## 4 Simulation Results and Discussion
### Simulation Results of Corona Characteristics under Different Factors  
Through simulation, we can not only investigate the dynamic behavior of charged particles in gas space and analyze the microscopic process of the initiation and development of corona discharge at the tip, but we can also further analyze the macroscopic characteristics of corona discharge. In the following, with the changes in geometric structures of the wire tip defect and air pressure conditions, the characteristics of corona inception voltage and discharge current are carefully studied. When the background air pressure is 1013 hPa and the temperature is 293.15 K, the variation of corona inception voltage in response to changes in the radius \(R\) of wire, the curvature radius \(r\), and the height \(h\) of the tip is obtained by simulation. Then, the applied voltage is further increased to 1.1 times the corona inception voltage and the relationship between the amplitude of the pulse current and the radius \(R\) of wire, the curvature radius \(r\), and the height \(h\) of the tip is calculated. The simulation results are shown in Figures 13-15. By analyzing the curves in Figure 13, it can be seen that when the curvature radius \(r\) of the tip is 0.1 mm, at the same value of \(R\), the corona inception voltage gradually decreases with an increase in the tip' height; for example, when the value of \(R\) is 10 mm, an increase in the tip's height from 2 mm to 20 mm causes the corona inception voltage to decrease by 52.4%. Moreover, at the same tip height, the corona inception voltage decreases with a decrease in the wire's radius. Taking the tip's height \(h\) of 2 mm as an example, when the wire's radius is reduced by 5 mm, the corona inception voltage is reduced by 22.9%. Figure 14: Corona inception voltage under different tip curvature radii and conductor radii (tip’s height \(h\) of 8 mm). Figure 13: Corona inception voltage under different tip height and wire radius (tip’s curvature radius \(r\) of 0.1 mm). Figure 15: Pulse amplitude under different geometries. Furthermore, in Figure 14, the given height \(h\) of the tip is 8 mm, and the curves obtained show that at the same value of \(R\), the larger the curvature radius of the tip, the higher the corona voltage; when the curvature radius of the tip increases from 0.1 mm to 0.5 mm, the increase in corona inception voltage is between 27.7% and 37.5%. And, at the same curvature radius of the tip, the larger the wire's radius, the higher the corona voltage. When the wire's radius is expanded from 5 mm to 10 mm, the corona inception voltage is increased by 32.3-41.7%. It can be concluded from the above that when the wire's radius \(R\) is smaller, the curvature radius \(r\) of the tip is smaller, and the tip's height is higher, corona discharge occurs more easily at the tip of the conductor. Figure 15 shows the variation in corona current under different structures of defects on the surface of a wire. When the value of \(r\) is 0.1 mm-0.5 mm, the value of \(h\) is 2 mm-20 mm, and the value of \(R\) is 5 mm, 7.5 mm, and 10 mm. It can be seen from Figure 15 that when the applied voltage is 1.1 times the corona inception voltage, the amplitude of the current pulse decreases with a decrease in the curvature radius of the tip and increases with an increase in the wire's radius and a decrease in the tip's height. In order to study the characteristics of corona discharge under different air pressure conditions, the given simulation conditions are as follows: the gas pressure varies from 600 hPa to 1013 hPa, the background temperature is 293.15 K, and the value of \(r\) is 0.1 mm, the value of \(h\) is 6 mm, and the value of \(R\) is 5 mm. The obtained curves of corona inception voltage and the amplitude of corona current are shown in Figure 16.  
The analysis for Figure 16 shows that when the gas pressure rises from 600 hPa to the standard atmospheric pressure, the corona inception voltage rises from 13.5 kV to 24.5 kV, and the amplitude of current pulse drops from 2.43 \(\mu\)A to 2.21 \(\mu\)A.