Generator dynamic state estimation method based on robust volume Kalman filtering

Abstract

The invention discloses a generator dynamic state estimation method based on robust volume Kalman filtering, which is characterized by comprising the following steps of: S1, setting an initial value, predicting an error covariance at a moment k, decomposing the error covariance by using a singular value decomposition method, and calculating a volume point of a state quantity at the moment; s2, calculating a measurement estimation value and a Kalman gain at the moment k; s3, selecting a proper robust method according to a robust principle, and correcting the state prediction value or the Kalman gain; s4, calculating a state estimation value and an estimation error covariance at the moment k; and S5, judging whether any robust method is selected in the current state or not, if so, compensating the estimation error covariance, and if not, continuing to execute the steps S2-S4, and calculating the state estimation value at the next moment. According to the method, the problem of dynamic state estimation of the generator under the condition that statistical characteristics of abnormal noise or measurement noise are deviated from actual conditions or even unknown is solved.

Description

Technical Field

[0001] The invention relates to the technical field of power systems, and in particular to a generator dynamic state estimation method based on robust cubature Kalman filtering. Background Art

[0002] State perception technology is one of the important means of situational awareness in power systems. State estimation based on measured data from PMUs can improve data accuracy and provide more reliable data support for coordinated optimization of distribution networks, load regulation, and distributed power output. In addition, synchronous generators also occupy an inestimable position in power systems. When a fault occurs in the power system, the state of the generator during the electromechanical transient process after the fault can be estimated to obtain an estimated value close to the actual state. Then, taking appropriate measures can effectively curb the expansion of the fault and maximize the recovery of economic losses. Therefore, conducting research on dynamic state estimation of generators is of great significance for real-time safety supervision and online fault diagnosis of power systems.

[0003] When the accurate statistical characteristics of noise and system models are known, the relevant algorithms can effectively solve the problem of dynamic state estimation of nonlinear systems; however, in actual engineering operations, due to the influence of environmental changes, production factors and other interferences, there may be abnormal Gaussian white noise or other noise that does not obey the Gaussian distribution in the measurement noise; these complex noises will cause the statistical characteristics of the measurement noise to be inconsistent with the prior probability distribution; in order to solve the problem of noise uncertainty, a model adaptive algorithm is added on the basis of Kalman filtering; this algorithm obtains noise characteristics that are closer to the real noise by connecting multiple filters in parallel and continuously comparing multiple filtering results; however, this method has a high transmission error of the sensor and high computational pressure, and is difficult to implement in engineering applications; some scholars have proposed using the new information vector and residual to adaptively adjust the noise covariance matrix, but when there is a sudden noise mutation, the noise cannot be properly processed.

[0004] Aiming at the problem of generator dynamic state estimation when the environmental noise may contain abnormal noise due to factors such as natural environment and industrial production, or the statistical characteristics of the measured noise deviate from the actual or even are unknown, a generator dynamic state estimation method based on robust cubature Kalman filtering is provided. Summary of the invention

[0005] The purpose of the present invention is to overcome the existing defects and provide a generator dynamic state estimation method based on robust cubature Kalman filtering, which solves the problem of generator dynamic state estimation when the statistical characteristics of abnormal noise or measurement noise deviate from the actual situation or are even unknown.

[0006] The technical solution to achieve the above purpose is: A method for estimating a generator dynamic state based on robust cubature Kalman filtering, characterized by comprising: Step S1, setting the initial value, predicting the error covariance at time k, decomposing the error covariance using the singular value decomposition method and calculating the volume point of the state quantity at that time; Step S2, calculating the measurement estimate value and Kalman gain at time k; Step S3, selecting a suitable robustness method according to the robustness principle to correct the state prediction value or Kalman gain; Step S4, calculating the state estimation value and estimation error covariance at time k; Step S5, determine whether any anti-error method is selected for the current state. If yes, compensate the estimated error covariance. If not, no compensation is required, and continue to execute steps S2-S4 to calculate the state estimate value at the next moment.

[0007] Preferably, in step S1, singular value decomposition is used instead of Cholesky decomposition in the robust cubature Kalman filter algorithm to decompose the error covariance and calculate the volume point of the state quantity at that moment.

[0008] Preferably, in step S3, the measurement innovation and noise covariance matrix are used to set the anti-error principle, and the principle is used to introduce the innovation vector to directly adjust the state prediction value or to adjust the proportion of the measurement prediction value in the filter by modifying the Kalman gain.

[0009] Preferably, in step S3, the relationship between the size of the innovation vector and the statistical characteristics of the measurement noise is a determining factor in determining whether to perform robustness and which robustness method to select. Therefore, the upper and lower limits are set according to the statistical characteristics of the noise, and the innovation vector and the upper and lower limits are combined for judgment, so as to select a suitable robustness method, that is, Measuring covariance and measurement news Size is closely related, so The measured prediction value at the moment is the center of the circle, Draw a circle with radius as the measuring circle, and then and Draw two correction circles for the radius, called correction circles and correction circle ,in, and is the adjustment factor, the range is [0.6, 0.9], and let When there is no bad measurement, the measuring circle is on the correction circle. If there is a bad measurement or a sudden change in state, the measurement circle will be located within the correction circle. In addition, the measured predicted values ​​at this time need to be processed for robustness.

[0010] Preferably, in step S3, it is assumed that express The diagonal components, which are the measurement errors of the variables in the corresponding dimensions, and are the judgment thresholds of the two correction circles respectively, and the robustness criterion can be summarized as: When measuring the new information The absolute value of the component When , no anti-difference is required; when When , it is considered that the state variable has a sudden change, and the measured predicted value is processed for robustness; when When , it is considered that there is a bad measurement, and the increase in measurement information is considered to be caused by the bad measurement, so the Kalman gain is reduced and the proportion of measurement in filtering is reduced; The specific anti-error method is expressed by the following formula: ; In the formula, is the robustness coefficient, about When selecting the value of , it is necessary to consider the measurement accuracy of the state variables corresponding to the measurement system, and it can be adjusted according to actual conditions; is the first on the diagonal of the Kalman gain matrix Quantity, is the Kalman gain adjustment factor, and the selection range is [0.5, 0.9].

[0011] Preferably, in step S4, the state estimation value is determined by the state prediction value and the measurement information.

[0012] Preferably, in step S5, if any robustness method is selected, the estimation error covariance is compensated, and the compensation formula is as follows: ; In the formula, is the compensation matrix for the estimated error covariance, is the estimated error covariance matrix, , are the influence of noise on the estimated covariance, is the measurement covariance Take the square root.

[0013] The beneficial effects of the present invention are as follows: in view of the problems of weak tracking ability and unstable filtering of the cubature Kalman filter algorithm in the dynamic state estimation of the generator, the present invention proposes a robust cubature Kalman filter algorithm based on singular value decomposition. The algorithm uses singular value decomposition to replace the original Cholesky decomposition, which can avoid the situation where the prior covariance matrix is ​​negative definite, and can improve the stability of the filtering; the robustness principle is set by using the measurement innovation and the noise covariance matrix, and the state prediction value or the Kalman gain matrix is ​​directly corrected, thereby reducing the amount of calculation and obtaining a more accurate state estimation value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of a method for estimating a dynamic state of a generator based on robust cubature Kalman filtering according to the present invention; Figure 2 It is a schematic diagram of the robustness judgment criterion in the present invention. DETAILED DESCRIPTION

[0015] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance.

[0016] The present invention will be further described below in conjunction with the accompanying drawings.

[0017] like Figure 1 As shown, a method for estimating a generator dynamic state based on robust cubature Kalman filtering is characterized by comprising: Step S1, set the initial value, predict the error covariance at time k, use the singular value decomposition method to decompose the error covariance and calculate the volume point of the state quantity at that time.

[0018] In the embodiment, singular value decomposition is used instead of Cholesky decomposition in the robust cubature Kalman filter algorithm to decompose the error covariance and calculate the volume point of the state quantity at that moment.

[0019] In the embodiment, based on the characteristics that the inertia and excitation flux of the generator rotor will not change suddenly when it is in working state, it is concluded that the angular velocity and power angle of the generator will not change suddenly during the electromechanical transient process of the power network, and the constraints of the dynamic equation of the generator are met. Therefore, based on this characteristic, the estimation of the generator state quantity is realized through the dynamic state estimation method, which can not only reduce the random error in the phasor measurement, but also improve the measurement accuracy of the PMU, and lay a good foundation for the estimation of the generator at the next moment. It can also provide more reliable data for the power system in the electromechanical transient process to ensure the safe and stable operation of the power system.

[0020] The cubature Kalman filter is a nonlinear filtering algorithm based on the Gaussian hypothesis and established using the Bayesian estimation theory, which is abbreviated as CKF. The Bayesian estimation is based on the likelihood function, and the posterior probability of the target state is estimated by using 2n volumetric points with equal weight coefficients to approximate it. This solves the problem of the integral of the product of the nonlinear function and the Gaussian probability density when solving the problem. The spherical-surface radial principle is then used to convert the target integral in the rectangular coordinate system into the target integral in the polar coordinate system. The converted target function is then integrated on the spherical surface and radially.

[0021] The cubature Kalman filter algorithm may have problems such as weak tracking ability and reduced or even divergent filtering algorithm accuracy when dealing with nonlinear dynamic systems. The cubature Kalman filter algorithm uses the Cholesky method to decompose the estimated error covariance matrix. There are also some problems in this process. For example, if the estimated error covariance matrix is ​​non-positive definite or asymmetric positive definite, it may lead to reduced filtering accuracy, or the state covariance matrix may become a sparse matrix during the operation of the filtering algorithm, or even cause the Cholesky method to fail to decompose the estimated error covariance matrix. Therefore, the singular value decomposition (SVD) decomposition is used instead of the Cholesky decomposition to avoid the situation where the prior covariance matrix is ​​negative definite and improve the stability of the filter. Then, the measurement innovation and noise covariance matrix are used to set the anti-error rule, and the state prediction value is directly adjusted by using the rule or the proportion of the measured value in the filter is adjusted by modifying the Kalman gain, thereby reducing the influence of abnormal measurement prediction value on the state estimation value.

[0022] Step S2, calculating the measurement estimation value and Kalman gain at time k.

[0023] Step S3, selecting a suitable robustness method according to the robustness principle to correct the state prediction value or the Kalman gain.

[0024] In the embodiment, the measurement innovation and the noise covariance matrix are used to set the anti-error principle, and the innovation vector is introduced to directly adjust the state prediction value or the proportion of the measurement prediction value in the filter is adjusted by modifying the Kalman gain.

[0025] In the embodiment, the relationship between the size of the innovation vector and the size of the statistical characteristics of the measurement noise is a determining factor in determining whether to perform anti-error and which anti-error method to select. Therefore, the upper and lower limits are set according to the statistical characteristics of the noise, and the innovation vector and the upper and lower limits are combined for judgment, so as to select a suitable anti-error method, that is, Measuring covariance and measurement news Size is closely related, so The measured prediction value at the moment is the center of the circle, Draw a circle with radius as the measuring circle, and then and Draw two correction circles for the radius, called correction circles and correction circle ,in, and is the adjustment factor, the range is [0.6, 0.9], and let When there is no bad measurement, the measuring circle is on the correction circle. If there is a bad measurement or a sudden change in state, the measurement circle will be located within the correction circle. In addition, the measured predicted values ​​at this time need to be processed for robustness.

[0026] In the embodiment, Figure 2 As shown, suppose, express The diagonal components, which are the measurement errors of the variables in the corresponding dimensions, and are the judgment thresholds of the two correction circles respectively, and the robustness criterion can be summarized as: When measuring the new information The absolute value of the component When , no anti-difference is required; when When , it is considered that the state variable has a sudden change, and the measured predicted value is processed for robustness; when When , it is considered that there is a bad measurement, and the increase in measurement information is considered to be caused by the bad measurement, so the Kalman gain is reduced and the proportion of measurement in filtering is reduced; The specific anti-error method is expressed by the following formula: ; In the formula, is the robustness coefficient, about When selecting the value of , it is necessary to consider the measurement accuracy of the state variables corresponding to the measurement system, and it can be adjusted according to actual conditions; is the first on the diagonal of the Kalman gain matrix Quantity, is the Kalman gain adjustment factor, and the selection range is [0.5, 0.9].

[0027] Step S4, calculating the state estimation value and estimation error covariance at time k.

[0028] In the embodiment, the state estimate is determined by the state prediction value and the measurement innovation; however, when the target state value at the next moment suddenly changes or the noise statistical characteristics do not conform to the actual situation, the difference between the prior state prediction value and the measurement prediction value at the next moment will be large, that is, the measurement innovation will increase, further causing the state estimation result to deviate from the true value; the principle of strong tracking filtering is to introduce a fading factor to compensate for the large prediction error and thus make the state estimate closer to the true value; in this way, it is believed that the prior state prediction value can be directly adjusted using the innovation vector, so that it can be ensured that when the state quantity suddenly changes, the filter can also respond in time to "catch up" with the change of the target state; this method is not only simple and intuitive, but also has a small amount of calculation; on the other hand, due to the nonlinear system and the presence of environmental noise and interference, bad measurement values ​​may occur from time to time; when bad measurement occurs, the innovation vector will also increase. If the measurement value continues to be used for filtering, the state estimate will deviate far from the true value, and even eventually cause filtering divergence; in this case, the Kalman gain can be directly adjusted to reduce the proportion of the measurement value in the filtering, thereby improving the accuracy of the filtering.

[0029] Step S5, determine whether any anti-error method is selected for the current state. If yes, compensate the estimated error covariance. If not, no compensation is required, and continue to execute steps S2-S4 to calculate the state estimate value at the next moment.

[0030] In the embodiment, if any robustness method is selected, the estimation error covariance is compensated, and the compensation formula is as follows: ; In the formula, is the compensation matrix for the estimated error covariance, is the estimated error covariance matrix, , are the influence of noise on the estimated covariance, is the measurement covariance Take the square root.

[0031] The present invention analyzes the conditions of Gaussian white noise and biased Gaussian white noise respectively, and the proposed robust cubic Kalman filtering algorithm based on singular value decomposition has higher accuracy and stronger robustness than the algorithm without adding robustness.

[0032] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some or all of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating a generator dynamic state based on robust cubature Kalman filtering, characterized in that: include: Step S1, setting the initial value, predicting the error covariance at time k, decomposing the error covariance using the singular value decomposition method and calculating the volume point of the state quantity at that time; Step S2, calculating the measurement estimate value and Kalman gain at time k; Step S3, selecting a suitable robustness method according to the robustness principle to correct the state prediction value or Kalman gain; Step S4, calculating the state estimation value and estimation error covariance at time k; Step S5, determine whether any anti-error method is selected for the current state. If yes, compensate the estimated error covariance. If not, no compensation is required, and continue to execute steps S2-S4 to calculate the state estimate value at the next moment.

2. A method for estimating a generator dynamic state based on robust cubature Kalman filtering according to claim 1, characterized in that: In the step S1, singular value decomposition is used to replace the Cholesky decomposition in the robust cubature Kalman filter algorithm, so as to decompose the error covariance and calculate the volume point of the state quantity at that moment.

3. The method for estimating the dynamic state of a generator based on robust cubature Kalman filtering according to claim 1, characterized in that: In step S3, the measurement innovation and noise covariance matrix are used to set the anti-error principle. Using this principle, the innovation vector is introduced to directly adjust the state prediction value or the proportion of the measurement prediction value in the filter is adjusted by modifying the Kalman gain.

4. The method for estimating the dynamic state of a generator based on robust cubature Kalman filtering according to claim 3, characterized in that: In step S3, the relationship between the size of the innovation vector and the statistical characteristics of the measurement noise is the determining factor for determining whether to perform robustness and which robustness method to choose. Therefore, the upper and lower limits are set according to the statistical characteristics of the noise, and the innovation vector and the upper and lower limits are combined for judgment, so as to select the appropriate robustness method, that is, Measuring covariance and measurement news Size is closely related, so The measured prediction value at the moment is the center of the circle, Draw a circle with radius as the measurement circle, and then and Draw two correction circles with radius, called correction circles and correction circle ,in, and is the adjustment factor, the range is [0.6, 0.9], and let When there is no bad measurement, the measuring circle is on the correction circle. If there is a bad measurement or a sudden change in state, the measurement circle will be located within the correction circle. In addition, the measured predicted values ​​at this time need to be processed for robustness.

5. The method for estimating the dynamic state of a generator based on robust cubature Kalman filtering according to claim 4, characterized in that: In step S3, it is assumed that express The diagonal components, which are the measurement errors of the variables in the corresponding dimensions, and are the judgment thresholds of the two correction circles respectively, and the robustness criterion can be summarized as: When measuring the new information The absolute value of the component When , no anti-difference is required; when When , it is considered that the state variable has a sudden change, and the measured predicted value is processed for robustness; when When , it is considered that there is a bad measurement, and the increase in measurement information is considered to be caused by the bad measurement, so the Kalman gain is reduced and the proportion of measurement in filtering is reduced; The specific anti-error method is expressed by the following formula: ； In the formula, is the robustness coefficient, about When selecting the value of , it is necessary to consider the measurement accuracy of the state variables corresponding to the measurement system, and it can be adjusted according to actual conditions; is the first on the diagonal of the Kalman gain matrix Quantity, is the Kalman gain adjustment factor, and the selection range is [0.5, 0.9].

6. The method for estimating the dynamic state of a generator based on robust cubature Kalman filtering according to claim 5, characterized in that: In step S4, the state estimation value is determined by the state prediction value and the measurement information.

7. The method for estimating the dynamic state of a generator based on robust cubature Kalman filtering according to claim 5, characterized in that: In step S5, if any robustness method is selected, the estimation error covariance is compensated, and the compensation formula is as follows: ； In the formula, is the compensation matrix for the estimated error covariance, is the estimated error covariance matrix, are the influence of noise on the estimated covariance, is the measurement covariance Take the square root.

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