CN112465010A - DKPCA and KFDA-based transformer fault detection and classification method - Google Patents

DKPCA and KFDA-based transformer fault detection and classification method Download PDF

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CN112465010A
CN112465010A CN202011340810.3A CN202011340810A CN112465010A CN 112465010 A CN112465010 A CN 112465010A CN 202011340810 A CN202011340810 A CN 202011340810A CN 112465010 A CN112465010 A CN 112465010A
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李鹏
张起
郎恂
高莲
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Abstract

The invention discloses a DKPCA and KFDA transformer fault detection and classification method, which comprises the steps of firstly collecting transformer operation data under the normal working condition of a transformer, and preprocessing the collected data; then establishing the correlation of the time-lag augmentation matrix reserved data, and extracting the characteristic information of the original data through the nonlinear mapping of the kernel function; establishing SPE and T through extracted score vectors2Statistics detecting occurrence of a fault; calculating the contributions RBC of each variable to the two statistics in the process, and determining the variable causing the fault; and finally, evaluating a fault variable by using KFDA to determine the fault type. According to the method, the DKPCA method is introduced into a transformer fault diagnosis method, so that the autocorrelation characteristic of the measured variable is kept, meanwhile, nonlinear characteristic information is accurately extracted, and the fault detection accuracy is improved; contribution system of introducing KFDA (Kalman Filter and data acquisition) to fault variableAnd the measurement is used for training and learning, so that the fault diagnosis precision of the transformer is improved.

Description

DKPCA and KFDA-based transformer fault detection and classification method
Technical Field
The invention belongs to the technical field of power transformer fault diagnosis of a power distribution network, relates to a transformer fault detection and classification method based on DKPCA and KFDA, and particularly relates to a low-voltage transformer fault detection and classification method of the power distribution network based on DKPCA and KFDA algorithms.
Background
Power transformers are used to convert different voltage levels in an electrical power system and are an important guarantee of reliability in the electrical power system. In order to ensure the reliability and safety of the power grid, maintenance personnel need to periodically acquire the operating state parameters of the transformer, and analyze the operating condition of the transformer through the parameters. However, manual maintenance depends on manual experience, the working efficiency is low, subjectivity is high, and the risk of transformer failure is increased. Therefore, under the background of artificial intelligence, the development of the intelligent transformer fault detection and diagnosis method has important practical significance.
At present, a method for analyzing Dissolved Gas (DGA) in transformer oil becomes a main method for judging the internal fault property of a transformer in a power system. The most common method in the DGA method is the three-ratio judgment method, so that the fault judgment accuracy is low, the existing fault detection method based on machine learning is difficult to mine the time sequence relation between measurement data, a nonlinear process is adopted before and after the fault occurs, and the reliability of the conventional machine learning method in transformer fault diagnosis needs to be improved.
Dynamic Kernel Principal Component Analysis (DKPCA) as a novel data-driven technique can well process dynamic nonlinear data. The basic idea is to obtain the dynamic characteristics among data by constructing a time lag matrix, and then map the data to a high-dimensional space by utilizing the nonlinear mapping of a kernel matrix, so that the time sequence correlation of the original data is kept, and meanwhile, the data which is difficult to separate is also separated in the high-dimensional space. Based on this, the feature information of the original data is extracted, and the time-series correlation features of the data are retained.
The Kernel Fisher Discriminant Analysis (KFDA) is used for determining the sample type according to the characteristics and the discriminant indexes of the sample data, and in order to solve the problem of nonlinear classification of fault contribution statistics, input data are subjected to kernel function nonlinear mapping, Fisher linear discriminant is used in a high-dimensional space, and the precision of fault diagnosis is improved.
In conclusion, the invention provides the transformer fault detection and classification method based on DKPCA and KFDA, which can effectively improve the transformer fault detection and classification precision and improve the operation reliability of the transformer.
Disclosure of Invention
In summary, in order to improve the fault classification accuracy of the power transformer, the invention provides a transformer fault detection and classification method based on DKPCA and KFDA. Firstly, extracting characteristic variables containing dynamic characteristics from massive redundant transformer state information through dynamic kernel principal component analysis, and utilizing T2Detecting whether the fault occurs by SPE statistics; and finally, calculating the contribution RBC corresponding to the fault statistics, and judging the fault category according to a KFDA classifier.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a transformer fault detection and classification method based on DKPCA and KFDA comprises the following steps:
step 1, collecting transformer operation data, and performing normalization processing on the collected data by adopting a Z-score method to enable the mean value of the processed data to be zero and the variance to be 1;
step 2, superposing vectors at s moments before t moment after each variable to form a time lag augmentation matrix X(s) so as to reflect the dynamic relation between the variables;
step 3, finding the optimal hypersphere defined by the eigenvector v, establishing a dynamic kernel matrix to separate fault variables, reserving the maximum variance information according to the defined dynamic kernel principal element objective function, and establishing SPE and T through the extracted score vector2Statistics detecting occurrence of a fault;
step 4, respectively calculating each variable pair T in the process2Contribution of statistics
Figure BDA0002798546550000021
Contribution to SPE statistics
Figure BDA0002798546550000022
Drawing a work contribution histogram, and judging a variable causing the fault according to the maximum contribution degree in the fault contribution graph;
and 5, determining the fault type of the transformer according to the KFDA judgment result.
Further, the step 1 further includes:
acquiring transformer operation data comprises acquiring dissolved gas data in transformer oil, transformer electrical test data and transformer insulating oil characteristic test data under the normal working condition of a transformer as a training sample set; taking the collected data as a training sample set x ∈ Rn×mWhere n is the number of measurement samples, each sample containing m observations; and carrying out normalization processing on the acquired data by adopting a Z-score method, wherein the formula is as follows:
Figure BDA0002798546550000031
after the mean value mu and the standard deviation sigma of the acquired data are calculated, the mean value of the processed data is 0 and the variance is 1 through the formula.
Further, the data of the dissolved gas in the transformer oil comprises H2、C2H2、CH4、C2H6、C2H4And the total hydrocarbon content; also included are the gas production rate of total hydrocarbons and CO2The ratio of the content of the stage CO gas; the transformer electrical test data comprise transformer dielectric loss factors, winding leakage current, insulation resistance and winding direct-current resistance phase difference; the transformer insulating oil characteristic test data comprise dielectric loss of insulating oil, water content in oil and furfural content.
Further, the step 2 further comprises:
after each normalized variable is superposed with the vectors of s times before t time, a time-lag augmentation matrix X(s) is established to reflect the dynamic relation between the variables, and a dynamic kernel matrix is established to separate fault variables
Figure BDA0002798546550000032
In the formula: x is the number oftRepresenting the samples taken at time t, s represents the time lag, and n is the number of samples.
Further, the step 3 further includes:
selecting kernel function as radial basis kernel function K ═ exp (— | | x-y | | | sweet wind path2/2σ2) Mapping the measurement sample to high-dimensional feature space, mapping a time-lag augmentation matrix X(s) to phi(s), and then establishing a data covariance matrix under the feature space
Figure BDA0002798546550000033
In the formula: phii(t: t-s) is the mapped dynamic data augmentation matrix;
carrying out eigenvector decomposition on the covariance matrix to find the optimal hypersphere defined by the eigenvector v
Figure BDA0002798546550000034
In the formula: alpha is alphaiIs a coefficient vector, v is a feature vector;
computing a dynamic kernel matrix
K＝<Φi(t:t-s),Φj(t:t-s)>
The centralization treatment is carried out under the characteristic space, so that
Figure BDA0002798546550000041
Core matrix centralization
Figure BDA0002798546550000042
In the formula: i isnIs an identity matrix;
objective function by dynamic kernel principal elements
Figure BDA0002798546550000043
In the formula: k is a dynamic kernel matrix;
solving for a score vector
Figure BDA0002798546550000044
Wherein the number of principal elements retained is determined using a cumulative variance contribution ratio criterion (R)CPV＞95％)；
Establishing a Squared Prediction Error (SPE) and Hotelling's T based on the extracted score vector2Statistics determine control limits for faults:
T2＝[t1,t2,…,tk]Λ-1[t1,t2,…,tk]T
Figure BDA0002798546550000045
in the formula: lambda-1And the inverse matrix of the diagonal matrix formed by the principal component eigenvalues is represented.
Further, the step 4 further includes:
calculating T2Contribution of statistics
Figure BDA0002798546550000046
And contribution of SPE statistics
Figure BDA0002798546550000047
Figure BDA0002798546550000048
Figure BDA0002798546550000049
In the formula: v. ofiIs the ith feature vector, xnewIs a new sample.
Further, the step 5 further includes:
dividing transformer faults into C types, wherein the fault variable number is N and is recorded as r ═ r1,r2,...,rCH, class i contains NiOne sample is recorded as
Figure BDA0002798546550000051
After nonlinear mapping, r → phi (r)i) The mean value after mapping the ith sample in the high-dimensional space is miThe mean value after mapping all samples is m;
Figure BDA0002798546550000052
Figure BDA0002798546550000053
in the formula:
Figure BDA0002798546550000054
representing the ith class jth sampling vector in the feature space;
calculating intra-kernel dispersion SWAnd degree of interspinous divergence SB
Figure BDA0002798546550000055
Figure BDA0002798546550000056
In the formula: m isiThe mean value of the i-th sample after mapping, and m is the mean value of all samples after mapping;
establishing Fisher criterion in high-dimensional space
Figure BDA0002798546550000057
In the formula: w is aφIs any non-zero column vector;
and judging the fault type by adopting the Mahalanobis distance.
Compared with the prior art, the method has the advantages that:
1) the invention captures the dynamic correlation of the data along with the time change by constructing the time-delay augmentation matrix, and the extracted dynamic characteristics can comprehensively analyze the data potential information.
2) And a better data separation effect is obtained by utilizing the nonlinear mapping of the kernel function.
3) And identifying fault variables according to the contribution RBC corresponding to the fault statistics, so that the fault reason can be clarified.
4) And further classifying fault variables through KFDA (Kalman Filter/data acquisition) to improve the fault classification precision.
Drawings
Fig. 1 is a flow chart of a DKPCA-FDA based transformer fault detection and diagnosis method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a DKPCA and KFDA-based transformer fault detection and diagnosis method, the flow chart of which is shown in FIG. 1 and is specifically implemented according to the following steps:
step 1: acquiring transformer operation data, and performing normalization processing on the acquired data by adopting a Z-score method to ensure that the mean value of the processed data is zero and the variance is 1;
further, the step 1 also comprises the following implementation process of collecting dissolved gas data in oil under the normal working condition of the transformer, electrical test data of the transformer and characteristic test data of insulating oil as a training sample set;
further, the step 1 should also include the following implementation processes: the data of dissolved gas in transformer oil comprises H2、C2H2、CH4、C2H6、C2H4The content of various gases such as total hydrocarbon, the gas production rate of the total hydrocarbon and CO2The ratio of the content of the stage CO gas; the electrical test data of the transformer comprise dielectric loss factors of the transformer, winding leakage current,The phase difference of the insulation resistance and the winding direct-current resistance; the insulating oil characteristic test data comprise dielectric loss of the insulating oil, water content in the oil and content of furfural.
Further, the step 1 should also include the following implementation processes: dissolved gas data in transformer oil, transformer electrical test data and insulating oil characteristic test data acquired under normal working condition are used as a training sample set x ∈ Rn×mAnd the real-time collected data of dissolved gas in the transformer oil, the electrical test data of the transformer and the characteristic test data of the insulating oil are used as a training sample set x ∈ Rn×mWhere n is the number of measurement samples, each sample containing m observations;
further, the step 1 should also include the following implementation processes: and (3) normalizing the measured data by adopting a Z-score method, wherein the mean value of the processed data is 0, and the variance is 1.
Figure BDA0002798546550000061
After calculating the mean μ and standard deviation σ of the measurement data, the mean of the processed data was made 0 and the variance was made 1 by equation (1).
Step 2: superposing vectors s times before t time after each variable to form a time lag augmentation matrix X(s) so as to reflect the dynamic relation among the variables and establish a dynamic kernel matrix separation fault variable;
further, the step 2 should also include the following implementation processes: establishing a time-lag augmentation matrix to reflect the dynamic relationship between the data:
Figure BDA0002798546550000071
further, the step 2 should also include the following implementation processes: determining the time s of the time-lag matrix through a recurrence formula, wherein the specific method comprises the following steps:
1.s＝0；
2. executing PCA algorithm and calculating all principal elements;
3.j＝n×(s+1)，r(s)＝0；
if jth principal element is linear
5.Then j＝j-1，r(s)＝r(s)+1；
6.
Figure BDA0002798546550000072
7.End if
8.While rnew(s)＞0
9.Do s＝s+1，go to step 2；
10.Else output s；
11.End
And step 3: finding out the optimal hypersphere defined by the eigenvector v, establishing a dynamic kernel matrix to separate fault variables, reserving the maximum variance information according to the defined dynamic kernel principal element objective function, and establishing SPE and T through the extracted score vector2Statistics detecting occurrence of a fault;
further, the step 3 should also include the following implementation processes: selecting kernel function as radial basis kernel function K ═ exp (— | | x-y | | | sweet wind path2/2σ2) Mapping the measurement sample to high-dimensional feature space, mapping a time-lag augmentation matrix X(s) to phi(s), and then establishing a data covariance matrix under the feature space
Figure BDA0002798546550000073
Carrying out eigenvector decomposition on the covariance matrix to find the optimal hypersphere defined by the eigenvector v
Figure BDA0002798546550000074
Further, the step 3 should further include the following processes: computing a dynamic kernel matrix
K＝<Φi(t:t-s),Φj(t:t-s)> (5)
The centralization treatment is carried out under the characteristic space, so that
Figure BDA0002798546550000081
Core matrix centralization
Figure BDA0002798546550000082
Further, the step 3 should further include the following processes: objective function by dynamic kernel principal elements
Figure BDA0002798546550000083
Solving for a score vector
Figure BDA0002798546550000084
Wherein the number of principal elements retained is determined using a cumulative variance contribution ratio criterion (R)CPV＞95％)。
Further, the step 3 should further include the following processes: establishing a Squared Prediction Error (SPE) and Hotelling's T based on the extracted score vector2Statistics determine control limits for faults:
T2＝[t1,t2,…,tk]Λ-1[t1,t2,…,tk]T (7)
Figure BDA0002798546550000085
and 4, step 4: respectively calculating each variable pair T in the process2Contribution of statistics
Figure BDA0002798546550000086
Contribution to SPE statistics
Figure BDA0002798546550000087
Drawing a work contribution histogram, and judging a variable causing the fault according to the maximum contribution degree in the fault contribution graph;
further, the step 4 should further include the following processes: t is2Contribution of statistics
Figure BDA0002798546550000088
And contribution of SPE statistics
Figure BDA0002798546550000089
Respectively is as follows;
Figure BDA00027985465500000810
Figure BDA00027985465500000811
and 5: determining the fault type of the transformer according to a KFDA (Kalman Filter/direct Current) judgment result;
further, the step 5 should further include the following processes: dividing transformer faults into C types, wherein the fault variable number is N and is recorded as r ═ r1,r2,...,rCH, class i contains NiOne sample is recorded as
Figure BDA00027985465500000812
After nonlinear mapping, r → phi ri) The mean value after mapping the ith sample in the high-dimensional space is miThe mean value after mapping all samples is m;
Figure BDA0002798546550000091
Figure BDA0002798546550000092
further, the step 5 should further include the following processes: calculating intra-kernel dispersion SWAnd degree of interspinous divergence SB；
Figure BDA0002798546550000093
Figure BDA0002798546550000094
Further, the step 5 should further include the following processes: establishing Fisher criterion in a high-dimensional space:
Figure BDA0002798546550000095
further, the step 5 should further include the following processes: judging the fault type by adopting the Mahalanobis distance;
further, the step 5 should further include the following processes: the failure categories and corresponding gas compositions are shown in table 1.
TABLE 1 Fault types and corresponding gas composition tables
Main gas component Secondary gas component Type of failure
H2 / The water or oil containing bubbles
CO、CO2 / Aging of oil
CH4 C2H4 Oil superheating
CH4、C2H4、CO、CO2 H2、C2H6 Severe overheating of oil and paper
H2、CH4 C2H2、C2H6 Oiled paper insulation partial discharge
CH4、C2H2、H2 / Spark discharge in oil
H2、C2H2、CH4 C2H4、C2H6 Electric arc in oil
H2、C2H2、CO、CO2 CH4、C2H6、C2H4 Electric arc in oil and paper
In the above formulae (1) to (15), xtRepresenting the samples taken at time t, s represents the time lag, n is the number of samples, phii(t: t-s) is the mapped dynamic data augmentation matrix, αiIs a coefficient vector, v is a feature vector, InIs an identity matrix, K is a dynamic kernel matrix, Λ-1An inverse matrix, v, representing a diagonal matrix of principal component eigenvaluesiIs the ith feature vector, xnewIs a new sample of the sample, and,
Figure BDA0002798546550000096
representing the ith class of jth sample vectors, m, in a feature spaceiIs the mean value of the i-th sample after mapping, m is the mean value of all samples after mapping, wφIs any non-zero column vector.

Claims (10)

1. A transformer fault detection and classification method based on DKPCA and KFDA is characterized in that:
step 1, collecting transformer operation data, and performing normalization processing on the collected data by adopting a Z-score method to enable the mean value of the processed data to be zero and the variance to be 1;
step 2, superposing vectors at s moments before t moment after each variable to form a time lag augmentation matrix X(s) so as to reflect the dynamic relation between the variables;
step 3, finding the optimal hypersphere defined by the eigenvector v, establishing a dynamic kernel matrix to separate fault variables, reserving the maximum variance information according to the defined dynamic kernel principal element objective function, and establishing SPE and T through the extracted score vector2Statistics detecting occurrence of a fault;
step 4, respectively calculating each variable pair T in the process2Contribution of statistics
Figure FDA0002798546540000011
Contribution to SPE statistics
Figure FDA0002798546540000012
Drawing a work contribution histogram, and judging a variable causing the fault according to the maximum contribution degree in the fault contribution graph;
and 5, determining the fault type of the transformer according to the KFDA judgment result.
2. The transformer fault detection and classification method according to claim 1, wherein the step 1 further comprises:
acquiring transformer operation data comprises acquiring dissolved gas data in transformer oil, transformer electrical test data and transformer insulating oil characteristic test data under the normal working condition of a transformer as a training sample set;
taking the collected data as a training sample set x ∈ Rn×mWhere n is the number of measurement samples, each sample containing m observations;
and carrying out normalization processing on the acquired data by adopting a Z-score method, wherein the formula is as follows:
Figure FDA0002798546540000013
after the mean value mu and the standard deviation sigma of the acquired data are calculated, the mean value of the processed data is 0 and the variance is 1 through the formula.
3. The transformer fault detection and classification method according to claim 2, wherein the step 2 further comprises:
after each normalized variable is superposed with the vectors of s times before t time, a time-lag augmentation matrix X(s) is established to reflect the dynamic relation between the variables, and a dynamic kernel matrix is established to separate fault variables
Figure FDA0002798546540000021
In the formula: x is the number oftRepresenting the samples taken at time t, s represents the time lag, and n is the number of samples.
4. The transformer fault detection and classification method according to claim 3, wherein the step 3 further comprises:
selecting kernel function as radial basis kernel function K ═ exp (— | | x-y | | | sweet wind path2/2σ2) Mapping the measurement samples to a high-dimensional feature space, and mapping a time-lag augmentation matrix X(s) intoPhi(s), and then establishing a data covariance matrix under the feature space
Figure FDA0002798546540000022
In the formula: phii(t: t-s) is the mapped dynamic data augmentation matrix;
carrying out eigenvector decomposition on the covariance matrix to find the optimal hypersphere defined by the eigenvector v
Figure FDA0002798546540000023
In the formula: alpha is alphaiIs a coefficient vector, v is a feature vector;
computing a dynamic kernel matrix
K＝<Φi(t:t-s),Φj(t:t-s)>
The centralization treatment is carried out under the characteristic space, so that
Figure FDA0002798546540000024
Core matrix centralization
Figure FDA0002798546540000025
In the formula: i isnIs an identity matrix;
objective function by dynamic kernel principal elements
Figure FDA0002798546540000026
s.t.αTKα＝1
In the formula: k is a dynamic kernel matrix;
solving for a score vector
Figure FDA0002798546540000027
Wherein the number of principal elements retained is determined using a cumulative variance contribution ratio criterion (R)CPV＞95％)；
Establishing a Squared Prediction Error (SPE) and Hotelling's T based on the extracted score vector2Statistics determine control limits for faults:
T2＝[t1,t2,…,tk]Λ-1[t1,t2,…,tk]T
Figure FDA0002798546540000031
in the formula: lambda-1And the inverse matrix of the diagonal matrix formed by the principal component eigenvalues is represented.
5. The transformer fault detection and classification method according to claim 4, wherein the step 4 further comprises:
calculating T2Contribution of statistics
Figure FDA0002798546540000032
And contribution of SPE statistics
Figure FDA0002798546540000033
Figure FDA0002798546540000034
Figure FDA0002798546540000035
In the formula: v. ofiIs the ith feature vector, xnewIs a new sample.
6. The transformer fault detection and classification method according to claim 5, wherein the step 5 further comprises:
classifying transformer faults into C-type faultsThe variable number is N, and is recorded as r ═ r1,r2,...,rCH, class i contains NiOne sample is denoted as ri＝{ri 1,ri 2,...,ri NiR → phi (r) after nonlinear mappingi) The mean value after mapping the ith sample in the high-dimensional space is miThe mean value after mapping all samples is m;
Figure FDA0002798546540000036
Figure FDA0002798546540000037
in the formula: phi (r)i j)(i＝1,...,m；j＝1,...,ni) Representing the ith class jth sampling vector in the feature space;
calculating intra-kernel dispersion SWAnd degree of interspinous divergence SB
Figure FDA0002798546540000038
Figure FDA0002798546540000041
In the formula: m isiThe mean value of the i-th sample after mapping, and m is the mean value of all samples after mapping;
establishing Fisher criterion in high-dimensional space
Figure FDA0002798546540000042
In the formula: w is aφIs any non-zero column vector;
and judging the fault type by adopting the Mahalanobis distance.
7. The transformer fault detection and classification method according to any one of claims 2 to 6, characterized in that:
the data of the dissolved gas in the transformer oil comprises H2、C2H2、CH4、C2H6、C2H4And the total hydrocarbon content.
8. The transformer fault detection and classification method according to any one of claims 2 to 6, characterized in that:
the transformer electrical test data comprise transformer dielectric loss factors, winding leakage current, insulation resistance and winding direct-current resistance phase difference.
9. The transformer fault detection and classification method according to any one of claims 2 to 6, characterized in that:
the transformer insulating oil characteristic test data comprise dielectric loss of insulating oil, water content in oil and furfural content.
10. The transformer fault detection and classification method according to claim 7, characterized in that:
also included are the gas production rate of total hydrocarbons and CO2Ratio of the gas content of the stage CO.
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Cited By (3)

* Cited by examiner, † Cited by third party
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CN113469257A (en) * 2021-07-07 2021-10-01 云南大学 Distribution transformer fault detection method and system
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CN113469257A (en) * 2021-07-07 2021-10-01 云南大学 Distribution transformer fault detection method and system
CN113657556A (en) * 2021-09-23 2021-11-16 华北电力大学 Gas turbine inlet guide vane system fault diagnosis method based on multivariate statistical analysis
CN113657556B (en) * 2021-09-23 2023-12-26 华北电力大学 Gas turbine inlet guide vane system fault diagnosis method based on multivariate statistical analysis
CN117290670A (en) * 2023-11-27 2023-12-26 南京中鑫智电科技有限公司 Transformer bushing insulation state estimation method based on enhancement filter algorithm
CN117290670B (en) * 2023-11-27 2024-01-26 南京中鑫智电科技有限公司 Transformer bushing insulation state estimation method based on enhancement filter algorithm

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