# Detecting Grounding Grid Orientation: Transient Electromagnetic Approach
## 4 Performance Evaluation and Results' Analysis
### Simulation Model  
The simulation model shown in Figure 5 features a square grid of dimensions 4 m \(\times\) 4 m. The conductors are labeled \(C_{1}\) to \(C_{12}\) and arranged such that the mesh dimensions are 2 m \(\times\) 2 m. The conductors were cylindrical steel rods of radius 0.01 m and conductivity 4.032 \(\times 10^{6}\) S/m. The soil considered was homogeneous with electrical resistivity equal to 5 \(\Omega\)m. The grounding grid was buried 0.5 m under the Earth's surface. The transmitter coil of radius 0.15 m was excited with a 16 A pulse current of a trapezoidal wave. The secondary magnetic field was recorded 0.05 m above the surface at the center of the transmitter coil after each 10 \(\upmu\)s for a total of 100 time samples after the transmitter coil current was turned off. The transmitter coil was moved in a circle of radius 1 m along points \(P_{1}\) to \(P_{8}\) such that the angular displacement between adjacent points was 0.785 rad. The circle was centered at Node 5 acting as pole, which in general must be identified from the position of the vertical conductor. According to IEEEstd 80-2013 [5], the length of the grounding grid branches varies from 3 m to 7 m. Therefore, the radius of the circle must be constrained to be between 0 m and 3 m.  
Employing the inversion calculation for the secondary magnetic field of Figure 5, the corresponding equivalent resistivity \(\rho_{r}\) is plotted in Figure 6. Here, \(\rho_{r}\) is high at points \(P_{1}\), \(P_{3}\), \(P_{5}\), and \(P_{7}\), illustrating the presence of conductors \(C_{4}\), \(C_{10}\), \(C_{3}\), and \(C_{9}\) at analogous points. For instance, the equivalent resistivity at \(P_{1}\) was high due to the opposite flow of eddy currents \(I_{3}\) and \(I_{4}\) in \(C_{4}\). Keeping in view the rectangular geometry of a typical grounding grid and the characteristics of the polar coordinate system, it is inferred from Figure 6 that the grid was oriented parallel in the plane of the Earth (parallel to the substation boundary). Furthermore, the secondary magnetic field along \(P_{1}\) to \(P_{8}\) is shown in Figure 7. Here, the average value of the magnetic field is plotted against each point. Due to the fact that the magnetic field from a medium is inversely proportional to its resistivity, Figure 7 shows an inverse relation with Figure 6. Therefore, \(\overline{H_{z}}\) was low at \(P_{1}\), \(P_{3}\), \(P_{5}\), and \(P_{7}\), confirming \(C_{4}\), \(C_{10}\), \(C_{3}\), and \(C_{9}\).  
Figure 5: Simulation model featuring the square grounding grid of dimensions 4 m \(\times\) 4 m and mesh spacing 2 m. Conductors are labeled \(C_{1}\) to \(C_{12}\) and nodes 1 to 9. \(I_{1}\) to \(I_{4}\) are the induced eddy currents whose direction of flow is indicated by arrows. The TEM system is moved 0.05 m above the surface along circle of radius 1 m from point \(P_{1}\) to \(P_{8}\).  
Figure 6: Equivalent resistivity \(\rho_{r}\) along the circle from \(P_{1}\) to \(P_{8}\). High \(\rho_{r}\) at \(P_{1}\), \(P_{3}\), \(P_{5}\), and \(P_{7}\) corresponds to the presence of conductors C\({}_{4}\), \(C_{10}\), \(C_{3}\), and \(C_{9}\). \(C_{4}\) at 0 rad, \(C_{10}\) at 1.57 rad, \(C_{3}\) at 3.14 rad, and \(C_{9}\) at 4.71 rad along the circle showed the parallel orientation of the grid in the plane.