# A Comparison of Electrical Breakdown Models for Polyethylene Nanocomposites
## 1 Introduction  
Power cables are the main equipment in urban transmission grids and offshore wind power transmission [1; 2; 3; 4; 5; 6]. Direct current (DC) power cables have the advantages of long transmission distance, large transmission capacity, and low power loss, and they are the key electrical equipment for large-scale reception of new energy power generation. Under the action of DC voltage, the power cable has no capacitive current and can realize long-distance power transmission. The aging of the insulating material of power cables under the DC electric field is slow, and its lifespan is greatly prolonged [1; 3; 4; 5; 6]. Moreover, the breakdown electric field of the insulating material under DC voltage is 2-3 times higher than that under AC voltage [7], which improves the safety margin of the DC power cable. Low-density polyethylene (LDPE) is the main insulating material of power cables, and its electrical insulation performance is important for the safe and reliable operation of power cables [1; 2; 3; 4; 5; 6]. Polymer nanocomposites (PNCs) have excellent properties, such as lower electrical conductivity, higher breakdown electric field, less space charges, higher thermalstability, and higher mechanical strength [5; 6; 8; 9; 10; 11; 12]. PNCs, known as third-generation insulating materials, have broad application prospects. The experimental results demonstrate that doping a relatively low content of nanoscale fillers in polyethylene can form deep traps, leading to the reduction in the electrical conductivity of the nanocomposites and the improvement in the breakdown strength [5; 6; 9; 11; 12; 13; 14]. Advanced LDPE nanocomposites can be used as insulating materials for DC power cables [5; 6; 12] and energy storage capacitors [15; 16], improving the capacity of power cables to transmit electrical energy and the energy storage density of capacitors. Power cables and energy storage capacitors are key equipment for the centralized transmission of large-scale offshore wind power, providing support for the supply of clean energy to cities. It is generally believed that the excellent electrical properties of polymer nanocomposites originate from the interfacial region between the nanoparticles and the polymer matrix [6; 12]. The multi-core interfacial region model proposed by [PERSON] et al. [17; 18] and the multi-region structure model proposed by [PERSON] et al. [19] show that deep traps are formed in nanocomposites when a small amount of doping is used. Deep traps near the electrodes trap more charges and reduce the number of charges injected. This can suppress the space charge accumulation, reduce the electric field concentration, and improve the breakdown electric field. By comparison, traps with higher energies can reduce the effective charge carrier mobility, reduce electrical conductivity and Joule heating, and improve breakdown performance. The interfacial region models proposed by [PERSON] et al. [20] and [PERSON] et al. [21] show that the interfacial regions not only form deep traps, but also constrain the motion of molecular chains. Under the action of the Coulomb force, the molecular chains undergo directional displacement, which affects the size of the surrounding free volumes. This, in turn, changes the breakdown performance of nanodielectrics. The interfacial region models show that increasing the trap level and/or the interaction between molecular chains in the interfacial regions can improve the breakdown strength of polymer nanocomposites. Experiments and simulations indicate that the breakdown of polymer materials under a strong electric field is related to physical processes such as electric field distortion and electron energy gain. [PERSON] et al. [22] used pulsed electroacoustic equipment to test the space charge distributions and the electric field distributions of LDPE under the action of a strong electric field. It was found that positive space charge packets are formed in LDPE when the electric field is higher than a threshold value.