Introduction

Dissolved Gas Analysis is the most common and effective method for detecting transformer faults. It can immediately predict internal transformer failures, which generally avoids huge economic losses.

A transformer in service is exposed to two types of stresses: electrical and thermal [1]. Due to these stresses, the transformer oil and paper decompose, releasing a set of gases that reduce their dielectric strength. The nature and quantity of each dissolved gas produced in transformer oil can indicate the internal condition of the transformer.

The most common gases produced by the decomposition of oil are: ethane (C2H6), ethylene (C2H4),acetylene (C2H2), methane (CH4) and hydrogen (H2) [2], these differ mainly in the intensity of the energy which is dissipated by the fault [1], [3]. In addition tocarbon dioxide (CO2) and carbon monoxide (CO) that are formed as a result of the decomposition of paper [4], while, the nitrogen (N2) and the Oxygen (O2) are the non-fault gases.

There are many approaches developed for the analysis of dissolved gases in transformer oil and interpret their meaning including IEC Ratio, DORNENBURG Ratio, Rogers Ratio, Duval Triangle and Pentagon, and,Key Gas method. However, these techniques have certain limitations such as the existence of non-decision areas and erroneous results [5]. To overcome this situation, several artificial intelligence techniques have been used to improve the diagnostic accuracy of power transformers, such as fuzzy logic inference systems [6], artificial neural networks [7], hybrid grey wolf optimization [4], support vector machines and K-nearest neighbors [8][9], and have impressive performance [10][11][12].

In this paper, we examine the use of the Naive Bayes and the Decision Tree algorithms in faults identification. The originality comes from the introduction of several input vectors formed using widely known DGA techniques in order to identify the most suitable input data which gives the best performance of each algorithm and achieves the best prediction of fault in power transformers.

This article is arranged as follows, in the second section, we describe the collection of DGA data then the construction of the proposed input space followed by a brief presentation of the two classification algorithms used; Decision Tree (DT) and Naïve Bayes (NB). The results of implementing the two algorithms using our proposed input vectors are discussed in the third section where, the best input vector for each technique has been identified. Finally, the conclusions from this work were summarized and potential future work was mentioned.

Methodology

Data collection

The construction of our proposed input space needs gas concentration values. For this purpose, samples of transformer oil are taken periodically to check the gasesformed [12].Generally, mixtures of all gases are present in an oil sample, where the relative amount of each, could be an indicator of the existing faults, such as, partial discharges (PD), thermal faults > 700 °C (T3), thermal faults of 300 °C to 700 °C (T2), thermal faults < 300 °C (T1), high energy discharges (D2) and low energy discharges (D1) [4].

In this work, a database of 481 samples has been used in training and testing the proposed methods. This database has been extracted from the literature [13].The distribution of the training and the testing samples according to their fault type is shown in Table 1.

Proposed Input vectors:

The following attributes have been considered in the construction of our proposed input vectors: 1. Using the concentration of the usual five key gases in ppm:

𝑋𝑋 = [𝐶𝐶 𝑎𝑎 , 𝐶𝐶 𝑏𝑏 ](6)

Where

𝐶𝐶 𝑎𝑎 = 1 3 ∑ (𝑎𝑎 𝑖𝑖 +𝑎𝑎 𝑖𝑖+1 )(𝑎𝑎 𝑖𝑖 𝑏𝑏 𝑖𝑖+1 −𝑎𝑎 𝑖𝑖+1 𝑏𝑏 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0 ∑ (𝑎𝑎 𝑖𝑖 𝑏𝑏 𝑖𝑖+1 −𝑎𝑎 𝑖𝑖+1 𝑏𝑏 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0(7)

And

𝐶𝐶 𝑏𝑏 = 1 3 ∑ (𝑏𝑏 𝑖𝑖 +𝑏𝑏 𝑖𝑖+1 )(𝑏𝑏 𝑖𝑖 𝑎𝑎 𝑖𝑖+1 −𝑏𝑏 𝑖𝑖+1 𝑎𝑎 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0 ∑ (𝑏𝑏 𝑖𝑖 𝑎𝑎 𝑖𝑖+1 −𝑏𝑏 𝑖𝑖+1 𝑎𝑎 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0(8)

The a i are calculated by the equations:

𝑎𝑎 0 = %𝐶𝐶𝐻𝐻 4 cos � 𝜋𝜋 2 � 𝑎𝑎 1 = %𝐶𝐶 2 𝐻𝐻 4 cos � 𝜋𝜋 2 + 𝜑𝜑� 𝑎𝑎 2 = %𝐶𝐶 2 𝐻𝐻 2 cos � 𝜋𝜋 + 2𝜑𝜑�(9)

And the b i could be obtained by replacing ''cos'' with ''sin'' in the last equations with α = 2π/3 7. Using Duval's pentagon coordinates:

𝑋𝑋 = [𝐶𝐶 𝑎𝑎 , 𝐶𝐶 𝑏𝑏 ](10)

Where

𝐶𝐶 𝑎𝑎 = 1 6 ∑ (𝑎𝑎 𝑖𝑖 +𝑎𝑎 𝑖𝑖+1 )(𝑎𝑎 𝑖𝑖 𝑏𝑏 𝑖𝑖+1 −𝑎𝑎 𝑖𝑖+1 𝑏𝑏 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0 ∑ (𝑎𝑎 𝑖𝑖 𝑏𝑏 𝑖𝑖+1 −𝑎𝑎 𝑖𝑖+1 𝑏𝑏 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0(11)

And

𝐶𝐶 𝑏𝑏 = 1 6 ∑ (𝑏𝑏 𝑖𝑖 +𝑏𝑏 𝑖𝑖+1 )(𝑏𝑏 𝑖𝑖 𝑎𝑎 𝑖𝑖+1 −𝑏𝑏 𝑖𝑖+1 𝑎𝑎 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0 ∑ (𝑏𝑏 𝑖𝑖 𝑎𝑎 𝑖𝑖+1 −𝑏𝑏 𝑖𝑖+1 𝑎𝑎 𝑖𝑖 ) 𝑘𝑘−1 𝑖𝑖=0(12)

The a i are calculated using the following equations:

𝑎𝑎 0 = %𝐻𝐻 2 cos � 𝜋𝜋 2 � 𝑎𝑎 1 = %𝐶𝐶 2 𝐻𝐻 6 cos � 𝜋𝜋 2 + 𝜑𝜑� 𝑎𝑎 2 = %𝐶𝐶𝐻𝐻 4 cos � 𝜋𝜋 2 + 2𝜑𝜑� 𝑎𝑎 3 = %𝐶𝐶 2 𝐻𝐻 4 cos � 𝜋𝜋 2 + 3𝜑𝜑� 𝑎𝑎 4 = 𝐶𝐶 2 𝐻𝐻 4 cos � 𝜋𝜋 2 + 4𝜑𝜑�(13)

Also, the b i could be obtained by replacing ''cos'' with ''sin'' in the last equations with α = 2π/5. 8. In this case, a combination of two of the previously mentioned input vectorshas been done, Roger's and DORNENBURG's ratios:

Where {Ca1, Cb1} are calculated using the triangle method, while Cb2} are calculated according to the pentagon one.

AI techniques: 2.3.1. Naive Bayes

The NAIVE BAYES algorithm is a simple probabilistic classifier that uses Bayes theorem,which is given by the following equation [14]:

𝑃𝑃(𝑥𝑥|𝑦𝑦) = 𝑃𝑃(𝑦𝑦 |𝑥𝑥)×𝑃𝑃(x) 𝑃𝑃(𝑦𝑦) (16)

Where 𝑃𝑃(𝑥𝑥|𝑦𝑦)refers to the subsequent possibility of the hypothesis x conditioned by some evidence y and𝑃𝑃(x) is the prior probability of x.

Decision tree

The decision tree algorithm is a non-parametric supervised machine learning's classifier used to split data into a set of branches. The construction of the tree is conducted from top to bottom in a recursive divide-and-conquer manner. The Decision Tree classifier training is based on finding the best split at each node as long as the full data set is not analyzed [15]. The said principle leads to the idea of partitioning the feature space until the interrupt criterion is satisfied in each list, or until all points in a given leaf belong to one class. Figure 1 illustrates the basic structure of a decision tree.

Construction of decision tree:

In order to select the best variable to split, the Decision Tree uses the information gain. The equation for calculating information gain is as follows:

𝐺𝐺𝑎𝑎𝑖𝑖𝐺𝐺(𝑇𝑇, 𝐴𝐴) = 𝐸𝐸𝐺𝐺𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑦𝑦(𝑇𝑇) − ∑ 𝑇𝑇 𝑖𝑖 𝑇𝑇 𝐸𝐸𝐺𝐺𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑦𝑦(𝑇𝑇 𝑖𝑖 ) 𝐺𝐺 𝑖𝑖=1(17)

Where 𝐺𝐺𝑎𝑎𝑖𝑖𝐺𝐺(𝑇𝑇, 𝐴𝐴) is the information gain of set T (training data) on an attribute A and 𝑇𝑇 𝑖𝑖 is a subgroup of T for which: A has value i.

The Entropy of node T is defined as:

𝐸𝐸𝐺𝐺𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑦𝑦(𝑇𝑇) = − ∑ 𝐸𝐸(𝑖𝑖) log 𝐸𝐸(𝑖𝑖) 𝐺𝐺 𝑖𝑖=1(18)

Where 𝐸𝐸(𝑖𝑖) is the proportion of T belonging to a class i.

Results and discussion:

To evaluate the performance of Naïve Bayes and Decision tree algorithms using our proposed input vectors according to six types of transformer faults, a set of 481 samples has been used to train and test the two methods; 67% of the dataset were used for the training and 33% for the testing, using the MATLAB software. Table 2 shows the results of the implementation of the two classifiers using the proposed input vectors. From Table 2, it is easy to see that the highest prediction accuracy is obtained using vector 9 (combined Duval's pentagon and triangle) with the Naïve Bayes algorithm (86.25%). Whereas, in the case of the Decision Tree, the input vector 4 (Roger's four-ratio method) gives the highest prediction accuracy, up to 83.75%.

In order to deepen the study, the performance of each algorithm with its appropriate input vector was evaluated based on the accuracy of each fault type diagnosis (Figure 2). From Figure 2, it is clear that the performance of each algorithm differs depending on the type of fault. For example, in the case of the partial discharges (PD), the Naïve Bayes has the best performance, while, in the case of medium thermal fault (T2), the Decision Tree has the superiority in such fault recognition. Overall, the Naïve Bayes algorithm remains the one with the greatest precision.

Conclusion:

The Naïve Bayes and the Decision Tree classification algorithms were used to identify power transformer faults. A dataset of 481 samples was employed and 9 different input vectors were considered. The Naive Bayes algorithm achieved a diagnostic accuracy of 86.25% when using the 9th input vector (Duval's triangle-pentagon coordinates combination), compared to 83.75% in the case of the Decision Tree using the 4th input vector (ROGER's four-ratio). These diagnostic results show an improvement in the identification of transformer faults over other traditional DGA methods. Significant differences in diagnostic accuracy were obtained when using the same classification algorithm with different input vectors, this investigation shows the appropriate input vector for the diagnosis of power transformers using the Naive Bayes and the Decision Tree algorithms.

In a future work, we will extend the proposed input space using other input vectors with an improved machine learning algorithm.