The resistance of the grid to remote earth depends mainly on the area it covers and on soil resistivity. IEEE 80 first estimates it with a disc formula (minimum value), completes it with the length of buried conductor and the depth, and for grids with rods offers the Schwarz equations. Electrodes embedded in concrete act as auxiliary electrodes.
Short answer. Grid resistance is the opposition that the set of buried conductors and rods offers to current flowing into remote earth. IEEE Std 80-2013 estimates it in stages. A disc formula gives the minimum value and depends only on area and resistivity. Another adds the length of buried conductor, and a third adds the depth. For grids with rods, the Schwarz equations combine conductors and rods.
Why resistance is calculated
Estimating the total resistance to remote earth is one of the first steps in defining the size and basic layout of the grid. Clause 14.2 explains that it depends mainly on the area the grid will occupy, which is almost always known at the start of the design. Where this figure sits within the whole procedure is covered in substation grounding design with IEEE 80.
That resistance sets the GPR, which is the maximum grid current multiplied by the resistance. It is not, however, the measure of safety. A low value is not enough, because what counts are the step and touch voltages. Clause 14.1 also clarifies that a high-resistivity surface layer does not make the voltages worse: it only increases the contact resistance of the foot, so higher voltages can be tolerated.
Simplified calculation
The guide proposes three successive equations for uniform soil, with ρ in Ω·m, A the grid area in m², L_T the total length of buried conductor in m and h the grid depth in m:
| Equation | What it represents | Expression |
|---|---|---|
| 55 | Minimum value: a metal disc at zero depth | R_g = ρ/4 · √(π/A) |
| 56 | Upper limit (Laurent and Nieman): a term for the conductor length is added | R_g = ρ/4 · √(π/A) + ρ/L_T |
| 57 | Sverak equation: adds the effect of depth | R_g = ρ · [ 1/L_T + 1/√(20A) · ( 1 + 1/(1 + h·√(20/A)) ) ] |
The second equation recognizes that a set of conductors has higher resistance than a solid plate. The difference decreases as the buried length increases and tends to zero when the length is infinite. For grids without rods, equation 57 gives results practically equal to the Schwarz equation. If rods are combined with a grid, adding the length of the rods to that of the conductors gives a somewhat conservative estimate of L_T, because rods are usually more effective per meter.
An example from the standard itself
In the Annex B example, a square 70 m × 70 m grid (4900 m²) without rods, with 1540 m of conductor at 0.5 m depth and 400 Ω·m soil, gives 2.78 Ω with equation 57. The EPRI computer program gives 2.67 Ω. With the other two equations and the same data the results are about 2.53 Ω (equation 55) and 2.79 Ω (equation 56).
The guide also compares values calculated with equation 56 and measured at five substations (Table 9). At the sandy loam substation of 800 Ω·m, for example, the calculation gave 4.97 Ω and the measurement 4.10 Ω. The standard clarifies that, if the average of all measured resistivities is used, equation 56 usually gives a resistance higher than the measured one; the values in the table were calculated with the lowest average resistivity measured at each site. Resistivity is measured as explained in soil resistivity measurement with the Wenner method.
The Schwarz equations
Schwarz developed a set of equations for homogeneous soil with horizontal electrodes (the grid) and vertical electrodes (the rods). Its parts are three resistances: that of the grid conductors (R₁), that of all the rods (R₂) and the mutual resistance between the two groups (R_m). The total resistance of the system is obtained by combining them:
R_g = (R₁ · R₂ − R_m²) / (R₁ + R₂ − 2 R_m) (equation 58)
The combined resistance of grid and rods is lower than that of each component alone, but higher than that of the two in parallel. The expressions for R₁, R₂ and R_m depend on resistivity, area, the length of conductor and rods, their diameters and two coefficients, k₁ and k₂, which are read from charts according to the grid shape and depth. Kercel gave equations for them and other authors extended the method to two-layer soil.
Primary electrodes
The resistance of any primary electrode, one designed to discharge the fault current into the soil, depends on soil resistivity and on the size and layout of its conductors. In arrangements with many crossing conductors and many rods in the same area, the mutual resistance between elements weighs heavily (clause 14.4).
Electrodes embedded in concrete
Buried in the soil, concrete is hygroscopic and behaves as a semiconducting medium of 30 Ω·m to 200 Ω·m, depending on moisture. In medium or highly resistive soils, a conductor or rod embedded in concrete has lower resistance than one buried directly. Clause 14.6 notes that this is both an advantage and a problem:
- It is impractical to build foundations where the interior steel is not connected to the structure, because the semiconducting nature of concrete already provides an electrical connection.
- A small direct current can corrode the reinforcing steel. Approximately 0.01% of the alternating current is rectified at the interface between the steel and the concrete.
- Corroded steel occupies about 2.2 times its original volume and can crack the concrete. A very high current that vaporizes the moisture can also crack it.
The guide gives a dc corrosion potential threshold of about 60 V, below which there is no corrosion. With precautions, embedded electrodes can be used as auxiliary electrodes. It is recommended to connect the anchor bolts and angle stubs to the reinforcing steel, to make sure the primary electrodes (grid and rods) carry most of the fault current, and to use soil enhancement material in high-resistivity areas.
What resistance value to require
The guide does not set a single normative resistance value, because safety depends on the voltages. Reference values set by local codes are covered in grounding of distribution substations and in ground resistance testing.
We do your grounding study
We estimate the resistance of your grid with the resistivity of your site, evaluate rods, depth and soil treatment when needed, and verify it with step and touch voltages. For a first estimate you can use our free grounding resistance tool. See our engineering design and studies service, done remotely and worldwide, or write to us through contact.
Related guides
- IEEE 80: Substation Grounding Safety
- Ground Potential Rise (GPR) in Substations: Definition and Calculation
- Substation Grounding Design: IEEE 80 Method
- Ground Resistance Test: Fall-of-Potential and IEEE 81
- Industrial Grounding: Design, Testing and Codes
References
- IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding: clauses 14.1 (usual requirements), 14.2 (simplified calculation; equations 55 to 57; Table 9), 14.3 (Schwarz equations; equation 58), 14.4 (primary electrodes), 14.5 (soil treatment) and 14.6 (concrete-encased electrodes); Annex B, example 1.
- E. Sverak, J. Laurent, J. Nieman and F. Schwarz, studies on grid resistance, cited in IEEE Std 80-2013.
Frequently asked questions
Which factor has the greatest influence on grid resistance?
The area it covers. IEEE 80 states that it is the most important geometric factor: the larger the grounded area, the lower the resistance and the lower the ground potential rise. Soil resistivity and the total length of buried conductor come next.
Does the calculated resistance match the measured one?
It comes close, but does not match. The guide compares calculated and measured values at five substations; for example, at the 2000 Ω·m substation the calculation gave 25.7 Ω and the measurement 39.0 Ω. The values were calculated with the lowest average resistivity measured at each site. If the average of all resistivities is used, the equation usually gives a value higher than the measured one.
Do the concrete foundations of structures work as electrodes?
They work as auxiliary electrodes. Buried, concrete behaves as a semiconducting medium of 30 Ω·m to 200 Ω·m, depending on its moisture, and an embedded metallic element has lower resistance than one buried directly. The guide recommends that most of the fault current be carried by the primary electrodes, the grid and the rods.