# Quantifying the Effect of Catalysts on the Lifetime of Transformer Oil
## 4 Results
### Changes in the UV-Vis Region of the Electromagnetic Spectrum
As shown in Figure 3a,b, the calculated R\({}^{2}\) values range from 0.986 to 0.996, which is sufficient for the subsequent derivation of the endpoint criterion for the UV-Vis_\(\lambda\)max parameter, as well as for quantifying the remaining lifetime of the tested mineral oil. Considering that the endpoint criterion for UV-Vis_\(\lambda\)max is not standardized and has not been reported to date, it was necessary to derive it using one of the standardized measurement techniques. For this purpose, values measured for the same oil without the presence of any catalysts but under the same experimental conditions using the standardized dielectric dissipation factor (tan \(\delta\)) measurements (published previously [26]) were used. In this earlier study, the measurement of tan \(\delta\) was performed according to EN 60247 [32] and was repeated three times for each aging time and temperature. The tan \(\delta\) measurement represents a traditional and proven technique, and is recognized by the professional community as a standard in the diagnostics of transformer insulation systems. Using this method and the results presented earlier [26], it is possible to validate not only the UV-Vis spectroscopy, but also the other methods that provide appropriate trends in the variables, and in this manner, easily determine when the oil reaches the true end of its technical life. However, this technique also has some disadvantages; for instance, the measurement is time-intensive, the results can be affected by the humidity, and the measuring procedure requires a fairly large volume of oil (at least 120 mL for one test). The study [26] provided three times to reach the endpoint criterion of tan \(\delta\) (tan \(\delta\) = 0.04) corresponding to the three temperatures of thermo-oxidative aging used: 2197 h at 110 \({}^{\circ}\)C, 1177 h at 120 \({}^{\circ}\)C, and 556 h at 130 \({}^{\circ}\)C. Hence, it was possible to derive the endpoint criterion for UV-Vis_\(\lambda\)max indirectly using these times according to the process outlined in Figure 4, which demonstrates this procedure for a temperature of 110 \({}^{\circ}\)C. The actual values of the endpoint criterion for UV-Vis_\(\lambda\)max and times to achieve these criteria for C+ samples were then calculated by solving the cubic equations using Cardano formulas. This procedure led to three slightly different endpoint criteria corresponding to three different temperatures of thermo-oxidative aging, as shown in Table 1. This table also summarizes the fitting parameters of the cubic equations and the times used to achieve each endpoint criterion. From these times, it was possible to quantify how much catalysts reduced the lifetime of the test oil from the perspective of UV-Vis spectroscopy. This parameter is referred to as \"Reduction in lifetime\" in Table 1, and means the percentage reduction in lifetime for oil-containing catalysts (C+) compared to oil without catalysts (C-). As observed from Table 1, depending on the aging temperature used, the reduction in oil lifetime by catalysts ranged from 35 to 45%. The temperature dependence of these values may indicate a nonlinear process of sludge formation in the oil. Nevertheless, the overall high values of oil lifetime reduction, as quantified by UV-Vis spectroscopy, point to the dominant catalytic role of the copper and Kraft paper in the aging process of the transformer insulation system, and in this respect, confirm the recent conclusions of [PERSON] et al. [14]. The obtained results also demonstrate the advantage of using UV-Vis spectroscopy for the quantification of oil discoloration, i.e., for instance, for the accurate and fast quantification of the color scale shown in Figure 2.