Problem statement

A power transformer's likelihood of failure depends on the behavior of its subsystems, which include the insulation system (IEEE Standards Association, 2017). The insulation of a transformer can be diagnosed through a set of electric tests, among them the Megger DC resistance test (Torkaman and Karimi, 2015), the dissipation factor tan-δ test (Malpure and Baburao, 2008), the power factor tip-up test (IEEE Standards Association, 2000), the dielectric frequency response test (IEC, 2006), and frequency response analysis (Sardar et al., 2017). These tests require the transformer to be off-line, which leads to economic impacts for the owner.

On the other hand, a DGA test can be performed with an online transformer and allows detecting the presence of different gases associated with its condition (IEEE Standards Association, 2019; IEC, 2015). Thus, this test might allow identifying the condition of a transformer's insulation based on statistical inference from a set of samples taken from a group of power transformers. This can help reduce the need to frequently disconnect transformers in order to perform insulation tests, as well as its economic impact.

Contributions

The main contribution of this paper lies in the existence of a correlation between two states of the DGA test and the Megger DC resistance test (regular and bad states). This finding was obtained from a statistical treatment applied to a set of real data on these two types of tests from 337 industrial power transformers. This encourages the application of the DGA test to predict potential insulation damages and reduce the need for off-line tests and their economic impact.

State of the art

In the area of dielectric oils chromatography, the interpretation of the gases present in a sample allows diagnosing faults in power transformers, such as the degradation of their insulation system (Díaz and Schmidt, 2014; Dhini et al., 2020). The analysis consists of taking a dielectric oil sample and testing it in an accredited laboratory with a calibrated chromatograph, in order to obtain quantitative results regarding its gas composition, which are expressed in parts per million (ppm) and as a percentage (%).

Currently, the focus of DGA analysis consists of characterizing the behavior of combustible gases in the transformer with the aim of estimating the possible trends throughout its lifespan (Dukarm, 2019), in addition to estimating any internal failures of the equipment which may be derived from the aging of its insulation system (oil and paper) due to both thermal and electrical factors (Mahmoudi et al., 2019). Carrying out DGA analysis on a regular basis allows observing the evolution of gases in the transformer, but there is no clear relationship between electrical failures and gas trends. Failures are usually determined via preventive electrical tests that directly evaluate transformer components (Fofana and Hadjadj, 2016) but require the disconnection of the equipment. However, there are four main DGA analysis techniques that are complementary and have the potential to detect failures in equipment components without affecting operation continuity (Juris et al., 2020).

Recent works have combined current DGA analysis techniques with more complex modeling and probabilistic tools to improve status monitoring in power transformers. Some works use tools such as fuzzy logic and artificial neural networks (Prasojo et al., 2020; Aciu et al., 2021 ; Patekar and Chaudhry, 2019; Saravanan et al., 2020), which allow for fault prediction and a better interpretation of the states of the transformer based on gas levels. On the other hand, the work by Aizpurua etal. (2019) focuses on the combination of probabilistic methods and soft computing to improve health monitoring in transformers under conditions of uncertainty.

Document structure

This article is organized as follows: the Introduction section presents the problem, a review of the state of the art and the contributions of our developed work; the section titled DGA techniques describes the theory associated with current DGA techniques for dielectric oil in transformers; the Methodology section presents the two models applied, the first of which is of the statistical type and focuses on the behavior of trends in fuel gases in addition to applying the theory of correlation of variables, while the second is a technical model to characterize the state of dielectric oil in transformers by applying the current techniques of DGA tests; in the Results section, the results obtained with the proposed models in their corresponding case studies are presents; and the Conclusions section draws the main conclusions of this study.

Doernenburg analysis

Doernenburg analysis, or the Doernenburg ratios method, is employed to determine whether the origin of a transformer failure is thermal or electrical in nature, upon the basis of a group of relationships between the concentrations of different gases present in the transformer oil. This technique considers the concentration of Methane (CH₄), Hydrogen (H₂), Acetylene (C₂H₂), Ethane (C₂H₆), and Ethylene (C₂H₄). The Doernenburg ratios are calculated as follows:

According to this interpretation method, the failures can be as follows: (a) thermal failures, which can occur when the transformer load exceeds the rated capacity over long periods of time, accelerating the natural rate of oil decomposition, generally at temperatures between 125 and 600 ^oC; (b) Corona effect failures, which is a low-energy partial discharge that occurs when dielectric oil is ionized, likely evolving into discharges in the cellulose of the insulating paper; and (c) internal arc failures, which is a short-duration, high-intensity discharge that can compromise the solid insulation of the transformer, where the oil has started its deterioration process (Piegar et al., 2015). Table 1 shows the conditions of the Doernenburg ratios for each type of fault.

Table 1: Doernenburg fault diagnosis

Source: (IEEE Standards Association, 2019)

Key gas analysis

This technique analyzes the individual concentration of gases. According to the temperature variations to which the oil is subjected, it is possible to find higher concentrations of certain gases. For instance, when there is an electrical failure, the temperature rises inside the transformer tank, and high concentrations of combustible gases are liberated. The key gas technique yields an estimate of gas generation for different temperature ranges in the transformer tank (IEEE Standards Association, 2008; Wannapring et al., 2016).

According to Rogers (1978) and IEEE Standards Association (2008), the key gases analyzed with this method and their possible fault diagnoses are as follows:

Ethylene. When the concentration of this gas exceeds 63%, failure due to overheating in the oil is suspected, as it has lost its cooling and insulating properties (i.e., thermal mineral oil failure). Typically, this type of failure is associated with a predominant concentration of ethylene and smaller proportions of ethane, methane, and hydrogen.

Carbon monoxide. If the concentration of this gas exceeds 92%, overheating is suspected in the cellulose due to fluctuations in the transformer's operating temperature, which is derived from load changes (i.e., thermal mineral oil and cellulose fault).

Hydrogen. If the hydrogen concentration exceeds 86%, failure by corona effect is suspected. Low-energy partial discharges predominantly generate hydrogen, with small amounts of methane and traces of ethylene and ethane.

Hydrogen and acetylene. If the predominant gases are hydrogen and acetylene, exceeding concentrations of 60 and 30%, respectively, the fault is most likely of the electric arc type. In this case, the oil undergoes a breakdown in its structure and tends to evaporate in small quantities.

Rogers analysis

Rogers analysis, or the Rogers ratios method, evaluates gas concentration ratios to diagnose faults while considering the transformer tank's operation temperature. This technique evaluates ratios from Equations (1) and (2). Moreover, it incorporates the ratio between the concentrations of ethylene and acetylene (5) (Syafruddin and Nugroho, 2020).

This fault identification technique that the temperature failures in the transformer tank are independent of electrical failures such as partial discharges (Wang, 2003). Thus, it allows identifying five types of failure, namely low-temperature thermal failure, which can be caused by the inrush current or high charging periods; thermal failure below 700 ^oC, typical of equipment with long periods of operation; thermal failure over 700 ^oC, which can be caused by the loss of the oil's cooling capacity; low-energy density arcing; partial discharges (Corona effect); and high-energy arcing, which can be caused by high energy discharges.

Table 2 presents the Rogers ratios for each type of fault. The limitation of this technique is that there can be many cases where the ratios do not meet the conditions established by the method, so the failure cannot be identified.

Table 2: Rogers fault diagnosis

Source: (Sarria-Arias et al., 2014)

Duval analysis

The Duval triangle analysis may be the most complete fault interpretation technique, as it allows identifying the six basic types of faults established in IEEE Standards Association (2019), plus mixtures of electrical and thermal faults. The Duval equations shown in (6)-(8) determine the percentages of methane (X), ethylene (Y), and acetylene (Z) over the sum of the three concentrations. These gases correspond to the increasing energy content or temperature faults: methane for low energy/temperature faults, ethylene for high energy/temperature faults, and acetylene for very high/temperature/arcing faults.

Graphically, the concentrations of the gases shown above correspond to the coordinate axes of an equilateral triangle, and the intersection of lines parallel to the axes allows finding the zone of possible failure in a transformer. Figure 1 shows the Duval triangle and its different fault zones, and Table 3 presents their corresponding diagnoses.

Figure 1: Duval triangle for fault diagnosis

Source: (Sarria-Arias et al., 2014)

Table 3: Duval fault diagnosis

Source: (Sarria-Arias et al., 2014)

The mixed fault zone (DT) allows classifying both thermal and electrical failures. This is a factor related to equipment that operates for long periods of time, as characteristic gases will necessarily be generated for both types of failure.

DGA tests

Dissolved gas chromatography testing in a power transformer consists of systematically calculating the concentrations of the combustible gases present in a sample of dielectric oil. Its results are quantitative and are expressed in parts per million (ppm) and as a percentage (%).

The results obtained for each of the combustible gases are compared with the ranges stipulated by Table 1 of the IEEE Std. C57.104-2008 (Dissolved gas concentrations) (IEEE Standards Association, 2019). These ranges in ppm have been classified and are presented in Table 4.

Table 4: Transformer conditions and ppm gas ranges for the separate gases method

Source: (IEEE Standards Association, 2019)

According to Table 4 and the criteria established by the IEEE, condition 1 represents a transformer in a normal operating state, condition 2 denotes an equipment that must be analyzed using at least one of the DGA techniques, condition 3 implies failures in the oil (all the DGA techniques must be applied), and condition 4 represents a high probability that the oilis undergoing decomposition, so the transformer must be intervened by the manufacturer and be temporarily or permanently withdrawn from operation.

Analysis of Case I

For this case, out of the 337 transformers, a total of 44 DGA tests reported conditions 2 (regular) or 3 (bad), while, regarding the Megger DC tests, there was a total of 45 transformers with conditions 3 (regular) or 4 (bad). Out of these, there were only 38 transformers that had one of the DGA conditions and one of the Megger DC test states in common. Table 7 shows the conditions of these 38 power transformers.

Table 7: DGA and Megger DC condition values for Case I

Source: Authors

To calculate the correlation coefficient, Equations (10) and (11 ) were used, where X̄ represents the transformer's DGA test condition, is its Megger DC test state, and X and Y denote the averages of each condition, which were 2,2894 and 3,2632 respectively. Table 8 presents the results of each term in Equation (10).

Table 8: Transformer correlation coefficient for Case I

Source: Authors

The results obtained show a covariance of 0,1650 and a correlation coefficient of 0,8045. The latter indicates that, if a transformer is in condition 2 (regular) or 3 (bad) in the DGA tests, then it can be said that its insulation is at least in condition 3 (regular) or in condition 4 (bad) of the Megger DC test, with a correlation of 80,45%.

The correlation coefficient obtained was subjected to the hypothesis test described in Table 9, with H₀ being the null hypothesis and H₁ the alternative hypothesis. A t-test based on Student's t-distribution with N - 2 degrees of freedom and a standard deviation calculated with Equation (12) was applied to evaluate the hypotheses by means of the t0 statistic (Equation (13)).

Table 9: Hypotheses raised to asses the significance of the correlation coefficient

Source: Authors

The t-test states that, if t₀ > t _(α/2,N-2), the null hypothesis is rejected, which means that the correlation coefficient of the population is different from 0, i.e., there is a relationship between the variables. On the other hand, if t₀ ≤ t _(α/2,N-2), the null hypothesis is accepted, meaning that the correlation of the population is equal to 0.

In the current study case, t₀ = 8,1269, and the selected significance level was α = 0,05, which gives t _(α/2,N-2) = 2,0281. These results lead to the rejection of the null hypothesis, which means that the sample comes from a population where the correlation is not equal to 0, with a confidence level of 95%.

Analysis of Case II

In this case, the number of transformers with a DGA test condition 1 (normal) was 292, and the transformers with the Megger DC resistance test conditions 3 and 4 were the same 45 of Case I. When comparing the conditions for these transformers, it was found that only seven of them share the conditions described above.

In these transformers, the PI meets two out of the three configurations of the Megger DC test, and the one that did not comply with the standard exhibits a value close to that required. In these protocols, the behavior of Case I was not observed; three or two configurations of the Megger DC test were not met, and their results were far from the required limit.

By applying correlation theory to the data in Table 10, it is observed that X̄ = 1 and = 1. The covariance, as well as the standard deviations S_X and S_Y, have values equal to 0, so the correlation coefficient is an indeterminacy.

Table 10: DGA and Megger DC condition values for Case II

Source: Authors

When a total combustible gases (TDCG) analysis was conducted in these seven transformers, it was found that the highest concentration was 384 ppm and the lowest one was 65 ppm (Table 11). Both values match the normal conditions of the IEEE Std. C57.104-2008 (IEEE Standards Association, 2019), with 0-720 ppm being the allowed range.

Table 11: Total combustible gases (TDCG) conditions for Case II

Source: Authors

The irregular insulation results can be attributed to climatic conditions when the Megger DC tests were run, as a high humidity directly affects the measurement. For this case, it is not possible to apply variable correlation theory, since the DGA and Megger states are the same for all tests. A larger sample would be needed to identify new relationships between the states analyzed.

Analysis of Case III

When the aforementioned DGA techniques were applied to the transformers, it was found that most of them showed no identifiable faults. The majority of the faults found via the Doernenburg, key gas, and Rogers methods were thermal in nature, whereas the Duval technique reported a higher percentage of low-energy partial discharge electrical failures.

In the Doernenburg analysis, 92,88% of the transformers showed no faults. Only 21 transformers reported failures, which were classified according to the Doernenburg ratios (Table 1). 11 of these could not be identified, since at least one of the ratios was indeterminate, implying the need to rerun the tests. As for the rest, eight faults were identified as thermal and two as internal arc failures (Figure 5).

Figure 5: Results for the transformers analyzed via the Doernenburg technique

Source: Authors

When comparing the Doernenburg analysis results against those of the correlation analysis, it was noted that there were more transformers in regular and bad conditions than transformers with identifiable faults according to the Doernenburg analysis.

The key gas technique also classified the majority of the transformers as being in a normal state. The most representative failure with this method was cellulose overheating, with carbon monoxide being the representative gas (Figure 6).

Figure 6: Results regarding relative gas distribution in the 337 power transformers

Source: Authors

As for the Rogers ratios method, 31,45% of the transformers were not suitable for analysis due to indeterminacies in the ratios, 20,47% did not have faults, 15,43% reported faults at low temperatures, and the rest exhibited thermal faults below 700 ^oC. No electrical faults were found with this method, which supports its ability to better predict thermal faults.

According to the Duval triangle, 81,31% of the results correspond to lower-intensity partial discharge electrical faults, which are typical of transformers with long periods of operation. Even though this is a minor fault type, it is likely that it will evolve into more critical faults in the triangle. This is the only method that identified more faulty transformers in comparison with the correlation analysis, given that Duval analysis evaluates failures in early stages, while correlation requires more advanced failure conditions.