## 1 Introduction  
With the rapid development of the economy and the strategic adjustment of energy structures, the development and utilization of renewable energy has become an important way to improve electricity use in daily life. At present, there are two major problems in the production and use of energy. One is that the distribution of energy production areas and major energy consumption areas is extremely uneven, as renewable energy is generally located far away from cities. There is an urgent need to build low-loss, large-capacity, long-distance power transmission channels. The other is limited by the absorption capacity of the traditional power system. Direct current (DC) transmission can be connected to the asynchronous power grid, which greatly reduces the difficulty of grid network dispatching. Thus, high-voltage (HV) and ultra-high-voltage (UHV) direct current transmission can solve the two problems of large-scale and long-distance transmission of electric energy and new energy consumption [1, 2, 3]. When transmission lines cross rivers and seas, or in densely populated urban areas, power cables need to go underground, so the outer layer needs to be surrounded by insulation materials. Cross-linked polyethylene (XLPE)insulation material has excellent electrical and mechanical properties, as well as low costs. It has become the most prominently used insulation material for high-voltage power cables. However, in the service process, space charges are accumulated locally, which distorts the electric field stress, leading to the breakdown of insulating materials, reducing the service life and failing to meet the growing social demand for the voltage level of high-voltage cables [4; 5; 6; 7]. Therefore, in order to reinforce the breakdown strength of insulating material, researchers have carried out a lot of work. Ultra-clean technology is one of the effective methods, which can not only reduce impurities but also maintain material cleanliness. It has been practically applied in the cable manufacturing process, and the breakdown strength of materials has been significantly improved. However, this technology has a limitation due to the maximum breakdown strength of the material itself, and we need to find another way to further improve the breakdown strength [8]. In order to obtain XLPE insulated power cable with the ability to withstand a higher voltage level, the problem of insulation material breakdown caused by space charge accumulation is usually solved by adding a space charge inhibitor. By adding a voltage stabilizer, electrical aging caused by charge accumulation under strong electric fields of polymer insulation can be inhibited, and the electrical resistance of polymer insulation material can be improved [9]. Voltage stabilizers can withstand partial discharge, mitigate strong electric fields, inhibit macromolecular degradation and capture high-energy electrons [10]. A voltage stabilizer is usually a small molecular aromatic compound, which has poor compatibility with saturated aliphatic polymer. During the long-term operation of cables, the voltage stabilizer is easy to migrate and precipitate due to the high working temperature and large working field strength. The migration and precipitation of the voltage stabilizer will leave defects in the original place, which will reduce the electrical resistance of polymer insulation materials [11]. In order to fundamentally solve the problem of migration and precipitation of the voltage stabilizer, small molecular aromatic compounds with the function of voltage stabilizers can be grafted onto the polyethylene chain by a chemical reaction [9]. The issue of space charge is very complex, and its generation, transportation, and attenuation characteristics are related to the microstructure, impurities, temperature, electric field strength, and crystal state of the dielectric. Therefore, the issue of space charge has always been a hot topic in the field of insulation research.