Power transformer fault diagnosis based on dissolved gas analysis by support vector machine

Electric Power Systems Research 83 (2012) 73–79

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Power transformer fault diagnosis based on dissolved gas analysis by support vector machine Khmais Bacha, Seifeddine Souahlia ∗ , Moncef Gossa Unit of research: Control, Monitoring and Reliability of the Systems, Higher School of Sciences and Technology of Tunis, 5, Taha Hussein Street – Tunis, Postal Box 56, Bab Menara 1008, Tunisia

a r t i c l e

i n f o

Article history: Received 26 April 2011 Received in revised form 21 July 2011 Accepted 20 September 2011 Available online 21 October 2011 Keywords: Dissolved gas analysis Support vector machine Transformer fault diagnosis

a b s t r a c t This paper presents an intelligent fault classification approach to power transformer dissolved gas analysis (DGA). Support vector machine (SVM) is powerful for the problem with small sampling (small amounts of training data), nonlinear and high dimension (large amounts of input data). The standard IEC 60599 proposes two DGA methods which are the ratios and graphical representation. According the experimental data, for the same input data, these two methods give two different faults diagnosis results, what brings us to a problem. This paper investigates a novel extension method which consists in elaborating an input vector establishes by the combination of ratios and graphical representation to resolve this problem. SVM is applied to establish the power transformers faults classification and to choose the most appropriate gas signature between the DGA traditional methods and a novel extension method. The experimental data from Tunisian Company of Electricity and Gas (STEG) is used to illustrate the performance of proposed SVM models. Then, the multi-layer SVM classifier is trained with the training samples. Finally, the normal state and the six fault types of transformers are identified by the trained classifier. In comparison to the results obtained from the SVM, the proposed DGA method has been shown to possess superior performance in identifying the transformer fault type. The SVM approach is compared with other AI techniques (fuzzy logic, MLP and RBF neural network); the proposed method gives a good performance for transformers fault diagnosis. The test results indicate that the novel extension method and the SVM approach can significantly improve the diagnosis accuracies for power transformer fault classification. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Power transformers are important equipments in power systems. Any fault in the power transformer may lead to the interruption of the power supply and accordingly. So it is of vital importance to detect the incipient fault of the transformer as early as possible. Diagnosis of potential faults concealed inside power transformers is the key of ensuring stable electrical power supply to consumers [1]. Condition monitoring and software-based diagnosis tools are central to the implementation of efficient maintenance management strategies for many engineering applications including power transformers [2]. Dissolved gas analysis (DGA) has been widely recognized as an effective diagnostic technique for power transformers faults detection. The analysis of specific dissolved gas concentrations in insulation oil of a transformer gives the knowledge about a

∗ Corresponding author. Tel.: +216 97 689358. E-mail addresses: [email protected] (K. Bacha), [email protected] (S. Souahlia), [email protected] (M. Gossa). 0378-7796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2011.09.012

transformer state, and therefore, allows taking the necessary preventive actions [3]. In the past years, various fault diagnosis techniques have been proposed, including the conventional key gas method used in Ref. [4], ratio method presented in Ref. [5] and Ref. [6], and graphical representation method introduced in Ref. [7]. However, the identification of the faulted location by the traditional method is not always an easy task due to the variability of gas data and operational natures. Recently, artificial intelligence techniques have been extensively used with the purpose of developing more accurate diagnostic tools based on DGA data. Shintemirov et al. [3] proposed the Genetic Programming (GP) method for transformer fault detection. In Ref. [8], the fuzzy logic is used with three and four digit codes containing the fault information are created based on the fuzzy logic to achieve better result. The method is applied to three transformers to diagnose the fault by analyzing the dissolved oil based on fuzzy logic. The back propagation (BP)-based artificial neural nets (ANN) described in Ref. [4] can identify complicated relationships among dissolved gas contents in transformer oil and corresponding fault

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Table 1 Fault type used in analysis.

Table 4 Diagnosis using the ratio method (IEC 599) [11].

Fault type

Fault type code

Fault type

C2 H2 /C2 H4

CH4 /H2

C2 H4 /C2 H6

Partial discharge Low energy discharge High energy discharge Thermal faults T < 300 ◦ C Thermal faults 300 < T < 700 ◦ C Thermal faults T > 700 ◦ C

PD D1 D2 T1 T2 T3

PD D1 D2 T1 T2 T3

<0.1 >1 0.6–2.5 <0.1 <0.1 <0.1

<0.1 0.1–0.5 0.1–1 >1 >1 >1

<0.2 >1 >2 <1 1–4 >4

2. Dissolved gas in the transformer oil

Table 2 Interpretation gas dissolved in the oil [11]. Gas detected

Interpretation

2.1. Transformers fault types

Oxygen (O2 ) Oxide carbon (CO) Dioxide carbon (CO2 ) Hydrogen (H2 )

Transformer seal fault Cellulose decomposition Cellulose decomposition Electric discharge (corona effect, low partial discharge) Electric fault (arc, spark) Thermal fault (overheating local) Secondary indicator of thermal fault Secondary indicator of an arc or serious overheating

Dissolved gas analysis (DGA) is a sensitive and reliable technique to identify the power transformers faults. By using this technique, it is possible to discriminate fault in a great variety of oil-filled equipment. IEC Publication 60599 [11] provides a coded list of faults detectable by DGA [12]. Table 1 tabulates the fault types and the codes addressed in this paper.

Acetylene (C2 H2 ) Ethylene (C2 H4 ) Ethane (C2 H6 ) Methane (CH4 )

2.2. DGA interpretation methods types. The BP determines the optimal connection weights and bias terms to achieve the most accurate diagnosis model for DGA. In Ref. [9] the authors describe how mapping a neural network into a rule-based fuzzy inference system leads to knowledge extraction. This mapping makes explicit the knowledge implicitly captured by the neural network during the learning stage, by transforming it into a set of rules. This method is applied to transformer fault diagnosis using dissolved gas-in-oil analysis. Such the AI techniques can deal with complex and nonlinear problems and implement empirical risk minimization to minimize the error on the training data. However, support vector machine (SVM) implements the principle of structural risk minimization in place of experiential risk minimization [10]. At present, SVM has been applied successfully to solve faults classification problem. In this paper, the proposed combination of ratios and graphical representation method is applied to resolve the problem of the conflict between the various DGA methods. SVM classification was developed to automate the evaluation on the power transformers state and chooses the most appropriate gas signature. Ideally, the proposed approach can overcome the above drawback and improve the diagnosis accuracies for transformer fault classifications. In this study, four types of DGA methods are employed as the inputs of the extended SVM classifiers for fault classification the key gas, the ratios, the graphical representation method and the combination of the ratios, and graphical representation methods. This paper consists of five sections. Section 2 illustrates principles of the faults types and DGA methods. Section 3 presents the regression arithmetic of SVM. Section 4 presents our power transformers fault diagnosis based on SVM and discusses the experimental results. Finally, Section 5 provides some important conclusions that we have drawn from this study.

Many interpretative methods based on DGA to detect the incipient fault nature have been reported. In this paper, three of the DGA methods were studied: - Gas key method; - IEC Ratios method; - the graphical representation method. 2.2.1. Key gas method In this key gas method, we need five key gas concentrations: hydrogen (H2 ), methane (CH4 ), acetylene (C2 H2 ), ethylene (C2 H4 ) and ethane (C2 H6 ) available for consistent interpretation of the fault. IEC 60599 standard establishes an interpretation by which five gases H2 , CH4 , C2 H2 , C2 H4 and C2 H6 can be used to detect different types of faults. Table 2 shows the diagnostic interpretations applying various key gas concentrations. The ppm concentration typical values range observed in power transformers according to IEC 60599 are given in Table 3. 2.2.2. IEC Ratios method The IEC Ratios method utilizes five gases H2 , CH4 , C2 H2 , C2 H4 and C2 H6 . These gases are used to produce a three gas ratios: C2 H2/ C2 H4 , CH4 /H2 and C2 H4 /C2 H6 . Table 4 shows the IEC standard for interpreting fault types and gives the values for the three key-gas ratios corresponding to the suggested fault diagnosis. When key-gas ratios exceed specific limits, incipient faults can be expected in the transformer. 2.2.3. The graphical representation The graphical representation method using Duval’s triangle is described in Appendix B of IEC 60599:1999 standard [13]. The concentrations (in ppm) of CH4 , C2 H2 and C2 H4 are expressed as a percentage of the total (CH4 + C2 H4 + C2 H2 ) and

Table 3 Concentration typical values observed in transformers [11]. Gas

H2

CH4

C2 H6

C2 H4

C2 H2

CO

CO2

Concentration (ppm)

60–150

40–110

50–90

60–280

3–50

540–900

5100–13,000

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where w denotes the weight vector and b denotes the bias term. w and b are used to define the position of the separating hyper-plane by which should satisfy the constraints:

⎧ ⎨ yk (w · xk + b) ≥ 1, k = 1, 2, . . . , m

(2)

⎩ min 1 w2 2

According to Lagrangian principle, the above problem can be transformed to its corresponding form as follows [15]:

 1 T ˛k [yk (wT xk + b) − 1] w w− 2 m

L(w, b, ˛) =

k=1

Fig. 1. Coordinates and fault zones of the triangle [7].

where ˛k are the Lagrange coefficients (˛k > 0). According to the condition of optimality:

Table 5 Graphical representation method zone limits [11]. PD D1 D2 T1 T2 T3

98% CH4 23% C2 H4 23% C2 H4 4% C2 H2 4% C2 H2 15% C2 H2

100% CH4 13% C2 H2 13% C2 H2 10% C2 H4 10% C2 H4 50% C2 H4

(3)

∂L(w, b, ˛) = 0, ∂w 100% C2 H2 38% C2 H4

29% C2 H2

100% C2 H4

∂L(w, b, ˛) =0 ∂b

(4)

We have the following equations:

⎧ m  ⎪ ⎪ ⎪ w= ˛k · xk · yk ⎪ ⎪ ⎨ k=1

(5)

m ⎪  ⎪ ⎪ ⎪ ˛k · yk = 0 ⎪ ⎩ k=1

Hence, from Eqs. (3) and (5), the dual problem is:

⎧ m  ⎪ 1 ⎪ ⎪ max ˛k − ˛k ˛j yk yj (xk xj ) ⎪ ⎪ 2 ⎪ ⎪ k=1 k,j ⎪ ⎨ ∀k,

˛k ≥ 0

(6)

⎪ ⎪ ⎪ m ⎪ ⎪ ⎪ ˛ y = 0 ⎪ ⎪ k k ⎩ i=1

We define the support vectors VS any vector xk as: yk [(w0 · xk ) + b0 ] = 1

(7)

This is equivalent to Eq. (8):

Fig. 2. Separation of two classes by SVM.



VS = { xk  ˛k > 0} for k = 1, 2, . . . , m define a point (%CH4 , %C2 H4 , %C2 H2 ) in a coordinate system represented as a triangular diagram (Fig. 1), which has been subdivided in different zones. Each zone is related to a certain type of fault. Zone DT in Fig. 1 corresponds to mixtures of thermal and electrical faults. We can translate Fig. 1 in a table that gives the limits of each fault which are summarized in Table 5. 3. Basic concept of SVM SVM analysis seeks to find an optimal separating hyper-plane by maximizing the margin between the separating data, as illustrated in Fig. 2 [14], where the filled circles are the support vectors and the unfilled circles are the training data. The regression approximation estimates a function according to a given data set T = {xk ,yk }k m , where xk denotes the input vector, yk ∈ {− 1 ; 1} denotes the corresponding output value and m denotes the total number of data patterns, the SVM regression function is: f (x) = w.x + b =

m  k=1

wk · xk + b = 0

(1)

(8)

The ranking function class (x) is defined by Eq. (9):

⎡

class (x) = sign[(w0 · x) + b0 ] = sign ⎣

n 

⎤

˛i yi (xi .x) + b0 ⎦

(9)

xi ∈ VS

If class (x) is less than 0, x is the class −1 else it is a class 1. However for nonlinear cases, there is insufficient space for classifying the inputs. So, we need a larger space. We must therefore resolve Eq. (10):

⎧ m  ⎪ 1 ⎪ ⎪ max ˛k − ˛k ˛j yk yj (xk )(xj ) ⎪ ⎪ 2 ⎪ ⎪ k=1 k,j ⎪ ⎨ ∀k,

0 ≤ ˛k ≤ C

⎪ ⎪ ⎪ m ⎪  ⎪ ⎪ ⎪ ˛k yk = 0 ⎪ ⎩

(10)

k=1

with C is the margin parameter. K(xk , xj ) = (xk ) · (xj ) is a positive kernel function definite on Rn based on Mercy condition [16]. From the above analysis, it can be concluded that SVM is decided by training samples and kernel function. The construction and

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Table 6 Transformer characteristics used for DGA samples. No.

1

2

3

4

5

6

P (MVA) V (kV)

150 235/15.5

4 15.5/6.8

2 6.6/0.4

42.5 230/11

25 150/30

40 150/30

No.

7

8

9

10

11

12

P (MVA) V (kV)

50 150/90

40 90/30

100 225/90

15 90/30

30 90/30

20 90/30

selection of kernel function is important to SVM. But the kernel function is often given directly in practice. Some common kernel functions are shown as follows [15]: • The linear Kernel function: K(x, x ) = x · x

(11)

• The polynomial kernel function: K(x, x ) = (x · x )

d

or (c + x · x )

d

(12)

• Gaussian radial basis function: K(x, x ) = exp





x − x 2 −

2 2

(13)

• Sigmoïd kernel function:



K(x, x ) = tanh(˛0 (x, x ) + ˇ0 )

Fig. 3. Diagnostic model of power transformer based on SVM classifiers.

(14)

4. Transformers faults classification based on SVM 4.1. DGA training and testing data This study employs dissolved gas content data in power transformer oil from chemistry laboratory of the Goulette central of Tunisian Company of Electricity and Gas (STEG). The data is divided into two data sets: the training data set (94 samples) and the testing data set (30 samples). The extracted DGA data contain not only the five key gas concentrations, three ratios and three relative percentages but also the diagnosis results from on-site inspections. The training data sets have been evaluated using various methods DGA and the corresponding judgments related to seven classes have been provided: normal unit (46 samples), partial discharge (2 samples), low energy discharge (3 samples), high energy discharge (17 samples), low temperature overheating (4 samples), middle temperature overheating (7 samples) and high temperature overheating (15 samples). The transformer characteristics used for the taking of mineral oil samples are given in Table 6. From January 2008 to December 2009, the transformer was internally examined. The SVM faults classification is performed using traditional DGA methods and the proposed DGA method as gas signature. 4.2. Diagnosis model conception based on SVM classifier As shown in Fig. 3, the diagnostic model includes six SVM classifiers which are used to identify the seven states: normal state and the six faults (PD, D1, D2, T1, T2 and T3). With all the training samples of the states, SVM1 is trained to separate the normal state from the fault state. When input of SVM1 is a sample representing the normal state, output of SVM1 is set to +1; otherwise −1. With the samples of single fault, SVM2 is trained to separate the discharge fault from the overheating fault. When the input of SVM2 is a sample representing discharge fault, the output of SVM2 is set to +1; otherwise −1. With the samples of discharge fault, SVM3 is trained to separate the high-energy discharge (D2) fault from the partial

Table 7 Codification output of SVM.

No fault PD D1 D2 T1 T2 T3

svm1

svm2

svm3

+1 −1 −1 −1 −1 −1 −1

+1 +1 +1 −1 −1 −1

−1 −1 +1

svm4

svm5

svm6 −1 +1

−1 −1 +1

−1 +1

discharge (PD) and low energy discharge (D1) fault. When the input of SVM3 is a sample representing the D2 fault, the output of SVM3 is set to +1; otherwise −1. With the samples of overheating fault, SVM4 is trained to separate the high temperature overheating (T3) fault from the low and middle temperature overheating (T1 and T2) fault. When the input of SVM4 is a sample representing the T3 fault, the output of SVM5 is set to +1; otherwise −1. SVM5 is trained to separate the middle temperature overheating (T2) fault from the low temperature overheating (T1) fault. When the input of SVM5 is a sample representing the T2 fault, the output of SVM5 is set to +1; otherwise −1. SVM6 is trained to separate the partial discharge (PD) fault from the low energy discharge (D1) fault. When the input of SVM6 is a sample representing the D1 fault, the output of SVM6 is set to +1; otherwise −1. All the six SVMs adopt polynomial and Gaussian as their kernel function. In SVM, the parameters  and C of SVM model are optimized by the cross validation method. The adjusted parameters with maximal classification accuracy are selected as the most appropriate parameters. Then, the optimal parameters are utilized to train the SVM model. So the output codification is presented in Table 7. 4.3. Proposed method implementation The training procedure and choice of SVM parameters for training is very important for classification. Fig. 4 presents the process of

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Table 8 The SVM key gas method classification performance. SVM kernel function

False alarm rate (%)

Non-detection rate (%)

Polynomial Gaussian

0 0

40 (12/30) 26.7 (8/30)

Table 9 The SVM ratios method classification performance. SVM kernel function

False alarm rate (%)

Non-detection rate (%)

Polynomial Gaussian

0 0

26.7 (8/30) 23.3 (7/30)

Table 10 The SVM graphical representation method classification performance. SVM kernel function

False alarm rate (%)

Non-detection rate (%)

Polynomial Gaussian

0 0

23.3 (7/30) 16.7 (5/30)

4.4. Experimental results and discussions The SVM faults classification is performed using several DGA methods as gas signature. Fig. 4. Proposed method implementation basic steps.

optimizing the SVM parameters with the cross validation method, which is described below.

Step 1: Load of the training data which are 94 samples training. Step 2: Data generation: the data were generated by considering a normal state mode and a failure mode. Step 3: Parameters initialization: we can choose the initial parameters as follows. • Kernel function type: polynomial and Gaussian • Kernel option () = 1 • C=1 Step 4: Training of SVM with the function svm class. Step 5: Load of the testing data which are 30 samples training. Step 6: Display of the results and the essential support vectors. Step 7: Determination of the hyper-parameter. Step 8: Determination of the C parameter values according to a logarithmic scale going from 1 to 1000. Step 9: Selection of the C and  parameters values with the cross validation method. Step 10: The SVMs are trained and tested using the appropriate values of these parameters.

4.4.1. SVM key gas Firstly, we will classify the faults using key gas as input data. The performance of key gas method is analyzed in terms false alarm rate and non-detection rate for polynomial and Gaussian kernel functions as shown in Table 8. According to the results, we find that the Gaussian kernel function is more efficient for system fault diagnosis, but this method does not give excellent results. So, we must propose an alternative method. 4.4.2. SVM ratios Secondly, we will classify the faults using ratios as input data. The test set is again fed to the SVM in order to verify if it classifies and estimates correctly. Table 9 tabulates the results by representing the false alarm rate and the non-detection rate for two kernel functions. From Table 9, we note that the Gaussian kernel function is more efficient system fault diagnosis. 4.4.3. SVM graphical representation Now, we will classify the faults using graphical representation as input. The diagnosis results for test set with the polynomial and Gaussian kernel functions are listed in Table 10. According to test results, we find that the Gaussian kernel function gives a better diagnosis compared to the polynomial kernel function.

Table 11 Tested gas data of transformer and diagnosis by ratios and graphical representation methods. No.

1 2 3 4 5 6 7 8

H2

19.3 27 23 21 160 180 345 30.4

CH4

103 30 63 34 130 175 112.3 117

C2 H6

159 23 54 5 33 75 27.5 44.2

C2 H4

19 2.4 10 47 96 50 51.5 138

C2 H2

0.6 0.1 0.3 62 0.1 4 58.8 0.1

AFC

T1 or T2 No fault or T1 T1 or T2 No fault or D2 No fault or T2 No fault or T2 D1 or D2 T2 or T3

SVM diagnosis SVMR

SVMG

T1 No fault T1 No fault T2 No fault D1 T2

T2 T1 T2 D2 No fault T2 D2 T3

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Table 12 The SVM combination method classification performance.

Table 14 Comparison of the proposed method with other AI methods.

SVM kernel function

False alarm rate (%)

Non-detection rate (%)

Polynomial Gaussian

0 0

16.7 (5/30) 10 (3/30)

Table 13 False alarm rate and non-detection rate of the four DGA methods. DGA methods

False alarm rate (%)

Non-detection rate (%)

Key gas Ratios Graphical representation Combination ratios and graphical representation

0 0 0 0

26.7 (8/30) 23.3 (7/30) 16.7 (5/30) 10 (3/30)

Note the problem of conflict between the methods of ratios and graphical representation is not resolved. To demonstrate this problem, various power transformers DGA results are tested. The detailed gas data are shown in Table 11, where the AFC expresses the actual fault type, SVMR and SVMG are the classification results by the SVM with Gaussian kernel function using ratios and graphical representation methods, respectively as input data. Consequently, we propose a combination method of these two methods. 4.4.4. SVM combination of ratios and graphical representation Finally, we will classify the faults using combination of ratios and graphical representation as input data. The false alarm rate and the non-detection rate of diagnostic systems for different membership functions are illustrated in Table 12. From Table 12, we note that the Gaussian kernel function shows highly accurate classification of fault diagnosis procedure. Note the problem of conflict between the methods of ratios and graphical representation is resolved. 4.4.5. Comparative investigation of SVM classification According to test results of the four inputs data classified by the SVM, we conclude that the Gaussian kernel function gives the best results. To select the most significant gas analysis method, we compare the false alarm rate and non-detection rate of four inputs data types which are given in Table 13. The actual result indicates the classification accuracies obtained by using the combination of ratios and graphical representation method is higher than those of gas signature for the classification by SVM. To conclude, faults classification by the SVM technique can be achieved by the combination of ratios and graphical representation method using the Gaussian kernel function. 4.5. Performance comparison For comparing artificial intelligence methods, we have also applied the Fuzzy approach and ANN to detect faults. Table 14 compares the performance of the proposed method and other AI approaches. The MLP (Multi-Layer Perceptron) and RBF (radial basis function) have the advantages of a fast learning process, a learning stage without any iteration for updating weights, robust ability, and adaptation capability [17]. However, MLP and RBF also require large amounts of training data, and need to adjust the parameters of the hidden activation function. The parameters are determined by experience or by using the optimum method to tune the network parameters and connecting weights such as the Genetic algorithm. The Fuzzy logic approach needs to determine the

AI approaches

False alarm rate (%)

Non-detection rate (%)

Diagnostic accuracy (%)

Fuzzy logic MLP RBF a SVM

6.7 0 0 0

6.7 20 13.3 10

86.7 80 86.7 90

a

The proposed method.

linguistic variables, membership functions with “low”, “medium”, and “high” descriptions for each gas signature, and inference rule base. Membership functions are used to translate judgments into numerical expression where the most uses are Gaussian, trapezoidal and triangular functions. During numerical testing, MLP and RBF have four-layer architecture with 6 input nodes, 7 output nodes, and 19 hidden nodes. The Fuzzy approach has 6 input variables, with each variable having 3 membership functions, 7 output variables with 3 membership functions, and 353 inference rules. The results confirm that the proposed method also provides high confidence for transformer fault diagnosis. 5. Conclusion In this paper, the SVM technique is implemented for the faults classification using the dissolved gas analysis for power transformers. The DGA methods studied are key gas, ratios, graphical representation and our proposed combination ratios and graphical representation method. The effectiveness of SVM diagnosis has been analyzed with polynomial and Gaussian functions. The real data sets are used to investigate its feasibility in forecasting the DGA methods in power transformer oil. According to test results, it is found that the combination ratios and graphical representation method is more suitable as a gas signature and the SVM with the Gaussian function has a better performance than the other kernel function in diagnosis accuracy. The accuracy of the multi-layer SVM for faults diagnosis is comparable to conventional methods due to their great facilities for study. Compared with other AI approaches, the proposed method shows good performance for fault diagnosis. The proposed method can be applied to online diagnosis of incipient faults in transformers. The experimental results reveal the potential of the proposed approach for forecasting the DGA method in power transformer oil. Acknowledgements This work was supported by the Tunisia Company of Electricity and Gas (STEG). The authors would like to express their gratitude to all the people who have directly or indirectly contributed towards the successful completion of this technical paper. References [1] S.-w. Fei, X.-b. Zhang, Fault diagnosis of power transformer based on support vector machine with genetic algorithm, Expert Systems with Applications 36 (2009) 11352–11357. [2] A. Akbari, A. Setayeshmehr, H. Borsi, E. Gockenbach, I. Fofana, Intelligent agentbased system using dissolved gas analysis to detect incipient faults in power transformers, IEEE Electrical Insulation Magazine 26 (6) (2010) 27–40. [3] A. Shintemirov, W. Tang, Q.H. Wu, Power transformer fault classification based on dissolved gas analysis by implementing bootstrap and genetic programming, IEEE Transactions on Systems, Man, and Cybernetics—Part C: Applications and Reviews 39 (January (1)) (2009) 69–79. [4] Y.-j. Sun, S. Zhang, C.-x. Miao, J.-m. Li, Improved BP neural network for transformer fault diagnosis, Journal of China University of Mining & Technology 17 (March (1)) (2007) 138–142.

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