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Earth Grid Design

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Grid length *

Grid width *

Conductor spacing *

Burial depth

Conductor diameter

Conductor material

Sized by IEEE 80-2013 Eq. 37 with the Table 1 constants of the material.

Ambient temperature

°C

Grid joint type

Sets T_m in Eq. 37 = min(joint limit, material fusing temperature) (IEEE 80 §11.3). Default bolted (250 °C).

T_m override

°C

Optional explicit T_m that overrides the joint type, e.g. a connector qualified to IEEE Std 837 for a higher temperature. Blank = from the joint type. Not above the material's fusing temperature (IEEE 80 Table 1).

Number of ground rods

Rod length

Rod diameter

Soil resistivity *

Ω·m

Grid fault current *

Fault clearing time

Body weight

Surface layer resistivity

Ω·m

Surface layer thickness

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Calc number

Tag number

Title

Description

Revision

Company name

Project number

Prepared by

Project name

Client company

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Your Company

Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name

Project: Project Name
Project No.: P001
Client: Client Name

Earth Grid Design (IEEE Std 80)

Earth grid design and safety assessment per IEEE Std 80-2013.

1. Input Parameters

Grid geometry, soil, and fault parameters:

Parameter	Symbol	Value	Notes
Soil Resistivity	\rho	100 Ω·m	Measured soil resistivity
Fault Current	I_f	10 kA	Maximum grid fault current
Clearing Time	t_s	500 ms	Fault clearing time
Grid Length	L	60 m
Grid Width	W	40 m
Conductor Spacing	D	6 m
Burial Depth	h	500 mm
Conductor Diameter	d	12.8 mm	Copper, annealed soft-drawn
Ground Rods	n_r	20	3.0m each
Surface Resistivity	\rho_s	3 kΩ·m	Crushed rock layer
Surface Thickness	h_s	100 mm
Body Weight		70 kg	Cb = 0.157

2. Surface Layer Derating Factor (Cs)

Derating factor for high-resistivity surface layer (IEEE 80 eq. 27):

Formula: $$ \begin{aligned} C_s &= 1 - \frac{0.09 \left(1 - \frac{\rho}{\rho_s}\right)}{2 h_s + 0.09} \\ &= 1 - \frac{0.09 \left(1 - \frac{100}{3000}\right)}{2 \times 0.1 + 0.09} \\ &= 0.7 \end{aligned} $$

3. Grid Geometry

Number of conductors and total horizontal length: Total length with rods: LT = 920.0 m

Formula: $$ \begin{aligned} n_x &= \left\lfloor \frac{L}{D} \right\rfloor + 1 \\ &= \left\lfloor \frac{60}{6} \right\rfloor + 1 = 11 $$ \\ &= \left\lfloor \frac{W}{D} \right\rfloor + 1 \\ &= \left\lfloor \frac{40}{6} \right\rfloor + 1 = 7 $$ \\ &= n_y \times L + n_x \times W \\ &= 7 \times 60 + 11 \times 40 = 860 \; \text{m} \end{aligned} $$

4. Grid Resistance (Rg)

Grid resistance, IEEE 80-2013 Eq. 57 (Sverak); the depth factor applies to the area term only:

Formula: $$ \begin{aligned} R_g &= \rho \left[ \frac{1}{L_T} + \frac{1}{\sqrt{20 A}} \left( 1 + \frac{1}{1 + h \sqrt{20/A}} \right) \right] \\ &= 100 \left[ \frac{1}{920} + \frac{1}{\sqrt{20 \times 2400}} \left( 1 + \frac{1}{1 + 0.5 \sqrt{20/2400}} \right) \right] \\ &= 1.0016 \; \Omega \end{aligned} $$

5. Tolerable Touch Voltage

Maximum allowable touch voltage for 70kg body (IEEE 80 eq. 32):

Formula: $$ \begin{aligned} E_{touch} &= \left(1000 + 1.5 \, C_s \, \rho_s \right) \frac{C_b}{\sqrt{t_s}} \\ &= \left(1000 + 1.5 \times 0.7 \times 3000 \right) \frac{0.157}{\sqrt{0.5}} \\ &= 921 \; \text{V} \end{aligned} $$

6. Tolerable Step Voltage

Maximum allowable step voltage for 70kg body (IEEE 80 eq. 29):

Formula: $$ \begin{aligned} E_{step} &= \left(1000 + 6 \, C_s \, \rho_s \right) \frac{C_b}{\sqrt{t_s}} \\ &= \left(1000 + 6 \times 0.7 \times 3000 \right) \frac{0.157}{\sqrt{0.5}} \\ &= 3020 \; \text{V} \end{aligned} $$

7.1 Mesh Spacing Factor (Km)

Geometric spacing factor for mesh voltage (IEEE 80 eq. 81):

Formula: $$ \begin{aligned} K_m &= \frac{1}{2\pi} \left[ \ln\left(\frac{D^2}{16hd} + \frac{(D+2h)^2}{8Dd} - \frac{h}{4d}\right) + \frac{K_{ii}}{K_h} \ln\frac{8}{\pi(2n-1)} \right] \\ &= 0.72 \end{aligned} $$

7.2 Step Spacing Factor (Ks)

Geometric spacing factor for step voltage (IEEE 80 eq. 83):

Formula: $$ \begin{aligned} K_s &= \frac{1}{\pi} \left( \frac{1}{2h} + \frac{1}{D+h} + \frac{1}{D} \left(1 - 0.5^{n-2}\right) \right) \\ &= 0.42 \end{aligned} $$

7.3 Irregularity Factor (Ki)

Correction factor for grid irregularity (IEEE 80 eq. 89):

Formula: $$ K_i = 0.644 + 0.148 \, n = 0.644 + 0.148 \times 8.69 = 1.93 $$

8. Mesh Voltage (Em)

Maximum mesh (touch) voltage at grid surface (IEEE 80 eq. 80):

Formula: $$ \begin{aligned} E_m &= \frac{\rho \cdot I_f \cdot K_m \cdot K_i}{L_C + L_R} \\ &= \frac{100 \times 10000 \times 0.72 \times 1.93}{860 + 60} \\ &= 1511 \; \text{V} \end{aligned} $$

9. Step Voltage (Es)

Maximum step voltage at grid perimeter (IEEE 80 eq. 84):

Formula: $$ \begin{aligned} E_s &= \frac{\rho \cdot I_f \cdot K_s \cdot K_i}{0.75 \, L_C + 0.85 \, L_R} \\ &= \frac{100 \times 10000 \times 0.42 \times 1.93}{0.75 \times 860 + 0.85 \times 60} \\ &= 1164 \; \text{V} \end{aligned} $$

10. Ground Potential Rise (GPR)

Maximum ground potential rise during fault:

Formula: $$ GPR = I_f \times R_g = 10000 \times 1.0016 = 10016 \; \text{V} $$

11. Grid Conductor Sizing

IEEE 80-2013 Eq. 37 with the Table 1 constants for Copper, annealed soft-drawn (fusing temperature 1083 °C). Joint type Bolted / pressure-type (incl. compression) connector: Tm = min(250, 1083) = 250 °C: Selected standard size: 50 mm²

Formula: $$ \begin{aligned} k &= 1000 \sqrt{\frac{TCAP \cdot 10^{-4}}{\alpha_r \, \rho_r} \ln\frac{K_0 + T_m}{K_0 + T_a}} \\ &= 1000 \sqrt{\frac{3.42 \times 10^{-4}}{0.00393 \times 1.72} \ln\frac{234 + 250}{234 + 40}} \\ &= 170 \; \text{A}\sqrt{\text{s}}/\text{mm}^2 $$ \\ &= \frac{I_f \sqrt{t_c}}{k} = \frac{10000 \times \sqrt{0.5}}{170} = 41.7 \; \text{mm}^2 \end{aligned} $$

12. Safety Assessment

Touch Voltage: Em = 1511 V vs E_touch = 921 V: FAIL
Step Voltage: Es = 1164 V vs E_step = 3020 V: PASS

OVERALL: FAIL - Grid Design Unsatisfactory

Grid Resistance: Rg = 1.002 ohm
GPR = 10016 V
Conductor: min 41.7 mm2 -> 50 mm2

Approval:

This calculation has been reviewed and approved by:

Created By
Engineer Name
Date: ..........................

Checked
By: .............................
Date: ..........................

Approved
By: .............................
Date: ..........................

Client Approved
By: .............................
Date: ..........................

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