## 6 Conclusions  
1. Low concentrations of nanoparticles can improve the quality of transformer oil, but the enhancement of breakdown voltage is not significant. On the other hand, high concentrations of nanoparticles not only fail to improve the quality of transformer oil but also reduce the breakdown voltage. Analysis of the experimental results revealed that the current stage's appropriate choice was a concentration of 0.01 g/L of TiO\({}_{2}\) nanoparticles, which could significantly improve the breakdown voltage of transformer oil without significantly compromising its quality. 2. The relationship curve between the breakdown voltage absolute value of TiO\({}_{2}\) nanomodified transformer oil and temperature exhibited a \"V\" or \"U\" shape. Within the range of \(-\)30 \({}^{\circ}\)C to 30 \({}^{\circ}\)C, the breakdown voltage of the nanofluid was higher than that of pure oil, but the amplitude of improvement compared to pure oil was the smallest around \(-\)10 \({}^{\circ}\)C to 0 \({}^{\circ}\)C. Within the range of 0 \({}^{\circ}\)C to 30 \({}^{\circ}\)C, the breakdown voltage of the nanofluid increased with temperature, and the amplitude of improvement compared to pure oil also increased. Within the range of \(-\)30 \({}^{\circ}\)C to 0 \({}^{\circ}\)C, the breakdown voltage of the nanofluid increased with decreasing temperature, and the amplitude of improvement compared to pure oil also increased. Within the temperature range of \(-\)30 \({}^{\circ}\)C to \(-\)10 \({}^{\circ}\)C, the breakdown voltage could be increased by 13% to 15%; within the range of \(-\)10 \({}^{\circ}\)C to 0 \({}^{\circ}\)C, it could be increased by 8% to 9%; within the range of 0 \({}^{\circ}\)C to 30 \({}^{\circ}\)C, it could be increased by 18% to 21%. 3. The moisture content had a significant impact on the breakdown voltage of TiO\({}_{2}\)-nanomodified transformer oil: the higher the moisture content, the lower the breakdown voltage. Regardless of whether the moisture content was high or low, the breakdown voltage of nanofluids was higher than that of pure oil, and the lowest breakdown voltage occurred at 0 \({}^{\circ}\)C. Compared to oil samples with low moisture content, when the moisture content is high, within the experimental temperature range, nanofluids exhibited a smaller amplitude of breakdown voltage enhancement compared to pure oil; however, the percentage enhancement was greater. Figure 22: Microscopic schematic diagram of the adsorption effect of nanoparticles on charged particles under a uniform electric field. 4. Regardless of whether TiO\({}_{2}\) nanomodified transformer oil or pure oil was used, the breakdown voltage under non-uniform electric fields was lower than that under slightly non-uniform electric fields. However, the breakdown voltage of pure oil exhibited instability under non-uniform electric fields, and the dispersion of breakdown voltage could be significantly reduced by adding TiO\({}_{2}\) nanoparticles. 5. The simulation results indicated that the addition of nanoparticles led to a certain adsorption effect on charged particles and facilitates their low-rate movement while carrying them. This validates the mechanism of nanomaterials enhancing the breakdown voltage of transformer oil, which is attributed to the hindrance of nanoparticle particles on the directed motion of charged particles in the oil. However, it should be noted that the model in this paper was established on the basis of numerous approximations and assumptions, and further research is needed to validate the specific mechanism. Conceptualization, C.Q. ; Methodology, Y.H. and Y.X. ; Software, C.Q. ; Validation, J.S. ; Investigation, Y.H. and H.L. ; Resources, Y.X. ; Data curation, H.L. ; Writing--original draft, Y.H. ; Writing--review & editing, J.S. ; Supervision, L.L. and Y.X. ; Project administration, L.L. ; Funding acquisition, C.Q. All authors have read and agreed to the published version of the manuscript.