Transformer Fault Early Warning Analysis Based on Hierarchical Clustering Combined with Decision Trees

Abstract

The issues of low accuracy, poor generality, high cost of transformer fault early warning, and the subjective nature of empirical judgments made by field maintenance personnel are difficult to solve with the traditional measurement methods used during the development of the transformer. To construct a transformer fault early warning analysis, this study recommends a data-fusion-based decision tree approach for merging electrical quantity signals with a non-electrical amount of vibration signals. By merging a decision tree inference with actual operation data, a clustering center, and an early warning model, this method creates a transformer fault early warning model with self-learning ability and adaptive capabilities. After reasonable verification, the method becomes more universal and interpretable, and it can successfully conduct an early warning of transformer faults.

1. Introduction

The demands for the safe and reliable functioning of transformers are increasing in line with the grid technology’s fast growth. In-service testing of transformers is crucial for their safe and reliable operation as they are a key element of the power system. The fault rate of transformers rises as they are used a lot, impairing their regular operation and even endangering the whole electrical grid [1,2]. Therefore, in order to promptly discover the hidden danger of transformer fault and avoid unexpected accidents, if the operation of transformer could offer an early warning and take effective measures to troubleshoot the transformer before it fails, then it will considerably lower the rate of fault of transformer operations. It is of great significance to condition based maintenance and stability improvement of transformer equipment [3,4].

Transformer fault early warning is to detect the state of the research object, collect state information, analyze and process the data, and help on-site operators determine the fault of the transformer. The primary research data source is vibration data or other signal data, and the corresponding early warning model is established using state estimation, neural networks [5,6], deep learning [7,8], and other methods in order to provisionally realize the fault early warning within specific conditions and ranges. When using a neural network to establish a transformer early warning model, a large number of transformer data sets are required and any insufficient data set can affect the prediction accuracy of the model. Hence, to ensure the versatility and flexibility of transformer fault early warning, improving the degree of fault early warning is an inevitable trend in the development of the early warning field.

Currently, dissolved gas analysis (DGA) is used to detect oil samples in the field of transformer fault early warning. Judging the insulation performance of transformers and solving the problem of oneness and low reliability could be a direct method for early warning against transformer faults [9,10]. In addition, the subjectivity and uncertainty in the manual empirical judgment which cannot achieve the ideal effect in actual analysis. To increase field maintenance and operational effectiveness, a more comprehensive approach to early warning of transformer fault types is therefore required. If a tiny amount of gas is produced by overheating during transformer operation, the associated insulation material will also begin to break down quickly, producing an excessive amount of gas. By identifying and mining historical data, the literature [11] proposes an online early warning approach for the probability distribution of specific gas history data and its precise categorization in the transformer condition space to issue transformer fault early warning. Transformer surface vibration signals for predictive judgment are the foundation of the literature [12]. The winding vibration information is mostly connected to current, and core vibration during the early fault warning process. The aforementioned methods can only be used in conjunction with unique gases produced by the transformer to achieve transformer fault early warning. Due to limited historical data, it is difficult to collect a large amount of multi-dimensional transformer data for a comprehensive testing [13,14,15]. Most of the detection data mentioned above are non-electrical quantities. Effectively determining the causal link between voltage level, power level, and other electrical parameters and failures is challenging. Fault early warning [16,17,18] does not really accomplish comprehensive coverage of data sources.

In addition, the computational complexity of the fault early warning method based on statistical analysis and artificial intelligence will increase exponentially with the increase in the input data dimension [19], which seriously increases the difficulty of the fault early warning method application. These supervised learning methods are relatively dependent on the label information of the data samples. Hence, this makes it difficult to obtain the hidden information concealed in the data and unable to generate a good early warning result.

To solve the above problems, it is necessary to combine data-driven technologies and adopt a transformer fault early warning method that combines unsupervised and supervised learning to achieve equipment status early warnings and gradually improve the level of equipment fault early warning. Therefore, this paper proposes a method for early warning of transformer operational status using a combination of agglomerative hierarchical clustering and decision trees, which collects data from multiple-dimensional transformer, such as electrical quantities and non-electrical quantities. Firstly, use the idea of data mining to study the vibration characteristics of different electrical quantities of transformers and apply hierarchical clustering to cluster division. Secondly, establish a decision tree model based on vibration cluster categories, identifying the vibration characteristic information that leads to the division of power quality problems in the power grid, i.e., harmonics and three-phase unbalanced, with the vibration characteristic information of light load and heavy load that reflects load changes. Analyze the abnormal vibration characteristics of transformers and realize a comprehensive early warning analysis of transformer operation fault. This method provides new ideas for traditional analysis methods which analyze the vibration signals for transformer faults early warning.

2. Analysis of Transformer Vibration Characteristics Supported Power Quality

2.1. Effect of Different Types of Electrical Quantities on Vibration

When a transformer is in operation, changes in electrical parameters such as supply voltage and load current effect the vibration signal of the transformer, which mainly comes from the vibration of the winding and iron core, depending on the magnetostriction and electromagnetic force of the silicon steel sheet (ampere force) role [20].

The electromagnetic force is caused by the leakage magnetic field of the iron core on the winding current. The winding vibration is caused by the electromagnetic force on the winding energized by the current in the leakage field, and changes in the load current affect the winding vibration during steady operation [21,22]. Magnetostriction of the core silicon steel sheet is the main cause of core vibration. The dimensions of the ferromagnetic material change periodically under the action of an alternating external magnetic field [23,24]. The acceleration of core vibration caused by this phenomenon is proportional to the square of the supply voltage [25], and changes in the supply voltage affect the vibration of the core. Therefore, for a comprehensive and correct analysis of transformer vibration characteristics, each variety of electrical quantities, transformer voltage and current, have to be compelled to be thought of comprehensively.

Based on the above analysis, it is clear that to effectively analyze the vibration characteristics, electrical quantities need to be classified first, i.e., load variations during normal transformer operation versus abnormal operating conditions when power quality problems exist. Based on the definition of power quality, the following types of typical transformer electrical quantities are considered:

Load change is a regular phenomenon during transformer operation, load change corresponds to transformer winding current change, according to the ampere force formula:

$$\mathrm{f}=I\cdot (L\times B)=ILB\sin \alpha$$

(1)

In Equation (1), I is the current flow through winding; B is the leakage flux density acting on the winding; α is the angle between the line length vector L and B; L is the wire length.

From (1), it can be seen that the electromagnetic force on the winding will change with a constant leakage flux B and further affect the vibration characteristics.

• Content of the higher current harmonics

The higher current harmonics are caused by non-linear loads. When transformer currents contain a harmonic component, it can be seen from the ampere force Equation (1) that the electromagnetic forces on the winding will also have a harmonic component, which affects the vibration characteristics.

• Three-phase current imbalanced

When the three-phase currents are unbalanced, the currents flowing through the three-phase winding are inconsistent, resulting in uneven forces on the three-phase winding. Again, according to the ampere force Equation (1), the vibration characteristics will change.

Based on the aforementioned analysis, it was discovered that a vibration propagation mechanism model was constructed based on common grid power quality issues, such as harmonic currents and three-phase unbalanced, with various types of electrical quantities that can reflect changes in load for light and heavy loads, as shown in Figure 1. As a result, the relationship between electrical quantities and transformer vibration was based on this model.

2.2. Vibration Signal Analysis Based on Fourier Transform

This paper analyzes the vibration signal of a dry-type transformer with a capacity of 400 KVA and 10 KV to 400 V in a power distribution room and analyzes 2 types of power quality problems combined with light load and heavy load, respectively. The experiments are based on 60 s sampling data. Split the time-domain curves of different types of electrical quantities into 440 consecutive sets of data with a time window of 200 ms, and then perform Fourier transform on the vibration data of each window to obtain the vibration amplitude-frequency characteristic curves of different electrical quantities from 50 Hz to 2400 Hz. Since the load change is the normal working state of the transformer, in order to facilitate the comparison of the vibration characteristics caused by power quality problems, the vibration characteristics of the light load and heavy load conditions are first to be analyzed here.

• Vibration signal analysis of transformers at light and heavy loads

The vibration signal of the transformer during light load and heavy load operation is shown in Figure 2a,b. Under light load conditions, the current flowing through the transformer winding changes less, resulting in a smaller change in the electromagnetic force on the winding with constant leakage flux, and the corresponding vibration signal is mainly concentrated in the low-frequency band, especially with a larger signal amplitude of 100 Hz integer times. At heavy load, due to the winding amperage, the new winding vibration will be superimposed with the core vibration, after non-linear propagation thus appearing high harmonic vibration components, so that the high-frequency vibration harmonic components increase significantly at heavy load.

• Analysis of vibration signals in transformers when harmonic currents are flowing

The vibration signal of the transformer when harmonic currents are flowing is shown in Figure 3a. The nonlinear load is what causes the harmonic current. The magnetostrictive properties of a transformer will alter when its current contains harmonic components, which will also have an impact on the vibration properties. The vibration signal’s inter harmonic components now considerably rise.

• Vibration signal analysis in transformers with three-phase unbalanced

Vibration signal analysis when the transformer flows through a three-phase unbalanced current as shown in Figure 3b. When the three-phase current is unbalanced, the current flowing through the three-phase winding is inconsistent, resulting in uneven forces on the three-phase winding. According to the ampere force Formula (1), the vibration characteristics will change, the vibration signal under the three-phase unbalanced condition appears inter harmonic, and the amplitude of each frequency band has increased.

3. Clustering Based on Power Quality

From the above analysis, it is clear that there is a causal relationship between transformer electrical quantities and vibration characteristics. We can perform unsupervised learning-clustering [26] on vibration characteristics based on power quality, directly train models based on actual working condition data, and solve current problems of insufficient number of samples in the fault sample data training model to realize a transformer fault early warning model with self-adaptive and self-learning capabilities. In the actual operation of transformers, we usually have no prior knowledge of the label information of various electrical quantities and the high dimensional of data set. Therefore, this paper introduces an unsupervised learning hierarchical clustering [27] algorithm for feature extraction of the data sets for principal component analysis, which does not need a pre-set variety of clusters and incorporates a clear hierarchical data structure. It can also be used as a common method for detecting data anomalies, which has been widely utilized in the field of transformer fault early warning. We apply the implementation of an automatic clustering of vibration characteristics based on the power quality.

3.1. Inter Class Distance Metric

For the distance metric between any two classes [28], the following four methods are widely used.

• Single Linkage [29]: The shortest distance of all data points in 2 clusters is used to represent the distance between the 2 classes.

$${{\displaystyle d}}_{\min }({{\displaystyle c}}_i,{{\displaystyle c}}_j)=\underset{{{\displaystyle x}}_i\in {{\displaystyle c}}_j,{{\displaystyle x}}_{ji}\in {{\displaystyle c}}_{ji}}{{\displaystyle \min }}dis\mathrm{tance}({{\displaystyle x}}_i,{{\displaystyle x}}_j)$$

(2)

2.

Complete Linkage [30]: The longest distance of all data points in 2 clusters is used to represent the distance between the 2 classes.

$${{\displaystyle d}}_{\max }({{\displaystyle c}}_i,{{\displaystyle c}}_j)=\underset{{{\displaystyle x}}_i\in {{\displaystyle c}}_j,{{\displaystyle x}}_{ji}\in {{\displaystyle c}}_{ji}}{{\displaystyle \min }}dis\mathrm{tance}({{\displaystyle x}}_i,{{\displaystyle x}}_j)$$

(3)

3.

Average Linkage: The average distance between all data points in 2 clusters is used to represent the distance between the 2 classes.

$${{\displaystyle d}}_{avg}({{\displaystyle c}}_i,{{\displaystyle c}}_j)=\frac{1}{\left|{{\displaystyle c}}_i\right|{{\displaystyle c}}_{ji}|}{\displaystyle \sum }_{{{\displaystyle x}}_i\in {{\displaystyle c}}_i}{\displaystyle \sum }_{{{\displaystyle x}}_{ji}\in {{\displaystyle c}}_{ji}}dis\mathrm{tance}({{\displaystyle x}}_i,{{\displaystyle x}}_j)$$

(4)

4.

Ward Linkage [31]: The distance between 2 classes is represented by the sum of the squares of the deviations between all data points in the 2 clusters.

$$E={\displaystyle \sum }_{i=1}^k{\displaystyle \sum }_{x\in {{\displaystyle c}}_i}{{\displaystyle \left|\right|x-{{\displaystyle u}}_i\left|\right|}}_2^2$$

(5)

The agglomerative hierarchical clustering methodology introduced in this paper contains a direct impact on the effectiveness of the cluster, reckoning on the selection of the inter-class distance live. By introducing the Elbow method of SSE [32] metrics for cluster analysis, the best variety of clusters and distance metrics were picked. As shown in Figure 4a,b, the Elbow method has the best silhouette coefficient for the A–C ward measurement method at the inflection purpose of the curve because of the optimum range of clusters for four categories. Therefore, in this experiment, A–C ward connection method is selected as the distance measurement of agglomerative hierarchical clustering.

3.2. Agglomerative Hierarchical Clustering

The data on the vibration characteristics of the various electrical quantities of transformers are used as input for the agglomerative hierarchical clustering, the optimal cluster number and ward’s linkage method are used to conduct row clustering according to the principle of distance similarity, and the clustering cluster categories of different electrical quantities are obtained [33].

From the clustering results in Figure 5, it can be seen that automatic clustering of vibration characteristics based on different electrical quantities of the transformer can be achieved by agglomerative hierarchical clustering, which reflects the real operating conditions of the transformer and validates the above analysis. The transformer vibration characteristics data in this experiment belongs to high-dimensional data, and the clustering effects corresponding to different dimensions are different. Therefore, it is necessary to analyze different dimensions under the same number of clusters.

3.3. Comparison of Different Dimensions

To realize a clustered analysis of the various dimensions of transformers vibration characteristics involves the introduction of principal meta-analysis [34], i.e., reducing the dimension of data, which can remove the influence of some noises. However, some vital data might be lost, though, given the correlation that usually exists within the actual information itself. It can reduce the loss of information as much as possible while reducing the dimension, so as to achieve the best clustering effect.

From the comparison of the clustering evaluation in Figure 6, it can be seen that when the same cluster number is four categories, the silhouette coefficient value of relatively low-dimensional data is high and produces the best clustering effect. Thus, the choice of 8-dimensional data for clustering in this paper has higher adaptability.

4. Decision Tree Modeling Based on Clustering

4.1. Data Pre-Processing

Based on the above agglomerative hierarchical clustering, the clustering results of different power quality conditions of transformers are used as the labels of this experimental transformer operating conditions’ data sets, and the continuous problem of continuous transformer vibration spectrum attribute values are discretely divided by introducing the supervised learning-ID3 decision tree algorithm [35,36]. The spectrum data set was divided into “large”, “medium” and “small” attributes and coded into three attributes, i.e., 0: “medium “, 1: “large”, 2: “small”, and the individual spectrum was divided as shown in

Table 1. Spectrum attribute data table.

Number	50 Hz	100 Hz	150 Hz	200 Hz	250 Hz	300 Hz	350 Hz	400 Hz	Cluster
0	large	small	large	Small	medium	medium	small	large	1
1	large	small	large	Small	medium	medium	small	large	1
2	medium	medium	large	Small	small	medium	medium	small	1
…	…	…	…	…	…	…	…	…	…
437	large	small	large	Medium	large	medium	medium	medium	3
438	large	small	large	Medium	large	medium	medium	medium	3
439	large	small	medium	Medium	large	medium	medium	medium	3

.

4.2. Model Calculations

The information gain is used as a metric for the classification criteria in the ID3 algorithm, and the attribute with the greatest information gain is selected as a node division.

• Information entropy

Assume that there are n categories of samples in the current set D, and the proportion of the k category is $p_k$ (k = 1,2,…, n), then the information entropy of D is defined as:

$$Ent(D)=-{\displaystyle \sum }_{k=1}^{\left|n\right|}{{\displaystyle p}}_k{{\displaystyle \log }}_2^{{{\displaystyle p}}_k}$$

(6)

where the smaller the value of Ent(D), the higher the purity of D.

• Information gain

The information gain is predicated on information entropy. Suppose there are double values for the discrete attribute ‘a’, if attribute AN is used to divide the data, m branch nodes are going to be generated. Where the branch node contains all the samples in D that take the value of attribute ‘a’, i.e., the sample set is $D_i$. The larger the number of samples, the greater the influence of the branch node. Therefore, the information gain obtained by dividing the sample D with attribute a can be calculated as follows:

$$Gain(D,a)=Ent(D)-{\displaystyle \sum }_{i=1}^m\frac{\left|{{\displaystyle D}}_i\right|}{\left|D\right|}Ent({{\displaystyle D}}_i)$$

(7)

In Equation (7), the number of samples contained in different branch nodes varies, and the branch nodes are given weights (denotes the number of samples contained in D, respectively).

In general, a larger information gain implies a larger purity gain obtained by using attribute a for segmentation.

4.3. Early Warning Model Analysis

The cluster numbers for the different electrical quantities of the transformer working conditions were established based on the information provided above. Constructing decision trees based on analyzing the correlations between branch qualities and categories. Aiming at the frequent occurrence of abnormal events in transformer operation, along with the reasoning of decision tree and clustering spectrum heat map, the ID3 decision tree is used to deduce the relationship between vibration anomalies and faults as well as the correlation between anomalous characteristics and fault types. Figure 7 illustrates the specific process for the construction of a transformer fault early warning model and reasonable prediction of transformer fault types.

Mechanical faults are one of the more frequent transformer defects, and they require attention during transformer operation and maintenance. This paper performs the screw loosening fault experiment based on the actual operating conditions data and performs the following analysis in order to verify the validity of the fault early warning method in this paper. If a mechanical fault occurs in a transformer, it can cause the vibration signal to highlight the strong non-linear characteristics and the high vibration component in the frequency spectrum.

The specific analysis of the early warning model is as follows:

• The quick Fourier rework (FFT) is used to extract the particular operating conditions of the transformer, i.e., harmonics, light load, heavy load and three-phase unbalanced, with four electrical quantities equivalent to the vibration characteristics 50–2400 Hz continuous 440 information, as a sample set for data processing of transformer fault early warning model.
• The agglomerative hierarchical clustering algorithm is used to achieve automatic clustering of vibration features based on different electrical quantities of the transformer, with the optimal number of clusters determined by the Elbow method and the optimal dimension of clustering determined by the silhouette coefficient,
• Obtain the clustering categories based on agglomerative hierarchical clustering, output as a transformer sample data set, and a supervised learning decision tree is used to build an early warning model.
• The initial clustering center is calculated according to the maximum-minimum distance algorithm [37]. Each vibration cluster’s distance is then calculated using the cluster center when the transformer fault happens, and select the working condition with the least distance, i.e., the abnormality—is chosen.

5. Case Verification

5.1. Example Analysis

Based on the above analysis, it can be seen that agglomerative hierarchical clustering can realize automatic clustering of vibration characteristics of different electrical quantities of transformers. However, it is difficult to analyze the vibration spectrum information and spot the vibration spectrum info of various electrical quantities. Hence, the establishment based on decision tree reasoning is conducted for the transformer early warning model. The inputs to the model information for harmonics, light load, heavy load and three-phase unbalanced throughout actual operating conditions. The outputs are the vibration clusters corresponding to the different electrical quantities, namely the electrical quantity category. Where cluster one is harmonic, cluster two is light load, cluster three is three-phase unbalance and cluster four is heavy load. Based on the decision tree, we can identify the spectrum characteristic information that leads to the division of vibration clusters. The frequency information of vibration cluster can be analyzed with a clustering spectrum heat map, as shown in the Figure 8 and Figure 9.

Based on the decision tree and clustering spectrum heat map, it can be seen that the 150 Hz and 400 Hz vibration signal information gain of the light load is larger and is firstly divided at the root node of the vibration spectrum decision tree. The three-phase unbalanced in each phase vibration spectrum appears 50 Hz, 350 Hz, and the spectral components of equal odd harmonic are the result of harmonic intrusion generated by the zero-sequence current when the system operates asymmetrically. When the transformer flows through harmonic currents, the vibration characteristics change significantly, mainly as a result of magnetostriction caused by 100 Hz and 400 Hz vibration. The harmonic amplitude is significantly amplified, while the amplitude of the 350 Hz vibration signal is lower. However, there is also a certain 50 Hz vibration component. The harmonics can therefore be distinguished from the three-phase unbalanced at the 350 Hz, 50 Hz or 500 Hz, 300 Hz, and 200 Hz leaf nodes. Whereas the 100 Hz vibration component of heavy loads increases, there is also a certain 50 Hz vibration component. The difference in amplitude between the 50 Hz vibration signal and that in the three-phase unbalanced is large, so that heavy loads can be distinguished from the three-phase unbalanced at the 50 Hz or 100 Hz lobe nodes.

5.2. Transformer Fault Analysis

Based on the above transformer fault warning model, according to the clustering spectrum heat map, different types of spectrum amplitudes have significant differences, which can be inferred that the transformer has abnormal vibration and corresponding electrical conditions. Based on an equivalent electrical condition, it is found that the reasoning results of the decision tree has changed, and it can be inferred that the transformer has abnormal vibration. Therefore, when the transformer fault type is reasonably speculated and the transformer fault early warning analysis is realized, the accuracy of early warning will be greatly improved. When a fault happens within an actual operation of transformer, the corresponding decision tree reasoning and clustering spectrum heat map shown in Figure 10 and Figure 11, the following analysis is made:

It can be seen from Figure 11 that the 400 Hz vibration amplitude of Cluster 1, 100 Hz vibration amplitude of Cluster 2 and Cluster 4, and 50 Hz and 400 Hz vibration amplitude of Cluster 3 are large, while the amplitude of other frequency spectrums is relatively small. When the transformer fault happens, the amplitude at 150 Hz, 200 Hz, 300 Hz, 350 Hz, 400 Hz, and 450 Hz of Cluster 2 will increase considerably, the spectrum amplitudes under other working conditions are basically unchanged. Compared with the normal spectrum, abnormal vibration occurs at this time.

The initial cluster centers under normal conditions are: [0, 413, 197, 81, 51], when the transformer fault happens, the initial cluster centers are: [0, 211], and the distribution characteristics of the clusters do not change. After calculating the distance between each vibration cluster and the cluster center is calculated, it is found that the distance between the cluster center at light load and fault is the smallest, indicating that the light load operation is abnormal at this time.

As it can be seen from Figure 11, the vibration characteristic information causing light load division is 150 Hz and 400 Hz. Once the transformer fault happens, the reasoning results modification underneath an equivalent 150 Hz and 400 Hz branches and it can be inferred that the transformer has abnormal vibration.

From the above three aspects, it can be seen that the transformer has abnormal vibration during light load operation, and high frequency vibration components appear in the frequency spectrum. Therefore, it can be inferred that this abnormal vibration is likely caused by mechanical fault under light load. For example, if some parts are loose (such as the core threading screw of the iron core is not tight), or the winding is deformed, the transformer should be stopped for inspection.

6. Conclusions

In this paper, the transformer fault early warning method based on the combination of agglomerative hierarchical clustering and decision tree to analyze the transformer vibration signal is proposed. Based on the experimental verification, the conclusions are as follows, the traditional transformer fault early warning method struggles to solve the problem of poor generality of early warning.

• An agglomerative hierarchical clustering has been introduced to demonstrate that vibration characteristics associated with various electrical quantities of the transformer can be automatically clustered to reflect the transformer’s actual operating conditions.
• The method in this paper is adaptive to the sample data and verifies that there is indeed a causal relationship between transformer electrical quantities and vibration characteristics, allowing inference about transformer vibration characteristics, reasonably predict of fault types, and explain the vibration mechanism of faults, which are not available within the traditional method of transformer fault early warning.

This experiment is based on the actual operation condition data on site, without fault sample data, combined with the agglomerative hierarchical clustering and decision tree method to establish an early warning model. Using the decision tree for analysis, reasoning and comparison, reasonably predicts the fault type, timely eliminates the potential safety hazards in the actual operation process of the transformer and improves the stability of the transformer operation. Compared with the fault early warning method using fault data, the early warning result of this method has good universality.