Effect of Tree Quantity and Distribution on the Electric Field under Transmission Lines

Abstract

The electric field of transmission lines has serious negative impacts on residents’ production and life with the expansion of high voltage engineering. In order to study the influence of trees on the electric field of ultra-high voltage transmission lines, this paper conducted three-dimensional simulation calculations of the power frequency electric field of transmission lines based on the tree quantity and distribution. Firstly, in order to study the pattern of electric field strength distribution in transmission lines, the electric field strengths of transmission lines of different voltage levels were compared; the maximum-power-frequency electric field intensity of ultra-high voltage transmission lines occurs below the edge conductor. Secondly, by changing the number of trees, it was concluded that the electric field strength below the edge conductor gradually decreases with the number of trees. Finally, the maximum electric field strength value at 1.5 m below the edge conductor and the width of the transmission corridor decreased by changing the layout of the trees. The results show that studying the impact of a tree’s electromagnetic parameters on the power frequency electric field strength under transmission lines can help reduce the electric field strength and decrease the width of transmission corridors, which is of great significance for line design and cost savings.

1. Introduction

With the rapid development of the world economy, the construction scale of ultra-high voltage transmission lines continues to increase, but their power frequency electric fields have also had serious negative impacts on residents’ production and life. At the same time, dense ultra-high voltage transmission lines span vast land, greatly affecting the natural landscape and environment. By planting trees to form green belts, not only can the width of power transmission corridors be reduced, but the impact of power transmission lines on the surrounding environment can also be minimized. Therefore, studying the influence of tree electromagnetic parameters on the power frequency electric field of transmission lines is of great significance for line design and cost savings.

According to relevant research, the electromagnetic interference of transmission lines can have a certain negative impact on the human body. Ron et al. [1] confirmed that ionizing radiation is one of the few known risk factors for acoustic neuroma through radiation therapy and dental X-ray studies. Greenland et al. [2] discussed that radiation in residential areas is one of the main reasons for the increase in the incidence rate of childhood leukemia. Attwell [3] proposed that the electrical stimulation generated by low-frequency electric fields can slightly affect visual processes and motor coordination. Therefore, since 1996, the World Health Organization (WHO) has organized over 60 countries and multiple international organizations to conduct global research on the “International Electromagnetic Field Program”. In addition, in order to ensure the safety and efficiency of power transmission, corridors need to be opened up along the path of high-voltage transmission line construction. However, the high-voltage transmission corridor requires a large amount of land to be requisitioned, and the width of the ultra-high voltage corridor is over 100 m. Economically developed areas have high electricity consumption, while land resources are scarce. Therefore, the contradiction between high-voltage transmission corridors and local land tension has become very prominent, and as the width of transmission corridors increases, the cost also increases sharply. For example, the cost of land occupation and demolition for the Xiangjiaba to Shanghai ultra-high voltage transmission line is far greater than the cost of the project construction itself [4]. Due to the above reasons, complaints and disputes about long-distance and high-capacity ultra-high voltage transmission line corridors are gradually increasing. According to statistics, since 2010, the number of complaints and petitions regarding the electromagnetic environmental impact of high-voltage transmission and transformation projects in China has been increasing at a rate of 10% per year. With the widespread construction of ultra-high voltage, the annual growth rate has exceeded 15% in the past three years [5]. Therefore, it is crucial to predict the power frequency electric field of transmission lines, reduce the electric field strength, and minimize the area of transmission corridors.

At present, the prediction of the power frequency electric field in transmission lines often adopts calculation methods such as the charge simulation method (CSM), finite difference method, moment method, and finite element method. Among them, the simulated charge method is based on the uniqueness principle of electrostatic fields, with high computational efficiency and strong real-time performance, and has been widely applied. The principle of CSM is to replace the free charges continuously distributed on the electrode surface or the bound charges continuously distributed on the dielectric interface with a set of discretized simulated charges and then use the superposition principle to superimpose the field generated by the discrete simulated charges in space, thereby obtaining the spatial electric field distribution equivalent to the original continuous distributed charges [6,7,8]. 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. Rankovi ć 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. Lai 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. Djekidel 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, King and Krajewski [12,13] studied the electric field distribution when high-voltage transmission lines are close to buildings. Mei 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.

Trotsenko 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. Ismail 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. Guo et al. [18] monitored and analyzed the mid-frequency electric and magnetic fields in four areas, namely, an unvegetated area, lawn, shrubs, and tall trees, under the same operating conditions of 110 k V overhead transmission lines, and concluded that the effect of plants on the mid-frequency electric field is obvious; specifically, the weakening rate of the mid-frequency electric field of the tall trees is more than 90%. The above studies almost all concluded that trees can reduce the field strength of transmission lines, but they have not been applied to actual transmission and transformation projects.

Most studies have shown that trees have a weakening effect on the electromagnetic field of transmission lines, but few are applied to specific scenarios, this paper focuses on the design of transmission line corridors, by changing the number and distribution of trees, to design appropriate transmission corridors, save the cost of actual engineering, and reduce the impact of transmission lines on residents’ living and survival.

Therefore, the paper proposed using the simulated charge method to calculate the power frequency electric field of transmission lines and obtain the distribution of the transverse electric field intensity at 1.5 m on the ground under different voltage levels. The conclusion is that the maximum electric field intensity of AC transmission lines occurs below the side conductors. Through the method of three-dimensional simulation calculation, the influence of tree size on the power frequency electric field of 500 kV transmission lines was obtained, which can provide a reference for reducing the power frequency electric field of ultra-high voltage transmission lines and reducing the width of transmission corridors. The detailed contributions and novelty of this paper are as follows:

(1)

By conducting three-dimensional simulation calculations of the electric field on transmission lines with and without overhead ground wires, the model of transmission lines without overhead ground wires is more efficient and quick.

(2)

The maximum power frequency electric field of the transmission line occurs below the edge conductor, and when the phase angle of voltage A is 30 degrees, the electric field strength is symmetrical about the center of the transverse measurement point. This result indicates that the field strength below the edge conductor needs to be given special attention and protection.

(3)

The proposed method is feasible and effective, which has been verified by simulating the three-dimensional electric field of tree green belts at different locations. It further provides suggestions based on the research results for reducing the width of transmission corridors and serves as a reference for future research in this field.

2. Charge Simulation Method Solving Electric Field near Transmission Lines

2.1. Evaluation Criterion

According to the “Electromagnetic Environment Control Restrictions” and “Technical Guidelines for Environmental Impact Assessment” in China (0.05 kHz), the electric-field-monitoring probe of ultra-high voltage transmission lines needs to be installed at a height of 1.5 m above ground, and the electric field limit amplitude in residential areas is 4 kV/m. The International Commission on Non-ionizing Radiation Protection (INCIRP) specifies guidelines for these E-fields from the perspective of public exposure at the ground level and sets it to 5 kV/m at 50 Hz [19,20].

2.2. Field Equation

Due to the fact that the span of transmission lines is much smaller than their operating wavelength, the induced electric field generated by time-varying magnetic fields is much smaller than the Coulomb electric field generated by their own charges. Therefore, the line voltage and line current of the transmission line remain almost constant along the span direction. Meanwhile, because the radius of the transmission line is much smaller than the installation height and parallel to the ground, and the voltage and current vary in a three-phase symmetrical sine law, it can be considered that the transmission line is uniformly distributed by line charges, and its power frequency electric field strength value is often calculated using the charge simulation method (CSM). The field equation of the simulated charge method is shown below.

$${\nabla }^2\phi =-{\displaystyle \frac{\rho }{\epsilon }}\mathrm{or}{\nabla }^2\phi =0$$

(1)

$${\left.\phi \right|}_{L_1}=f_1(P)$$

(2)

$${\phi }_1={\phi }_2, {\epsilon }_1{\displaystyle \frac{\partial {\phi }_1}{\partial n}}-{\epsilon }_2{\displaystyle \frac{\partial {\phi }_2}{\partial n}}=0$$

(3)

where $\phi$ is the potential, $\rho$ is the density of the charged body, and $\epsilon$ is the dielectric constant of the medium. The meanings of ${\phi }_1$ and ${\phi }_2$ are the potential at the interface between two media, and ${\epsilon }_1$ and ${\epsilon }_2$ are the dielectric constants of the two media, respectively. $L_1$ is the boundary of a given potential, p is the point on the boundary, and $f_1$ is the Dirichlet boundary condition.

However, in practical engineering applications, the free charges inside the conductor and the bound charges at the interface are unknown and cannot be obtained through boundary conditions. Therefore, the simulated charge method uses continuous point charges, line charges, or surface charges to replace unknown charges while ensuring that the boundary conditions remain unchanged, in order to obtain simulated charges. Then, select matching points on the surface of the wire with a known potential that are equal in number to the simulated charges and use them to calculate the coefficient matrix based on the relative position between the matching points and the simulated charges [21]. At the same time, combine the given boundary conditions to write the potential equation for the transmission line wire:

$$\left[P\right]\left[\tau \right]=\left[\phi \right]$$

(4)

where [P] is the l-order potential coefficient matrix, [$\tau$] is the column vector of line charge density, and [$\phi$] is a potential column vector.

The calculation accuracy is verified through several verification points on the surface of the wire. If it does not meet the accuracy requirements, the position, number, and shape of the simulated charge will be re-selected. Finally, by satisfying the precision requirements of discrete line charge density, the potential and electric field values at any point can be calculated based on the superposition principle. The flow chart of the simulated charge method is shown in Figure 1, where $∆\Phi$ is the relative error.

For transmission lines or bus bars, line charges are generally selected to be arranged at the center of the conductor for equivalent substitution. For some complex-shaped power equipment, more general point charges can be used for the corresponding arrangement.

In order to facilitate the analysis of three-dimensional transmission lines, simulated line charges are selected to calculate the voltage distribution around the wires. In the three-dimensional coordinate system, the wire is divided into basic line charge units of length L, and the amount of charge carried by each line charge unit also follows a linear distribution [22,23,24]. The three-dimensional line charge units are shown in Figure 2.

Assuming the length of the basic unit of linear charge is L, the starting point of the unit is P₁, the ending point is P₂, and the proportional calculation parameter is denoted as u (0 ≤ u ≤ L), the coordinates P (X, Y, Z) of any point on the basic unit can be expressed as a function of u.

$$\left\{\begin{array}{c}X(u)=x_1+{\displaystyle \frac{l}{L}}u\\ Y(u)=y_1+{\displaystyle \frac{m}{L}}u\\ Z(u)=z_1+{\displaystyle \frac{n}{L}}u\end{array}\right.$$

(5)

where l = x₂ − x₁, m = y₂ − y₁, and n = z₂ − z₁.

If the charge densities at the two ends of a line charge unit are τ(0) = τ₁ and τ(L) = τ₂, the charge density of the entire unit can be characterized by the charge densities at both ends.

$$\tau \left(u\right)={\tau }_1+{\displaystyle \frac{{\tau }_2-{\tau }_1}{L}}u=b+au$$

(6)

where b = τ₁, and a = (τ₂ − τ₁)/L.

According to the numerical calculation formula in the electromagnetic field calculation method, the potential of a line charge unit Q (x, y, z) at any point in the field can be expressed as

$$\phi ={\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle {\int }_0^L\frac{\tau \left(u\right)}{D}du}$$

(7)

where is the distance D between the simulated charge point and the calculation point. Assuming u = Lt (0 ≤ t ≤ 1), then D is

$$D=\sqrt{{\left(x_1+lt-x\right)}^2+{\left(y_1+mt-y\right)}^2+{\left(z_1+nt-z\right)}^2}$$

(8)

After substituting Equations (6) and (8) into (7), they can be simplified as

$$\phi ={\displaystyle \frac{L}{4\pi {\epsilon }_0}}{\displaystyle {\int }_0^1\frac{At+B}{\sqrt{E{t}^2+Ft+G}}dt}$$

(9)

where A = aL, B = b, E = l² + m² + n², F = −2[l(x − x₁) + m(y − y₁) + n(z − z₁)], and G = (x − x₁)² + (y − y₁)² + (z − z₁)².

Substitute the linear charge density into Formula (9), and then perform integration simplification according to the integration formula, expressed as

$$\begin{array}{l}\phi ={\displaystyle \frac{L}{4\pi {\epsilon }_0}}\left[{\displaystyle \frac{2E+F}{2\sqrt{E^3}}}\ln {\displaystyle \frac{2E+F+2\sqrt{E\left(E+F+G\right)}}{F+2\sqrt{EG}}}-{\displaystyle \frac{1}{E}}\left(\sqrt{E+F+G}-\sqrt{G}\right)\right]{\tau }_1\\ +{\displaystyle \frac{L}{4\pi {\epsilon }_0}}\left[{\displaystyle \frac{-F}{2\sqrt{E^3}}}\ln {\displaystyle \frac{2E+F+2\sqrt{E\left(E+F+G\right)}}{F+2\sqrt{EG}}}+{\displaystyle \frac{1}{E}}\left(\sqrt{E+F+G}-\sqrt{G}\right)\right]{\tau }_2\end{array}$$

(10)

3. Prediction Model and Validation

3.1. Prediction Model

Most studies on the electric field of transmission lines ignore factors such as sag and span and treat transmission lines as two-dimensional models for calculation. This simplified calculation can greatly reduce computation time, but it has a significant impact on the distribution of electric fields and computational accuracy. Therefore, this article establishes a three-dimensional power frequency electric field mathematical model for ultra-high voltage transmission lines considering sag and uses the model charge method to calculate the electric field. Assuming that the axial direction of the transmission line is the x-axis, the lateral direction is the y-axis, and the direction perpendicular to the ground is the z-axis. An overhead transmission line with a suspension point of equal height and uniform span can be described using a periodic catenary equation [25].

$$z={\displaystyle \frac{L}{a}}[\cosh {\displaystyle \frac{a(x-kL)}{L}}-\cosh {\displaystyle \frac{a}{2}}]+H,-{\displaystyle \frac{L}{2}}\le x-kL\le {\displaystyle \frac{L}{2}}$$

(11)

where $a=\gamma L/{\sigma }_0$ is the horizontal stress coefficient of the wire, ${\sigma }_0$ is the horizontal stress of the wire, $\gamma$ is the specific load of the wire, L is the span of the transmission line, and k is an integer.

The ultra-high voltage transmission line adopts the form of split conductors. When calculating using the simulated charge method, the number of conductors and span length will greatly affect the calculation time. Because the geometric dimensions of the split wire are much smaller than the distance between the field sources, the equivalent radius can be used for calculation [26]:

$$R_{eq}=\sqrt[s]{sr{R}^{s-1}}$$

(12)

where s is the number of split wires, r is the radius of the subwire, and R is the radius of the split wire circle.

3.2. Validation of Predictive Models

Assuming the rated voltage of the transmission line is positive sequence 1000 kV, the phase angle of voltage A is 30 degrees, the three-phase voltage is defined by Equation (13), and each phase conductor adopts 8× LGJ-500/45, with a splitting spacing of 0.4 m. The conductor arrangement is an equilateral triangle, with side conductors at a height of 30.33 m from the ground, middle conductors at a height of 48.33 m from the ground, and a line span of 400 m. The overhead ground wire adopts LHBGJ-120/70, with a ground height of 60 m. The annual average temperature is 20 °C, with no wind or ice. The maximum sag of the transmission line is calculated to be 10.33 m. The three-dimensional calculation model of the ultra-high voltage transmission line is shown in Figure 3.

$$\left\{\begin{array}{c}{V}_A(t)=V\cos (\omega t+\pi /6)\\ V_B(t)=V\cos (\omega t-\pi /2)\\ V_C(t)=V\cos (\omega t-7\pi /6)\end{array}\right.$$

(13)

where $V_A$, $V_B$, and $V_C$ are the voltage values of the three phases, $V$ is the voltage amplitude, $\omega$ is the angular frequency, and t is time.

Among them, the transverse measurement position is a straight line at 1.5 m above the ground and x = 0, denoted as T1. The longitudinal measurement position is a straight line at 1.5 m above the ground and y = −7.5, denoted as L1. The conductivity and dielectric constant of the materials related to the prediction model are shown in

Table 1. Material parameters of model.

Material	Relative Dielectric Constant	Conductivity (S/m)
air	1	2 × 10−14
ground	10	1 × 10−4
trunk	9	0.002
crown of a tree	9	0.004
wire	1	3.8 × 107

[27,28]. Among them, the electrical resistivity of the tree trunk is taken from the actual measured values, and the average electrical resistivity at a distance of 2 m is taken from the crown of the tree.

3.2.1. Simplification of the Transmission Line Model

To improve the efficiency of calculations and reduce operating time, the influence of overhead ground wires on the power frequency electric field strength of transmission lines was studied. A comparison chart of power frequency electric field strength with and without overhead ground wires was obtained through three-dimensional simulation calculations [29,30]. From Figure 4, it can be seen that the trend of the power frequency electric field intensity of both with respect to lateral distance is the same. The maximum power frequency electric field intensity values for transmission lines without and with overhead ground wires are 9.85 kV/m and 9.65 kV/m, respectively, with an error within 5%. Therefore, subsequent 3D electric field simulation calculations can be performed based on the model without overhead ground wires.

3.2.2. Comparison of Results

The measurement position is T1, and the measuring equipment used is the PMM8053A portable electromagnetic field analyzer from Italy, which measures cloudy weather, a temperature of 35 °C, and a relative humidity of 62% on that day. Using the center of the line as the coordinate origin and the ground projection point, the measuring point is 1.5 m above the ground. Measurements are taken along the transverse direction of the line, with points taken at intervals of 2 m. The measurement time for each point shall not be less than 1 min, and the reading shall be taken after the data display is essentially stable. The power frequency electric field calculated from the three-dimensional transmission model, the actual transmission line, and the three-dimensional simulation are compared as shown in Figure 5. The electric field distribution cloud map calculated from the three-dimensional simulation is shown in Figure 6. As shown in the figure, the predicted values of the model are essentially consistent with the measured values, and the distribution pattern is consistent, which verifies the correctness of the calculation model in this paper and lays the foundation for further research on the influence of tree quantity on the electric field of transmission lines.

To study the influence of the power frequency electric field on transmission lines of different voltage levels, this paper conducted simulation calculations on transmission lines of various ultra-high voltage levels based on the above three-dimensional simulation calculation model. The transmission lines of each voltage level were arranged in an equilateral triangle, and their position coordinates are shown in

Table 2. Position coordinates of transmission lines.

Wireway	Coordinate of Wire Position (x, y) (m)
	110 kV Line	220 kV Line	500 kV Line	1000 kV Line
A	(−3.5, 16.57)	(−5.4, 19.20)	(−7.5, 24.89)	(−18.8, 30.33)
B	(0, 18.57)	(0, 24.20)	(0, 34.49)	(0, 48.33)
C	(3.5, 16.57)	(5.4, 19.20)	(7.5, 24.89)	(18.8, 30.33)
Splitting distance	0.25 m	0.4 m	0.45 m	0.4 m
Phase conductor	2× LGJ-200/30	2× LGJ-240/40	4× LGJ-400/35	8× LGJ-500/45

. Figure 7 shows the horizontal distribution of the power frequency electric field at different voltage levels.

By analyzing the graph, this article draws the following four conclusions:

(1)

When the phase angle of voltage A is 30 degrees, the variation curve of its power frequency electric field strength with lateral distance is symmetrical about the middle conductor.

(2)

The maximum power frequency electric field strength of AC transmission lines occurs below the edge conductors, so the protection of power frequency electric fields on transmission lines should focus on the area below the edge conductors, and relevant measures should be taken to reduce the electric field strength to below 4 kV/m.

(3)

The amplitude of the electric field strength directly below the side conductor of typical 500 kV and 1000 kV tower-type AC overhead transmission lines in this article exceeds relevant domestic and foreign standards. The maximum amplitude of the electric field intensity directly below the side conductor of a typical 1000 kV tower-type AC overhead transmission line reached 9850 V/m, and the maximum amplitude of the electric field intensity directly below the side conductor of a typical 500 kV tower-type AC overhead transmission line reached 5810 V/m, both exceeding ICNIRP’s 5000 V/m power frequency electric field public exposure reference level and China’s 4000 V/m power frequency electric field environmental limit standard. This part of the area may be prone to accidents such as step voltage, and residents should avoid crossing as much as possible. However, due to the existence of transmission corridors, there is generally no long-term exposure of human bodies here, and such environmental risks are temporary and accidental.

(4)

The typical power frequency electric field values of 220 kV and 110 kV transmission lines in this article are less than 4 kV/m, meeting the requirements for power frequency electric field strength in residential areas. The maximum amplitude of the electric field strength directly below the side conductor of typical tower-type AC overhead transmission lines of 220 kV and 110 kV is 3300 V/m and 2350 V/m, respectively, which does not exceed the ICNIRP reference level and China’s environmental protection standards. It can be considered safe to be located below these two types of AC overhead transmission lines.

4. Effect of Tree Quantity and Distribution on Power Frequency Electric Field

Xing’an larch is one of the widely distributed tree species in Northeast China because of its adaptability and low soil requirements. In this paper, we will simulate and calculate the number and row position of Xing’an larch and apply the 500 kV voltage excitation to study the effect of tree size on the transmission line, and an equivalent model of transmission line and trees is shown in Figure 8. Meanwhile, A, B and C are the three-phase conductors of the transmission line.

4.1. Effect of Tree Quantity

It is assumed that the model and all parameters of trees are the same. On one side, the coordinates of the first tree are (0, 7.5), and the wheelbase between the center points of adjacent trees is 3 m. On the other side, the coordinates of the first tree are (0, −7.5), and the axial spacing between the center points of adjacent trees is 3 m. Meanwhile, the layout of trees is symmetrical about x = 0.

According to the conclusion obtained from transverse measurements, the maximum electric field intensity of the AC transmission line is below the side conductor, so this paper investigates the distribution of the industrial frequency electric field by changing the number of trees below the side conductor.

In this paper, assuming that the green belt formed by trees is symmetrical along the lateral conductor, the number of trees is set to 9, 19, 29, 54, and 133, respectively. So we can obtain the field strength distribution at 1.5 m above the ground for different numbers of trees, as shown in Figure 9. Then, the measurement path was selected as L1, and the variation curves of the electric field intensity under the lateral conductor with longitudinal distance were plotted for different numbers of trees, as shown in Figure 10. The maximum field strength values at the longitudinal measurement points for different numbers of trees are shown in

Table 3. Electric field strength for different numbers of trees.

Number	0	9	19	29	54	133
Electric field strength (kV/m)	5.60	5.32	5.10	4.86	3.79	1.19

.

In Figure 9, the cloud diagram of electric field distribution at a height of 1.5 m above the ground shows that the distribution of electric field intensity gradually weakens with the increase in the number of trees. It can be seen more intuitively in Figure 10 that, as the number of trees increases, the field strength below the side conductor decreases gradually. When the number of trees increased to 54, the field strength below the side conductor was reduced to below 4 kV/m. When the number of trees increased to 133, the green belt formed by the trees spread all over the transmission line below the side conductor, and the electric field strength at the longitudinal measurement point was 1.19 kV/m, which is 78.75% lower than that when there are no trees.

4.2. Effect of Tree Distribution

Therefore, it is possible to move the green belt of trees to the inside of the corridor, so as to achieve the purpose of reducing the width of the transmission corridor and reducing the electric field intensity below the side conductor [31,32]. The curve of the change of the value of the industrial frequency electric field intensity with the longitudinal distance at the longitudinal measurement point below the side conductor is shown in Figure 11.

As can be seen from Figure 11, when the tree green belt is laid from 15 m to 9 m of the transmission corridor, the maximum power frequency electric field strength of the longitudinal measurement point of the side wire is 3.71 kV/m. After retaining a certain safety margin, the electric field strength value is still less than 4 kV/m, and the width of the transmission corridor is reduced by 40%, which is of great significance for reducing the power frequency electric field of the transmission line and the width of the transmission corridor.

5. Conclusions

In this paper, through the study of transmission lines about different voltage levels, the basic law of power frequency electric field change under transmission lines is obtained, and the influence of a tree’s electromagnetic parameters on the power frequency electric field distribution of 500 kV transmission lines is studied by changing the number and location of trees. The following main conclusions were drawn:

(1)

The change trend of power frequency electric field strength with lateral distance is the same for transmission lines with and without overhead ground lines, and the error of the maximum power frequency electric field strength of both is within 5%, so in order to improve the calculation efficiency and reduce the calculation memory, the 3D electric field simulation calculation of transmission lines can be calculated according to the model without overhead ground lines.

(2)

When the phase angle of voltage A is 30 degrees, the change curve of its power frequency electric field strength with lateral distance is symmetrical about the middle conductor, and the maximum value of its power frequency electric field strength appears below the side conductor.

(3)

With the increase in the number of trees, the maximum value of power frequency electric field strength below the side conductor decreases gradually. Therefore, it is possible to move the green belt of trees to the inside of the corridor, so as to achieve the purpose of reducing the width of the transmission corridor and reducing the electric field strength below the side conductor.

However, some limitations can be expected. The simulated charge method used in this paper is the most classical algorithm, which is not combined with the method of calculating the electric field strength, so it is not comprehensive and efficient. In addition, the tree model in this paper is only a Xing’an larch model, which may not be suitable for the requirements of most regions.

For future work, we intend to use more integrated algorithms to predict the electric field strength of transmission lines and calculate the impact of different tree types on the width of transmission corridors.