Dissolved Gas Analysis (DGA) is one of the most used techniques for assessing the condition of oil-filled power transformers. Electrical and thermal stresses inside the transformer decompose the oil-paper insulation system, generating gases such as hydrogen (H₂), methane (CH₄), ethane (C₂H₆), ethylene (C₂H₄), acetylene (C₂H₂), carbon monoxide (CO), and carbon dioxide (CO₂) [1][11]. Each gas or combination of gases is associated with specific types of defects. Several methods are used to interpret the results of dissolved gas analysis (DGA), including the key gas method, gas ratio methods like the Rogers ratio, and graphical methods such as the Duval triangle [12][13]. In addition, the international standards IEC 60599 [11] and IEEE C57.104 [1] provide guidelines for interpreting dissolved gas concentrations and identifying transformer faults. Although discharge gas analysis (DGA) is an effective diagnostic tool, it has certain limitations. The results can be difficult to interpret when multiple faults occur simultaneously, and periodic oil samples may not be sufficient to detect rapidly developing faults. Consequently, DGA is often combined with other diagnostic techniques to provide a more complete assessment of transformer condition [4][14].

Furan analysis is widely used to assess the aging of paper insulation in power transformers. As paper insulation ages under thermal and oxidative stress, cellulose gradually breaks down and releases furan compounds into the insulating oil. These compounds include 2-furfural (2-FAL), 5-hydroxymethyl-2-furfural (5-HMF), and other related compounds [15][16]. Among these, 2-furfural (2-FAL) is the most used indicator for assessing the aging of paper-based insulation materials, as it is relatively stable and closely linked to cellulose degradation [17]. While DGA analysis detects electrical and thermal defects, furan analysis provides direct information on the condition of paper insulation. Since the concentration of 2-furfural (2-FAL) is closely related to the degree of polymerization (DP) of cellulose, it is commonly used to assess the aging of the insulation and estimate the transformer’s remaining service life [3][18]. Although furan analysis is primarily used to assess the long-term aging of paper insulation, it is less effective for detecting rapidly developing failures. In addition, factors such as oil replacement, operating temperature, and humidity can affect furan concentrations. For this reason, furan analysis is often combined with other diagnostic techniques, such as DGA and moisture measurement, to obtain a more comprehensive assessment of transformer condition [19].

BDV test is employed to evaluate the insulating performance of transformer oil. Over time, thermal, electrical, and chemical aging gradually degrades the oil, leading to the formation of moisture, sludge, dissolved gases, and other contaminants that reduce its dielectric strength [20]. According to IEC 60156, the test consists of applying an alternating voltage that increases continuously at a rate of 2 kV/s between two electrodes immersed in a sample of oil until dielectric breakdown occurs. To ensure the reliability of the results, six consecutive breakdown tests are performed, and the average of the measured breakdown voltages is reported as the BDV value of oil [21]. The relationship between oil dielectric strength and the BDV value is described in the IEEE C57.106 standard [22]. In practice, a BDV value below 30 kV generally indicates significant oil degradation and requires additional investigations as well as corrective maintenance measures [23][24].

The acids present in the oil come from its decomposition or oxidation. They may also come from external sources, such as atmospheric contamination. The measure is made with Color-Indicator Titration technique according to ASTM D974. The standard unit of measure is mg KOH/g. During transformer operation, oxidation gradually generates polar byproducts, particularly organic acids, which leads to an increase in the acid number (AN). Fresh oil insulation contains little or no acidic compounds, whereas a high AN value in service aged oil generally indicates oxidation or contamination by materials such as varnish, paint, or other foreign substances. Consequently, the acid number is widely recognized as a valuable indicator of oil aging, oxidation, nitration, and contamination, making it an important parameter for assessing the condition of transformers. According to industry recommendations, oil regeneration should be considered when the acid number reaches 0.20 mg of KOH/g [23].

Moisture is one of the main factors affecting the performance and service life of transformer insulation systems. It is present in both insulating oil and paper insulation, where it reduces dielectric strength and accelerates insulation aging [25]. At high temperatures, it can also cause the formation of bubbles, which increases the risk of insulation failure [25]. The moisture content of transformer oil is generally measured in parts per million (ppm) using a Karl Fischer titration. The distribution of moisture between the insulating oil and the paper insulation depends on the temperature and the moisture equilibrium within the insulation system [26].

Although the presence of moisture does identify specific transformer faults, it significantly accelerates insulation aging and degradation. As a result, moisture is an important parameter for assessing the full condition of the transformer [19].

3.1.1. Dataset Description

The dataset used in this study was collected from 101 power transformers in service on the Ivorian transmission grid. Sampling of 101 transformers was conducted between September 1 and September 15, 2025. The 101 transformers were inspected as part of the public utility’s regular preventive maintenance program. The measurements were taken from October 6 to October 10, 2025. A complete observation consists of 17 variables. These transformers cover a wide range of voltage levels, powers ratings, and operating conditions, providing a realistic overview of transformer performance in the field.

The fleet includes transformers that were commissioned between the mid-1960s and recent years, exhibiting varying degrees of aging and insulation conditions. Their technical characteristics range from small distribution transformers to large transmission units operating at voltages up to 225 kV. This diversity makes the dataset particularly well-suited for studying various degradation mechanisms, since transformer aging is influenced by operating history, load conditions, and environmental factors [2].

To obtain a more comprehensive assessment of the transformer’s condition, diagnostic parameters from several categories were considered and grouped into three diagnostic categories, as shown in Table 1.

Table 1.Categories of diagnostic parameters considered in this study.

Each diagnostic parameter provides information about a different aspect of transformer degradation. When used together, they allow a more complete and reliable assessment of transformer condition [19].

3.1.2. Data Cleaning and Reconstruction

Field data collected from operating transformers often contains missing values, inconsistent data formats, and incomplete historical information. Consequently, the dataset has been preprocessing to improve data quality and ensure consistent results. First, all diagnostic data were organized into a structured database, in which each transformer was treated as a separate observation and each diagnostic measurement served as an input feature.

3.1.3. Missing Value Treatment

Some diagnostic measurements were missing from the dataset. To retain all records related to transformers and ensure consistent analysis, the missing values were replaced using median imputation, as shown in Equation (1):

Median imputation was used because transformer diagnostic data often contains extreme values associated with failure conditions. Unlike the mean, the median is much less influenced by these values, making it a more robust choice for handling missing data [27].

The number of missing values for each seven variables was as follows: TDCG: (0); BDV: (0); moisture: (0); 2-FAL: (0); CO₂: (0); acidity: (0); and transformer age: (4). Median imputation was performed before calculating the HI and conducting multivariate analysis. The median for each variable was calculated based on the available observations for the fleet. The variables were then standardized using z-scores prior to PCA analysis and K-means clustering.

To improve diagnostic performance, two additional features (transformer age and gas aggradation indicator) were derived from the initial measurements through.

Transformer age was included as an additional parameter, since insulation degradation is largely related to cumulative operating time and thermal aging [27]. It was calculated using Equation (2):

where A g e i denotes the age of transformer i, Y r e f is the reference year used in this study, and Y c o m m , i is the commissioning year of transformer i.

The Total concentration of Dissolved Combustible Gas (TDCG) was used as an complete indicator of gas production associated with transformer failures. In accordance with the definition given in Equation (3), the TDCG value was calculated as the sum of the main combustible gases dissolved in the insulating oil. To further improve the interpretation of failures, gas aggregation indicators were also considered [28][29].

where T D C G is the total dissolved combustible gas concentration (ppm), G i denotes the concentration of the i t h combustible gas (ppm), and n = 6 (H₂, CH₄, C₂H₆, C₂H₄, C₂H₂, and CO) is the number of combustible gases considered.

Transformer degradation is influenced by several electrical, thermal, and chemical stresses that occur simultaneously. To capture these various aspects into a single indicator, a multiparameter HI was developed by [30][31]. This approach estimates the HI of transformers through a three-step evaluation process. First, the dissolved gas analysis factor (DGAF) is calculated with the concentrations of the seven key dissolved gases using Equation (4):

where S i is the condition score assigned to the ith dissolved gas according to the applicable diagnostic standard, W i is the weighting factor reflecting its relative importance, and i represents the seven characteristic gases (H₂, CH₄, C₂H₆, C₂H₄, C₂H₂, CO, and CO₂).

Next, the Oil Quality Factor (OQF) is determined by evaluating the main physicochemical properties of the insulating oil, including dielectric breakdown voltage, acidity, and moisture content. The OQF is calculated using the weighted average formulation given in Equation (5):

where S i denotes the condition score of the i^th oil quality parameter, W i is its corresponding weighting factor, and i refers to the three oil properties considered in the assessment.

The weighting factors assigned to each diagnostic parameter and the corresponding score are presented in Table 2 and Table 3 for the DGAF and the OQF, respectively.

Table 2. DGAF parameters [30][32].

Table 3. oil quality parameters [30][32].

Similarly, the evaluation of paper insulation condition using furan is presented in Table 4. The score of DGAF and OQF calculated are also classified into five levels, as shown in Table 5.

Finally, the global HI is obtained by combining the different diagnostic indicators into a single metric, as shown in Equation (6). Details of HIFj and Kj indices for each parameter are presented in Table 6. Table 7 presents the final assessment of transformers condition based on the transformer HI methods.

Table 4.Furan factor ranking [30].

Table 5.Assement the score of DGAF and OQF [30][32].

where K j is the weight factor indicating the significance of each input to the final health index and H I F j is the health index factor of each input, as shown in Table 6.

Table 6.Health index assessment [30][32].

Table 7. Health index final assessment [30][32].

Figure 1 illustrates the relationship between water saturation and tan δ measured at 90˚C. Most transformers have a water saturation of less than 20% and exhibit relatively low tan δ values. However, tan δ generally tends to increase with water saturation. Several transformers with higher moisture levels also exhibit higher dielectric losses, indicating that moisture may contribute to the degradation of the oil-paper insulation system. Water can increase electrical conductivity and polarization losses, thereby altering the dielectric response of insulating materials. Previous studies have also shown that the dielectric behavior of transformer insulation is strongly influenced by humidity and temperature [33]. Nevertheless, this relationship is not consistent across all transformers. Some units with water saturation exceeding 20% maintain low tan δvalues, while a transformer with water saturation of approximately 17% exhibits an unusually high dissipation factor. These observations indicate that moisture may contribute to an increase in dielectric losses, but it is not the only factor involved. Oil oxidation, polar contaminants, insulation aging, temperature can also affect tan δ.

From the perspective of the health index, water saturation and tan δ should be considered complementary indicators rather than interchangeable ones. Water saturation describes the moisture condition of the insulation system, while tan δ reflects the entire dielectric losses associated with moisture, aging byproducts, and contamination. Including both parameters thus provides a more complete picture of insulation degradation.

In sum, Figure 1 shows that higher water saturation is generally associated with greater dielectric losses. However, neither of these two parameters, taken alone, can’t reliably describe the condition of the transformer’s insulation. Combining them with other physicochemical and electrical indicators therefore provides a more reliable assessment.

Figure 2 illustrates the relationship between carbon monoxide (CO) concentration and 2-furfural (2-FAL) content. Some transformers with a 2-FAL content of less than 1 mg/L have CO concentrations ranging from less than 100 ppm to more than 1,400 ppm. This wide dispersion indicates that the two indicators do not exhibit a strong linear relationship.

Other units with 2-FAL concentrations exceeding 2 mg/L also show relatively high CO concentrations, suggesting advanced degradation of the cellulose insulation. However, this trend is not consistent across the entire dataset. For example, transformers with 2-FAL levels above 3 mg/L have CO concentrations from approximately 450 to 1,200 ppm. Similarly, some units exhibit high CO levels despite relatively low 2-FAL levels. These differences may be related to operating temperature, oxygen availability, oil replacement or treatment, paper type, loading history, and the migration of degradation products between the solid insulator and the oil [34].

Although both variables are associated with cellulose aging, they reflect different degradation processes. CO is primarily produced by the thermal decomposition and oxidation of paper insulation. In contrast, 2-FAL is a more specific marker of cellulose depolymerization, although its concentration can be affected by oil replacement, moisture, temperature, and adsorption by the paper.

In the context of HI, CO and 2-FAL should be treated as complementary indicators rather than interchangeable ones as explained earlier.

The entire graph suggests a certain correlation between high CO concentrations and high 2-FAL levels in several old transformers, but this relationship remains weak and inconsistent across the population of transformers. Presenting Spearman’s correlation coefficient would allow us to quantify this association while limiting the influence of outliers.

Figure 1. Relationship between water saturation and the dielectric dissipation factor (tan δ) measured at 90˚C.

Figure 2. Cellulose aging: 2-FAL versus CO.

Figure 3 shows the Pearson correlations between the selected transformer condition indicators and the HI. The results reveal several significant relationships between oil quality, cellulose aging, gas generation, and the global condition of the transformers.

The HI index shows its strongest correlations with humidity (r = −0.73), total dissolved combustible gases (TDCG, r = −0.70), CO₂ (r = −0.67), and 2-FAL (r = −0.62). Moderate negative relationships are also observed with age (r = −0.57), acidity (r = −0.49), and CO (r = −0.47). In contrast, the BDV shows a positive correlation with the HI index (r = 0.55). These results indicate that higher moisture content, gas concentrations, acidity, and furan levels, and transformer age, are generally associated with lower HI index values, while higher dielectric strength corresponds to a better condition of the transformer. Several condition indicators are also closely related. Moisture shows a positive correlation with 2-FAL (r = 0.68), acidity (r = 0.62), CO₂ (r = 0.54), and age (r = 0.52). These relationships are consistent with the combined effects of moisture accumulation, oil oxidation, and cellulose aging. BDV shows a negative correlation with moisture (r = −0.57), CO₂ (r = −0.37), 2-FAL (r = −0.36), and TDCG (r = −0.32). This suggests that dielectric strength generally decreases as humidity and aging-related byproducts accumulate. However, these correlations remain moderate, confirming that the BDV is influenced by several factors and cannot independently describe the overall condition of the insulation system.

This correlation analysis shows that transformer aging results from several interconnected electrical, thermal, chemical, and moisture-related processes. This finding justifies the use of a multiparameter diagnostic framework.

Figure 3.Pearson correlation matrix of transformer condition indicators and the HI.

Table 8 shows the HI scores for 20 transformers. Based on the proposed HI, the 101 transformers were grouped into five condition categories. As shown in Figure 4, the largest group consists of 35 units with HI scores ranging from 85 to 100, indicating that approximately one-third of the fleet is in very good condition. The intermediate ranges of 30 to 50 and 50 to 70 contain 20 and 21 transformers, respectively, while 14 units fall within the 70 to 85 range. Only 11 transformers have scores below 30, representing the smallest group, but also the one of greatest concern.

The distribution suggests that the global condition of the transformer fleet is generally satisfactory, although a considerable number of units show moderate to significant deterioration. Transformers with lower HI scores may be affected by several interacting factors, such as increased humidity, dielectric losses, oil degradation, dissolved gases, and cellulose aging. These units require closer monitoring and additional testing or corrective actions. By combining multiple condition indicators into a single index, the proposed HI provides a clear overview of the fleet while helping to identify the transformers that require the most attention. This classification can facilitate inspection planning, maintenance prioritization, and long-term asset management decisions.

Table 8. HI scores for 20 transformers.

Figure 4.Distribution of transformers across health index condition ranges.

Principal component analysis (PCA) and the K-means clustering method were used to assess whether the five condition categories defined by the proposed HI corresponded to the multivariate diagnostic structure of the transformer fleet. Given that the variables used in PCA and the K-means algorithm largely overlap with the diagnostic data from the HI index, this analysis was not intended to serve as an independent validation. Rather, it aimed to determine whether the multivariate structure of the underlying measures corresponded to the categories of conditions established by the index.

PCA was performed on seven diagnostic variables including total dissolved combustible gas (TDCG) concentration, breakdown voltage (BDV), moisture, 2-furfural (2-FAL), carbon dioxide (CO₂), acidity, and transformer age. Before analysis, the variables were standardized using z-scores, as they are expressed in different units and have widely varying numerical ranges. This transformation gives each variable equal initial weight and prevents high amplitude measurements to dominate the principal components.

The first two principal components explain 63.58% of the total variance, with PC1 accounting for 50.19% and PC2 for 13.39%. PC1 reflects the entire condition of transformer insulation system as shown in Figure 5. Moisture, 2-FAL, acidity, CO₂, TDCG, and age all have a positive effect on this parameter, while BDV has a negative effect. PC1 can therefore be interpreted as a measure of general degradation axis. The PC2 component primarily displays differences between indicators of gas and oil acidity. TDCG and CO₂ have positive loading coefficients, while acidity has a strongly negative loading coefficient. This component makes it possible to distinguish transformers characterized by gas production from those exhibiting oil oxidation.

Figure 6 shows the transformers scores on the PC1-PC2 plane, with observations colored according to their HI category. It reveals a clear transition in the condition of the transformers along PC1. Units classified as “very good” are concentrated on the negative side, while most of those classified as “very poor” appear at high positive values. Good, fair, and poor transformers fall mainly between these two extremes. This gradual progression supports the HI classification, since a deterioration in condition is generally associated with movement from left to right. PC2 highlights the differences among units with a similar general condition. Its greater dispersion within the “Poor” and “Very Poor” groups suggests that severely damaged transformers do not exhibit the same degradation profile. Some may be primarily affected by gas production, while others may indicate more pronounced effects related to moisture, acidity, or paper aging.

The adjacent categories overlap particularly Good, Fair and Poor, because the deterioration of transformers occurs gradually rather than in distinct stages. The extreme groups are more clearly distinguished, while the intermediate categories reflect transitional stages.

In general, the graph provides significant statistical support for the health index groups, without suggesting that they constitute entirely distinct populations.

Figure 5.Variable loadings on PC1 and PC2.

The K-means clustering method was applied directly to the seven normalized diagnostic variables: TDCG, BDV, moisture, 2-FAL, CO₂, acidity, and transformer age. The analysis was performed in Python using scikit-learn version 1.8.0. The algorithm used k-means++ initialization, 50 independent initializations, a maximum of 300 iterations, a convergence tolerance of 10−4, and a fixed random seed of 42 to ensure reproducibility.

Solutions ranging from k = 2 to k = 7 were evaluated using the silhouette coefficient, the Davies-Bouldin index, the Calinski-Harabasz index, and inertia as shown in Figure 7. The highest silhouette coefficient (0.347) and Calinski-Harabasz index (48.104) were obtained for k = 2, indicating that two clusters provide the clearest natural separation in the dataset. However, the proposed HI classifies the condition of transformers into five operational categories. Consequently, the solution k = 5 was selected to assess the consistency between the clusters resulting from the data analysis and these predefined categories. For k = 5, the silhouette coefficient was 0.297 and the Davies-Bouldin index was 1.315, indicating moderate separation in the seven-dimensional feature space.

Figure 6. PCA score plot colored by health index category.

Figure 8 presents the K-means seven variables projection. The five clusters contained 31, 31, 30, 3, and 6 transformers, respectively. Their average HI values were 96.6%, 76.3%, 45.1%, 31.2%, and 15%, respectively, indicating a clear overall progression in the condition of transformers, from best to worst. The agreement with the five categories of the health index was partial, as shown in Table 9, with an adjusted Rand index of 0.312, a normalized mutual information score of 0.407, and an optimal agreement rate of 60.4%. The strongest agreement was observed for the “Very Good” and “Very Poor” categories, while greater overlap was found among the intermediate categories.

For visualization, the clusters obtained from the seven variables were projected onto the PC1-PC2 plane to illustrate the cluster structure; the K-means analysis, meanwhile, was performed in the full seven-dimensional space.

On the whole, principal component analysis (PCA) and the K-means algorithm provide data-driven evidence that the proposed health status categories follow a technically significant status gradient within the transformer fleet. The results support the consistency of the healthiest groups and most deteriorate, while revealing gradual transitions and multiple degradation profiles among the intermediate categories. Consequently, this analysis confirms the internal statistical consistency of the HI classification.

Figure 7.K-means model-selection metrics for seven standardized variables.

Table 9.Agreement between Health Index Categories and K-Means Cluster Assign-ments.

To illustrate the practical application of the proposed HI, two transformers with different operating conditions were examined. Table 10 presents the values determined based on the complete (electrical and physicochemical) analysis of oil.

Transformer T1 shows high concentrations of dissolved gases, related to thermal activity and possible localized overheating. However, its moisture and acidity levels remain low, indicating limited aging of the insulation. Nevertheless, its breakdown voltage and oil leaks should continue to be closely monitored. Transformer T7 is in poorer condition. Its test results indicate the possible presence of electrical discharges, high moisture content, oil degradation, particle contamination, and leaks. The condition index confirms this difference: T1 scored 42.39% and T7 scored 33.70%, placing both units in the “Poor” category, with T7 requiring special attention.

Although conventional techniques are essential for identifying individual defects, interpreting their results separately may not provide a clear picture of the transformer’s entire condition. The proposed HI overcomes this limitation by integrating the available diagnostic information into a single condition score. The index thus preserves the diagnostic value of each test while making it easier to identify differences in severity level. This case study highlights its usefulness as a complementary decision-making tool for comparing units, establishing maintenance priorities, and selecting transformers that require further examination.

Figure 8.K-means clusters obtained from the seven standardized diagnostic variables and projected onto the PC1-PC2 plane. The X markers represent the projected cluster centroids.

The proposed HI provides asset managers a way to assess the global condition of a transformer fleet. By combining the results of dissolved gas analysis, acidity, moisture content, dielectric performance, and insulation aging indicators into a single index, this method facilitates comparisons between transformers with different operational histories and degradation profiles. Transformers with high HI values may continue to be monitored regularly, while those in an intermediate condition may undergo additional testing or preventive maintenance. Units with low ratings should be prioritized for a thorough inspection, corrective action, or replacement planning. The HI index proves particularly useful when conventional tests yield mixed results. For example, one transformer may have high concentrations of combustible gases while still maintaining acceptable oil quality, whereas another may show moderate abnormalities across several diagnostic parameters. Evaluating each measurement separately can make it difficult to determine which unit requires priority attention. The proposed approach synthesizes these results and provides a more balanced view of the overall condition. However, the final score should not replace individual diagnostic methods, as detailed test results are still necessary to identify the primary failure and select the appropriate maintenance action. At the fleet level, this classification can facilitate risk-based maintenance, inspection planning, budget allocation, and long-term investment planning. It can also help public utilities to identify units that are deteriorating before they reach a critical condition, thereby reducing the risk of unplanned outages. When considered in addition with the transformer’s load, the consequences of a failure, and its maintenance history, the proposed HI provides a practical basis for making technically asset management decisions.

Table 10.Parameters values based on the complete oil analysis for the two transformers studied.