DGA via DTM [7] applies the percentages of three critical gases, namely methane (CH₄), ethylene (C₂H₄), and acetylene (C₂H₂), to determine the internal faults that occurred in a transformer. These gases are plotted on a triangular diagram, such that concentration ratios of the gases determine the location inside specified zones of the triangle, namely Partial Discharge (PD), low-energy thermal faults (T1, T2), high-energy thermal faults (T3), and electrical discharges (D1, D2), mixed thermal and electrical fault (DT) using Figure 1 . The concentration ratios can be calculated using the following Equation (1), (2), and (3) [7] .

$\%{\text{CH}}_4=\frac{{\text{CH}}_4}{{\text{CH}}_4+{\text{C}}_2{\text{H}}_4+{\text{C}}_{\text{2}}{\text{H}}_2}\times 100$ (1)

$\%{\text{C}}_{\text{2}}{\text{H}}_4=\frac{{\text{C}}_{\text{2}}{\text{H}}_4}{{\text{CH}}_4+{\text{C}}_{\text{2}}{\text{H}}_4+{\text{C}}_{\text{2}}{\text{H}}_2}\times 100$ (2)

$\%{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}=\frac{{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}}{{\text{CH}}_4+{\text{C}}_{\text{2}}{\text{H}}_4+{\text{C}}_{\text{2}}{\text{H}}_2}\times 100$ (3)

DGA severity, that assess the condition of transformers by classifying their internal fault types through DGA is shown in Table 1 . Each fault type (PD, T1, T2, T3, D1, D2, DT) identified via the DTM is assigned a numerical severity between 0.1 and 1.0.

The severity represent the risk level associated with each fault, where higher severity corresponds to less critical faults, and lower severity indicate more critical internal fault conditions.

For example, a PD fault might receive a severity of 0.85 due to its relatively minor impact, while a D2 fault, linked to high-energy discharges causing major damage, could be scored at 0.25. By translating fault categories into severity-based rating, Table 1 assists converting qualitative fault type data into a quantitative format suitable for integration into the overall THI model.

OQA is employed to evaluate the condition of transformer insulating oil, which is essential for both cooling and insulating of the transformer. Three parameters were utilized: breakdown voltage, acidity, and water content. Breakdown voltage indicates the oil’s ability to withstand electrical stress; a low breakdown voltage suggests possible contamination or degradation. Acidity measures the chemical ageing of the oil, with higher acidity pointing to the presence of by-products that can accelerate insulation deterioration. Water content is also essential, as even small amounts of water can impair the insulating properties of the oil and hasten the deterioration of insulating paper. Collectively, these parameters offer insights into the overall condition of the transformer oil. Table 2 shows the severity of OQA parameters (breakdown voltage, acidity and water content).

The OQA severity is calculated via Equation (4)

$\text{OQA}\text{severity}=\frac{\left(x\times 0.169\right)+\left(y\times 0.139\right)+\left(z\times 0.108\right)}{0.169+0.139+0.108}$ (4)

where x = breakdown voltage’s severity, y = Acidity’s severity × 0.139, and z = water content’s severity.

Each parameter applied a severity from 0.1 to 1.0, where a higher severity means better oil condition. For instance, a high breakdown voltage accompanied by low amounts of acidity or water content will almost have a severity of 0.9, suggesting that it is healthy insulating oil. Conversely, lower breakdown voltage or higher quantities of water content or acidity mean deterioration and lessen the severity. These severity account for the quality of the oil and are further aggregated with their respective weighted score [11] (i.e., 0.169, 0.139, and 0.108 for breakdown voltage, acidity, and water content respectively) to find the OQA severity, which contributes to the overall THI model.

FFA is used to evaluate the condition of insulating paper of transformer, which naturally deteriorates over time due to heat, chemical reactions, and electrical stress. As the paper ages, it produces chemical by-products called furans, which dissolve into the insulating oil. By measuring these furans, FFA provides an estimate of how damaged the insulating paper has become. A critical metric in this assessment is called Degree of Polymerization (DP), which reflects the strength of the cellulose fibres within the paper. A high DP indicates healthy, well-preserved insulation, while a low DP signals ageing insulation.

However, directly determining DP involves removing and testing the insulation, which is impractical for active transformers. Instead, FFA estimates DP indirectly through models such as the Chendong model, which translates furan concentrations into approximate DP values as in Equation (5).

$\text{DP}=\frac{1.51-\log 2\text{FAL}}{0.0035}$ (5)

The Chendong model’s ability for providing non-invasive, precise estimations of insulating paper’s condition makes it a valuable instrument in transformer diagnostics. FFA severity is listed in Table 3 .

The FFA severity is from 0.1 to 1.0, where better DP values receiving higher rating, indicating healthier insulation. This scoring permits furan statistics to be translated into a measurable health indicator, contributing substantially to the overall THI model.

The combination of DGA, OQA, and FFA weighted scores gives a complete THI. Each analysis offers independent information about the transformer’s insulation system. Yet, while combined, yields an assessment of the transformer’s health. THI is calculated by combining the weighted scores of DGA, OQA, and FFA (see Table 4 ) using Equation (6).

$\text{THI},\%=\left(a+b+c\right)\times 100$ (6)

Table 4 shows how DGA, OQA, and FFA contributes to the health index of a transformer: DGA (34.8%), OQA (21.6%), and FFA (43.6%). FFA having the very highest weight because insulating paper degradation is irreversible.

The THI (Equation (6)) is then compared with Table 5 , which classify the transformer’s condition as Good, Fair, Poor, or Very Poor.

Based on the THI classification, the suggested actions are as follows: for a “Good” rating, continue data collection at a 1-year interval; for “Fair,” adjust the data collection frequency to every 6 months; for “Poor,” decrease the transformer loading; and for “Very Poor,” plan for significant repair, upgrade, or replacement.