Free Tool · IEEE 80-2013 · IEC 61936-1
Substation Earthing Grid
Calculate grid resistance R_g, ground potential rise GPR, touch and step voltages, and recommended conductor size for substation earthing grids. Implements IEEE 80-2013 (Sverak formula, Onderdonk sizing) with IEC 61936-1 EU compliance reference.
Frequently Asked Questions
What is the Sverak formula for grid resistance?
The Sverak formula (IEEE 80-2013 §16.3) gives grid resistance as:
R_g = ρ/L_T + ρ/√(20·A) × (1 + 1/(1 + h·√(20/A)))
where ρ is soil resistivity (Ω·m), L_T is total buried conductor length (m), A is grid area (m²), and h is burial depth (m). It is more accurate than the earlier Schwarz equations for typical rectangular grids and is the preferred method in IEEE 80-2013.
How does the C_s surface layer derating factor work?
When crushed rock or concrete (high-resistivity surface layer ρ_s > ρ_soil) is placed on top of the grid area, it increases the contact resistance under a person's foot. The factor C_s (IEEE 80-2013 Eq. 27) reduces the effective foot resistance from ρ_s to an intermediate value, which raises the tolerable touch/step voltages — making the design easier to pass.
Typical values: 100 mm of crushed rock (ρ_s ≈ 3 000 Ω·m) on 100 Ω·m soil → C_s ≈ 0.74. No surface layer → C_s = 1.0 (worst case for tolerability, lowest tolerable voltage).
What is GPR and why does it matter?
Ground Potential Rise (GPR = I_G × R_g) is the maximum voltage that the earth grid can reach with respect to remote earth during a fault. It determines the hazard to anyone touching grounded metalwork, and drives the touch/step voltage calculations. GPR must also be communicated to adjacent utilities (telecom, pipelines) whose equipment may be connected to the substation earth grid.
What is the Onderdonk equation used for conductor sizing?
The Onderdonk (fusing) equation (IEEE 80-2013 §11.3 Eq. 37) sizes the conductor so it will not melt during a ground fault:
A_mm² = I / √( TCAP / (t × α_r × ρ_r × 10⁴) × ln((K_0 + T_m)/(K_0 + T_a)) )
Material constants (TCAP, ρ_r, α_r, K_0, T_m) are from IEEE 80-2013 Table 1. For 10 kA, 0.5 s, copper: A_min ≈ 120 mm² → use standard 150 mm² (240 kcmil).
What is the difference between IEEE 80 and IEC 61936-1?
IEEE 80-2013 is the primary North American guide for substation grounding design, covering grid resistance, GPR, mesh/step voltages, and conductor sizing in detail. IEC 61936-1 (Power installations > 1 kV AC) is the European standard that references earthing requirements and acceptable touch/step voltage levels — it broadly aligns with IEEE 80 for the engineering fundamentals but uses slightly different body impedance models and national annexes (e.g. CENELEC HD 637 S1 in some EU countries). This calculator implements IEEE 80-2013 as the primary calculation engine.
How many conductors per direction should I use?
A common starting point is to target a mesh spacing D of 5–10 m for transmission substations and 3–5 m for distribution substations. For a 50 × 50 m grid with 5 m spacing you need 10 conductors per direction. Tighter meshes reduce the mesh voltage (E_touch) but increase cost. The calculator lets you iterate quickly — if the touch voltage check fails, increase the conductor count until it passes.