Accuracy Improvement of Transformer Faults Diagnostic Based on DGA Data Using SVM-BA Classiﬁer

energies

Article Accuracy Improvement of Transformer Faults Diagnostic Based on DGA Data Using SVM-BA Classiﬁer

Youcef Benmahamed 1 , Omar Kherif 1 , Madjid Teguar 1, Ahmed Boubakeur 1 and Sherif S. M. Ghoneim 2,*

1 Research Laboratories, National Polytechnic School (ENP), B.P 182, El-Harrach, Algiers 16200, Algeria; [email protected] (Y.B.); [email protected] (O.K.); [email protected] (M.T.); [email protected] (A.B.) 2 Electrical Engineering Department, College of Engineering, Taif University, Taif 21944, Saudi Arabia * Correspondence: [email protected]

Abstract: The main objective of the current work was to enhance the transformer fault diagnostic accuracy based on dissolved gas analysis (DGA) data with a proposed coupled system of support vector machine (SVM)-bat algorithm (BA) and Gaussian classifiers. Six electrical and thermal fault classes were categorized based on the IEC and IEEE standard rules. The concentration of five main combustible gases (hydrogen, methane, ethane, ethylene, and acetylene) was utilized as an input vector of the two classifiers. Two types of input vectors have been tested; the first input type considered the five gases in ppm, and the second input type considered the gases introduced in the percentage of the sum of the five gases. An extensive database of 481 had been used for training and testing phases (321 data samples for training and 160 data samples for testing). The SVM model conditioning parameter “λ” and penalty margin parameter “C” were adjusted through the bat algorithm to develop a maximum accuracy rate. The SVM-BA and Gaussian classifiers’ accuracy was

Citation: Benmahamed, Y.; Kherif, evaluated and compared with several DGA techniques in the literature. O.; Teguar, M.; Boubakeur, A.; Ghoneim, S.S.M. Accuracy Keywords: transformer faults; SVM-BA classiﬁer; DGA; DGALab Improvement of Transformer Faults Diagnostic Based on DGA Data Using SVM-BA Classiﬁer. Energies 2021, 14, 2970. https://doi.org/10.3390/ 1. Introduction en14102970 The insulation system state of the power transformers is responsible for determining the transformers’ lifetime. It is generally exposed to a couple of defects arising from Academic Editor: Ayman El-Hag overheating, paper carbonization, arcing, and discharges of low or high energy [1–3]. These faults might accelerate the insulation degradation, affecting the transformer reliability and Received: 15 April 2021 lifetime [4]. Early detection of these faults can avoid the undesired abnormal operating Accepted: 19 May 2021 Published: 20 May 2021 conditions or transformer outages [5,6]. Several DGA techniques in the literature were proposed to detect the faults in trans-

Publisher’s Note: MDPI stays neutral formers, but in some cases, these DGA techniques’ diagnostic accuracy is inadequate. with regard to jurisdictional claims in The dissolved gas analysis (DGA) technique considers one of the fastest and economical published maps and institutional affil- techniques widely used to diagnose the transformer fault types of the insulation system [7]. iations. The insulating oil decomposes into hydrocarbon products, which are categorized as combustible and incombustible gases. The five main combustible gases are Hydrogen (H2), Methane (CH4), Acetylene (C2H2), Ethylene (C2H4), and Ethane (C2H6), which might be generated within the oil during a faulty mode [1]. The concentrations of these gases were used as an input vector to interpret the DGA results in transformer oil, associated with six Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. basic electrical and thermal faults [4,8]. Different DGA techniques have been developed This article is an open access article to diagnose the transformer faults, including graphical DGA methods (e.g., [1,9–11]) and distributed under the terms and artificial intelligence techniques (e.g., [12,13]). Improved coupled techniques have also conditions of the Creative Commons been developed to diagnose multiple transformer faults and quantitatively indicate each Attribution (CC BY) license (https:// fault’s likelihood (e.g., [14]). creativecommons.org/licenses/by/ Artificial intelligence techniques such as artificial neural networks (ANN) can combine 4.0/). with the traditional DGA techniques to enhance the diagnostic accuracy of the transformer

Energies 2021, 14, 2970. https://doi.org/10.3390/en14102970 https://www.mdpi.com/journal/energies Energies 2021, 14, 2970 2 of 17

faults, such as the California State University Sacramento artificial neural network method (CSUS-ANN) [13]. The CSUS-ANN DGA technique used the gas concentration percentage from the five main combustible gases as inputs to the backpropagation neural network to determine the transformer faults based on the training process of DGA samples with knowing transformer fault types. Ghoneim and Taha [15] proposed a new approach (clustering) to enhance the diagnostic transformer faults by developing new gas ratios with the IEC ratios and defining its limits to improve diagnostic accuracy. The traditional IEC code 60599 and Rogers’ four ratios gave a poor diagnostic accuracy of the transformer faults. Enhancing the diagnostic accuracy by modifying the two previous DGA methods’ ratio limits using the particle swarm optimization with fuzzy logic is presented [6]. The conditional probability in [16] introduced a new concept using the likelihood of the faults’ occurrence and the likelihood of un-occurrence of the fault via the mean and standard deviation of the two events’ DGA samples. The conditional probability of the fault occurrence is identified using the multivariate normal probability density function. Three scenarios were developed depending on how to separate among the different faults. All these techniques are merged into one software package (DGALab), which is own as in [17] to facilitate the comparison process between them and any new proposed DGA techniques with the advantage of using an extensive database of DGA samples [17,18]. In this paper, SVM-BA and Gaussian classifiers have been used to detect faults within an oil-immersed power transformer. The concentration of gases in the ppm and percentage of the sum of the five main combustible gases have been used as an input vector for Gaussian and SVM classifiers. Kernel parameter λ and penalty margin C of the SVM model have been optimized by a Bat algorithm (SVM-BA) to adjust the model, getting a high diagnostic accuracy. Electrical and thermal transformer faults have characterized the output of each classifier including partial discharge (PD), low energy discharges (D1), high energy discharges (D2), thermal faults < 300 ◦C (T1), thermal faults of 300 ◦C to 700 ◦C (T2), and thermal faults > 700 ◦C (T3) [1]. The performance of each classifier has been investigated in terms of accuracy rate. A total of 481 sample datasets have been considered, where two-thirds were used for the training process (321 samples) while the rest was used for the testing process (160 samples). A comparative study was accomplished with the other DGA techniques in the literature to identify the proposed DGA technique’s diagnostic improvement. The current work presents a classification technique (SVM-BAT and Gaussian classifiers) to enhance the transformer faults’ diagnostic accuracy, which considers one of the new trends in condition monitoring and diagnostics of power system assets.

2. Problem Formulation Highly reliable transformers are mainly made of iron core and windings; both are placed in the oil tank ﬁlled with insulating oil, as shown in Figure1. Mineral insulating oil is the most common type of oil used in outdoor transformers [19]. This insulating oil has signiﬁcant dielectric strength so that it can withstand a pretty high voltage. It also reduces heat generated by transformer windings employing the cooler (radiators, air fans, ... ). Therefore, the heat generated in the transformer results in a temperature rise in the internal transformer structures. Under electrical and thermal stresses, different hydrocarbon gases are liberated due to the insulating oil decomposition. Particular gases characterize each type of fault. For instance, hydrogen concentration, produced by ionic bombardment, increases with partial discharges within a transformer oil. In this context, a general review about the gases produced during the deterioration of mineral oil and their interpretation has been detailed in [10]. Energies 20212021,, 1414,, 2970x FOR PEER REVIEW 3 of 16 17

Figure 1. Oil-immersedOil-immersed power power transformer cross-section.

MineralEarly-stage insulating detection oil is of the these most faults common should ty bepe carriedof oil used out in to outdoor avoid the transformers undesired abnormal operating conditions or transformer outages. For this purpose, periodic monitor- [19]. This insulating oil has significant dielectric strength so that it can withstand a pretty ing of the oil should be conducted during transformer service, whether in-situ or at the high voltage. It also reduces heat generated by transformer windings employing the laboratory, using a multi-stage gas-extractor (a device for sampling transformer oil) [10]. In cooler (radiators, air fans, …). Therefore, the heat generated in the transformer results in general, the most important gases are Hydrogen (H ), Methane (CH ), Acetylene (C H ), a temperature rise in the internal transformer structures.2 Under electrical4 and thermal2 2 Ethylene (C H ), and Ethane (C H ). The distribution of these gases is related to the type of stresses, different2 4 hydrocarbon 2gases6 are liberated due to the insulating oil decomposition. transformer fault, and the rate of gas generation can indicate the severity of the fault [5,20]. Particular gases characterize each type of fault. For instance, hydrogen concentration, pro- In [6], the authors have collected 481 samples associating with the six different faults duced by ionic bombardment, increases with partial discharges within a transformer oil. as indicated in the Introduction (i.e., PD, D1, D2, T1, T2, and T3). The number of samples In this context, a general review about the gases produced during the deterioration of associated with each fault is given in Table1. mineral oil and their interpretation has been detailed in [10]. TableEarly-stage 1. Database distribution.detection of these faults should be carried out to avoid the undesired abnormal operating conditions or transformer outages. For this purpose, periodic monitoring of theDefect oil should be conducted Interpretationduring transformer service, whether Number ofin-situ Samples or at the laboratory, PDusing a multi-stage gas-extractor Partial discharge (a device for sampling transformer 48 oil) [10]. In general, the most important gases are Hydrogen (H2), Methane (CH4), Acetylene (C2H2), D1 Low energy discharges 79 Ethylene (C2H4), and Ethane (C2H6). The distribution of these gases is related to the type of transformerD2 fault, and the rate High of energygas gene dischargesration can indicate the severity 126 of the fault [5,20]. T1 Thermal faults of <300 ◦C 95 In [6], theT2 authors have Thermal collected faults 481 of samples 300 ◦C to associating 700 ◦C with the six 48 different faults as indicated in the Introduction (i.e., PD, D1, D2, T1, T2, and T3). The number of samples T3 Thermal faults of >700 ◦C 85 associated with each fault is given in Table 1. All 481 Table 1. Database distribution.

DefectThedatabase set has beenInterpretation exploited in the present investigationNum tober detect of Samples and identify faults.PD As shown in this table,Partial only discharge separated faults (no combined faults) have48 been considered. The fault detection has been examined using the concentration of each dissolved gas. D1 Low energy discharges 79 Since the weight percent of the gases as mentioned earlier would result in an inopportunely D2 High energy discharges 126 small number, concentration in parts per million, or ppm, has been considered for each gas. T1 Thermal faults of < 300 °C 95 Furthermore, percent concentration of the total sum was also used, where each sample T2 Thermal faults of 300 °C to 700 °C 48 X = [x , x ,..., x ] is scaled as follows: T31 2 5 Thermal faults of > 700 °C 85 All X 481 = × X 5 100% (1) ∑i=1 xi

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The database set has been exploited in the present investigation to detect and identify faults. As shown in this table, only separated faults (no combined faults) have been considered. The fault detection has been examined using the concentration of each dissolved gas. Since the weight percent of the gases as mentioned earlier would result in an inopportunely small number, concentration in parts per million, or ppm, has been considered for each gas. Furthermore, percent concentration of the total sum was also used, where Energies 2021, 14, 2970 each sample X = [x1, x2, …, x5] is scaled as follows: 4 of 17 𝑋 X = 100% (1) ∑ 𝑥 TheThe faultsfaults diagnostic diagnostic method method has has been been carried carried out out elaborating elaborating two two different different classiﬁers, classifi- namelyers, namely Gaussian Gaussian and SVM-BA.and SVM-BA. The ﬂowchartThe flowchart given given in Figure in Figure2 summarizes 2 summarizes the various the var- stagesious stages of the of diagnostic the diagnostic approach. approach.

FigureFigure 2.2.Flowchart Flowchart ofof thethe problemproblem formulation.formulation.

3.3. ClassificationClassification Approach Approach ForFor both,both, Gaussian Gaussian and and SVM-BA, SVM-BA, classifier, classifier the, concentrationsthe concentrations in percentages in percentages and ppm and ofppm the fiveof the dissolved five dissolved gases have gases been have used been as anused input as an vector, input denoted vector, bydenotedX = [x 1by, x 2X,..., = [x1x, 5x]2,, associated…, x5], associated with a particular with a particular class of faultclass (denoted of fault (denoted by y) representing by y) representing the classifier the decisionclassifier (classifierdecision (classifier output). output).

3.1.3.1. GaussianGaussian ClassifierClassifier InIn thisthis part,part, the Gaussian Gaussian classification classification is is used used as as a aprobabilistic probabilistic learning learning method method for forconstructing constructing a classifier a classifier by applying by applying Bayes’ Bayes’ theorem. theorem. It concerns It concerns the conditional the conditional and mar- and marginal probabilities of two random events. The classifier is based on the comparison of ginal probabilities of two random events. The classifier is based on the comparison of the the posterior probability P (wi|x): posterior probability P (wi|x):

P(𝑃x(|w𝑥|i𝑤)P )( w𝑃i()𝑤) P(w𝑃(i|𝑤x)|𝑥=) = , i =, 𝑖1, 2, = . 1,2 .,...,6 . , 6 (2)(2) P(𝑃x)(𝑥)

wherewhereP P (x|w (x|wii)) isis thethe conditionalconditional probabilityprobability (likelihood)(likelihood) givengiven by:by:

6 P(x|wi) = ∏ P(xk|wi) (3) k=1

and P(x) is the unconditional density that normalizes the posteriors, computed as follows:

6 P(x) = ∑ P(x|wi)P(wi) (4) i=1

in which P(wi) is the prior probability of each class. Energies 2021, 14, 2970 5 of 17

Firstly, the training phase has been carried out for constructing the parameters of the Gaussian model. In this phase, 321 samples of the data set have been reserved to determine the Gaussian distributions, consisting of the mean value (µ) and the matrix covariance (σ) of the gas concentration for each defect class. Since the number of samples differs from one fault to another, every distribution is multiplied by a weight corresponding to its samples’ number on the database’s total size. In the next step, Gaussian has been employed to compute the conditional probability P (x|wi) as indicated in Equation (3), where the posterior probability is calculated using the probability density function of a univariate normal distribution as follows:

2 1 (xk−m) 1 − 2 2 P(xij|wk) = √ e σ (5) 2πσ2 Since it is required to know the likelihood of observing the k-th sample while con- sidering all the different distributions, one can sum the likelihood of observing the given sample from each possible Gaussian, using:

exp[− 1 X − µ)Tσ−1(X − µ) P(x |w ) = 2 (6) k i 6/2p (2π) |σ|

in which, |σ| and σ−1 denote the determinant and inverse of the covariance matrix σ. Each Gaussian model’s parameters (i.e., variance, mean, and weight) have been addressed to cluster the data and estimate those having the same parameters. Moreover, a maximum likelihood estimate (MLE) was used to ﬁnd the optimal mean and variance, maximizing the data’s likelihood. After training the model, the classiﬁer output ideally ends up with six distributions on the same axis. Depending on the axis’s location, each Energies 2021, 14, x FOR PEER REVIEWtesting sample (a total of 160 testing ones) is placed in one of the defect classes.6 of 16 Figure3

illustrates the different steps of the Gaussian classiﬁer.

FigureFigure 3. Flowchart 3. Flowchart formulating formulating the problem the problem using using Gaussian Gaussian classiﬁer. classifier.

3.2. SVM Classifier Coupled with BA SVMs techniques are used in the problem of classification, regression, and prediction models [21]. For the classification problems, hyperplanes are required in a multidimen- sional space separating data points of both fault classes. These hyperplanes are used to distinguish between every two classes (yi and yj) of faults associated with two different input vectors (Xi and Xj) [22–24]. Among these hyperplanes, it is suggested to find the one that has the maximum margin (denoted by M). In this light, the classification becomes an optimization problem where hyperplanes represent the decision boundaries that help classify the data points. Usually, an orthogonal vector (denoted by ω) to the hyperplane defined by:

𝜔=[𝜔,𝜔,...,𝜔] (7) which is used in combination with an input vector (Xi) to define the hyperplane function, h, as follows [22]:

ℎ(𝑋)=𝑤 . 𝑋 +𝜔 =𝜔 +𝜔.𝑥 (8)

The 𝜔 is the bias term required to determine the position of separating hyperplane (i.e., h (X) = 0). A learning strategy of One-to-One is selected. It is assumed that Xi is of class “1” if h (Xi) ≥ 0 and, consequently, it is of class “−1” elsewhere. Assuming that Xi and Xj are the two closest points on each side of the hyperplane (different classes), the equations for the hyperplanes h (Xi) and h (Xj) become:

ℎ(𝑋)=𝑤 .𝑋 +𝜔 =1 (9) and

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3.2. SVM Classifier Coupled with BA SVMs techniques are used in the problem of classification, regression, and prediction models [21]. For the classification problems, hyperplanes are required in a multidimen- sional space separating data points of both fault classes. These hyperplanes are used to distinguish between every two classes (yi and yj) of faults associated with two different input vectors (Xi and Xj)[22–24]. Among these hyperplanes, it is suggested to find the one that has the maximum margin (denoted by M). In this light, the classification becomes an optimization problem where hyperplanes represent the decision boundaries that help classify the data points. Usually, an orthogonal vector (denoted by ω) to the hyperplane defined by: ω = [ω1, ω2,..., ωk] (7) which is used in combination with an input vector (Xi) to define the hyperplane function, h, as follows [22]: k T h(Xi) = w . Xi + ω0 = ω0 + ∑ ωi.xi (8) i=1

The ω0 is the bias term required to determine the position of separating hyperplane (i.e., h (X) = 0). A learning strategy of One-to-One is selected. It is assumed that Xi is of class “1” if h (Xi) ≥ 0 and, consequently, it is of class “−1” elsewhere. Assuming that Xi and Xj are the two closest points on each side of the hyperplane (different classes), the equations for the hyperplanes h (Xi) and h (Xj) become:

T h(Xi) = w . Xi + ω0 = 1 (9)

and T h(Xi) = w . Xi + ω0 = −1 (10) Differencing these equations and dividing both sides by the magnitude of the ω, we obtain: 2 X −X = (11) i j ||ω||

Xi − Xj is the distance between the two hyperplanes. From the expression (11), it is clear that the maximization of the margin implies the minimization of the weight vector ω used to deﬁne the hyperplane. A soft-margin SVM is utilized for nonlinear classes to provide freedom to the model misclassifying some data points by minimizing the number of such samples [23]. For this purpose, slack variable non-negatives ζi is introduced in the hyperplane equation. Consequently, the optimization problem becomes:  k  1 k k2 +  Min : 2 ω C ∑ ζi i=1 (12)  Such that : yi(ω.xi + ω0) ≥ 1 − ζi  ∀i, 0 < ζi < 1 i = 1, 2, . . . , k C represents the margin parameter, which can be seen as a regularization parameter. The corresponding Lagrangian dual problem is given by:

k k 1 2 L(ω, ω0, ζ, α) = kωk + C ∑ ζi − ∑ αi[yi(ωixi + ω0) − 1+ζi) (13) 2 i=1 i=1

αi are Lagrange coefﬁcients (multipliers). In such circumstances, the Karush–Kuhn–Kucker conditions are [14]:

k k 1 2 L(ω, ω0, ζ, α) = kωk + C ∑ ζi − ∑ αi[yi(ωixi + ω0) − 1+ζi) (14) 2 i=1 i=1 Energies 2021, 14, 2970 7 of 17

Setting the derivatives as mentioned earlier of the Lagrangian and ω0 individually to 0, it follows that the Lagrangian expression should be maximized under the constraint:

k ∑ αiyi = 0 (15) i=1

and it also yields C = αi + ζi (16) Since the data are assumed as non-separable, the feature space has been enlarged by a characteristic function Φ known as Kernel function. Every data point has been mapped into high-dimensional space through a particular transformation Φ: X 7→ φ (X). Polynomial Kernel function of d–degree has been used in this investigation as follows [23]:

0 d K xi, xj = (C + x.x ) (17)

which veriﬁes the following condition: φ(xi).φ xj = K xi, xj (18)

In this case, the optimization problem after rearrangement becomes as follows:

 k k k  Max α − 1 α α y y (x ) x  : ∑ i 2 ∑ ∑ i j i jΦ i Φ j  i=1 i=1 j=1 Subject to : ∀i ∈ {1, 2, . . . , k}, C ≥ αk ≥ 0 (19)  m   ∑ αi.xi = 0 i=1

SVM parameters consisting in: • Kernel parameter λ (conditioning parameter equivalent σ in RBF kernel [24]); • penalty parameter C (margin parameter); and • degree d of the Kernel polynomial. significantly affect the accuracy of predicting model. To further improve the accuracy rate, the bat algorithm (BA) has been elaborated in this investigation to optimize the SVM parameters. BA is part of meta-heuristic algorithms for global optimization, intended (by Xin-She Yang in 2010) to simulate prey’s sensing distance and avoid obstacles using micro- bats echolocation behavior [23]. In BA, the aim is reached by determining the optimum parameters C and λ that give the best accuracy rate of the SVM classifier. The degree of a polynomial kernel has been fixed at d = 1, 2, and 3. Figure4 illustrates the different steps of the coupled SVM-BA classifier. In the beginning, BA parameters have been initialized. Table2 lists the detailed settings for the BA values used to optimize the SVM model. Energies 2021, 14, 2970 8 of 17 Energies 2021, 14, x FOR PEER REVIEW 9 of 16

FigureFigure 4.4. FlowchartFlowchart formulatingformulating SVM-BASVM-BA Classiﬁer.Classifier.

TableThe parameter 2. Parameters fi denotes of Bat algorithm. the frequency, which is computed as follows: =+ β Parameterfiminmaxmin f (f -) f Value (21) in which β is a Populationrandom number size ranging between 0 and 1. 50 It is worth notingLoudness that the searching space has been bounded 0.5 by Cmin = 10−6 and Cmax = −7 0.1 for the parameterFrequency ( fCmin againstand fmax λ)min = 10 and λmax = 0.7 for the second0 and 20 parameter λ. More- over, the pulseNumber rate increased of iterations according to the iteration number as 600 follows: Pulse rate𝑟 = 𝑟 + [1−𝑒𝑥𝑝(−𝛾𝑡)] 0.5 (22) while the loudness decreased by: Therefore, BA generates a population of the SVM parameters (C, λ). For each couple, 𝐴 = 𝜎𝐴, 0 < 𝜎 < 1 (23) the initial position p and velocity v have been randomly selected. Each couple’s fitness has been evaluated to extract the best global position (denoted by p∗). This means that the training4. Experimental dataset is Work used to train the SVM classifier for each position, while the testing dataset is usedDuring to calculate transformers’ the accuracy operation, rate. This the latterinsulati representson of transformer the ratio between coils is thesubjected number to ofhigh correctly electrical classified and thermal samples stresses (Nc) tocausing the total corro numbersion of of some test samplesinsulating (N material). After this particles step, theand position decomposition and velocity of some of each insulating individual oil areparticles updated producing using the different following types expressions: of gases. These gases dissolve in the transformer oil. At the beginning of any slight fault, the gases pt+1 = pt + vt are not released largely enough to operatei thei gasi protection device that does not cause(20) vt+1 = vt + (pt − p∗) f instantaneous breakdown, but the itransformeri efficiencyi i is reduced. Thet gases thatt+1 were used to diagnose the transformers’ state include Hydrogent (H2), where vi and vi are current, and the next velocities correspond to the existing pi and Methane (CHt+1 4), Acetylene (C2H2), Ethylene (C2H4), Ethane (C2H6), carbon monoxide (CO), the next pi positions, respectively. and carbon dioxide (CO2). Hence, chromatographic analysis (CA) of dissolved gases in

Energies 2021, 14, 2970 9 of 17

The parameter fi denotes the frequency, which is computed as follows:

fi = fmin + ( fmax − fmin)β (21)

in which β is a random number ranging between 0 and 1. −6 It is worth noting that the searching space has been bounded by Cmin = 10 and −7 Cmax = 0.1 for the parameter C against λmin = 10 and λmax = 0.7 for the second parameter λ. Moreover, the pulse rate increased according to the iteration number as follows:

t+1 0 ri = ri + [1 − exp(−γt)] (22)

while the loudness decreased by:

t+1 0 Ai = σAi , 0σ < 1 (23)

4. Experimental Work During transformers’ operation, the insulation of transformer coils is subjected to high electrical and thermal stresses causing corrosion of some insulating material particles and decomposition of some insulating oil particles producing different types of gases. These gases dissolve in the transformer oil. At the beginning of any slight fault, the gases are not released largely enough to operate the gas protection device that does not cause instantaneous breakdown, but the transformer efﬁciency is reduced. The gases that were used to diagnose the transformers’ state include Hydrogen (H2), Methane (CH4), Acetylene (C2H2), Ethylene (C2H4), Ethane (C2H6), carbon monoxide (CO), and carbon dioxide (CO2). Hence, chromatographic analysis (CA) of dissolved gases in transformer oils is considered as an analysis method that reveals small percentages of dissolved gases in the oil. The CA of gases indicates the transformers’ condition in the early stage of the fault occurrence. Thus, the transformers can be preserved and decrease the transformer failure before a transformers’ complete breakdown occurs. The CA results’ accuracy depends on drawing the transformer’s oil sample, extracting the dissolved gases from the oils’ samples, and adjusting the analyzer device. The CA must be carried out at the start of the transformers’ operation, and its results are considered a reference when analyzing this transformer later. American Society for Testing and Materials (ASTM) D3612-2 [24] indicates the dissolved gases’ extracting procedures from the transformer oils’ samples using gas chromatography (GC). The GC consists of the mobile phase (including three types of gases the carrier gas, the fuel gas, and zero air), the sample injector, the column, the columns’ oven, the detector, and the data system. Oil samples were prepared and ﬁlled with glass vials by a sampling device. Then, they were placed into the Autosampler unit. Hence, one by one, the samples were analyzed, and inserted into the oven at 80 ◦C. The dissolved gases are extracted by increasing the temperature by moving the oil sample. Hence, the extracted gases are injected into the GC to accomplish the gases’ analysis [25]. Figure5 illustrates the oil samples’ drawing process from the transformer and the GC device (8890 Gas Chromatograph (GC) System and 7697A Headspace Sampler, Agilent, USA). The GCs’ analysis results are shown in Figure6, illustrating the time required to extract each gas and its concentration in ppm. The chromatograph provides a signal with time, which produces the familiar chromatogram. The chromatogram signal can be converted into a list of peak times and sizes by either manual or electronic means [26]. Energies 2021, 14, x FOR PEER REVIEW 10 of 16

transformer oils is considered as an analysis method that reveals small percentages of dissolved gases in the oil. The CA of gases indicates the transformers’ condition in the early stage of the fault occurrence. Thus, the transformers can be preserved and decrease the transformer failure before a transformers’ complete breakdown occurs. The CA results’ accuracy depends on drawing the transformer’s oil sample, extracting the dissolved gases from the oils’ samples, and adjusting the analyzer device. The CA must be carried out at the start of the transformers’ operation, and its results are considered a reference when analyzing this transformer later. American Society for Testing and Materials (ASTM) D3612-2 [24] indicates the dissolved gases’ extracting procedures from the transformer oils’ samples using gas chromatography (GC). The GC consists of the mobile phase (including three types of gases the carrier gas, the fuel gas, and zero air), the sample injector, the column, the columns’ oven, the detector, and the data system. Oil samples were prepared and filled with glass vials by a sampling device. Then, they were placed into the Autosampler unit. Hence, one by one, the samples were analyzed, and inserted into the oven at 80 °C. The dissolved gases are extracted by increasing the temperature by moving the oil sample. Hence, the extracted gases are injected into the GC to accomplish the gases’ analysis [25]. Figure 5 illustrates the oil samples’ drawing process from the transformer and the GC device (8890 Gas Chromatograph (GC) System and 7697A Headspace Sampler, Ag- ilent, USA). The GCs’ analysis results are shown in Figure 6, illustrating the time required Energies 2021, 14, 2970 to extract each gas and its concentration in ppm. The chromatograph provides a10 signal of 17 with time, which produces the familiar chromatogram. The chromatogram signal can be converted into a list of peak times and sizes by either manual or electronic means [26].

Energies 2021, 14, x FOR PEER REVIEWFigure 5. Drawing the oil sample from the transformer and the 8890 Gas Chromatograph (GC)11 of 16 Figure 5. Drawing the oil sample from the transformer and the 8890 Gas Chromatograph (GC) SystemSystem andand 7697A7697A HeadspaceHeadspace Sampler,Sampler, Agilent, Agilent, USA. USA.

Figure 6. GasGas Chromatography Chromatography result.

5. Results Results and and Discussions Discussions A database database set of of 481 481 samples samples has has been been exploi exploitedted to to evaluate evaluate each each classifiers’ classifiers’ accuracy accuracy rate.rate. As As stated stated in in Section Section 22,, 321321 samplessamples ofof thethe datadata setset werewere usedused inin thethe trainingtraining phase,phase, while the rest was used for testing (160 samples).samples). The data distribution was based on the holdout method; more than 60% of the database must be reserved for the training phase (2/3 for for the the training training set set and and the the remaining 1/3 as as the the test test set) set) [27]. [27]. Both Both data parts were randomlyrandomly selected, selected, and and they they were were used used in inall allsimulations. simulations. DGA DGA results results in percentages in percentages (i.e., percentages(i.e., percentages of the of total the total sum) sum) and and ppm ppm have have been been considered considered an an input input vector vector for for both classifiers.classifiers. As As mentioned mentioned previously previously for for SVM, SVM, the Kernel polynomial and a one-to-one learninglearning strategystrategy werewere selected. selected. The The classifiers’ classifiers’ results results were were compared compared regarding regarding inspection inspection(the (the real real fault fault in the in transformer)the transformer) as in as Table in Table3. In 3. Table In Table3, some 3, some cases cases were were illustrated illustrated to toexplain explain the the comparison comparison between between the the SVM-BA SVM-BA and and Gaussian Gaussian classifier classifier for gasesfor gases in ppm in ppm and andgases gases percentages. percentages.

Table 3. Diagnosis results of some cases.

Gaussian SVM-BA (In- SVM-BA (In- Gaussian (In- Inspec- (Input H2 CH4 C2H2 C2H4 C2H6 put Vector in put Vector in put Vector in tion Vector in ppm) Percentage) Percentage) ppm) 2587.2 112.25 0 1.4 4.704 PD PD D2 * PD PD 6870 1028 5500 900 79 D1 D1 D1 D1 D2 * 84 6 86 14 1 D2 D2 T3 * D1 * D1 * 92 27 0 7 67 T1 T1 T3 * T1 T1 960 4000 6 1560 1290 T2 T3* T3 * T2 T3 * 1374 2648 298 5376 628 T3 T3 T3 T3 T3 (*) denotes that diagnosis is wrong based on the inspection.

Not only the type of input vector influences the accuracy rate in the SVM algorithm, but in the experience of previous investigations, the degree of the polynomial kernel can also affect the diagnostic accuracy [28]. Figure 7 shows the impact of vector input type on the classification performance for the SVM-BA classifier’s evolution during the optimization process. This latter has been illustrated in Figure 7a,b when the input vector calculates gases in percentages and ppm, respectively, with different polynomial kernel degrees.

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Table 3. Diagnosis results of some cases.

SVM-BA Gaussian SVM-BA Gaussian H2 CH4 C2H2 C2H4 C2H6 Inspection (Input Vector (Input Vector (Input Vector (Input Vector in ppm) in ppm) in Percentage) in Percentage) 2587.2 112.25 0 1.4 4.704 PD PD D2 * PD PD 6870 1028 5500 900 79 D1 D1 D1 D1 D2 * 84 6 86 14 1 D2 D2 T3 * D1 * D1 * 92 27 0 7 67 T1 T1 T3 * T1 T1 960 4000 6 1560 1290 T2 T3* T3 * T2 T3 * 1374 2648 298 5376 628 T3 T3 T3 T3 T3 (*) denotes that diagnosis is wrong based on the inspection.

Not only the type of input vector influences the accuracy rate in the SVM algorithm, but in the experience of previous investigations, the degree of the polynomial kernel can also affect the diagnostic accuracy [28]. Figure7 shows the impact of vector input type on the classification performance for the SVM-BA classifier’s evolution during the optimiza- Energies 2021, 14, x FOR PEER REVIEW 12 of 16 tion process. This latter has been illustrated in Figure7a,b when the input vector calculates gases in percentages and ppm, respectively, with different polynomial kernel degrees.

90 Accuracy rate (%) rate Accuracy

86 d = 2 d = 1 d = 3

0 100 200 300 400 500 600 Iteration (a) 88

80 Accuracy rate (%) rate Accuracy

d = 1 d = 2 d = 3

0 50 100 150 200 250 300 Iteration

(b)

Figure 7.Figure SVM-BA 7. classifierSVM-BA evolution classiﬁer duri evolutionng the optimization during the process: optimization (a) DGA in process: percentage; (a) ( DGAb) in percentage; DGA in ppm. (b) DGA in ppm. For a given degree of Kernel polynomial, it is clear that 300 iterations are mainly sufficient for the convergence of the SVM-BA algorithm. The results showed that the SVM- BA classifier’s accuracy rate is quite sensitive to the degree of Kernel polynomial. For an input vector taken in percentages as shown in Figure 7a, the maximal accuracy rate is 93.13% with d = 2 and 3 against 91.88% with d = 1. On the other hand, notably lower results have been found in Figure 7b for an input vector in ppm where the highest accuracy is 87.5% obtained for d = 1 against 82.5% and 78.13% for d = 2 and 3, respectively. However, the convergence for d = 3 is very fast compared to those found for d = 2 and d = 1. The previous simulation, related to the SVM-BA classifier and shown in Figure 7, is repeated 50 times to find the best accuracy rate to provide more credibility of the obtained results. Figure 8 illustrates an example of the accuracy rate versus the number of runs (i.e., executions) when using DG in percentages as an input vector for the SVM-BA classifier. These results have been computed for the Kernel polynomial of d = 1, 2, and 3 degrees.

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For a given degree of Kernel polynomial, it is clear that 300 iterations are mainly sufficient for the convergence of the SVM-BA algorithm. The results showed that the SVM-BA classifier’s accuracy rate is quite sensitive to the degree of Kernel polynomial. For an input vector taken in percentages as shown in Figure7a, the maximal accuracy rate is 93.13% with d = 2 and 3 against 91.88% with d = 1. On the other hand, notably lower results have been found in Figure7b for an input vector in ppm where the highest accuracy is 87.5% obtained for d = 1 against 82.5% and 78.13% for d = 2 and 3, respectively. However, the convergence for d = 3 is very fast compared to those found for d = 2 and d = 1. The previous simulation, related to the SVM-BA classifier and shown in Figure7, is repeated 50 times to find the best accuracy rate to provide more credibility of the obtained results. Figure8 illustrates an example of the accuracy rate versus the number of runs (i.e., Energies 2021, 14, x FOR PEER REVIEW 13 of 16 executions) when using DG in percentages as an input vector for the SVM-BA classifier. These results have been computed for the Kernel polynomial of d = 1, 2, and 3 degrees.

94 d = 1 d = 2 d = 3 (%) Accuracy rate

91 0 10 20 30 40 50 Number of runs FigureFigure 8. 8.The The accuracy accuracy rate rate of of the the SVM-BA SVM-BA classiﬁer classifier over over the the running running number. number.

InIn Figure Figure8 ,8, the the best best accuracy accuracy rate rate obtained obtained for for different different executions executions is is located located between between 91%91% and and 94%. 94%. The The global global best best results results related related to to the the accuracy accuracy rate rate obtained obtained for for several several runs runs areare presented presented in in Table Table4. 4. Additionally, Additionally, DGA DGA has has been been elaborated elaborated in in ppm ppm and and percentages percentages forfor the the input input vector. vector.

TableTable 4. 4.The The accuracy accuracy rate rate for for both both classiﬁers classifiers after after 50 50 executions. executions.

SVM-BA Classifier Gaussian SVM-BA Classifier Gaussian d = 1 d = 2 d = 3 d = 1 d = 2 d = 3 DGA in percentages 69.37 % 93.13% 93.75% 93.75% DGA in DGA in ppm69.37 % 93.13%32.75 % 87.50% 93.75% 82.50% 93.75% 78.13% percentages DGAFor in SVM-BA, ppm the 32.75results % are given for 87.50% three degrees of 82.50% Kernel polynomial. 78.13% After 50 executions, it was found that the maximal accuracy rate was 93.75% with d = 2 and 3 againstFor 93.13% SVM-BA, with the d = results 1 obtained aregiven when foremploying three degrees an input of vector Kernel in polynomial. percentages. AfterWhen 50using executions, the dissolved it was gases found in that ppm the as maximal input ve accuracyctor for the rate SVMBA, was 93.75% the computed with d = 2 andresults 3 againstdecreased 93.13% to 87.50% with d for= 1 d obtained = 1 against when 89.75% employing for d = an2 and input 3. This vector implies in percentages. that the SVM-BA When usingclassifier the dissolvedgives a better gases accuracy in ppm rate as for input an vectorinput vector for the given SVMBA, in percentages. the computed On the results other decreasedhand, Gaussian to 87.50% classifier for d = gives 1 against the lowest 89.75% accuracy for d = 2 andrate 3.of This32.75% implies when that the the input SVM-BA vector classifieremployed gives in ppm a better compared accuracy to rate an foraccuracy an input ra vectorte of 66.25% given inwhen percentages. the input On vector the other is in hand,percentages. Gaussian This classifier ascertainment gives the demonstrates lowest accuracy the rateconcentration of 32.75% whenof gases the in input percentages vector employedto differentiate in ppm between compared a particul to anar accuracy defect from rate the of 66.25%other ones. when the input vector is in For the Gaussian classifier, it should be noted that the results have been dramatically improved when the real part of the posterior probability given by the expression (6) is employed. In this case, the accuracy rate has been increased to 70% for percentages input in while it remains the same (i.e., 32.75%) for an input vector in ppm. Such findings suggest using the real part of posterior Probability in Gaussian classifier with an input vector in percentages. Compared to other literature results, the SVM-BA classifier has good accuracy and has high abilities to diagnose the transformer fault classes with simple codes. The overall accuracy obtained in [6] for the same database in ppm is a good example of this.

6. Validation and Overall Accuracy of the Proposed SVM-BA Classifier The SVM-BA and Gaussian classifiers are compared with various classification algorithms used in the DGALab interface to evaluate the proposed method’s accuracy [17]. The free DGALab software package is available in [18]. DGALab involves the Duval tri-

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percentages. This ascertainment demonstrates the concentration of gases in percentages to differentiate between a particular defect from the other ones. For the Gaussian classifier, it should be noted that the results have been dramatically improved when the real part of the posterior probability given by the expression (6) is employed. In this case, the accuracy rate has been increased to 70% for percentages input in while it remains the same (i.e., 32.75%) for an input vector in ppm. Such findings suggest using the real part of posterior Probability in Gaussian classifier with an input vector in percentages. Compared to other literature results, the SVM-BA classifier has good accuracy and has high abilities to diagnose the transformer fault classes with simple codes. The overall accuracy obtained in [6] for the same database in ppm is a good example of this.

6. Validation and Overall Accuracy of the Proposed SVM-BA Classifier The SVM-BA and Gaussian classifiers are compared with various classification algorithms used in the DGALab interface to evaluate the proposed method’s accuracy [17]. The free DGALab software package is available in [18]. DGALab involves the Duval triangle method, IEC code 60599, Roger’s four ratios, modified IEC code and Modified Rogers’ 4 ratios, clustering method, conditional probability, and California State University Sacra- mento artificial neural network method (CSUS-ANN). The details of the whole algorithms are cited in [15–17]. A comparison among all these mentioned methods was carried out based on the individual fault accuracy and overall accuracy rate (Table5). The last row in Table5 illustrates the total number of samples used for testing purposes and the overall accuracy of each DGA method for comparison purposes. From the evaluation exposed in Table5, the SVM-BA provides the best overall accuracy rate (93.75%). This superiority came from the ability of SVM to classify the complex and extensive data set. Moreover, the coupling of SVM with the BAT algorithm enabled the right choice of parameters which gave the highest possible accuracy rate. The nearest overall accuracy of the proposed method is the modified IEC code, which showed an 88.75% overall accuracy rate. The worst overall accuracy rate is the Rogers’ four ratio DGA method, for which the overall accuracy is 53.75%. The results in Table5 are recapitulated in Figure9 in a histogram form. Energies 2021, 14, 2970 14 of 17

Table 5. Accuracy rate table of different techniques.

Duval IEC Rogers’ 4 Modiﬁed Modiﬁed Rogers’ Conditional ACT Clustering CSUS ANN SVM-BA Gaussian Triangle Code-60599 Ratios IEC Code 4 Ratios Probability PD 16 93.75 43.75 37.5 8.5 75 93.75 100 8.5 87.5 81.25 D1 26 76.92 26.92 0 76.92 84.61 84.61 76.92 69.23 92.31 34.61 D2 42 85.71 66.66 73.80 90.47 88.09 85.71 97.61 92.85 95.24 78.57 T1 32 65.62 53.125 90.62 93.75 93.75 93.75 87.5 93.75 93.75 90.62 T2 16 50 68.75 25 93.75 93.75 31.25 81.25 43.75 87.5 0 T3 28 100 82.14 57.14 89.28 89.28 85.7 82.14 71.42 96.48 100 All 160 80 58.12 53.75 88.75 88.12 82.5 88.12 80 93.75 69.37 Energies 2021, 14, x FOR PEER REVIEW 14 of 16

angle method, IEC code 60599, Roger’s four ratios, modified IEC code and Modified Rog- ers’ 4 ratios, clustering method, conditional probability, and California State University Sacramento artificial neural network method (CSUS-ANN). The details of the whole algorithms are cited in [15–17]. A comparison among all these mentioned methods was carried out based on the individual fault accuracy and overall accuracy rate (Table 5).

Table 5. Accuracy rate table of different techniques.

Modi- Condi- Duval IEC Rog- fied Modified Cluster- tional CSUS Gauss- ACT Trian- Code- ers’ 4 Rogers’ SVM-BA IEC Code ing Probabil- ANN ian gle 60599 Ratios 4 Ra- ity tios PD 16 93.75 43.75 37.5 8.5 75 93.75 100 8.5 87.5 81.25 D1 26 76.92 26.92 0 76.92 84.61 84.61 76.92 69.23 92.31 34.61 D2 42 85.71 66.66 73.80 90.47 88.09 85.71 97.61 92.85 95.24 78.57 T1 32 65.62 53.125 90.62 93.75 93.75 93.75 87.5 93.75 93.75 90.62 T2 16 50 68.75 25 93.75 93.75 31.25 81.25 43.75 87.5 0 T3 28 100 82.14 57.14 89.28 89.28 85.7 82.14 71.42 96.48 100 All 160 80 58.12 53.75 88.75 88.12 82.5 88.12 80 93.75 69.37

The last row in Table 5 illustrates the total number of samples used for testing purposes and the overall accuracy of each DGA method for comparison purposes. From the evaluation exposed in Table 5, the SVM-BA provides the best overall accuracy rate (93.75%). This superiority came from the ability of SVM to classify the complex and extensive data set. Moreover, the coupling of SVM with the BAT algorithm enabled the right choice of parameters which gave the highest possible accuracy rate. The nearest overall accuracy of the proposed method is the modified IEC code, which showed an 88.75% overall accuracy rate. The worst overall accuracy rate is the Rogers’ four ratio DGA

Energies 2021, 14, 2970 method, for which the overall accuracy is 53.75%. The results in Table 5 are recapitulated15 of 17 in Figure 9 in a histogram form.

100 Duval IEC 90 Rogers4 Ratios 80 Modified IEC Modified Rogers4 ratios 70 Clustering Probability 60 CUSU SVM-BA 50 Gaussian 40 Accuracy Accuracy (%) rate 30

0 PD D1 D2 T1 T2 T3 All Fault types Figure 9. Histogram of accuracy rates.

7. Conclusions This paper proposed a newnew DGADGA techniquetechnique usingusing anan SVM-BASVM-BA classifierclassifier toto enhanceenhance the transformer faults’ diagnostic accuracy. Five main combustible dissolved gas concen- 2 4 2 6 2 4 2 2 trations (H(H2, CH4,,C C2HH6, ,CC 2HH,4 ,and and C CH2H)2 )were were used used as as an an input input vector vector top the SVM-BASVM-BA classifier to identify the transformer fault type. The concentration of five dissolved gases was used in ppm and in percentages. A total of 481 samples was collected from the chemi- cal laboratory and literature, categorized into 321 data samples for training and 160 data samples for testing processes. The SVM-BA classifier results indicated the following: • An accuracy rate of 93.75% has been achieved when the input vector in percentage with d = 2 and 3 degrees. • The coupled SVM-BA classifier’s test results revealed the classifier’s ability to enhance the transformer faults’ diagnostic accuracy rather than the other DGA techniques in the literature. • The overall accuracy of SVM-BA was 93.75%, which is higher than that of the modified IEC code (88.75%). • It recommended determining the expected remaining life of the transformer based on the state of the insulation system.

Author Contributions: Conceptualization: Y.B.; methodology: O.K.; software: Y.B.; validation, M.T.; formal analysis: O.K.; investigation, resources, data curation: S.S.M.G.; writing—original draft preparation: Y.B.; writing—review and editing: All authors, visualization, supervision: A.B.; project administration: S.S.M.G.; funding acquisition: S.S.M.G. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by TAIF UNIVERSITY RESEARCHERS SUPPORTING PROJECT, grant number “TURSP-2020/34” and “The APC was funded by SHERIF GHONEIM”. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors would like to acknowledge the ﬁnancial support received from Taif University Researchers Supporting Project Number (TURSP-2020/34), Taif University, Taif, Saudi Arabia. Energies 2021, 14, 2970 16 of 17

Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the study’s design; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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