Substation earthing
Substation grid resistance (Sverak, IEEE 80)
- where
- grid resistance, Sverak (Ω)
- soil resistivity (Ω·m)
- total buried horizontal conductor length (m)
- area occupied by the grid (m²)
- grid burial depth (m)
- Laurent–Niemann estimate (Ω)
Explain this equation
Estimates the resistance of a meshed substation earth grid in uniform soil, for early design and for EPR estimates before a computer model is built.
A is the area covered by the grid and LT the total length of buried horizontal conductor. The 1/√(20A) term is the resistance of a plate of the same area; 1/LT accounts for the grid being made of wires rather than a solid plate; the h term corrects for burial depth. RLN is the simpler Laurent–Niemann form with an equivalent radius √(A/π).
A dense grid behaves almost like a solid plate, so area is what matters most. The 20 inside the roots comes from Sverak's fit to the plate result and reduces to roughly ρ/(4r) for a shallow grid.
A 70 m × 70 m grid with 1540 m of conductor in 400 Ω·m soil gives 2.78 Ω. Doubling the conductor length within the same area gives only a few per cent less; doubling the area cuts R by about 30 %.
Watch out: rods are not included in LT, and two-layer soil can change the answer a great deal.
Resistance to remote earth of a meshed substation earth grid in uniform soil.
Enter your values to see the result.
Good to know
Sverak’s formula (IEEE 80-2013 Eq. 52) adds a depth correction to the Laurent–Niemann estimate ρ/(4r) + ρ/LT used in EREC S34 (formula R4). For most grids the first term dominates: R falls roughly with the square root of area, and adding more conductor inside the same area helps little. IEEE 80 Example 1: 70 m × 70 m, 1540 m of conductor, 0.5 m deep, 400 Ω·m → 2.78 Ω.
Common mistake
Counting rods in LT. Rods are handled separately (EREC S34 R5/R6 or IEEE 80 Schwarz equations); include only horizontal conductor in LT.
Limits
Uniform soil, grid without rods, burial 0.25–2.5 m. Two-layer soil, rods and long irregular shapes need the Schwarz equations or a computer model (as EREC S34 and TS 41-24 recommend for primary substations).
Sources
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.