I indicated that the Earthing Systems Design Steps process has (3) main steps::
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:
Today, I will explain The Methods for Performing of Grounding System Design Calculations.
You can preview the following Articles for more info:
Grounding System Design Calculations
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.

1 Standards
Standards used for ground
calculations of Domestic, commercial and industrial premises are:

2 What do we need to
calculate?
There are many parameters to be
calculated when designing grounding systems for Domestic, commercial and
industrial premises as follows:
Notes:

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

First: Equations Method

1 Prerequisites
The following information is required
/ desirable before starting the calculation:

2 Earth/grounding
electrode resistance Calculations
Sometimes it called
“Resistance to Earth calculations” and can be obtained either by using BS or
IEEE standards rules as it will be explained in below.

Second: Using BS 7430
Standard
The most common types of electrodes
included in BS 7430 are as follows:

2.1 Vertical Rods
The resistance to earth of a vertical
rod electrode is given by the following equations:
a In Metric Units:
Where:
R is the resistance to earth in ohms,
ρ is the resistivity of the soil, in
Ωm,
L is the length of electrode, in
meters,
D is the diameter of the rod in
meters.
b in English Units:
Where:
R is the resistance to earth in ohms,
ρ is the resistivity of the soil, in
Ωm,
L is the length of electrode, in
feets,
D is the diameter of the rod in
inches.
Example#1:
For a vertical rod electrode having
20mm diameter and 3 m length, calculate the resistance to earth noting that
soil resistivity is 50 Ωm.
Solution:
The resistance to earth of a vertical
rod electrode is given by the following equation:
R=
ρ * { loge (8L / d) 1 } / 2ΠL = 50 * { log_{e} (8*3 / 0.02)
1 } /2*3.14*3 = 16.1 ohm
Example#2:
For a vertical rod electrode having
25mm diameter and 2 m length, calculate the resistance to earth noting that
soil resistivity is 30 Ωm.
Solution:
The resistance to earth of a vertical
rod electrode (R) in ohms is given by the following equation:
R=
ρ * { loge (8L / d) 1 } / 2ΠL = 30 * { log_{e} (8*2 / 0.025)
1 } /2*3.14*2 = 13.0 ohm

2.2 Parallel connection of
aligned rods
Multiple electrodes in parallel yield
lower resistance to ground than a single electrode. Multiple rods are
commonly used to provide the low grounding resistance required by
highcapacity installations. Adding a second rod does not, however, provide a
total resistance of half that of a single rod, unless the two are several rod
lengths apart.
a From BS 7430:
The resistance Rt in ohms (Ω) of n vertically driven rods set
s metres apart may be
calculated from:
where:
ρ is the resistivity of
soil, in ohm metres (Ωm);
L is the length of the electrode, in
metres (m);
n is the number of rods;
s is the spacing between the rods, in
metres (m).
b as per IEEE 142:
A useful rule is that grounding
systems of 2–24 rods placed one rod length apart in a line, hollow triangle,
circle, or square will provide a grounding resistance divided by the number
of rods and multiplied by the factor F taken from Table2.
Notes:

2.3 For horizontal
strip electrode (circular or rectangular section)
The resistance Rta in ohms (Ω) of a strip or round
conductor may be calculated from:
Where:
Rta = Resistance in ohms,
ρ is the resistivity of soil, in
ohm metres (Ωm);
L is the length of the strip or
conductor, in metres (m);
h is the depth of the electrode,
in metres (m);
d is the diameter of the round
conductor or diameter of the equivalent cross sectional area of the strip, in
metres (m).
Note:
Paralleling of Strips
When two or more strips in straight
lengths, each of length L in metres (m) and a separation distance s metres are laid parallel
to each other and connected together at one end only the combined resistance
may be calculated from the following equation:
Rn = FR1
Where:
Rn is the resistance of n conductors in
parallel, in ohms (Ω)
R1 is the resistance of a single strip of
length L, calculated from the
preceding Rta equation, in ohms (Ω).
F has the following value:

2.4 For Plates
electrodes
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}.
Notes:

2.5 For structure
steelwork
Foundation metalwork in concrete may be
used as a ready made and effective earth electrode. The total electrode area
formed by the underground metalwork of large structure may often be used to
provide an earth resistance lower then that obtainable by other methods;
overall values well below 1 Ω are obtainable.
The resistance to earth of a
reinforced concrete foundation can be estimated by assuming the following:
So, the resistance to earth of a
reinforced concrete foundation will be given 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 Table3,
The combined effect of
all similar footings Rtot in ohms (Ω), assumed to be arranged in an
approximately rectangular plan, may be determined from the following:
Where:
R1 is the resistance of
one footing, in ohms (Ω);
λ is the factor from
Table 4;
ρ is the resistivity of
soil, in ohm metres (Ωm);
s is the spacing of
footings, in metres (m);
n is the number of
footings used as electrodes (see the note to Table 4).
Note:
Notes:

26 resistance of an
electrode surrounded by an infill of materials (such as bentonite or concrete)
In this
case, The following equation will be used:
Where:
ρ Is the
resistivity of soil in ohm metres (Ωm),
ρ_{c} Is the
resistivity of infill material in ohm metres (Ωm),
d is the
diammeter of electrode in meter,
L is the
driven length of electrode in meter.
Note:

2.7 Three rods at the
vertices of an equilateral triangle
The resistance Re in ohms (Ω) of three interconnected
rods set out at the vertices of an equilateral triangle [see Figure 1a ]
of side s metres length may be
calculated from:
The resistance of various constructions of
horizontally placed simple earthing electrodes can be calculated using the
following equation:
Where:
ρ is the resistivity of
soil, in ohm metres (Ωm);
L is the length of rod, in metres (m);
d is the diameter of rod, in metres (m);
s is the length of one side of the
equilateral triangle, in metres (m).

2.8 Two strips set at right
angles to each other meeting at one corner
The resistance RL in ohms (Ω) of two strips of equal
length set at 90° with one corner touching [see Figure 1b ] may be
calculated from:
Where:
ρ is the resistivity of
soil, in ohm metres (Ωm);
L is the total length of strip in metres
(m);
h is the depth of burial in metres (m);
d is the diameter of the round conductor
or diameter of the equivalent cross sectional area of the strip in metres (m)

2.9 Three strips set at
120° meeting at the star point all of equal length
The resistance RS in ohms (Ω) of a star arranged strip
[see Figure 1c ] may be calculated from:
Where:
ρ is the resistivity of
soil, in ohm metres (Ωm);
L is the total length of strip in metres
(m);
h is the depth of burial in metres (m);
d is the diameter of the round conductor
or diameter of the equivalent cross sectional area of the strip in metres
(m).

2.10 Four strips set in a
cruciform
The resistance Rcr in ohms (Ω) of four strips set out
in a cruciform [see Figure 1d] may be calculated from:
Where:
ρ is the resistivity of
soil, in ohm metres (Ωm);
L is the total length of strip in metres
(m);
h is the depth of burial in metres (m);
d is the diameter of the round conductor
or diameter of the equivalent cross sectional area of the strip in metres
(m).

Now, We finish the first method of grounding design calculations: Equations Method, the other methods of grounding design calculations are summarized in the below table.
Methods of Grounding Design
Calculations
There are many methods can be used for
performing Grounding System Design Calculations But the common methods
are:

In the next Article, I will explain Other
Methods of Grounding Design Calculations. Please, keep
following.
excuse me in this" part:2.7 Three rods at the vertices of an equilateral triangle" where is the soil resistivity in the equation
ReplyDeleteNice to read it
ReplyDeletehi may I know where to find the source of equations for k1 and k2? Just want to verify the source so that we can proceed to indicate it. Thanks a lot!
ReplyDelete