## 4 Influence of Ageing on Charge Transport Properties and Discussion
### Discussion  
The aging effects of ac superimposed harmonic voltage on insulating materials are mainly from electrical and thermal effects [22]. The general law of electrical aging of insulating materials under continuous voltage is \(U^{\tau}\tau=\) constant, where \(U\) is the voltage applied to the dielectric, \(\tau\) is the lifespan of the dielectric, and \(r\) is an index related to the properties of the dielectric. It is shown that \(r\) is generally 7-9, which means that the lifespan of the insulating material is shortened by about 50% for every 10% increase in voltage [22]. Harmonics cause overvoltage of power cables, accelerating the aging of their insulating dielectrics and shortening the overall life of the power cables [4]. In addition, it is generally believed that the lifespan of insulation materials in power equipment will be reduced by 50% for every 8 \({}^{\circ}\)C increase in temperature [18]. When the power cable is operated in a power supply containing harmonics, the power loss is greatly increased due to harmonic overvoltage, overcurrent, and overload. According to the heating power formula under the condition of sine wave voltage \(\Delta P=\omega CUtan\delta\), the heating power of the insulation material in the presence of harmonics can be calculated. Here, \(\omega\) is the angular frequency, \(C\) is the capacitance, and tan \(\delta\) is the loss angle. Under the same voltage, the thermal effect of higher harmonics on the insulating material is more obvious. Grid harmonics will cause abnormal heating of power equipment and affect the service life of power equipment [23].  
The power cable terminals suffer from temperature rise under power frequency voltage superimposed harmonics, and are also affected by the normal electric field and the strong tangential electric field. Chemical reactions, such as cross-linking and molecular chain breakage, gradually occur inside the silicone rubber insulation material of cable terminals subjected to thermal and electrical effects. These chemical reactions will cause changes in the trap levels and densities inside the silicone rubber insulation. The surface potential decay measuring results show that the trap energy level of the silicone rubber insulation material gradually decreases, and the density of shallow traps gradually  
Figure 9: Contour plot of the carrier mobility in the plane of the trap density and trap energy at the electric field of 2.5 kVmm\({}^{-1}\), temperature of 20 \({}^{\circ}\)C, and \(\alpha\) of \(2\times 10^{8}\).  
increases, as shown in Figure 7. The carrier hopping model was used to establish the relationship between the traps and the carrier mobility or conductivity of silicone rubber. The analytical expression of the carrier mobility indicates that the reduction of the trap energy will promote the thermally assisted hopping of carriers. Increasing the trap density results in a decrease in the average spacing between traps, making it easier for carriers to migrate between the two traps. The combined effects of the trap level and trap density lead to the increase in the carrier mobility and conductivity of the silicone rubber insulation as the aging time increases, as shown in Figure 5. The increase in conductivity will also increase the dielectric loss, as shown in Figure 3b. The trend of the dielectric characteristics changing with the aging time shows that the electrical and thermal effects of power frequency voltage superimposed harmonics cause the degradation of silicone rubber. This makes the cable terminal a vulnerable part in power cables and increases the failure probability of the power cables [4]. Therefore, the insulation material modification and structure optimization methods need further research for power cable terminals. This will improve the anti-aging performance of the cable terminal insulation material and improve the operational reliability of power cables [9; 24].