阅读说明：本技术 基于tls-esprit的变压器油纸绝缘扩展德拜等效电路参数辨识方法 (TLS-ESPRIT-based transformer oil paper insulation expansion Debye equivalent circuit parameter identification method ) 是由 刘庆珍 苏凯强 于 2021-09-08 设计创作，主要内容包括：本发明涉及一种基于TLS-ESPRIT的变压器油纸绝缘扩展德拜等效电路参数辨识方法。该方法根据扩展德拜等效模型下去极化电流为指数函数叠加的物理特性,通过对样本数据构造的Hankel矩阵进行奇异值分解,根据奇异值变化率确定极化支路数,然后借助总体最小二乘-旋转矢量不变技术(TLS-ESPRIT)算法得到各极化支路的弛豫系数和时间常数,代入德拜等效电路参数辨识公式实现各极化支路电阻、电容参数的辨识。该发明方法避免了人为取点的主观性、极化支路数的不确定性,对具有噪声干扰的实测去极化电流起到了去噪作用,准确唯一地实现了变压器油纸绝缘扩展德拜等效电路参数的辨识。(The invention relates to a TLS-ESPRIT-based transformer oil paper insulation expansion Debye equivalent circuit parameter identification method. According to the method, according to the physical characteristic that depolarization current under an expanded Debye equivalent model is superposed by an exponential function, singular value decomposition is carried out on a Hankel matrix constructed by sample data, the number of polarization branches is determined according to the singular value change rate, then the relaxation coefficient and the time constant of each polarization branch are obtained by means of a total least square-rotation vector invariant technology (TLS-ESPRIT) algorithm, and the relaxation coefficient and the time constant are substituted into a parameter identification formula of the Debye equivalent circuit to realize the identification of the resistance and capacitance parameters of each polarization branch. The method avoids the subjectivity of artificial point taking and the uncertainty of the number of polarization branches, has a denoising effect on the actually measured depolarized current with noise interference, and accurately and uniquely realizes the identification of the transformer oil paper insulation expansion Debye equivalent circuit parameters.)

1. A transformer oil paper insulation expansion Debye equivalent circuit parameter identification method based on TLS-ESPRIT is characterized by comprising the following steps:

s1, acquiring depolarized current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm by the depolarized current data;

s2, performing singular value decomposition on the Hankel matrix constructed in the S1 to obtain singular values of the matrix;

step S3, calculating the relative change rate of each singular value, and determining the polarization branch number n of the expanded Debye equivalent circuit;

step S4, solving the time constant of each branch circuit by the rotation space invariant technology (ESPRIT);

step S5, solving the relaxation coefficients of all branches through Total Least Squares (TLS);

step S6, the time constant and relaxation coefficient of each branch are substituted into a parameter identification formula to obtain the parameters of the expanded DE-Bay equivalent circuit of the transformer.

2. The TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method according to claim 1, wherein the step S1 is implemented as follows:

step S11, measuring depolarization current data x (i) (1, 2,3, …, N) of the oiled paper transformer by using a PDC instrument, wherein it is ensured that the depolarization current is a discrete current sequence composed of equally spaced sampling points in the measurement process;

step S12, constructing a Hankel matrix using the depolarization current data x (i) measured in step S11:

wherein L is N/3.

3. The TLS-ESPRIT-based transformer oil-paper insulation extension Debye equivalent circuit parameter identification method of claim 2, wherein in the step S2, the singular value decomposition of the Hankel matrix X is performed in the following specific manner:

carrying out singular value decomposition on the Hankel matrix X to obtain X ═ SVD^TIn the formula: s is a (N-L) × (N-L) dimension left singular vector matrix; d is a (L +1) × (L +1) dimension right singular vector matrix; v is a diagonal matrix of dimension (N-L) × (L +1), the diagonal element σ of which matrix_i(1 ≦ i ≦ h, h ═ min (N-L, L +1)) is the singular values of matrix X, and they are arranged in descending order.

4. The TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method according to claim 3, wherein the step S3 is implemented as follows:

step S31, calculating a singular value change rate:

step S32, determining the number of polarization branches according to the singular value change rate: since the singular value will be at a certain demarcation point sigma_k+1The rate of change of the rear part approaches 0, i.e. delta_k+1The number k of the previous point is regarded as the effective signal order, i.e. the number n of the polarization branches.

5. The TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method according to claim 3, wherein the step S4 is implemented as follows:

step S41, intercepting the front n columns of the right singular vector matrix D and recording as the matrix D₀D is₀Delete the first row to get D₁D is₀Delete last row to get D₂Constructing a matrix D₃＝[D₁,D₂]；

Step S42, for D₃Singular value decomposition is carried out to obtain a right singular vector matrix P, and P is equally divided into 4 sub-matrixes

Step S43, calculatingOf the non-zero characteristic root λ_iCalculating the time constant τ_i＝-1/(f_s×ln|λ_iL) where f_sIs the sampling frequency.

6. The TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method according to claim 5, wherein the step S5 is implemented as follows:

step S51, feature root λ obtained in step S43_iSubstituting the following least square method to obtain the parameter b_i：

Step S52, calculating relaxation coefficient A_i＝|b_i|。

7. The TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method according to claim 6, wherein the step S6 is implemented as follows:

according to the obtained tau_iAnd A_iSubstituting the equivalent resistance polarization resistance and the polarization capacitance parameters into the following formulas to obtain equivalent resistance polarization resistance and polarization capacitance parameters:

in the formula of U₀For the application of a DC charging voltage to the insulating medium, t_cIs the charging time.

Technical Field

The invention relates to the technical field of response modeling and aging evaluation of oil-paper insulation transformer media, in particular to a TLS-ESPRIT-based transformer oil-paper insulation expansion Debye equivalent circuit parameter identification method.

Background

The medium response method is a nondestructive detection method for diagnosing the insulation state of the oiled paper, the medium response experiments performed on the oiled paper insulation mainly comprise a planned depolarization current experiment (PDC), a return voltage experiment (RVM) and a frequency domain medium response experiment (FDS), and the research on the medium response method in recent years has been changed from the step of directly extracting characteristic quantities from experimental data to the step of modeling a medium relaxation process, so that the process and mechanism of medium response are deeply understood and researched.

The method is characterized in that a mathematical model is established, so that different medium response experiments have unified theoretical explanation, and different measurement processes are mutually verified through a medium response model, wherein the extended Debye model is a mathematical model widely applied to corresponding modeling of the oil paper insulating medium, and can accurately reflect the complicated polarization process of the oil paper insulating non-uniform medium.

Under the description of the extended Debye model, the depolarization current is in the form of superposition of sub-spectral lines of exponential functions, and the key for identifying parameters of each branch of the extended Debye model is to obtain a relaxation coefficient and a time constant of a depolarization current exponential superposition term; the TLS-ESPRIT algorithm is a mode identification algorithm, can effectively distinguish signals and noise, improves the filtering effect on actually-measured PDC current with noise interference, and further accurately identifies the parameters of the signals. The method is mainly applied to parameter identification of the oil paper insulation expansion Debye model.

Disclosure of Invention

The invention aims to provide a TLS-ESPRIT-based transformer oil paper insulation expansion Debye equivalent circuit parameter identification method, which can accurately, uniquely and objectively identify transformer oil paper insulation expansion Debye equivalent circuit parameters.

In order to achieve the purpose, the technical scheme of the invention is as follows: a transformer oil paper insulation expansion Debye equivalent circuit parameter identification method based on TLS-ESPRIT comprises the following steps:

s1, acquiring depolarized current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm by the depolarized current data;

s2, performing singular value decomposition on the Hankel matrix constructed in the S1 to obtain singular values of the matrix;

step S3, calculating the relative change rate of each singular value, and determining the polarization branch number n of the expanded Debye equivalent circuit;

step S4, solving the time constant of each branch circuit by the rotation space invariant technology (ESPRIT);

step S5, solving the relaxation coefficients of all branches through Total Least Squares (TLS);

step S6, the time constant and relaxation coefficient of each branch are substituted into a parameter identification formula to obtain the parameters of the expanded DE-Bay equivalent circuit of the transformer.

In an embodiment of the present invention, the step S1 is specifically implemented as follows:

step S11, measuring depolarization current data x (i) (1, 2,3, …, N) of the oiled paper transformer by using a PDC instrument, wherein it is ensured that the depolarization current is a discrete current sequence composed of equally spaced sampling points in the measurement process;

step S12, constructing a Hankel matrix using the depolarization current data x (i) measured in step S11:

wherein L is N/3.

In an embodiment of the present invention, in step S2, a specific manner of performing singular value decomposition on the Hankel matrix X is as follows:

carrying out singular value decomposition on the Hankel matrix X to obtain X ═ SVD^TIn the formula: s is a (N-L) × (N-L) dimension left singular vector matrix; d is a (L +1) × (L +1) dimension right singular vector matrix; v is a diagonal matrix of dimension (N-L) × (L +1), the diagonal element σ of which matrix_i(1 ≦ i ≦ h, h ═ min (N-L, L +1)) is the singular values of matrix X, and they are arranged in descending order.

In an embodiment of the present invention, the step S3 is specifically implemented as follows:

step (ii) ofS31, calculating the singular value change rate:

step S32, determining the number of polarization branches according to the singular value change rate: since the singular value will be at a certain demarcation point sigma_k+1The rate of change of the rear part approaches 0, i.e. delta_k+1The number k of the previous point is regarded as the effective signal order, i.e. the number n of the polarization branches.

In an embodiment of the present invention, the step S4 is specifically implemented as follows:

step S41, intercepting the front n columns of the right singular vector matrix D and recording as the matrix D₀D is₀Delete the first row to get D₁D is₀Delete last row to get D₂Constructing a matrix D₃＝[D₁,D₂]；

Step S42, for D₃Singular value decomposition is carried out to obtain a right singular vector matrix P, and P is equally divided into 4 sub-matrixes

Step S43, calculatingOf the non-zero characteristic root λ_iCalculating the time constant τ_i＝-1/(f_s×ln|λ_iL) where f_sIs the sampling frequency.

In an embodiment of the present invention, the step S5 is specifically implemented as follows:

step S51, feature root λ obtained in step S43_iSubstituting the following least square method to obtain the parameter b_i：

Step S52, calculating relaxation coefficient A_i＝|b_i|。

In an embodiment of the present invention, the step S6 is specifically implemented as follows:

according to the obtained tau_iAnd A_iSubstituting the equivalent resistance polarization resistance and the polarization capacitance parameters into the following formulas to obtain equivalent resistance polarization resistance and polarization capacitance parameters:

in the formula of U₀For the application of a DC charging voltage to the insulating medium, t_cIs the charging time.

Compared with the prior art, the invention has the following beneficial effects:

1. the invention starts from Debye fitting of depolarization current, identifies the parameters of the oil paper insulation expansion Debye model, can play a role in filtering field measurement, and has uniqueness in parameter identification;

2. compared with the traditional method of fitting from the tail end, the method avoids the difference and inaccuracy caused by the subjectivity of manual point taking;

3. compared with methods such as cubic differential spectrum decomposition and vector matching, the method has no complicated steps such as complicated differentiation, time-frequency domain conversion and the like, and has no intermediate error introduced by the complicated steps.

4. Compared with the Prony algorithm with multiple sampling intervals, the method can identify the unique polarization branch number and equivalent circuit parameters at one time without fitting for multiple times according to different branch numbers.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention.

FIG. 2 is a schematic diagram of a PDC testing experiment using a DIRANA instrument, in accordance with an embodiment of the present invention.

FIG. 3 is a schematic diagram of an extended Debye equivalent circuit.

Fig. 4 is a depolarization current raw curve of the voltage regulator according to the embodiment of the present invention.

FIG. 5 is a comparison of a TLS-ESPRIT algorithm fit curve with a raw curve according to an embodiment of the present invention.

Detailed Description

The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.

As shown in fig. 1, the method for identifying parameters of transformer oil paper insulation expansion debye equivalent circuit based on TLS-ESPRIT of the present invention includes the following steps:

step S1, acquiring depolarized current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm by the depolarized current data;

s2, performing singular value decomposition on the Hankel matrix to obtain singular values of the matrix;

step S3, determining the polarization branch number n of the expanded Debye equivalent circuit by calculating the relative change rate of each singular value;

step S4, solving the time constant of each branch circuit by the rotation space invariant technology (ESPRIT);

step S5, solving the relaxation coefficients of all branches through Total Least Squares (TLS);

step S6, the time constant and relaxation coefficient of each branch are substituted into a parameter identification formula to obtain the parameters of the expanded DE-Bay equivalent circuit of the transformer.

The invention will be described in further detail below with reference to the accompanying figures 2-5 and specific embodiments.

In specific implementation, the identification method of the equivalent circuit parameters of the oil paper insulation expansion Debye based on the TLS-ESPRIT algorithm comprises the following steps:

1. firstly, according to step S1, depolarization current measurement is performed on 1 retired induction voltage regulator manufactured in 10 th 1983 and having model number TDJA-a0/0.5, 2000V charging voltage is applied, charging time is 5000S, depolarization current obtained by the test is an equally spaced depolarization current sequence with a sampling interval of 1S, and a current curve is shown in fig. 4.

2. According to the steps S2 and S3, the singular value change rate of each point is obtained as shown in the following Table 1 (only the first 8 points are listed for space limitation):

TABLE 1 distribution of singular value variation rates

Number i	1	2	3	4	5	6	7	8
									Singular value variation rate deltai	0.9517	0.9342	0.0578	0.0553	0.0409	0.0103	0.0093	0.0449

According to step S33, the change rate delta of the singular value is generally determined_iIf < 0.1, it can be considered to be approximately 0. As can be seen from Table 1, the condition that the singular value change rate approaches to 0 is satisfied when the number i.gtoreq.3, so the number n of polarization branches is 2.

3. According to the steps S4 and S5, the relaxation coefficient A of each polarization branch is solved_iAnd time constant τ_iAs shown in table 2 below:

TABLE 2 relaxation coefficients and time constants of the branches

Curve fitting was performed according to the obtained parameters, and the fitting results are shown in fig. 5. To measure the closeness of the fitted curve to the actually measured curve, the fitting accuracy is definedWhere x is the actual measurement signal, x^△Fitting the signal, | | | is a two-norm operator. The larger the AFI, the higher the fitting accuracy. When the AFI is more than 10, the fitting precision requirement can be met. AFI in this example is 35.3709, meeting the accuracy requirement.

4. According to step S6, the polarization resistance R of each polarization branch is solved_iAnd a polarization capacitor C_iThe parameter identification process is completed, and the results are shown in table 3 below:

TABLE 3 polarization resistance and polarization capacitance of each branch

The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.