## 4 Discussion  
The electric field dependent molecular ionization has been proved to be the dominant contributor to streamer development in transformer oil, which has a great effect on breakdown strength of transformer oil [22; 23; 24]. In transformer oil, ionization occurs at streamer tip with a high electric field, generating positive ions and electrons. The highly mobile electrons swept back towards the positive electrode, leaving positive ions to form a net space charge region near the streamer tip, as presented in Figure 7a. These space charges slowly propagate towards the ground electrode and enhance the electric field towards the ground electrode [25]. So, the streamers tend to propagate straightly towards the ground electrode showing filamentary pattern, and breakdown happens when streamers extend throughout the gap. It is clear that the breakdown event is closely associated with charge transport process, which in turn, is influenced by the trap characteristics of transformer oil.  
To investigate the effects of nanoparticle materials on the trap characteristics of transformer oil, thermally stimulated currents (TSC) were measured. It is believed that TSC measurements can be used to investigate the nature and origin of charge carrier traps in dielectric, including the change of the density and energy level of the trap sites [26]. Figure 8 presents results on TSCs of pure oil and three types of nanofluids. It can be seen that the thermally stimulated currents are increased with the addition of nanoparticles. The trap characteristics including energy level and total trapped charges were calculated as shown in Table 1[26; 27]. The trap density is proportional to the total trapped charge if one-level of trap distribution is assumed [26]. It is indicated that the trap energy level of transformer oil is nearly unchanged by the addition of nanoparticles, which is  
Figure 7: The electric field distribution in pure oil (**a**) and nanofluids (**b**).  
trap [14]. However, the trap densities are significantly increased by 65.5% and 59.0% in Fe\({}_{3}\)O\({}_{4}\) and TiO\({}_{2}\) nanofluids, respectively. In Al\({}_{2}\)O\({}_{3}\) nanofluid, the increase is only 14.6%. These results agree well with the effects of nanoparticle materials on breakdown and prebreakdown characteristics of nanofluids presented above.  
By introducing more shallow traps, the probability of capturing electrons is more likely increased, meanwhile decreasing the energy of fast electrons during these trapping and de-trapping process in shallow traps. In all, the presence of Fe\({}_{3}\)O\({}_{4}\) and TiO\({}_{2}\) nanoparticles greatly increases the density of shallow traps and forms more negative charges in the oil. As a result, the electric field is changed due to the superposition of space-charge field created by these negative space charges with applied electric field, as presented in Figure 7b. The electric field towards ground electrode is weakened, making it hard for positive streamers in Fe\({}_{3}\)O\({}_{4}\) and TiO\({}_{2}\) nanofluids to propagate towards ground electrode. Moreover, the electric field between the space charge region and the positive electrode is enhanced, contributing to generate lateral branches. In comparison with streamers containing one or two main filaments, streamers with more branches can reduce the tip field due to mutual electrical shielding [5; 28], which further slows down the propagation velocity of streamers, improving the positive breakdown strength. Whereas in Al\({}_{2}\)O\({}_{3}\) nanofluid, the increase of breakdown strength is slight due to limited increase of trap density.