A Method of Winding Fault Classification in Transformer Based on Moving Window Calculation and Support Vector Machine

Abstract

Winding fault is one of the most common types of transformer faults. The frequency response method is a common diagnosis method for winding fault detection. In order to improve the feature extraction ability of the frequency response curve before and after the winding fault, this paper proposes a winding fault feature extraction method based on the moving window algorithm to improve the Euclidean distance and correlation coefficient and uses a support vector machine to diagnose winding fault. “Moving window meter algorithm” refers to the fixed moving window width and window moving interval, scanning the entire frequency response curve from the initial point to the end point of the frequency response curve, using the correlation coefficient (CC) and Euclidean distance (ED) to calculate the mathematical index of each window. The mathematical index of each window is used as the characteristic quantity of fault type classification. Finally, the grid search algorithm is used to optimize the support vector machine to classify and identify the type of winding fault. At the same time, the standard support vector machine s(SVM) and back propagation neural network algorithm (BPNN) are compared with the support vector machine optimized by the grid search method to diagnose the fault type. The research shows that the improved correlation coefficient and Euclidean distance using the moving window algorithm are more sensitive to winding faults than the traditional calculation methods. The combination of the two calculation methods makes up for the shortcomings of their respective methods. The fault features obtained meet the requirements of the support vector machine for fault diagnosis, and the grid search method-optimized support vector machine classification algorithm has a good classification and recognition effect on the identification of fault types. The effectiveness and superiority of this method are further illustrated.

1. Introduction

As an important equipment for voltage conversion and power transmission in the power system, the safe and stable operation of power transformers is of vital importance for the power supply of the grid [1,2]. The power system is generally operated symmetrically in three phases in which the transformer, as a key piece of equipment in the power system along with its operation performance, is the key to the stable and symmetrical operation of the power system, so it therefore needs accurate fault diagnosis. Due to the surge in demand for electrical energy in social life, the capacity of the power system is expanding, and the level of short-circuit current in the whole system is rising, thus making the operating environment of power equipment, such as transformers, more complex [3]. According to the statistics of each power grid, it is known that among the types of transformer faults, winding faults account for 30% of the total transformer faults [4]. Transformer winding deformation is mainly caused by short-circuit current and mechanical shock during installation, where axial and radial forces generated by short-circuit current cause transformer winding displacement, and distortion and other deformations are the most common faults in the winding [5]. Most of the transformer winding failures are due to minor faults that cannot be detected and overhauled in time, which cause transformer winding failures due to the cumulative effect and eventually bring huge losses to the power grid. In order to carry out effective prevention of winding faults, it is essential to carry out winding detection studies.

At present, many scholars have carried out research on the diagnosis of winding faults. The frequency response analysis (FRA) method [6] is widely used in the test to detect whether transformer winding is deformed because of its advantages of better repeatability and higher sensitivity in the actual process.

In transformer winding at input source frequencies above 1 kHz, ignoring the role of the core, the winding can be equated to a circuit model consisting of parameters, such as capacitance, inductance, and resistance, etc. Since changes in the winding structure size and position are associated with the parameters of the equivalent circuit model, and when the winding undergoes deformation, it causes changes in parameters, such as inductance and capacitance, in the equivalent circuit model, resulting in changes in the resonance point of the transfer function. Therefore, the change in the characteristics of the frequency response curve can reflect the winding state change [7,8]. Transformer winding fault diagnosis methods generally use the frequency response curves of the fault and normal state for comparison, and the characteristics reflected by the response curves are used as the basis for winding fault diagnosis. Since the frequency response curves of the same type of faults will show the same or similar characteristic patterns, the transformer winding faults can be diagnosed by extracting the fault characteristics from the fault and standard frequency response curves [9,10]. The current industry practice is to use the relevant IEEE standards in North America or IEC standards in most other countries. However, in the Chinese industry, the correlation coefficient method is usually used for the fault diagnosis of windings according to DL/T 911-2016 “frequency response analysis of power transformer winding deformation” [11], which divides the frequency response frequency range into three frequency bands, which are the low-frequency band (1 kHz to 100 kHz), the medium-frequency band (100 kHz to 600 kHz), and the high-frequency band (600 kHz to 1 MHz), and the fault is diagnosed by calculating the correlation coefficient values in each of the three frequency bands. Because the frequency response curve amplitude after winding fault has the same difference within the roughly divided frequency band interval, the extracted characteristic quantities are not enough to reflect the variation pattern between different fault types and to make an effective diagnosis of transformer winding fault types [12,13,14].

In this paper, in order to improve and optimize the shortcomings of the correlation coefficient feature extraction method in the three frequency bands and facilitate the extraction of more effective winding fault classification and identification features, a “moving window meter algorithm” is proposed to improve the correlation coefficient and Euclidean distance methods, and Euclidean distance is used to make up for the shortcomings of the correlation coefficient calculation method. The correlation coefficient and Euclidean distance calculated by the moving window calculation method are used as the characteristic quantities of winding fault, and then the grid search method is used to optimize the support vector machine to classify and identify the winding fault types. At the same time, the two classification algorithms are compared with their fault diagnosis rates to further highlight the effect of classification and identification.

2. Moving Window Calculation Method

The “moving window calculation method” is a method used to extract the characteristics of the frequency response curve after a winding fault by using the calculated correlation coefficient and Euclidean distance as the characteristic quantity for winding fault type diagnosis. The basic principle of this method is that the frequency response curve is composed of several data points measured in the winding operation state, and each frequency point has its corresponding frequency response amplitude, and the amplitude change of the frequency point is caused by the winding state change. Therefore, the amount of fixed frequency response amplitude movement is used, that is, the width of the fixed “moving window”. This window sweeps from the starting amplitude point of the frequency response curve to the ending amplitude point at a fixed moving interval, thus sweeping through the entire detection range of frequency response amplitude points. In order to ensure that the moving window can sweep through all amplitude points on the frequency response curve, the width of the window should be larger than the window moving interval. Within each fixed-width window, a mathematical indicator value can be calculated based on the number of frequency response amplitude points within the window, and a window center frequency point can also be calculated, and each mathematical indicator value can be used as a characteristic quantity of the winding fault type. The basic principle of this method is shown in Figure 1.

In this paper, we propose to improve the correlation coefficient and Euclidean distance by using the moving window calculation method, and the mathematical index calculated from each window is used as the characteristic value to diagnose the fault type. The formulas of the correlation coefficient and Euclidean distance for the moving window calculation method are shown in Equations (1) and (4):

$$MW-CC\left(i\right)=\frac{{\displaystyle \sum _{i=1,j=1}^{NF(i),L}\left(\left(X_j-{\overline{X}}_{w_i}\right)\left(Y_j-{\overline{Y}}_{w_i}\right)\right)}}{\sqrt{{\displaystyle \sum _{i=1,j=1}^{NF(i),L}{\left(X_j-{\overline{X}}_{w_i}\right)}^2{\displaystyle \sum _{i=1,j=1}^{NF(i),L}{\left(Y_j-{\overline{Y}}_{w_i}\right)}^2}}}}$$

(1)

$${\overline{X}}_{w_i}=\frac{1}{n}{\sum }_{j=1}^{L}Xj$$

(2)

$${\overline{Y}}_{w_i}=\frac{1}{n}{\sum }_{j=1}^L{Y}_j$$

(3)

$$\begin{gathered} MW-ED\left(i\right)=\parallel X-Y\parallel =\sqrt{{\left(X-Y\right)}^T\left(X-Y\right)} \\ =\sqrt{{\sum }_{j=1}^L\left(X_j-Y_j\right)} \end{gathered}$$

(4)

where $MW-CC$ and $MW-ED$ are the CC and ED of the moving window calculation method, respectively; $X$ is the frequency response curve of the winding in the normal state; $Y$ is the frequency response curve of the winding in the operating state; ${\overline{X}}_{w_i}$ and ${\overline{Y}}_{w_i}$ are the average values of the frequency response amplitude in the $i\text{-}\mathrm{th}$ moving window.

The number of eigenvolumes calculated over the entire frequency range in Figure 1, and the equations for the center frequency corresponding to each window are shown in Equations (5) and (6), respectively

$$NF=\left|\frac{\left(D{B}_{\mathrm{end}}-D{B}_{\mathrm{start}}\right)-L}{L_{\mathrm{step}}}\right|+1$$

(5)

$$f_m\left(i\right)=\left|\frac{f_1^{\left(i\right)}+\dots +f_L^{\left(i\right)}}{L}\right|i=1,2,\dots ,NF$$

(6)

where $L$ is the width of the moving window; $NF$ is the number of eigenvolumes; $L_{\mathrm{step}}$ is the window moving spacing; $D{B}_{\mathrm{start}}$ is the initial frequency point amplitude; $D{B}_{\mathrm{end}}$ is the ending frequency point amplitude; $f_m$ is the frequency corresponding to the center point of the window; $f_L^{\left(i\right)}$ is the $L\text{-}\mathrm{th}$ frequency point of the $i\text{-}\mathrm{th}$ window.

The size of the width of the moving window does not affect the numerical calculation. The smaller the width of the window selection, the more obvious the value of the difference in the reflected frequency response curve obtained will be, but it is susceptible to noise interference in the application. The larger the width of the window selected, the smaller the value of the window calculated, making the difference in the reflected frequency response curve smaller. Therefore, the application of the “moving window calculation method” to calculate the correlation coefficient and Euclidean distance, need to reflect the resonance point changes as much as possible, so the window to move the distance less than the distance between adjacent resonance points.

3. Transformer Winding Fault Simulation Analysis

3.1. Winding Fault Simulation Settings

In order to further illustrate that the moving window calculation method of the correlation coefficient and Euclidean distance methods to deal with the frequency response curve method before and after the winding fault can better extract the difference of reflecting the frequency response curve and that the extracted features can effectively diagnose the fault type, this paper carries out the simulation analysis of the equivalent circuit model of transformer winding and establishes the simulation equivalent circuit model of winding as shown in Figure 2, where $L_i$ denotes the self-inductance of the $i\text{-}\mathrm{th}$ pie winding; $K_i$ is the equivalent longitudinal capacitance of the $i\text{-}\mathrm{th}$ pie winding; $C_i$ denotes the capacitance of the $i\text{-}\mathrm{th}$ pie winding to ground; $R_1$ and $R_2$ denote the equivalent resistance of the measurement line; $U_{in}$ is the input excitation voltage source; $V_1$ and $V_2$ are the measured first and end voltage signals, respectively. The structure of a simulated transformer is a single-phase continuous winding. The winding is composed of 7 cakes. The power parameters [15] of the transformer winding are simulated by Maxwell software. The equivalent circuit parameters of the calculated winding are shown in

Table 1. Transformer winding equivalent circuit parameters.

Parameter	Capacitance to Ground (pF)	Equivalent Longitudinal Capacitance (pF)	Inductance (mH)
Value	1024	21.9	36.9

. The main parameters of the transformer and the basic parameters of the winding structure are shown in

Table 2. The main parameters of the single-phase transformer.

Parameter	Value
Rated capacity/kVA	24,000
Rated voltage at HV side/kV	$550/\sqrt{3}$
Rated voltage at LV side/kV	20
Rated current at high and low voltage sides/A	755.8/12,000
Turns at HV and LV sides	508/32

and

Table 3. Physical dimensions of the investigated transformer winding.

Parameter	Value/mm	Parameter	Value/mm
Conductor width	6.95	Coil height	560
Conductor height	11.2	Inner diameter of winding	240
Average turn length	1884	Outer diameter of winding	360
Insulation paper thickness	2.95	Pad width	40
Oil channel height	8	Thickness of space bar	24

, respectively.

In the simulation using PSpice software, a sweep signal is input at the first end of the winding with $U_{in}$ frequency range of 1 kHz~1 MHz and 1021 sweep points, and the sweep voltage signal at the first end of the winding and the voltage signal at the response end are measured by a voltage measurement probe to obtain the frequency response characteristic curve of the winding.

Since the equivalent circuit model of transformer winding is directly related to the size and location of the winding inside the transformer case, when the winding is deformed, the equivalent parameters in the circuit model will also change, and the relationship between different fault types and power parameters is reflected in the literature [16], according to which the power parameters of the circuit model are changed to simulate different winding fault types. In this paper, three winding fault types: radial deformation (RD), short-circuit turns (SC), and axial deformation (AD) are mainly simulated, and the location of the fault is set in the 1st, 3rd, 4th, 6th, and 7th cakes. The depth of radial deformation convexity is 18 mm, which is about 5% of the average radius of the winding, and the degree of deformation of each cake is determined by the number of radial deformations; axial deformation is determined by the height of each cake convexity in the order of 0.4 mm, 0.8 mm, 1.2 mm, and 1.6 mm. The axial deformation is determined by the number of radial deformations; the axial deformation is achieved by the height of each cake bump of 0.4 mm, 0.8 mm, 1.2 mm, 1.6 mm, 2 mm, and 2.4 mm; each cake has 20 turns, and the degree of short-circuit deformation between turns is achieved by each cake short circuit of 1 turn, 2 turns, 3 turns, 4 turns, and 5 turns. Therefore, the degree of failure is 5% to 25% for each category. By changing the winding fault location and fault degree, 25 sets of samples can be obtained for each fault type, and a total of 75 sets of simulation samples are obtained.

3.2. Winding Fault Simulation Analysis

The window width of the moving window is set to 40, and the moving interval is 3, so that the number of characteristic parameters calculated for each mathematical index is 328. Since the simulation sampling is nonequal frequency interval sampling, it is not possible to use the equal interval frequency shift, and the difference between the frequency response curve of fault and normal winding is reflected in the amplitude of the frequency point, so this paper adopts the fixed moving window width (i.e., the number of amplitude values) and the window shift interval (i.e., the number of amplitude shift intervals) and then extracts the characteristic values of different fault types by calculating the correlation coefficient and Euclidean distance, which is a method more applicable in practical applications.

The frequency response curves of each fault type at different degrees are obtained by simulation, and the control curve consisting of the window eigenvalue and the center frequency point obtained by the moving window calculation method of the correlation coefficient is located in the lower part of the frequency response curve, as shown in Figure 3b,c; the control curve consisting of the window eigenvalue and the center frequency point obtained by the moving window calculation method of Euclidean distance is located in the upper part of the frequency response curve, as shown in Figure 4b,c.

From Figure 3a, it can be seen that the correlation coefficients of radial deformation faults at different degrees in the low-, middle-, and high-frequency bands are all greater than 0.994, which indicates that the winding is in a normal condition according to the winding fault judgment criteria, which is completely inconsistent with the actual situation and further indicates that the correlation coefficients in the three frequency bands cannot make an effective diagnosis of winding faults. From Figure 3b, it can be seen that the improved correlation coefficient using the moving window is able to drop to 0.52 at 100 kHz and above, and at greater than 1 kHz, the correlation coefficient is greater than 0.9. This further indicates that the improved correlation coefficient of the “moving window calculation method” is more reflective of the transformer winding fault than the traditional correlation coefficient method. This further indicates that the improved correlation coefficient of the “moving window calculation method” can reflect the transformer winding fault better than the traditional correlation coefficient method, which is also better to make quantitative judgment about the faulty winding. However, the correlation coefficient is only sensitive to the frequency change of the resonance point, but not sensitive enough to the amplitude change of the resonance point and cannot distinguish two frequency response curves with similar shapes but different sizes, as can be seen from the high-frequency part of Figure 3b and Figure 4b. So, in order to make up for this shortcoming, the Euclidean distance improved by the moving window calculation method is introduced, and the Euclidean distance to the amplitude change of the resonance point can be intuitively expressed by Figure 4a. As can be seen, three frequency bands under the Euclidean distance can reflect the degree of winding failure but cannot make a quantitative standard judgment of the fault and cannot effectively reflect the characteristics of the winding fault type. Figure 4b shows that using the moving window calculation of the Euclidean distance obtained by the eigenvalue can more comprehensively reflect the frequency response curve in the amplitude change and can be different in size but similar to the curve of amplitude, as can be seen in the high-frequency part of Figure 4b.

When the same degree of axial, radial, and interturn short-circuit faults occur at the same location, the improved Euclidean distance and correlation coefficients using the moving window calculation method are shown in Figure 3c and FIgure 4c, and it can be seen from the figure that when the most serious axial, radial, and interturn short-circuit faults occur in the winding, the difference among the three fault characteristics of the CC pairs calculated by the moving window is small, and the difference between the interturn short circuit and the other two faults is obvious. The distribution of the three ED faults calculated by the moving window is obviously different. Between 10 kHz and 100 kHz, there is a certain difference between the radial deformation fault and the other two. Between 100 kHz and 1 MHz, there is a great difference between the interturn short circuit and the radial and axial faults. The effective features among the three faults are extracted by using the combination of CC and ED, which is also convenient for the algorithm to classify and identify the faults.

4. SVM-Based Winding Fault Classification Results

4.1. Classification Principle of Support Vector Machine

The support vector machine (SVM) [17,18,19,20,21] is a machine learning algorithm proposed by Vapnik et al. Compared with other algorithms, the SVM can obtain better classification results in the case of limited sample data. For linearly divisible samples, the SVM mainly searches for the optimal hyperplane in the space; in the case of linearly indivisible samples, the low-dimensional, indivisible samples need to be mapped to the high-dimensional space by the kernel function, and the optimal hyperplane is selected in the high-dimensional space to classify the samples.

In general, the samples are linearly indistinguishable, so the optimal hyperplane needs to be sought by mapping the samples to a high-dimensional divisible space using kernel functions. From the literature [20], it is known that the use of Gaussian radial basis kernel function is better than other kernel functions for classification. The expression form of the Gaussian kernel function is shown in Equation (7).

$$f_m\left(i\right)=\left|\frac{f_1^{\left(i\right)}+\dots +f_L^{\left(i\right)}}{L}\right|i=1,2,\dots ,NF$$

(7)

On this basis, linear indistinguishable samples can be classified, and the classification decision function is expressed as

$$f\left(x_i\right)=sgn\left({\sum }_{i=1}^m{\alpha }_i{y}_{i}K\left(x_i,x_j\right)+b\right)$$

(8)

The penalty coefficient $C$ and kernel function $g$ are very important parameters in the SVM, where $C$ mainly plays a role in influencing the distance between the support vector and the decision surface, which further influences the differentiation of the data, while the kernel function $g$ mainly maps the nonlinear data from the low-dimensional space to the high-dimensional space, and the size of the dimension also affects the result of the sample training, which further influences the classification result of the classification function. The choice of penalty coefficient $C$ and kernel function $g$ affects the classification effect of the SVM, so it is necessary to choose the optimal parameters, and the parameter search method used in this paper is the grid search method. The method uses a grid search method to divide the $(C,g)$ to be searched into different searched intervals according to certain steps, selects $(C,g)$ in different intervals, and then substitutes the determined parameters into the kernel function for calculation, determines whether the output value is the optimal value, and repeats the above operation until the optimal parameter $(C,g)$ is found. The flowchart of winding fault classification recognition by the grid search method-optimized SVM is shown in Figure 5.

4.2. Support Vector Machine Classification Results

In order to verify the accuracy of the SVM for transformer winding fault diagnosis, this paper uses the obtained simulation data and cross-validation method to verify.

According to the principle of cross-validation, the sample data need to be grouped, with one part as the test sample, and the other part as the validation sample. In this paper, three types of faults: axial deformation, radial deformation, and interturn short circuit are set up, and each fault type consists of 656 eigenvalues obtained from the correlation coefficient and Euclidean distance calculated by the improved moving window calculation method, with a total of 25 groups of samples. Fifteen groups of data from each fault type are selected as training samples, and another 10 groups of data are used as validation samples, and then the support vector machine is used to classify the fault types before. The three fault types are labeled as 1, 2, and 3 for radial deformation, axial deformation, and turn-to-turn short circuit, respectively, and the training samples are trained with the optimized support vector machine classification method using the grid search method to obtain the discriminant function for optimal classification. When the optimal parameters (〖C,g〗) of the support vector machine were obtained by using the eigenvalues calculated from the input correlation coefficients and Euclidean distance, and the optimal transformer winding fault classification model was established using the grid search method, and the test samples were diagnosed, the SVM classification results are shown in Figure 6. From the fault type classification results in Figure 6, it can be seen that the fault type comprehensive recognition rate reaches 96.67%; in particular, two kinds of faults, radial deformation and axial deformation, can be completely recognized. Among them, the optimal parameter search results are shown in Figure 7.

In order to better compare the effects of selecting different feature values on the fault diagnosis results and to illustrate the reasonableness of selecting the calculated values of the correlation coefficient and Euclidean distance as feature values, the same training set and validation set were used, and the three categories of correlation coefficient, Euclidean distance, and the combination of both were used as feature inputs, and the SVM optimized by the grid search method was used to build the diagnosis model.

It can be seen from Figure 8 that when only the correlation coefficient is used as the characteristic input, the fault diagnosis rate is 73.33%; when only the Euclidean distance is used as the feature input, the fault diagnosis rate is 86.67%, and the fault diagnosis rate using Euclidean distance as the feature input is higher, indicating that the diagnostic model obtained as the feature input has higher accuracy, mainly because the correlation coefficient is not sensitive to the amplitude change of harmonic points in the frequency response curve and cannot fully express the characteristics of fault types. The accuracy of fault diagnosis using the correlation coefficient and Euclidean distance as feature input is 96.67%, and the fault diagnosis rate is higher when the combination of the two is used as the feature input, which further shows that the combination of the two can better make up for the shortcomings of their traditional methods and better reflect the characteristics of fault types. Extracting Euclidean distance and correlation coefficient feature samples based on the moving window algorithm can well meet the requirements of the support vector machine for winding fault type recognition. The optimization of the grid search method also better improves the fault recognition rate of the SVM.

In order to verify the superiority of the fault diagnosis model using the grid search method-optimized SVM, the standard SVM, BPNN (Back Propagation Neural Network), and grid search algorithm-optimized SVM were used as inputs to diagnose the fault types, and multiple iterations were performed to select the optimal diagnosis accuracy as shown in

Table 4. Diagnostic accuracy of different methods.

Classification Methods	Accuracy (%)
SVM	76.67%
BPNN	60%
SVM-GS	96.67%

. As can be seen from the table, the grid search-optimized SVM has a higher fault identification rate than the conventional SVM and BPNN when the combination of Euclidean distance and correlation coefficient calculated by moving windows is used as the input features, further verifying the effectiveness of the method.

5. Conclusions

(1)

This paper proposes a method to extract features based on the moving window calculation method to improve the correlation coefficient and Euclidean distance to provide a new method to deal with the frequency response curve before and after the winding fault. The improved method is more sensitive to the winding fault than the traditional calculation method, while the combination of two mathematical index calculation methods can compensate for the shortcomings of the respective traditional methods, which is also conducive to the extraction of effective fault type features.

(2)

The grid search method is used to optimize the support vector machine to classify and identify winding fault types. Through the comparison of the fault accuracy of three classification algorithms, standard SVM, BPNN, and grid search algorithm-optimized support vector machine, we found that the features extracted by the moving window algorithm meet the requirements of the support vector machine for fault identification, The grid search algorithm-optimized support vector machine has the highest accuracy and the best effect on fault type recognition, which further verifies the effectiveness of the proposed classification algorithm.

(3)

The moving window method mainly used in this paper has a certain novelty, but the commonly used calculation formula is used in the quantitative mathematical indicators. At the same time, there are only three types of fault classification and identification, which have certain limitations. Follow-up research needs to adopt more new mathematical indicators and carry out classification and identification research on a variety of fault types.