CN113779914B - TLS-ESPRIT-based transformer oil paper insulation extension Debye equivalent circuit parameter identification method - Google Patents
TLS-ESPRIT-based transformer oil paper insulation extension Debye equivalent circuit parameter identification method Download PDFInfo
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Abstract
The invention relates to a TLS-ESPRIT-based transformer oil paper insulation extension Debye equivalent circuit parameter identification method. According to the physical characteristics that depolarization current is an exponential function superposition under an extended debye equivalent model, 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 time constant of each polarization branch are obtained by means of a total least squares-rotation vector invariant technology (TLS-ESPRIT) algorithm, and the relaxation coefficient and time constant are substituted into a debye equivalent circuit parameter identification formula to realize identification of resistance and capacitance parameters of each polarization branch. The method provided by the invention avoids the subjectivity of artificial point taking and the uncertainty of polarization branch numbers, has the denoising effect on the actually measured depolarization current with noise interference, and accurately and uniquely realizes the identification of the transformer oil paper insulation extended debye equivalent circuit parameters.
Description
Technical Field
The invention relates to the technical field of medium response modeling and aging evaluation of oil paper insulation transformers, 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 testing method for diagnosing the insulating state of the oilpaper, and medium response experiments performed on the oilpaper insulation mainly comprise a planned depolarization current experiment (PDC), a recovery voltage experiment (RVM) and a frequency domain medium response experiment (FDS), so that the research on the medium response method in recent years has been changed from directly extracting characteristic quantities from experimental data to modeling a medium relaxation process, and deeply understanding and researching the process and mechanism of the medium response.
The mathematical model is established to ensure that different medium response experiments have unified theoretical explanation, and different measurement processes are mutually verified through the medium response model, wherein the extended debye model is a mathematical model which is widely applied to modeling corresponding to the oilpaper insulating medium, and can accurately reflect the complex polarization process of the oilpaper insulating inhomogeneous medium.
Under the description of an extended debye model, depolarization current is in the form of superposition of exponential function sub-spectral lines, and the key of 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 item; the TLS-ESPRIT algorithm is a modal identification algorithm, can effectively distinguish signals from noise, improves the filtering effect on the actually measured PDC current with noise interference, and further accurately identifies the parameters of the signals. The application of the algorithm to the parameter identification of the oilpaper insulation extended debye model is the main work of the invention.
Disclosure of Invention
The invention aims to provide a TLS-ESPRIT-based transformer oil paper insulation extension debye equivalent circuit parameter identification method, which can accurately, uniquely and objectively identify transformer oil paper insulation extension debye equivalent circuit parameters.
In order to achieve the above purpose, the technical scheme of the invention is as follows: a TLS-ESPRIT-based transformer oil paper insulation extended Debye equivalent circuit parameter identification method comprises the following steps:
s1, obtaining depolarization current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm from the depolarization current data;
s2, performing singular value decomposition on the Hankel matrix constructed in the step S1 to obtain singular values of the matrix;
s3, calculating the relative change rate of each singular value, and determining the number n of polarization branches of the extended Debye equivalent circuit;
s4, solving the time constants of the branches through a rotation space invariant technology (ESPRIT);
s5, solving the relaxation coefficients of each branch through Total Least Squares (TLS);
and S6, bringing the time constant and the relaxation coefficient of each branch into a parameter identification formula to obtain the parameters of the extended DE Bayer 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) (i=1, 2,3, …, N) of the oilpaper transformer by using a PDC instrument, wherein the depolarization current is ensured to be a discrete current sequence formed by equally-spaced sampling points in the measuring process;
step S12, constructing a Hankel matrix by using the depolarization current data x (i) measured in step S11:
where l=n/3.
In one embodiment of the present invention, in step S2, the specific way of performing singular value decomposition on the Hankel matrix X is as follows:
singular value decomposition is performed on Hankel matrix X to obtain X=SVD T Wherein: s is an (N-L) x (N-L) dimensional Zuo Jiyi vector matrix; d is a right singular vector matrix of (L+1) x (L+1) dimensions; v is an (N-L) x (L+1) -dimensional diagonal matrix having diagonal elements sigma i (1.ltoreq.i.ltoreq.h, h=min (N-L, l+1)) is the singular value of matrix X, and it is arranged in descending order.
In an embodiment of the present invention, the step S3 is specifically 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 singular values will be at some demarcation point sigma k+1 The post-change rate approaches 0, i.e. delta k+1 The point is the boundary point between the actual current signal and the noise signal, and the number k before the point is regarded as the effective signal order, i.e. the polarization branch number n.
In an embodiment of the present invention, the step S4 is specifically implemented as follows:
s41, intercepting the first n columns of the right singular vector matrix D and marking the first n columns as the matrix D 0 D is to 0 Deleting the first row to obtain D 1 D is to 0 Deleting the last line to obtain D 2 Constructing matrix D 3 ＝[D 1 ,D 2 ]；
Step S42, pair D 3 Singular value decomposition is carried out to obtain a right singular vector matrix P, and the P is equally divided into 4 submatrices
Step S43, calculatingNon-zero characteristic root lambda of (2) i Calculating a time constant τ i ＝-1/(f s ×ln|λ i I), where f s Is the sampling frequency.
In an embodiment of the present invention, the step S5 is specifically implemented as follows:
step S51, feature root lambda obtained in step S43 i Substituting the following least square method to obtain the parameter b i ：
Step S52, calculating the relaxation coefficient A i ＝|b i |。
In an embodiment of the present invention, the step S6 is specifically implemented as follows:
based on the obtained τ i And A i Substituting the following formula to obtain equivalent resistance polarization resistance and polarization capacitance parameters:
in U 0 To apply a DC charging voltage to an insulating medium, t c Is 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 parameters of the oilpaper insulation extended Debye model, can play a role of filtering on site 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 subjectivity of manual point taking;
3. compared with the methods of three-time differential spectrum, vector matching and the like, the method has no complex steps of complex differentiation, time-frequency domain conversion and the like, and also has no intermediate errors caused by the complex 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 PDC test run using a DIRANA instrument in accordance with an embodiment of the invention.
Fig. 3 is a schematic diagram of an extended debye equivalent circuit.
Fig. 4 is a plot of the depolarization current of a voltage regulator according to an embodiment of the present invention.
FIG. 5 is a comparison of a TLS-ESPRIT algorithm fitted curve and an original curve according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is specifically described below with reference to the accompanying drawings.
As shown in FIG. 1, the TLS-ESPRIT-based transformer oil paper insulation extended Debye equivalent circuit parameter identification method comprises the following steps:
s1, obtaining depolarization current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm from the depolarization current data;
s2, performing singular value decomposition on the Hankel matrix to obtain singular values of the matrix;
s3, determining the number n of polarization branches of the extended Debye equivalent circuit by calculating the relative change rate of each singular value;
s4, solving the time constants of the branches through a rotation space invariant technology (ESPRIT);
s5, solving the relaxation coefficients of each branch through Total Least Squares (TLS);
and S6, bringing the time constant and the relaxation coefficient of each branch into a parameter identification formula to obtain the parameters of the extended DE Bayer equivalent circuit of the transformer.
The invention will be described in further detail with reference to fig. 2-5 and the specific examples.
In specific implementation, the identification method of the oilpaper insulation extended debye equivalent circuit parameters based on the TLS-ESPRIT algorithm comprises the following steps:
1. first, according to step S1, depolarization current measurement is performed on 1 retired induction voltage regulator manufactured in 10 months of 1983 and model TDJA-A0/0.5, 2000V charging voltage is applied, charging time is 5000S, depolarization current obtained by testing is an equidistant depolarization current sequence with sampling interval of 1S, and current curve is shown in fig. 4.
2. According to steps S2 and S3, the singular value change rate of each point is obtained as follows in Table 1 (the space is limited and only the first 8 points are listed):
TABLE 1 singular value Rate of change distribution
| Number i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Singular value change rate delta i | 0.9517 | 0.9342 | 0.0578 | 0.0553 | 0.0409 | 0.0103 | 0.0093 | 0.0449 |
According to step S33, generally when the singular value change rate delta i When < 0.1, it can be approximately considered to approach 0. As can be seen from Table 1, when the number i is not less than 3, the condition that the singular value change rate approaches 0 is satisfied, so that the number n of polarization branches is 2.
3. Solving the relaxation coefficient A of each polarization branch according to the steps S4 and S5 i And a time constant tau i As shown in table 2 below:
TABLE 2 relaxation coefficients and time constants for the branches
Curve fitting was performed according to the obtained parameters, and the fitting result is shown in fig. 5. To measure the closeness of the fitting curve and the actual measurement curve, the fitting precision is definedWherein x isActual measurement signal, x △ Fitting the signal, wherein the I is a two-norm operator. The larger the AFI, the higher the fitting accuracy. When AFI is more than 10, the fitting accuracy requirement can be considered to be met. Afi= 35.3709 in this example, meets the accuracy requirement.
4. According to step S6, solving the polarization resistance R of each polarization branch i And polarization capacitor C i The parameter identification process was completed and the results are shown in table 3 below:
TABLE 3 polarization resistance and polarization capacitance of each branch
The above is a preferred embodiment of the present invention, and all changes made according to the technical solution of the present invention belong to the protection scope of the present invention when the generated functional effects do not exceed the scope of the technical solution of the present invention.
Claims (4)
1. The TLS-ESPRIT-based transformer oil paper insulation extended debye equivalent circuit parameter identification method is characterized by comprising the following steps of:
s1, obtaining depolarization current data, and constructing a Hankel matrix of a TLS-ESPRIT algorithm from the depolarization current data;
s2, performing singular value decomposition on the Hankel matrix constructed in the step S1 to obtain singular values of the matrix;
s3, calculating the relative change rate of each singular value, and determining the number n of polarization branches of the extended Debye equivalent circuit;
s4, solving the time constants of the branches through a rotation space invariant technology (ESPRIT);
s5, solving the relaxation coefficients of each branch through Total Least Squares (TLS);
s6, bringing the time constant and the relaxation coefficient of each branch into a parameter identification formula to obtain parameters of the extended DE Bayer equivalent circuit of the transformer;
the step S1 is specifically implemented as follows:
step S11, measuring depolarization current data x (i) (i=1, 2,3, …, N) of the oilpaper transformer by using a PDC instrument, wherein the depolarization current is ensured to be a discrete current sequence formed by equally-spaced sampling points in the measuring process;
step S12, constructing a Hankel matrix by using the depolarization current data x (i) measured in step S11:
wherein l=n/3;
in step S2, the specific way of performing singular value decomposition on the Hankel matrix X is as follows:
singular value decomposition is performed on Hankel matrix X to obtain X=SVD T Wherein: s is an (N-L) x (N-L) dimensional Zuo Jiyi vector matrix; d is a right singular vector matrix of (L+1) x (L+1) dimensions; v is an (N-L) x (L+1) -dimensional diagonal matrix having diagonal elements sigma i (1.ltoreq.i.ltoreq.h, h=min (N-L, l+1)) is the singular value of matrix X, and it is arranged in descending order;
the step S3 is specifically 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 singular values will be at some demarcation point sigma k+1 The post-change rate approaches 0, i.e. delta k+1 The point is the boundary point between the actual current signal and the noise signal, and the number k before the point is regarded as the effective signal order, i.e. the polarization branch number n.
2. The TLS-ESPRIT-based transformer oil paper insulation extended debye equivalent circuit parameter identification method of claim 1, wherein the step S4 is specifically implemented as follows:
s41, intercepting the first n columns of the right singular vector matrix D and marking the first n columns as the matrix D 0 D is to 0 Deleting the first row to obtainD 1 D is to 0 Deleting the last line to obtain D 2 Constructing matrix D 3 ＝[D 1 ,D 2 ]；
Step S42, pair D 3 Singular value decomposition is carried out to obtain a right singular vector matrix P, and the P is equally divided into 4 submatrices
Step S43, calculatingNon-zero characteristic root lambda of (2) i Calculating a time constant τ i ＝-1/(f s ×ln|λ i I), where f s Is the sampling frequency.
3. The TLS-ESPRIT-based transformer oil paper insulation extended debye equivalent circuit parameter identification method of claim 2, wherein the step S5 is specifically implemented as follows:
step S51, feature root lambda obtained in step S43 i Substituting the following least square method to obtain the parameter b i ：
Step S52, calculating the relaxation coefficient A i ＝|b i |。
4. The TLS-ESPRIT-based transformer oil paper insulation extended debye equivalent circuit parameter identification method of claim 3, wherein said step S6 is specifically implemented as follows:
based on the obtained τ i And A i Substituting the following formula to obtain equivalent resistance polarization resistance and polarization capacitance parameters:
in U 0 To apply a DC charging voltage to an insulating medium, t c Is the charging time.
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