**4. Conclusions**

In this paper, simulations and experiments were carried out to investigate the accumulation characteristics of cellulose, copper, and mixed particles in mineral oil under DC voltage. The DC breakdown voltages of mineral oil with di fferent particle concentrations were measured. The conclusions obtained from this study are as follows.

The simulation model was able to reveal the process of particle bridging in mineral oil under DC voltage. The simulation results showed that as the experiment duration increased, particle accumulation became more evident. The accumulation concentration of mixed particles was the largest, followed by cellulose particles and metal particles, which is in agreemen<sup>t</sup> with the experimental results. In the particle accumulation experiments, it was also obvious that metal particles have di fficulty forming stable bridges, while bridges of mixed particles were the densest and thickest among the tested compounds. Moreover, the larger the initial concentration of particles, the more obvious the accumulation phenomenon as well as the electrical field distortion.

The properties of particles determine the accumulation shapes, conductivity characteristics, and variation law of breakdown voltages. The increasing degrees of saturated current in contaminated oil compared to clean oil in decreasing order were found to be mixed particles, metal particles, and cellulose particles. Moreover, metal particles were also shown to play a more prominent part in electrical field distortion than cellulose particles. Therefore, the breakdown voltage of mineral oil contaminated by cellulose particles was larger than that of mineral oil containing copper particles. Nevertheless, it is noteworthy that cellulose particles along with metal particles cannot have a superposition e ffect on the conductivity characteristics and electrical field distortion of insulation oil.

The test and computational results indicated that changes in the electrical field distribution together with an increase in conductivity collectively a ffect the breakdown strength of mineral oil. The bridge formation of particles under DC electrical field was shown to significantly improve the conductivity of oil, which is one of main reasons for the decrease in breakdown strength of mineral oil containing particles. The simulation results of the particle accumulation model showed that as the duration of the experiment increased, the range of electrical field distortion caused by particles accumulation gradually expanded, which is also one of main reasons for the decrease in the DC breakdown strength of mineral oil containing particles.

**Author Contributions:** Designed the experiments, did the motion characteristics experiments and breakdown voltage measurement, wrote the paper, M.D.; improved the simulation method, analyzed the experiment data and revised the paper, J.H.; contributed discussion, R.L., L.C., J.Z., and F.L.

**Funding:** This research was funded by [National Key R&D Program of China] gran<sup>t</sup> number [2017YFB0902704], [Science and Technology Project of State Grid Corporation-Research on Insulation Defect Analysis and Testing Technology of UHV Converter Transformer], [Joint Funds of the National Natural Science Foundation of China] gran<sup>t</sup> number [U1866603], [Funds for Innovative Research Groups of China] gran<sup>t</sup> number [51321063].

**Conflicts of Interest:** The authors declare no conflict of interest.
