# FEM Analysis and Sensor-Based Measurement Scheme of Current Distribution for Grounding Electrode
## 3 Calculation and Analysis of Current Distribution
### Current Density and Potential Distribution  
#### 3.3.1 Three-layer Soil Model  
In order to analyze the distribution characteristics of current density and potential value on the redefined X and Y coordinate planes, 130 sets of data are taken between 0 and 0.6m in the X and Y coordinate directions. Figures 6-8 are the curves of the current density and potential of the linear, cross-shaped, and ring-shaped grounding electrodes under the three-layer soil model. The distribution curves in Figures 7 and 8 almost completely coincide, so a dot-line plot is adopted for graphing purposes.  
The following analysis can be obtained from the current density and potential distribution curves of different grounding electrodes under the three-layer soil model:  
For the linear grounding electrode, the maximum current density is about 67.4 A/m\({}^{2}\), and the highest value is probably located at the surface directly above the two ends of the linear grounding electrode. The current peak value of 65.9 A/m\({}^{2}\) also appears at the position where the Y coordinate is located at 0.25 and 0.35 m. At the boundary of the model, the current density drops to 25 A/m\({}^{2}\)  
Figure 5: Current density and potential distribution with different grounding electrodes. (**a**) Current density for linear grounding electrode; (**b**) current density for cross-shaped grounding electrode; (**c**) current density for ring-shaped grounding electrode; (**d**) potential distribution for linear grounding electrode; (**e**) potential distribution for cross-shaped grounding electrode; (**f**) potential distribution for ring-shaped grounding electrode.  
Secondly, the maximum potential is on the ground surface directly above the center of the linear grounding electrode, and the peak value is about 278 V.  
The maximum current density of the cross-shaped grounding electrode is about 55.9 A/m\({}^{2}\), and the highest value is located where the X coordinate is 0.2 and 0.4 m, while the Y coordinate is 0.2 and 0.4 m. Besides, the maximum potential is located on the ground surface directly above the center of the cross-shaped grounding electrode body, and the peak value is about 261 V.  
Figure 8: Current density and potential distribution curves for the ring-shaped grounding electrode. (**a**) Potential distribution curves in the X and Y directions; (**b**) current density distribution curves in the X and Y directions.  
Figure 6: Current density and potential distribution curves for the linear grounding electrode. (**a**) Potential distribution curves in the X and Y directions; (**b**) current density distribution curves in the X and Y directions.  
Figure 7: Current density and potential distribution curves for the cross-shaped grounding electrode. (**a**) Potential distribution curves in the X and Y directions; (**b**) current density distribution curves in the X and Y directions.  
For the ring-shaped grounding electrode, the maximum current density is about 43 A/m\({}^{2}\), which is a circular area about 0.15 m from the center point. In a circular region of 0.05 m from the center, the surface current density is close to 0, and there are two smaller current peaks of about 1 A/m\({}^{2}\). At the boundary of the soil model, the current density drops to 24 A/m\({}^{2}\). On the other hand, the maximum potential is about 173 V on the ground surface directly above the ring-shaped grounding electrode body.  
For the cross-shaped and ring-shaped grounding electrodes, the current density and potential distribution curves in both X and Y coordinates are completely overlapped. The reason for this overlapping is that the cross-shaped and ring-shaped grounding electrodes are completely symmetrical. Further, the surface current density directly above the center of the three grounding electrodes' bodies is close to 0. Meanwhile, at the boundary of the soil model, the surface potential drops to 0.