When to use: Get a preliminary estimate of substation ground grid resistance using Sverak's simplified IEEE 80 formula, plus the standard IEEE 80 tolerable touch and step voltage limits for a 50 kg body. This is an educational, preliminary screening tool — final substation grounding grid design requires a full IEEE 80 study including grid current division, X/R ratio, actual mesh/step voltage from grid geometry, and field soil resistivity testing, by a qualified engineer.
This is a preliminary educational estimate using simplified IEEE 80 equations (Sverak's grid resistance formula and the standard 50 kg tolerable touch/step voltage equations). Final substation grounding grid design requires a full IEEE 80 study — including fault current division between the grid and other return paths, X/R ratio and DC offset, actual mesh and step voltage computed from grid conductor spacing/geometry, and field-measured soil resistivity (often modeled as a two-layer soil) — performed by a qualified engineer.
This tool provides a preliminary, educational estimate of substation ground grid resistance using Sverak's simplified IEEE 80 formula, plus the standard IEEE 80 tolerable touch and step voltage limits for a 50 kg body weight. It is intended for early-stage screening and learning — final substation grounding grid design requires a full IEEE 80 study performed by a qualified engineer, including grid current division, X/R ratio, actual mesh/step voltage from grid geometry, and field soil resistivity testing.
Sverak's widely published simplified formula estimates the resistance-to-remote-earth of a buried ground grid as Rg = ρ·[1/L + (1/√(20A))·(1 + 1/(1+h√(20/A)))], where ρ is the soil resistivity (Ω·m), A is the area enclosed by the grid (m²), h is the burial depth (m), and L is the total buried conductor length (m, including all grid conductors and any ground rods). This formula is widely used for preliminary grid sizing because it only needs grid area, burial depth, and total conductor length rather than the full grid layout (conductor spacing, number of parallel conductors, rod placement), and it converges to reasonable accuracy for typical grid geometries.
Lower resistivity soil, greater grid area, and more buried conductor length all reduce grid resistance. Because uniform-soil resistivity from a single Wenner test is itself an approximation of real, often layered soil, treat the resulting Rg as a preliminary estimate — final designs typically use a two-layer (or multi-layer) soil model from full soil resistivity testing.
IEEE 80 defines tolerable touch and step voltage limits based on the energy a human body can safely absorb during a ground fault before the protective device clears it. For a 50 kg body weight, the standard equations are Etouch50 = (1000 + 1.5·Cs·ρs)·0.116/√ts and Estep50 = (1000 + 6·Cs·ρs)·0.116/√ts, where ρs is the resistivity of a surface material (such as crushed rock) placed over the native soil, ts is the fault clearing time in seconds, and Cs is a surface-layer derating factor computed from Cs = 1 − [0.09·(1 − ρ/ρs)] / (2hs + 0.09) using the surface layer thickness hs (m).
A high-resistivity surface layer (crushed rock is typically in the rough range of 2,000-3,000 Ω·m, though it varies with material and moisture) substantially raises the tolerable touch and step voltage by increasing the contact resistance between a person's feet and the ground, which is why crushed rock or similar surfacing is standard practice in substation yards. Faster fault clearing time (smaller ts) also raises the tolerable voltage, since a shorter shock duration is safer for a given voltage.
This calculator estimates grid resistance and the tolerable (safe) touch/step voltage limits — it does not compute the actual mesh voltage (Em) or step voltage (Es) that would appear at the surface during a real fault, which depends on the detailed grid geometry (conductor spacing, grid shape, number of ground rods, corner/edge effects) through IEEE 80's geometric factors Km, Ki, Kii, and Kh. It also does not perform fault current division analysis (only a fraction of total system ground fault current typically returns through the grid rather than through shield wires or remote earth), and it assumes a uniform single-layer soil rather than the layered soil models often needed for accurate results. A complete substation grounding design compares the actual computed mesh/step voltage against these tolerable limits — this tool only produces the tolerable-limit side of that comparison, plus a preliminary resistance estimate.
There is no single universal target — acceptable grid resistance depends on the fault current magnitude, system grounding, and the resulting ground potential rise (GPR) relative to tolerable touch/step voltages for the specific site. Historically some utilities used rough guideline targets like 1 ohm or less for large substations and up to a few ohms for smaller ones, but the governing check under IEEE 80 is always the actual touch/step voltage from a full study, not resistance alone.
A high-resistivity surface layer (like crushed rock, typically very roughly 2,000-3,000 Ω·m depending on material, size, and moisture) greatly increases the contact resistance between a person's feet and earth during a fault, which raises the tolerable touch and step voltage limits substantially compared to bare native soil. This is why crushed rock surfacing is standard in outdoor substation switchyards.
Touch voltage is the potential difference between an energized structure (like a grounded equipment frame) and the ground at a point a person could touch while standing nearby, with hand-to-both-feet as the current path. Step voltage is the potential difference between two points on the ground surface one stride apart (foot-to-foot), which a person could experience while walking near a fault. IEEE 80 sets separate tolerable limits for each because the body's current path and impedance differ.
No. Grid resistance affects the overall ground potential rise (GPR = Rg × fault current returning through the grid), but personnel safety is governed by the local mesh and step voltages at the surface, which depend on grid geometry (conductor spacing, rod placement) — not resistance alone. A grid can have low resistance yet still have unsafe local touch/step voltages if conductor spacing is too wide; a full IEEE 80 study computing Em and Es against the tolerable limits is required to confirm safety.
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