A low-voltage transformer fault diagnosis method and system

Abstract

The present invention relates to a low-voltage transformer fault diagnosis method and system, which belongs to the field of transformer fault diagnosis technology, and includes the following steps: collecting transformer operating status data and converting it into quantitative description data to construct an observation matrix; using the principal component analysis (PCA) algorithm to extract features from the matrix, and realizing data dimensionality reduction by calculating the eigenvalue contribution rate, thereby significantly reducing the amount of subsequent calculations; using the reduced-dimensional data as the input of a support vector data description (SVDD) model to output a fault sample set; applying a cluster analysis algorithm to classify the fault samples to obtain accurate fault diagnosis results. Compared with traditional methods, the present invention innovatively combines PCA dimensionality reduction technology with the SVDD model. While ensuring diagnostic accuracy, the dimensionality reduction process guided by the eigenvalue contribution rate effectively reduces the computational complexity and improves the efficiency of fault diagnosis. The present invention is particularly suitable for the real-time status monitoring and fault warning requirements of low-voltage transformers in power systems.

Description

Technical Field

[0001] The present invention relates to a low-voltage transformer fault diagnosis method and system, belonging to the technical field of transformer fault diagnosis. Background Art

[0002] Low-voltage current transformers (LVCTs) are key components in power grids, converting high currents from high- or low-voltage systems into low currents for use in low-voltage systems, such as instrumentation, automatic control, and relay protection. LVCTs not only significantly reduce power system costs but also effectively ensure the safety of power workers, earning them widespread application. In recent years, with the rapid development of ultra-high voltage (UHV) transmission technology in my country, the requirements for voltage levels have become increasingly stringent, and the operating environment of LVCTs has become increasingly harsh. Therefore, the ability to accurately and real-timely diagnose LVCT faults is of great practical significance.

[0003] Prior art, such as the Chinese patent application with publication number "CN112596016A," discloses a transformer fault diagnosis method based on the integration of multiple one-dimensional convolutional neural networks. The method comprises the following steps: S1. Acquiring the transformer's original fault signal to generate a fault dataset, which is then rationally segmented into a training dataset and a test dataset; S2. Normalizing each fault sample in the training and test datasets; S3. Constructing three convolutional neural network models with different activation functions and training each convolutional neural network model separately; S4. Testing the fault classification of the trained convolutional neural network models on the test dataset to obtain the classification accuracy prediction results for each sample, and then deriving the final output through a majority voting ensemble strategy. However, the aforementioned patent relies heavily on a large amount of training data, particularly fault status data, to train the multiple CNN models. In practical applications, obtaining sufficient and high-quality fault status data can be challenging. While CNN models perform well in fault identification, the computational complexity of training and inference for multiple CNN models is high, potentially impacting real-time performance. This can be particularly challenging to deploy in resource-constrained environments, such as embedded systems. Summary of the Invention

[0004] In order to solve the above problems in the prior art, the present invention proposes a low voltage transformer fault diagnosis method and system.

[0005] The technical solutions of the present invention are as follows:

[0006] In one aspect, the present invention provides a method for diagnosing a low-voltage transformer fault, comprising the following steps:

[0007] Determining an operating state of a low-voltage transformer, obtaining operating data of the low-voltage transformer, and converting the operating data of the low-voltage transformer into operating data quantitatively describing the low-voltage transformer according to the operating state;

[0008] An observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and a principal component analysis algorithm (PCA) is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors.

[0009] Calculating the contribution rate of the eigenvalue, and performing dimensionality reduction processing on the measurement matrix based on the contribution rate and the eigenvector to obtain a measurement matrix after dimensionality reduction;

[0010] The observation matrix after dimension reduction is used as the input of the support vector data description model SVDD, and the fault class samples are output;

[0011] The fault samples are analyzed based on the cluster analysis algorithm to obtain the low-voltage transformer fault diagnosis results.

[0012] As a preferred embodiment, the operating state of the low-voltage transformer includes a normal operating state, a fixed deviation state, a drift deviation state, a ratio deviation state, and an accuracy distortion state. According to the operating state, the operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer, specifically:

[0013] The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula:

[0014] ;

[0015] The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows:

[0016] ;

[0017] The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula:

[0018] ;

[0019] The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows:

[0020] ;

[0021] The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows:

[0022] ;

[0023] Where, Indicates the quantitative description of the operating data of the low voltage transformer, Indicates the transformer ratio, represents the sine function, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, Indicates the operating data of the low voltage transformer. represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

[0024] As a preferred embodiment, an observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and the principal component analysis algorithm PCA is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors. The specific steps are as follows:

[0025] The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows:

[0026] ;

[0027] ;

[0028] Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points;

[0029] The observation matrix is constructed based on the measurement data and is expressed as follows:

[0030] ;

[0031] ;

[0032] Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix;

[0033] Calculate the covariance matrix of the observation matrix, which is expressed as:

[0034] ;

[0035] Where, represents the covariance matrix, represents the mean of the observation matrix;

[0036] Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows:

[0037] ;

[0038] ;

[0039] Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors.

[0040] As a preferred embodiment, the contribution rate of the eigenvalue is calculated, and the dimension reduction processing of the measurement matrix is performed based on the contribution rate and the eigenvector to obtain the reduced dimension measurement matrix. The specific steps are:

[0041] Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as:

[0042] ;

[0043] ;

[0044] Where, represents the eigenvalue spectrum, represents the number of eigenvalues;

[0045] Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as:

[0046] ;

[0047] Where, Indicates the number of statistically large eigenvalues ;

[0048] Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction dimension.

[0054] As a preferred embodiment, the measurement matrix after dimensionality reduction is used as the input of the support vector data description model SVDD to output fault class samples. The specific steps are as follows:

[0055] The support vector data description model SVDD is expressed as follows:

[0056] ;

[0057] Where, represents the minimum function, represents the optimal hypersphere, Indicates the center of the sphere, represents the radius, represents the relaxation factor, represents the regularization parameter, represents the constraints, Represents the observation matrix after dimensionality reduction No. elements, represents the norm of a vector;

[0058] Based on the Lagrange duality theory, the support vector data description model SVDD is expressed in dual form:

[0059] ;

[0060] Where, represents the maximum function, represents the objective function, 、 represents the Lagrange coefficient, Represents the observation matrix after dimensionality reduction No. elements, Represents the observation matrix after dimensionality reduction No. elements;

[0061] The reduced-dimensional observation matrix corresponding to the Lagrange coefficient that satisfies the constraints The elements of , based on the support vector The optimal hypersphere of the support vector data description model SVDD is obtained, which is expressed as follows:

[0062] ;

[0063] Where, Indicates the support vectors;

[0064] The decision function of the support vector data description model SVDD is obtained based on the optimal hypersphere , expressed as:

[0065] ;

[0066] ;

[0067] Where, Represents the observation matrix after dimensionality reduction Any element of Indicates the support vectors;

[0068] like , then it is judged as a target class sample, otherwise it is judged as a fault class sample and output.

[0069] As a preferred embodiment, the fault samples are analyzed based on the cluster analysis algorithm to obtain the low voltage transformer fault diagnosis result, and the specific steps are as follows:

[0070] Construct a fault sample set based on the fault class samples, which can be expressed as follows:

[0071] ;

[0072] Where, represents the set of fault samples, represents the number of fault samples, Indicates the Fault samples;

[0073] The analysis steps of the cluster analysis algorithm are as follows:

[0074] S1. Determine the optimal number of clusters :

[0075] S101, setting the initial value of the number of clusters to 1;

[0076] S102, based on the spatial information entropy of the fault sample set The calculation method of the fault sample set and the first Information entropy of subclasses The information entropy of the current subclass is calculated by the calculation method; the subclasses are divided by setting the spatial information entropy threshold;

[0077] Among them, the spatial information entropy of the fault sample set is The calculation method is expressed as follows:

[0078] ;

[0079] ;

[0080] Where, represents the complexity function, represents the logarithmic function, represents the probability function;

[0081] The first Information entropy of subclasses The calculation method is expressed as follows:

[0082] ;

[0083] Where, Represents the first subclasses, Represents the fault sample set The characteristic value of the fault class samples in the subclass;

[0084] S103, according to the first Information gain of subclasses The calculation method calculates the information gain of the current subclass and records it;

[0085] Among them, the first Information gain of subclasses The calculation method is expressed as follows:

[0086] ;

[0087] ;

[0088] Where, represents the information entropy of the fault sample set, Represents the observation matrix The value is the measurement data The probability of Indicates logarithm operation with base 2;

[0089] S104, perform a +1 operation on the number of clusters, and execute step S102 until the number of clusters reaches a preset cluster threshold, and then execute step S105;

[0090] S105. Select the number of clusters corresponding to the minimum information gain from the recorded information gains as the optimal number of clusters ;

[0091] S2. Select the initial cluster center:

[0092] S201, according to the fault sample set Fault samples The spatial density The calculation method calculates the spatial density of each fault class sample;

[0093] Among them, the first Fault samples The spatial density The calculation method is expressed as follows:

[0094] ;

[0095] Where, Indicates the Fault samples, Indicates the Fault samples;

[0096] S202, according to the first Fault samples The radius of the field The calculation method calculates the neighborhood radius of each sample;

[0097] Among them, the first Fault samples The radius of the field The calculation method is expressed as follows:

[0098] ;

[0099] Where, represents the exponential function;

[0100] S203, according to the first Fault samples The local density The calculation method calculates the local density of each sample;

[0101] Among them, the first Fault samples The local density The calculation method is expressed as follows:

[0102] ;

[0103] S204, selecting the fault class sample with the largest local density as the initial cluster center;

[0104] S3. Calculate the Euclidean distance between the fault class samples that are not the initial cluster center in the fault sample set and each cluster, and divide them into the cluster with the closest Euclidean distance;

[0105] S4. Calculate the new cluster center of each subclass, expressed as:

[0106] ;

[0107] Where, Indicates the The new cluster centers of the subclasses, Indicates the The number of fault class samples in the subclass, Indicates the The first subcategory Fault samples;

[0108] S5. Re-cluster all fault samples according to the new cluster center. If the clustering results of two adjacent clustering are consistent, the clustering analysis algorithm step ends and the clustering result is output as the low-voltage transformer fault diagnosis result; otherwise, execute step S3;

[0109] The low voltage transformer fault diagnosis result includes fixed deviation, drift deviation, ratio deviation and accuracy distortion.

[0110] In another aspect, the present invention further provides a low-voltage transformer fault diagnosis system, comprising:

[0111] Data acquisition and preprocessing module: determines the operating state of the low-voltage transformer, obtains the operating data of the low-voltage transformer, and converts the operating data of the low-voltage transformer into operating data quantitatively described by the low-voltage transformer according to the operating state;

[0112] Feature extraction module: constructs an observation matrix based on the operation data quantitatively described by the low-voltage transformer, and uses the principal component analysis algorithm PCA to extract features from the observation matrix to obtain eigenvalues and eigenvectors;

[0113] Data modeling module: calculates the contribution rate of the eigenvalue, and performs dimensionality reduction processing on the observation matrix based on the contribution rate and the eigenvector to obtain the reduced-dimensional observation matrix;

[0114] Fault sample identification module: takes the reduced-dimensional observation matrix as the input of the support vector data description model (SVDD) and outputs fault samples;

[0115] Fault diagnosis module: Analyzes fault samples based on cluster analysis algorithm to obtain low-voltage transformer fault diagnosis results.

[0116] As a preferred embodiment, the operating state of the low-voltage transformer includes a normal operating state, a fixed deviation state, a drift deviation state, a ratio deviation state, and an accuracy distortion state. According to the operating state, the operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer, specifically:

[0117] The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula:

[0118] ;

[0119] The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows:

[0120] ;

[0121] The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula:

[0122] ;

[0123] The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows:

[0124] ;

[0125] The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows:

[0126] ;

[0127] Where, Indicates the quantitative description of the operating data of the low voltage transformer, Indicates the transformer ratio, represents the sine function, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, Indicates the operating data of the low voltage transformer. represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

[0128] As a preferred embodiment, an observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and the principal component analysis algorithm PCA is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors. The specific steps are as follows:

[0129] The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows:

[0130] ;

[0131] ;

[0132] Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points;

[0133] The observation matrix is constructed based on the measurement data and is expressed as follows:

[0134] ;

[0135] ;

[0136] Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix;

[0137] Calculate the covariance matrix of the observation matrix, which is expressed as:

[0138] ;

[0139] Where, represents the covariance matrix, represents the mean of the observation matrix;

[0140] Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows:

[0141] ;

[0142] ;

[0143] Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors.

[0144] As a preferred embodiment, the contribution rate of the eigenvalue is calculated, and the dimension reduction processing of the measurement matrix is performed based on the contribution rate and the eigenvector to obtain the reduced dimension measurement matrix. The specific steps are:

[0145] Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as:

[0146] ;

[0147] ;

[0148] Where, represents the eigenvalue spectrum, represents the number of eigenvalues;

[0149] Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as:

[0150] ;

[0151] Where, Indicates the number of statistically large eigenvalues ;

[0152] Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as:

[0153] ;

[0154] ;

[0155] ;

[0156] ;

[0157] Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction dimension.

[0158] The present invention has the following beneficial effects:

[0159] 1. The present invention uses the principal component analysis algorithm (PCA) to extract features from the operating data of the low-voltage transformer, effectively extracting the main features in the data, reducing the interference of noise and redundant information on fault diagnosis, and thus improving the accuracy of fault diagnosis.

[0160] 2. The present invention can quickly process the operating data of the low-voltage transformer and output the fault diagnosis results in real time, which helps to promptly discover and handle transformer faults, avoid fault expansion, and ensure the stable operation of the power system.

[0161] 3. The present invention introduces the application of the support vector data description model (SVDD), which enables the present invention to have a strong recognition ability for slight changes in the transformer operating data, can accurately judge the operating status of the transformer under different working conditions, and enhance the robustness of the system.

[0162] 4. The present invention reduces the amount of data for subsequent calculations, lowers the computational complexity, and improves the efficiency of fault diagnosis by calculating the contribution rate of eigenvalues and performing dimensionality reduction processing on the observation matrix. BRIEF DESCRIPTION OF THE DRAWINGS

[0163] Figure 1 The present invention is a flowchart for implementing the method.

[0164] Figure 2 This is a curve diagram of operating data changes of the low-voltage transformer in normal operating state of the present invention.

[0165] Figure 3 This is a curve diagram of the operating data change of the low-voltage transformer in a fixed deviation state according to the present invention.

[0166] Figure 4This is a curve diagram of the operating data change of the low-voltage transformer in the drift deviation state of the present invention.

[0167] Figure 5 This is a curve diagram of the operating data of the low-voltage transformer in the transformation ratio deviation state of the present invention.

[0168] Figure 6 This is a curve diagram of the operating data change of the low-voltage transformer in the accuracy distortion state of the present invention.

[0169] Figure 7 Schematic diagram of the maximum number of PCA features of the present invention.

[0170] Figure 8 This is a schematic diagram of the SVDD training results of the present invention.

[0171] Figure 9 Schematic diagram of SVDD anomaly detection results of the present invention.

[0172] Figure 10 This is the information gain change curve of the present invention.

[0173] Figure 11 This is a schematic diagram of the results of the improved cluster analysis algorithm proposed in this invention. DETAILED DESCRIPTION

[0174] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0175] It should be understood that the step numbers used herein are only for convenience of description and are not intended to limit the order in which the steps are to be executed.

[0176] It should be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0177] The terms “include” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0178] The term "and / or" refers to and includes any and all possible combinations of one or more of the associated listed items.

[0179] Example 1:

[0180] See also Figure 1 The present invention provides a low voltage transformer fault diagnosis method, comprising the following steps:

[0181] Determining an operating state of a low-voltage transformer, obtaining operating data of the low-voltage transformer, and converting the operating data of the low-voltage transformer into operating data quantitatively describing the low-voltage transformer according to the operating state;

[0182] An observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and a principal component analysis algorithm (PCA) is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors.

[0183] Calculating the contribution rate of the eigenvalue, and performing dimensionality reduction processing on the measurement matrix based on the contribution rate and the eigenvector to obtain a measurement matrix after dimensionality reduction;

[0184] The observation matrix after dimension reduction is used as the input of the support vector data description model SVDD, and the fault class samples are output;

[0185] The fault samples are analyzed based on the cluster analysis algorithm to obtain the low-voltage transformer fault diagnosis results.

[0186] A low-voltage current transformer typically consists of a primary winding, a secondary winding, an iron core, a frame, and a housing. Its basic operating principle is based on magnetic induction theory, achieving a change between voltage and current through the induction of a magnetic field. When current passes through one side of the transformer, it generates a magnetic field within the transformer's iron core, generating an induced current on the other side. Under normal load conditions, the secondary current of a low-voltage transformer is proportional to the current in the main circuit. After a voltage reduction step, the voltage of the secondary current is reduced to a safe range. In real-world production, the operating state of a low-voltage current transformer is affected by a variety of factors. By analyzing the impact of different operating states of a low-voltage transformer, a quantitative description is established.

[0187] As a preferred embodiment, the operating state of the low-voltage transformer is determined, the operating data of the low-voltage transformer is obtained, and the operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer according to the operating state, which is expressed as follows:

[0188] (1)

[0189] The operating status of the low voltage transformer includes normal operating status, fixed deviation status, drift deviation status, ratio deviation status and accuracy distortion status;

[0190] The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula:

[0191] (2)

[0192] Formula (1) is the general expression format for quantitative description. In formula (2), the measurement error of the operating data of the quantitative description of the low-voltage transformer under normal operating conditions is 0, so there are only two items.

[0193] The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows:

[0194] (3)

[0195] The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula:

[0196] (4)

[0197] The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows:

[0198] (5)

[0199] The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows:

[0200] (6)

[0201] In the formula, in the formula, Indicates the quantitative description of the operating data of the low voltage transformer, 、 Indicates the operating data of the low voltage transformer. represents the measurement error, represents the systematic error, Indicates the transformer ratio, 、 represents Gaussian white noise, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

[0202] The complexity of low-voltage current transformer operating environments and the diversity of their fault states make fault diagnosis a high-dimensional, nonlinear, and massive data mining problem. Furthermore, the data inevitably contains a large amount of duplicate and redundant information, which affects the computational efficiency and accuracy of the fault diagnosis algorithm. Therefore, the first step in low-voltage current transformer fault diagnosis is data dimensionality reduction and feature extraction.

[0203] PCA is a classic method in the field of data analysis. It transforms correlated high-dimensional data into a set of uncorrelated low-dimensional data through orthogonal transformation. These low-dimensional data are called principal components.

[0204] As a preferred embodiment, an observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and the principal component analysis algorithm PCA is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors. The specific steps are as follows:

[0205] The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows:

[0206] ;

[0207] ;

[0208] Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points, Indicates the number of sampling points index;

[0209] The observation matrix is constructed based on the measurement data and is expressed as follows:

[0210] ;

[0211] ;

[0212] Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix, Indicates the index of observation times;

[0213] Calculate the covariance matrix of the observation matrix, which is expressed as:

[0214] ;

[0215] Where, represents the covariance matrix, represents the mean of the observation matrix;

[0216] Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows:

[0217] ;

[0218] ;

[0219] Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors, Represents the covariance matrix element index.

[0220] As a preferred embodiment, the contribution rate of the eigenvalue is calculated, and the dimension reduction processing of the measurement matrix is performed based on the contribution rate and the eigenvector to obtain the reduced dimension measurement matrix. The specific steps are:

[0221] Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as:

[0222] ;

[0223] ;

[0224] Where, represents the eigenvalue spectrum, represents the number of eigenvalues;

[0225] Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as:

[0226] (7)

[0227] Where, Indicates the number of statistically large eigenvalues ;

[0228] Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as:

[0229] ;

[0230] ;

[0231] ;

[0232] ;

[0233] Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction dimension.

[0234] After PCA decomposition, the original dimensional data is converted into The principal component form of unrelated dimensions realizes the elimination of redundant information in the data. The principal components contain most of the useful information in the original data, so they can replace the original high-dimensional data for subsequent fault diagnosis analysis.

[0235] Based on practical experience, low-voltage current transformer failures are rare events. Since the system remains normal most of the time, it's often difficult to obtain sufficient fault state data for model training during the training phase. This limits the use of traditional supervised pattern recognition methods like support vector machines (SVMs) and neural networks.

[0236] SVDD is a one-class classifier within a Bayesian framework. Its fundamental principle is to find an optimal hypersphere with the smallest possible radius in feature space that encompasses as many target class samples as possible while excluding non-target class samples. Therefore, during model training, SVDD only requires target class samples to obtain the optimal hypersphere.

[0237] As a preferred embodiment, the measurement matrix after dimensionality reduction is used as the input of the support vector data description model SVDD to output fault class samples. The specific steps are as follows:

[0238] The support vector data description model SVDD is expressed as follows:

[0239] ;

[0240] Where, represents the minimum function, represents the optimal hypersphere, Indicates the center of the sphere, represents the radius, represents the relaxation factor, represents the regularization parameter, represents the constraints, Represents the observation matrix after dimensionality reduction No. elements, represents the norm of a vector;

[0241] Based on the Lagrange duality theory, the support vector data description model SVDD is expressed in dual form:

[0242] ;

[0243] Where, represents the maximum function, represents the objective function, 、 represents the Lagrange coefficient, Represents the observation matrix after dimensionality reduction No. elements, Represents the observation matrix after dimensionality reduction No. elements, 、 Represents a general index;

[0244] The reduced-dimensional observation matrix corresponding to the Lagrange coefficient that satisfies the constraints The elements of , based on the support vector The optimal hypersphere of the support vector data description model SVDD is obtained, which is expressed as follows:

[0245] ;

[0246] Where, Indicates the support vectors;

[0247] The decision function of the support vector data description model SVDD is obtained based on the optimal hypersphere , expressed as:

[0248] ;

[0249] ;

[0250] Where, Represents the observation matrix after dimensionality reduction Any element of Indicates the support vectors, represents the inner product;

[0251] like , then it is judged as a target class sample, otherwise it is judged as a fault class sample and output.

[0252] Cluster analysis algorithm is a classic unsupervised clustering method that divides samples into different subclasses based on the size of the Euclidean distance between them. It has the advantages of simple principle and efficient algorithm. However, the performance of cluster analysis algorithm is affected by the number of clusters. The selection of the initial cluster center has a great influence on how to choose the optimal number of clusters. There is currently no better method for determining the initial cluster center. To address the above issues, this paper proposes an improved cluster analysis algorithm based on information gain and local density. First, the concept of information gain of clustering is given, and the amount of information in the sample space under different partitions is quantitatively evaluated by the size of the information gain. The number of categories corresponding to the minimum information gain is the optimal number of clusters. ; Then the concept of sample local density is given. Local density comprehensively considers the number of samples and sample distance information in the neighborhood. The samples with the largest local density are selected as the initial cluster centers. The initial cluster centers selected in this way are not only located in the area with the densest sample distribution, but also the distances between different cluster centers are far.

[0253] As a preferred embodiment, the fault samples are analyzed based on the cluster analysis algorithm to obtain the low voltage transformer fault diagnosis result, and the specific steps are as follows:

[0254] Construct a fault sample set based on the fault class samples, which can be expressed as follows:

[0255] ;

[0256] Where, represents the set of fault samples, represents the number of fault samples, Indicates the Fault samples;

[0257] The analysis steps of the cluster analysis algorithm are as follows:

[0258] S1. Determine the optimal number of clusters :

[0259] S101, setting the initial value of the number of clusters to 1;

[0260] S102, based on the spatial information entropy of the fault sample set The calculation method of the fault sample set and the first Information entropy of subclasses The information entropy of the current subclass is calculated by the calculation method; the subclasses are divided by setting the spatial information entropy threshold;

[0261] Among them, the spatial information entropy of the fault sample set is The calculation method is expressed as follows:

[0262] ;

[0263] ;

[0264] Where, represents the complexity function, represents the logarithmic function, represents the probability function;

[0265] The first Information entropy of subclasses The calculation method is expressed as follows:

[0266] ;

[0267] Where, Represents the first subclasses, Represents the fault sample set The characteristic value of the fault class samples in the subclass;

[0268] S103, according to the first Information gain of subclasses The calculation method calculates the information gain of the current subclass and records it;

[0269] Among them, the first Information gain of subclasses The calculation method is expressed as follows:

[0270] ;

[0271] ;

[0272] Where, represents the information entropy of the fault sample set, Represents the observation matrix The value is the measurement data The probability of Indicates logarithm operation with base 2;

[0273] S104, perform a +1 operation on the number of clusters, and execute step S102 until the number of clusters reaches a preset cluster threshold, and then execute step S105;

[0274] S105. Select the number of clusters corresponding to the minimum information gain from the recorded information gains as the optimal number of clusters ;

[0275] S2. Select the initial cluster center:

[0276] S201, according to the first Fault samples The spatial density The calculation method calculates the spatial density of each fault class sample;

[0277] Among them, the first Fault samples The spatial density The calculation method is expressed as follows:

[0278] ;

[0279] Where, Indicates the Fault samples, Indicates the Fault samples;

[0280] S202, according to the first Fault samples The radius of the area The calculation method calculates the neighborhood radius of each sample;

[0281] Among them, the first Fault samples The radius of the field The calculation method is expressed as follows:

[0282] ;

[0283] Where, represents the exponential function;

[0284] S203, according to the first Fault samples The local density The calculation method calculates the local density of each sample;

[0285] Among them, the first Fault samples The local density The calculation method is expressed as follows:

[0286] ;

[0287] S204, selecting the fault class sample with the largest local density as the initial cluster center;

[0288] S3. Calculate the Euclidean distance between the fault class samples that are not the initial cluster center in the fault sample set and each cluster, and divide them into the cluster with the closest Euclidean distance;

[0289] S4. Calculate the new cluster center of each subclass, expressed as:

[0290] ;

[0291] Where, Indicates the The new cluster centers of the subclasses, Indicates the The number of fault class samples in the subclass, Indicates the The first subcategory Fault samples;

[0292] S5. Re-cluster all fault samples according to the new cluster center. If the clustering results of two adjacent clustering are consistent, the clustering analysis algorithm step ends and the clustering result is output as the low-voltage transformer fault diagnosis result; otherwise, execute step S3;

[0293] The low voltage transformer fault diagnosis result includes fixed deviation, drift deviation, ratio deviation and accuracy distortion.

[0294] In order to verify the effectiveness of the method proposed in this invention, the Monte Carlo method is used to simulate and generate experimental data corresponding to the normal operating state and four fault states according to equations (2) to (6). The parameter settings during the simulation process are shown in Table 1.

[0295] Table 1 Simulation parameter setting table

[0296]

[0297] See also Figure 2-6 , presenting curves of simulated data under five different states. During the validation process, 1000 sets of normal state data were simulated and used as training samples for training the SVDD optimal classification surface. During the testing phase, 100 sets of normal state data and 100 sets of each of the four fault state data were simulated, totaling 500 sets of test samples, to evaluate and verify the fault diagnosis performance of the proposed method.

[0298] See also Figure 7 , Figure 7 The eigenvalue spectrum obtained by using PCA to perform dimensionality reduction analysis and feature extraction on the training samples is given. It can be seen that the first three eigenvalues are significantly larger than the remaining eigenvalues. According to formula (7), the number of large features calculated with the eigenvalue contribution rate exceeding 90% as the criterion is 3, indicating that after using PCA to perform dimensionality reduction decomposition on the original data, the three-dimensional principal components are extracted to form the eigenvector.

[0299] See also Figure 8-9 , Figure 8 The projection of the optimal hypersphere obtained by training the SVDD classifier using the eigenvectors onto the two-dimensional plane is presented. It can be seen that the optimal hypersphere obtained during the training phase encompasses all training samples within the sphere, and there is a certain amount of loose space between the sphere and the training data to avoid overfitting, indicating that the model has a certain degree of robustness.

[0300] The results of fault detection using the optimal hypersphere on the test data set are as follows: Figure 9 As shown, it can be seen that all fault state samples (square □) are classified outside the classification surface and are correctly judged as "fault". At the same time, most normal state samples (◇) are classified within the classification surface and are correctly judged as "normal". Only 2 groups of "normal" state samples are classified outside the classification surface and are incorrectly judged as "fault".

[0301] See also Figure 10-11 ,After completing the fault detection of the transformer using SVDD, it is necessary to ,perform further cluster analysis on the samples judged as “faulty” by SVDD, so as to ,effectively distinguish different fault states. Figure 10 The information gain of the clustering process using the improved cluster analysis algorithm is given as the number of clusters increases. From the change curve, it can be seen that when the number of clusters (the horizontal axis in the figure) is 4, the corresponding information gain is the smallest, that is, the optimal number of clusters determined by the method proposed in this invention is 4, which is consistent with the actual simulation data setting.

[0302] Figure 11 The clustering results obtained by clustering data of different fault states using the proposed improved clustering analysis algorithm are given. Figure 11 It can be seen that after clustering, the three types of fault state data, namely fixed deviation, drift deviation and ratio deviation, show a high degree of clustering, and there are also obvious differences between the three types of data. The distribution of precision distortion state data is relatively loose, and the clustering is weaker than that of the other three states, and there is a small amount of overlap between the samples and the ratio deviation state.

[0303] right Figure 9 and Figure 11The results shown in Table 2 are combined to obtain the fault diagnosis results of the proposed SVDD combined with improved cluster analysis algorithm. As can be seen, the proposed method achieves a diagnostic accuracy exceeding 96% for all five different transformer states, with the accuracy reaching 100% for the fixed deviation and drift deviation states. The average fault diagnosis accuracy of the proposed method for all five states is 98.3%, validating the effectiveness of the proposed method.

[0304] Table 2 Fault diagnosis results

[0305] normal Fixed deviation Drift deviation Ratio deviation Precision distortion Accuracy 98% 100% 100% 97.5% 96.3%

[0306] In order to further verify the effectiveness of the method proposed in the present invention, the unimproved cluster analysis algorithm and the BP neural network method were used to perform fault diagnosis on the transformer's five different state data. The unimproved cluster analysis algorithm, as an unsupervised clustering method, can achieve fault diagnosis without the need for training data. As a supervised clustering method, the BP neural network requires five different state data as training sets to complete model training during the training phase. Therefore, during the training phase, we simulated 1,000 groups of normal state data and 100 groups of four fault state data as training samples. Table 3 further illustrates the sample number settings of different methods in the experiment. It can be seen that the main difference between the three methods lies in whether training samples are required. The unsupervised cluster analysis algorithm method does not require training samples at all. The method proposed in the present invention only needs to generate normal state data as training samples, while the supervised BP neural network requires training data for all states.

[0307] Table 3 Different sample set division methods

[0308]

[0309] Table 4 shows the fault diagnosis results for each state obtained by the cluster analysis algorithm (setting the number of clusters to 5) and the BP neural network method. It can be seen that for the two samples of normal state and fixed deviation state, the classification performance of the supervised BP neural network method is better than the unsupervised cluster analysis algorithm, but for the other three fault states, the classification performance of the BP neural network is lower than the cluster analysis algorithm. The reason is that as a supervised classification method, under unbalanced samples, the BP neural network tends to judge the category with a small number of samples as the category with a large number of samples, thereby obtaining a higher average accuracy. Comparing Table 4 with Table 1, it can be seen that the method proposed in the present invention can obtain the highest accuracy for all five different states of the mutual inductor, and the average accuracy is improved by 5.3% compared with the cluster analysis algorithm and 4.5% compared with the BP neural network. The above results verify the superiority of the method proposed in the present invention under the conditions of unbalanced sample sets.

[0310] Table 4 Fault diagnosis results of different methods

[0311] normal Fixed deviation Drift deviation Ratio deviation Precision distortion Cluster analysis algorithm 94% 100% 95.3% 96.2% 93.3% BP neural network 100% 100% 94.2% 94.5% 91.7%

[0312] Furthermore, Table 5 shows the fault diagnosis results obtained by the three methods when the samples are balanced (1000 samples for each of the five states). It can be seen that the performance of the BP neural network is significantly improved under balanced samples, with the classification accuracy for each state being superior to that of the cluster analysis algorithm. The proposed method also achieves a comparable accuracy for each state as the BP neural network, demonstrating that the proposed method is suitable not only for unbalanced datasets but also for balanced datasets, and exhibits greater adaptability than the other two methods.

[0313] Table 5. Fault diagnosis results of different methods (balanced data set)

[0314] normal Fixed deviation Drift deviation Ratio deviation Precision distortion Cluster analysis algorithm 96.7% 100% 98.9% 97.6% 96.8% BP neural network 98.7% 100% 100% 99.5% 99.2% The method proposed by the present invention 99% 100% 100% 99.5% 98.8%

[0315] Example 2:

[0316] The present invention also provides a low-voltage transformer fault diagnosis system, comprising:

[0317] Data acquisition and preprocessing module: determines the operating state of the low-voltage transformer, obtains the operating data of the low-voltage transformer, and converts the operating data of the low-voltage transformer into operating data quantitatively described by the low-voltage transformer according to the operating state;

[0318] Feature extraction module: constructs an observation matrix based on the operation data quantitatively described by the low-voltage transformer, and uses the principal component analysis algorithm PCA to extract features from the observation matrix to obtain eigenvalues and eigenvectors;

[0319] Data modeling module: calculates the contribution rate of the eigenvalue, and performs dimensionality reduction processing on the observation matrix based on the contribution rate and the eigenvector to obtain the reduced-dimensional observation matrix;

[0320] Fault sample identification module: takes the reduced-dimensional observation matrix as the input of the support vector data description model (SVDD) and outputs fault samples;

[0321] Fault diagnosis module: Analyzes fault samples based on cluster analysis algorithm to obtain low-voltage transformer fault diagnosis results.

[0322] As a preferred embodiment, the operating state of the low-voltage transformer includes a normal operating state, a fixed deviation state, a drift deviation state, a ratio deviation state, and an accuracy distortion state. According to the operating state, the operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer, specifically:

[0323] The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula:

[0324] ;

[0325] The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows:

[0326] ;

[0327] The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula:

[0328] ;

[0329] The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows:

[0330] ;

[0331] The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows:

[0332] ;

[0333] Where, Indicates the quantitative description of the operating data of the low voltage transformer, Indicates the transformer ratio, represents the sine function, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, Indicates the operating data of the low voltage transformer. represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

[0334] As a preferred embodiment, an observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer, and the principal component analysis algorithm PCA is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors. The specific steps are as follows:

[0335] The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows:

[0336] ;

[0337] ;

[0338] Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points;

[0339] The observation matrix is constructed based on the measurement data and is expressed as follows:

[0340] ;

[0341] ;

[0342] Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix;

[0343] Calculate the covariance matrix of the observation matrix, which is expressed as:

[0344] ;

[0345] Where, represents the covariance matrix, represents the mean of the observation matrix;

[0346] Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows:

[0347] ;

[0348] ;

[0349] Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors.

[0350] As a preferred embodiment, the contribution rate of the eigenvalue is calculated, and the dimension reduction processing of the measurement matrix is performed based on the contribution rate and the eigenvector to obtain the reduced dimension measurement matrix. The specific steps are:

[0351] Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as:

[0352] ;

[0353] ;

[0354] Where, represents the eigenvalue spectrum, represents the number of eigenvalues;

[0355] Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as:

[0356] ;

[0357] Where, Indicates the number of statistically large eigenvalues ;

[0358] Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as:

[0359] ;

[0360] ;

[0361] ;

[0362] ;

[0363] Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction dimension.

[0364] In the embodiments of the present application, "at least one" refers to one or more, and "more" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can represent: a, b, c, a and b, a and c, b and c or a and b and c, where a, b, c can be single or multiple.

[0365] Those skilled in the art will appreciate that the various units and algorithm steps described in the embodiments disclosed in the present invention can be implemented by a combination of electronic hardware, computer software, and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0366] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0367] In the several embodiments provided in this application, if any function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of this application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory; hereinafter referred to as: ROM), random access memory (Random Access Memory; hereinafter referred to as: RAM), magnetic disk or optical disk, and other media that can store program code.

[0368] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A low voltage transformer fault diagnosis method, characterized in that: The following steps are involved: Determining an operating state of a low-voltage transformer, obtaining operating data of the low-voltage transformer, and converting the operating data of the low-voltage transformer into operating data quantitatively describing the low-voltage transformer according to the operating state; An observation matrix is constructed based on the operation data quantitatively described by the low-voltage transformer. The principal component analysis algorithm PCA is used to extract features from the observation matrix to obtain eigenvalues and eigenvectors. The specific steps are as follows: The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows: ； ； Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points; The observation matrix is constructed based on the measurement data and is expressed as follows: ； ； Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix; Calculate the covariance matrix of the observation matrix, which is expressed as: ； Where, represents the covariance matrix, represents the mean of the observation matrix; Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows: ； ； Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors; Calculate the contribution rate of the eigenvalue, and perform dimensionality reduction processing on the measurement matrix based on the contribution rate and the eigenvector to obtain the reduced-dimensional measurement matrix. The specific steps are: Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as: ； ； Where, represents the eigenvalue spectrum, represents the number of eigenvalues; Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as: ； Where, Indicates the number of statistically large eigenvalues ; Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as: ； ； ； ； Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction Dimensions; The observation matrix after dimension reduction is used as the input of the support vector data description model SVDD, and the fault class samples are output; The fault samples are analyzed based on the cluster analysis algorithm to obtain the low-voltage transformer fault diagnosis results.

2. The low voltage transformer fault diagnosis method according to claim 1, characterized in that: The operating status of the low-voltage transformer includes a normal operating state, a fixed deviation state, a drift deviation state, a ratio deviation state, and an accuracy distortion state. The operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer according to the operating status, specifically: The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula: ； The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows: ； The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula: ； The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows: ； The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows: ； Where, Indicates the quantitative description of the operating data of the low voltage transformer, Indicates the transformer ratio, represents the sine function, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, Indicates the operating data of the low voltage transformer. represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

3. The low voltage transformer fault diagnosis method according to claim 1, characterized in that: The reduced-dimensional observation matrix is used as the input of the support vector data description model SVDD to output fault class samples. The specific steps are as follows: The support vector data description model SVDD is expressed as follows: ； Where, represents the minimum function, represents the optimal hypersphere, Indicates the center of the sphere, represents the radius, represents the relaxation factor, represents the regularization parameter, represents the constraints, Represents the observation matrix after dimensionality reduction No. elements, represents the norm of a vector; Based on the Lagrange duality theory, the support vector data description model SVDD is expressed in dual form: ； Where, represents the maximum function, represents the objective function, 、 represents the Lagrange coefficient, Represents the observation matrix after dimensionality reduction No. elements, Represents the observation matrix after dimensionality reduction No. elements; The reduced-dimensional observation matrix corresponding to the Lagrange coefficient that satisfies the constraints The elements of , based on the support vector The optimal hypersphere of the support vector data description model SVDD is obtained, which is expressed as follows: ； Where, Indicates the support vectors; The decision function of the support vector data description model SVDD is obtained based on the optimal hypersphere , expressed as: ； ； Where, Represents the observation matrix after dimensionality reduction Any element of Indicates the support vectors; like , then it is judged as a target class sample, otherwise it is judged as a fault class sample and output.

4. The low voltage transformer fault diagnosis method according to claim 3, characterized in that: The fault samples are analyzed based on the cluster analysis algorithm to obtain the low voltage transformer fault diagnosis results. The specific steps are: Construct a fault sample set based on the fault class samples, which can be expressed as follows: ； Where, represents the set of fault samples, represents the number of fault samples, Indicates the Fault samples; The analysis steps of the cluster analysis algorithm are as follows: S1. Determine the optimal number of clusters : S101, setting the initial value of the number of clusters to 1; S102, based on the spatial information entropy of the fault sample set The calculation method of the fault sample set and the first Information entropy of subclasses The information entropy of the current subclass is calculated by the calculation method; the subclasses are divided by setting the spatial information entropy threshold; Among them, the spatial information entropy of the fault sample set is The calculation method is expressed as follows: ； ； Where, represents the complexity function, represents the logarithmic function, represents the probability function; The first Information entropy of subclasses The calculation method is expressed as follows: ； Where, Represents the first subclasses, Represents the fault sample set The characteristic values of the fault class samples in the subclasses; S103, according to the first Information gain of subclasses The calculation method calculates the information gain of the current subclass and records it; Among them, the first Information gain of subclasses The calculation method is expressed as follows: ； ； Where, represents the information entropy of the fault sample set, Represents the observation matrix The value is the measurement data The probability of Indicates logarithm operation with base 2; S104, perform a +1 operation on the number of clusters, and execute step S102 until the number of clusters reaches a preset cluster threshold, and then execute step S105; S105. Select the number of clusters corresponding to the minimum information gain from the recorded information gains as the optimal number of clusters ; S2. Select the initial cluster center: S201, according to the fault sample set Fault samples The spatial density The calculation method calculates the spatial density of each fault class sample; Among them, the first Fault samples The spatial density The calculation method is expressed as follows: ； Where, Indicates the Fault samples, Indicates the Fault samples; S202, according to the first Fault samples The radius of the field The calculation method calculates the neighborhood radius of each sample; Among them, the first Fault samples The radius of the field The calculation method is expressed as follows: ； Where, represents the exponential function; S203, according to the first Fault samples The local density The calculation method calculates the local density of each sample; Among them, the first Fault samples The local density The calculation method is expressed as follows: ； S204, selecting the fault class sample with the largest local density as the initial cluster center; S3. Calculate the Euclidean distance between the fault class samples that are not the initial cluster center in the fault sample set and each cluster, and divide them into the cluster with the closest Euclidean distance; S4. Calculate the new cluster center of each subclass, expressed as: ； Where, Indicates the The new cluster centers of the subclasses, Indicates the The number of fault class samples in the subclass, Indicates the The first of the subclasses Fault samples; S5. Re-cluster all fault samples according to the new cluster center. If the clustering results of two adjacent clustering are consistent, the clustering analysis algorithm step ends and the clustering result is output as the low-voltage transformer fault diagnosis result; otherwise, execute step S3; The low voltage transformer fault diagnosis result includes fixed deviation, drift deviation, ratio deviation and accuracy distortion.

5. A low voltage transformer fault diagnosis system comprising: Data acquisition and preprocessing module: determines the operating state of the low-voltage transformer, obtains the operating data of the low-voltage transformer, and converts the operating data of the low-voltage transformer into operating data quantitatively described by the low-voltage transformer according to the operating state; Feature extraction module: Build an observation matrix based on the quantitative description of the operation data of the low-voltage transformer, use the principal component analysis algorithm PCA to extract features from the observation matrix, and obtain eigenvalues and eigenvectors. The specific steps are as follows: The measurement data is obtained by setting sampling points for the quantitative description of the operation data of the low-voltage transformer and sampling, which can be expressed as follows: ； ； Where, Represents the operating data that quantitatively describes the low-voltage transformer No. The measurement data obtained from observations, represents the transpose of the matrix, Indicates the The operation data of low voltage transformer is quantitatively described by the sampling points No. The measurement data obtained from observations, Indicates the number of sampling points; The observation matrix is constructed based on the measurement data and is expressed as follows: ； ； Where, represents the observation matrix, represents the total number of observations, represents the dimension of the observation matrix; Calculate the covariance matrix of the observation matrix, which is expressed as: ； Where, represents the covariance matrix, represents the mean of the observation matrix; Perform eigendecomposition on the covariance matrix to obtain eigenvalues and eigenvectors, which can be expressed as follows: ； ； Where, represents the covariance matrix eigenvalues, represents the covariance matrix feature vectors; Data modeling module: Calculate the contribution rate of the eigenvalue, perform dimensionality reduction processing on the observation matrix based on the contribution rate and eigenvector, and obtain the reduced-dimensional observation matrix. The specific steps are as follows: Arrange the eigenvalues from large to small to get the eigenvalue spectrum, which can be expressed as: ； ； Where, represents the eigenvalue spectrum, represents the number of eigenvalues; Calculate the contribution rate of the eigenvalue, record the eigenvalue with a contribution rate greater than or equal to 90% as the large eigenvalue, and count the number of large eigenvalues , expressed as: ； Where, Indicates the number of statistically large eigenvalues ; Project the observation matrix onto The subspace consisting of the eigenvectors corresponding to the largest eigenvalues , and obtain the observation matrix after dimensionality reduction , expressed as: ； ； ； ； Where, Indicates the The eigenvectors corresponding to the largest eigenvalues are Represents the observation matrix after dimensionality reduction The first element of Represents the observation matrix after dimensionality reduction The number of elements, Represents the observation matrix after dimensionality reduction Dimensions; Fault sample identification module: takes the reduced-dimensional observation matrix as the input of the support vector data description model (SVDD) and outputs fault samples; Fault diagnosis module: Analyzes fault samples based on cluster analysis algorithm to obtain low-voltage transformer fault diagnosis results.

6. The low voltage transformer fault diagnosis system according to claim 5, characterized in that: The operating status of the low-voltage transformer includes a normal operating state, a fixed deviation state, a drift deviation state, a ratio deviation state, and an accuracy distortion state. The operating data of the low-voltage transformer is converted into operating data quantitatively described by the low-voltage transformer according to the operating status, specifically: The quantitative description of the operating data of the low-voltage transformer under the normal operating state is expressed by the formula: ； The quantitative operating data of the low-voltage transformer under the fixed deviation state is expressed as follows: ； The quantitative description of the operating data of the low-voltage transformer under the drift deviation state is expressed by the formula: ； The quantitative operating data of the low-voltage transformer under the ratio deviation state is expressed as follows: ； The quantitative operating data of the low-voltage transformer under the accuracy distortion state is expressed as follows: ； Where, Indicates the quantitative description of the operating data of the low voltage transformer, Indicates the transformer ratio, represents the sine function, 、 represents zero mean, 、 The variance is 、 Gaussian white noise, Indicates the operating data of the low voltage transformer. represents the angular frequency, Indicates the initial phase, represents a normal distribution, Indicates time, represents a fixed deviation, represents a constant, Indicates the failure rate.

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