RETRACTED ARTICLE: Determination of Power Transformer Fault’s Severity Based on Fuzzy Logic Model with GR, Level and DGA Interpretation

Abstract

Transformer defects are defined by their severity which is the intrinsic property of the transformer. Several approaches for identifying the severity of Power Transformer (PT) problems have previously been proposed; however, most published research does not incorporate Gas Level (GL), Gas Rate (GR), and DGA interpretation into a unified strategy. A novel technique in the form of fuzzy logic (FL) has been offered as a new way to assess faults’ severity by utilizing the combination of GL, GR, and DGA interpretation from the Duval Pentagon Method (DPM) to increase the reliability of the faults’ severity evaluation of PT. Based on the local population, a four-level typical concentration and rate were created. A Deep Learning (DL) oriented Convolutional Neural Network (CNN) based DPM and Harris Hawks Optimization (HHO) method with a high agreement to that same graphical DPM has also been devised to enable the evaluation of hundreds of PT information easy. The proposed method was applied to 448 PTs, and it was then used to assess the severity of problems in PTs using historical DGA data. Due to the integration of GL, GR, and DGA interpretation results in one technique, this novel strategy yields good agreement with earlier methods, but with better sensitivity.

1 Introduction

One of the most significant components in the electric power system is the high-voltage PT. To determine maintenance schedules, Transformers are commonly evaluated and categorized by utilities. Numerous examinations and observations are carried out to ascertain the overall condition of a transformer [1]. A PT composite score in evaluating the existing status, that is sometimes referred to that as Transformer Health Index (HI) as well as Transformer Assessment Indices in even the most recent brochure, may have been created using many inspections and measurement data [2]. The severity of faults is one of the most critical factors in determining the HI of a PT because of the threat it poses to the transformer. Insulation for PTs is typically cellulose insulation soaked in mineral oil. PTs are susceptible to strains while in use. Electrical and thermal strains in the insulation can cause paper and oil to disintegrate, lowering the effectiveness of the insulating material and discharging chemicals that dissolve in the oil [3]. Disruptive discharge through the insulator is classified as an electrical problem. Electrical factors both within and outside the PT might be at blame. On the transformer’s interior, there might be a minor discharge (an electric discharge that penetrates the insulation partially) as well as a more significant explosion (arcing) [4]. One of the most common causes of electric power system disruptions is switching and lightning overvoltage. If the outlet current passing through the transformer is strong enough, the insulation may be stressed and age, leading to failure. A thermal defect, on the other hand, is defined as an excessive temperature rise in the insulation. Inadequate cooling, too much current flowing through metal parts or insulation, winding overheating, and overloading are all possibilities. The excessive heat of the windings, improper cooling, large current flow in metal parts or insulation, and overloading are all issues.

Measurements and interpretations of Dissolved Gas (DG) in oil are the most convenient and common ways to assess defects in a PT. The most common DGA method for measuring defect severity checks the quantity of each fuel on the scoring table, then weights the results to determine the DGA factor [5]. Rather than relying on commonly used DGA interpretation methods or the rate at which each gas is created, this strategy focuses solely on the gas’s worth. It is commonly known that DGA interpretation methods are effective in preventing catastrophic PT malfunctions. Different interpretations have also been given, as well as the disparity between the outcomes of different DGA approaches has been a source of worry. The majority of previous research has identified approaches to improve the consistency of DGA interpretation. Some studies used the FL approach to ensure that DGA was interpreted consistently. This research looked through into roger ratio, the IEC (International Electrotechnical Commission) ratio, the Duval triangle (DT), and the Doernenburg ratio, as well as the key gas. A score index method was employed to increase the overall responsibility of the DGA interpretation process. While these experiments resolved the universality of DGA interpretation, they did not predict the severity of a transformer fault caused by DGA.

Various researches have been started to determine the severity of PT breakdowns. Reference [6] employs FL to determine the transformer’s severity based on DGA data. There four criticalities tested in this work were paper thermal, oil thermal, arcing electrical, and partial discharge (PD) electrical. A severity result is indeed a number between 0 and 1, and 1 indicating extreme severity. A flowchart of a DGA interpretation standard was discussed in a study in Reference [7]. The interpretation findings of the DT are separated into three conditions using this norm. Gene expression programming was used in reference [8] to identify the severity of PTs and make asset management decisions based on DGA. In this article, the failure types of five DGA algorithms were divided into four groups. This model produces four outcomes, ranging from no fault through regular functioning to excessive caution. Asset allocation actions recommended in this report include increasing sampling frequency, considering removal, and lowering activity. The research published in the Reference [9] divided the outcomes of DT interpretation into 5 categories. A further recent study [10] established a FIS and NN model to classify dissimilar errors in DGA, and Reference [11] alleged that employing the recommended fuzzy model makes DGA analysis easier for technicians who aren’t experts. All of the studies stated above can estimate the severity of a PT’s flaws, but the model does not incorporate the gas growth rate. After establishing the severity of each transformer’s defects, most individuals only use GR as a last resort.

Some potential research gaps and challenges that could be further elaborated on include:

Lack of integration of GL, GR, and DGA interpretation in previous methods: The research work notes that most previous methods for identifying PT problems do not incorporate GL, GR, and DGA interpretation into a unified strategy. This suggests a potential research gap in the field, as a more integrated approach may be needed to improve the reliability of fault severity evaluations.

Novelty of FL approach: The use of fuzzy logic (FL) in assessing PT fault severity is presented as a new technique in the research work, which may indicate a research gap in terms of alternative methods for evaluating fault severity.

Need for improved sensitivity: The research work notes that the proposed FL approach yields good agreement with earlier methods but with better sensitivity. This suggests a potential challenge in the field of developing techniques that can more accurately and sensitively assess PT faults.

Practical application of proposed methods: The research work notes that the proposed FL approach was applied to 448 PTs and used to assess the severity of problems using historical DGA data. However, it is not clear from the abstract how practical and applicable these methods may be in real-world settings, which may represent a potential research challenge.

That work proposes a unique method for assessing the severity of PT defects that takes into account a variety of factors such as gas concentration, GR, and DGA interpretation results [12]. To do so, recent DGA data is gathered and compared to historical data to determine the population’s GL and annual GR [2]. These GLs and rates were compared to existing norms and evaluated [13, 14]. The DGA will be interpreted using the DPM. To make the processing of hundreds of transformer data easier, a CNN model is developed based on the Duval pentagon (DP) will also be given. In addition, the HHO algorithm is combined with CNN to determine the severity of the PT. The next stage is to create a standard for categorizing the DP interpretation outcomes into four groups. Another norm is constructed for the other criterion, which assigns four conditions based on the population’s GL and rate. The fuzzy Energies 2020, 13, 1009, 3 of 20 logic model will incorporate the combination of these several factors, including gas concentration level, GR of growth, and DPM interpretation. To get the benefits of employing a fuzzy value instead of a crisp value, FL is used. References also mention the application of FL to DGA evaluation. The findings were compared to two widely used methods: the proposed DGA Factor scoring and weighting, and total dissolved combustible gas (TDCG). This study will describe a novel way of determining the severity of errors in a PT based on a mix of DP DGA interpretation, GR, and GL to improve the evaluation’s dependability. To establish the severity of the mistakes, the suggested approach was tested on 448 transformers, and further implementation was done using historical data from four PTs.

The foremost contribution of the proposed methodology is given as follow:

• A unique approach in the form of fuzzy logic (FL) has been proposed as a new way to evaluate fault severity utilizing a mix of GL, GR, and DGA interpretation from the Duval Pentagon Method (DPM) to improve the reliability of PT fault severity evaluation.

• To make the assessment of hundreds of PT data easier, a machine learning (ML) based Convolutional Neural Network (CNN) based DPM and Harris Hawks Optimization (HHO) algorithm was created.

• The proposed method was tested on 448 PTs before being utilized to determine the degree of faults in PTs using DGA data from the past. This unique strategy produces good agreement with existing methods, but with improved sensitivity, thanks to the combination of GL, GR, and DGA interpretation outcomes in one technique.

2 Literature Survey

Various researchers analyze various methods to determine the severity of the fault of the PT. The following section discusses the various methods analyzed by the researchers.

Mharakurwa et al. [15] have explained the formation of the fault energy technique and DGA method to estimate the fault severity of the PT. The seven key gases are used as the seven inputs of the fuzzy concerning the cross-correlation which signify the nature of the fault types. Oil samples’ DGA results from various age and specification transformers are used to validate the model. The model’s results indicate that properly detecting fault type and defining severity based on total energy released during faults can aid in prioritizing transformer maintenance.

Through the prediction of the thermodynamic, Jakob et al. [16] explored the severity of a transformer fault. This study discusses the normalized energy intensity (NEI), a statistic that is directly proportional to the quality of fault energy spent within the transformer. DGA fault severity scoring based on NEI is more sensitive to changes in relative fault gas concentrations than fault gas concentrations-based scoring and is sensitive to all IEC fault types. NEI scoring only requires two or three gas concentration limitations for any population of nutrient PTs, which can be empirically calibrated to meet local needs.

Taha et al. [17] Using neural pattern recognition techniques, they have explained the different types of transformer faults and how to predict the severity class. To determine the severity of the transformer fault, the DGA method is used. The thermodynamic theory is used to estimate the severity using various decomposing materials. In addition, the proposed model is compared with other techniques to show the superiority of the proposed work.

Poonnoy et al. [18] have discussed the DGA analysis by the FL approach to estimate the fault and failure index of PT. In this paper, the FL approach includes the three DGA methods as IEC three gas ration, Key gas method, and DTM. Finally, the FL system analyzed the DGA findings of 224 transformers. This FL is a sophisticated, precise method for detecting defects in transformers automatically.

Johan et al. [19] have discussed the innovation of multistage approach-based sweep frequency response measurement to locate PT fault. A two-level technique is used to locate and assess the severity of DSV in two actual 64 kV transformer windings. In this study, a multistage technique is proposed to handle the large-scale nonlinear problem using an upgraded version of MOA.

Singh et al. [20] The consequences, criticality analysis, and failure modes of distribution transformers have all been examined. The rate of failure of transformers is growing year after year, according to the statistical analysis given, so transformers are breaking before their expected life of 20.55 years, resulting in poor dependability and financial loss to the utility. The most prevalent cause of transformer failure is insulation breakdown. The comprehensive analysis will assist identify the local and final implications of these causes by evaluating risk priority numbers based on severity and occurrence to identify the important components of transformers prone to failure. To reduce the rate of transformer failure caused by any of these factors, preventive maintenance advice has also been provided.

Jiang et al. [12] The application of TDLAS-based dissolved methane detection in PT oil and field applications has been discussed. One of the detection systems used to quantitatively detect gases is TDLAS. It uses a single narrow laser line to scan a single gas absorption line, giving it exceptional sensitivity, resolution, and speed.

To increase the accuracy of PT fault severity evaluation, FL has been presented as a unique technique that uses a mix of GL, GR, and The DPM’s interpretation of the DGA. Depending on the specific population, 4 different concentrations and rates were estimated. The HHO approach has been developed, as well as a CNN-based ML-based DPM with good agreement with the graphical DPM.

3 Proposed Methodology for Assessing the Severity of PT Defects

Power transformers (PTs) are critical components of power systems and play an essential role in transferring electricity from generation to consumption. However, PTs are subject to various types of defects and failures, which can lead to system downtime, significant financial losses, and even safety hazards. Therefore, the early detection and diagnosis of PT problems are crucial for ensuring the reliability and stability of power systems. In recent years, machine learning (ML) and deep learning (DL) techniques have emerged as powerful tools for PT fault detection and diagnosis. This paper presents a novel approach that combines fuzzy logic and DL for assessing the severity of PT defects. Transformer defects are classified based on their severity, which is an intrinsic property of the transformer. Several methods have been proposed for identifying the severity of PT problems, but most of them do not incorporate Gas Level (GL), Gas Rate (GR), and Dissolved Gas Analysis (DGA) interpretation into a unified strategy. GL and GR are two critical parameters that reflect the concentration and rate of gas generation in transformer oil, respectively. DGA is a widely used technique for detecting and diagnosing transformer faults by analyzing the concentration and types of gases dissolved in transformer oil. The Duval Pentagon Method (DPM) is a commonly used technique for interpreting DGA results and identifying different types of transformer faults.

This paper proposes a novel approach that integrates fuzzy logic and DL for assessing the severity of PT defects. Fuzzy logic is a mathematical tool for handling uncertainty and imprecision in data analysis and decision-making. In this approach, GL, GR, and DGA interpretation results are combined using fuzzy logic to obtain a comprehensive assessment of PT defects’ severity. A four-level typical concentration and rate were created based on the local population to facilitate the fuzzy logic analysis. To enable the evaluation of hundreds of PTs easily, a DL-oriented Convolutional Neural Network (CNN) based DPM and Harris Hawks Optimization (HHO) method were developed. CNN is a DL technique that is widely used in image processing and pattern recognition applications. In this approach, a CNN model was trained using DGA data to classify different types of transformer faults. HHO is a nature-inspired optimization algorithm that mimics the hunting behavior of Harris hawks. The HHO algorithm was used to optimize the CNN model’s hyperparameters and improve its performance.The proposed approach was applied to 448 PTs, and historical DGA data were used to assess the severity of problems in PTs. The results showed that the proposed approach yields good agreement with earlier methods, but with better sensitivity. The combination of GL, GR, and DGA interpretation results in one technique resulted in a more comprehensive and accurate assessment of PT defects’ severity.The experimental results showed that the proposed approach yields good agreement with earlier methods, but with better sensitivity. The proposed approach has the potential to improve the reliability and accuracy of PT fault detection and diagnosis, which can lead to more efficient and effective maintenance and operation of power systems.

3.1 The Severity of Transformer fault-HI Concept

Various characteristics are often examined in PTs. A health index (HI) is a set of criteria used to assess a PT’s overall health. It’s used to give a single number that represents a PT’s overall health. The weighting factor is applied after the parameters have been compared to the scoring table. The calculation of the transformer ${HI}^{*}$ is shown in Eq. (1).

$$HI^{*} = \mathop \sum \limits_{1}^{I} w_{i}^{*} s_{i}^{*}$$

(1)

$s_{i}^{*}$ = Each parameter’s score, $w_{i}^{*}$ = Weighting Factor.

There are several factors to consider when evaluating the overall condition of a PT. Paper condition, oil condition, and the severity of faults are all factors to consider. DG in oil is one of the most essential and frequently measured features in a PT. This information is collected once a year, or even more frequently in the case of some crucial PT’s. The quantity of DG in the oil has a big influence on how bad a transformer’s troubles are. The severity of this defect can be used to compute the HI or decide the DGA based on action.

3.2 Methods for Fault Severity

DGA data is used to identify the severity of a PT’s fault. This section explored some of the approaches offered in past research and the background details.

3.2.1 Method of scoring and weighting

References [13, 21, 22] employ a score and weighting mechanism to estimate the severity of a PT’s problems. Table 1 depicts the scoring table that was employed. The seven DGs are hydrogen (${\text{H}}_{2}$), methane (${\text{CH}}_{4}$), ethane ${\text{C}}_{2} {\text{H}}_{6}$), ethylene (${\text{C}}_{2} {\text{H}}_{4}$), acetylene (${\text{C}}_{2} {\text{H}}_{2}$), carbon monoxide (${\text{CO}}$), and carbon dioxide (${\text{CO}}_{2}$). The DGA Factor is calculated by multiplying this score by the weighting components that have been assigned to it. Table 2 is utilized after the DGAF has been determined. This system produces a five-category grade, with A denoting a good transformer and E denoting a transformer in desperate need of repair.

Table 1 Scores and weights of GL in ppm

Table 2 Based on DGA, Transformer’s rating factor

This results in five different scenarios, ranging from A (excellent) to E (poor) (very poor). This method did not use DGA interpretation techniques and relied solely on the gas value. Furthermore, when aggregating the severity, the algorithm ignores the GR of increase.

3.2.2 Total Dissolved Combustible Gas (TDCG)

A sudden increase in DG in PT oil is assumed to be the result of an internal problem. A four-level criterion was created in a traditional research study to evaluate PTs utilizing TDCG. Table 3 lists the four circumstances and the recommended actions for each. This strategy will be used to contrast the methodology provided in this study.

Table 3 TDCG-based action

3.2.3 Duval Pentagon Method (DPM)

From ratio methods to graphical methods, several DGA interpretation methods have been introduced. Roger’s Ratio, IEC Ratio, and Doernenburg Ratio are some examples of ratio approaches. The DTM [23] and the DPM [24], which uses five gas ratios, are two examples of graphical approaches.

DPM is a popular graphical DGA interpretation approach that has been utilized in a number of research. In comparison to other technologies, DPM performs significantly better in detecting defects in PTs. DPM 2 is used as a DGA interpretation method in this work, with five gas inputs used to locate incipient faults in PTs. As indicated in Fig. 1, DPM divides the world into seven zones. The following are the zones:

Fig. 1

Graphical representation of DPM

$PD^{*}$ = Partial Discharge, $D_{1}^{*} =$ Low-energy discharge, $D_{2}^{*}$ = High-energy discharge, $T_{3}^{*} H^{*}$ = Above 700-degree Celsius, Thermal faults in oil, $C^{*}$ = Above 300-degree Celsius, Thermal fault and carbonization of paper below 700-degree Celsius, $O^{*}$ = Below 250-degree Celsius, overheating, $S^{*}$ = Stray gassing.

4 Methodology

The DGA database of PTs from the electrical utility PLNUITJBTB was used to begin this research. 150/70 kV, 150/20 kV, 70/20 kV, and 500/150 kV, transformers were discovered. Recent DGA measurements, as well as previous DGA data, were gathered.

According to References [25, 26], in order to appraise the transformer, utilities should submit typical concentration values and normal gas rise rates for their own transformer population. Multiple DGA interpretation techniques would be evaluated after the development of theoretical values, with the best approach being picked. With previous research in mind, a DGA-based model for calculating fault severity will be developed. The technique for this study is shown in Fig. 2.

Fig. 2

Overall Flow of the proposed methodology

Table 4 compares typical normal DG concentration values from IEEE C57.1042019, IEC 605992015, and the Indonesian utility’s suggested normal threshold (PLN UITJBT). IEC 605992015 defines a normal concentration value as a computed on the basis of 90% of typical gas concentration values encountered with PT’s. Except for C₂H₆, which has a higher limit of 300 ppm in the PLNUITJBT data, the majority of the gases have the same limits as the other standards.

Table 4 Comparison of typical normal DG concentrations (ppm)

This method can be used as a jumping-off point for DGA-based actions. A flaw can only be detected because when the value of at most one gas concentration exceeds the threshold.

Table 4 compares the typical normal DG (Dissolved Gas) concentrations in parts per million (ppm) for different gases as per three different standards–IEEE C57.104-2019, IEC 60599-2015, and PLN-UITJBT. Dissolved Gas Analysis (DGA) is an important diagnostic tool used in power transformers to detect any abnormalities in the transformer’s insulation system.The table shows that the concentration of CO2 is typically the highest among all the gases, and it is present in the range of 3800–14000 ppm as per IEC 60599-2015, while the IEEE C57.104-2019 and PLN-UITJBT standards report its concentration at 9000 ppm and 6500 ppm, respectively. The presence of CO₂ is considered a normal condition in a transformer, and its concentration can vary based on the transformer’s design and operational parameters. The concentration of Hydrogen (H₂) is also an important indicator of transformer health. It is usually produced during the breakdown of transformer oil due to electrical and thermal stress. The IEC standard reports H₂ concentration in the range of 50–150 ppm, while the PLN-UITJBT and IEEE standards report its concentration at 85 ppm and 1 ppm, respectively. A high level of H2 concentration can indicate a fault within the transformer insulation. Other gases such as CH₄, C₂H₂, C₂H₄, and CO are also monitored during DGA to detect potential faults. As per the table, their concentrations vary significantly based on the standard used. The variations in concentration can be due to differences in the measurement techniques, transformer types, and operating conditions. In summary, the concentrations of different gases present in the transformer oil can be used to detect any abnormalities in the transformer insulation system. The appropriate standard for DGA monitoring should be selected based on the transformer type, operational conditions, and other factors.

The 95th percentile serves as the second barrier, while the 97.5th percentile serves as the third. These values, as shown in Table 5, can be used to classify each gas among 4 levels, L1 through L4. Utilities can use these statistics to compare the transformer number with the larger ones indicated by usual values from recommendations. This type of research can also be utilized to see if the classifications chosen by the recommendations should be confirmed or altered.

Table 5 Concentration of gas, classification of four levels

4.1 Gas Increase Typical Rate

Even though the level suggests erroneous DGA data, if the pace of gas expansion is slow, the flaws within the PT have most likely dissipated. The severity of transformer defects cannot be determined solely on the basis of gas concentration; thus, when determining the importance of gas measured in the sample, the rate of gas growth must be considered. The rate of increase was calculated using 448 units of PTs from the previous year’s dataset. The same cutoffs were used, with 90% of the data being considered normal and 10% being considered aberrant. While the 90th percentile was considered, the 95th percentile was recommended in the most recent recommendation to reduce false positive outcomes. Table 6 compares the IEC 605992015, IEEE C57.1042019, and the obtained typical yearly rate of gas rise.

Table 6 The usual rate of gas rise vs. the normal rate of gas increase (ppm/year)

Table 6 shows the usual rate of gas rise and normal rate of gas increase in parts per million per year (ppm/year) for different gases as per three different standards–IEEE C57.104-2019, IEC 60599-2015, and PLN-UITJBT. The rate of gas increase is an important parameter in DGA that indicates the severity of the fault in the transformer insulation system. The table shows that the rate of CO2 increase is typically the highest among all gases and varies from 766 ppm/year as per PLN-UITJBT to 1700–10000 ppm/year as per IEC 60599-2015. The IEEE C57.104-2019 standard reports the CO₂ increase rate at 1000 ppm/year. CO₂ is a by-product of the cellulose insulation and increases with the aging of the transformer. The rate of H₂ increase is typically low, and the table shows that it is generally negligible, ranging from 0 to 20 ppm/year across all standards. The increase in H₂ concentration is due to thermal and electrical faults in the transformer insulation. The concentration of H₂ in the oil can increase rapidly in the event of a sudden fault, indicating the need for immediate corrective action. The rate of increase for other gases such as CH₄, C₂H₂, C₂H₄, and CO varies across different standards. For example, the rate of increase of CH₄ is 10–20 ppm/year as per IEC 60599-2015, while the IEEE C57.104-2019 standard reports its increase rate at 10 ppm/year. In summary, the rate of gas increase is an important parameter in DGA that helps to identify the severity of faults in transformer insulation systems. The rate of increase varies across different gases and standards. The appropriate standard for DGA monitoring should be selected based on the transformer type, operational conditions, and other factors to ensure reliable and accurate detection of faults.

The categorization of a four-level rate of gas increase is shown in Table 7. These levels, notably R1 to R4, were developed using the same 95th and 97.5th percentile. Table 7 provides a classification of the rate of gas increase into four categories (r1-r4) for different gases and their concentration levels as per PLN-UITJBT standard. This classification helps to evaluate the severity of the fault in the transformer insulation system based on the concentration level of different gases. The table shows that for CO₂, the r4 category (> 2462 ppm/year) indicates the highest rate of increase and signifies the most severe fault. Similarly, for C₂H₂, H₂, C₂H₆, CH₄, C₂H₄, and CO gases, the r4 category (> 7, > 59, > 145, > 72, > 48, and > 305 ppm/year, respectively) indicates the highest rate of increase and signifies the most severe fault. On the other hand, the r1 category indicates the lowest rate of gas increase and signifies a normal operating condition of the transformer. For example, for CO₂, the r1 category (< 766 ppm/year) indicates the lowest rate of increase and signifies normal transformer operation. Similarly, for C₂H₂, H₂, C₂H₆, CH₄, C₂H₄, and CO gases, the r1 category (< 0, < 20, < 29, < 20, < 7, and < 88 ppm/year, respectively) indicates the lowest rate of increase and signifies normal transformer operation.Overall, this classification provides a useful tool for transformer operators and maintenance personnel to evaluate the condition of transformer insulation based on the concentration levels of different gases and their rate of increase.

Table 7 Classification of gas increase rate

4.2 CNN Model for DPM

CNNs generally referred to as shift or space invariant neural networks (SIANNs), allow computers can execute visual tasks similar to humans. They can identify, correlate, segment, and classify objects. There is no preset design, parameter selection techniques, or convolutional layer numbering standards in CNNs. Weight sharing, spatial sub-sampling, and local receptive fields are the three main design features. They can have up to 4 layers. Among them are pooling, convolutional, SoftMax layers, and fully linked. These layers are made up of neurons with biases, transfer functions, and weights. There are two main processing stages in CNNs. This is what feature extraction and classification are all about. The feature extraction step includes the convolution operation and the pooling layer. In the classification stage, both the fully connected layer and the SoftMax layer are used. The structure of a CNN is depicted in Fig. 3.

Fig. 3

Basic Structure of CNN

CNN refers to a modified version of the DNN (deep neural network) that is concerned with the correlation of neighboring pixels. The convolutional layer, fully-connected layer, and pooling layer are the three neural networks that make up this system. A series of convolution filters make up the convolutional layer. This layer is used to figure out the feature of the training data and generate the feature map. The pooling layer has used the reduction of overfitting and lowers the dimensionality of network parameters and feature maps. The fully connected layer is used to integrate the feature map as a feature vector. The randomly specified patches are taken as input and modifications are made at the training stage. After the completion of the training, the network utilizes the modified patches for the prediction and validation of the results. There are two types of transformation in the CNN, the first transformation is convolution where the pixels are convolved with the filter. The second one is subsampling.

4.3 HHO Algorithm

Harris hawks’ pursuit behavior, which is a cooperative approach to chasing, inspired the HHO algorithm. The HHO algorithm has been employed in a range of scientific applications with great success. The hawks try to surprise and pounce on their victim (rabbit) in various methods. The pursuit kinds are chosen by Harris hawks based on the prey’s flying path. The three stages of HHO are pouncing, tracking, and attacking. The Fig. 4 depicts the phases of the HHO algorithm.

Fig. 4

The phases of HHO. $SB$ is a Soft besiege; $HB$ is the Hard besiege; $PRD$ is the Progressive rapid dives; $RL$ is the random location

The exploration phase of the HHO algorithm is for waiting, seeking, and discovering the desired pursuit. The shift from exploration to exploitation is the HHO’s second stage, and the Exploitation phase, which is dependent on the prey’s residual energy, is the third. Hawks utilize two types of besieging to hunt rabbits from various directions: SB (soft besiege) and HB (hard besiege), with SB being the most common and HB being the least common.

• Exploitation

• Exploration

• Exploration to Exploitation Transition

4.3.1 Exploration Process

Every step has been examined in order to determine the best method for the Harris Hawks. The Harris hawks’ location can be calculated using the formula below:

$$x^{*} \left( {Iter + 1} \right) = \left\{ {\begin{array}{*{20}l} {x_{rand}^{*} \left( {Iter} \right) - r_{1} \left| {x_{rand}^{*} \left( {Iter} \right) - 2r_{2} x^{*} \left( {Iter} \right) if q_{*} \ge 0.5,} \right.} \hfill \\ {\left( {x_{rabit}^{*} \left( {Iter} \right) - x_{m}^{*} \left( {Iter} \right)} \right) - R_{3} \left( {LB + R_{4} \left( {UB - LB} \right)} \right) if q_{*} < 0.5 } \hfill \\ \end{array} } \right.$$

(2)

The current iteration is represented in the available population as Y rand*, R I where i = 1,2,3,4,… q_*. The rabbit position is represented by the symbol Y rabit*, and these digits are picked at random from the range of 0 to 1.

$$Z_{m}^{*} \left( {Iter} \right) = \frac{1}{{N_{*} }}\mathop \sum \limits_{i = 1}^{{N_{*} }} X_{i}^{*} \left( {Iter} \right),$$

(3)

$Z_{m}^{*}$ = each hawk’s position (solution), $N_{*}$ = Hawks’ size, $Z_{i}^{*}$ = place of all hawk.

4.3.2 Process of Exploration to Exploitation Transition

In this section, the power of the rabbit is determined using the following equation:

$$E^{*} = 2E_{0}^{*} \left( {1 - \frac{Iter}{{T^{*} }}} \right),$$

(4)

$E^{*}$ represents the rabbit’s external power. $T^{*}$ is the iteration’s maximum size, The Inlet energy from every stage is $E_{0}^{*}$, with − 1 < $E_{0}^{*}$ > 1. HHO identifies the rabbit state based on $E_{0}^{*}$ variation.

4.3.3 Exploitation Process

HHO takes the soft round when the |E* | is more than 0.5 and the hard round when the |E* | is less than 0.5. When it comes to the prey’s escape tactic, HHO employs four different techniques: SB and HB, PRD when the target is difficult to capture and advance quick jumps when the prey is easy to grab. A |E* | value larger than 0.5 indicates the prey has adequate energy to flee.

4.3.4 Process of Soft Surround

$${\varvec{r}} \,{\text{and}}\,e^{* } \ge \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} .$$

This process is modeled using the equation below:

$$x^{*} \left( {Iter + 1} \right) = \Delta x^{*} \left( {Iter} \right) - e^{*} \left| {J^{*} x_{rabbit}^{*} \left( {Iter} \right) - x^{*} \left( {Iter} \right)} \right|,$$

(5)

$$\Delta x^{*} \left( {Iter} \right) = x_{rabbit}^{*} \left( {Iter} \right) - x^{*} \left( {Iter} \right),$$

(6)

$\Delta Z^{*}$ is the difference between the prey’s location vectors?. $J^{*}$ is the 2 $\left( {1 - R_{s} } \right)$ The severity of the prey′s jump during the escaping stage?. $R_{s}$ is the Random number between the range of 0 and 1?

4.3.5 Process of Hard surround

Here the rapid dives $R$ ≥ ½ and energy $\left|{E}^{*}\right|$ ≥ ½.

The following equation describes the current situation:

$$x^{*} \left( {Iter + 1} \right) = x_{rabbit}^{*} \left( {Iter} \right) - E^{*} \left| {\Delta x\left( {Iter} \right)} \right|$$

(7)

4.3.6 Process of Advanced Rapid Dives when Soft Surround

$R$ Is ≤ ½ and $\left| {E^{*} } \right|$ is ≥ 1/2,

Hawks find the next purpose for soft surround using the equation below.

$$G^{*} = x_{rabbit}^{*} \left( {Iter} \right) - E^{*} \left| {J^{*} x_{rabbit}^{*} \left( {Iter} \right) - x^{*} \left( {Iter} \right)} \right|$$

(8)

Using the below relation, the hawks can dive,

$$H^{*} = Y^{*} + R^{*} \times lf\left( d \right)$$

(9)

$d$ is the Issue dimension, $R_{1 \times d}^{*}$ = Random vector along with levy flight.

$$lf\left( d \right) = 0.01 \times \frac{{\mu^{*} \times \sigma^{*} }}{{\left| {\vartheta^{*} } \right|^{\frac{1}{b}} }}.\sigma^{*} = \left( {\frac{{\rho \left( {1 + b} \right) \times sin\left( {\frac{\pi b}{2}} \right)}}{{\rho \left( {\frac{1 + b}{2}} \right) \times b \times 2^{{\left( {\frac{b - 1}{2}} \right)}} }}} \right).b = 1.5$$

(10)

$\vartheta^{*}$ and $\mu^{*}$ = Random amounts between the range of 0 and 1.

Updating the hawk’s location,

$$x^{*} \left( {Iter + 1} \right) = \left\{ {\begin{array}{*{20}c} {g^{* } if \;f\left( {g^{*} } \right) < f\left( {x^{*} \left( {Iter} \right)} \right)} \\ {h^{*} if\; f\left( {x^{*} } \right) < f\left( {x^{*} \left( {Iter} \right)} \right)} \\ \end{array} } \right.$$

(11)

4.3.7 Process of Advanced Rapid Dives when Hard Surround

$R$ Is less than 1/2 and $\left| {E^{*} } \right|$ is less than 1/2, The hawks’ behavior is replicated here since they were close to the rabbit in the current study.

$$x^{*} \left( {Iter + 1} \right) = \left\{ {\begin{array}{*{20}c} {g^{* } if \;f\left( {g^{*} } \right) < f\left( {x^{*} \left( {Iter} \right)} \right)} \\ {h^{*} if\; f\left( {h^{*} } \right) < f\left( {x^{*} \left( {Iter} \right)} \right)} \\ \end{array} } \right.$$

(12)

$$g^{* } = x_{rabbit}^{*} \left( {Iter} \right) - e^{*} \left| {j^{*} x_{rabbit}^{*} \left( {Iter} \right) - x^{*} \left( {Iter} \right)} \right|$$

(13)

$$h^{*} = g^{*} + r^{*} \times lf\left( d \right)$$

(14)

$$x_{m}^{*} \left( {Iter} \right) = \frac{1}{{N_{*} }}\mathop \sum \limits_{i = 1}^{{N_{*} }} x_{i}^{*} \left( {Iter} \right)$$

(15)

The HHO optimization is combined with CNN to accurately estimate the fault severity.

The implementation of the DPM into the assessment after the level’s classification and threshold. An ML-based CNN with DPM has been developed using the MATLAB tool to make assessing hundreds of PT data easier. In several studies, the utilization of the ML in PT assessment has also been stated. By characteristic all the coordinates in the DPM graph, the advancement of the model is initiated which coordinates of the boundaries are as follows with respect to the reference [24];

${\varvec{PD}}^{\user2{*}}$: (0, 24.5), (0, 33), (− 1, 24.5), (− 1, 33),

${\varvec{D}}_{1}^{\user2{*}}$: (0, 40), (38, 12), (32, − 6), (4, 16), (0, 1.5),

${\varvec{D}}_{2}^{\user2{*}}$: (4, 16), (32, − 6), (24, − 30), (− 1, − 2),

${\varvec{T}}_{3}^{\user2{*}}$: (24, − 30), (− 1, − 2), (− 6, − 4), (1, − 32),

${\varvec{T}}_{2}^{\user2{*}}$: (1, − 32), (− 6, − 4), (− 22.5, − 32),

${\varvec{T}}_{1}^{\user2{*}}$: (− 22.5, − 32), (− 6, − 4), (− 1, − 2), (0, 1.5), (− 35, 3),

${\varvec{S}}^{\user2{*}}$: (− 35, 3), (0, 1.5), (0, 24.5), (0, 33), (− 1, 24.5), (− 1, 33), (0, 40),

${\varvec{T}}_{3}^{\user2{*}} {\varvec{H}}^{\user2{*}}$: (− 24, − 30), (− 3.5, − 3), (2.5, − 32),

${\varvec{C}}^{\user2{*}}$: (2.5, − 32), (− 3.5, − 3), (− 11, − 8), (− 21.5, − 32),

${\varvec{O}}^{\user2{*}}$: (− 21.5, − 32), (− 11, − 8), (− 3.5, − 3), (− 1, − 2), (0, 1.5), (− 35, 3).

The next step is calculating the relative percentage of each of the five gases after getting the boundaries and plotting the coordinates: ${\text{C}}_{2} {\text{H}}_{2}$, ${\text{H}}_{2}$, ${\text{C}}_{2} {\text{H}}_{6}$, ${\text{CH}}_{4}$, ${\text{C}}_{2} {\text{H}}_{4}$.

The coordinates of five relative gas percentages are then plotted into the pentagon. The next step is to find the centroid of the pentagon generated by five relative gas percentage coordinates. The equation is used to compute the area of the pentagon (2). The coordinates of five relative gas percentages are then plotted into the pentagon. Using the Eqs. (3) and (4), the centroid ${x}^{*}$ $\left({cx}^{*}\right)$ and centroid ${y}^{*}$ $\left({cy}^{*}\right)$ of a pentagon are calculated.

$$a^{*} = \frac{1}{2}\mathop \sum \limits_{i - 0}^{{n^{*} - 1}} \left( {x_{i}^{*} y_{i + 1}^{*} - x_{i + 1}^{*} y_{i}^{*} } \right)$$

(16)

$$centroid_{{x^{*} }}^{*} = \frac{1}{{6a^{*} }}\mathop \sum \limits_{i - 0}^{{n^{*} - 1}} \left( {x_{i}^{*} + x_{i + 1}^{*} } \right)\left( {x_{i}^{*} y_{i + 1}^{*} - x_{i + 1}^{*} y_{i}^{*} } \right)$$

(17)

$$centroid_{{y^{*} }}^{*} = \frac{1}{{6a^{*} }}\mathop \sum \limits_{i - 0}^{{n^{*} - 1}} \left( {y_{i}^{*} + y_{i + 1}^{*} } \right)\left( {x_{i}^{*} y_{i + 1}^{*} - x_{i + 1}^{*} y_{i}^{*} } \right)$$

(18)

Create a training database with the inputs (cx*) and (cy*) and the targets PD*, D 1*, D 2*, O*, C*, S*, T 3* H*. Using fivefold cross-validation, 961 training data sets were examined. Three machine learning models have been trained and tested: the Support Vector Machine (SVM), the K-Nearest Neighbor (KNN), and CNN. Table 8 provides a comparison of the performance of various machine learning (ML) based Duval Pentagon Method (DPM) models for assessing transformer faults’ severity. The table shows three types of ML models, namely, Convolutional Neural Network (CNN), Support Vector Machine (SVM), and K-Nearest Neighbor (KNN), along with their corresponding accuracy values.The first model, CNN, achieves an accuracy of 99%, indicating that it correctly identified the severity of faults in the majority of the transformers. The second model, SVM, achieved an accuracy of 97.5%, which is also a high accuracy level, but slightly lower than that of the CNN model. Finally, the third model, KNN, achieved an accuracy of 94.4%, which is still a good accuracy level but lower than the other two models.

Table 8 ML-based DPM performance comparison

Overall, these results indicate that the CNN model is the most effective in accurately identifying transformer faults’ severity among the three ML models evaluated in this study. It is important to note that the specific performance of these models may vary depending on the dataset used, the specific parameters of the models, and other factors.

Following that, real transformer data was used to put the CNN-based DPM to the test. A total of 127 transformers were used to test the model, all of which have been identified as aberrant DGA information. Five DGes from the 127 transformers were evaluated using graphical DPM. The (cx*) and (cy*) were calculated using Eqs. (2), (3), (4) and then placed into the CNN-based DPM.

Table 8 presents a performance comparison of different machine learning (ML) models for detecting diesel particulate matter (DPM) using their accuracy values. The three models compared in the table are Convolutional Neural Network (CNN), Support Vector Machine (SVM), and K-Nearest Neighbors (KNN). The table shows that the CNN model achieved the highest accuracy of 99%, indicating the best performance in detecting DPM. The SVM model achieved an accuracy of 97.5%, which is also a relatively high accuracy value. The KNN model achieved an accuracy of 94.4%, which is slightly lower than the other two models. Overall, the table suggests that the CNN model is the most effective ML model for detecting DPM. However, it is important to note that other factors, such as the availability and quality of training data, computational resources, and model complexity, may also influence the selection of an appropriate ML model for a particular application.

Table 9 shows 10 examples from 127 real transformer DGA data. 98.8% of the time, the graphical DPM and the forecast made using the established model coincided. When detecting the type of transformer failure based on DPM interpretation, The trained model has a good correlation with the graphical DPM and could be used to analyze hundreds of data points quickly. Figure 5 Confusion matrix.

Table 9 10 examples of DPM prediction using CNN

Fig. 5

Confusion matrix

The table provides 10 examples of DPM (dissolved gas analysis) prediction using a CNN (convolutional neural network) along with the input values and predicted DPM values for each example. The input values include the concentrations of various gases such as H₂, CH₄, C₂H₂, C₂H₄, C₂H₆, along with the coordinates of two points (cx and cy). The predicted DPM values are denoted with different symbols, including D1*, S*, O*, PD*, D2*, and T3* H*. It is important to note that the table lists 14 examples instead of 10. The CNN-based DPM prediction model achieved high accuracy, as reported in Table 8. The actual accuracy of the model can vary depending on the size and quality of the training data and other parameters used in the model. The examples in Table 9 demonstrate the ability of the CNN model to accurately predict DPM values for a range of input values, with predicted DPM values ranging from as low as -18.54 to as high as 32.51. Overall, the results suggest that the CNN model can be an effective tool for predicting DPM values based on input gas concentrations and other relevant parameters.

4.4 Norm Development of Fault Severity

The proposed method is depicted in Fig. 6. Table 4 will be used to compare DGA data. The transformer is considered normal if all of the gases are within normal amounts (Condition 1). Apply DPM if the concentration of one of the gases exceeds that of a typical normal gas. The level of the gas as well as the rate of growth will be evaluated. The DPM, GL, and GR measurements will be used as input to the DGA-based judgment procedure for determining the severity of a PT’s problems.

Fig. 6

Proposed flowchart

The outcomes of a PT’s fault severity model are five condition types:

Normal = ${A}^{*}$; Acceptable = ${B}^{*}$; Need for caution = ${C}^{*}$; Poor = ${D}^{*}$; Very poor = ${E}^{*}$.

These classifications, as well as the activities that should be taken as a result, are depicted in Table 10.

Table 10 Faults’ severity of transformer model’s output power

Table 10 provides a summary of the recommended actions for different levels of fault severity detected by the model’s output power. Condition A* indicates that the transformer is operating normally, and the recommended action is to measure the dissolved gas analysis (DGA) yearly. Condition B* indicates that the transformer is acceptable, but some caution is necessary. The recommended action is to measure the DGA yearly and check the rate of generation. Condition C* indicates that the transformer requires caution, and the recommended action is to measure the DGA in half-yearly intervals and check the rate of generation. Condition D* indicates that the transformer is in poor condition and extreme caution is necessary. The recommended action is to measure the DGA in monthly intervals, check the rate of generation, and discuss with the manufacturer to confirm the electrical test. Condition E* indicates that the transformer is in very poor condition, and the recommended action is to measure the DGA weekly, check the rate of generation, and consider service and further investigation. In summary, the severity of the transformer faults detected by the model’s output power determines the recommended actions, ranging from yearly DGA measurement for normal operation to weekly DGA measurement, rate of generation checking, manufacturer discussion, and further investigation for very poor conditions.

Several classic research publications have developed a standard for categorizing DGA interpretation throughout the format of a flowchart. The flowchart has been modified with the help of citation [27] to show how DPM results are interpreted under four conditions.

Initially, compare the five gases such as ${\text{C}}_{2} {\text{H}}_{2}$, ${\text{H}}_{2}$, ${\text{C}}_{2} {\text{H}}_{6}$, ${\text{CH}}_{4}$, ${\text{C}}_{2} {\text{H}}_{4}$ into values of typical concentration in Table 4. ${\text{CO}}$ and ${\text{CO}}_{2}$ were the only two gases not included in this study. These gases will be utilized in a separate investigation to assess the severity of paper damage. Following is an example of how to utilize Fig. 6. Apply DPM if the normal limit (L1) is exceeded by at least one gas. Report normal or Condition 1 if none of the other options are available. If DPM is causing S, check your rate (Stray Gas). If the annual growth rate (GR) exceeds R1, indicate condition 2, else report normal. Figure 7 depicts a flowchart that develops four distinct scenarios, spanning from Condition 1 to Condition 4.

Fig. 7

Form DPM results, four—condition classification flowchart

The GL and rate should be checked after the DPM has been checked. Table 5 determines the GL, while Table 7 determines the GR. The maximum GR and GL are determined using Table 11. As a result, four classes are produced. The following is an illustration of how Table 11 can be used. Regardless of the rate, report the condition when the maximum GL reaches L1. Report condition 2 if the maximum GL is 2 and the maximum GR is 2 or 3, and so on.

Table 11 Selected condition depending on the gas level and rate

Based on DPM interpretation, rate of gas, and level of gas, two conditions have been assigned thus far. Table 12 combines the conditions from Fig. 6 flowchart with Table 11’s GL and rate. Table 12 produces five severity levels for faults, ranging from ${A}^{*}$ to ${E}^{*}$, with ${ND}^{*}$ for “not defined.” Here’s an example: When the DPM flowchart yields C1, the severity of the problems is reported as A. If the DPM flowchart is C2 and the GL rate is C2, the fault severity is B*. The following result section introduces FL, which is utilized to fulfill this condition.

Table 12 GL, GR based on DPM’s norm of fault severity

4.5 Fuzzy Logic

To improve the reliability of the faults’ severity evaluation of power transformer, a new approach in the form of fuzzy logic (FL) has been presented as a new way to analyses faults’ severity employing the combining of GL, GR, and DGA interpretations from the Duval Pentagon Method (DPM). The fuzzy logic method is a computerized calculation tool that simulates expert knowledge, experience, and automatic judgment without requiring human intervention. To aid in standardizing the total decision of various DGA interpretation techniques, fuzzy logic models have been developed. The model’s input variables are the seven main gases in parts per million (ppm). Each model’s output is separated into three sets of membership functions, each of which contains thermal (oil and/or cellulose overheating) and electrical (corona and arcing) faults that might be recognized using DGA. Several interpretive techniques were employed to locate these faults. Show the given below Fig. 8 flowchart for a fuzzy logic model.

Fig. 8

Flowchart for a fuzzy logic model

To find these faults, multiple interpretation methods were used. The combustible gas generation-temperature chart specifies the temperature range at which gases are formed inside an oil-filled transformer. At lower temperatures than oil breakdown, cellulosic thermal decomposition releases ${\text{CO}}$ and ${\text{CO}}_{2}$, and detectable amounts of these gases can be detected at typical operating temperatures. The ${\text{CO}}_{2}$/${\text{CO}}$ ratio is utilized to make a sure selection on the paper degrading situation. This ratio, however, is not a reliable measure of paper health because it can occur under normal operating conditions due to oil degradation. For a more thorough assessment of the paper condition, further tests such as furan analysis or, if feasible, degree of polymerization (DP) should be performed. Oil thermal breakdown begins at a higher temperature, at 350 degrees Celsius, and ${\text{C}}_{2} {\text{H}}_{4}$ production begins. ${\text{H}}_{2}$ generation exceeds that of all other gases at around 450 °C, resulting in low-intensity discharges such as partial discharge and extremely low-level intermittent arcing. More ${\text{C}}_{2} {\text{H}}_{2}$ is created at around 700 °C, resulting in high-intensity arcing or a continuous discharge percentage.

In the output membership functions depicted in Fig. 9, membership functions (F4) and (F6) are added to reflect the normal operation and “out of code” scenarios that ratio approaches may lead to for some DGA data. The faults are organized on a scale of 0 to 8 starting from normal condition (F4) to sustained arcing fault (F3) to identify transformers’ critical ranking based on DGA values, as illustrated in Fig. 9.

Fig. 9

Fuzzy logic models output membership functions

Based on several DGA interpretation methodologies, a collection of fuzzy logic rules in the form of (IF-AND-THEN) statements linking the input to the output variables is produced. Each fuzzy model is created using MATLAB’s graphical user interface tool, which fuzzifies each input into distinct sets of membership functions. The defuzzification approach employs the center-of-gravity, with the desired output ${x}_{0}$ determined as:

$$x_{0} = \frac{{\smallint x.\mu_{c} \left( x \right)dx}}{{\smallint \mu_{c} \left( x \right)dx}}$$

${\mu }_{c} \left(x\right)$-output’s membership function.

For each DGA interpretation method (IEC, Duval, Roger, key gas, and Doerenburg) listed in Section ‘Dga interpretation techniques,’ a fuzzy logic model is created. The fuzzy logic created for the IEC ratio approach is detailed below. For the other approaches listed, the same procedure was utilized to build fuzzy logic models.

The number of gases contained in the oil sample determines the input membership functions for the three ratios (${\text{C}}_{2} {\text{H}}_{2}$/${\text{C}}_{2} {\text{H}}_{4}$, ${\text{CH}}_{4}$/${\text{H}}_{2}$, and ${\text{C}}_{2} {\text{H}}_{4}$/${\text{C}}_{2} {\text{H}}_{6}$) used in the IEC approach. As illustrated in Fig. 3, a set of fuzzy rules that connect the input parameters to the output are established. ${\text{C}}_{2} {\text{H}}_{2}$/${\text{C}}_{2} {\text{H}}_{4}$ (0.15), ${\text{CH}}_{4}$/${\text{H}}_{2}$ (2.5) and ${\text{C}}_{2} {\text{H}}_{4}$/${\text{C}}_{2} {\text{H}}_{6}$ (5), as identified in one transformer oil sample using DGA, are used to evaluate the model. The numerical output of the fuzzy logic model is 7.44, which corresponds to F3 (arcing fault). This result indicates that the transformer under study has a substantial criticality that requires immediate attention.

5 Result and Discussion

The information from the PT DGA was gathered and analyzed. To determine the severity of defects, three methods were used: The first was based on References [9, 28, 29], the second was TDCG (as specified in Reference [30], and the third was the FL model’s suggested approach.

5.1 FLM

Based on DPM interpretation, GL, and GR, the approach provided in this study divides PT failures into five categories. The FL model was created and tested using MATLAB. The severity of the problems is depicted in Fig. 8. (FLM). GL FL, GR FL, GL and rate FL, DPM FL, and Faults’ Severity FL are the five FLMs that have been constructed. Figure 8 shows the hierarchical structure of this model. Figure 9 depicts the use of trapezium membership functions in DPM FL’s input membership functions. Figures 10, 11, 12, 13, 14 demonstrate input membership functions for five gas concentrations in ppm. The data in Table 5 was used to generate these input membership functions. This method has the advantage of using fuzzy values rather than traditional crisp values. This allows for the division of a gas concentration into two levels, each having its own membership level.

Fig. 10

Fuzzy IEC rules

Fig. 11

FLC model for fault severity

Fig. 12

Input membership functions

Fig. 13

Output membership function of gas

Fig. 14

Input membership function of GL

Figure 11’s flowcharts, Table 11’s GL, and rate, and Table 12’s defect severity standard are then used to assign the rules.

Figure 12 depicts the gas’s input membership functions in FLC models.

Figure 13 demonstrates the output membership function of the gas in the FLC model.

Figures 14, 15, and 16 demonstrate the GL, DPM interpretation level, and gas rate input membership functions for the PT.

Fig. 15

Input membership function of DPM interpretation results

Fig. 16

Input membership function of GR

Figure 17 demonstrates the output membership function of DPM of gas, level of gas, level of GR, and DPMFL.

Fig. 17

Output membership function of DPM of gas, GL, rate, and DPMFL

Figure 18 demonstrates the output graph of the FL model. This is the three-dimensional graph with respect to rate, DPM, and DPMFL.

Fig. 18

Output graph of FL

Figure 19 demonstrates the membership function of input variables of DPMFL and level rate FL.

Fig. 19

Input variable membership function of DPMFL and Level rate of FL

Figures 17, 20 illustrates the accuracy graph of CNN with DPM in which a bold blue line is mentioned as a training smoothed line, a light blue line is mentioned as a training line, and a black dotted line is mentioned as a validation line.

Fig. 20

Accuracy graph

Figure 21 illustrates the graph of the loss signal of CNN with DPM in which a bold red line is mentioned as smoothed training line, a light red line is mentioned as a training line, and a dotted black line is mentioned as a validation line. After that, the FL implementation will be applied to the DGA data from in-service PTs. In the following section, we’ll go over the findings.

Fig. 21

Loss graph

5.2 Faults Severity

Depending on the DPM interpretation, FL, GR, and GL were employed to assess the severity of flaws. The method of evaluating the suggested model is described in this section. The initial step was to acquire as much recent DGA of in-service PT data as possible. These PTs fall into the same categories as those used to calculate typical values and rates. These transformers will be subjected to the fault severity model to determine the severity of the PT population as a result of faults. Two different methodologies were compared to the results. This FL was then used to assess the severity of PT faults over a four-year period using historical data on four transformers, confirming the model’s applicability in assessing the severity of PT errors using historical data. The transformer’s transformation.

5.3 Result and Discussion

In the faults severity approach, there are five FL models: GL FL, GL GR FL and rate FL, DPM FL, and Faults Severity FL. Figure 11 illustrates the model’s hierarchical structure. The suggested technique is compared to a variety of previously published methodologies, as well as the application of the fault severity method to PT’s historical data in this part.

5.3.1 Fault Severity of a Transformer

Using DGA data from the in-service PT, the severity of issues was evaluated. Recent DGA data from in-service PTs were analyzed and compared to other previously presented approaches to validate the outcomes of the proposed approach. To evaluate the suggested fault severity FL models, five gases were used (H₂, C₂H₆, C₂H₄, CH₄, and C₂H₂). CO and CO₂ were not included in this inquiry as they will be employed in a separate study to determine the degree of paper deterioration. The suggested fault severity method had a signed agreement with the other techniques for the 26 PT’s. Most other approaches resulted in condition A for transformers with normal faults of severity. In a few other circumstances, though, there are some distinctions.

Thermal flaws with paper carbonization above 300 °C and below 700 °C, GL maximum (max) of 3, and GR maximum of 1 were observed in case 14. Case 14 would have been in the C (Need Caution) condition, according to the HIDGA technique. This would be caused to rather high amounts of a variety of gases, as shown by a maximum GL of 3. Despite the fact that numerous gases had large concentrations, the rate of rising was slow. Condition B will be assigned to this PT in this proposed manner. Case 17 has a similar outcome. Because of the addition of the GR of growth, the severity of the predicted defects is more sensitive in some circumstances Transformer 26 was riddled with flaws. The DPM result for Transformer 26 indicates that the transformer has a high-energy discharge. Furthermore, there was proof of a high level and rate. According to Table 10, utilities should double-check transformer 26 on weekly DGA readings, examine that rate, and consider withdrawing it from service for further inquiry.

Figure 22 demonstrates the class of distribution with respect to frequency, in which ${C}^{*}$ is reached 37 Hz frequency, ${D}_{1}^{*}$ is 82 Hz, ${D}_{2}^{*}$ is 50 Hz, ${O}^{*}$ is 48 Hz, ${PD}^{*}$ is 137 Hz, ${S}^{*}$ is 110 Hz, and ${T}_{3}^{*}{H}^{*}$ is 40 Hz. In addition, here the ${PD}^{*}$ reached the maximum frequency.

Fig. 22

Class of distribution with respect to frequency

5.3.2 Historical Data of Fault Severity of PT

Using historical data from four PTs, more implementations were made. Once a year, the amount of DG in the transformer oil was measured. Table 13 shows the degree of flaws in four PTs over the course of four years. Despite the DPM interpretation of C* or O*, the gas concentration level of five PTs does not exceed 1, and so this transformer is assigned normal faults severity. A similar example can be seen in Transformer 2. The severity of problems increased in the second year for transformer 3 in Table 13. The concentration level surpassed level one, and the annual GR of rising sped to level four. As a result, the severity of ‘needs for caution’ issues grows. Level 4 had the highest GL, and the DPM interpretation findings revealed that transformer 4 has thermal failures over 300 °C and below 700 °C with paper carbonization. Furthermore, the GR of increase of transformer 4 was quite strong from the second-year forward. As a result, the severity of transformer 4 defects is bad. Monthly DGA readings are required, as well as a quick oil treatment. Table 13 demonstrates the four years fault severity of the PT.

Table 13 Fault severity determination of four years PT

From the above analysis, this is proved that the proposed system is superior to the other conventional approaches. In other cases, several differences are available. Because of the suggestion of a rise in GR, the proposed fault severity is sometimes more sensitive and selective. The proposed method can be utilized to evaluate previous PT DGA data. Table 14 presents a comparison of the performance metrics of the proposed method with existing works. The table shows the fault severity accuracy (%) achieved by each approach. The fuzzy logic methodology proposed in [15] achieved an accuracy of 94.7%, NPR [17] achieved 98%, the fuzzy logic approach proposed in [18] achieved an accuracy of 95%, and FMECA [19] achieved 97.2%. The proposed method achieved an accuracy of 98.8%, which is higher than all the existing works. This table demonstrates that the proposed method outperforms existing works in terms of fault severity accuracy. It shows the effectiveness of the proposed approach in accurately detecting faults in the system. Therefore, it can be concluded that the proposed method is a reliable and efficient approach for fault diagnosis in the system.

Table 14 Comparisons of performance metric with existing works

5.3.3 Discussion

The study aimed to propose a new methodology for assessing the severity of faults in transformers by using dissolved gas analysis (DGA) data. The proposed approach was compared to other conventional approaches, and the results showed that the proposed method outperformed existing works in terms of fault severity accuracy. The methodology employed five different fault severity models: GL FL, GL GR FL and rate FL, DPM FL, and Faults Severity FL. The FL model was used to evaluate the severity of faults in in-service PTs using recent DGA data. The suggested approach was found to have a good agreement with other techniques, and in some cases, it was more sensitive and selective. The method was also used to assess the severity of faults in four PTs over a four-year period, and the results showed that the proposed method was reliable and efficient in detecting faults in the system. The study concluded that the proposed methodology can be used as an effective tool for fault diagnosis in transformers.

6 Conclusion

In this paper, a fault severity assessment approach for power transformers using DGA was proposed. The proposed approach employed fuzzy logic and decision-making techniques to assess the severity of transformer faults. Five FL models were proposed, and their hierarchical structure was presented. To make the evaluation of hundreds of PTs easier, a CNN-based DPM was built and tested. The proposed approach was compared with several existing methodologies, and its performance was found to be superior to other approaches in terms of fault severity accuracy. The proposed approach was validated using historical data from four transformers, and the results demonstrated its reliability and efficiency in detecting faults. Therefore, it can be concluded that the proposed method is a useful tool for fault diagnosis and assessment in power transformer systems. In future, it is planned to expand the work to other types of transformers: The proposed method can be applied to other types of transformers, such as distribution transformers, to determine the severity of their faults based on GL, GR, and DGA interpretation. In addition, it is also planned to investigate other fuzzy logic techniques: Future research can investigate other fuzzy logic techniques, such as Adaptive Neuro-Fuzzy Inference System (ANFIS), to determine the performance and accuracy of different fuzzy logic approaches in evaluating transformer fault severity.