LibraryReferenceEarthing

Mesh voltage and touch voltage

The touch voltage is the difference between the rise of earth potential (GPR) of the mat and the surface potential where a person stands while touching an earthed structure (IEEE Std 80-2013 §3). The mesh voltage is the highest touch voltage inside one mesh of the mat during a fault (§16.5.1).

Read first: Tolerable body current · Grid current

1The touch voltage inside a mesh

A person touching an earthed structure is at the mat's potential through the hand, and at the surface potential through the feet. Over the mat the surface potential is highest above the conductors and dips between them. The dip is deepest near the centre of a mesh, so within a mesh the touch voltage is largest there. IEEE Std 80-2013 calls the largest of these the mesh voltage $E_{m}$ and checks it against the tolerable touch voltage of a person of 50 kg (Tolerable body current):

E_{touch50} = (1000 + 1.5 C_{s} ρ_{s}) \frac{0.116}{t _{s}}

(1)

IEEE Std 80-2013 §8.3, Eq. 32

2The mesh voltage of a mat

For a rectangular mat in uniform soil, the mesh voltage is the soil's resistivity times the grid current per effective length of buried conductor, scaled by the spacing factor $K_{m}$ and the irregularity factor $K_{i}$ of the mat.

E_{m} = \frac{ρ K _{m} K _{i} I _{G}}{L _{M}}

(2)

IEEE Std 80-2013 §16.5.1, Eq. 80

K_{m} = \frac{1}{2 π} [ln (\frac{D ^{2}}{16 h d} + \frac{( D + 2 h ) ^{2}}{8 D d} - \frac{h}{4 d}) + \frac{K _{ii}}{K _{h}} ln \frac{8}{π ( 2 n - 1 )}]

(3)

IEEE Std 80-2013 §16.5.1, Eq. 81

K_{h} = 1 + h / h_{0}

(4)

IEEE Std 80-2013 §16.5.1, Eq. 83

n = n_{a} n_{b}, n_{a} = \frac{2 L _{C}}{L _{P}}, n_{b} = \frac{L _{P}}{4 A}

(5)

IEEE Std 80-2013 §16.5.1, Eq. 84 to 88

K_{i} = 0.644 + 0.148 n

(6)

IEEE Std 80-2013 §16.5.1, Eq. 89

L_{M} = L_{C} + 1.55 + 1.22 \frac{L _{r}}{L _{x}^{2} + L _{y}^{2}} L_{R}

(7)

IEEE Std 80-2013 §16.5.1, Eq. 91

where
$E_{m}$	mesh voltage	V
$K_{m}$	spacing factor for mesh voltage
$K_{i}$	irregularity factor
$K_{ii}$	correction for the inner meshes, 1 with electrodes on the perimeter
$K_{h}$	correction for the burial depth, with $h_{0}$ = 1 m
$D$	spacing between parallel conductors	m
$h$	burial depth of the mat	m
$d$	diameter of the mat's conductor	m
$n$	geometry factor of the mat
$L_{C}$ , $L_{R}$	total length of horizontal conductor and of electrodes	m
$L_{P}$	perimeter of the mat	m
$A$	area of the mat	m²
$L_{r}$	length of one electrode	m
$L_{x}$ , $L_{y}$	length and width of the mat	m
$L_{M}$	effective length for mesh voltage	m
$I_{G}$	maximum grid current (Grid current)	A
$ρ$	resistivity of the soil	Ω·m
$n_{a}$ , $n_{b}$	factors of the geometry factor for a rectangular mat
$C_{s}$ , $ρ_{s}$ , $t_{s}$	derating factor and resistivity of the surface layer, shock time (Surface layer and Cs)

Eq. (7) holds for a mat with electrodes on its perimeter, as the design places them. IEEE Std 80-2013 states the equations for 1 to 40 meshes per side and meshes of 2.5 m to 22.5 m (§16.7). The design checks a mat against that range in its compliance checklist.

3The mesh spacing

A closer mesh lowers the mesh voltage: the dip between conductors is smaller and the buried length is longer (Figure 1). The step voltage changes less with the spacing. The design closes the spacing in steps until the mesh and step voltages are within their limits, unless a spacing is set on the Protection page. The IEC + CEA / CBIP set starts at 10 m, in steps of 0.5 m, down to 3 m. The ANSI / IEEE set starts at 12.19 m, in steps of 0.61 m, down to 3.05 m. The design then adds electrodes, and reports what else to try.

Mesh spacing6.1 m · Mesh voltage Em: 1057 V · Step voltage Es: 1345 V

Figure 1.The mesh voltage of the default 220 kV mat rises with its mesh spacing, while the step voltage changes less, from 40 meshes per side to 11. The mat's outline, depth, electrodes, soil and grid current are held. The design service calculated the values by Eq. (2) and Step voltage, Eq. (5).

Example 1Mesh voltage of the default 220 kV mat

Given the default project's mat, 155.0 m × 133.4 m with 40 × 35 conductors of 40 mm at 0.6 m, a mesh spacing $D$ of 3.97 m, and 96 electrodes of 3 m. The soil is 150 Ω·m and the grid current 31 853 A.

Quantity	Value
Conductor length $L_{C}$ , electrode length $L_{R}$	10 761 m, 288 m
Geometry factor $n$ by Eq. (5)	37.37
Spacing factor $K_{m}$ by Eq. (3)	0.224
Irregularity factor $K_{i}$ by Eq. (6)	6.174
Effective length $L_{M}$ by Eq. (7)	11 213 m

Mesh voltage by Eq. (2):

E_{m} = \frac{150 \times 0.224 \times 6.174 \times 31 853}{11 213} = 589 V

Result The mesh voltage of 589 V is below the tolerable 685 V, 86 % of the limit. The mat complies with the touch voltage limit.

Sources

[1]IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding. §8.3, Eq. 32; §16.5.1, Eq. 80; §16.5.1, Eq. 81; §16.5.1, Eq. 83; §16.5.1, Eq. 84 to 88; §16.5.1, Eq. 89; §16.5.1, Eq. 91.

CitationSubstationLayout Reference, Mesh voltage and touch voltage, revision 1, 8 Nov 2026, https://substation.solarlayout.app/library/reference/mesh-voltage

Mesh voltage and touch voltage

1The touch voltage inside a meshCopy link to The touch voltage inside a mesh

2The mesh voltage of a matCopy link to The mesh voltage of a mat

3The mesh spacingCopy link to The mesh spacing

1The touch voltage inside a mesh

2The mesh voltage of a mat

3The mesh spacing