## 1 Introduction  
Ultra-high-voltage direct-current (HVDC) transmission is the main power transmission mode in the project \"Power from West to East\" in China [1, 2]. When there are burrs, broken strands, loose strands, and other tip defects on the surface of the DC transmission line conductor, it is easy to produce a corona discharge at the defect. A corona discharge of transmission lines produces acoustic, optical, and thermal effects, as well as electric energy loss, and the high-frequency electromagnetic pulse generated by the discharge also has a negligible impact on radio communication. Therefore, it is of practical significance to study the characteristics of corona discharge and the influencing factors of DC conductor surface defects [3]. At present, many studies have been carried out on corona discharge on the surface of DC transmission lines at home and abroad [4, 5, 6, 7, 8, 9, 10, 11]. These studies pay attention to the physical process of the generation and development of corona discharge and the influence of environmental parameters on corona discharge characteristics such as corona initial voltage, discharge current, and corona loss. Given air temperature and density, [PERSON] et al. [4] studied the propagation characteristics of a positive streamer in an air gap. Their results showed that the average electric field and maximum charge density required for a streamer bridging the gap can be significantly affected by an increase in temperature or a decrease in density; in addition, the effect of density is less strong than that of temperature. For air pressure, in the range of 400 hPa to 1013 hPa, [PERSON] et al. [5] thoroughly analyzed a positive streamer discharge in the air. It was observed that electron concentration decreases by an order of magnitude with a decrease in pressure, while the electric field in the streamer head is rarely affected. In terms of humidity research, the following are representative [6; 7; 8]: [PERSON] and [PERSON] [6] proposed a numerical model to incorporate the effect of water vapor on corona plasma. The results of the simulation showed that the distribution of electron number density and electron kinetic energy are insensitive to variations in relative humidity due to the relatively low water content. [PERSON] [7] carried out some experimental studies at different humidity levels to obtain the variation of the electric field strength near a wire as well as the distribution of charge density after the occurrence of a corona. Results showed that the impact of increasing humidity on the two are clearly opposite. In detail, at high humidity (>70%), charge density increases while the electric field strength decreases. Aiming at other influencing factors, scholars investigated the effects of rain intensity on the corona inception voltage (CIV) and corona loss (CL) of HVDC lines through indoor experiments [9]. The effect of high altitudes on the CIV of HVDC lines was also measured by using a mobile corona cage in [10]. In [11], the relationship between audible noise (AN) and conductor surface gradients was investigated for stranded conductors, and it was found that increased conductor surface gradients increased AN levels. The research above shows that a DC corona shows different behavior under conditions of specific natural environments and environmental meteorological parameters (temperature, humidity, air pressure, rain, high altitudes, etc. ), which have an important and complex impact on the corona discharge of conductor surfaces [12; 13; 14]. As for corona discharge occurring at the tip defects of wire surfaces, there are, however, few studies focused on the influence of the geometric structures of tip defects on a corona discharge. Moreover, it can be seen from the existing literature that current research on the corona discharge of conductors is mainly based on analysis of macroscopic discharge characteristics (CIV, CL, AN, etc.) and microscopic particle processes (electric field, electric potential, etc.).