**1. Introduction**

The research on insulator contamination characteristics is the fundamental research of external insulation in power systems, and it is of great significance to master the contamination characteristics of the insulator for the design, operation, and maintenance of external insulation [1–6]. Given the existence of the contamination, the insulation performance of insulators has changed greatly [7–9]. Contamination degree, leakage current, and pollution flashover voltage are important parameters for evaluating insulation performance of the insulator, and researchers have carried out a lot of research on them [10–14]. However, these researches were based on the surface that has been adhered to the contamination. The contribution on reduction of contamination accumulation and the physical properties of contamination is limited. Therefore, it is necessary to carry out research on related characteristics regarding accumulating contamination particles.

In recent years, researchers have carried out a lot of research on contamination accumulation characteristics through a variety of ways, including theoretical research, natural contamination accumulation experiments, artificial simulation experiments, and simulation analysis; especially in the research of the movement characteristics and deposition characteristics of contaminated particles from the microscopic point of view [15–27]. In theoretical research, Wang et al. [15] have analyzed the forces of particles moving around the insulator in detail, where they found that polarization force has little effect on the movement of particles, and fluid drag force plays an important role

under high wind speed. Horenstein et al. [16] considered that the electric field force has a great influence on the movement of particles, especially for particles with a size less than 10 μm, after a wind tunnel simulation experiment and theoretical deduction. However, when the particle size is greater than 10 μm, the effect of fluid drag force on the particle trajectory will gradually increase. At low wind speed, Li et al. [17] thought that the energy loss was mainly caused by the inelastic collision of particles, and the friction loss caused by the relative motion of particles and surface during the collision. However, at high wind speed, the particles will experience elastic-plastic deformation, and thus generate energy loss [18].

Furthermore, researchers have also used fluid dynamics simulation software to study contamination accumulation characteristics. Jiang et al. [19] found that under the condition of horizontal wind, the collision coefficient of the contaminated particles on the upper surface of the insulator increases with the increase of particle size and wind speed, but the collision coefficient of the bottom surface is always at a low level. Nan et al. [20] also obtained the same conclusion through an artificial simulation experiment and simulation analysis. In addition, they found that the change of wind direction had obvious influence on the contamination distribution of double umbrella insulators. Wang et al. [21] suggested that the collision mass of particles increases rapidly with the increase of wind speed, and the shape of the umbrella skirt at the bottom surface has an important influence on the collision characteristics. Zhang et al. considered that the contamination degree of windward and leeward of the insulator increased with the increase of wind speed, whilst the contamination degree of crosswind side showed a decreasing trend. As a result, a great deal of contamination accumulates on the windward and leeward, but the crosswind surfaces are relatively clean [22]. Lv et al. [23–25] thought that under the same wind speed, the contamination degree in the DC (direct current) electrical field is much more than that in the AC (alternating current) and no electrical field. Furthermore, under the conditions of AC and no electrical field, the deposition amount of contamination at low wind speed was relatively low. Even under the condition of high wind speed, the increase amount of contamination was very limited.

In general, the current literature shows that researchers paid more attention to the amount of contamination accumulated from contaminated particles. However, researchers seldom studied and analyzed the size distribution characteristics of adhered particles. With the increase of the frequency of haze and other microclimate phenomena in recent years, the difference of adhered particle size distribution on the insulator surface will have some influence on the contamination characteristics, pollution flashover characteristics, etc. [26]. Therefore, it is necessary to study size distribution characteristics of contaminated particles on the insulator surface.

After measuring many contamination samples, it was found that the size distribution of contaminated particles had some significant statistical characteristics. To explore the reasons of these distribution characteristics, a physical model of collision and adhesion between particles and surface was established. In addition, the influences of different factors on the adhesion were studied respectively. The research of this paper can effectively explain that the size distribution characteristics of adhered particle are easy to focus on a specific range. Furthermore, the work of this paper can provide theoretical support for more accurate external insulation researches in the future, such as artificial contamination simulation experiments and the influence of particle size distribution on pollution flashover.

#### **2. Size Distribution Characteristics of Adhered Particle**

#### *2.1. Measurement Method*

To study microscopic topography and particle size distribution of the particles adhered to the insulator surface, scanning electron microscopy (SEM) and laser particle size analyzer were used to study contamination. To observe microscopic topography of the particles in the contamination sample, a small amount of the contamination sample was adhered by conductive tape from the insulator

surface, and samples were placed in a scanning electron microscope (VEGA TS5136XM, TESCAN Corporation, Brno, Czech) for observation. In addition, when collecting the particles, the force should be uniform, and the contaminated sample should not be squeezed to avoid destroying the shape and size of the particles. To measure particle size distribution of contamination samples, the contamination on the insulator surface was collected into clean sealed bags with a clean brush, and the numbers were recorded. Mastersizer 2000 laser particle size analyzer (Malvern Panalytical Corporation, Malvern, UK) was used to analyze the particle size of contamination samples. The measurement range of the Mastersizer 2000 laser particle size analyzer is from 20 nm to 2000 μm, and the reappearance rate is better than 0.5%, and the accuracy is better than 1%, which effectively met the measurement requirements. In addition, some of contamination was easily soluble in water, easily causing measurement errors. Therefore, alcohol was used as substrate, and the method of wet dispersion measurement was carried out.
