is the adjustment factor.

[0146] The matrix form of the synchronous generator state estimation discrete model is generated based on the adjusted kernel function, and the method of iteratively updating the state error covariance and measurement noise covariance is:

[0147]

[0148] in,

[0149] definition

[0150] Multiply both sides of formula (18) by M k -1 have to:

[0151] A=Bx k +ε k (19)

[0152] in, ε k =A-Bx k

[0153] According to the Gaussian kernel function, G σ (e)

[0154] κ p =diag{G σ (e1),G σ (e2),…,G σ (e m )} (20)

[0155] κ r =diag{G σ (e m+1 ),G σ (e m+2 ),…,G σ (e n )} (twenty one)

[0156] In the formula, m represents the number of measurements, n = 2m;

[0157] The state error covariance and the measurement noise covariance R k Updated to:

[0158]

[0159] (3) In the measurement update phase of the synchronous generator, the state error covariance matrix is ​​iteratively adjusted through the iterative CKF based on the LM (Levenberg-Marquardt) principle, the Kalman gain is calculated, the state quantity is iteratively cycled and a specific threshold is set to limit the number of iterations, and the state prediction value and state error covariance of time k steps are calculated.

[0160] Iteratively adjust the state error covariance matrix:

[0161]

[0162] Where j represents the number of iterations, the damping parameter μ is used to correct the state error covariance matrix, and then the corrected covariance matrix is ​​used for iterative observation update

[0163] Generate a set of volume points based on the prediction step:

[0164]

[0165] After measuring the function, the volume point propagation is:

[0166] Z i,kk-1 =h(χ i,kk-1 ,u k ) i=1,2,…,2n (26)

[0167] Compute the quantity measure means and interaction covariances:

[0168]

[0169] Calculate the Kalman filter gain and state prediction value:

[0170]

[0171] When the state quantity satisfies Then the iteration stops, where The state prediction value and state error covariance of the kth step are output as follows:

[0172]

[0173] (4) In the measurement update phase of the synchronous generator, the process noise covariance and the measurement noise covariance are adaptively iteratively updated based on the new information residual between the state quantity and the estimated quantity and used for the next prediction.

[0174] Design a sliding window adaptive update Q based on the residual between the quantity measurement and the estimation quantity k and R k :

[0175]

[0176] Where m is the window length, e i is the residual between the state quantity and the estimated value;

[0177] Then, update the process noise covariance and measurement noise covariance:

[0178]

[0179] Effect verification

[0180] In order to verify the effectiveness of the method of the present invention (AKMCC-CKF algorithm), it was compared with other traditional algorithms.

[0181] In the IEEE10 machine 39 bus system, a large number of tests were performed under different working conditions, such as Gaussian noise, non-Gaussian noise and innovative outlier noise. At t=0.5s, a three-phase short circuit fault was set to occur at bus 16; at t=0.7s, the fault was cleared. The initial values ​​of all input variables are considered known, using steady-state power flow values. The sampling frequency of the PMU is 50Hz. In order to obtain more statistically significant conclusions, a Monte Carlo experiment of N=200 was performed for each case. In addition, the traditional UKF, traditional CKF, MCC-CKF algorithm and the proposed AKMCC-CKF algorithm were also executed from the system and test module to evaluate the effectiveness of the method of the present invention.

[0182] In order to digitize the estimation accuracy of these algorithms, the mean absolute error (MAE) is introduced as an evaluation indicator:

[0183]

[0184] Among them, m represents the dimension of measurement; represents the estimated value of the state; x kk Indicates the actual measurement value.

[0185] Designing for non-Gaussian noise and outliers for synchronous generator dynamic state estimation:

[0186] Under non-Gaussian noise conditions, the heavy-tailed non-Gaussian noise R generated by mixed Gaussian noise k To analyze;

[0187] R k ~(1-α)N(0,p1)+αN(0,p2)

[0188] Where N(0,p1) represents Gaussian noise with 0 as mean, pi as covariance, α as proportional coefficient, indicating the degree of mixing, α = 0.05. p1 and p2 represent the covariance of two Gaussian noises, p1 = 10 -11 I,p2=5×10-6 I;

[0189] When there is an outlier disturbance, multiple outlier values ​​of the state variables are set between t=1.5s and t=1.7s.

[0190] like Figure 2-Figure 9 As shown in the figure, under the condition of non-Gaussian and outlier interference, the estimated value of UKF deviates seriously from the true value, while CKF uses third-order spherical radial volume adjustment to find sampling points, and the estimation result is better than UKF. In contrast, MCC-CKF and AKMCC-CKF are significantly better than the other two methods, which shows that the proposed kernel adaptive strategy can adjust to the appropriate kernel width in real time during the estimation process. The MCC criterion with kernel adaptation plays a huge role in suppressing the adverse effects of non-Gaussian noise. In addition, compared with MCC-CKF, AKMCC-CKF has higher estimation accuracy, which is because the latter introduces an adaptive algorithm to update and correct the estimated Q k and R k The proposed method can meet the time-varying characteristics of process noise and measurement noise during generator operation, and exhibits higher robustness and effectiveness.

[0191] Table 1 shows the comparison of MAE of different methods under two working conditions

[0192]

[0193] The comparison of MAE of the four methods under two working conditions is listed in Table 1. It is easy to see from Table 1 that the mean absolute error of the proposed AKMCC-CKF method is the smallest among the four methods, showing a higher estimation accuracy. Experiments show that the kernel adaptive strategy using maximum correlation entropy can suppress the negative impact of non-Gaussian noise and outlier noise on filtering accuracy.

[0194] Example 2

[0195] This embodiment provides a synchronous generator dynamic state estimation system based on kernel adaptive maximum correlation entropy CKF, including:

[0196] The first processing module is configured to: establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide k steps, select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated;

[0197] The second processing module is configured to: introduce a kernel adaptive maximum correlation entropy criterion in the measurement update phase of the synchronous generator, dynamically adjust the kernel parameters based on the kernel adaptive strategy of the introduced kernel adaptive maximum correlation entropy criterion; generate a matrix form of a discrete model of the synchronous generator state estimation based on the adjusted kernel function, and then iteratively update the state error covariance and the measurement noise covariance;

[0198] The third processing module is configured to: in the measurement update phase of the synchronous generator, iteratively adjust the state error covariance matrix, calculate the Kalman gain, iteratively cycle the state quantity and set a specific threshold, limit the number of iterations, and calculate the state prediction value and state error covariance of the time k step through iterative CKF based on the LM principle;

[0199] The fourth processing module is configured to: in the measurement update phase of the synchronous generator, adaptively and iteratively update the process noise covariance and the measurement noise covariance based on the innovation residual between the state quantity and the estimation quantity and use them for the next prediction.

[0200] It should be noted that the system embodiment of this embodiment is similar to the method embodiment of Embodiment 1, so the description is relatively simple, and the relevant parts can refer to the method of Embodiment 1.

[0201] Example 3

[0202] An embodiment of the present application also provides an electronic device, including: a memory and a processor, the memory and the processor are connected via a bus communication, a computer program is stored in the memory, and the computer program can be run on the processor, thereby implementing the steps in the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF disclosed in Example 1 of the present application.

[0203] An embodiment of the present application also provides a computer-readable storage medium, on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps in the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlated entropy CKF as disclosed in Example 1 of the present application are implemented.

[0204] The embodiment of the present application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps in the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF as disclosed in Embodiment 1 of the present application.

[0205] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0206] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, devices or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0207] The description of the above embodiments is only used to help understand the method of the present application and its core idea; at the same time, for a person skilled in the art, according to the idea of ​​the present application, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A method for dynamic state estimation of synchronous generator based on kernel adaptive maximum correlation entropy CKF, characterized in that: The following steps are included: (1) Establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide it into k steps, and select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated; (2) In the measurement update phase of the synchronous generator, the kernel adaptive maximum correlation entropy criterion is introduced, and the kernel parameters are dynamically adjusted based on the kernel adaptive strategy based on the kernel adaptive maximum correlation entropy criterion; Generate the matrix form of the synchronous generator state estimation discrete model based on the adjusted kernel function, and then iteratively update the state error covariance and measurement noise covariance; (3) In the measurement update phase of the synchronous generator, the state error covariance matrix is ​​iteratively adjusted, the Kalman gain is calculated, the state quantity is iteratively cycled and a specific threshold is set to limit the number of iterations, and the state prediction value and state error covariance of the time step k are calculated through the iterative CKF based on the LM principle; (4) In the measurement update phase of the synchronous generator, the process noise covariance and the measurement noise covariance are adaptively iteratively updated based on the new information residual between the state quantity and the estimated quantity and used for the next prediction.

2. The method for dynamic state estimation of synchronous generator based on kernel adaptive maximum correlation entropy CKF according to claim 1 is characterized in that: In step (1), the fourth-order continuous model of the synchronous generator is established as: For synchronous generators, consider the fourth-order continuous differential equation in the local dq coordinate system: Where δ is the rotor angle in radians of the generator, ω is the unit rotor speed, ω0=2πf0 is the angular frequency rating, H and K D are the inertia constant and damping coefficient respectively, and the parameter T m and T e are mechanical torque and electrical gap torque respectively, E fd is the internal field voltage, variable e′ d and e′ q are the transient voltages along the local d and q axes, respectively, and the parameter T d ′0 and T q ′0 is the open circuit time constant along the d and q axis directions respectively; x d and x q are the synchronous reactances along the d-axis and q-axis respectively; x′ d and x′ q are the transient reactances related to the d-axis and q-axis respectively; i d and i q are the stator currents in the d-axis and q-axis directions respectively; The method of discretizing the fourth-order continuous model of synchronous generator into a discrete state space model is: Simplify formula (1) to: Among them, c represents the continuous time model, x represents the d and e′ q The state variables composed of c and v c represents process noise and measurement noise, and their covariances are Q k and R k , f c (·) represents the nonlinear state transfer function, h c (·) is the measurement function, u is the input variable, and y is the output variable; u=[T m E fd i R i I ] T (3) y=[δωe R e I ] T (4) Discretize a continuous-time model into discrete form: Where k represents the instantaneous moment of kΔt, Δt represents the sampling interval, and w k and v k They are respectively k and R k process noise and measurement noise; The discrete state transfer function is obtained using the improved Euler method: Measurement function h c (·) is represented as: y k =h c (x k ,u k )+v k (9) The method for estimating the one-step state prediction value and state error covariance of the state quantity is: Setting up the state matrix And the corresponding estimated covariance matrix 2n volume points are generated: x i,k-1 =x k-1 +ξ i S k-1 i=1,2,…,2n (10) Among them, S k-1 Indicates P k-1 Perform Cholesky decomposition, χ i,k-1 is the newly generated volume point, ξ i represents the i-th column of the identity matrix with dimension n×n; The volume point is calculated through the state transfer function to obtain the state prediction value and state error covariance: In the formula, represents the transformed cubic point, is the state prediction value, P k|k-1 is the corresponding state error covariance, and the superscript T represents the matrix transpose operation.

3. The method for dynamic state estimation of synchronous generator based on kernel adaptive maximum correlation entropy CKF according to claim 2 is characterized in that: In step (2), the kernel adaptive strategy of the kernel adaptive maximum correlation entropy criterion introduced is: The maximum correlation entropy is a criterion for describing the correlation between two random variables. For any two random variables M and N, the maximum correlation entropy is defined as follows: V(M,N)=E[κ(M,N)]=∫κ(m,n)F MN (m,n)dmdn (14) Among them, F MN (m,n) is the joint distribution function of M and N, E[·] represents the expected distribution function; The Gaussian kernel function is used as the kernel function of the maximum correlation entropy, that is, Where, σ is the kernel width; Due to the unknown nature of the joint distribution function, the mean of the Gaussian kernel function is used to obtain the relevant entropy estimation result: Based on the pseudo-Huber weight function, the kernel width is adaptively updated: in, is the residual, ρ is the adjustment factor; The matrix form of the synchronous generator state estimation discrete model is generated based on the adjusted kernel function, and the method of iteratively updating the state error covariance and measurement noise covariance is: in, definition Multiply both sides of formula (18) by M k -1 have to: A=Bx k +e k (19) in, ε k =A-Bx k According to the Gaussian kernel function, G σ (e) κ p =diag{G σ (e1),G σ (e2),…,G σ (And m )} (20) κ r =diag{G σ (e m+1 ),G σ (e m+2 ),…,G σ (e n )} (21) In the formula, m represents the number of measurements, n = 2m; The state error covariance and the measurement noise covariance R k Updated to:

4. The method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF according to claim 3 is characterized in that: Through iterative CKF based on the LM principle, the state error covariance matrix is ​​iteratively adjusted: Where j represents the number of iterations, the damping parameter μ is used to correct the state error covariance matrix, and then the corrected covariance matrix is ​​used for iterative observation update Generate a set of volume points based on the prediction step: After measuring the function, the volume point propagation is: Z i,kk-1 =h(χ i,kk-1 ,u k ) i=1,2,…,2n (26) Compute the quantity measure means and interaction covariances: Calculate the Kalman filter gain and state prediction value: When the state quantity satisfies Then the iteration stops, where The state prediction value and state error covariance of the kth step are output as follows:

5. The method for dynamic state estimation of synchronous generator based on kernel adaptive maximum correlation entropy CKF according to claim 4 is characterized in that: Design a sliding window adaptive update Q based on the residual between the quantity measurement and the estimation quantity k and R k : Where m is the window length, e i is the residual between the state quantity and the estimated value; Then, update the process noise covariance and measurement noise covariance:

6. A synchronous generator dynamic state estimation system based on kernel adaptive maximum correlation entropy CKF, characterized in that: include: The first processing module is configured to: establish a fourth-order continuous model of the synchronous generator, and in the process of dynamic state prediction of the synchronous generator, discretize the fourth-order continuous model of the synchronous generator into a discrete state space model, divide k steps, select y = [δωe R e I ] T As the state quantity, the one-step state prediction value and state error covariance of the state quantity are estimated; The second processing module is configured to: introduce a kernel adaptive maximum correlation entropy criterion in the measurement update phase of the synchronous generator, and dynamically adjust the kernel parameters based on the kernel adaptive strategy of the introduced kernel adaptive maximum correlation entropy criterion; Generate the matrix form of the synchronous generator state estimation discrete model based on the adjusted kernel function, and then iteratively update the state error covariance and measurement noise covariance; The third processing module is configured to: in the measurement update phase of the synchronous generator, iteratively adjust the state error covariance matrix, calculate the Kalman gain, iteratively cycle the state quantity and set a specific threshold, limit the number of iterations, and calculate the state prediction value and state error covariance of the time k step through iterative CKF based on the LM principle; The fourth processing module is configured to: in the measurement update phase of the synchronous generator, adaptively and iteratively update the process noise covariance and the measurement noise covariance based on the innovation residual between the state quantity and the estimation quantity and use them for the next prediction.

7. An electronic device, characterized in that: include: at least one processor, and a memory coupled to the at least one processor; The memory stores a computer program, and the computer program can be executed by the at least one processor to implement the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed, the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF as claimed in any one of claims 1 to 5 can be implemented.

9. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the method for dynamic state estimation of a synchronous generator based on kernel adaptive maximum correlation entropy CKF as described in any one of claims 1 to 5 is implemented.

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