Surface voltages and resistance of grounding systems of grid and rods in two-layer earth by the rapid Galerkin´s moment method

The point matching moment method has been the prime candidate for grounding system analysis. The regular method yields accurate results as long as the segmentation is very fine. This means a large number of basis functions and frequently requires a super computer. In the present paper, we propose an alternate moment method in the Galerkin´s form. This form is variational (i.e. with error reduction property) which allows for very few basis functions, resulting in a very fast convergence but still gives less than 2% error in the grounding resistance. Each basis function in this form can be a whole rod with uniform current distribution, representing a vertical driven rod or a horizontal rod across a whole grid. Such basis functions give good results in the grounding resistance, it is obvious that they need not give good results in the voltages (ground potential rise, touch, and step) on the earth surface near the grid intersections. To correct this, a second type of basis functions namely spheres is added at the intersections. Since the intersections are few, the total number of basis functions is still small. With such basis functions added, however, the resulting voltages now have errors generally less than 4%. With such high accuracy and small matrix size (≈10×10 to 50×50) in the moment method it is easy to do parametric studies, even for an extensive grounding system