Substation earthing
Transferred potential to a remote point (hemispherical approximation)
- where
- earth-return current (A)
- earth potential rise (V)
- earth electrode resistance (Ω)
- soil surface potential at distance x (V)
- soil resistivity (Ω·m)
- distance from the electrode centre (m)
- transferred voltage between the conductor and local earth (V)
Explain this equation
Estimates the voltage that a metallic conductor connected to the substation earth can carry to a remote point, or bring into the site from remote earth: fences, pipes, cable sheaths and telecoms pairs.
IE is the current leaving the electrode, found from EPR and RE. Vx is the potential of the soil surface at distance x, modelling the electrode as an equivalent hemisphere. UTr is the difference between the conductor, which sits at the full EPR, and the local soil at x.
Around a hemisphere current spreads evenly in all directions, so the soil potential falls as 1/x. The equivalent radius ρ/(2πRE) is the hemisphere that would have the same resistance as the real electrode.
A 2144 V EPR from a 1.43 Ω electrode in 100 Ω·m soil leaves about 240 V in the soil at 100 m, so about 1.9 kV appears on a conductor bonded at the substation. Doubling x halves Vx.
Watch out: the model is poor within a few electrode widths of the site, and conductors earthed along their route will carry less than this.
Estimates the voltage a metallic conductor (fence, pipe, cable sheath, telecoms pair) bonded at one end can impose at a remote point, using the potential of the soil at that distance.
Enter your values to see the result.
Good to know
The electrode is replaced by a hemisphere of the same resistance (radius ρ/(2πRE)). Soil potential then falls as 1/x, so Vx = ρIE/(2πx). A conductor earthed at the substation and taken to point x carries the full EPR there, giving EPR − Vx between it and local earth; a conductor earthed remotely and brought into the site sees the same difference. Rearranged, x = ρIE/(2πV) gives the distance to the 430 V or 650 V HOT-zone contour.
Common mistake
Assuming a conductor is safe because it leaves the substation fence. Close in, most of the EPR is transferred; the transferred share only falls off slowly as 1/x.
Limits
Uniform soil, compact electrode, point well beyond the electrode (x several times its size). Ignores the conductor’s own impedance and its earthing along the route, which can reduce the transferred voltage. EREC S34 gives more detailed methods for EPR contours and transferred potentials.
Sources
- ENA EREC S34 Issue 2 (2018) A guide for assessing the rise of earth potential at electrical installations
- BS EN 50522 Earthing of power installations exceeding 1 kV a.c. (2010; superseded by EN 50522:2022)
- ENA TS 41-24 Issue 2 Guidelines for the design, installation, testing and maintenance of main earthing systems in substations (consultation text, Tables 1 and 2)
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.