## 3 Experimental Results and Analysis
### Effect of Water Content on the Breakdown Characteristics of Oil in the Nanotransformer  
In accordance with [PERSON]'s law, the moisture content in transformer oil can be represented by Equation (2). \[S=\frac{Q}{10.772\rho_{MO}} \tag{2}\]  
In the equation, \(S\) represents the moisture content in transformer oil (ppm), \(Q\) represents the electrolysis charge (mc), and \(\rho_{MO}\) represents the density of the transformer oil at standard temperature and pressure (kg/m\({}^{3}\)). Three different moisture levels (26 ppm, 61 ppm, and 85 ppm) of nanoparticle oil samples and the corresponding pure oil samples with the same moisture content were selected to conduct breakdown experiments. The aim was to compare and analyze the enhancement effect of TiO\({}_{2}\) nanoparticles on the breakdown voltage of oil samples under different moisture levels. The experimental results of pure oil at various water contents are shown in Figure 7, with the overall variation trend of the curve exhibiting a \"U\" shape. From the figure, it can be observed that, for any given temperature, the breakdown voltage of oil samples with low water contents was higher than that of samples with high water contents, and the minimum breakdown voltage occurred at \(0\)\({}^{\circ}\)C. For oil samples with high water contents, the rate of increase in breakdown voltage was slower for temperatures ranging from \(-10\)\({}^{\circ}\)C to \(10\)\({}^{\circ}\)C compared to samples with low water contents, while the rate of increase in breakdown voltage was faster for temperatures below \(-10\)\({}^{\circ}\)C in samples with high water contents. The experimental results of nanofluid at different water contents are shown in Figure 8. Numerically, the breakdown voltage was higher than that of pure oil, with the maximum value occurring at \(30\)\({}^{\circ}\)C at approximately 75 kV. Through comparison with Figure 7, it can be observed that, when the temperature was above \(0\)\({}^{\circ}\)C, the enhancement of the breakdown voltage by the nanomaterial in transformer oil was more significant. However,  
Figure 7: Experimental results of pure oil at different water contents. when the water content in the oil was high, the improvement effect of the nanoparticle on the breakdown voltage was limited, and the enhancement magnitude was relatively small. The experimental results of the two oil samples are summarized in Figure 9, which shows that the breakdown voltage of nanofluid was higher than that of pure oil at different water contents. Starting from \(-10\)\({}^{\circ}\)C, as the temperature decreased, and the impact of the nanomaterial on the breakdown voltage of transformer oil became more significant, with a more pronounced enhancement. Within the temperature range of 0 \({}^{\circ}\)C to 30 \({}^{\circ}\)C, the enhancement of the breakdown voltage of transformer oil by the nanomaterial became increasingly apparent with the increase in temperature. It can be observed that the water content in transformer oil had a significant impact on its breakdown voltage. As the temperature decreased, the breakdown voltage showed a decreasing trend followed by an increasing trend, with an overall curve variation resembling a \"U\" shape. When the water content in the oil was 26 ppm, the minimum breakdown voltage for both types of oil occurred at 0 \({}^{\circ}\)C. At this point, the lowest breakdown voltage for pure oil was 19.9 kV, while the breakdown voltage for nanoparticle fluid was 21.3 kV, resulting in an increase of 7.03% in breakdown voltage. When the water content in the oil was 61 ppm and 85 ppm, the lowest breakdown voltage did not exceed 10 kV. Compared to pure oil, the nanoparticle fluid exhibited an increase of 9.80% and 8.99% with respect to breakdown voltage, respectively. Figure 8: Experimental results of nanofluid at different water contents. Figure 9: Effect of water content on the breakdown voltage of the two oil samples.