# FEM Analysis and Sensor-Based Measurement Scheme of Current Distribution for Grounding Electrode
## 1 Introduction  
HVDC transmission systems have reached a voltage level of \(\pm\)1100 kV, and the stable operation of the grounding electrode is critical for the reliable operation of HVDC systems [1]. The grounding electrode can not only form a loop when the DC system is operating in a single-pole operating status but also balances the neutral point potential of the converter transformer [2; 3]. Besides, soil resistivity determines the current distribution, hence it is necessary to investigate the current distribution in the vicinity of the grounding electrode considering different soil textures [4].  
The disadvantages of the HVDC transmission project are that the electrical parameters of the grounding electrode still rely on the manual collection and the degree of automation is insufficient [5]. The resistivity in the soil where the grounding electrode is located will change with the changes in environmental temperature and humidity, while there are frozen soil and seasonally frozen soil in many areas [6]. At present, many scholars have conducted in-depth research on these topics. [PERSON] et al. used the complex image method to calculate the potential distribution of multi-layer soil betweengrounding electrodes in a DC transmission system and analyzed the influence of deep layers such as the crust, mantle, and core for the potential distribution on Earth's surface [7]. [PERSON] et al. used the finite element method to study the surface potential distribution of typical soil models and multi-layer soil models [8]. [PERSON] et al. developed a grounding electrode monitoring system that can collect the grounding current, temperature, and humidity at the grounding electrode site [9].  
The finite element method has been frequently used to calculate the current distribution in the soil near the grounding electrode [10; 11; 12; 13; 14]. The finite element method has been widely used in the study of grounding electrode current characteristics, but to better analyze it in engineering, real-time current monitoring is also needed. If a large DC flows from the grounding electrode into the soil, it will harm the surrounding metal pipes, transformers and other power equipment, and even humans or livestock. Therefore, it is necessary to study and design a weak current measurement device to be placed in the soil around the grounding electrode.  
In this paper, three-layer and mixed-layer soil models are proposed to calculate the current distribution in the vicinity of the grounding electrode, which considers the influence of frozen soil and the electric field. Experiments were set up to simulate the current distribution for extremely cold weather conditions, in which different magnitudes of the current flow into the ground, and the depth of the grounding electrode, the resistivity of the soil, and the location of the current measuring device were investigated. Finally, a \"drainage wire\" with a Hall sensor-based method is proposed to measure the leakage current in the soil under the simulation test platform, and a weak current measurement device range from 0 to 50 mA is designed. Then, the reliability and accuracy of the measuring device are verified.  
The remaining parts of the paper are as follows: in Section 2, the models to calculate the current distribution with frozen soil are described, and Section 3 presents the simulation of current and potential dispersion. In Section 4, the experimental results are analyzed.