Experimental design and data analysis and optimization of mechanical condition diagnosis for transformer sets

Bingshuang Chang; Jian Xin; Miaomiao Fu; Vishal Jagota; Mukesh Soni; Samrat Ray

doi:10.1515/nleng-2022-0215

Article Open Access

Experimental design and data analysis and optimization of mechanical condition diagnosis for transformer sets

Bingshuang Chang , Jian Xin , Miaomiao Fu , Vishal Jagota , Mukesh Soni and Samrat Ray

Published/Copyright: August 5, 2023

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From the journal Nonlinear Engineering Volume 12 Issue 1

Abstract

The typical power transformer diagnosis approach is imprecise and unstable. A support vector machine classification algorithm is proposed, by designing an algorithm program that can improve the accuracy and speed of energy transformer diagnosis, the vibration signals of the surface twisting in different states are extracted by wavelet packet energy spectrum signal processing method, it is verified that the curve similarity between the vibration simulation model and the measured data is greater than 0.98, proving the simulation model’s validity. The calculation technique of online short circuit inductance is developed from the equivalent transformer model, and the variation error of simulation results is less than 0.05% when compared to the real transformer characteristics. The suggested state diagnostic technique successfully compensates for the drawbacks of the reactance method, which is incapable of detecting and judging the slightly loose or faulty winding. The method’s accuracy and superiority, as well as the practicability of the state diagnosis system, are demonstrated.

Keywords: transformer; mechanical state; experimental design; data analysis

1 Introduction

With the development of China’s power grid intelligent construction and the rise in demand for power equipment condition maintenance, the reliability of power transformer operation and the comprehensiveness of condition maintenance are becoming increasingly important. Accurate evaluation and diagnosis of transformer state in operation is the foundation for detecting potential transformer faults, as well as a primary guarantee for the safe operation of power systems [1]. It should be noted that power transformers are essential components of all power systems, including high voltage (HV) supply, medium voltage (MV), and low voltage (LV) distribution. Transformers are costly, so it will be interesting to see whether there is a method to lower the production costs, while boosting longevity [2,3]. Mechanical state of winding in the existing diagnostic techniques and standards for winding mechanical state include difficulties such as off-line judgement, single diagnosis signal, erroneous diagnosis findings for small failures, and inadequate data sources [4]. However, power transformers are inevitably subjected to a variety of short circuit current effects during operation, leading the winding to acquire a latent fault of mechanical damage, posing a major threat to the transformer’s normal operation [5,6]. Therefore, the state grid basic and prospective (academician team) science and technology project “Research on Online Multi-information Fusion State Evaluation method of Power Transformer” is taken as the background of the project. Taking S 11-M-500/3-5 oil-immersed power transformer as the research object, in combination with the multi-state and multi-parameter signal analysis and information fusion theory, in-depth research has been carried out using the state assessment and diagnosis method, simulation modeling and system development. The main research has been carried out based on the theoretical study of the mechanical state features of transformer twisting, the multi-physical field coupling simulation vibration model, and the finite element model of short circuit inductance. An online calculation method for short circuit inductance is proposed [7]. The induced current, voltage, flux leakage distribution, displacement distribution, and vibration acceleration of each phase winding in the simulation model are calculated. It is proposed to extract the value of transformer short circuit reactance (SCR) and winding fundamental frequency vibration characteristic from transformer SCR and winding fundamental frequency vibration. A wavelet packet energy spectrum signal processing method for feature extraction was proposed, and the fuzzy C clustering algorithm was used to validate the method’s classification effectiveness. The characteristic rule of vibration signal change in transformer windings in different states was obtained [8]. The multi-physical field coupling simulation vibration model and the finite element model of short circuit inductance were built using the theoretical study of mechanical state features of transformer twisting. Power grid intelligent construction is becoming increasingly significant, as is a trend for power electronics quality management, the reliability of power transformer operation, and the conciseness of state servicing.

The short circuit impedance is a significant component in determining the efficiency of a transformer. The short circuit impedance is the proportion of the rated voltage to be given to the transformer’s primary coil when the transformer is shorted and indeed the primary winding has rated current. It represents the impedance of the transformer. The greater the conductivity voltage, the better the control will be. Ortiz et al. proposed introducing parameter identification theory to calculate the short circuit impedance, the fault features of the internal twisting of the transformer include leakage inductance, resistance, and other parameters, and the fault size of the internal winding of the transformer can be judged by the change degree of the characteristic parameters [9].

The article is organized into five sections: Section 1 provides the global overview of power transformer diagnosis method and winding mechanical condition diagnosis, Section 2 covers the research work done in the traditional transformer winding deformation diagnosis methods, Section 3 covers the transformer mechanical characteristics, Section 4 discusses the results of experimental analysis of the current study. Major conclusion drawn from the study is presented in Section 5.

2 Literature review

Yang et al. suggested the online short circuit impedance calculation process, which was applied to the online transformer winding monitoring, and proposed the online SCR calculation method through the energy method. Depending on the analysis of transformer errors, an online observing system for SCR of transformer windings was developed [10]. During the short circuit condition, the lower the impedance voltage, the larger the short circuit current. When transformers are paralleled, only short circuit impedance controls voltage, load distribution, and short circuit current. Zhao et al. proposed online calculation of transformer SCR by using online parameter identification theory, and developed an online monitoring system for power transformer windings [11].

Evidence theory and support vector machine theory are used to develop a diagnosis model for winding mechanical condition. The notion of hierarchical state diagnosis was introduced, with assessment coming first, followed by diagnosis, and theories including information entropy, fuzzy theory, and D–S evidence theory, and support vector machine (SVM) was organically integrated into the state diagnostic model [12]. The SVM is presented as an effective fault detection technique for oil-immersed transformers relying on dissolved gases analysis (DGA) with maximum broad generalization ability; however, the SVM’s applicability is severely limited due to the challenges in selecting appropriate SVM parameters [13,14]. Vapnik presented SVM as a novel machine learning approach in the 1990s [15], which is based on the statistical theory and structural risk reduction and completely assures its high generalization capacity in theory. SVMs are frequently utilized in fault diagnosis, including fault diagnosis of analogue circuits [16,17], fault diagnosis of generator sets [18,19], and so on. Support vector machine with genetic algorithm (SVMG) was used to diagnose power transformer faults by Fei and Zhang [20]. For power transformer breakdown diagnosis, Bacha et al. [21] suggested a multi-layer SVM classifier that utilized combined ratios and graphical representation as gas characteristics. Wei et al. [22] suggested a novel technique for DGA feature prioritization and classification, and the new gas features were utilized to train an SVM optimized using particle swarm optimization (PSO), which produced the greatest classification accuracy. Koroglu and Demircali [23] constructed a multi-layer SVM model employing Gaussian radial basis as the kernel function, which was improved using grid search (GS), genetic evolution, differential evolution, and PSO algorithms. Yuan et al. [24] presented a chemical reaction optimization and twin SVM-based transformer defect diagnostic model. A transformer defect diagnostic model based on hybrid SVM and enhanced evolutionary PSO was suggested by Illias and Zhao [25].

3 Transformer mechanical characteristics

In the electrical characteristics of transformer winding mechanical condition diagnosis, domestic and foreign scholars have carried out a lot of research works, there are some offline testing methods and diagnosis equipment. The idea of transformer winding diagnosis based on electrical characteristics is to regard the winding itself as a unassertive straight two-port network constituting of resistors, inductors and capacitors. When the size or shape of the winding changes, the division of leakage of magnetic field at the corresponding fault will change, resulting in the exchange of corresponding division parameters such as self-inductance, capacitance, and mutual inductance [26]. According to this principle, domestic and foreign scholars put forward the frequency response process, LV pulse process, low pressure pulse analysis, and short circuit impedance process and other traditional transformer winding deformation diagnosis methods, the further study of each diagnostic method can improve the diagnostic method and the diagnostic accuracy.

3.1 Frequency response

According to the transformer equivalent circuit theory, the transformer is equivalent to a passive straight two-port network constituting of straight inductance, resistance, and capacitance parameters, the characteristic curve of the winding can be expressed by the unit impulse response function h _(t) in the time domain and the transfer function H _(jω) in the frequency domain, where H _(jω) is the Fourier transform of h _(t).

3.2 Low pressure pulse analysis

The diagnostic idea behind the LV pulse process is similar to that of the frequency reply process: an input sinusoidal signal is converted into a LV pulse signal origin, and the disfigurement of the twisting is determined by comparing the twisting’s reply waveform to the LV pulse. A fixed LV pulse signal is applied to one end of the transformer twisting under test during the trial as shown in Figure 1, while the pulse signal of the input and reply ends is recorded by the signal recorder, and the signal is analyzed in the time and frequency domain, and the change in the frequency response curve before and after the test is compared to determine the state of the transformer internal twisting.

Figure 1

Schematic test drawing of least voltage pulse process.

3.3 SCR

The short circuit impedance process examines the twisting deformation, displacement, and other mechanical faults by contrasting the short circuit impedance changes. The transformer short circuit impedance is the equivalent impedance inside the transformer when the impedance at the load side of the transformer is zero. The leakage reactance of the twisting can be evaluated by calculating the leakage inductance of the transformer twisting, and the change in leakage inductance is determined by the size of the internal twisting [27]. The specific calculation process of the short circuit impedance is shown in the given formulas (1) and (2):

(1) Z k = ∣ R 1 + j X 1 + R 12 + j X 12 ∣ = ( R 1 + R 12 ) 2 + ( X 1 + X 12 ) 2 = V / 1 ,

(2) R k = R 1 + R 12 = P / I 2 .

Figure 2 shows the vibration signal and spectrum analysis of a power transformer in normal operation. The vibration information generated by the cooling system, such as an oil pump and a fan, is within the frequency range of less than 100 Hz. The fundamental frequency of the winding is 100 Hz, which acts as the main frequency under the action of load current and magnetic flux leakage, and the vibration information of the winding is an integer multiple of the basic frequency. The core is accompanied by other high-order harmonic components in addition to the fundamental frequency of 100 Hz vibration due to the impact of the magnetostrictive nonlinear nature of the silicon steel sheet. The main vibration of transformer is mainly caused by loading voltage and load electricity, and its vibration frequency mainly includes the high harmonic components of fundamental frequency of 100 Hz and integral multiples of fundamental frequency.

Figure 2

Vibration signal and spectrum analysis of transformer in normal operation.

The vibration signal of the twisting is basically concentrated at the fundamental frequency of 100 Hz, accompanied by the vibration in the frequency domain of 200–500 Hz, the amplitude of the fundamental frequency is proportional to the square of the load current. Core vibration signals are mainly concentrated at 100–800 Hz and basically attenuate to after 1,000 Hz [28]. The amplitude of fundamental frequency is proportional to the square of the voltage. Therefore, the vibration changes around 100 Hz base band can be used to diagnose the faults such as the loosening of the winding preload force and the degree of deformation.

When the load current passes through the transformer winding, the electric force will be generated under the action of the surrounding leakage magnetic field. When the transformer winding vibrates mechanically, the current in the winding is transferred to the surface of the transformer oil tank via the insulating oil and connecting parts. The current in the winding of the transformer in steady state operation is given by formula (3):

(3) i t = I cos ω t ,

where I is the effective value of steady short circuit current, and ω is the angular frequency of the power frequency current.

The value of the leakage magnetic field at the position of the transformer coil is a time-varying function. With the vibration of the winding and the change in the position of the conductor, the distribution of the leakage magnetic field in space is time-varying. The discrete magnetic field value is transformed into continuous distribution function of the position of each wire, and the force condition of each wire is calculated. In the calculation of magnetic leakage field, according to Biot-Savart’s law, the magnetic induction intensity generated by conductor I′ at a certain point is given by Eq. (4):

(4) B → t = u 0 4 π i t ∫ i ′ d l ′ × r 0 r 2 .

For a given point, except that i _i is a variable, all other phases are constants. Therefore, the current steady state value is calculated according to the static field, and the corresponding magnetic flux leakage (MFL) B _t can be equivalent to

(5) B → t = k → I cos ω t .

For the specified transformer, in addition to the elastic coefficient K, other parameters are all fixed values, the elastic coefficient is related to the winding compression force. The insulation of transformer winding includes insulation pad and inter-turn insulation. The insulation pad is made of laminated wood fiber board with multiple pores. In the transformer oil, the paper board absorbs the transformer oil, and the oil is squeezed out from the paper board under the state of compression. When the pressure is relieved or reduced, the oil enters the board again, and the insulating pad (board) is subjected to sudden pressure, the oil pressure gradually decreases when the oil flows outward until it overcomes the resistance. The elastic coefficient of the pad changes with the change in the pressure, and the relation can be written as

(6) σ = a ε + b ε 3 .

Assuming that the elastic coefficients of the upper and lower insulation pads are the same, the elastic coefficients of the insulation pads are given by

(7) K i = K B + K H = 2 d σ d ε = 2 ( a ε + 3 b ε 2 ) .

By combining Eqs. (6) and (7), the relationship between the elastic coefficient and winding compression force can be obtained. As shown in Figure 3, when the winding becomes relaxed due to the decrease in the compression force, the elastic coefficient decreases. Let ( K − 4 M i ω 2 ) go down, causing the amplitude of vibration acceleration of the coil to increase, and when the elastic coefficient decreases to the same as 4 M i ω 2 , the vibration acceleration reaches the maximum and resonance phenomenon occurs. Therefore, during the operation of the transformer, the variation the in winding compression force can be reflected by the amplitude change in periodic vibration signal.

Figure 3

Relationship between elastic coefficient and compression force.

3.4 SVM classification algorithm

The basic idea of SVM classification algorithm is to minimize risk through immobilized experience, input questions can be directly mapped into higher dimensional inner product space to avoid the impact of dimensional disaster. Therefore, when solving the problem of small sample size and high recognition pattern, SVM classification algorithm can get the global optimal solution in the simplest way. The maximum probability avoids the local minimum and simplifies the algorithm structure, SVM classification algorithm has great advantages in the same type of algorithms. Set the sample set in the D-dimension vector, assuming there are 11 samples in the sample set, namely, { ( x i , y i ) , = 1 , 2 , … , n } , and all samples satisfy y ∈ { + 1 , − 1 } , then hyperplane Eq. (8) can be obtained

(8) ω ⋅ x + b = 0 ,

where b is a constant. In this case, the sample set of linear classification plane satisfies y i [ ω x i + b ] ≥ 0 and i = 1 , 2 , … , n . In this case, the support vector is taken as the training set of hyperplane samples under the premise of supporting the optimal classification plane. Through the Lagrange function shown in formula (9), formula (10) for solving the minimum value is obtained

(9) L ( ω , a , b ) = 1 2 ω ω − ∑ i = 1 n α i [ y i ( ω x i + b ) − 1 ] ,

(10) min L ( ω , b , a ) = 1 2 ω − y i ( α ω x i + b ) ,

where L ( ω , b , a ) represents the best training sample closest to the classification surface; and min L ( ω , b , a ) represents the sample with the smallest value among these training samples. The decision tree for reconstruction of multi-class classifiers is obtained. The increasing input dimension will lead to the reduction in operation efficiency. The SVM classification algorithm is designed to solve the hierarchical structure problem of DTBSVM and improve the diagnostic accuracy and speed of DTBSVM-based power transformer mechanical state diagnosis.

In the designed DTBSVM-based power transformer mechanical state diagnosis method, SVM classification algorithm is used, to a certain extent, the diagnostic accuracy and algorithm running speed of DTBSVM diagnosis method are improved, and a set of fault diagnosis algorithm flow based on DTBSVM is designed. When solving the problem of the number of intersecting samples in the class domain, the optimal solution cannot be obtained by the hierarchical distribution of decision tree, and the vector projection method can be used for two classes of samples through the domain. When the method is implemented, we need to consider whether the vector projection is linear or nonlinear, and the two classes have different calculation methods. When the vector projection is a linear distribution, the calculation formula (11) for the center point of the sample can be obtained

(11) m i = 1 n ∑ j = 1 n x j ,

where n is the number of samples in the sample set, m _i represents the average eigenvalue of the center point of the sample in class i samples; x _i is the jth sample in the sample set X = { x 1 , x 2 , … x n } .

When the vector projection is nonlinear distribution, the space distance of sample features can be measured by calculating Euclidean distance, the Euclidean distance of any two samples in the feature space is calculated using formula (12)

(12) d H ( x , y ) = K ( x , y ) − 2 K ( x , y ) + K ( x , y ) .

4 Experimental analysis

A fault diagnosis method based on DTBSVM is designed. Theoretically, the structure of the algorithm is greatly optimized and the accuracy and speed of diagnosis results are improved. In order to verify whether this method can truly optimize the algorithm compared with the traditional generalized regression neural network fault diagnosis method, radial basis function neural network fault diagnosis method, and BP neural network fault diagnosis method, the following experiments are designed. When applying the studied power transformer fault diagnosis method and the three traditional power transformer fault diagnosis methods to the experiment, first, the parameters of the power transformer need to be set, and a 220 kV power transformer is selected for the preventive test. The test results are shown in Table 1.

Table 1

Initial test results of power transformers

Test item	Number of tests			Mean value of test
Test item	First time	Second time	Third time	Mean value of test
Winding DC resistance	0.52%	0.54%	0.56%	0.53%
Winding absorption ratio	1.24	1.26	1.36	1.29
Winding medium	0.29%	0.32%	0.36%	0.35%
Microwater content	18.00 mg/L	16.00 mg/L	15.00 mg/L	17.65 mg/L
Oil medium	1.68%	1.74%	1.56%	1.63%
Oil breakdown voltage	55.00 kV	63.00 kV	53.00 kV	58.00 kV
Core grounding current	32.00 mA	35.00 mA	39.00 mA	36.00 mA

The parameters of the four power transformer mechanical condition diagnosis methods required in this experiment are adjusted, and 15 nodes in the transformer are set, the output value of each node is detected, the status of the power transformer is judged based on the output value, and the diagnosis result is given, according to the data in Table 1. To identify the benefits and drawbacks of the four diagnostic approaches, the errors, diagnostic accuracy, and algorithm operation time were compared based on the diagnostic findings.

The diagnostic output results of the DTBSVM-based fault diagnosis method, the traditional generalized regression neural network fault diagnosis method, the radial basis function neural network fault diagnosis method, and the BP neural network fault diagnosis method in the experiment can be obtained through the test records, as shown in Table 2.

Table 2

Test results

Method	Average error	Maximum change	Diagnosis accuracy (%)	Performance period
DTBSVM	0.2526	0.3451	92.7	47 s
Generalized regression	0.3005	0.4026	89.5	1 min 6 s
Radial basis function	0.2963	0.4659	87.3	59 s
BP Network	0.2561	0.5038	80.6	45 s

Among the four diagnostic results of mechanical state of power transformers, only DTBSVM method has the lowest mean error and maximum change and the highest diagnostic accuracy, the running time is not the least, but the difference from the shortest running algorithm is only 2 s. The algorithm used in BP neural network fault diagnosis method is shorter, but the diagnosis accuracy of this method is poor. Thus, it can be known that among the four power transformer state diagnosis methods set up in the experiment, only the DTBSVM-based power transformer mechanical state diagnosis method designed in this work is the most practical, the error value, diagnostic accuracy, and algorithm optimization are in the leading state, which are more superior to the other three methods.

5 Conclusion

An online calculation method of SCR was proposed to establish the multi-field coupling vibration simulation model of the winding based on the basic “Research on online Multi-information Fusion State Assessment method for Power transformers” of the State Grid, based on the theoretical study of mechanical state characteristics of transformer windings and the finite element model of SCR. The technique of extracting transformer SCR and winding fundamental frequency vibration characteristic value is investigated, and a fundamental frequency vibration and SCR assessment system is built. When comparing the simulation results with the actual parameters of the transformer, the variation error is within 0.05%, proving the validity of the simulation model. The calculation method of online SCR is deduced by transformer equivalent model, and the variation error is within 0.05%. Proving the validity of the simulation model, the results show that the proposed state diagnosis method can effectively compensate for the shortcomings of the reactance method for the detection and judgement of slight loosening of the winding and failure type, as well as the accuracy and superiority of the method and the state diagnosis system’s practicability.

Funding information: This work is not funded externally.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: Authors state no conflict of interest.
Data availability statement: Data used for present work can be made available on genuine request from the corresponding author.

References

[1] Leibl M, Ortiz G, Kolar JW. Design and experimental analysis of a medium-frequency transformer for solid-state transformer applications. IEEE J Emerg Sel Top Power Electron. 2017;5(1):110–23.10.1109/JESTPE.2016.2623679Search in Google Scholar

[2] Abu-Elanien AEB, Salama AAB, Bartnikas R. A Techno-Economic Method for Replacing Transformers. IEEE Trans Power Deliv. 2011;26(2):817–2910.1109/TPWRD.2010.2091289Search in Google Scholar

[3] Georgilakis PS, Tsili MA, Souflaris AT. A heuristic solution to the transformer manufacturing cost optimization problem. J Mater Process Technol. 2007;181(1–3):260–6.10.1016/j.jmatprotec.2006.03.034Search in Google Scholar

[4] Czyz P, Guillod T, Krismer F, Huber J, Kolar JW. Design and experimental analysis of 166 kW medium-voltage medium-frequency air-core transformer for 1:1-DCX applications. IEEE J Emerg Sel Top Power Electron. 2021;99:1.10.1109/JESTPE.2021.3060506Search in Google Scholar

[5] Wang G, Liu Y, Chen X, Yan Q, Sui H, Ma C, Zhang J. Power transformer fault diagnosis system based on Internet of Things. J Wireless Com Network. 2021;21:1–24.10.1186/s13638-020-01871-6Search in Google Scholar

[6] Metwally I. Failures, monitoring and new trends of power transformers. IEEE Potentials. 2011;30(3)36–43.10.1109/MPOT.2011.940233Search in Google Scholar

[7] Ozdemir S, Balci S, Altin N, Sefa I. Design and performance analysis of the three-level isolated DC-DC converter with the nanocyrstalline core transformer. Int J Hydrog Energy. 2017;42(28):17801–12.10.1016/j.ijhydene.2017.02.158Search in Google Scholar

[8] Wang J, Si D, Tian T, Ren R. Design and experimental study of a current transformer with a stacked PCB-based on B-dot. Sensors. 2017;17(4):820.10.3390/s17040820Search in Google Scholar PubMed PubMed Central

[9] Ortiz G, Leibl MG, Huber JE, Kolar JW. Design and experimental testing of a resonant DC–DC converter for solid-state transformers. IEEE Trans Power Electron. 2017;32(10):7534–42.10.1109/TPEL.2016.2637827Search in Google Scholar

[10] Yang Z, Fu P, Jiang J, Liu X, Huang Y, Liu Q, et al. Analysis of anti-short circuit strength on windings for ITER-PPEN power transformer. Fusion Eng Des. 2017;121(Oct):319–24.10.1016/j.fusengdes.2017.05.033Search in Google Scholar

[11] Zhao T, Zhang X, Wang M, Mao W, Wang X. Module power balance control and redundancy design analysis of cascaded PV solid-state transformer under fault conditions. IEEE J Emerg Sel Top Power Electron. 2020;99:1.10.1109/JESTPE.2020.2964950Search in Google Scholar

[12] Rashidi M, Altin N, Ozdemir S, Bani-Ahmed A, Nasiri A. Design and implementation of a LLC resonant solid state transformer. IEEE Trans Ind Appl. 2020;99:1.10.1109/TIA.2020.2982847Search in Google Scholar

[13] Malarvel M, Singh H. An autonomous technique for weld defects detection and classification using multi-class support vector machine in X-radiography image. Optik. 2021;231:Article ID 166342. 10.1016/j.ijleo.2021.166342.Search in Google Scholar

[14] Meng J, Singh M, Sharma M, Singh D, Kaur P, Kumar R. Online monitoring technology of power transformer based on vibration analysis. J Intell Syst. 2021;30(1):554–63.10.1515/jisys-2020-0112Search in Google Scholar

[15] Cortes C, Vapnik V. Support-vector networks Mach Learn. 1995;20(3):273–97. 10.1007/bf00994018.Search in Google Scholar

[16] Zhang C, He Y, Yuan L, He W, Xiang S, Li Z. A novel approach for diagnosis of analog circuit fault by using GMKL-SVM and PSO. J Electron Test Theory Appl. 2016;32:531–40.10.1007/s10836-016-5616-ySearch in Google Scholar

[17] Zhang A, Chen C, Jiang B. Analog circuit fault diagnosis based UCISVM. Neurocomputing. 2016;173:1752–60.10.1016/j.neucom.2015.09.050Search in Google Scholar

[18] Dong BY, Ren G. Analog circuit fault diagnosis using AdaBoost with SVM-based component classifiers. Adv Mater Res. 2012;591:1414–7.10.4028/www.scientific.net/AMR.591-593.1414Search in Google Scholar

[19] Liu CL, Qi WX. Research on fault diagnosis method of wind turbine based on wavelet analysis and LS-SVM. Adv Mater Res. 2013;724:593–7.10.4028/www.scientific.net/AMR.724-725.593Search in Google Scholar

[20] Fei S, Zhang X. Fault diagnosis of power transformer based on support vector machine with genetic algorithm. Expert Syst Appl. 2009;36:11352–7.10.1016/j.eswa.2009.03.022Search in Google Scholar

[21] Bacha K, Souahlia S, Gossa M. Power transformer fault diagnosis based on dissolved gas analysis by support vector machine. Electr Power Syst Res. 2012;83:73–9.10.1016/j.epsr.2011.09.012Search in Google Scholar

[22] Wei C, Tang W, Wu Q. Dissolved gas analysis method based on novel feature prioritisation and support vector machine. IET Electr Power Appl. 2014;8:320–8.10.1049/iet-epa.2014.0085Search in Google Scholar

[23] Koroglu S, Demircali A. Diagnosis of power transformer faults based on multi-layer support vector machine hybridized with optimization methods. Electr Mach Power Syst. 2016;44:2172–84.10.1080/15325008.2016.1219427Search in Google Scholar

[24] Yuan F, Guo J, Xiao Z, Zeng B, Zhu W, Huang S. A transformer fault diagnosis model based on chemical reaction optimization and twin support vector machine. Energies. 2019;12:960.10.3390/en12050960Search in Google Scholar

[25] Illias HA, Zhao WL. Identification of transformer fault based on dissolved gas analysis using hybrid support vector machine-modified evolutionary particle swarm optimisation. PLoS One. 2018;13:e0191366.10.1371/journal.pone.0191366Search in Google Scholar PubMed PubMed Central

[26] Lavrinovich VA, Mytnikov AV, Li H. Advanced technology of transformer winding condition control based on nanosecond probing impulse. Resour Effic Technol. 2016;2(3):111–17.10.1016/j.reffit.2016.07.003Search in Google Scholar

[27] Eddiai A, Meddad M, Rguiti M, Chérif A, Courtois C. Design and construction of a multifunction piezoelectric transformer. J Aust Ceram Soc. 2019;55(1);19–24.10.1007/s41779-018-0206-3Search in Google Scholar

[28] Bulus M. Sample size determination and optimal design of randomized/non-equivalent pretest-posttest control-group designs. Adiyaman Univ J Edu Sci. 2021;11(1):48–69.10.17984/adyuebd.941434Search in Google Scholar

Received: 2022-03-01

Revised: 2022-06-23

Accepted: 2022-06-24

Published Online: 2023-08-05

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2022-0215

Keywords for this article

transformer; mechanical state; experimental design; data analysis

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