## 1 Introduction
Abundant studies have shown that an external magnetic field significantly affects the stability and insulation properties of nanomagnetic fluids, making nanomagnetic fluids that are prepared with nanoparticles such as Fe\({}_{3}\)O\({}_{4}\) unsuitable for transformers [24; 25; 26; 27]. AlN-based nanotransformer oil can effectively improve the thermal conductivity, positive polarity lightning impulse breakdown voltage, and partial discharge inception voltage of transformer oil. Compared to regular oil, it can increase these properties by 7%, 50%, and 20%, respectively, with the most outstanding positive polarity lightning impulse breakdown characteristics observed when the nanoparticle concentration is 0.127% [28; 29]. For plant-oil-based BN nanofluids, the breakdown strength at 63.2% probability and 5% probability increases by 30% and 33%, respectively, when the mass fraction of BN nanoparticles is 0.05 wt.% [30]. Adding Al\({}_{2}\)O\({}_{3}\) to mineral oil can significantly improve the alternating current breakdown voltage under high-moisture conditions and reduce dielectric loss [31]. Furthermore, Al\({}_{2}\)O\({}_{3}\) nanofluids can slow down the aging of insulating oil and paperboard, with the insulation properties of aged nanofluids improved compared to pure oil and oil-immersed paperboards [32]. For SiO\({}_{2}\)-nanomodified transformer oil, the addition of SiO\({}_{2}\) nanoparticles does not effectively enhance insulation properties when the moisture content is low. However, with higher moisture contents, it can significantly increase the breakdown field strength [33], and SiO\({}_{2}\) nanoparticles can effectively improve the insulation properties of aged transformer oil [34]. [PERSON] and [PERSON] et al. conducted experiments to verify that Fe\({}_{3}\)O\({}_{4}\), TiO\({}_{2}\), and Al\({}_{2}\)O\({}_{3}\) nanoparticles all have an enhancing effect on the breakdown voltage of transformer oil. Additionally, there exists an optimal mass concentration for each nanoparticle, i.e., 0.03 g/L, 0.01 g/L, and 0.02 g/L, respectively. It can be observedthat TiO\({}_{2}\) nanotransformer oil has the smallest optimal mass concentration, indicating that using the least amount of TiO\({}_{2}\) nanoparticles can greatly reduce the breakdown voltage, thus reducing economic costs in practical applications. Furthermore, among the three types of nanoparticles, TiO\({}_{2}\) nanoparticles exhibit the highest relative dielectric constant [35; 36]. TiO\({}_{2}\), a white inorganic material, is an n-type wide bandgap semiconductor that exists in two stable forms, rutile and anatase, at room temperature. Due to its excellent properties, such as enhanced surface charge carrier density and improved charge transport, TiO\({}_{2}\) has been a focus of research in the field of insulating materials. Semiconductor TiO\({}_{2}\) nanoparticles can increase the alternating current breakdown voltage of transformer oil. By modifying the microstructure and dispersion of TiO\({}_{2}\) nanoparticles, the thermal aging resistance and resistance to the water degradation of transformer oil can be significantly improved [37]. Additionally, TiO\({}_{2}\) nanoparticles can effectively suppress the streamer development length of oil-immersed paperboards under positive lightning impulse conditions, reduce the streamer propagation velocity, and accelerate streamer dissipation velocity [38]. [PERSON] studied the influence of 10 nm spherical TiO\({}_{2}\) nanoparticles, 5 nm spherical TiO\({}_{2}\) nanoparticles, and 5 nm rod-shaped TiO\({}_{2}\) nanoparticles on the AC breakdown voltage of transformer oil. The results showed that the addition of 10 nm spherical TiO\({}_{2}\) nanoparticles had the most significant effect on increasing the AC breakdown voltage, with an improvement of 111.9% [39].