Soil investigation and model
Reduce four-pin field measurements to apparent resistivity, fit a two-, three- or four-layer earth model (IEEE Std 81-2025 §7.3, §7.6), and derive the equivalent uniform resistivity used by the closed-form IEEE 80 equations.
Survey data
Wenner puts the four pins at equal spacing a. Schlumberger keeps the two inner potential pins close together and moves the outer current pins out, so the spacing entered is AB/2, half the distance between the current pins.
Enter the apparent resistivity if the instrument already reports ρₐ, or the raw resistance R if it reports ohms — the program applies the array formula for you.
One row per pin spacing you measured, smallest
first. At least three rows are needed to fit a two-layer model and six (better eight
or more) for three layers; a roughly logarithmic ladder of spacings — 1, 1.5, 2, 3,
4, 6, 9, 12, 16, 20, 30 m — resolves the layers best.
| # | Pin spacing a (m)? | ρₐ (Ω·m)? | R (Ω)? | Traverse? |
|---|
Model options
Automatic fits two layers and, when that fit is worse than 3 % RMS or the curve falls and rises again (H-type) or rises and falls (K-type), also fits three; with nine or more readings and a three-layer fit still worse than 3 %, it also tries four. The third layer is kept only if it lowers the misfit by at least a fifth and passes an F test of its two extra parameters at the 5 % level, so noise is not mistaken for a layer. Three layers need at least six readings and four at least nine; the middle layer's resistivity and thickness are often traded against each other (equivalence), and the result says which combination of them the readings actually fix.
m
Depth of cover over the buried earthing conductors, measured from finished ground level to the top of the conductor. Typically 0.5–0.8 m.
m
How far the ground rods reach below the buried grid, not their total length. Leave 0 if there are no rods. It only affects which layer the model is averaged over.
How the two fitted layers are collapsed into the single ρ that the IEEE 80 closed-form equations need. A grid's current goes about one grid radius deep, however shallow the grid is buried, so the grid-size rule treats the grid as a disc of the same area on the layered soil. Automatic uses it whenever the grid area is known; the grid page's Pull inputs recomputes it for the actual grid. The depth-weighted average suits small electrodes only. Upper layer only is not conservative when ρ₂ is higher than ρ₁.
m²
Area enclosed by the earthing grid. It sets how deep the grid's current reaches and therefore which layer dominates. Leave empty if not yet known — Pull inputs on the grid page recomputes the equivalent resistivity with the grid's own area and length.
A single bad reading — a pin in a stone, a buried pipe, a misread range — drags a least-squares fit towards itself. With this on, the residuals of the fit are scaled by their median absolute deviation; a reading more than three robust standard deviations (and at least 5 %) from the curve is set aside, one at a time, and the model refitted. At most a fifth of the readings can be set aside. The excluded readings are listed so you can re-measure them.
Readings from more than one traverse? Give each row its traverse name (for example N–S, E–W). All rows are fitted together, and each traverse with three or more readings is also fitted on its own to show whether the soil varies across the site.
Apparent resistivity curvemeasured vs fitted
Section through the modelled soilto scale
Model and residuals
Enter at least three measurement points and run the fit.
Earth-fault current
Line-to-earth fault current to IEC 60909-0, then the maximum grid current IG = Df·Sf·Cp·3I₀ of IEEE Std 80-2013 clause 15.
Source data
Network + transformer data builds the sequence impedances from the supply short-circuit level. Use sequence impedances if the utility gave you Z₁ and Z₀ directly, or 3I₀ if you already know the earth-fault current.
kV
Nominal line-to-line voltage of the faulted system, not the phase voltage.
–
IEC 60909 voltage factor. 1.1 for maximum fault current above 1 kV — it accounts for the highest operating voltage, tap changers and load flow.
kA
The total earth-fault current at the site — three times the zero-sequence current. Fill this in to bypass the impedance calculation entirely; leave it blank to let the program compute it.
Grid current factors
s
How long the fault lasts before the protection clears it, including breaker operating time. This sizes the conductor and sets the decrement factor.
s
How long a person could be in contact with the fault. Usually the same as the fault duration, but IEEE 80 lets you use a shorter time where high-speed reclosing means the person is not exposed for the whole event.
Hz
–
The fraction of the earth-fault current that actually leaves the grid into the soil. The rest returns through overhead earth wires, cable sheaths and neutrals, and never raises the site potential. 0.6 means 60 %.
–
Allowance for future growth of the fault level over the life of the installation. 1.0 for no growth, 1.25 to design for a 25 % increase.
Indicative Sf values for a grid of about 1 Ω (a rough summary, not values from a standard) — click to apply:
Or estimate Sf from IEEE Std 80-2013 Table C.1 (100 % remote contribution): Sf = |Zeq| / |Zeq + Rg|.
Ω
Shield wires and fault location
IEEE Std 80-2013 clause 15.9 and Annex C: the fault current that returns through the soil — and so raises the grid — is what the shield wire of the line does not carry back. Here the shield wire and tower footings of one outgoing line are solved as a ladder, with the voltage the phase current induces in the shield wire, and the fault is moved along the line: a fault at the first towers outside the station often puts more current into the grid than one inside it.
Ω
Resistance of this station's grid to remote earth — from the grid page or the numerical solver.
km
Length of the outgoing line to the remote station.
km
Average distance between towers.
Ω
Average footing resistance of one tower; 10–25 Ω is typical.
Ω
Earth resistance of the station at the far end, to which the shield wire is bonded.
Ω·m
Sets the depth of the earth return in Carson's equations.
Ω/km
a.c. resistance of the overhead earth wire (0.33 Ω/km is a 7/3.25 mm steel-cored aluminium wire; galvanised steel is 2–4 Ω/km).
m
Geometric mean radius of the shield wire.
m
Average distance between the faulted phase and the shield wire; it sets the mutual coupling.
One or two shield wires on the faulted line. Two wires bonded at every tower are solved as one bundle with their mutual impedance, (z_s + z_m)/2 per km — not half the impedance of one wire.
m
Distance between the two shield wires of a line (used with two wires, here and for the other and parallel lines).
Ω
Positive-sequence impedance of this station's own source (transformer and network behind it), as R+jX, e.g. 0.5+5j.
Ω
Zero-sequence impedance of this station's own source — the earthed transformer neutral.
Ω
Positive-sequence impedance of the source at the far end of the line.
Ω
Zero-sequence impedance of the source at the far end.
Ω/km
Positive-sequence impedance of the line per kilometre.
Ω/km
Zero-sequence impedance of the line per kilometre.
Ω
Combined input impedance of every other line's shield wire and distribution neutral bonded to the grid. Blank: none.
km
One length per span, from the station outwards, where the spans differ. Given, they replace the line and span lengths above (the line length is their sum).
Ω
One footing resistance per intermediate tower, from the station outwards — measured values where you have them. There is one tower fewer than there are spans. Given, they replace the single value above.
Every other line leaving the station with a shield wire, one per row as: length (km), span (km), footing resistance (Ω), remote station earth (Ω)[, number of shield wires]. Each ladder is solved with the same shield-wire data and soil and put in parallel with the grid, in addition to the impedance in the box above. Two shield wires are taken as a bundle with their mutual impedance, at the spacing above.
A line that runs beside the faulted one over the whole route, with its towers at the same places and ending at the same remote station: separation between the line centres (m), its footing resistance (Ω), and optionally its number of shield wires, their spacing and the distance from the faulted phase to them (default: the separation). Its shield wires are coupled to the faulted phase and to every other shield wire (Carson, shield wires at one height) and the corridor is solved as one network. A line on a different route belongs under Other outgoing lines.
Cable sheaths — earth-fault return
A substation fed by cable: for an earth fault at the far end the fault current returns partly in the cable sheaths and armour and partly through the soil — only the soil part raises the earth. The sheaths are solved as a ladder between the two end earths and any earthed joints or link boxes, with the faulted core inducing its voltage in every section (ENA EREC S34 Appendix D generalised). The result is the split factor of the cable, the earth current and potential at each end and the voltage of every joint.
kA
The earth-fault current at the faulted end, from the fault current above (3I₀).
km
Length of the cable route between the two substations.
Ω
Earth resistance of the substation at the source end.
Ω
Earth resistance of the substation at the far end.
Ω/km
a.c. resistance of one cable's metallic sheath or screen per km, from the cable data sheet.
Ω/km
Resistance of the armour per km where it is bonded with the sheath; it is taken in parallel.
m
Mean radius of the sheath (half its mean diameter).
For single-core cables the three sheaths, bonded together at the ends, act as one return conductor; their geometry sets its self impedance and its coupling to the faulted core.
m
Centre-to-centre spacing of the single-core cables.
Identical cable circuits between the same two substations.
Distances from A of the joints or link boxes whose sheaths are earthed through their own electrode.
Ω
Earth resistance of each earthed joint or link box.
Single-point bonded sheaths carry no earth-fault return current: the whole fault current then flows through the soil. Cross-bonded sheaths are solved section by section with the transpositions at the link boxes; with equal minor sections the result is the same as bonded at both ends.
The minor sections from A, three for every major section; they must add up to the route length. The sheaths are earthed at A, at B and at every major joint (with the joint earth resistance above); the link boxes between are taken as open, their voltage limiters not conducting.
The core with the earth fault. In flat formation the result depends on it; in trefoil it does not.
m
Centre distance between parallel circuits laid side by side (cross-bonded model only).
Where the earth fault is.
Ω·m
Average soil resistivity along the route (sets the depth of the earth-return path).
Then the current returns to a remote source and also leaves through A's earth (EREC S34 D.2.3); unticked, A's transformer neutral is the source (D.2.1).
Results
Enter the source data and calculate.
Decrement factor vs fault duration
Grid current along the lineshield-wire ladder
Solve the ladder to see where the fault puts the most current into the grid.
Earthing conductor sizing
Thermal sizing to IEEE Std 80-2013 Eq. (37)/(45) and the IEC 60364-5-54 adiabatic equation, plus the minimum sizes required by IEC 60364-5-54 Tables 54.1 and 54.2.
Design current
kA
The current the earthing conductor itself has to carry, which is not always the full site fault current — a grid conductor carries only its share.
s
Time the conductor carries that current. The heating is adiabatic, so the required area grows as the square root of this time.
–
Accounts for the d.c. offset in the first cycles, which heats the conductor more than the a.c. value alone. Take the value computed on the fault-current page; 1.0 ignores the offset.
°C
Ambient soil or air temperature the conductor starts from. A higher starting temperature leaves less room before the fusing limit and increases the area.
Material and joints
Sets the conductivity, fusing temperature and thermal capacity used in the IEEE 80 equation. Copper-clad steel is the usual compromise between cost and theft resistance.
The joint, not the conductor, usually sets the temperature limit. An exothermic weld can go to the copper fusing point; a bolted joint must stay below 250 °C or it loosens and its resistance rises.
Material for the parallel IEC 60364-5-54 adiabatic check, which uses a k factor rather than the IEEE 80 formula.
Where the conductor runs and what covers it. This sets the initial and final temperatures, and therefore k — a bare buried conductor may run hotter than one bundled with cables.
mm²
Cross-section of the line conductor the protective conductor runs with, used for the S/2 and 16 mm² rules of IEC 60364-5-54 Table 54.2 (BS 7671 Table 54.7). Leave 0 if you are not sizing a PE from a line size.
BS 7671 Table 54.1: "protected against corrosion" means a sheath. A bare conductor buried in soil is not protected and must be at least 25 mm² copper or 50 mm² steel, whatever the thermal calculation says; IEC 60364-5-54:2011 (542.3.1, Table 54.1) asks the same 25 mm² of copper, 50 mm² where a lightning protection system is connected, and 10 mm round (78.5 mm²) hot-dip galvanized steel. A sheathed conductor may be 16 mm², or 2.5 mm² copper if it is also mechanically protected.
IEC 60364-5-54:2011 Table 54.1: a bare copper earthing conductor buried in soil must be 50 mm² (not 25 mm²) where the earth electrode also serves a lightning protection system (IEC 62305-3).
Which thermal criterion sizes the conductor (docs/THEORY.md §4). An HV substation grid designed to IEEE 80 is sized by IEEE 80 with the joint temperature, which is where welded joints save copper; an LV protective or earthing conductor is sized to IEC 60364-5-54. Taking the larger of the two is the safe choice when both standards apply or the basis is not yet fixed. The Table 54.1 minimum applies in every case. Record the basis in the design report.
Results
Enter the design current and run.
Required area vs fault duration
Substation / power-plant earth grid — IEEE Std 80-2013
The complete design procedure of Figure 33: tolerable voltages, grid resistance (Sverak and Schwarz), ground potential rise, mesh and step voltages, and automatic refinement until the design complies.
Site and safety data
Ω·m
Uniform soil resistivity used by the closed-form equations. Take the equivalent value from the soil model page rather than a single field reading.
Picking a material fills in its wet resistivity below. The surface layer is the crushed rock or asphalt on top of the natural soil, not the soil itself.
Ω·m
Resistivity of the surface layer when wet — always use the wet figure, because that is the unfavourable case for a person standing on it.
m
Thickness of the crushed-rock or asphalt layer. 0.102 m is 4 inches, the value used in the IEEE 80 Annex B worked example. Set 0 for bare soil.
s
Duration of the shock a person could receive. It appears under a square root in the tolerable-voltage formula, so halving it raises the limits by about 40 %.
IEEE 80 gives limits for a 50 kg and a 70 kg body. 50 kg gives the lower, more conservative limits and is the usual choice where the public has access.
kA
The part of the earth-fault current that actually flows from the grid into the soil: IG = Df · Sf · Cp · 3I₀. Use “Pull inputs” to take it from the fault-current page rather than entering the raw fault current here.
Grid geometry
m
Overall plan length of the buried grid, edge to edge — the area the conductors enclose, not the length of one conductor.
m
Overall plan width of the buried grid, edge to edge.
m
Centre-to-centre distance between adjacent parallel grid conductors — the size of one mesh. The IEEE 80 equations assume the same spacing both ways, so a 70 m grid at D = 7 m has eleven conductors in each direction. Reducing D is the most direct way to bring the mesh voltage down.
m
Depth of cover from finished ground level to the top of the buried conductors. Usually 0.5 m; deeper burial lowers the touch voltage but barely changes the grid resistance.
m
Diameter of the grid conductor itself, in metres — 0.01 m is a 10 mm round conductor, roughly 79 mm². It enters the mesh-voltage geometry factor only, so it has a weak effect on the result.
The closed-form equations need the true area, perimeter and conductor length of an L-, T-shaped or irregular grid (IEEE 80 Eq. (91)–(93) and Example B.4): enter them in the fields that appear. Lx and Ly are then the maximum dimensions. IEEE 80 validated the equations for square, rectangular, triangular, T- and L-shaped grids; for a genuinely irregular outline use the numerical solver page as well.
Sverak is the standard closed form for a grid with or without rods. Schwarz treats the conductors and the rods as two coupled electrodes and is better when the rods dominate. Automatic chooses between them.
Compliance
Run the evaluation.
Layout
Section
Spacing sweep
Detailed results
Grid layout
Section through the gridsurface layer, burial depth, spacing, rods
Mesh and step voltage vs conductor spacing
All computed quantities
Run the evaluation.
Numerical analysis — boundary-element solver
Arbitrary electrode geometry in uniform or layered soil (up to four layers), or two soils side by side across a vertical boundary. The buried metal is discretised into segments held at a common potential; solving for the leakage-current distribution gives the true earth resistance, the surface potential field and the touch and step voltages everywhere — without the shape restrictions of the closed-form equations.
Soil and current
Ω·m
Resistivity of the upper soil layer. For a uniform earth, put the single value here and leave the lower layer blank.
Ω·m
Resistivity of the lower layer. Leave blank to solve a uniform earth.
m
Depth from ground level to the boundary between the first and second layers.
Ω·m
Resistivity of a third layer below the second, extending to any depth. Leave blank for a two-layer earth. The solver then uses the exact image expansion of the three-layer earth, and every conductor that crosses an interface is split there.
m
Thickness of the second layer, so the third layer starts at the top-layer thickness plus this value. Needed only with ρ₃.
Ω·m
Resistivity of a fourth layer below the third, extending to any depth. Leave blank for three layers or fewer.
m
Thickness of the third layer, so the fourth starts at the sum of the three thicknesses above it. Needed only with ρ₄.
Ω·m
Resistivity of the soil beyond a vertical boundary — a fault, a buried rock face, the edge of a backfilled area or of a lake. The soil is then ρ₁ on one side and ρ′ on the other, each uniform to any depth, and the solution is exact (images in the boundary). Use it with ρ₁ only: leave the lower layers blank.
m
A point of the boundary line on the plan: its x coordinate, in the coordinates of the electrode elements.
m
The y coordinate of the same point.
°
The direction, measured anticlockwise from the x axis, in which you cross the boundary into the ρ′ soil: 0° puts ρ′ at larger x (the boundary runs parallel to y), 90° at larger y, 180° at smaller x.
A
Current injected into the electrode system, in amperes — note that the grid page asks for the same quantity in kA, so 1.908 kA is 1908 A here.
m
Length each conductor is chopped into before solving. Shorter segments give a more accurate answer and a slower solve; 2–3 m suits a substation grid.
pts
Number of points across the scanned area in each direction, so 61 means the surface potential is evaluated on a 61 × 61 grid. Raise it for a smoother map, at the cost of solve time.
m
The stride length used to evaluate step voltage — the distance between a person's feet. IEEE 80 and IEC 60364 both use 1 m.
The leakage current crowds towards the free end of every conductor — the grid corners, rod tips — and so do the touch and step voltages. With this on, the segment at each conductor end is halved three times towards the end. On the IEEE 80 Annex B grid it gives with uniform 3 m segments the corner touch voltage of a uniform 0.5 m mesh, at a quarter of the unknowns.
%
After the solution, the segments within 3 m of the worst touch and step points (and of their mirror images) are halved and the model solved again, until both voltages change by less than this percentage — 0.5 % is a good value. It removes the local discretisation error where the verdict is decided; the convergence check under Accuracy and soil studies still measures the global one.
Where people can touch earthed metal — equipment, structures, gates — one per line as name: x0, y0, x1, y1 (a rectangle, m), optionally followed by its own limit in volts. With zones the touch voltage is checked only there. Without them it is checked wherever a person standing on the soil is within 1 m of buried metal, or inside a mesh — so the empty notch of an L-shaped grid no longer counts.
Electrode geometry
| Element | Parameters |
|---|
Import from a DXF site drawing
Reads an ASCII DXF of the earthing layout. Lines and polylines on a conductor layer become buried conductors (arcs as chords), circles there become rings; points, small circles and blocks on a rod layer become driven rods; each polyline on a fence layer becomes a fence. The unit is taken from the drawing ($INSUNITS) unless a scale is given.
Save the plan from AutoCAD, BricsCAD, QCAD or LibreCAD as DXF, ASCII or binary, any release from R12 on. DWG cannot be read. Put the grid conductors, the rods and the fence on separate layers.
m
Depth of the imported conductors and of the rod tops.
m
Radius of the imported conductors.
m
Length of every imported rod.
m
Radius of every imported rod.
m per unit
Metres per drawing unit: 0.001 for a drawing in millimetres. Leave blank to use the unit stored in the drawing.
Site drawings are often in survey co-ordinates far from the origin; moving the layout keeps the numbers readable. The offset is reported.
Unticked, each fence is isolated and floats at the potential the soil imposes; the value can be changed per fence in the table.
Touch voltage is reported wherever a person on the soil is within 1 m of
buried metal or inside a mesh (or only in the touch zones, when given); step voltage is
reported over the whole scanned area, in the worst direction. A fence is
checked on its own: its touch voltage is the fence potential minus the surface
potential within 1 m on either side. Set bonded to 1 to connect it to the
grid, 0 to leave it isolated (it then floats at the potential the soil imposes). Insulated
fence sections and gates are entered as several open outlines (closed 0), one per section.
A pier or strip footing is a reinforced-concrete foundation used as an electrode: its
bar cage becomes one equivalent bar inside a concrete cylinder, whose resistivity
ρc (30–100 Ω·m moist, a few hundred dry) adds to the soil's.
A plate is a thin solid metal rectangle in contact with the soil — an earth plate, or a
raft's reinforcement taken as one sheet. It is cut into narrow strips, finer at the
edges where the current crowds, and its resistance is within 0.3 % of an exact plate
solution. Plates are solved by this page and its studies; the non-equipotential and
lightning models take wire electrodes only.
Transferred potential
A pipe, rail, cable screen or bare earth wire that leaves the station carries part of its potential rise out (IEEE Std 80 clause 17.3). The conductor has series impedance with earth return and leaks into the soil. A bare or coated conductor is solved together with the station, so its own leakage changes the soil potential round the station and beside the route; an insulated screen or a rail is solved as a lossy line driven by the bond and by the soil potential the station imposes along the route. It uses the soil, current and electrodes above.
Coated: leakage set by the coating resistance. Bare: leakage into the soil along its length. Insulated: no leakage, so the whole station potential reaches the far end. Rail: leakage given as rail-to-earth resistance.
m
Where the conductor leaves the station, in the same co-ordinates as the electrodes.
°
The route is a straight line in this direction: 0° along +x, 90° along +y.
m
Length from the station to the far end.
m
Depth of the conductor; the soil potential along the route is taken at this depth.
m
Outer radius of the pipe, rail-equivalent or screen.
Sets the internal impedance. Steel at 50 Hz carries the current in a skin about 2 mm deep, which makes it several times more resistive than at d.c.
m
Wall of a pipe or thickness of a screen; blank for a solid conductor.
Ω/km
From the cable data sheet, for a screen or wire. Overrides the value worked out from the metal and wall.
Ω·m²
Specific coating resistance of a coated pipe: about 10³ for a poor or old coating, 10⁴ typical, 10⁵–10⁶ for a new polyethylene coating.
Ω·km
Rail-to-earth resistance of one kilometre of track: 2–20 Ω·km is typical for ballasted track.
Bonded: the metal takes the GPR at the station end. Insulating joint: it is lifted only by the soil it passes through.
Earthed locally ties the far end to the soil there through the resistance below; remote ties it to 0 V, as a cable screen bonded to another substation's earth does.
Ω
Used when the far end is earthed.
For a bare or coated conductor: the route is cut into segments that leak into the soil together with the grid's, so the current it draws, the GPR and the soil beside the route all include its own leakage. Against the full circuit-field model this is within 1–3 %; the one-way line model it replaces (shown for comparison) read the touch voltage beside a bare wire two to three times high. Off: the one-way model alone.
m
Distances from the station where a person can touch the metal — valve pits, crossings, cabinets. The far end is always checked.
A route that is not straight, as points x, y; x, y; … from the station outwards. It replaces the start and direction above; the length still sets how far the conductor runs (the last leg is extended).
Lightning response
The electrodes above under a lightning current, solved in the frequency domain as thin wires in a lossy half-space (the electromagnetic model of the Theory & reference page, §10.7). It gives the harmonic impedance, the potential rise for a first and a subsequent stroke, and the impulse coefficient, in uniform or layered soil, with or without soil ionisation. Concrete foundations are included with their concrete.
Layered: the exact (Sommerfeld) solution of the stratified soil, with ρ₁ … ρ₄ and the thicknesses above; each layer gets the same frequency dependence and ε_r. Uniform: one resistivity, ρ₀ below.
Ω·m
With a uniform soil: the low-frequency resistivity of the soil around the electrode. Blank uses ρ₁ of the soil card.
Used when the soil is taken as constant with frequency; 10 is the usual assumption.
Soil resistivity and permittivity fall with frequency, strongly above about 300 Ω·m. CIGRE TB 781 recommends taking it into account above 300 Ω·m and requires it above 700 Ω·m; constant parameters are conservative.
m
Where the down-conductor meets the electrode. The nearest node of the model is used.
The TB 781 first stroke has the concave front and second peak of measured first strokes; the Heidler one rises smoothly in 8.4 µs. Both subsequent strokes peak in about 0.8 µs.
kA
31.1 kA is the median of Mount San Salvatore. The response is linear, so the potential scales with it.
kA
11.8 kA is the median of Mount San Salvatore.
MHz
The model is checked to 10 MHz. Lowering it makes the segments longer and the solution faster.
Large currents break the soil down around the electrode, which then behaves as a larger one. The CIGRE and IEEE resistance R/√(1 + i/I_g), I_g = E₀ρ/(2πR²), replaces R in the resistive part of the response (Grcev 2009). It lowers the first-stroke peak most; recommended for electrodes up to about 30 m.
kV/m
Field at which the soil breaks down: 400 kV/m in CIGRE TB 63, 300 kV/m in IEEE Std 1243. Values from 300 to 1500 kV/m are published; a higher value is the cautious choice.
Accuracy and soil studies
Each study re-solves the electrodes and soil above. The convergence check halves the segments and estimates the converged values. The seasonal study replaces the top of the soil by a dry or frozen layer. The uncertainty study draws soil models from the fitted model's covariance (page 1) and gives the spread of the results and the probability of meeting the limits.
×
How many times more resistive the top soil is at the driest time of year than when it was measured. 1.5–3 is common; IEEE Std 80 §13.4 and IEEE Std 81 §7.3 warn that the survey is one moment of the year.
m
Depth to which the soil dries out.
Ω·m
Resistivity of frozen top soil, often several thousand Ω·m. Leave blank where the ground does not freeze.
m
Depth of frost penetration.
Number of soil models drawn. Each one is a full solution, so 20 samples take about a minute for a substation grid in layered soil. The result states the 95 % confidence interval of each probability and how many samples would narrow it to ±5 %.
Latin hypercube divides each soil parameter's distribution into as many equally likely bands as there are samples and draws one sample in each band, so even 20 samples cover the tails evenly; the percentiles are steadier than with random sampling for the same number of solutions (McKay, Beckman and Conover, 1979).
Conductor impedance — non-equipotential solution
The solver above holds all buried metal at one potential. A large grid, steel conductors or low soil resistivity break that: the fault current enters at one point and loses voltage along the conductors. This solves the same electrodes at power frequency with the conductors' internal impedance and their self and mutual inductance with earth return and compares the result with the equipotential one. Fences are solved too: their posts and buried wire leak current, the fabric joins them above ground, and a bonded fence is connected to the grid node nearest to it.
Sets the internal impedance. Steel at 50 Hz carries its current in a skin about a millimetre deep and has several times the resistance it has at d.c.
Hz
Power frequency.
Where the fault current enters the grid — the transformer neutrals or the faulted equipment — one per line as x, y, share. The shares are normalised. The nearest grid node is used.
Optimise the grid
Searches for the cheapest rectangular grid that meets the tolerable touch and step voltages of the grid page, using this solver and the soil above: the number of conductors, unequal spacing drawn towards the edges (where a uniform grid's mesh voltages are highest), and rods on the perimeter. The result can be loaded into the electrode table.
m
Length of the area to cover.
m
Width of the area to cover.
m
Depth of the grid conductors.
m
Radius of the grid conductor.
m
Length of the rods tried on the perimeter.
per m
Relative cost of one metre of grid conductor, installed.
per m
Relative cost of one metre of rod, installed.
Fall-of-potential test
IEEE Std 81 clause 8. Plans the test of the electrodes above — how far out the current electrode must go and where the potential probe must stand — and, with the readings, interprets it. The test current is injected into the electrodes and returned through a driven rod; the whole curve R(x) is computed for this geometry and soil, so the 61.8 % rule is checked rather than assumed.
°
Direction of the traverse, measured from +x towards +y.
IEEE Std 81 and the 61.8 % rule measure the probe and current-electrode distances from the centre of the electrode. On site they are often taped from its edge; choose that if your readings were taken so — the probe position for the true value then moves well below 61.8 % for a large grid.
°
Angle between the probe line and the current line: 0 for the usual straight traverse, 90 for the 90° method.
%
The plan recommends the shortest current-electrode distance whose 61.8 % reading is within this.
m
Distance to the current electrode in the test you made, measured as chosen above.
Measured readings, one per line as probe distance (m), resistance (Ω), with distances measured as chosen above. The model curve is scaled to them: the factor gives the resistance the test implies, and the agreement of the shapes says whether the soil model is right.
Surface potential
3-D potential
Touch / step map
Profile
Current distribution
Geometry
Section
Earth-surface potential
Potential surface
Touch voltage (GPR − Vsurface)
Potential, touch and step voltage along a traverse
Leakage current per segment
Electrode geometry (3-D)
Electrodes in the soil section
Results
Add at least one electrode element and solve.
Governing values — the verdict of this page
The checks that decide whether the design complies. For each quantity the largest value from the solution above and from every study run on the same electrodes, soil and current is taken — the convergence check, seasonal soil, the 95th percentile of the soil-uncertainty study and the non-equipotential solution — and the study it came from is named. A study run before the electrodes or soil were changed is listed as out of date and left out. The design report and the drawing stamp use these values. They update by themselves after every solution and study.
Run the numerical solution first.
Buildings and homes — IEC 60364 / BS 7671
Earth electrode selection, protective conductor sizing, earth-fault loop impedance, maximum disconnection times and RCD selection for TN-S, TN-C-S, TT and IT installations.
Installation
The first letter is how the supply is earthed, the second how the installation is: TN uses a protective conductor back to the source, TT uses its own local electrode, IT has no direct source earth.
V
Nominal voltage between a line conductor and earth — 230 V in a 400 V three-phase system.
Ω·m
Soil resistivity at the electrode location, used to compute the resistance of each electrode you add below.
m
Typical distance between the electrodes you add below (for example from the foundation centre to a corner rod). Bonded electrodes in the same soil raise each other's potential, so they never combine like resistors in parallel. Leave empty to assume they are close together, which is the conservative choice.
Final circuits must disconnect faster than distribution circuits: 0.4 s against 5 s in a TN system at 230 V.
Ω
Resistance and reactance of the line conductor from the origin of the installation to the point of the fault. Together with the PE impedance and Z_e it makes up the fault loop.
Ω
Impedance of the protective conductor over the same route back to the source. In a TT system the return is through the soil instead, so this is not used.
Ω
The part of the fault loop outside the installation — the supply transformer and the service cable. The distributor declares it; 0.35 Ω is a common assumed value for a TN-C-S supply. For a TT supply enter the source side only (transformer, service cable and the source earth electrode RB); the installation electrode RA is added by the program.
V
The touch voltage that may be held indefinitely. 50 V a.c. in ordinary dry conditions; 25 V where the standard calls for reduced limits, such as agricultural premises.
Protective device
The device that has to clear the earth fault. An RCD trips on residual current and so does not depend on the fault current being large. For a fuse of unknown make the IEC 60269 gates give a current that operates every compliant fuse-link — safe but on the high side; the manufacturer's curve gives the tightest answer.
A
For an MCB or fuse this is the rated current in amperes. For an RCD it is the rated residual operating current IΔn, so type 0.03 for a 30 mA device.
Earth electrodes
| Type | Parameters | R (Ω) |
|---|
Compliance
Add an electrode and run the assessment.
Details
Electrode section
Electrode resistance vs soil resistivity
Earth pit — electrode in low-resistivity backfill
Pit
A rod driven or set in a bored hole filled with backfill (BS 7430 9.5.7; CBIP 302 Fig. 8.2), or a plate laid at the bottom of a dug earth well (Iranian earthing regulation, Art. 15–22). The plate is modelled as a horizontal disc of the same area.
Ω·m
Measured resistivity of the soil around the pit. Use the value for the depth of the electrode.
m
Length of the rod in the hole. The rod is assumed to start at the surface.
m
Diameter of the rod — 16 mm copper-bonded steel is common. IEC 62561-2 Table 3 asks for at least 14–15 mm; the Iranian regulation (Art. 24) 12 mm copper, 16 mm steel.
m²
One face of the plate. The Iranian regulation (Art. 15) asks for at least 1 × 0.5 m; IEC 62561-2 for 0.5 × 0.5 m.
m
Depth of the plate centre. Lay it in permanently moist ground (Art. 16) and at least 0.6 m deep (Art. 22, BS 7430 9.5.2).
mm
Copper ≥ 2 mm, galvanized steel ≥ 3 mm (Iranian regulation, Art. 15).
Backfill
Use the manufacturer's declared resistivity for a commercial compound (IEC 62561-7) or a soil-box measurement for a site mix such as salt–charcoal–clay. Salt leaches away and must be renewed (IEEE 80 14.5).
Ω·m
Leave empty to use the value of the chosen material.
m
A bored hole is typically 0.3 m (CBIP 302); a dug well 0.8–1.0 m.
m
Top of the backfill column. CBIP 302 fills the top of the hole with excavated soil.
m
Bottom of the backfill. Empty: the bottom of the rod, or 0.2 m below the plate.
–
Ratio of the dry-season soil resistivity to the measured value (§11.6). The backfill is assumed to stay moist — keep it watered.
Group, loading and housing
–
Equal pits in a straight line, bonded together.
m
At least the electrode depth (Iranian regulation, Art. 49); twice the rod length makes good use of each pit.
Ω
The program finds how many pits are needed in the dry season. The Iranian regulation (Art. 64) asks for less than 2 Ω for the total earthing resistance of a substation.
A
Current into the whole group, for the current-density check of BS 7430 9.8. Leave empty to skip.
s
Duration of the fault current.
IEC 62561-5:2023 load classes for the inspection pit cover and housing.
Earth pit results
Set the pit and run the calculation. The field around the electrode and its backfill is solved numerically (axisymmetric finite volumes); for a full-length rod column the BS 7430 formula is shown alongside.
Pit resistance vs hole diameter
Lightning protection earth termination — IEC 62305-3
LPS class parameters, the minimum electrode length l₁ from Figure 3, Type A and Type B earth terminations, down-conductor spacing and the separation distance s.
Structure and LPS
Class I protects against the widest range of stroke currents and demands the most; class IV the least. It comes from the risk assessment of IEC 62305-2, not from this page.
Ω·m
Soil resistivity at the structure, which sets the minimum electrode length l₁ required for this class.
m²
Plan area enclosed by the structure at ground level. It is used to find the mean radius of the ring electrode, re = √(A/π).
m
Perimeter of the structure at ground level, which sets how many down-conductors are needed.
Type B is a ring or foundation electrode round the whole structure and is the normal choice. Type A is separate radial or vertical electrodes, one at each down-conductor, and suits small structures.
m
Diameter of the ring conductor, in metres — 0.01 m is a 10 mm round conductor.
m
Depth of cover over the ring electrode, typically 0.5 m and at least 0.5 m clear of the foundation.
m
Diameter of each vertical electrode in a Type A arrangement, in metres — 0.016 m is a standard 16 mm rod.
m³
Volume bounded by the outer faces of the foundation in contact with the soil (plan area × depth below ground for a basement), if you are using the bonded, continuous reinforcement as the electrode. Leave blank to size a ring instead.
Risk management — IEC 62305-2:2024
The 2024 edition's single risk R = RL1 + RL2 (injury to people and physical damage) against RT = 10⁻⁵ per year, and the frequency of damage F of internal systems against the FT you set, both zone by zone. The least LPS class, entrance bonding SPDs and coordinated SPDs that meet both are found; the LPS class can then be used for the earth termination above.
Surge protection — IEC 62305-4
Selection and coordination of the SPDs at the service entrance and the sub-board: the impulse current each Type 1 SPD must take, the effective protection level with its connecting leads, the protection condition at the equipment and the decoupling length between stages.
Sets the maximum lightning current, half of which is taken to enter the services (IEC 62305-1 Annex E).
Number of metallic services (power, telecom, pipes) among which the current divides.
Conductors of the power service (L1, L2, L3, N = 4).
kA
Impulse current rating (10/350) per mode of the service-entrance SPD.
kV
Protection level of the Type 1 SPD.
A spark gap needs about 10 m of cable (or a decoupling inductor) to a downstream MOV stage.
m
Length of cable between the Type 1 and the Type 2 SPD.
kV
Protection level of the sub-board SPD.
kA
Nominal discharge current (8/20).
m
Total length of the SPD's connecting leads (phase and earth). Each metre adds about 1 kV.
m
Cable length from the last SPD to the protected equipment. Over 10 m the voltage can double by reflection.
kV
Rated impulse withstand voltage of the equipment (IEC 60664-1 categories I–IV: 1.5, 2.5, 4, 6 kV at 230/400 V).
kV
Voltage induced in the circuit loop by nearby flashes; matters only for circuits longer than 10 m.
IEC 62305-4:2024 C.2.3.1.1: where a failure is critical, allow for the voltage doubling of oscillations and keep U_p ≤ 0.5·U_w.
For the simplified I_imp per protection mode, Tables C.3 and C.4.
IEC 60364-5-53 connection types; CT2 puts the summed current of the line conductors through the N–PE gap.
Compliance
Run the design.
Details
Minimum electrode length l₁ vs soil resistivity
Under the lightning impulse — effective length and effective area
Run the design.
What the front actually reaches
Effective radius versus front time
Air termination and protection zone — IEC 62305-3
Where the flash is intercepted, and which volume that interception actually protects. The rolling sphere is rolled numerically over the structure and the terminations, so the result holds for any arrangement; the protective angle and the mesh method are shown beside it for comparison.
Structure
The class sets the rolling sphere radius: 20 m for I, 30 m for II, 45 m for III and 60 m for IV. A smaller sphere reaches into more places, so a higher class is a harder test.
m
Width of the structure measured across the elevation being drawn — the left-to-right direction of the section view.
m
Depth of the structure into the page. It is not used by the elevation; it sets the roof area for the plan-coverage and mesh checks.
m
Height from ground level to the roof surface. Set 0 for open ground, such as a tank farm or a switchyard protected by masts.
m
The surface being protected. Leave blank to protect the roof when there is a structure and the ground when there is not; enter a level to protect something else, such as the top of a tank.
m
Leave blank to use the mesh size the class requires. Enter a value only to test a layout you already have.
Air terminations
| x (m) | y (m) | Height (m) | Base (m) |
|---|
x runs across the section and y into the page, both measured from the
centre of the structure. Height is the length of the rod or mast itself; leave the base
level blank to stand it on the roof when it falls inside the footprint and on the ground
when it falls outside.
Compliance
Add a termination and evaluate.
Rolling sphere
Protected area
Protective angle
Mesh method
Rolling sphere — elevation
Protected area — plan
Protective angle method
Mesh method — roof plan
All computed quantities
Evaluate the arrangement.
System neutral grounding — IEEE Std 142
Choose between solid, low-resistance, high-resistance, reactance and ungrounded systems; size the neutral earthing resistor; check whether the system is effectively grounded for surge-arrester selection.
System
kV
Nominal line-to-line voltage of the system whose neutral is being earthed.
Hz
km
Total route length of cable connected to the system. Cable capacitance to earth is what makes an unearthed system charge up, so this drives the earth-fault current.
µF/km
Zero-sequence capacitance to earth per phase per kilometre, from the cable data sheet. Around 0.25 µF/km for medium-voltage XLPE.
km
Route length of overhead line. Its capacitance to earth is far smaller than a cable's, so it contributes much less charging current.
kVA
Total rating of motors connected to the system, used for their contribution to the charging current.
kVA
Total rating of transformers connected to the system, used the same way.
Tick this if a single earth fault must not trip the plant. It pushes the recommendation towards high-resistance or unearthed operation, which keeps running with one phase earthed.
Tick this if any load is connected between a phase and the neutral. Such loads need a stable neutral, which rules out high-resistance earthing.
Leave on Recommend automatically to have the program choose from the system data, or force a method to see what it would require.
A
The earth-fault current you want the neutral earthing resistor to let through. High resistance keeps it at or just above the charging current; low resistance is typically 200–600 A to give relays something to see.
s
How long the resistor must carry that current before the protection clears the fault. 10 s is the usual rating; continuous rating costs much more.
Results
Run the evaluation.
Grounding method comparison
Design report
Assemble every module that has been run into one printable document, in English or Persian. Charts are captured from the modules and embedded in the report.
Document details
The Persian version is laid out right-to-left with translated headings and verdicts; numbers and formulas stay left-to-right.
Captures the section drawings and charts from every module that has been run and embeds them in the document.
Sections included
Preview
Construction drawings
Turn the design into a drawing set for the contractor and the manufacturers: register and general notes, earth-grid layout plan, typical sections, earth pit, main earthing terminal, connection and bonding details, conductor selection chart, lightning earth termination, earthing schematics and the bill of materials. Sheets follow ISO 5457 / ISO 7200 / ISO 128; every installation rule on them is checked and quoted with its clause.
Title block
Each sheet is numbered prefix-code, e.g. ES-DWG-101 for the layout plan. Use the owner's document numbering if there is one.
The plans pick the largest preferred scale (ISO 5455) that fits the sheet, so a large grid comes out at a better scale on A1.
Drafting options
By default the drawings use the size selected in conductor sizing, raised to the minimum for the electrode duty where it is smaller (50, 25 or 16 mm², BS EN 50522 Table C.1 / IEC 60364-5-54 Table 54.1). Choose a size to override it.
Sets the smallest buried bare copper electrode. BS EN 50522 Table C.1 and IEC 60364-5-54 Table 54.1 ask for 50 mm² where the electrode also serves lightning protection, 25 mm² (the value in brackets) for protection against electric shock only, and allow 16 mm² where experience shows that the risk of corrosion and mechanical damage is extremely low. Automatic chooses lightning duty when a lightning protection system is designed or surge arresters are bonded to the grid.
m
Length of one extensible rod section (commonly 1.2, 1.5, 2.4 or 3 m). Sets the number of sections and couplings in the bill of materials.
Draws the fence inside the perimeter conductor and the fence earthing detail (IEEE 80, 17.3: perimeter conductor about 1 m outside the fence).
m
m
No.
Rods furthest from the centre (the corners first) are placed in inspection pits with test links so that they can be measured.
No.
%
Sheets
Generate the drawings.
Preview
The sheets appear here.
Design-rule verification of the drawings
Every installation rule shown on the drawings is checked here, with its clause.
Bill of materials
Theory — the physics and mathematics behind every page
The complete teaching companion: where each equation comes from, the derivations,
worked examples, and how to read a verdict. The same text is in
docs/THEORY.md, and docs/METHODS.md is the condensed
equation reference.