Earth Potential Rise - Calculations

Calculations

In principle, the potential of the earth grid V_grid can be calculated using Ohm's Law if the fault current (I_f) and resistance of the grid (Z_grid) are known.

While the fault current from a distribution or transmission system can usually be calculated or estimated with precision, calculation of the earth grid resistance is more complicated. Difficulties in calculation arise from the extended and irregular shape of practical ground grids, and the varying resistivity of soil at different depths.

At points outside the earth grid, the potential rise decreases. The simplest case of the potential at a distance is the analysis of a driven rod electrode in homogeneous earth. The voltage profile is given by the following equation.

where

is a point beyond the edge of the earth grid.

is the voltage at distance from the earth grid, in volts.

is the resistivity of the earth, in Ω·m.

is the earth fault current, in amperes.

This case is a simplified system; practical earthing systems are more complex than a single rod, and the soil will have varying resistivity. It can, however, reliably be said that the resistance of a ground grid is inversely proportional to the area it covers; this rule can be used to quickly assess the degree of difficulty for a particular site. Programs running on desktop personal computers can model ground resistance effects and produce detailed calculations of ground potential rise, using various techniques including the finite element method.