Earthing Systems Design
Steps

And I explained the first step: Data Collection in the following Articles:
I explained the second step: Data Analysis in the following Articles:
And I explained What we are going to design for grounding system in any building in the following Articles:
And, in Article " Grounding Design Calculations – Part One ", I indicated the following:
Grounding System Design
Calculations according to type of the building
The procedures for performing the Grounding System Design
Calculations can differ slightly according to the type of the building
as follows:

First: Domestic,
commercial and industrial premises
We mean by domestic, commercial and
industrial premises, all installations up to 1,000 V ac and 1,500 V dc 
between phases, with some minor exceptions.

Methods of Grounding Design
Calculations
There are many methods can be used for
performing Grounding System Design Calculations But the common methods
are:

In this Article, I explained the first method of grounding design calculations: Equations Method.
Today, we will solve some examples using the Equations Method but from BS 7430 – issued in 1998.
You can preview the following Articles for more info:
Examples for Grounding System Design Calculations by using the Equations Method from BS 7430 – issued in 1998.
Some Rules/Equations
from BS 7430: 1998 Revision

Example#1:
For three rods placed in equilateral
triangle, calculate the resistance to earth noting that:
Solution:
For three rods placed in equilateral
triangle, λ = 1.66 (From BS7430:1998)
Step#1: Calculate The Resistance Of
One Rod
Therefore: R = 6.70 ohms
Step#2: Calculate The Resistance Of
The (3) Parallel Rods
Where, R = 6.70 ohms; λ = 1.66; n = 3
So, Rn = 2.02 ohms.

2
Horizontal strip or round conductor electrodes
For a strip or round conductor
electrode the resistance R, in ohms is given by the following equation:
Where:
L is the length of the
strip or conductor, in metres (m);
h is the depth of
electrode, in metres (m);
w is the width of strip
or diameter of conductor, in metres (m);
ρ is the resistivity of
soil, in ohm metres (7·m);
P and Q are coefficients given in
Table3 for different arrangements of electrode.

Example#2:
For a building, 17m width and 35m
length, Calculate the earth resistance by using the following electrode
types:
Noting that The measured sand soil
resistivity ρ = 70.3 Ω.m.
Solution:
Case#1: Design Using Vertical Copper
Bonded Steel Rod as in Fig.1
The resistance of one vertical rod
calculated as follow:
So,
R=
70.3 * { loge (8*3 / 0.015) 1 } /2*3.14*3 = 23.79 ohm
The combined resistance of rod
obtained from the following equation:
Where:
R: Resistance of one rod in isolation
in ohm,
S: Distance between adjacent rods, in
m
ρ: Resistivity of soil, Ωm,
λ: Factor depend on number of electrode,
n: Number of electrodes = 4
α= 70.3/2 π*23.79*5 = 0.094,
Rn = 23.79 {(1+1*0.094)/2}=7.46 ohm
by use 4 pits
Take into account the resistance of
cable connecting all rods of cross section area 120mm2 cu:
Where:
R = Resistance in ohms,
ρ = Soil resistivity in ohm metres
(Ωm),
L = Length of electrode in metres,
w = Width of strip or diameter of
circular electrode in metres,
h = Depth of electrode in metres,
P and Q = Coefficients for different
arrangements of electrode which given in table2
L : Length of cable = 25m,
h : Depth of cable = 0.5m,
w : Diameter of cable 120mm2 cu =
0.017m
The combined earth resistance of the 4 rods and
cable will be as follows:
It's recommended to bonding the earth
pits to the concrete foundation of building, and the earth resistance of
reinforcing column calculated by the following equation:
Where:
R = Resistance in ohms,
ρ = Soil resistivity in ohm metres
(Ωm),
ρ_{c} = Concrete resistivity
in ohm metres (Ωm),
L = Length of reinforcing rod below
ground level in metres,
δ= thickness of concrete between rods
and soil in meters,
Z = geometric mean distance of rod
cluster in meters from Table4,
From Table4, we find Z equal to:
a: radius of reinforcing rod, s:
distance between reinforcing rods (s = 0.03m, a = 0.008m so Z= 0.045m)
so, R= 14.38 ohm
The combination resistance of earth copper
rods & cable with reinforcing concrete electrode: R1= 1.99 Ohm, R2 =
14.38 Ohm
Case#2: Design Using Copper Lattice
Plate as in Fig.2
The resistance to earth of a plate
electrode is given by the following equation:
Where:
R = Resistance in ohms,
ρ = Soil resistivity in ohm metres
(Ωm),
A = The Area of one face of the
plate, in m^{2}.
By using 4 buried plates:
R1=R2=R3=R4=36.7 Ohm
The combination resistance of earth
copper plats and the resistance of cable connecting all plates
The combination resistance of earth
copper plate & cable and reinforcing concrete electrode
at the end,for this example, we find that:
Ground Resistance in Case#1: Using Vertical Copper Bonded Steel Rod = 1.74 ohm < Ground Resistance in Case#2: Design Using Copper Lattice Plate = 1.82 ohm.

To download a Solved example for Grounding Design Calculations of small substation using Equations method from BS 74302011 Revision, please click on the link.
In the next Article, I will explain Other Methods of Grounding Design Calculations. Please, keep following.
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