Fault-tolerant cubature Kalman filtering-based multi-machine power system elastic state estimation method

Abstract

The invention discloses a fault-tolerant cubature Kalman filtering-based multi-machine power system elastic state estimation method. The method comprises the following steps of establishing a multi-machine power system dynamic state estimation model considering sensor abnormality; initializing parameter values of the state estimation method; calculating a state prediction value and a prediction error covariance matrix at the moment k; whether a fault occurs or not is judged by calculating filtering innovation of a state estimation method; and introducing a fault-tolerant factor to enforcedly execute correction filtering innovation, and updating a state estimation value and a state error covariance matrix. According to the method provided by the invention, the dynamic state estimation model of the multi-machine power system under the abnormal condition of the sensor is established, the method capable of improving the fault-tolerant capability and the stability of the system under the abnormal condition is provided, stable state estimation is kept, and the stability and the reliability of the system can be improved.

Description

Technical Field

[0001] This invention relates to the field of power energy management technology. Specifically, this invention relates to a method for elastic state estimation of multi-machine power systems based on fault-tolerant volumetric Kalman filtering. This method is applicable when there are abnormal measurement values ​​in the power system, and can improve the robustness and operational stability of system state estimation through a dynamic fault-tolerant mechanism. Background Technology

[0002] Dynamic state estimation (DSE), as a core function of modern power energy management systems, overcomes the limitations of traditional static estimation methods that can only reflect the system state at a single moment through real-time state tracking and short-term prediction capabilities. It provides key support for advanced applications such as power system monitoring, situational awareness, and optimized control. Especially in the context of high penetration of new energy sources, facing the significant enhancement of system randomness, volatility, and nonlinearity, DSE technology has become an important technical means to ensure the safe and stable operation of power systems by abandoning static assumptions and realizing continuous tracking and prediction of state variables. Among them, dynamic state estimation of synchronous generators is particularly important due to its accurate capture of the dynamic characteristics of the system.

[0003] Current dynamic state estimation of power systems mainly employs Kalman filtering and its improved algorithms, including Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Capacitive Kalman Filter (CKF). EKF is suitable for weakly nonlinear systems through Jacobian matrix linearization, UKF performs well in moderately nonlinear systems using unscented transformation, while CKF, based on spherical radial integral, has an accuracy advantage in high-dimensional nonlinear scenarios, but is very sensitive to outliers.

[0004] In large nonlinear systems, sensor noise, communication failures, or sudden interference can all lead to measurement anomalies, resulting in incomplete or abnormal measurement data, which in turn affects the safe and stable operation of the power system. When dealing with large nonlinear systems, neither EKF, UKF, nor CKF can improve the robustness of dynamic state estimation methods in large nonlinear power systems with outliers. Summary of the Invention

[0005] This invention designs a resilient state estimation method for multi-machine power systems based on fault-tolerant cubature Kalman filter (FTCKF). When abnormal measurements exist in the power system, the robustness and operational stability of the system state estimation can be significantly improved through a dynamic fault-tolerant mechanism.

[0006] Specific technical solution: The first aspect of this invention provides a method for elastic state estimation of a multi-machine power system based on fault-tolerant volumetric Kalman filtering, comprising the following steps: 1) Establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies; The established discrete-time state-space model of the multi-machine power system is as follows: in, k +1 indicates a discrete-time index; It is the system's state vector; f and h It consists of a vector composed of nonlinear state transition functions and measurement functions; It is x k+1 The measurement vector, σ is a random vector describing the magnitude of outliers, when ρ k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no k+1 When =1, it indicates a system malfunction; w k and v k These are the system noise vector and the measurement noise vector, respectively. 2) Initialize the parameter values ​​for the fault-tolerant volumetric Kalman filter (FTCKF) state estimation method; The parameter values ​​include the initial values ​​for state estimation. The estimation error covariance matrix P0 and the system noise covariance matrix Q k And the measurement noise covariance matrix R k+1 ; 3) Perform state estimation using the traditional capacitive Kalman filter method, and calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; ① By decomposing the estimated error covariance matrix, volume points are generated: In the formula, P0 represents the estimation error covariance matrix; S k This indicates that P0 is obtained through Cholesky decomposition; Represents the generated volume point; {ξ i}, i=1,2,…,2n represents the i-th column of an n×n identity matrix; ② Calculate the volume point using the state transition function, and then calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; In the formula, fRepresents the state transition function. Represents the volume point after propagation. Q represents the matrix transpose operation. k+1 This represents the system noise covariance matrix at time k+1; 4) Calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; ① By decomposing the state prediction error covariance matrix P k+1|k Generate volume points and propagate them through measurement functions; In the formula, S k+1|k P represents k+1|k Obtained through Cholesky decomposition; x i,k+1|k Represents the generated volume point; {ξ i}, i=1,2,…,2n represents the i-th column of an n×n identity matrix; h represents the measurement propagation function. Represents the volume point after propagation; ②Calculation quantity measurement mean and interaction covariance matrix ; ③ Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 ; In the formula, R represents the estimated innovation covariance matrix. k+1 Let K represent the measurement noise covariance matrix at time k+1. k Indicates Kalman gain, This represents the actual measurement value at time step k+1. This represents the measurement value at time step k+1 predicted based on all available information at time step k; 5) Calculate the filtering innovation r at time k+1. k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, by introducing a fault tolerance factor λ in fault detection...k+1 ; (Correct): , ; (Fault): , ; The fault detection function is as follows: In the formula, This represents the estimation of the innovation covariance matrix; 6) Update the calculated state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; .

[0007] A second aspect of the present invention provides a resilient state estimation system for a multi-machine power system based on fault-tolerant commensurate Kalman filtering, characterized in that it comprises: The first processing module is configured to: establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies; The established discrete-time state-space model of the multi-machine power system is as follows: in, k +1 indicates a discrete-time index; It is the system's state vector; f and h It consists of a vector composed of nonlinear state transition functions and measurement functions; It is x k+1 The measurement vector, σ is a random vector describing the magnitude of outliers, when ρ k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no faults. k+1 When =1, it indicates a system malfunction; w k and v k These are the system noise vector and the measurement noise vector, respectively. The second processing module is configured to initialize the parameter values ​​of the fault-tolerant volume Kalman filter (FTCKF) state estimation method. The parameter values ​​include the initial values ​​for state estimation. The estimation error covariance matrix P0 and the system noise covariance matrix Q k And the measurement noise covariance matrix R k+1 ; The third processing module is configured to perform state estimation using the traditional capacitive Kalman filter method and calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; ① By decomposing the error covariance matrix, volume points are generated: In the formula, P0 represents the estimation error covariance; S k This indicates that P0 is obtained through Cholesky decomposition; Represents the generated volume point; {ξ i}, i=1,2,…,2n represents the i-th column of an n×n identity matrix; ② Calculate the volume point using the state transition function, and then calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; In the formula, f Represents the state transition function. Represents the volume point after propagation. Q represents the matrix transpose operation. k+1 This represents the system noise covariance matrix at time k+1; The fourth processing module is configured to calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; ① By decomposing the state prediction error covariance matrix P k+1|k Generate volume points and propagate them through measurement functions; In the formula, S k+1|k P represents k+1|k Obtained through Cholesky decomposition; x i,k+1|k Represents the generated volume point; {ξ i}, i=1,2,…,2n represents the i-th column of an n×n identity matrix; h represents the measurement propagation function. Represents the volume point after propagation; ②Calculation quantity measurement mean and interaction covariance matrix ; ③ Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 ; In the formula, R represents the estimated innovation covariance matrix. k+1 Let K represent the measurement noise covariance matrix at time k+1. k Indicates Kalman gain, This represents the actual measurement value at time step k+1. This represents the measurement value at time step k+1 predicted based on all available information at time step k; The fifth processing module is configured to calculate the filtering innovation r at time k+1. k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, a fault tolerance factor λ is introduced into the fault detection process. k+1 ; (Correct): , ; (Fault): , ; The fault detection function is as follows: In the formula, This represents the estimation of the innovation covariance matrix; The sixth processing module is configured to update and calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; .

[0008] A third aspect of the present invention provides an electronic device, comprising: At least one processor, and a memory coupled to said at least one processor; The memory stores a computer program that can be executed by the at least one processor to implement the resilient state estimation method for multi-machine power systems based on fault-tolerant volumetric Kalman filtering, as described above.

[0009] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed, enables the implementation of the resilient state estimation method for a multi-machine power system based on fault-tolerant volumetric Kalman filtering as described above.

[0010] The fifth aspect of the present invention provides a computer program product, including a computer program / instruction that, when executed by a processor, implements the resilient state estimation method for a multi-machine power system based on fault-tolerant volumetric Kalman filtering as described above.

[0011] Compared with existing state estimation methods for multi-machine power systems, the present invention has the following advantages and technical effects: This invention utilizes filtering innovation (the difference between measured and predicted values) to construct a detection statistic, and determines whether anomalies exist based on theoretical covariance. Once an anomaly is detected, a fault-tolerance factor is immediately introduced to forcibly reduce the impact of the current innovation on state estimation, dynamically correcting the state estimate and the state estimation error covariance matrix to prevent filter divergence. This fault-tolerance mechanism significantly improves the robustness and operational stability of the system state estimation. Attached Figure Description

[0012] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0013] Figure 2 Estimation results for generator 1 under Gaussian noise.

[0014] Figure 3 Comparison of dynamic estimation results of δ under abnormal measurement.

[0015] Figure 4 Comparison of dynamic estimation results of ω under abnormal measurement.

[0016] Figure 5 Abnormal measurement Comparison of dynamic estimation results.

[0017] Figure 6 Abnormal measurement Comparison of dynamic estimation results. Detailed Implementation

[0018] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0019] Example 1 like Figure 1 As shown in the figure, this embodiment provides a method for elastic state estimation of a multi-machine power system based on fault-tolerant volumetric Kalman filtering, which includes the following steps: (1) Establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies, which can be expressed as: in, k +1 indicates a discrete-time index; It is the system's state vector. f and h It consists of a vector composed of nonlinear state transition functions and measurement functions; It is x k+1 The measurement vector is ρ, and σ is a random vector describing the magnitude of the outlier. k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no k+1 When =1, it indicates a system malfunction; w k and v k These are the system noise vector and the measurement noise vector, respectively.

[0020] (2) Initialize the parameter values ​​of the fault-tolerant volumetric Kalman filter (FTCKF) state estimation method, including the initial values ​​of the state estimation. The estimated error covariance P0, and the system noise and measurement noise covariance matrices are respectively Q. k and R k+1 .

[0021] (3) Calculate the predicted state value at time k+1 And the state prediction error covariance matrix P k+1|k The calculation method is as follows: ① By decomposing the error covariance matrix, volume points are generated: In the formula, P0 represents the estimation error covariance; S k This indicates that P0 is obtained through Cholesky (matrix decomposition method); Represents the generated volume point; {ξ i}, where i=1,2,…,2n represents the i-th column of an n×n identity matrix.

[0022] ② Calculate the volume point using the state transition function, and then calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; In the formula, f Represents the state transition function. Represents the volume point after propagation. Q represents the matrix transpose operation. k+1 Let represent the system noise covariance matrix at time k+1.

[0023] (4) Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 The calculation method is as follows: ① By decomposing the prediction error covariance matrix P k+1|k Generate volume points and propagate them through measurement functions; In the formula, S k+1|k P represents k+1|k Obtained through Cholesky decomposition; x i,k+1|k Represents the generated volume point; {ξ i}, i=1,2,…,2n represents the i-th column of an n×n identity matrix; h represents the measurement propagation function. This represents the volume point after propagation.

[0024] ②Calculation quantity measurement mean and interaction covariance matrix ; ③ Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 ; In the formula, R represents the estimated innovation covariance matrix.k+1 Let K represent the measurement noise covariance matrix at time k+1. k Indicates Kalman gain, This represents the actual measurement value at time step k+1. This represents the measurement value at time step k+1 predicted based on all available information at time step k.

[0025] (5) Calculate the filtering innovation r at time k+1 k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, by introducing a fault tolerance factor λ in fault detection... k+1 ; (Correct): , ; (Fault): , ; The fault detection function is as follows: In the formula, This represents the estimation of the innovation covariance matrix; (6) Update the calculated state estimate at time k+1 and the state estimation error covariance matrix P k+1 ; .

[0026] Example 2 This embodiment provides a specific method for elastic state estimation of a multi-machine power system based on fault-tolerant volumetric Kalman filtering, which includes the following steps: (a) Model building Here, a fourth-order synchronous generator model is used to characterize the dynamic characteristics of the power system, and its mathematical expression is as follows: Where δ is the rotor angular radius of the generator in radians, ω is the unit rotor speed, and ω0 = 2π f 0 is the rated angular frequency, H and K D These are the inertial constant and damping coefficient, respectively, and parameter T. m and T e These are the mechanical torque and the electrical clearance torque, respectively, E fd For internal field voltage, variable and Let be the transient voltages along the local d-axis and q-axis, respectively, and the parameters be... and , respectively, are the open-circuit time constants along the d-axis and q-axis; x d and x q These are the synchronous reactances along the d-axis and q-axis, respectively; and These are the transient reactances associated with the d-axis and q-axis, respectively; i d and i q These are the stator currents along the d-axis and q-axis, respectively.

[0027] The discrete-space model of a generator can be simply described as follows: Where c represents the continuous-time model, and x is composed of δ, ω, and The state variables that make up the composition f c (·) is a nonlinear state transition function. h c (·) represents the measurement function, u is the input variable, and y is the output variable, as shown below: To perform dynamic state estimation of a generator, the continuous-time model must be discretized into a discrete form: σ is a random vector describing the size of outliers. When ρ k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no faults. k+1 When the value is 1, it indicates a system malfunction. k and v k These are the system noise vector and the measurement noise vector, respectively.

[0028] (b) Example Analysis To verify the effectiveness and practicality of the proposed FTCKF multi-machine power system elastic state estimation method, this invention uses an NPCC-48 machine 140 bus system as the test system. The NPCC-48 machine 140 bus system represents the northeast region of the EI system. 27 generators use a fourth-order model, and the remaining 21 generators use a second-order classical model. Therefore, there are a total of 150 state variables. For the NPCC system, 24 PMUs are installed on generators 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 16, 18, 19, 20, 21, 27, 28, 31, 32, 35, 36, 38, 44, and 45. In the simulation, the system experiences a sudden sensor anomaly or generator measurement data anomaly at t=1s, which is automatically cleared after 1s. The covariance matrix of process noise was set as a diagonal matrix, with values ​​on the diagonal being the square of 10% of the maximum state change; the covariance matrix of measurement noise was also a diagonal matrix, with values ​​on the diagonal being 0.012. The test interval was [0, 10 seconds], and the system dynamic state was estimated at a sampling rate of 120 samples per second. A total of 96 measurement data points were collected, provided by 24 performance monitoring units (PMUs).

[0029] For the system described in the above embodiment, the CKF algorithm and the FTCKF method proposed in this invention are used to test, verify and analyze abnormal measurement conditions in multi-machine power systems.

[0030] The dynamic state estimation results of generator G1 obtained by tracking and estimating the NPCC-48 machine 140 bus system using the different methods described above are as follows: Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown. In the NPCC 140-node system, for generator 1, under normal operating conditions, the estimation results of the traditional CKF method and the proposed FTCKF method are compared under normal Gaussian noise conditions. Figure 2 It can be seen that both methods exhibit excellent dynamic state tracking performance and can stably control the estimation error within the allowable range. Figure 3-6 The estimation results of generator 1 under abnormal measurement conditions (1-2 seconds) are presented. When the sensor fails, the conventional Kalman filter (CKF) exhibits significant estimation bias and fluctuations, requiring approximately 3 seconds to recover. In contrast, the fault-tolerant Kalman filter (FTCKF), through its fault-tolerance mechanism, maintains a smaller error during the abnormal period and quickly resumes tracking after the abnormality is resolved. This verifies the robustness of the fault detection Kalman filter in handling sudden measurement anomalies, demonstrating better robustness compared to the conventional Kalman filter.

[0031] To further conduct a quantitative comparative analysis of the state estimation results of different algorithms, the estimation error RMSE is used as a performance metric for performance comparison among different algorithms. The metric is defined as follows: In the formula y i Representing the actual values, i=1,2,3, For estimates, n=3 represents the number of system buses, and N represents the total number of simulation test cycles.

[0032] Table 1 presents the performance metrics of different algorithms for the dynamic estimation results of the system in the embodiment. The performance data in the table shows that, under abnormal conditions, the FTCKF state estimation method proposed in this invention outperforms the CKF method in all performance metrics, highlighting the superiority of the proposed method.

[0033] Table 1 Dynamic Estimation Results Indicators In summary, the following conclusions can be drawn: The FTCKF multi-machine power system elastic state estimation method proposed in this invention can improve the fault tolerance and stability of the system under abnormal conditions, maintain stable state estimation, and enhance the stability and reliability of the system.

[0034] Example 3 This embodiment provides a resilient state estimation system for a multi-machine power system based on fault-tolerant volumetric Kalman filtering, including: The first processing module is configured to: establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies; The second processing module is configured to initialize the parameter values ​​of the fault-tolerant volume Kalman filter (FTCKF) state estimation method. The third processing module is configured to perform state estimation using the traditional capacitive Kalman filter method and calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; The fourth processing module is configured to calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; The fifth processing module is configured to calculate the filtering innovation r at time k+1. k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, a fault tolerance factor λ is introduced into the fault detection process. k+1 ; The sixth processing module is configured to update the state estimate at time k+1 under the fault-tolerant mechanism. and the state estimation error covariance matrix P k+1 .

[0035] It should be noted that the system embodiment of this example is similar to the method embodiment of example 1, so the description is relatively simple. For relevant details, please refer to the method of example 1.

[0036] Example 4 This application also provides an electronic device, including: a memory and a processor, wherein the memory and the processor are connected via a bus for communication, and the memory stores a computer program that can run on the processor to implement the steps in the multi-machine power system elastic state estimation method based on fault-tolerant volumetric Kalman filtering disclosed in embodiment 1 of this application.

[0037] This application also provides a computer-readable storage medium storing a computer program / instruction, which, when executed by a processor, implements the steps in the fault-tolerant volumetric Kalman filter-based resilient state estimation method for multi-machine power systems disclosed in Embodiment 1 of this application.

[0038] This application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps in the fault-tolerant volumetric Kalman filtering-based resilient state estimation method for multi-machine power systems disclosed in Embodiment 1 of this application.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0040] Those skilled in the art will understand that embodiments of this application can be provided as methods, apparatus, or computer program products. Therefore, embodiments of this application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of this application can take the form of computer program products 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.

[0041] The above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​this application; at the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for elastic state estimation of a multi-machine power system based on fault-tolerant volumetric Kalman filtering, characterized in that, Includes the following steps: 1) Establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies; The established discrete-time state-space model of the multi-machine power system is as follows: in, k +1 indicates a discrete-time index; It is the system's state vector; f and h It consists of a vector composed of nonlinear state transition functions and measurement functions; It is x k+1 The measurement vector, σ is a random vector describing the magnitude of outliers, when ρ k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no faults. k+1 When =1, it indicates a system malfunction; w k and v k These are the system noise vector and the measurement noise vector, respectively. 2) Initialize the parameter values ​​for the fault-tolerant volumetric Kalman filter (FTCKF) state estimation method; The parameter values ​​include the initial values ​​for state estimation. The estimation error covariance matrix P0 and the system noise covariance matrix Q k And the measurement noise covariance matrix R k+1 ; 3) Perform state estimation using the traditional capacitive Kalman filter method, and calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; ① By decomposing the estimated error covariance matrix, volume points are generated: In the formula, P0 represents the estimation error covariance matrix; S k This indicates that P0 is obtained through Cholesky decomposition; Represents the generated volume point; {ξ i }, i=1,2,…,2n represents the i-th column of an n×n identity matrix; ② Calculate the volume point using the state transition function, and then calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; In the formula, f Represents the state transition function. Represents the volume point after propagation. Q represents the matrix transpose operation. k+1 This represents the system noise covariance matrix at time k+1; 4) Calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; ① By decomposing the state prediction error covariance matrix P k+1|k Generate volume points and propagate them through measurement functions; In the formula, S k+1|k P represents k+1|k Obtained through Cholesky decomposition; x i,k+1|k Represents the generated volume point; {ξ i }, i=1,2,…,2n represents the i-th column of an n×n identity matrix; h represents the measurement propagation function. Indicates the volume point after propagation; ②Calculation quantity measurement mean and interaction covariance matrix ; ③ Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 ; In the formula, R represents the estimated innovation covariance matrix. k+1 Let K represent the measurement noise covariance matrix at time k+1. k Indicates Kalman gain, This represents the actual measurement value at time step k+1. This represents the measurement value at time step k+1 predicted based on all available information at time step k; 5) Calculate the filtering innovation r at time k+1. k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, a fault tolerance factor λ is introduced into the fault detection process. k+1 ; The fault detection function is as follows: In the formula, This represents the estimation of the innovation covariance matrix; 6) Update the calculated state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; In the formula, This represents the estimated innovation covariance matrix.

2. A flexible state estimation system for a multi-machine power system based on fault-tolerant volumetric Kalman filtering, characterized in that, include: The first processing module is configured to: establish a discrete-time state-space model of a multi-machine power system that takes into account sensor anomalies; The established discrete-time state-space model of the multi-machine power system is as follows: in, k +1 indicates a discrete-time index; It is the system's state vector; f and h It consists of a vector composed of nonlinear state transition functions and measurement functions; It is x k+1 The measurement vector, σ is a random vector describing the magnitude of outliers, when ρ k+1 When ρ = 0, it indicates that the system has no faults; when ρ = 0, it indicates that the system has no faults. k+1 When =1, it indicates a system malfunction; w k and v k These are the system noise vector and the measurement noise vector, respectively. The second processing module is configured to initialize the parameter values ​​of the fault-tolerant volume Kalman filter (FTCKF) state estimation method. The parameter values ​​include the initial values ​​for state estimation. The estimation error covariance matrix P0 and the system noise covariance matrix Q k And the measurement noise covariance matrix R k+1 ; The third processing module is configured to perform state estimation using the traditional capacitive Kalman filter method and calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; By over-decomposing the estimation error covariance matrix, volume points are generated: In the formula, P0 represents the estimation error covariance matrix; S k This indicates that P0 is obtained through Cholesky decomposition; Represents the generated volume point; {ξ i }, i=1,2,…,2n represents the i-th column of an n×n identity matrix; ② Calculate the volume point using the state transition function, and then calculate the predicted state value at time k+1. And the state prediction error covariance matrix P k+1|k ; In the formula, f Represents the state transition function. Represents the volume point after propagation. Q represents the matrix transpose operation. k+1 This represents the system noise covariance matrix at time k+1; The fourth processing module is configured to calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; ① Over-decomposition state prediction error covariance matrix P k+1|k Generate volume points and propagate them through measurement functions; In the formula, S k+1|k P represents k+1|k Obtained through Cholesky decomposition; x i,k+1|k Represents the generated volume point; {ξ i }, i=1,2,…,2n represents the i-th column of an n×n identity matrix; h represents the measurement propagation function. Indicates the volume point after propagation; ②Calculation quantity measurement mean and interaction covariance matrix ; ③ Calculate the state estimate at time k+1 With the state estimation error covariance matrix P k+1 ; In the formula, R represents the estimated innovation covariance matrix. k+1 Let K represent the measurement noise covariance matrix at time k+1. k Indicates Kalman gain, This represents the actual measurement value at time step k+1. This represents the measurement value at time step k+1 predicted based on all available information at time step k; The fifth processing module is configured to calculate the filtering innovation r at time k+1. k+1 The fault detection function d is obtained by performing fault detection using statistical test results. k+1 Then, a fault tolerance factor λ is introduced into the fault detection process. k+1 ; The fault detection function is as follows: In the formula, This represents the estimation of the innovation covariance matrix; The sixth processing module is configured to update and calculate the state estimate at time k+1. and the state estimation error covariance matrix P k+1 ; In the formula, This represents the estimated innovation covariance matrix.

3. An electronic device, characterized in that, include: At least one processor, and a memory coupled to said at least one processor; The memory stores a computer program that can be executed by the at least one processor to implement the fault-tolerant volumetric Kalman filter-based resilient state estimation method for multi-machine power systems as described in claim 1.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, enables the implementation of the fault-tolerant volumetric Kalman filter-based elastic state estimation method for multi-machine power systems as described in claim 1.

5. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the resilient state estimation method for multi-machine power systems based on fault-tolerant volumetric Kalman filtering as described in claim 1.

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