## 1 Introduction  
The rapid growth of power grid capacity, the development of power electronics technology, and the wide utilization of a large number of power electronic devices and non-linear loads results in voltage and current distortions of the power system and generation of harmonic components [1]. Various iron core equipment, such as transformers, electromagnetic voltage transformers, and reactors;various ac/dc converters, such as rectifiers and inverters; bidirectional thyristors; and controllable switches can generate harmonic components during operation. Harmonics are also produced during the melting period of all kinds of steelmaking electric arc furnaces, during the welding period of ac arc welding machines, and at the moment of fracture of arc drawing during the opening and closing of high-voltage circuit breakers. Harmonic components in the power system will cause safety hazards to the normal operation of the power transmission, transformation, and power consumption; reduce the quality of power; and exacerbate the aging of internal insulation materials in power equipment, which may reduce the overall operating life of the power system [2]. Power cables are very common in urban power grids. In recent years, with the implementation of urban economic construction and power grid upgrading, the proportion of power cables in urban power grids has become larger and larger [3]. The cable rate of economically developed cities has exceeded 98%. The power cable network structure is becoming more and more complicated, and the continuous increase of the operating time has caused a deterioration of cable aging. The combined effect of these factors has led to more and more incidents of power cable failures [4]. For example, a cascade dielectric breakdown occurred in 150 kV power cable terminations caused by partial discharges under the large tangential electrical field components [5]. Silicone rubber with a high elasticity, wide service temperature range, and excellent electrical properties is used as the main insulation material in cable accessories used to connect cables and cables to other equipment of extra-high-voltage systems [4]. However, in the cable system, due to the compact structure, harsh operating environment, and other reasons, it is commonly acknowledged that the probability of flashover or breakdown of cable accessories is still much higher than that of the cable itself. Under normal operation, the maximum temperature of the cable may reach 90 \({}^{\circ}\)C. When the cable is overloaded or short-circuited, the temperature of the cable will rise to more than twice that during normal operation in a short time. Due to the unavoidable defects inside or outside the silicone rubber insulation material, during long-term operation, various slow and irreversible chemical and physical changes will occur inside the silicone rubber insulation material under electrical and thermal stresses. [PERSON] et al. revealed that the crosslinking by oxidation and thermal decomposition of chemical crosslinking are two main aging reactions in silicone rubbers, which will affect the macroscopic properties of the materials [6]. [PERSON] et al. found that Si-CH\({}_{3}\) bonds were reduced and Si-O-Si bonds were changed to a non-uniform distribution in field-aged silicone rubber insulators [7]. [PERSON] et al. investigated the electrical and material properties of silicone rubber aged under irradiation at high temperatures and found that the changes in the electrical properties are related to the chemical reactions inside the materials [8]. From a macro perspective, it is manifested by changes in the electrical properties of the insulating layer, such as increased dielectric loss, enhanced partial discharge, and electrical dendrites. When the aging reaches a certain level, premature failure of the insulating material will occur [9]. Harmonics can cause additional losses in cross-linked polyethylene power cables, causing a temperature rise in the insulating material.