A doubly-fed induction generator rotor speed estimation method based on maximum cross-correlation entropy weighting extended Kalman filter

Abstract

The application discloses a double-fed induction generator rotor speed estimation method based on maximum cross-correlation entropy weighting, and belongs to the field of motor control. The method creatively applies cross-correlation entropy theory to noise covariance estimation of EKF, and designs a complete algorithm system containing dynamic weighting, adaptive kernel bandwidth, mixed robust weighting and numerical reinforcement. The progressiveness is reflected in that the method comprehensively solves the shortcomings of traditional methods in response speed, parameter disturbance resistance and non-Gaussian noise resistance. Theoretical proof and comprehensive simulation experiments prove that the method has better estimation accuracy, robustness and reliability in complex industrial environments such as wind power generation.

Description

Technical Field

[0001] This invention belongs to the field of motor control, and specifically relates to a method for estimating the rotor speed of a doubly fed induction generator based on maximum cross-correlation entropy weighting using extended Kalman filtering. Background Technology

[0002] In the vector control system of a doubly-fed induction generator (DFIG), real-time and accurate acquisition of rotor speed is crucial for achieving maximum power point tracking and stable system operation. In actual wind farm environments, complex electromagnetic interference and variable operating conditions pose significant challenges to accurate speed estimation. Currently, the extended Kalman filter (EKF), a classic algorithm for state estimation in nonlinear systems, has been initially applied in sensorless control of DFIGs. However, the performance of traditional EKF is highly dependent on prior assumptions about the process noise covariance Q and measurement noise covariance R. In actual DFIG operation, due to nonlinear coupling, time-varying parameters (such as stator resistance variations), and randomly occurring non-Gaussian noise interference, a fixed noise covariance often leads to slow filter convergence and even divergence under extreme conditions. Although existing adaptive extended Kalman filters (AEKF) and random weighted extended Kalman filters (RWEKF) have made some improvements in handling noise uncertainty, the former has a significant response lag when faced with sudden noise, while the latter, due to the introduction of random weights, is prone to large fluctuations in the estimation results in steady state. Summary of the Invention

[0003] Given the shortcomings of existing technologies in terms of robustness, dynamic response speed, and steady-state accuracy when dealing with time-varying, non-Gaussian noise and parameter mutations in actual DFIG operation, the purpose of this invention is to provide an improved Cross-correlation Entropy Weighted Extended Kalman Filter (CWEKF) algorithm to overcome the above limitations and improve the overall performance of rotor speed estimation.

[0004] To solve the above-mentioned technical problems, the inventors, drawing on years of research experience in motor control and through extensive experimental research and continuous exploration and improvement, finally obtained the following technical solution: a rotor speed estimation method for a doubly-fed induction generator based on maximum cross-correlation entropy weighting, the method comprising the following steps:

[0005] S1: Construct a nonlinear state-space model of a doubly-fed induction generator that includes rotor current, rotor flux linkage, and rotor speed.

[0006] S2: Under the extended Kalman filter framework, obtain the measurement residual and state residual at the current moment;

[0007] S3: Set a sliding window to store the historical residual sequence. Based on the cross-correlation entropy theory, calculate the similarity between the current residual and each historical residual in the historical residual sequence, and dynamically generate weighting coefficients for estimating the measurement noise covariance and process noise covariance based on the similarity.

[0008] S4: Using the weighting coefficients obtained in step S3, adaptively update the measurement noise covariance matrix and the process noise covariance matrix;

[0009] S5: Combining regularization techniques with Huber robust weights, a hybrid weighting mechanism is constructed to perform positive definite processing on the updated covariance matrix, calculate the Kalman gain, and complete the state estimation update;

[0010] S6: Output the estimated rotor speed at the current moment.

[0011] More preferably, in step S1, the state vector of the nonlinear state-space model is x=[ , , ] T ,in For rotor current, For rotor flux linkage, The rotor speed is; the measurement vector is .

[0012] More preferably, in step S3, for the measurement residual, the first Historical residuals weight Calculated using the following formula:

[0013] in, Represents the cross-correlation entropy based on the Gaussian kernel function, where N is the sliding window length;

[0014] For the state residual, the first Historical residuals weight The calculation is performed using a similar formula, where the measurement residual is replaced by the state residual.

[0015] More preferably, step S3 further includes an adaptive kernel bandwidth adjustment step: calculating the noise mutation index of each component of the current measurement residual. ,in This represents the sample variance of the difference within the sliding window;

[0016] like If T is the chi-square test threshold, it is determined to be a noise mutation, and the kernel bandwidth is adjusted by the minimum value of the squared residual difference within the sliding window; otherwise, the kernel bandwidth is adjusted by the maximum value.

[0017] More preferably, in step S4, the measurement noise covariance matrix The estimated value is:

[0018] in, For weighted sample covariance, Let H be the prior state covariance matrix, and H be the measurement matrix.

[0019] More preferably, in step S5, the hybrid weighting mechanism constructs the final weights using the following formula. :

[0020] in, For weights based on cross-correlation entropy, Huber robust weights are defined as follows:

[0021]

[0022] in, To observe the residuals, This is the Huber threshold.

[0023] More preferably, in step S5, the positive definiteness process includes: before calculating the Kalman gain, adjusting the matrix S... k =HP k|k−1 H T +R k Add a small regularization term In the state covariance matrix After |k is updated, execute Operation, among which And δ is a small positive number, and I is the identity matrix.

[0024] More preferably, the estimation error of the method is eventually bounded by the mean square exponential, and its stability is achieved by constructing a Lyapunov function. And prove the existence of positive constants. , making Established and guaranteed, among which This represents the state estimation error.

[0025] More preferably, the sliding window length N=30, and the chi-square test threshold... Huber Robust Weight Threshold .in, It is the critical value of the chi-square distribution with 1 degree of freedom at a significance level of α=0.05; It is a balance point that ensures that when the data follows a normal distribution, the variance estimated using Huber is approximately 95% of the variance estimated using traditional least squares.

[0026] Furthermore, based on the improved cross-correlation entropy weighted extended Kalman filter algorithm described above, this invention also provides a sensorless control system for a doubly-fed induction generator. The system includes a processor and a memory, the memory storing a computer program. When the processor executes the computer program, it implements the steps of the above-described extended Kalman filter rotor speed estimation method for a doubly-fed induction generator based on maximum cross-correlation entropy weighting.

[0027] Compared with existing technologies, the extended Kalman filter-based rotor speed estimation method for doubly-fed induction generators based on maximum cross-correlation entropy weighting has the following advantages and advancements:

[0028] (1) This invention introduces cross-correlation entropy from information theory into the extended Kalman filter framework to quantify the local statistical similarity between the current residual and the historical residual, thereby serving as the basis for dynamically adjusting the noise covariance estimation weights. This breaks through the limitations of traditional EKF using fixed weights and AEKF using equal weights or simple adaptive rules.

[0029] (2) This invention calculates weights based on cross-correlation entropy. This enables the algorithm to fully utilize the statistical characteristics of historical information when the noise is stable, and to automatically reduce the interference of outdated historical data when the noise changes abruptly, thus achieving intelligent perception and adaptation to time-varying noise environments.

[0030] (3) This invention combines the chi-square test to detect the statistical characteristics of the residuals, based on whether the noise undergoes a sudden change ( ), dynamically adjust the bandwidth of the Gaussian kernel function ( By narrowing the bandwidth during noise abrupt changes to enhance sensitivity to differences, and widening the bandwidth during steady-state conditions to smooth estimations and retain effective information, a balance is struck between dynamic response speed and steady-state accuracy.

[0031] (4) This invention integrates cross-correlation entropy weights and Huber robust weights. The former handles general non-Gaussian noise, while the latter specifically suppresses anomalous residuals with large amplitudes. (This process involves attenuation), creating a dual protection.

[0032] (5) This invention utilizes regularization technology ( To ensure matrix invertibility, corrections are made through symmetry and positive definiteness. This prevents the covariance matrix from losing its positive definiteness during iteration, fundamentally avoiding filter divergence.

[0033] (6) For the first time, this invention rigorously proves the final boundedness of the mean square exponent of the estimation error of the proposed CWEKF algorithm by combining the Lipschitz condition of the DFIG system and the Lyapunov stability theory, thus theoretically ensuring the stable convergence of the algorithm under various working conditions. Attached Figure Description

[0034] Figure 1 Comparison of speed estimation and error of four algorithms under sudden speed change; (a) Speed ​​estimation diagram, (b) Speed ​​error comparison diagram.

[0035] Figure 2 Flux estimation diagrams for four algorithms under sudden changes in rotational speed.

[0036] Figure 3 Four algorithms for rotor current estimation in the αβ coordinate system under sudden speed changes.

[0037] Figure 4 The Q-value changes of four algorithms under sudden speed changes: (a) Q-value of EKF, (b) Q-value of EKF (first 4), (c) Q-value of AEKF, (d) Q-value of AEKF (first 4), (e) Q-value of RWEKF, (f) Q-value of RWEKF (first 4), (g) Q-value of CWEKF, (h) Q-value of CWEKF (first 4).

[0038] Figure 5 The changes in R-values ​​of the four algorithms under sudden changes in rotational speed.

[0039] Figure 6 : Comparison of speed estimation and error of four algorithms under sudden change; (a) speed estimation, (b) speed error.

[0040] Figure 7 : Rotor flux estimation using four algorithms under abrupt changes.

[0041] Figure 8 : Four algorithms for rotor current estimation under sudden changes.

[0042] Figure 9 : The Q-value changes of the three algorithms under mutation: (a) Q-value of AEKF, (b) Q-value of the first 4 AEKF, (c) Q-value of RWEKF, (d) Q-value of the first 4 RWEKF, (e) Q-value of CWEKF, (f) Q-value of the first 4 CWEKF.

[0043] Figure 10 : The changes in R values ​​of the two algorithms under mutation: (a) the changes in R values ​​of RWEKF, and (b) the changes in R values ​​of CWEKF.

[0044] Figure 11 Comparison of speed estimation and error of four algorithms under rotor current noise interference; (a) Speed ​​estimation diagram, (b) Speed ​​error comparison diagram.

[0045] Figure 12 Flux estimation diagrams for four algorithms under rotor current noise interference.

[0046] Figure 13 Rotor current estimation diagrams for four algorithms under rotor current noise interference.

[0047] Figure 14 The Q-value changes of the four algorithms under rotor current noise interference: (a) Q-value of AEKF, (b) Q-value of the first 4 AEKF, (c) Q-value of RWEKF, (d) Q-value of the first 4 RWEKF, (e) Q-value of CWEKF, (f) Q-value of the first 4 CWEKF.

[0048] Figure 15 The changes in R value for four algorithms under rotor current noise interference: (a) R change for RWEKF, (b) R change for CWEKF. Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] This invention proposes an improved cross-correlation entropy weighted extended Kalman filter algorithm, aiming to enhance the robustness and accuracy of DFIG rotor speed estimation. The following embodiments mainly focus on the following aspects:

[0051] (1) Based on Faraday's law of electromagnetic induction and the equation of mechanical motion, a DFIG nonlinear state-space model suitable for speed estimation is constructed, and the influence of cross-coupling terms on the estimation accuracy is clarified.

[0052] (2) The cross-correlation entropy theory in information theory is introduced to design a dynamic weighting scheme for residuals. The noise covariance weight is adaptively adjusted by the local similarity between the current residual and the historical residual, and an adaptive kernel bandwidth mechanism is constructed by combining the chi-square test to balance the dynamic response speed and steady-state accuracy of the algorithm.

[0053] (3) To address the potential numerical instability of the original algorithm under extreme conditions, a hybrid weighting mechanism is constructed by integrating Huber robust weights and orthogonalization to ensure the positive definiteness of the covariance matrix.

[0054] (4) The mean square exponential final bound of the CWEKF estimation error is proved using the Lipschitz condition and Lyapunov theory. In the MATLAB / Simulink environment, CWEKF is compared with algorithms such as EKF, AEKF, and RWEKF under various operating conditions including speed step changes, parameter mutations, and strong noise interference. This study aims to provide a more robust state estimation scheme for the DFIG sensorless control system, laying a theoretical foundation for the design of high-performance controllers in subsequent chapters.

[0055] Example 1: Construction of the mathematical model of a doubly-fed induction generator

[0056] To achieve sensorless speed estimation of DFIG, a state vector containing measurable rotor current is constructed. Rotor flux that cannot be directly measured And the key state variables that need to be estimated The control input vector represents the output of the rotor-side converter. of shaft and Shaft voltage is used to adjust the electromagnetic characteristics of the DFIG. The measurement vector is defined as the measured rotor current. The general form of the DFIG state equations is:

[0057] (4-1)

[0058] in, Representing the state nonlinear dynamics term, including , , , , . This represents Gaussian noise that follows a zero-mean Gaussian distribution. Its components are as follows:

[0059] (4-2)

[0060] (4-3)

[0061] (4-4)

[0062] (4-5)

[0063] (4-6)

[0064] Input matrix Defined as:

[0065] (4-7)

[0066] Rotor current , It can be directly measured by a current sensor. The measurement equation describes the observable output. With state vector The relationship between them is represented as:

[0067] (4-8)

[0068] in, To measure noise, To measure the noise covariance matrix. Measurement matrix. Used to extract rotor current components from the state vector. Represented as:

[0069] (4-9)

[0070] Example 2: CWEKF Algorithm Design

[0071] 1. Traditional Extended Kalman Filter

[0072] Traditional EKF can achieve state estimation of nonlinear systems, and its operation is divided into two stages: prediction and update. In the prediction stage, it utilizes... The posterior state estimate at time k and the nonlinear state function generate the state prediction at time k:

[0073] (4-10)

[0074] in Represents the sampling time. The nonlinear function... exist Linearization is performed at this point, and the Jacobian matrix is... By calculating all nonlinear functions The partial derivatives with respect to the state variables yield a 5x5 Jacobian matrix. :

[0075] (4-11)

[0076] Subsequently, the prior state estimation covariance is updated using the Jacobian matrix and the process noise covariance:

[0077] (4-12)

[0078] in It is the identity matrix. This is the discretized process noise covariance. In traditional EKF estimation, it is usually kept constant. .

[0079] During the update phase, the difference between the actual measured value and the predicted measured value is first calculated to obtain the measurement residual, which measures the degree of mismatch between the model and the measured value:

[0080] (4-13)

[0081] Subsequently, based on the statistical characteristics of state estimation error and measurement noise, the theoretical covariance of the measurement residuals is derived:

[0082] (4-14)

[0083] in To measure noise covariance, it is typically set to a fixed value in traditional EKF. .

[0084] Next, calculate the Kalman filter gain of the EKF:

[0085] (4-15)

[0086] Finally, the prior state estimate is corrected using the measurement residuals, and the state covariance matrix is ​​updated:

[0087] (4-16)

[0088] (4-17)

[0089] 2. Analysis based on the theory of cross-correlation entropy

[0090] Traditional EKF relies on a fixed process noise covariance. and measurement noise covariance This means that it treats all historical residuals the same way, making it unsuitable for time-varying noise environments. In contrast, cross-correlation entropy provides a non-linear similarity measure that can quantify local statistical dependencies between variables, thus effectively weighting dynamic residuals.

[0091] For two random variables and The cross-correlation entropy is defined as the expectation of the Gaussian kernel function of the difference between the two:

[0092] (4-18)

[0093] in for and The joint distribution function, For Gaussian kernel function:

[0094] (4-19)

[0095] in, , They are respectively , The dimensional components, For the first The kernel bandwidth of the Gaussian kernel function is dimensional. The Gaussian kernel function exhibits localization properties when... When (high similarity), The value is relatively large; when and When the differences are significant (low similarity), Approaching 0.

[0096] In practical applications, the joint distribution of residuals Since the value is unknown, the sample correlation entropy is used to approximate the theoretical correlation entropy. For the current residual... Historical residuals within the sliding window (length N) The sample correlation entropy is:

[0097] (4-20)

[0098] In the formula, The dimension of the residual vector is used to measure the residual. residual state .

[0099] 3. Residual weight design based on cross-correlation entropy

[0100] Based on the above analysis using the relevant entropy theory, the higher the similarity between historical and current residuals, the greater their weight in noise covariance estimation. For the measurement residual sequence within the sliding window... , No. Historical residuals The weights are defined as follows:

[0101] (4-21)

[0102] Among them, weight normalization .

[0103] When the measurement noise of DFIG stabilizes, the current residual Residual of History With high similarity, weight The similarity is relatively large, thus preserving effective information from historical residuals. When measurement noise changes abruptly, the similarity decreases, and the weights... It decreases accordingly. This correspondingly reduces the interference from outdated historical data.

[0104] State residuals are defined as the difference between the posterior state estimate and the prior state prediction. They reflect the amount of correction to the state estimate and are related to process noise.

[0105] (4-22)

[0106] Similarly, for the state residual sequence , No. Weights of each historical state residual Defined as:

[0107] (4-23)

[0108] in, The calculation is consistent with equation (4-21).

[0109] Example 3: Adaptive Kernel Bandwidth Analysis

[0110] 1. Residual statistical property detection

[0111] For the measurement residual sequence within the sliding window, calculate the sample mean of the i-th dimension residual. With sample variance :

[0112] (4-24)

[0113] (4-25)

[0114] Among them, adopt Perform unbiased variance estimation. Define the noise mutation index as the ratio of the current squared residuals to the sample variance:

[0115] (4-26)

[0116] For zero-mean Gaussian measurement noise ,therefore It follows a chi-square distribution with 1 degree of freedom. From the chi-square distribution table, the critical value at the 95% confidence level is... .like If the noise level changes abruptly, it is considered that the noise has changed; otherwise, the noise is in a stable state.

[0117] 2. Adaptive bandwidth

[0118] Combining the Silverman bandwidth criterion (used to determine the initial bandwidth under steady noise) and the noise mutation index, an adaptive bandwidth adjustment formula for the measurement residual is derived:

[0119] (4-27)

[0120] in, This is a Silverman constant, ensuring the kernel function has optimal smoothness when the noise is stable. When the noise abruptly changes (... When the minimum value of the squared residual difference is used as the bandwidth adjustment term, the bandwidth is reduced. This enhances the sensitivity of the correlation entropy to residual differences; when the noise is stable, the maximum value is used as an adjustment term to increase... Historical information is preserved. Similarly, the adaptive bandwidth of the state residuals... This can be achieved by modifying equations (4-24) to (4-27). Replace with It is derived that the threshold .

[0121] Example 4: and cross-correlation entropy weighted estimation

[0122] Using the covariance formula (4-14) from residual theory, the noise covariance is measured. It can be represented as:

[0123] (4-28)

[0124] Traditional AEKF uses unweighted sample covariance. approximate All residuals are treated equally. CWEKF uses the correlation entropy-weighted sample covariance instead of the theoretical expectation, which can adapt to time-varying noise.

[0125] (4-29)

[0126] Substituting equation (4-28) into equation (4-29), we get estimated value

[0127] (4-30)

[0128] Similarly, the covariance of state residuals and process noise is derived. Substitute equation (4-17) into equation (4-12) and rearrange.

[0129] (4-31)

[0130] By the definition of state residuals (4-32), its theoretical covariance is:

[0131] (4-32)

[0132] Rearranged equation (4-32), process noise covariance for

[0133] (4-33)

[0134] and Similarly, the estimation uses the correlation entropy weighted sample covariance approximation of the state residuals.

[0135] (4-34)

[0136] Substituting equation (4-34) into equation (4-33) and shifting the time step to k, we obtain The estimated value

[0137] (4-35)

[0138] Example 5: Optimization of Algorithm Numerical Stability

[0139] Although the CWEKF algorithm has extremely high estimation accuracy in steady state, it faces two key problems in actual calculations: first, the single cross-correlation entropy weight has limited ability to suppress extreme outliers (such as speed jumps); second, the covariance matrix update is prone to losing positive definiteness, leading to calculation divergence.

[0140] To address the aforementioned shortcomings, this embodiment optimizes the CWEKF algorithm from three aspects: matrix singularity suppression, mixed weight construction, and positive covariance definiteness. Equation (4-34) is rewritten as S k =HP k|k−1 H T +R k In order to ensure S k The reversibility and numerical stability of S k Modified to

[0141] (4-36)

[0142] in, =10 −8 Let I be the regularization parameter, and S be the regularization parameter. k An identity matrix of the same dimension. Based on the corrected... Kalman gain updated to

[0143] (4-37)

[0144] In addition, to enhance the CWEKF algorithm's ability to suppress extreme outliers, a dual-mechanism hybrid weight is constructed by fusing relevant entropy weights and Huber robust weights. The relevant entropy weights maintain adaptability to non-Gaussian noise, while the Huber weights specifically suppress the influence of anomalous residuals. The expression for the hybrid weights is as follows:

[0145] (4-38)

[0146] Among them, the relevant entropy weight Continuing the traditional CWEKF construction method, namely:

[0147] (4-39)

[0148] To observe the residuals, For the relevant entropy bandwidth, , For weighting coefficients, .

[0149] Huber Robust Weights Based on adaptive adjustment of residual norm, it is defined as follows:

[0150] (4-40)

[0151] in, The Huber threshold corresponds to 95% asymptotic efficiency, which can suppress abnormally large residuals while ensuring normal residual weights, thus preventing them from having an excessive impact on state updates.

[0152] To achieve adaptive adjustment of the noise covariance matrix, mixed weights are introduced. and The update process incorporates positive definiteness processing to ensure the mathematical properties of the covariance matrix. (Process noise covariance) Covariance of observation noise The update formula is

[0153] (4-41)

[0154] (4-42)

[0155] in, , Based on the basic noise covariance matrix, , This is the robust weighting coefficient, with a value range limited to [0.1, 5.0] to avoid parameter extremes. The introduction of this can prevent the problem of excessively small weights. Overflow problem. State covariance matrix. After the update, the positive definiteness is easily lost due to numerical errors, and symmetry and positive definiteness corrections are required.

[0156] (4-43)

[0157] Example 6: Convergence Analysis of the CWEKF Algorithm

[0158] To ensure the stability of CWEKF in DFIG rotor speed estimation, this embodiment uses Lyapunov theory and the Lipschitz condition to prove that its estimation error is exponentially bounded in the mean-square sense. For the DFIG nonlinear system and the CWEKF algorithm, the following assumptions are proposed:

[0159] Assumption 1: Nonlinear function The Lipschitz condition must be satisfied, i.e., there exists a constant. For any ,have:

[0160] (4-44)

[0161] Note: This assumption holds in physical systems because the DFIG model is smooth and its partial derivatives (Jacobi matrix) are bounded.

[0162] Assumption 2 (Bounded Noise): The mean square values ​​of process noise and measurement noise are bounded.

[0163] (4-45)

[0164] in, It is a positive number.

[0165] Assumption 3 (Bounded Covariance): The estimated noise covariance matrix and state covariance matrix both satisfy the boundedness condition:

[0166] (4-46)

[0167] (4-47)

[0168] In the formula, It is a positive number.

[0169] Based on the above assumptions, the following lemma is introduced for stability determination.

[0170] Lemma 1: Let It is a random process. If a random function exists... and positive real constants The following conditions must be met:

[0171] (4-48)

[0172] (4-49)

[0173] Then the random process It is bounded by the mean square exponent, that is, it satisfies

[0174] (4-50)

[0175] Proof: Define the state estimation error as... Therefore, proof is required. The mean square exponent is bounded.

[0176] First, we choose the Lyapunov function as:

[0177] (4-51)

[0178] According to hypothesis 3 (4-47), the inverse of the state covariance matrix satisfies:

[0179] (4-52)

[0180] Substituting equation (4-52) into equation (4-51), we get Upper and lower bounds:

[0181] (4-53)

[0182] The above equation satisfies the first condition in Lemma 1 (Equation 4-48), where the correlation coefficient is defined as:

[0183] (4-54)

[0184] Based on the state update equation (4-36) and the definition of estimation error, the updated estimation error can be rewritten as:

[0185] (4-55)

[0186] in This represents the prior estimation error.

[0187] Combining the state prediction equation (4-27) and hypothesis 1 (Lipschitz condition), the prior estimation error satisfies:

[0188] (4-56)

[0189] Substitute the error recursive equations (4-55) and (4-56) into the Lyapunov function and calculate the conditional expectation.

[0190] (4-57)

[0191] Expand the quadratic form and utilize noise and The independence of the terms (with the expected value of the cross term being zero) yields:

[0192] (4-58)

[0193] Among them, related items , and They are defined as follows:

[0194] (4-59)

[0195] (4-60)

[0196] (4-61)

[0197] The boundedness of T1, T2, and T3 is then analyzed.

[0198] Based on assumptions 2 and 3, and The norms of all are bounded. Let Let be the gain correlation coefficient, then we have

[0199] (4-62)

[0200] in, (Due to filter gain) (To ensure stability during the update phase) Explanation Bounded.

[0201] Similarly, based on the assumptions, there exists a constant. Make:

[0202] (4-63)

[0203] Therefore, we can know The terms are also bounded.

[0204] In summary, the difference in conditional expectations satisfies:

[0205] (4-64)

[0206] make and Then equation (4-64) completely satisfies the second condition of Lemma 1 (equation 4-49).

[0207] According to Lemma 1, the DFIG rotor speed estimation error is exponentially bounded in the mean-square sense. Thus, the stability of the CWEKF algorithm is theoretically proven.

[0208] Example 7: Experimental Verification and Result Analysis

[0209] 1. Simulation settings and algorithm parameter description

[0210] This experiment constructed a complete state estimation test platform for a doubly-fed induction generator (DFIG) to comprehensively evaluate the performance of four extended Kalman filter algorithms under different operating conditions. A 3kW DFIG was selected as the research object, with the following main physical parameters: stator resistance 3.127Ω, rotor resistance 3.55Ω, stator and rotor inductances 0.2533H and 0.2556H respectively, mutual inductance 0.2472H, number of pole pairs 3, and moment of inertia 0.1kg·m². The test platform employed discrete-time simulation with a sampling period of 1ms to ensure sufficient time resolution for capturing the dynamic characteristics of the generator.

[0211] In the state-space model, the state vector contains five key variables: the αβ component of the rotor current, the αβ component of the rotor flux linkage, and the rotor speed. In the experiment, the rotor speed reference values ​​were set to the rated speed of 1500 r / min and the synchronous speed of 1200 r / min. The measurement system only provides the αβ component of the rotor current to simulate the limited situation in actual industrial scenarios where information can only be obtained through current sensors. Since the rotor flux linkage and speed are state variables that cannot be directly measured, they need to be estimated in real time using a state observer. The algorithms compared in this experiment include the traditional EKF, AEKF, RWEKF, and the CWEKF proposed in this invention. To ensure the fairness of the comparison, each algorithm used the exact same initial conditions and covariance matrix settings.

[0212] To verify the superiority of the CWEKF algorithm, three typical operating conditions were designed for the experiment, covering scenarios ranging from ideal Gaussian noise to complex non-Gaussian noise and parameter perturbation. These conditions specifically included: sudden changes in rotor speed and stator resistance. Sudden changes and rotor current noise interference.

[0213] Regarding parameter configuration, the physical meaning and settings of the process noise covariance Q and measurement noise covariance R are as follows: Q 11 With Q 22 Corresponding to rotor currents shaft and The process noise of the axial component reflects the error and uncertainty of the current model, and the two are symmetrical; Q 33 With Q 44These represent the rotor flux linkages. shaft and The process noise of the axis components reflects the error of the flux linkage observation model; Q 55 This represents the process noise of the rotor speed, used to reflect the modeling error of the speed model.

[0214] The specific initial parameters for the experiment are set as follows: initial state Initial state covariance (Units are A², A², Wb², Wb², (rad / s)² respectively). Additionally, the sliding window length... Sampling time Chi-square test threshold The four algorithms shared the same initial value of noise covariance at the start of the experiment, i.e. , By observing the adaptive adjustment of the Q and R matrices under different operating conditions, this study will comprehensively evaluate the robustness and adaptability of the four algorithms under various practical application conditions.

[0215] 2. Scenario 1 (Experiment on Step Change of Rotor Speed)

[0216] Scenario 1 was used to test the dynamic response capabilities of the four algorithms under step changes in rotational speed. The total experiment duration was 20 seconds, and the rotational speed setpoints were as follows: 300 r / min for 0-8 seconds; stepping to 500 r / min at 8 seconds; stepping to 1000 r / min at 13 seconds; and suddenly dropping to 600 r / min at 16 seconds. Figure 1 The speed estimation curves of each algorithm and their error comparison are shown. The results show that all four algorithms can achieve accurate estimation during the stable operation phase, but they exhibit significant differences during the transient processes of sudden speed changes (8s, 13s, 16s).

[0217] Table 1 provides a detailed comparison of overshoot and response time after three step jumps. The data shows that, under the experimental model, the estimation accuracy of all four algorithms remains at a high level, with maximum speed deviations of approximately 4.86 r / min (EKF / AEKF) and 5.01 r / min (RWEKF / CWEKF), respectively. Notably, the response times of RWEKF and CWEKF are approximately 0.023 s shorter than those of EKF and AEKF. This is attributed to the real-time update mechanism of the Q and R matrices in these two algorithms, effectively balancing the dynamic response speed and steady-state performance of the system.

[0218] Table 1: Comparison of overshoot and response time for four algorithms

[0219]

[0220] also, Figure 2 and Figure 3 The results show that the rotor flux linkage trajectory remains stable during sudden speed changes, and the rotor current only experiences a brief distortion at the moment of the change and recovers quickly. The rotor current frequency adjusts synchronously with the speed change, which is consistent with the DFIG operating principle. Figure 4 and Figure 5 The dynamic adjustment of Q and R values ​​was analyzed. The parameters of EKF remained constant, while the Q values ​​of AEKF, RWEKF, and CWEKF showed higher sensitivity. In particular, CWEKF exhibited unique R-value adjustment characteristics at different rotational speeds: it utilized correlation entropy to quantify the local similarity of residuals, reduced the weight of historical data at abrupt changes to avoid interference, and increased the weight during the stable period to utilize statistical information, thus demonstrating optimal sensitivity.

[0221] Figure 4 and Figure 5 The changes in Q and R values ​​during the simulation process for four algorithms are shown. Specifically, Figure 4 (a) shows the Q value of the EKF algorithm at each time step, which remains constant throughout; Figure 4 Figures (c), (e), and (g) respectively illustrate the Q-value changes for the AEKF, RWEKF, and CWEKF algorithms. Figure 4 (d), (f), and (h) are magnified views of these three sets of curves, respectively. It can be observed that the Q-value components related to current and flux linkage fluctuate relatively little, while the Q-value components related to rotational speed change significantly. This phenomenon is highly consistent with the theoretical analysis results presented earlier.

[0222] A larger Q-value indicates lower confidence in the system model by the filter, leading to greater reliance on measurement data to correct state estimates; conversely, a smaller Q-value indicates higher confidence in the model and stronger measurement noise suppression capabilities. Figure 4 It can be seen that the Q-value adjustment mechanisms of AEKF, RWEKF and CWEKF are more sensitive, thus effectively ensuring the high accuracy of rotor current estimation.

[0223] Figure 5 The changes in R-values ​​for four algorithms at different time points are shown. Figure 5 As shown in (a) and (b), the R values ​​of EKF and AEKF remain constant. Figure 5As shown in (c) and (d), the R-values ​​of RWEKF and CWEKF change dynamically over time. RWEKF exhibits significant fluctuations only during sudden changes in rotational speed, consistent with its theoretical analysis: the R-value is amplified only when the residual exceeds a threshold to reduce the weight of outlier measurements, while remaining constant within the normal range. In contrast, the R-value of CWEKF exhibits different adjustment characteristics at different rotational speeds. This is because CWEKF utilizes correlation entropy to quantify the local similarity between the current residual and historical residuals, reducing the weight of historical residuals at the moment of sudden change to avoid interference from outdated data, and increasing the weight during stable operation to retain effective statistical information. Therefore, CWEKF demonstrates higher sensitivity in the dynamic adjustment of Q-values ​​and R-values.

[0224] 3. Scenario 2 (Stator Resistance) (Parameter mutation experiment)

[0225] Scenario 2 aims to test the four algorithms in terms of stator resistance. Dynamic response capability under abrupt change scenarios. The simulation time was set to 20 seconds, and the rotation speed was maintained at 1000 r / min throughout. hour, It suddenly increases to 1.5 times the initial value and lasts for 5 seconds, then... It will then return to its initial value. Figure 6 (a) and (b) show the speed estimation results and error curves of the four algorithms under this operating condition, respectively. Figure 6 (a) It can be seen that, in At the moment of the two sudden changes, the maximum errors in the estimated rotational speed of EKF and AEKF reached 118 r / min and 83 r / min, respectively; in contrast, the errors of RWEKF and CWEKF were successfully controlled within 5 r / min. Figure 7 for The comparison chart of flux linkage estimation under abrupt change conditions clearly shows that the flux linkage trajectory circles of RWEKF and CWEKF are more stable than the other two algorithms.

[0226] Figure 8 The rotor current estimation waveforms for four different algorithms are shown. Figure 6 The rotational speed changes in the two parameters are consistent, and the estimated currents of EKF and AEKF are in... Significant shifts occurred during the abrupt changes: the estimated current amplitude decreased significantly between 10 and 15 seconds; while the estimated currents of RWEKF and CWEKF fluctuated only slightly at the two abrupt change points of 10 and 15 seconds, remaining stable for the rest of the time.

[0227] The theoretical basis for this superior performance lies in the fact that RWEKF focuses on suppressing outliers, and its Q and R matrices are adjusted based on preset threshold segments. In contrast, CWEKF's Q-value changes continuously and is directly related to the noise distribution; by adjusting the kernel width, the algorithm's sensitivity to dynamic changes in small signals can be precisely controlled. Simultaneously, CWEKF's R-value can dynamically adapt to measurement reliability, effectively handling measurement fluctuations in non-Gaussian noise scenarios. Therefore, when... Even with parameter perturbations, RWEKF and CWEKF can still maintain high-accuracy speed estimation. The evolution of Q and R values ​​for each algorithm in scenario two is as follows: Figure 9 and Figure 10 As shown above, the experimental results are highly consistent with the theoretical analysis of CWEKF: the hybrid weighting mechanism can significantly weaken the influence of anomalous residuals, while accurate modeling quantifies the nonlinearity of the system, jointly ensuring the estimation robustness of CWEKF during parameter mutation processes.

[0228] 4. Scenario 3 (Rotor Current Noise Interference Experiment)

[0229] Scenario 3 is a rotor current noise interference scenario, in the current loop shaft and Bandwidth-limited white noise was injected simultaneously into the shaft, with the noise power set to 0.1W. Under these conditions, the Q parameter of CWEKF is deeply coupled with the noise distribution characteristics, enabling real-time matching of the noise's statistical regularity during the 10-15s noise injection period. Through adaptive adjustment of the kernel width, the algorithm effectively suppresses unnecessary fluctuations caused by small-signal noise. Simultaneously, the R parameter, based on a dynamic update mechanism of measurement reliability, accurately identifies noise interference and valid signals, ensuring precise capture of the motor's true state even in high-noise environments. Experimental results show that CWEKF's speed estimation error is controlled within ±5%, and its rotor current estimation accuracy is significantly better than other comparative algorithms, such as... Figure 11 As shown.

[0230] Depend on Figure 11 It is evident that, due to their reliance on fixed Q or R matrices, the EKF and AEKF algorithms suffer from rotational speed estimation errors exceeding ±30%, with curve fluctuations reaching over 300 r / min. Although RWEKF optimizes estimation performance using random weights, its error remains around ±8%. In contrast, CWEKF employs an adaptive kernel bandwidth mechanism to narrow the bandwidth during noise injection to enhance residual sensitivity, and then expands the bandwidth after system stabilization. Ultimately, CWEKF's estimation error is strictly limited to within ±5%, and the smoothness of the estimation curve exceeds 95%, fully validating the theoretical superiority of correlation entropy in handling non-Gaussian noise.

[0231] In CWEKF theory, Q and R are estimated in real time using correlation entropy-weighted residuals, which can dynamically match the statistical characteristics of non-Gaussian noise. Figure 14 and Figure 15 This has been verified. (By...) Figure 14 It can be seen that the Q value of AEKF fluctuates irregularly, while the Q value of RWEKF shows an abnormal jump of up to 50%. In stark contrast, the Q value of CWEKF adjusts very smoothly during the noise injection period (10s to 15s), with the fluctuation range controlled within 10%, which is highly consistent with the distribution characteristics of the injected noise (0.1W bandwidth-limited white noise). Figure 15 The results show that the R-value of RWEKF exhibits pulse-like fluctuations, while the R-value of CWEKF demonstrates a continuous dynamic adaptive process, with the adjustment amplitude positively correlated with noise intensity. This further verifies the superiority of the R-value estimation method based on measurement residual correlation entropy weighting in non-Gaussian scenarios. Simultaneously, this also confirms the boundedness of the mean square exponential of the estimation error, as proven by Lyapunov theory, meaning that CWEKF still does not face the risk of filter divergence under strong noise interference.

[0232] As can be seen from the above embodiments, in the sensorless speed estimation of doubly-fed induction generators, the traditional EKF algorithm suffers from low estimation accuracy and poor robustness due to the influence of model nonlinearity, time-varying noise, and parameter mutations. This embodiment proposes a correlation entropy weighted extended Kalman filter algorithm. Through theoretical derivation and simulation experiments, the following conclusions are drawn:

[0233] (1) By introducing the relevant entropy theory to design the dynamic weight of the residuals, the local similarity between the current residuals and the historical residuals is used to adaptively adjust the covariance estimation weights, thereby suppressing the interference of historical data. The adaptive kernel bandwidth is derived by combining the chi-square test and the statistical characteristics of the residuals, which balances the response speed to noise mutations and the steady-state accuracy, and solves the problems of poor adaptability of fixed Q and R matrices and response delay in the traditional EKF algorithm.

[0234] (2) A hybrid weighting mechanism was constructed by integrating Huber robust weights and regularization techniques to weaken the impact of abnormal residuals and ensure the invertibility of the covariance matrix. By optimizing the positive definite correction of the state covariance, filter divergence caused by matrix singularity under parameter mutations and strong noise was avoided, thus improving reliability under extreme conditions.

[0235] (3) Based on the Lipschitz condition and Lyapunov theory, the boundedness of the mean square exponent of the CWEKF estimation error was proved. Furthermore, simulation models established using MATLAB / Simulink and comparative experimental results show that the maximum speed estimation error of the CWEKF algorithm is ≤5 r / min, the response time is shortened by more than 65% compared to EKF, and the stator resistance... It exhibits optimal robustness under conditions of sudden changes and strong rotor current noise, meeting the requirements of sensorless DFIG control.

Claims

1. A method for estimating the rotor speed of a doubly-fed induction generator based on maximum cross-correlation entropy weighting using extended Kalman filtering, characterized in that, The method includes the following steps: S1: Construct a nonlinear state-space model of a doubly-fed induction generator that includes rotor current, rotor flux linkage, and rotor speed. S2: Under the extended Kalman filter framework, obtain the measurement residual and state residual at the current moment; S3: Set a sliding window to store the historical residual sequence. Based on the cross-correlation entropy theory, calculate the similarity between the current residual and each historical residual in the historical residual sequence, and dynamically generate weighting coefficients for estimating the measurement noise covariance and process noise covariance based on the similarity. S4: Using the weighting coefficients obtained in step S3, adaptively update the measurement noise covariance matrix and the process noise covariance matrix; S5: Combining regularization techniques with Huber robust weights, a hybrid weighting mechanism is constructed to perform positive definite processing on the updated covariance matrix, calculate the Kalman gain, and complete the state estimation update; S6: Output the estimated rotor speed at the current moment.

2. The method according to claim 1, characterized in that, In step S1, the state vector of the nonlinear state-space model is x=[ , , ] T ,in For rotor current, For rotor flux linkage, The rotor speed is; the measurement vector is .

3. The method according to claim 1, characterized in that, In step S3, for the measurement residual, the first Historical residuals weight Calculated using the following formula: in, Represents the cross-correlation entropy based on the Gaussian kernel function, where N is the sliding window length; For the state residual, the first Historical residuals weight The calculation is performed using a similar formula, where the measurement residual is replaced by the state residual.

4. The method according to claim 3, characterized in that, Step S3 also includes an adaptive kernel bandwidth adjustment step: calculating the noise mutation index of each component of the current measurement residual. ,in This represents the sample variance of the difference within the sliding window; like Where T is the chi-square test threshold, it is determined to be a noise mutation, and the kernel bandwidth is adjusted by the minimum value of the square of the residual difference within the sliding window; Otherwise, adjust the kernel bandwidth using the maximum value.

5. The method according to claim 1, characterized in that, In step S4, the measurement noise covariance matrix The estimated value is: in, For weighted sample covariance, Let H be the prior state covariance matrix, and H be the measurement matrix.

6. The method according to claim 1, characterized in that, In step S5, the hybrid weighting mechanism constructs the final weights using the following formula. : in, For weights based on cross-correlation entropy, Huber robust weights are defined as follows: in, To observe the residuals, This is the Huber threshold.

7. The method according to claim 1 or 6, characterized in that, In step S5, the positive definiteness process includes: before calculating the Kalman gain, adjusting the matrix S... k =HP k|k−1 H T +R k Add a small regularization term In the state covariance matrix After |k is updated, execute Operation, among which And δ is a small positive number, and I is the identity matrix.

8. The method according to claim 1, characterized in that, The estimation error of the method is eventually bounded by the mean square exponential, and its stability is achieved by constructing a Lyapunov function. And prove the existence of positive constants. , making Established and guaranteed, among which This represents the state estimation error.

9. The method according to claim 1, characterized in that, Sliding window length N=30, chi-square test threshold Huber Robust Weight Threshold .

10. A sensorless control system for a doubly-fed induction generator, characterized in that, The system includes a processor and a memory, the memory storing a computer program, and the processor executing the computer program to implement the steps of the extended Kalman filter-based doubly-fed induction generator rotor speed estimation method as described in any one of claims 1 to 9.

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