## 1 Introduction  
Polymer composites are increasingly used as the main components in various engineering applications. However, micro structural defects are the major damage form of polymer composites, and the damage is usually formed deep within the material, where detection and repair are difficult [1; 2; 3]. Moreover, the micro structural defects lead to the degradation of material performances, shortening the service lifespan of material. In the field of electrical insulating materials, reliable and durable insulating polymers are required for high voltage transmission in the power grid [4]. Cross-linked polyethylene (XLPE) insulated cables have been widely used in modern power grids due to their excellent electrical performances. The XLPE cable has become the main transmission equipment of urban power grid [5; 6; 7]. However, in the process of manufacture, laying, and operation, damage can inevitably occur in the polyethylene insulation layer, resulting in structural defects, such as micro-cracks and micro-holes [7; 8; 9]. Moreover, the outer surface of polyethylene at the joint is also easily scratched [9]. In the high electric field, micro structural damage can distort the electric field, which leads to partial discharge (PD) and electrical trees, causing new damage. Furthermore, the structural degradation can lead to the irreparable decline of material typical performances, such as breakdown strength [10; 11]. However, with the existing technologies it is difficult to detect and repair these micro damage defects in polyethylene [12; 13; 14; 15]. Therefore, the micro damage can directly threaten the normal operation of the power grid, and even cause catastrophic failures. If the insulating material has self-healing ability, that is, the material can repair the defect automatically at the initial stages of damage, the influence of structural damage on the insulating material will be greatly reduced. However, the existing research on self-healing materials rarely involve the high-voltage insulating material and its electrical performances [16; 17; 18; 19; 20]. Therefore, it is necessary to develop a self-healing polyethylene insulating composite and analyze its typical electrical performances, such as insulation strength, dielectric properties, and space charge characteristics. On the premise of guaranteeing the basic performances of polyethylene, the ability to self-heal damage is realized, fundamentally prolonging the service lifespan of insulated cables. Nowadays, self-healing technologies are mainly divided into two types: intrinsic and extrinsic [18; 19; 20; 21; 22]. In recent years, the research on self-healing electrical materials have focused on the intrinsic method [20; 21]. However, the intrinsic self-healing materials with grafting groups or the Diels-Alder reaction not only introduce many polar groups, but also require stricter reaction conditions [23; 24; 25]. Furthermore, the new self-healing soft electronics, such as dielectric elastomers, usually have a higher dielectric constant and smaller Young's modulus [26; 27]. Therefore, the intrinsic self-healing electrical materials cannot meet the application requirements of polyethylene high-voltage insulating materials. Compared with the intrinsic material, the extrinsic self-healing material has a more mature manufacturing process and better weatherability [22]. Thus, the extrinsic method is more conducive to the self-healing behavior of polyethylene insulating materials in complex operating environments. The extrinsic self-healing technologies mainly include microcapsules, hollow fibers, microvascular network, and mesoporous hollow microsphere [28; 29; 30]. Moreover, the microcapsule system not only has good stability and a high repair rate, but also has little damage to the structure of the matrix material. Therefore, the microcapsule system was selected to achieve the self-healing goal for the damage in insulating materials.