Method for evaluating insulation state of stator winding of high-voltage generator

Abstract

The invention discloses a high-voltage generator stator winding insulation state evaluation method, and relates to the technical field of power systems, and the method comprises the steps: building a high-voltage generator stator winding insulation expansion Debye model; performing modal decomposition on the depolarization current time sequence of the high-voltage generator stator winding based on a dynamic modal decomposition algorithm to obtain each order of modal with different physical meanings; performing sparse processing on each order of modality based on a fast iterative shrinkage threshold algorithm FISTA, separating a dominant modality from a false modality, solving and expanding a Debye model by using the dominant modality, and realizing accurate collaborative identification of the number of model branches and branch parameters; and based on a solving result, performing simulation and thermal aging experiments by adopting preset model parameters. The method solves the problems that an existing method is difficult to determine the number of expanded Debye model branches of high-voltage generator stator winding insulation, the physical significance of the model is not clear, and the anti-noise capacity of a model parameter identification method is poor.

Description

Technical Field

[0001] The invention relates to the technical field of power systems, and in particular to a method for evaluating the insulation state of a stator winding of a high-voltage generator. Background Art

[0002] As the core part of modern power systems, the reliable and stable operation of large high-voltage generator sets directly determines the safe and stable operation of power systems. When high-voltage generators are in operation, the stator windings are subjected to electrical stress, thermal stress, mechanical stress and environmental stress, and the insulation ages rapidly, which can easily lead to abnormal operation or even failure. Once a sudden failure occurs in the unit, it will cause huge economic losses and the consequences will be disastrous. Therefore, accurately evaluating the insulation status of high-voltage generator stator windings is crucial to ensure the safe and stable operation of power systems.

[0003] At present, researchers use the polarization and depolarization current method (PDC) to evaluate insulation status in the following steps: equivalent modeling of the time-domain dielectric response characteristics of insulation - establishing an extended Debye model of insulation, combining the PDC test current to obtain the specific parameters of the model, and judging the insulation status based on the amplitude and change law of the parameters. Therefore, the two keys to diagnosing the insulation status of high-voltage generator stator windings using this method are: establishing an extended Debye model that conforms to the epoxy-mica composite insulation system; and using PDC test data to accurately identify the model parameters.

[0004] However, existing methods make it difficult to determine the number of branches of the extended Debye model of high-voltage generator stator winding insulation, the physical meaning of the model is unclear, and the model parameter identification method has poor noise resistance. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, a method for evaluating the insulation status of a high-voltage generator stator winding is provided by the present invention, which solves the problems that the existing methods are difficult to determine the number of branches of the extended Debye model of the high-voltage generator stator winding insulation, the physical meaning of the model is unclear, and the model parameter identification method has poor noise resistance.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for evaluating the insulation state of a high-voltage generator stator winding, comprising the following steps:

[0007] S1: Establish an extended Debye model for stator winding insulation of high-voltage generators;

[0008] S2: Based on the dynamic mode decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings;

[0009] S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsely processed to separate the dominant mode from the false mode, and the dominant mode is used to solve the extended Debye model to achieve accurate collaborative identification of the number of model branches and branch parameters;

[0010] S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

[0011] Furthermore, the depolarization current of the extended Debye model in S1 is expressed as:

[0012]

[0013] τ i =R i ×C i

[0014] Among them, i depol is the depolarization current, U0 is the polarization voltage, R0 is the insulation resistance, R i is the resistance of branch i, n is the number of relaxation branches, t is the time, τ i is the relaxation time constant, A i is the current amplitude of branch i, t p is the polarization time, C i is the capacitance of branch i.

[0015] Furthermore, S2 includes the following sub-steps:

[0016] S21: Construct the depolarization current time series into a Hankel matrix, the formula is:

[0017]

[0018] Where C is the Hankel matrix, c(·) is the depolarization current sequence, a is the number of rows of the Hankel matrix, b is the number of columns of the Hankel matrix, and N is the number of depolarization current sampling points;

[0019] S22: Based on the dynamic mode decomposition algorithm, the first b-1 columns and the last b-1 columns of the Hankel matrix are taken to form a lead matrix and a lag matrix. The relationship between the lead matrix and the lag matrix is:

[0020] C2=KC1+ε

[0021] Among them, C1 is the leading depolarization current matrix, C2 is the lagging depolarization current matrix, K is the Koopman operator, and ε is the residual matrix;

[0022] S23: Perform singular value decomposition on the advance depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space;

[0023] S24: Solve the eigenvalues ​​and eigenvectors of the low-rank operator, and based on the solution results, obtain the various modes of different physical meanings of the extended Debye model of the stator winding insulation of the high-voltage generator.

[0024] Furthermore, in S23, the leading depolarization current matrix is ​​subjected to singular value decomposition, and the formula is:

[0025] C1=UΣV *

[0026] Where U is the left singular matrix, Σ is the singular value matrix, V is the right singular matrix, and the superscript * indicates the complex conjugate transpose of the matrix;

[0027] Construct a low-rank Koopman operator in a low-rank space, the formula is:

[0028]

[0029] Among them, K r is a low-rank operator, U r is the left singular matrix U after rank truncation, V r is the left singular matrix V after rank truncation, is the singular value matrix Σ after rank truncation.

[0030] Furthermore, the eigenvalue and eigenvector of the low-rank operator are solved in S24, and the formula is:

[0031] K r W=WΛ

[0032] Where W is K r The eigenvector matrix of K r The eigenvalue diagonal matrix of ;

[0033] The various modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are:

[0034]

[0035] Among them, Φ is the modal vector, φ1, φ2, …, φ r is modal.

[0036] Furthermore, S3 includes the following sub-steps:

[0037] S31: Establish the initial amplitude coefficients of each mode;

[0038] S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparse processing to separate the dominant mode from the false mode;

[0039] S33: According to the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is:

[0040]

[0041] Among them, τ m is the time constant of branch m, T s is the sampling time interval of PDC test, λ1,λ2,…,λ m is the eigenvalue corresponding to the dominant mode, A1, A2, …, A m is the amplitude coefficient of branch m.

[0042] Furthermore, the S31 includes the following sub-steps:

[0043] S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is:

[0044]

[0045] Among them, C1 is the leading depolarization current matrix, D α is the initial amplitude coefficient matrix, V and is the Vandermonde matrix containing the main insulation relaxation characteristics, the superscript T is the transpose of the matrix, α1,α2,…,α r is the initial amplitude coefficient of each mode, λ1,λ2,…,λ r is the eigenvalue corresponding to each mode;

[0046] S312: According to the leading depolarization current matrix including the initial amplitude coefficient, the reconstruction error caused by it is obtained, and the reconstruction error is solved to complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is:

[0047]

[0048] q=diag(V and VΣ * W) T

[0049] s=tra(Σ * Σ)

[0050] α=[α1α2…α r ] T

[0051] Among them, J(·) is the reconstruction error, α is the vector composed of the amplitude coefficients of each order mode, ||·|| F is the Frobenius norm, tra(·) is the trace of the matrix, P is the first parameter, q is the second parameter, s is the third parameter, and diag(·) is the column vector formed by taking the main diagonal elements of the matrix;

[0052] The vector α formed by the amplitude coefficients of each order mode is solved as follows:

[0053] α=P -1 q.

[0054] Further, the S32 includes the following sub-steps:

[0055] S321: Use 1-norm as regularization penalty function to establish the objective function H for optimizing the initial amplitude coefficients of each mode. The formula is:

[0056]

[0057] S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, so as to eliminate the false modes and achieve the separation of the dominant mode and the false mode.

[0058] Furthermore, the fast iterative shrinkage threshold algorithm FISTA is used in S322 to iteratively solve the objective function of optimizing the initial amplitude coefficients of each order mode, including the following sub-steps:

[0059] S3221: α=P -1 The α calculated by q is set as the initial value of iteration α0, the initial value of momentum term y1=α0, the initial value of momentum acceleration parameter t1=1, and the step size L is the Lipschitz constant of the objective function;

[0060] S3222: Perform gradient descent solution, the formula is:

[0061]

[0062] Among them, α' k is the value of α at the kth iteration, is the regularization penalty function f(α) at ​​point y k The gradient at y k is the momentum variable;

[0063] S3223: To α' k Perform soft threshold shrinkage to obtain the α for the next iteration k for:

[0064]

[0065] Among them, Shrink(·) is the soft threshold function, ε0 is the threshold of the soft threshold operation;

[0066] S3224: Update momentum acceleration parameter t k for:

[0067]

[0068] Among them, t k+1 is the updated momentum acceleration parameter t k ;

[0069] S3225: According to α k and t k+1 Update the momentum variable y for the next step k+1 for:

[0070]

[0071] S3226: Momentum variable y based on the next step k+1 , return to step S3222 to perform an iterative loop until the convergence condition is reached and the iteration is stopped. The convergence condition is:

[0072] ||α k -α k-1 ||≤ε end

[0073] Among them, ε end is the preset convergence threshold.

[0074] Furthermore, in S322, in order to eliminate the false modes, the amplitude of the false modes is set to zero, so that each dominant mode corresponds to the branch of the extended Debye model in a one-to-one manner. The formula is:

[0075] minJ(α),stE T α=0

[0076] Where E is a matrix whose column vectors are unit vectors.

[0077] The beneficial effects of the present invention are as follows: the present invention proposes an evaluation method based on sparse enhanced dynamic decoupling of depolarization current, which can automatically determine the number of branches of the extended Debye model of the main insulation of the stator winding of a high-voltage generator, and has a clear physical meaning. At the same time, the method has strong robustness and excellent identification accuracy. First, the modal decomposition of the depolarization current time series is performed based on the dynamic mode decomposition algorithm (Dynamic Mode Decomposition, DMD) to obtain various modes with different physical meanings. Subsequently, the fast iterative shrinkage threshold algorithm FISTA is introduced to perform sparse processing on each order mode, separate the dominant mode from the false mode, and use the dominant mode to solve the model parameters, so as to realize the automatic determination of the extended Debye model branches and the accurate identification of the model parameters. Finally, the accuracy of the method is verified by simulation experiments with preset model parameters, and the feasibility of the method is verified by evaluating the insulation state and characterizing the microscopic performance of stator bars under different thermal aging conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is a flow chart of a method for evaluating the insulation status of a high-voltage generator stator winding.

[0079] Figure 2 Wiring diagram for PDC test.

[0080] Figure 3 Schematic diagram of the expanded Debye model.

[0081] Figure 4 This is the identification result diagram with 5% noise.

[0082] Figure 5 Schematic diagram of stator bar sample dimensions. DETAILED DESCRIPTION

[0083] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0084] like Figure 1 As shown, a method for evaluating the insulation status of a high-voltage generator stator winding comprises the following steps:

[0085] S1: Establish an extended Debye model for stator winding insulation of high-voltage generators;

[0086] S2: Based on the dynamic mode decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings;

[0087] S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsely processed to separate the dominant mode from the false mode, and the dominant mode is used to solve the extended Debye model to achieve accurate collaborative identification of the number of model branches and branch parameters;

[0088] S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

[0089] The process of using the PDC method to evaluate the insulation status of high-voltage generator stator bars is as follows: Figure 2 In the test circuit shown, the slot of the wire rod is tightly attached to the copper foil and then connected to the test pole. The shielding rings on both sides of the copper foil are grounded to shield the influence of the surface current. The polarization voltage U0 is applied to the copper conductor of the wire rod to polarize the main insulation of the wire rod. During the test, the time domain dielectric response characteristics of the main insulation of the stator winding of the high-voltage generator can be equivalent to a multi-branch RC circuit composed of a series of series-parallel resistors and capacitors, which is called the extended Debye model, such as Figure 3 shown.

[0090] Each branch in the model represents a type of relaxation or conductance process. R0 is the insulation resistance, which represents the conductance process of the main insulation under the action of the electric field; C0 is the geometric capacitance, which represents the sum of the instantaneous polarization process of the main insulation. Since the instantaneous polarization process takes a very short time, the measurement equipment cannot record the response process; R i , C i The series branches represent various types of relaxation processes inside the main insulation. After equivalently evaluating the time domain dielectric response characteristics of the main insulation of the stator winding of the high-voltage generator, the following depolarization current is obtained.

[0091] The depolarization current of the extended Debye model in S1 is expressed as:

[0092]

[0093] τ i =R i ×C i

[0094] Among them, i depol is the depolarization current, U0 is the polarization voltage, R0 is the insulation resistance, R i is the resistance of branch i, n is the number of relaxation branches, t is the time, τ i is the relaxation time constant, A i is the current amplitude of branch i, t p is the polarization time, C i is the capacitance of branch i.

[0095] Therefore, to use the PDC method to evaluate the insulation status of high-voltage generator stator bars, we must first determine the number of relaxation branches n with clear physical meaning. On this basis, the test data is used to accurately solve the insulation resistance R0 and the branch relaxation strength coefficient A. i and the relaxation time constant τ i , only then can the insulation status evaluation of the stator bars of the high-voltage generator be realized.

[0096] In order to solve the problem of unclear physical meaning of the branch number of the extended Debye model, the present invention introduces the DMD algorithm to perform modal decomposition on the depolarization current time series to obtain each order mode with clear physical meaning. Subsequently, the fast iterative shrinkage threshold algorithm FISTA is introduced to perform sparse enhancement processing on each order mode, which improves the robustness of the identification method, separates the dominant mode from the false mode, and uses the dominant mode to solve the extended Debye model, realizing the accurate collaborative identification of the branch number and branch parameters of the extended Debye model of the stator winding insulation of the high-voltage generator.

[0097] The S2 includes the following sub-steps:

[0098] S21: Construct the depolarization current time series into a Hankel matrix, the formula is:

[0099]

[0100] Where C is the Hankel matrix, c(·) is the depolarization current sequence, a is the number of rows of the Hankel matrix, b is the number of columns of the Hankel matrix, and N is the number of depolarization current sampling points;

[0101] S22: Based on the dynamic mode decomposition algorithm, the first b-1 columns and the last b-1 columns of the Hankel matrix are taken to form a lead matrix and a lag matrix. The relationship between the lead matrix and the lag matrix is:

[0102] C2=KC1+ε

[0103] Among them, C1 is the leading depolarization current matrix, C2 is the lagging depolarization current matrix, K is the Koopman operator, and ε is the residual matrix;

[0104] S23: Perform singular value decomposition on the advance depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space;

[0105] S24: Solve the eigenvalues ​​and eigenvectors of the low-rank operator, and based on the solution results, obtain the various modes of different physical meanings of the extended Debye model of the stator winding insulation of the high-voltage generator.

[0106] In S23, the advance depolarization current matrix is ​​subjected to singular value decomposition, and the formula is:

[0107] C1=UΣV *

[0108] Where U is the left singular matrix, Σ is the singular value matrix, V is the right singular matrix, and the superscript * indicates the complex conjugate transpose of the matrix;

[0109] Construct a low-rank Koopman operator in a low-rank space, the formula is:

[0110]

[0111] Among them, K r is a low-rank operator, U r is the left singular matrix U after rank truncation, V r is the left singular matrix V after rank truncation, is the singular value matrix Σ after rank truncation.

[0112] The depolarization test of the stator winding of a high-voltage generator usually lasts 10-30 minutes. To ensure the test accuracy, the test sampling rate is usually not less than 20Hz, which results in an extremely large amount of data for a single test. It is time-consuming to directly solve the operator K, which is not conducive to the rapid dynamic decoupling analysis of the depolarization current data on site.

[0113] In order to speed up the calculation and prevent calculation divergence, the Koopman operator is approximated by low rank. Since the order of magnitude of noise in field tests is smaller than the order of magnitude of depolarization current, the rank truncation operation eliminates the influence of various test noises in field tests to a certain extent, thereby improving the robustness of this method. After a large number of test analyses, it was found that the steady-state value of the depolarization current is used as the rank truncation threshold and truncation can meet the subsequent calculation requirements, thus avoiding the problem of insufficient prior knowledge of on-site maintenance personnel and lowering the threshold for use of this method. Assuming the rank truncation is r, a low-rank operator K that can reflect the characteristics of the A matrix is ​​constructed in the low-rank space. r .

[0114] In S24, the eigenvalue and eigenvector of the low-rank operator are solved, and the formula is:

[0115] K r W=WΛ

[0116] Where W is K r The eigenvector matrix of K r The eigenvalue diagonal matrix of ;

[0117] The various modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are:

[0118]

[0119] Among them, Φ is the modal vector, φ1, φ2, …, φ r is modal.

[0120] Based on the DMD algorithm, dynamic decoupling of depolarization current is realized. However, each order mode after rank truncation still contains false modes caused by noise. In order to improve the robustness of the algorithm and realize the unique determination of the number of Debye branches of the stator winding insulation expansion of the high-voltage generator, the fast iterative shrinkage threshold algorithm FISTA is used to screen the amplitude coefficients of each order mode, separate the dominant mode from the false mode, and realize the accurate collaborative identification of the number of model branches and branch parameters.

[0121] The S3 comprises the following sub-steps:

[0122] S31: Establish the initial amplitude coefficients of each mode;

[0123] S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparse processing to separate the dominant mode from the false mode;

[0124] S33: According to the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is:

[0125]

[0126] Among them, τ m is the time constant of branch m, T s is the sampling time interval of PDC test, λ1,λ2,…,λ m is the eigenvalue corresponding to the dominant mode, A1, A2, …, A m is the amplitude coefficient of branch m.

[0127] The S31 comprises the following sub-steps:

[0128] S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is:

[0129]

[0130] Among them, C1 is the leading depolarization current matrix, D α is the initial amplitude coefficient matrix, V and is the Vandermonde matrix containing the main insulation relaxation characteristics, the superscript T is the transpose of the matrix, α1,α2,…,α r is the initial amplitude coefficient of each mode, λ1,λ2,…,λ r is the eigenvalue corresponding to each mode;

[0131] S312: According to the leading depolarization current matrix including the initial amplitude coefficient, the reconstruction error caused by it is obtained, and the reconstruction error is solved to complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is:

[0132]

[0133] q=diag(V and VΣ * W) T

[0134] s=tra(Σ * Σ)

[0135] α=[α1α2…α r ] T

[0136] Among them, J(·) is the reconstruction error, α is the vector composed of the amplitude coefficients of each order mode, ||·|| F is the Frobenius norm, tra(·) is the trace of the matrix, P is the first parameter, q is the second parameter, s is the third parameter, and diag(·) is the column vector formed by taking the main diagonal elements of the matrix;

[0137] The vector α formed by the amplitude coefficients of each order mode is solved as follows:

[0138] α=P -1 q.

[0139] By establishing the initial amplitude coefficients of each mode, it is convenient to use the amplitude coefficients to screen the modes later.

[0140] On the basis of determining the initial amplitude coefficient, in order to accurately screen the dominant mode representing the insulation relaxation characteristics of the high-voltage generator stator winding, the present invention introduces a penalty function to perform sparse enhanced iterative calculation, and minimizes the deviation between the dominant mode and mode containing key system information and the dynamic oscillation information contained in the leading depolarization current matrix C1, that is, the dominant mode and mode are used to achieve a hierarchical description of the leading depolarization current matrix C1. The improved optimization problem is:

[0141] minJ(α)+γf(α)

[0142] Among them, γ is the regularization parameter, and its size represents the sparsity of the penalty function. The larger the value, the higher the sparsity. f(α) is the regularization penalty function. Commonly used regularization penalty functions are 1-norm and 2-norm.

[0143] In order to save time in evaluating the insulation status of stator windings at the maintenance site, the 1-norm is selected as the regularization penalty function under comprehensive consideration of calculation time and calculation accuracy.

[0144] The S32 comprises the following sub-steps:

[0145] S321: Use 1-norm as regularization penalty function to establish the objective function H for optimizing the initial amplitude coefficients of each mode. The formula is:

[0146]

[0147] S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, so as to eliminate the false modes and achieve the separation of the dominant mode and the false mode.

[0148] By solving the objective function H, the optimal solution of α can be obtained, thereby effectively eliminating the false modes caused by various noises in the maintenance site test and improving the robustness of the algorithm. This scheme uses FISTA to iteratively solve formula H to eliminate false modal information in the system.

[0149] In the S322, the fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each order mode, including the following sub-steps:

[0150] S3221: α=P -1 The α calculated by q is set as the initial value of iteration α0, the initial value of momentum term y1=α0, the initial value of momentum acceleration parameter t1=1, and the step size L is the Lipschitz constant of the objective function;

[0151] S3222: Perform gradient descent solution, the formula is:

[0152]

[0153] Among them, α' k is the value of α at the kth iteration, is the regularization penalty function f(α) at ​​point y k The gradient at y k is the momentum variable;

[0154] S3223: To α' k Perform soft threshold shrinkage to obtain the α for the next iteration k for:

[0155]

[0156] Among them, Shrink(·) is the soft threshold function, ε0 is the threshold of the soft threshold operation;

[0157] S3224: Update momentum acceleration parameter t k for:

[0158]

[0159] Among them, t k+1 is the updated momentum acceleration parameter t k ;

[0160] S3225: According to α k and t k+1 Update the momentum variable y for the next step k+1 for:

[0161]

[0162] S3226: Momentum variable y based on the next step k+1 , return to step S3222 to perform an iterative loop until the convergence condition is reached and the iteration is stopped. The convergence condition is:

[0163] ||α k -α k-1 ||≤ε end

[0164] Among them, ε end is the preset convergence threshold.

[0165] When the optimal solution of α is obtained, in order to more intuitively screen the dominant mode, the convex optimization problem shown in the following formula is introduced, and the amplitude of the false mode is set to zero.

[0166] In the step S322, the amplitude of the false mode is set to zero to eliminate the false mode, so that each dominant mode corresponds to the branch of the extended Debye model. The formula is:

[0167] minJ(α),stE T α=0

[0168] Where E is a matrix whose column vectors are unit vectors.

[0169] The above-mentioned sparse process based on the fast iterative shrinkage threshold algorithm FISTA achieves the optimal amplitude coefficient α sp The accurate construction of provides a basis for the selection of dominant modes. sp Not 0, corresponding to the false mode α sp The dominant mode of the dielectric response of the stator winding main insulation is accurately screened out based on the characteristic of 0. According to the screening results, the various modes of the extended Debye model of the stator winding insulation of the high-voltage generator with different physical meanings are recalculated to obtain the parameters of the extended Debye model of the stator winding main insulation.

[0170] In one embodiment of the present invention, in order to verify the accuracy of the above algorithm, this embodiment uses MATLAB to generate the depolarization current time series of the three branches for branch identification, and the parameter settings of each branch are shown in Table 1. At the same time, in order to simulate the strong noise environment faced during on-site inspection, random noise is added to the three-branch simulation current data to simulate the interference in the on-site test. The depolarization current shows an exponential decay trend with time, so the signal-to-noise ratio at the end of the current is lower. This embodiment introduces random noise with a ratio of 1%, 3%, and 5% of the maximum noise amplitude to the current amplitude at the last moment of the depolarization current. In order to quantify the branch identification effect of this algorithm, the determination coefficient R is introduced. 2 and mean absolute percentage error MAPE.

[0171] Table 1 MATLAB simulation depolarization current branch parameters

[0172]

[0173] Coefficient of determination R 2 It is a statistical indicator used to evaluate the goodness of fit between the identified data and the original data. Its calculation formula is as follows. The value range is 0-1. R 2 The larger it is, the better the fitting effect is.

[0174]

[0175] Among them, c(i) is the measured current data, To identify current data.

[0176] The mean absolute percentage error (MAPE) is a statistical indicator to measure the accuracy of the prediction model. It represents the absolute percentage error between the predicted value and the actual value. The calculation formula is as follows: the smaller the MAPE value, the smaller the difference between the identification result and the original data.

[0177]

[0178] The depolarization current data under different noise conditions are identified, and the branch parameter results are shown in Table 2. Figure 4 The identification results under 5% noise are shown. As can be seen from the table and figure, as the noise amplitude gradually increases, the error of the identification result of this algorithm gradually increases, but even under 5% noise, the accuracy and robustness of this algorithm are still very good, and it is highly feasible to use this algorithm to diagnose the insulation status of stator windings in industrial sites.

[0179] Table 2 Identification results under different noise conditions

[0180]

[0181] In order to verify the practical application effect of the algorithm proposed in the present invention, a stator wire bar thermal aging verification test was carried out in the laboratory. The test sample selected a newly produced high-voltage generator stator wire bar with a rated voltage of 15.75kV and a rated capacity of 312MW. Its insulation grade is F class, the main insulation is an epoxy resin-mica-glass fiber system, and the manufacturing process is a low-glue vacuum pressure impregnation (VPI). During the experiment, a short wire bar sample was cut from the low-resistance paint section in the middle of the complete stator wire bar sample, and the sample length was 50cm. A 7cm low-resistance anti-corona tape was peeled off at both ends of the cut short sample, and a 0.3mm thick high-resistance anti-corona paint was applied at a distance of 2cm to 7cm from both ends. Subsequently, a 0.3mm thick low-resistance anti-corona paint was applied at a distance of about 5cm to 9cm from the edge as an overlap to prevent the electric field distortion at the interface between the low-resistance anti-corona tape and the high-resistance paint from affecting the test. The schematic diagram of the short sample preparation is shown in the figure. Figure 5 shown.

[0182] The prepared samples were subjected to heat aging test. The wire rod samples were placed in an electric constant temperature blast drying oven. The drying oven model was DHG-9640A, and its maximum temperature could be set to 200°C. During the heat aging process, the temperature in the oven was set to 180°C, and the aging time was 0d, 10d, 20d, and 30d. After each stage of aging, the wire rod samples were immediately subjected to PDC test. The polarization voltage was set to 3kV, and the polarization time and depolarization time were set to 300s.

[0183] The branch parameters of the depolarization current time series are identified, and the branch parameters are shown in Tables 3 to 6. It is not difficult to find from the table that with the increase of aging time, the number of branches of the equivalent Debye model of epoxy-mica insulation gradually increases, the relaxation strength of the branch also gradually increases, and the time constant gradually decreases. This is because long-term thermal aging causes the molecular chains in the macromolecular substances in the epoxy-mica insulation system to gradually break, and the substances gradually degrade into small molecular substances, which enhances the conductivity and interface polarization of the material.

[0184] Table 3 Identification results of thermal aging 0d

[0185]

[0186]

[0187] Table 4 Identification results of thermal aging for 10 days

[0188]

[0189] Table 5 Identification results of heat aging for 20 days

[0190]

[0191] Table 6 Identification results of heat aging for 30 days

[0192]

[0193] It can be seen that the R of the identification results under different aging conditions 2 All of them are greater than 0.9950, and the MAPE is less than 3%. It can be seen that in the laboratory environment where the noise level is lower than the field environment, the algorithm has good accuracy and robustness.

[0194] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the invention.

Claims

1. A method for evaluating the insulation status of a high-voltage generator stator winding, characterized in that: The following steps are involved: S1: Establish an extended Debye model for stator winding insulation of high-voltage generators; S2: Based on the dynamic mode decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings; S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsely processed to separate the dominant mode from the false mode, and the dominant mode is used to solve the extended Debye model to achieve accurate collaborative identification of the number of model branches and branch parameters; S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

2. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 1, characterized in that: The depolarization current of the extended Debye model in S1 is expressed as: t i =R i ×C i Among them, i depol is the depolarization current, U0 is the polarization voltage, R0 is the insulation resistance, R i is the resistance of branch i, n is the number of relaxation branches, t is the time, τ i is the relaxation time constant, A i is the current amplitude of branch i, t p is the polarization time, C i is the capacitance of branch i.

3. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 2, characterized in that: The S2 includes the following sub-steps: S21: Construct the depolarization current time series into a Hankel matrix, the formula is: Where C is the Hankel matrix, c(·) is the depolarization current sequence, a is the number of rows of the Hankel matrix, b is the number of columns of the Hankel matrix, and N is the number of depolarization current sampling points; S22: Based on the dynamic mode decomposition algorithm, the first b-1 columns and the last b-1 columns of the Hankel matrix are taken to form a lead matrix and a lag matrix. The relationship between the lead matrix and the lag matrix is: C2=KC1+ε Among them, C1 is the leading depolarization current matrix, C2 is the lagging depolarization current matrix, K is the Koopman operator, and ε is the residual matrix; S23: Perform singular value decomposition on the advance depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space; S24: Solve the eigenvalues ​​and eigenvectors of the low-rank operator, and based on the solution results, obtain the various modes of different physical meanings of the extended Debye model of the stator winding insulation of the high-voltage generator.

4. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 3, characterized in that: In S23, the advance depolarization current matrix is ​​subjected to singular value decomposition, and the formula is: C1=UΣV * Where U is the left singular matrix, Σ is the singular value matrix, V is the right singular matrix, and the superscript * indicates the complex conjugate transpose of the matrix; Construct a low-rank Koopman operator in a low-rank space, the formula is: Among them, K r is a low-rank operator, U r is the left singular matrix U, V after rank truncation r is the left singular matrix V after rank truncation, is the singular value matrix Σ after rank truncation.

5. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 4, characterized in that: In S24, the eigenvalue and eigenvector of the low-rank operator are solved, and the formula is: K r W=WΛ Where W is K r The eigenvector matrix of K r The eigenvalue diagonal matrix of ; The various modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are: Among them, Φ is the modal vector, φ1, φ2, …, φ r is modal.

6. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 5, characterized in that: The S3 comprises the following sub-steps: S31: Establish the initial amplitude coefficients of each mode; S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparse processing to separate the dominant mode from the false mode; S33: According to the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is: Among them, τ m is the time constant of branch m, T s is the sampling time interval of PDC test, λ1,λ2,…,λ m is the eigenvalue corresponding to the dominant mode, A1, A2, …, A m is the amplitude coefficient of branch m.

7. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 6, characterized in that: The S31 comprises the following sub-steps: S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is: Among them, C1 is the leading depolarization current matrix, D α is the initial amplitude coefficient matrix, V and is the Vandermonde matrix containing the main insulation relaxation characteristics, the superscript T is the transpose of the matrix, α1,α2,…,α r is the initial amplitude coefficient of each mode, λ1,λ2,…,λ r is the eigenvalue corresponding to each mode; S312: According to the leading depolarization current matrix including the initial amplitude coefficient, the reconstruction error caused by it is obtained, and the reconstruction error is solved to complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is: Among them, J(·) is the reconstruction error, α is the vector composed of the amplitude coefficients of each order mode, ||·|| F is the Frobenius norm, tra(·) is the trace of the matrix, P is the first parameter, q is the second parameter, s is the third parameter, and diag(·) is the column vector formed by taking the main diagonal elements of the matrix; The vector α formed by the amplitude coefficients of each order mode is solved as follows: α=P -1 Q.

8. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 7, characterized in that: The S32 comprises the following sub-steps: S321: Use 1-norm as regularization penalty function to establish the objective function H for optimizing the initial amplitude coefficients of each mode. The formula is: S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, so as to eliminate the false modes and achieve the separation of the dominant mode and the false mode.

9. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 8, characterized in that: In the S322, the fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each order mode, including the following sub-steps: S3221: α=P -1 The α calculated by q is set as the initial value of iteration α0, the initial value of momentum term y1=α0, the initial value of momentum acceleration parameter t1=1, and the step size L is the Lipschitz constant of the objective function; S3222: Perform gradient descent solution, the formula is: Among them, α' k is the value of α at the kth iteration, is the regularization penalty function f(α) at ​​point y k The gradient at y k is the momentum variable; S3223: To α' k Perform soft threshold shrinkage to obtain the α for the next iteration k for: Among them, Shrink(·) is the soft threshold function, ε0 is the threshold of the soft threshold operation; S3224: Update momentum acceleration parameter t k for: Among them, t k+1 is the updated momentum acceleration parameter t k ; S3225: According to α k and t k+1 Update the momentum variable y for the next step k+1 for: S3226: Momentum variable y based on the next step k+1 , return to step S3222 to perform an iterative loop until the convergence condition is reached and the iteration is stopped. The convergence condition is: ||a k -a k-1 ||≤e end Among them, ε end is the preset convergence threshold.

10. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 9, characterized in that: In the step S322, the amplitude of the false mode is set to zero to eliminate the false mode, so that each dominant mode corresponds to the branch of the extended Debye model. The formula is: min J(α), stE T α=0 Where E is a matrix whose column vectors are unit vectors.

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