# Effect of Tree Quantity and Distribution on the Electric Field under Transmission Lines
## 1 Introduction
Due to the significant difference in scale between transmission lines and the solution field, regional methods such as the finite element method and finite difference method involve large-scale air domain partitioning, resulting in a huge computational load. Although the successive mirror method can accurately calculate the power frequency electric field below the line, compared with the simulated charge method and moment method, the accuracy improvement is not significant and the computational complexity increases. Therefore, it is less commonly used in calculating the ground electric field. Usually, the analog charge method and moment method are commonly used. CSM has been widely used in the field of electric field numerical distribution calculation. [PERSON] et al. [9] proposed a generalized CSM, which establishes a three-dimensional generalized model for high-voltage substations with complex geometric structures. By combining multiple simulated charge types for electric field calculation, the accuracy of the three-dimensional electric field calculation results is improved. [PERSON] et al. [10] proposed a CSM for improving numerical conformal mapping, which constructs constraint equations using CSM and calculates charge and conformal radius using the Runge-Kutta method to obtain a new approximate conformal mapping function, thereby improving the accuracy of numerical conformal mapping and electric field distribution. [PERSON] et al. [11] propose a three-dimensional (3D) quasi-static model of the electric field produced by high voltage (HV) overhead power lines using a charge simulation method combined with intelligent optimization algorithms. The authors compare the simulation results with the calculation results of the 3D integration method and obtain good results. Various dielectrics and conductors under transmission lines can affect the distribution of the electric field. Among them, the academic community mainly focuses on the impact of buildings on the spatial distribution of the high-voltage transmission line industrial frequency electric field, shielding effect, and electric field distortion research. For example, [PERSON] and [PERSON] [12; 13] studied the electric field distribution when high-voltage transmission lines are close to buildings. [PERSON] et al. [14] showed that different types of buildings have different shielding effects on industrial frequency electric and magnetic fields generated by high-voltage transmission lines. At present, there are fewer studies on the effects of electric fields when transmission lines are adjacent to or pass through trees, and the following is a description of the relevant studies. [PERSON] et al. [15] analyzed the measurement results of a span field strength of a 330 kV UHV overhead transmission line. The influence of vegetation on the distribution of an electric field near overhead power lines was investigated, and conclusions were obtained: with an increase in the area of deciduous tree growth outside the edge of the transmission line right of way, the decrease in the electric field strength will be more significant. In ref. [16], an equivalent excitation source finite element method and an equivalent tree model were used to estimate the electric field shielding efficiency of the tree. It was concluded that the shielding effect of trees on the electric field of high-voltage transmission lines is obvious. [PERSON] et al. [17] used a row of natural trees to shade the HVTL which spans a very large area to reduce the electric field, and hence, the edge of the right of way (ROW) limits, the distance of the tree rows from the line and its effect on the ROW limits were studied and clarified. [PERSON] et al.