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.

And I explained Methods of Grounding Design Calculations of Domestic, commercial and industrial premises in the following Articles:
 Grounding Design Calculations – Part One and Grounding Design Calculations – Part Two: Equations Method and solved examples.
 Grounding Design Calculations – Part Three: Nomographs Method
 Grounding Design Calculations – Part Four: Excel Spreadsheets Method
 Grounding Design Calculations – Part Five and Grounding Design Calculations – Part Six: using Tables Method
 Grounding Design Calculations – Part Seven and Grounding Design Calculations – Part Eight: Using Online Earthing Calculators
 Grounding Design Calculations – Part Nine: Software Programs Method
You can preview the following Articles for more info:
Second: High And Medium
Voltage Electricity AC Substations

I began explaining Grounding Design Calculations for second type of buildings: AC Substations in Article " Grounding Design Calculations – Part Ten " where I explained the following:
 Design Procedures for grounding system design as per IEEE 80: Guide for safety in AC substation grounding,
 Step#1: Field Data Collection,
 Step#2: Earthing Grid Conductor Sizing.
Also in " Grounding Design Calculations – Part Eleven ", I explained Step#3: Calculation Of Tolerable Touch And Step Voltages.
Today, I will continue explaining other steps from the design procedures of grounding system for AC Substation.
Design
Procedures of Grounding System for AC Substations  Continued

Step#5:
Calculation Of The Preliminary Grid Resistance, Rg, Of The Grounding System
In Uniform Soil

1 Terms Definitions for
Step#5
Notes:

2 Required Values of the Earthing Grid Resistance Rg for AC Substations
Low values of resistance to remote earth
are required in order to minimize the ground potential rise GPR and consequently avoid dangerous touch and step voltages, for example:

3 Factors
Affecting The Earthing
Grid Resistance Rg Values
The earthing grid resistance
mainly depends on:
The area of the grounding system, which is usually known in the
early design stage, is the single most important geometrical factor in
determining the resistance of the grid. The larger the area grounded, the
lower the grid resistance and, thus, the lower the ground potential rise GPR.

4 Calculations Methods of Earthing Grid
Resistance, Rg, In Uniform Soil
IEEE Std 80 offers two alternative options for
calculating the earthing grid resistance (with respect to remote earth) as
follows:

4.1 The
Simplified Method
A First approximation: Rg for a
grounding system of circular metal plate at zero depth:
As a first approximation, a minimum value
of the substation grounding system resistance in uniform soil can be
estimated by means of the formula of a circular metal plate at zero depth as
follows:
Where:
Rg is the substation ground resistance in Ω,
ρ is the soil resistivity in Ω·m,
A is the area occupied by the ground grid in
m2.
B Approximation Refining: Rg for a grounding
system of a grid rod combination:
An upper limit of the substation ground
resistance in uniform soil can be obtained by Laurent and Niemann equation as
follows:
Where:
LT is the total buried length of conductors in
m.
This equation states the fact that the
resistance of any actual grounding system that consists of a number of
conductors is higher than that of a solid metallic plate. The difference will
decrease with the increasing length of buried conductors and will approach 0
for infinite LT, when the condition of a
solid plate is reached.
C Final Equation:
Finally, the simplified method equation as modified by Sverak to
include the effect of earthing grid depth will be as follows:
Where:
Rg is the substation ground resistance in Ω,
ρ is the soil resistivity in Ω·m,
A is the area occupied by the ground grid in
m2,
LT is the total buried length of conductors in
m,
h is the depth of the grid in m.

Example#1:
For a rectangular earthing grid
(see fig.2) with the following parameters is proposed:
Calculate the erthing grid resistance using
the simplified equation.
Solution:
Using the simplified equation,
the resistance of the earthing grid with respect to remote earth is:

4.2 The Schwarz Equations
The Schwarz equations are a series of equations that are more
accurate in modeling of grounding system in a homogeneous soil consisting of
horizontal (grid) and vertical (rods) electrodes as follows:
Where:
R1 ground resistance of grid conductors in Ω,
R2 ground resistance of all ground rods in Ω,
Rm mutual ground resistance between the group
of grid conductors, R1, and group of ground rods, R2 in Ω.
A Ground Resistance Of The Grid (R1):
Where:
ρ is the soil resistivity in Ω·m,
Lc is the total length of all connected grid
conductors in m,
a' is √ (a x 2h) for conductors buried at
depth h in m, or
a' is a for conductor on earth surface in m,
a is the crosssectional radius of conductor in m,
A is the area covered by conductors in m2,
k1, k2 are constant coefficients depending on the geometry of the grid.
B Ground Resistance Of The Rod Bed (R2):
Where:
Lr is the length of each rod in m,
LR is the Total Length Of All Rods,
b is the crosssectional radius of an earthing electrode in m,
nR number of rods placed in area A.
C Mutual Ground Resistance Between The
Grid And The Rod Bed (Rm):
Note:

4.2.1 Determination Of Coefficients K1 and K2
Coefficients
k1 and k2 can be determined by one of
the following two methods:
Method#1: from Curves as follows:
Method#2: from Equations as
follows:
A For coefficient k1:
The coefficient k1 can be approximated by the
following equations:
A For coefficient k2:
The coefficient k2 can be approximated by the
following equations:
Where in both cases, L/R is the lengthtowidth ratio of the
earthing grid.

Example#2:
For a square earthing grid with the following parameters
is proposed:
Calculate the erthing grid resistance using
Schwarz Equations.
Solution:
Step#1: Calculating Ground Resistance Of The Grid R1
ρ= Soil resistivity = 100,000
ohm.m
Lc
= Total
length of all connected grid conductors = 6 x 15 + 6 x 15 = 180 m
a'
= √ (a x 2h) = √(0.0055 x 2 x 1.5) = 0.1285
a = the raduis of conductor
in m = 0.011 /2 = 0.0055 m
A = the area covered by conductors in m2 = 15 x 15 = 225 m2
L/R
= lengthtowidth ratio = 15 / 15 =
1
Since, h = √A /10 ( because h
= 1.5 m and √A /6 = 15/10 =1.5)
then
k1 =  0.05 L/R + 1.2 = 1.15
k2= 0.10 L/R + 4.68 = 4.78
by applying R1 equation:
So, R1 = 2.9989 ohm
Step#2: Calculating Ground Resistance Of The Rod
Bed (R2):
Lr =
the length of each rod = 1.2
LR =
the Total Length Of All Rods = 1.2 x 10 rods = 12 m
b =
the crosssectional radius of an
earthing electrode = 0.019 / 2 = 0.0095 m
nR = number of rods placed in area = 10
by applying R2 equation:
So, R2 = 2.1394
ohm
Step#3: Calculating Mutual Ground Resistance
Between The Grid And The Rod Bed (Rm):
by applying Rm equation:
So, Rm = 2.3734 ohm
Step#4: Calculating The Erthing Grid Resistance Rg
by applying Rg equation:
So, Rg = 1.9995 ohm

In the next Article, I will explain Other Steps from the Design Procedures of Grounding System Design for AC Substation. Please, keep following.
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