## 1 Introduction  
The transformer bushing is an important part of transformer equipment, and the most commonly used nowadays are mainly oil-impregnated bushings. According to CIGRE report, more than 14% of DC system failures are caused by faults in the converter transformer and its bushings, and 56% of bushing failures are accompanied with fire, which is a serious threat to the safe and stable operation of power system [1]. In the AC bushing fault type statistics collected by State Grid Corporation of China from 2013 to 2018, bushing PD is in the top three in all equipment failures [2]. Furthermore, a structural defect is one of the most significant factors impeding the safe operation of bushings. During manufacturing process, immature local production processes and overvoltage accumulation may lead to structural defects [3]. Most of the PD test failures that occur in quality testing before sale by manufacturers are presumed to be due to small breaks and folds caused during the aluminum foil rolling process. The distortions of the electric field distribution are at these small breaks and folds, which leads to the abnormal space charge distribution and continuous PD. It is speculated that the cause of excessive PD is the small breaks and folds caused by the aluminum foil rolling process. PD is considered to be one of the most important reasons for insulation damage in electrical equipment, and PD occurs in weak insulation where the electric field is too concentrated. The distortions of the electric field distribution are at these small breaks and folds, which leads to abnormal space charge distribution and continuous PD. The electric field distortions of the bushing [4] are aggravated, causing the insulation to age and even fail. Long-time PD will continue to decompose the transformer oil to produce a large amount of acetylene gas, and then an explosion will occur. Currently, many research teams focus on deterioration of the oil-paper insulation layers and the finite element method of bushings. [PERSON] et al. [5] showed that the dielectric loss and capacitance increase significantly when the bushing condenser is exposed to moisture. [PERSON] and [PERSON] [6] studied the effect of moisture on incipient discharge voltage along the oil-paper intersection. [PERSON] et al. [7] investigated the effect of the air gap size in solids on the PD process. [PERSON] et al. [8] used the finite elements method (FEM) to calculate bushing degradation and optimize the design. [PERSON] et al. used FEM to optimize the insulation design of the end part of the transformer bushing [9]. [PERSON] et al. designed and analyzed the bushing electrothermal performance by FEM [10]. [PERSON] et al. proposed a new thermal model to estimate the hotspot temperature of the OIP bushing by FEM [11]. For the PD characteristics of an oil-impregnated pressboard system, the internal PD signal of a bushing insulation system can be detected by the pulse current method and the UHF method [12]. In addition, its space charge distribution can be measured using the electroacoustic pulse method [13], etc. However, the charge transfer characteristics and the discharge mechanism of the oil-paper insulation system cannot be tested with the current experimental methods. Therefore, an equivalent simulation model can be developed to better research the charge distribution and discharge characteristics of bushing foil layers. [PERSON] [14] and [PERSON] [15] proposed the use of a hydrodynamic model with Poisson's equation to represent the effect of space charge in the electric field. [PERSON] [16] referred this method into liquid PD and built a simulation of the streamer inside the liquid. Subsequently, [PERSON] [17] et al. used the finite element method in [PERSON]'s simulation and researched the space charge of needle-plane discharges with different parameters. However, the PD process and mechanism of defects of transformer bushing is not known.