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Grid resistance and GPR

The grid resistance $R_{g}$ is the resistance of the earth mat to remote earth. With the grid current it sets the rise of earth potential (GPR), the voltage of the whole mat above remote earth during a fault (IEEE Std 80-2013 §14.2, §16).

Read first: Soil resistivity and Wenner readings · Grid current

1The resistance of the mat

The resistance of a mat falls as its area grows and as the buried length grows, and it rises with the soil's resistivity. IEEE Std 80-2013 gives the Sverak equation for a mat of area $A$ and total buried length $L_{T}$ , with a correction for the burial depth $h$ .

R_{g} = ρ [\frac{1}{L _{T}} + \frac{1}{20 A} (1 + \frac{1}{1 + h 20/ A})]

(1)

IEEE Std 80-2013 §14.2, Eq. 52

R_{g} = \frac{ρ}{4} \frac{π}{A} + \frac{ρ}{L _{T}}

(2)

IEEE Std 80-2013 §14.2, Eq. 51

where
$R_{g}$	grid resistance	Ω
$ρ$	resistivity of the soil	Ω·m
$A$	area of the mat	m²
$L_{T}$	total buried length, conductor and electrodes	m
$h$	burial depth of the mat	m

The design takes Eq. (1) for the GPR and reports Eq. (2), the simplified estimate of Laurent and Niemann, beside it. Both are dominated by the area for a large mat: the term in $1/ L_{T}$ is small once the buried length is long.

2The rise of earth potential

GPR = I_{G} R_{g}

(3)

IEEE Std 80-2013 §16

where
$GPR$	rise of earth potential of the mat	V
$I_{G}$	maximum grid current (Grid current)	A

A touch voltage cannot exceed the GPR. If the GPR is below the tolerable touch voltage, the mesh check is not needed, by step 6 of the design procedure of IEEE Std 80-2013 (§16). If it is above, the mesh and step voltages are calculated and checked (Mesh voltage and touch voltage, Step voltage).

Example 1Grid resistance and GPR of the default 220 kV mat

Given the default project's mat of 20 677 m² at 0.6 m, with 10 761 m of conductor and 288 m of electrodes, $L_{T}$ = 11 049 m, in soil of 150 Ω·m. The grid current is 31 853 A (Grid current, Example 1).

Grid resistance by Eq. (1):

R_{g} = 150 [\frac{1}{11 049} + \frac{1}{20 \times 20 677} (1 + \frac{1}{1 + 0.6 20/ 20 677})] = 0.4758 Ω

Laurent and Niemann by Eq. (2): $R_{g}$ = 0.4758 Ω.

Rise of earth potential by Eq. (3):

GPR = 31853 \times 0.4758 = 15156 V

Result The GPR of 15 156 V is above the tolerable touch voltage of 685 V, so the mesh and step voltages are checked (Mesh voltage and touch voltage, Example 1).

Sources

[1]IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding. §14.2, Eq. 52; §14.2, Eq. 51; §16.

CitationSubstationLayout Reference, Grid resistance and GPR, revision 1, 8 Nov 2026, https://substation.solarlayout.app/library/reference/grid-resistance

Grid resistance and GPR

1The resistance of the matCopy link to The resistance of the mat

2The rise of earth potentialCopy link to The rise of earth potential

1The resistance of the mat

2The rise of earth potential