Ground Grid Resistance Calculator
Enter soil, grid geometry, fault current and clearing time to check mesh and step voltage against tolerable limits.
Step-by-step
- Enter valid values to begin.
Simplified IEEE Std 80-2013 method for a rectangular grid in uniform soil: Sverak Rg, tolerable touch and step voltage with surface-layer factor Cs, and the Km, Ki, Ks mesh and step equations. Rods are assumed on the perimeter. It does not model two-layer soil, irregular grids or transferred potentials. Use a verified earthing study (CDEGS, ETAP) for design.
Ground Grid Resistance: Making the Substation Safe to Stand In
Core Engineering Principles
When a fault sends current into the earth through a substation grid, the earth does not stay at zero volts. The ground potential rise (GPR) is the grid current times the grid resistance, and it can be several thousand volts. A person standing at the edge of the grid with a hand on a grounded steel structure is exposed to touch voltage, the difference between the GPR and the surface potential under their feet. A person walking across the yard sees step voltage between their feet. The job of the grid is to keep those two voltages below what the body can tolerate for the clearing time of the protection.
The tolerable limit follows the IEEE 80 body-current equation. For a 70 kg person, the limit is 0.157 / √t amps through the body, and the voltage limit also depends on the surface layer. A thin layer of crushed rock with 3,000 Ω·m resistivity adds series resistance to the feet and makes a big difference. The grid resistance itself, Rg, is estimated by the Sverak formula from soil resistivity, buried area, conductor length and depth. Then the mesh voltage Em and step voltage Es are calculated from geometry factors and compared with the tolerable limits.
Etouch = (1000 + 1.5 Csρs) × 0.157/√ts • Estep = (1000 + 6 Csρs) × 0.157/√ts • Em = ρ Km Ki IG / LM
NEC & Standard References
IEEE Std 80-2013 is the guide for safety in AC substation grounding and gives all of the equations used here: Equation 27 for the Sverak resistance, Equations 32 and 33 for tolerable touch and step voltage, and Equations 80 to 94 for mesh and step voltage factors. IEEE Std 81 covers measuring soil resistivity (Wenner four-pin) and grid resistance (fall-of-potential). NESC Rule 92 and 93 cover grounding of supply stations. IEEE Std 837 covers connections, and NEC 250.50 and 250.53 apply to building electrodes. The 0.116 body constant is for a 50 kg person, 0.157 for 70 kg. Soil resistivity varies with moisture and season; use the worst-case, dry-season measurement.1. Conductors: 10 runs of 40 m plus 7 runs of 60 m gives LC = 820 m.
2. Rg by Sverak = 1.02 Ω, so GPR = 3,000 × 1.02 = 3,045 V.
3. Cs = 0.70; tolerable touch = 921 V; tolerable step = 3,020 V.
4. Mesh voltage Em = 614 V and step voltage Es = 370 V. Both are under the limits, so the design passes. Take the rock away and the tolerable touch voltage falls below 300 V, and the same grid fails.
- Measure the soil. A guessed resistivity is the largest error in grid design. Use at least a Wenner survey at several spacings.
- Fault current split. Only the part of the fault current that returns through the earth, IG, counts. Overhead ground wires and cable shields carry the rest.
- Fences and transfer voltages. Bond the fence to the grid or isolate it, and watch for pipes and communication cables carrying GPR out of the site.
- Corrosion and joints. Use exothermic welds or listed compression connectors, and inspect the grid after any excavation.