Transformer winding mechanical fault diagnosis method based on closing transient acoustic vibration signal

The current conventional transformer winding fault diagnosis method mainly extracts the vibration signal through the time-frequency analysis method, which leads to poor diagnosis due to the lack of analysis of the transformer winding state. In this regard, a transformer winding mechanical fault diagnosis method based on the closing transient acoustic vibration signal is proposed. The closing vibration signals of the transformer in the normal and loose winding states are collected separately, the transformer winding force situation is analysed, and the transformer fault signal characteristics are extracted and combined with a fault classifier to construct a fault diagnosis model. In the experiments, the proposed method is verified for fault identification. The experimental results show that the proposed method has a high correct rate when used to identify different types of transformer faults, and has a more desirable fault diagnosis performance.


Introduction
Transformer electromagnetic force is mainly generated by the internal main magnetic flux and leakage flux with the energized winding.Concentric winding, for instance, is mainly an axisymmetric structure, so the distribution of leakage magnetic field can be decomposed along the axial and spoke direction, and electromagnetic force in the spoke direction and axial together causes the transformer winding cycle vibration.When the transformer is under load, the electromotive force on the winding under the rated load current will not have a large amplitude, so the vibration acceleration obtained by the winding is not very large.Transformer winding mechanical state failure means that under the action of mechanical force or electrodynamic force, the size or position of the winding has irreversible changes, specifically for the winding overall or local size change, body displacement, winding loosening and insulation pad off, etc. [1].The causes of mechanical failure of transformer windings can be summarized into four categories.The first is a variety of short-circuit accidents caused by transformer winding mechanical failure.When a short circuit fault occurs in the operating transformer, the magnitude of the inrush current is much higher than the normal operating rated current of the transformer, which generates a strong electromotive force in the winding.When the winding local mechanical strength cannot withstand the short circuit electromotive force, it will cause transformer winding deformation, insulation off and other mechanical failures, and even cause winding collapse and other larger transformer accidents.The second type of failure is that the winding design is unreasonable in the transformer factory and the defects in the production process lead to winding mechanical failure.The third type of failure is the mechanical failure of the winding caused by resonance.The factory preload force design of transformers makes the winding inherent vibration frequency away from the forced vibration of the electrodynamic force.When the transformer suffers from a short circuit, a strong impact leads to winding compression screw loosening, thus changing the winding inherent vibration frequency.When the inherent vibration frequency and electrodynamic excitation vibration frequency are close to the resonance phenomenon, the transformer vibration increases sharply, internal winding insulation falls off, and the pad is displaced.Mechanical failure, such as transformers continuing to run, will occur more accidents [2].The fourth type of failure is the cumulative effect of the winding resulting in mechanical failure.The transformer internal winding micro-deformation relative winding insulation performance and mechanical properties have been reduced.If the transformer continues to run when encountering a sudden short-circuit fault, under the strong short-circuit electrodynamic effect, winding insulation and mechanical properties will continue to deteriorate, resulting in a vicious cycle.Through in-depth research and repeated exploration of frequency response methods at home and abroad, the frequency response method has been used to test the winding deformation of power transformers.However, the frequency response method has its own shortcomings.For example, the type of winding deformation cannot be determined only through the frequency response function analysis, so the frequency response method in the mechanical state of the transformer winding diagnosis has certain limitations.In this paper, we propose a method to diagnose mechanical faults of transformer windings based on the closing transient acoustic vibration signal, aiming to improve the diagnostic accuracy and propose a corresponding maintenance strategy [3].

Transformer winding force analysis based on closing transient acoustic vibration signal
During normal operation, the transformer operates in the linear section of the magnetization curve, the core flux is not saturated, and the excitation current is very small, less than 10% of the rated current.After the winding is loosened, the high-frequency component of the transient vibration signal at the moment of closing is relatively large [4], taking a single-phase transformer as an example, the expression of the voltage equation at closing is shown below. 1 11 sin( ) where m U is the primary voltage amplitude, α is the voltage phase angle at closing, 1 N is the number of turns of the primary winding, φ is the core flux, 1 r is the primary equivalent resistance, and 1 i is the primary winding current [5].The average inductance of av L during steady-state operation is used to simulate the core excitation inductance of a single-phase transformer, and the above differential equation is solved by substituting the initial remanence of the transformer at the time of ( 2 ) According to Equation (2), when the transformer is closed at no load, the core flux is divided into the steady-state component and the transient component, where the amplitude of the transient component is affected by the closing angle and the remanent magnetism.If a=0, the flux reaches its maximum value after half a cycle of closing, which is much larger than the rated flux of the transformer, and the core is severely saturated, resulting in excitation inrush [6].
When a current flows in the winding, the current in the winding interacts with each other under the influence of leakage inductance to produce electromotive force.The leakage flux is usually decomposed into mutually perpendicular spoke leakage x B and axial leakage y B .According to the equation of Lorentz force, the formula for calculating the electromotive force generated in the transformer winding is as follows.
where J is the current density; B is the leakage density.Radial leakage x B is constant inside the winding and smaller at both ends, generating a radial electromagnetic force F, which is constant in the middle of the winding.The currents flowing through the high and low voltage windings of the transformer are in opposite directions, so the two windings are subject to a radial electromagnetic force that repels each other, with the inner low voltage winding subject to an inward radial pressure and the outer high voltage winding subject to an outward radial tension.x B is zero in the middle of the winding and maximum at both ends, generating an axial electromagnetic force x F is maximum at both ends and in opposite directions, generating a tendency to compress the winding [7].Spoke electromagnetic force to transformer insulation performance is damaged and leads to strong deformation of the winding.Axial electromagnetic force will cause the oil channel between the pad and the line cake loose, and the axial vibration of the line cake will also intensify the loose tendency, and even cause the winding collapse in severe cases.
The winding is subjected to an electrodynamic force proportional to the square of the current, and the fundamental frequency of vibration acceleration is twice the fundamental frequency of the current.The excitation inrush current is large in amplitude and contains a large number of high harmonics.Under its impact, the winding is subjected to a large electrodynamic force and the vibration is intensified and contains high harmonic components, which are transmitted to the surface of the tank [8].After the winding is loose, its ability to transmit vibration is affected, and the winding is loose so that the distribution of leakage magnetic field changes, which in turn changes the force and vibration of the winding.The winding is loose also leads to a reduction in the structural stiffness of the transformer, and the inherent frequency is reduced, which in turn leads to changes in the energy distribution of the vibration signal in different frequency bands.The compression force is crucial to the winding's resistance to short-circuit shocks.In the event of further short-circuit shocks, windings with a loose compression force may suffer serious faults such as short-circuiting and deformation [9].

Transformer vibration signal fault feature extraction
The analysis of the winding vibration characteristics of power transformers shows that when mechanical faults occur in transformers, such as winding deformation, winding turn-to-turn short circuit and winding preload loosening, etc. will cause changes in the winding, core and the whole transformer structure, resulting in changes in its modal parameters such as the intrinsic frequency, and thus the corresponding vibration signals will change accordingly [10].In order to make this change information more intuitive, this paper enables the determination of winding status by extracting the fault characteristics of the vibration signal.
Wavelet analysis is a time one scale signal analysis method.Its basic function is different from the infinite triangular basis function of the Fourier transform.Wavelet analysis becomes a finite length and can decay wavelet basis function.Wavelet analysis not only has adaptability to the signal, but also can achieve good localization characteristics in the time domain of the signal.Effective analysis of non-stationary signals provides a powerful fault diagnosis based on the vibration analysis method [11].
In addition, given the different time delays in the transmission of vibrations to the various measurement points on the tank wall, there will be different phase differences between the vibrations at each measurement point.When a fault occurs, the transmission characteristics of each measurement point will change to varying degrees, and this change will further alter the phase difference between the vibrations at each measurement point.Therefore, in order to investigate the spatial variability of the phase, the vibration waveforms of each measurement point are superimposed in the time domain with the position coordinates as weights to form the vibration centre of gravity trajectory.In this paper, wavelet packet decomposition is used to divide the signal under different frequency domains, extract the moisture value of the transformer vibration signal as a fault feature and provide a fault diagnosis method for power transformers [12].
When a fault occurs inside the transformer structure it can be reflected by a change in the vibration signal for transformer fault diagnosis.This can be shown concretely by the fact that when a transformer winding is loosened or deformed, the energy entropy of each frequency band after its wavelet packet decomposition will change.Therefore, the characteristic vector of the fault can be constructed based on the energy of each frequency band, which can be used as a criterion for analysis and comparison between different signals [13].
The transformer fault diagnosis is achieved by extracting the frequency band energy feature vector of the vibration signal, which is described as follows: (1) The transient vibration signals collected from the tank surface closing in the experiments and simulations are taken and the signals are decomposed by 3-layer wavelet packets.
(2) The signal reconstruction of the sub-band sequence obtained after wavelet packet decomposition is performed to obtain 8 wavelet packet reconstruction signals.
(3) The energy entropy of the eight decomposed reconstructed signals is obtained separately, and the obtained energy entropy is constructed as a feature vector, denoted as T. The specific expression is shown below.
The feature vectors are normalized by the following equation: (5) According to the above method, the signal feature vectors can be extracted and applied to the actual transformer fault diagnosis by comparing the corresponding feature values of different states.However, in order to ensure the validity of the feature vectors and the accuracy of fault diagnosis, it is necessary to monitor the operation of the transformer for a long time and analyze the obtained data, which is one of the problems to be solved in the current vibration analysis method applied to transformer condition monitoring letter.

Winding fault diagnosis model establishment
The identification and diagnosis of transformer winding faults can be regarded as a dichotomous problem, i.e., divided into two categories: "normal" and "fault".Usually, the training samples are prelabeled, and then the classifier is constructed and learned from the training samples.Support vector machines are developed from the optimal partitioning interface under the simplest linear divisibility.The so-called optimal partition line means that not only can the two classes of samples be correctly separated, but also the classification interval should be maximized.In most cases, the sample sets are nonlinearly separable from each other.In this paper, a fault sample type classifier is built to enable the classification and identification of faults to aid fault diagnosis [14].
The kernel function ( , ) is known and the mapping function Φ is obtained from its corresponding semi-positive definite kernel matrix.In this paper, the radial basis function (RBF) is chosen as the kernel function.In addition, ω is the maximum interval hyperplane normal vector, b is the displacement term, and the parameters of the maximum interval hyperplane are found for a given set of labeled samples ( , ) x x with number l.The maximum interval hyperplane normal vector and the displacement term are equivalent to the solution to the following optimization problem:  Based on the above classifier, a sample of power transformer tank wall vibration signal with known winding health is selected, and the parameters of vibration distribution characteristics are calculated for each set of vibration signals, including the horizontal and vertical coordinates of the center of gravity of vibration amplitude, as well as the main axis tilt angle and eccentricity of vibration center trajectory.The four quantization parameters are used as input x to the classifier, and the labels 1 and -1 are used as category markers for transformers belonging to "normal" or "fault".Some of the samples are randomly selected as training samples to calculate the parameters of the maximum interval hyperplane in the classifier.The rest of the samples are used as test samples and are fed into the trained support vector machine for classification and the classification results are compared with the labels to evaluate the effectiveness of the support vector machine classification [15].

Experimental preparation
In order to prove that the diagnostic effect of the transformer winding fault diagnosis method based on the closing transient acoustic vibration signal proposed in this paper is better than the conventional transformer winding fault diagnosis method, after the theoretical part of the design is completed, an experimental session is constructed to test the diagnostic effect of this paper's method.In order to improve the reliability of the experimental results, in addition to the method selected in this paper, two conventional methods were also selected as the experimental control group, and the test results of the three groups were compared, so as to verify the validity of the method in this paper.
The transformer under test is a three-phase control isolation transformer, Model S 13-M-100/10/0.4.The load cabinet and regulator are used to adjust the transformer load and voltage, and the data acquisition of the vibration signal on the surface of the box wall is carried out by the 365A vibration sensor of PCB, and the relevant parameters of the vibration sensor are shown in Table The signal data of each measurement point during normal operation and fault operation are collected and recorded, under different operating conditions such as no-load, short circuit, and load of the transformer.The signal data collected by the vibration sensor is transmitted to the data storage device through the data cable for storage experiments with an acquisition frequency of 25.6 kHz.

Analysis of test results
The diagnostic performance of the standard algorithm chosen for this experiment to compare the specific measure of correct diagnosis rate is shown in the following figure 2.

Figure2. Comparison of diagnostic results
From the experimental results, it can be seen that there are also differences in the diagnostic effects of different methods when diagnosing different types of faults.Through numerical comparison, it is obvious that the correct diagnosis rate of the transformer winding fault diagnosis method based on the closing transient acoustic vibration signal proposed in this paper is significantly higher than that of the two traditional diagnosis methods, and the diagnosis performance is more stable, which proves that the diagnosis method proposed in this paper has better diagnosis effect.

Conclusion
In this paper, a transformer winding diagnosis model is proposed on the basis of extracting the closing transient acoustic vibration signal, combining the quantized parameters of the vibration distribution characteristics into a feature vector, which is used as a sample input to the fault type classifier to determine the working state of the winding and realize the analysis and diagnosis of the transformer C represents the penalty coefficient and i ζ represents the relaxation coefficient.The above maximum interval hyperplane is determined by searching and selecting the appropriate values of ω and b, and then finding the optimal solutions of the normal vector and displacement terms of the maximum interval hyperplane.The process of establishing the transformer fault diagnosis model based on the closing transient acoustic vibration signal is shown in Figure 1.

Figure1.
Figure1.The establishment process of transformer fault diagnosis model based on closing transient acoustic vibration signal winding state and faults.The test results show that the model can achieve transformer winding fault diagnosis accurately and effectively.