There is no direct measurement device for space potential measurement under high-voltage transmission lines. In this paper, a method for measuring and calculating the near-ground potential under high-voltage transmission lines is proposed.
Modeling methods
The vertical electric field in the near-earth region below the high-voltage transmission line is approximately uniform. When the electric field strength value
E0 in the vertical direction and the height
h from the ground are known, the potential value can be calculated by Eq.1.

(1)
In this paper, a method for calculating the vertical electric field in the near-earth region is proposed. Place a metal spherical shell near the grounded area under the high voltage transmission line. The potential of the metal ball can be measured as
V0 by a voltage measuring device, as shown in Fig.1.

Fig.1

Fig.2
The surface charge distribution of the metal spherical shell is not uniform. According to the analog charge method, the analog charge can replace the surface charge of the metal sphere. Divide the metal sphere into
n simulated charge rings, as shown in Fig. 2. Find
n potential matching points on the sphere, each affected by the simulated charge and the vertical electric field. The equation is shown in Eq. 2, and the influence of the earth is replaced by the mirror method.

(2)
For each matching point,
n potential equations can be listed, and the equation system can be obtained as Eq. 3.

(3)
Among them,

,
n+1 unknowns,
n+1 equations, the electric field intensity
E0 of the uniform electric field under the transmission line can be solved. The potential value of the area near the ground below the high-voltage transmission line can be calculated according to Eq.1.
Results
In this paper, the simulation calculation of the near-ground potential under the high-voltage transmission line is carried out through the simulation experiment. The experimental results show that the method can obtain the potential under the high-voltage transmission line within a certain error range.
Conclusions
In this paper, the space potential value of the near-ground area under the high-voltage transmission line can be calculated by the analog charge method and the potential inversion method.