Abstract
In the electrical energy transmission and distribution sector, power transformers play an important role. Early fault diagnosis and prognosis are essential to ensure continuous operation and also to prepare a proper maintenance schedule based on the requirements. The occurrence of a fault in the transformer will lead to the formation of various gases inside the transformer tank. For fault diagnosis in the transformer, Dissolved Gas Analysis (DGA) is an excellent method. An Artificial Intelligence (AI) based fault diagnosis and prognosis system using dissolved gases in transformer oil is helpful to predict the health state of the transformer well in advance. Hence, based on the fault severity level, the remaining useful life of the transformer, fault type and current state of the transformer can be estimated effectively by imparting AI to the existing system. A Two-Tier Fuzzy Logic Controller (TTFLC) is proposed in this article to find the type of fault and health index (HI) of the transformer. For further fault prognosis, an effective Gated Recurrent Network (GRN) based deep learning enabled future learning estimator is used for predicting the Criticality Index (CI) of the Transformer. The performance of the proposed method is evaluated for both data from the IEEE data set and expert data collected from the southern Tamil Nadu region. The proposed system shows better results even in multivariate, complex process systems. The diagnosis accuracy of the proposed system is obtained as 95.28% and it compared with conventional methods such as Rogers Ratio Method (RRM), Duval Triangle Method (DTM) and Duval Pentagon Method (DPM) and other AI based methods such as Radial Basis Neural Network (RBNN), k-nearest neighbors (KNN). The diagnosis accuracy of other conventional and AI based methods are less than 90% for the collected dataset.
Keywords
Introduction
Electricity is an integral part of our day-to-day life and a life without electricity is inconceivable. The power which is generated in far-away locations is transmitted to various places for distribution [1]. The generated energy is stepped up before transmitting in order to avoid transmission losses. Therefore, Power transformers play a vital role in Electrical energy transmission and distribution. Oil-cooled power transformers should be periodically monitored and diagnosed to find faults and predict the fault severity level, to avoid unexpected failure. Also, if accumulated gases are not monitored properly then it may cause catastrophic failure and even lead to huge loss to society [2]. The prime sources for diagnosing the incipient fault in the transformer are oil and paper insulations. Over a period of operation or due to the occurrence of any fault, the oil and paper insulation present in the transformer will deteriorate and liberate various gases. If the gases liberated are not significant, they will get dissolved in the oil itself and it will not get sensed by protection devices.
By assessing the various dissolved gases in the oil, the health status of the transformer can be determined. The Dissolved Gas Analysis (DGA) is a well-established method for the early diagnosis of incipient fault in a Transformer. Out of several gases liberated from the transformer, nine gases such as nitrogen (N2), oxygen (O2), carbon-monoxide (CO), carbon-di-oxide (CO2), acetylene (C2H2), ethylene (C2H4), methane (CH4), ethane (C2H6) and hydrogen (H2) are sufficient to get useful information about the transformer condition [3]. According to the type of internal fault, only few gases evolved among the nine gases. The various gases evolved and its corresponding fault type is listed in Table 1.
Type of fault and corresponding gases evolved
Type of fault and corresponding gases evolved
The DGA is used to determine the type and quantity of gases present in the transformer oil. Further, the DGA results are used to prioritize the transformer maintenance schedule. The fault in the transformer are classified into 6 categories such as TF0: Normal state, TF1: Partial discharge, TF2: Overheating of transformer (thermal fault <300°C), TF3: Medium temperature phenomena (thermal fault 300°C to 700°C), TF4: Low density discharge (sparking), TF5: High temperature phenomena (thermal fault >700°C) and TF6: High density discharge (arcing).
For the past few decades, a lot of DGA methodologies were proposed by different researchers. Most of these methods are evolved based on human expertise rather than complex mathematical expressions. Some of the leading methodologies for DGA are Key Gas Method (KGM), Rogers Ratio Method (RRM), Doerenburg Ratio Method (DRM), Duval Triangle Method (DTM) and Duval Pentagon Method (DPM) [3–6]. The above mentioned existing methods namely, KGM, RRM and DRM are simple but less reliable and the results are not consistent, which leads to wrong fault diagnosis. DTM and DPM methods are commonly used for monitoring the health condition of the transformer, it is not suitable for identifying the normal state TF0 of the transformer. So, even during normal operating conditions, it might result in any low-level fault type. Also, the ratio methods are applicable only when a significant amount of gases are present based on the combination otherwise it will result in a false prediction. To overcome the drawbacks mentioned, Artificial Intelligence (AI) based fault diagnosis is getting attention among the researchers [7, 8]. When a transformer undergoes electrical and thermal stress, gases get evolved because of the decomposition of oil. The various conventional and intelligent methods used for DGA interpretation and the corresponding gases involved are mentioned in Table 2.
DGA methodologies
In [9], the fault diagnosis in oil-filled transformers is done by performing various condition monitoring tests. But, the overall HI of the transformer is not computed. The Degree of Polymerization (DP) of the solid insulation (paper) in the transformer is identified by the furan. In [10, 11], DP is used for the computation of the transformer End of Life (EoL) of the transformer.
In articles [12–15], all possible parameters which affect the health of a transformer are listed, also the author highlights the role of the expert system in fault diagnosis but the way to compute the health index is not addressed. In [16] health index is computed based on the grading method. The main drawback of this weighted HI method is defining a threshold between the different scores for fault diagnosis which cannot be determined exactly and there exists overlapping regions.
Among the various subsets of AI, the fuzzy logic controller is used in this paper for fault diagnosis and Health Index (HI) computation. Fuzzy logic techniques can provide a better solution for the above mentioned drawbacks. In fuzzy logic technique, there is no need for finding a sharp threshold between grades. A crisp threshold is sufficient for computing the overall HI of the transformer. In [17], fuzzy logic based health index calculation for oil-immersed transformers is investigated. However, computation related to diagnosing the type of fault and fault prognosis is not carried out. In article [18], fault prognosis using HI based on Markov Chain is discussed. In [19], the Markov model is used for determining the deterioration performance curve based on HI but the effectiveness of the model in a multivariate system is not discussed in detail. Based on the literature review, the following points are observed. Most of the DGA interpretation methods available in the literature are addressing the issues related to fault diagnosis. But in order to improve the reliability and to assess the health state of the transformer, computation of Health Index (HI) of the individual transformer is mandatory. Estimation of the Health index of the transformer quantifies the health state of the transformer but it will reveal only the current state of the transformer.
HI alone is not sufficient for fault prognosis in Transformer. Therefore HI along with the Criticality Index (CI) will reveal the complete evaluation of the performance of the transformer, which is useful in prioritizing deliberate decisions on transformers health assessment. Hence, to predict the progression of fault severity level in transformers, an efficient multivariate and time-dependent process system for fault prognosis is needed.
In order to accurately predict the future health condition, a fault prognosis network based on deep learning technology is highly solicited for this multivariate complex process system and it is adopted in this proposed system for determining the Criticality Index (CI). The most commonly available model for fault prognosis is Recurrent Neural Networks (RNNs).
In articles [33–35] a Deep Recurrent Neural Network (DRNN) is used for investigating the root cause analysis of faults. It is a group of neural networks building a sequential model which has the ability to keep previous inputs in the network’s memory and it is being trained with backpropagation through time, this will lead to the notorious gradient vanishing issue [36]. To overcome this, Gated Recurrent Network (GRN) is used in this prognosis model.
From the literature survey, it is evident that only a few research works are available in transformer fault prognosis using HI along with CI and that too is not effective for time-dependent systems.
To bridge the research gap in this field, AI based fault diagnosis and prognosis of power transformers are investigated and the schematic representation of the proposed system is given in Fig. 1. The transformer dissolved gas concentration is collected and given as input to the proposed two-tier fuzzy logic controller (TTFLC). The output of the diagnosis unit is Health Index (HI) and type of fault. The transformer fault prognosis unit is helpful in fault prognoses with the help of deep learning enabled future learning estimators. The Gated Recurrent Network (GRN) is used in the transformer fault prognosis unit for computing the Criticality Index (CI) of the transformer. Based on the HI and CI values fault severity level is computed.

Block diagram of proposed system.
The contribution of the research outcomes is summarized below, This article proposes a Two Tier Fuzzy Logic Controller (TTFLC) for identifying the condition of the transformer and for computing the health index of a transformer based on DGA. The proposed system also includes a fault prognosis network based on a deep learning technique in-order to compute the criticality index of a transformer. The proposed system is efficient and this hybrid AI system is sufficient to build an effective fault diagnosis and prognosis unit for estimating the fault severity of a Transformer using DGA.
Expert data systems of both in-service and faulty transformers are collected from various locations in the southern Tamil Nadu circles such as Virudhunagar, Tirunelveli, Tuticorin and Nagercoil during the year 2021. Nearly 233 transformer data are collected with different transformer capacity ranges from 8 MVA to 25 MVA. The service period of the transformer ranges from 1 year to 44 years. To strengthen the database and in order to perform comparative analysis, data from the IEEE data set and data available from journals are included. During normal operation, the gases in the oil are within the acceptable threshold limit and DGA acceptable and unacceptable limits as per IEEEC57.104-1978 standards (in parts per million (ppm)) are mentioned in Table 3. When a transformer undergoes thermal decomposition, the bonds in the oil break down and it evolves C2H4 and C2H6 as principal gases. Similarly overheating of solid insulation leads to paper related faults and it leads to the liberation of CO and CO2. This type of cellulose ageing or cellulose related fault is very dangerous and leads to catastrophic failure. When excessive H2, CH4 and C2H2 gases get evolved then it leads to an electrical related fault in the transformer. In the proposed Two Tier Fuzzy Logic Controller (TTFLC), two levels of different operations such as diagnosing the type of fault and estimating the health index are done in parallel.
DGA limits
DGA limits
In tier 1 of the proposed System, Health index computation is performed using Fuzzy logic. Five membership functions used for fuzzification are acetylene (C2H2), ethylene (C2H4), methane (CH4), ethane (C2H6) and hydrogen (H2). The gaussian membership function is used to represent the input variables and it is selected based on the nature of input. Also, the scaling was selected based on the IEEEC57.104-1978 standards. Five linguistic variables are used to represent the input and output membership function. The input linguistic variables are Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH). The output linguistic variables are Worst (W), Poor (P), Good (G), Very Good (VG) and Excellent (E). Instead of the mathematical model, rules are framed in the linguistic form of IF-THEN rules. Forty-one expert rules are framed and used in the fuzzy inferencing unit. For defuzzification of fuzzy variables, the centroid method is used. The membership functions of various input variables and output variables (in terms of ppm) are depicted in Fig. 2.

Membership functions of input variables in ppm (a) H2, (b) CH4, (c) C2H2, (d) C2H4, (e) C2H6 (f) output variables.
In tier 2 of the proposed fuzzy system, the type of fault is computed. The gases such as acetylene (C2H2), ethylene (C2H4), methane (CH4), ethane (C2H6), hydrogen (H2), carbon-monoxide (CO) and carbon-di-oxide (CO2) are considered as input membership functions. The gaussian membership function is used to represent the input variables. Based on the survey collected from the experts, three linguistic variables are used to represent the input and six linguistic variables are used to represent the output variable – a type of fault. The linguistic variables for the inputs are Low (L), Medium (M) and High (H). The linguistic variables for the output are TF0, TF1, TF2, TF3, TF4, TF5 and TF6. The limits for each fuzzy variable are selected based on IEEEC57.104-1978 standards. Thirty-three expert rules are framed and used in the fuzzy inferencing unit. For defuzzification of fuzzy variables, the centroid method is used. The membership functions of various input variables (in terms of ppm) are shown in Fig. 3.

Membership functions of input variables in ppm (a) H2, (b) CH4, (c) C2H2, (d) C2H4, (e) C2H6, (f) CO (g) CO2.
In this proposed system, Gated Recurrent Network (GRN) is used for the fault prognosis of the Transformer and the block diagram of GRN is shown in Fig. 4. It offers several advantages over conventional RNN such as very fast training capability, involves only a few parameters, uses less computational resources and has the ability of learning time-dependent sequential data. These features make GRN more robust in the field of fault prognosis and remaining useful lifetime estimation.

Block diagram of GRN.
The architecture of a single cell of GRU is shown in Fig. 5. GRN uses an update gate z(t) and reset gate r(t) for controlling the flow of information into and out of the memory respectively. These gates will decide whether the previous hidden state value is useful or not, if useful it will hold it else it will remove it. The reset gate will decide the rate of forgotten past useless information. This enables the feature of handling smaller datasets.

Architecture of GRU cell.
Let us consider a single unit, for that compute update weight using Equation (1), where Wz is the update weight matrix. When input Xt is given to the network unit, it is multiplied with Wz and information of previous t-1 units, h(t-1) is multiplied with Wz and both terms get added together. Sigmoidal activation function (σ) is applied and its value ranges from 0 to 1. This modeled update gate determines the amount of past information to be fetched in future.
The reset gate is useful for deciding the rate of forgetting the past information. Reset state equation rt is given in Equation (2) and it is similar to zt. The difference in zt and rt computation is based on weight and gate usage.
Where Wr is the reset weight matrix. The inflow of previous hidden state h(t-1) is controlled by candidate hidden state ht by using rt. If rt is zero, then the previous hidden state will be removed.
The current memory content state equation is given in Equation (3). It calculates element wise product (⊗) between the reset gate and h(t-1).
The current state h(t) is generated from
In the proposed system, raw data such as type of fault, age and load factor are given as input to the system. After normalization, data will be divided into several sequences and given as input to GRN. Based on the features extracted, Softmax regression classification model is applied to identify the Criticality Index (CI). To estimate CI for training data, a survey is conducted among technical experts and they are asked to assign weights ranging from 0 to 1 based on their previous experience on real time recorded results. The collected responses are averaged and used for CI labeling in the training dataset.
In the two tier fuzzy logic controller, the first tier of the fuzzy logic controller is used to determine the type of fault in the power transformer. The dissolved gases including CO and CO2 are the inputs and the type of fault will be the output which is also taken on the scale of (0 - 1). The confusion matrix of the proposed fault diagnosis system is shown in Fig. 6. The accuracy of the proposed system is 95.28%, error rate is 4.7%, sensitivity is 100%, specificity is 100% and prevalence is 18.88%. Also, there is no unresolved prediction observed in TTFLC, whereas the unresolved predictions are the main drawback of Rogers Ratio Method. The results obtained from the proposed TTFLC are compared with RRM, DTM, DPM, Radial Basis Neural Network (RBNN), k-nearest neighbors (KNN) and their performance is tabulated in Table 4. From the analysis, it is evident that the performance of the proposed system is far superior to other existing approaches.

Confusion matrix.
Comparison of successful prediction by various interpretation technique
An another fuzzy logic controller is used in the second tier of proposed TTFLC, to determine the health index of the power transformer whose inputs are various dissolved gases of the transformer and the output is the Health Index which is taken on the scale of (0 - 1) and level of health index is taken as Worst, Poor, Good, Very Good and Excellent which is useful for the diagnosing of transformer condition. In order to evaluate the HI of the transformer nearly 42 expert rules are used. Higher the value of HI, the better is the health of the transformer.
Upon successful computation of the health index of a transformer, it is easy to predict the Criticality Index of the transformer in order to prognosis the transformer health status. For calculating the value of CI, deep learning enabled future learning estimators based on GRN are used in this article. The parameters used for training the GRN are Age, Load Factor, actual fault type and expert knowledge on fault severity level. For training the GRN, nearly 173 transformer data are used and during the testing phase, 60 samples are tested. The Load Factor (LF) is computed using a linear method of load score calculation and the load history is characterized into 5 groups (say i = 0, 1, 2, 3, 4). These groups are based on the ratio of the number of monthly peak loads Si to the rated loading SB of the transformer [21]. The group values are classified based on the ratio value which ranges in the order of <0.6, 0.6 to 1, 1 to 1.3, 1.3 to 1.5 and >1.5 respectively. The load factor is computed by using the Equation (5).
For better performance, the value of CI obtained should be lower. In-order to assess the performance of the GRN, the performance parameters such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Mean Squared Error (MSE) are calculated using Equations (6 to 8). The predicted value (xi), mean value (
To prove the effectiveness of the proposed system for predicting the criticality index of the transformer, obtained results from GRN are compared with Long Short-Term Memory network (LSTM). The comparison results are tabulated in Table 5.
Performance evaluation
The obtained test results of the proposed system for sample data covering all types of fault is showcased in Table 6. Also, the mapping of HI with respect to CI assessment helps to identify the fault severity level of the transformer. This fault severity mapping helps to prioritize the maintenance schedule For CI and HI evaluation, it will be easy if they are combined and drawn in the form of a single graph. The entire region is classified into 5 zones namely healthy, routine maintenance, scheduled maintenance, immediate rectification and refurbishment. The zone classification is already an existing practice and it is addressed in literature. But the zone threshold as shown in Fig. 7 are formed based on expert knowledge and past history of 80 transformers which is taken under study. From the known data and the actual status of 80 transformers, HI and CI values are computed for those transformers and plotted in the graph. The zone under which the 80 transformers fall are compared with actual status and the results are closely associated. From this it is evident that based on the mapping of HI and CI scores, fault severity level can be identified and it is used to determine the strategic maintenance required for the transformer. In Fig. 7, each dot represents a transformer and the overall fault severity assessment result is shown in the plot. The healthy transformers are located in the top left sector, while the bottom right sector contains the equipment that requires immediate attention.
Sample data and results of HI and CI

HI and CI mapping of oil filled transformers.
In this article, DGA based fault diagnosis and prognosis of Transformer using Artificial intelligence are investigated. A two tier fuzzy logic controller is designed for Fault Diagnosis which integrates the DGA IEEE standards and expert knowledge. With the help of the proposed TTFLC, both the Health Index and transformer fault type is diagnosed. 233 different transformer oil samples are used for validating the results of the proposed TTFLC. The diagnosis accuracy of the proposed TTFLC is nearly 95.28%, which is far superior when compared to other existing methods addressed in the literature. Further, for predicting the fault severity level of transformers, a deep learning based network is designed. To evaluate the performance of the proposed system, a 43 year-old transformer with a complaint of arcing is tested in real-time. The collected samples from the corresponding transformer, along with its load factor, are given as input to the proposed system and the output obtained are TF6, HI = 0.386, and CI = 0.895. The results obtained from the proposed system are found to closely relate to the real condition of the transformer. This demonstrates that the proposed system is highly efficient and reliable in computing the type of fault, HI and CI values.
The findings of this study highlight the potential of the proposed system in improving the efficiency and accuracy of maintenance operations in the power industry. By providing reliable information on the condition of transformers, the system can assist in preparing maintenance schedules and prolonging the remnant life of transformers. This can result in significant cost savings and improved operational efficiency for power utilities. Overall, the proposed system has practical implications for the power industry and can contribute to the reliable and sustainable operation of power systems.
