**Journal Name:** Journal of Multidisciplinary Research and Reviews

**Article Type:** Research

**Received date:** 01 November, 2018

**Accepted date:** 12 November, 2018

**Published date:** 19 November, 2018

**Citation:** Gouda OE, Amer GM, Salim OM, Elsayed EA. (2018) Techniques used for Unequally Spaced Grounding Grid Design. J Multidis Res Rev. Vol: 1, Issu: 1 (01-09).

**Copyright:** © 2018 Gouda OE. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use,
distribution, and reproduction in any medium, provided the original author and source are credited.

# Abstract

Grounding system is one of the most important items of the power plants and substation systems design. The main purpose of power system substation grounding grids is to maintain reliable operation and provide protection for personnel and equipment during fault conditions. In any substation planning, economical and effective grounding system plays an essential role since absence of effective grounding grid can result in mal-operation of protective devices and hazardous for operators and substation equipment. Therefore, in this paper, the evolutional technique for unequally spaced grounding grid design is suggested. The design is based on hybridization of optimum compression ratio (OCR) and particle swarm optimization (PSO) techniques. This approach is purposed to control the grounding copper volume of the grounding system with the aid of controlling of unequally spaced grounding conductor lengths with respect to the safety measures. The proposed technique offers almost 20% of copper savings comparing with the optimum compression ratio method.

# Keywords

Ground grid, Optimum compression ratio, Particle swarm optimization, Ground potential rise, Step voltage, Touch voltage.

# Abstract

Grounding system is one of the most important items of the power plants and substation systems design. The main purpose of power system substation grounding grids is to maintain reliable operation and provide protection for personnel and equipment during fault conditions. In any substation planning, economical and effective grounding system plays an essential role since absence of effective grounding grid can result in mal-operation of protective devices and hazardous for operators and substation equipment. Therefore, in this paper, the evolutional technique for unequally spaced grounding grid design is suggested. The design is based on hybridization of optimum compression ratio (OCR) and particle swarm optimization (PSO) techniques. This approach is purposed to control the grounding copper volume of the grounding system with the aid of controlling of unequally spaced grounding conductor lengths with respect to the safety measures. The proposed technique offers almost 20% of copper savings comparing with the optimum compression ratio method.

# Keywords

Ground grid, Optimum compression ratio, Particle swarm optimization, Ground potential rise, Step voltage, Touch voltage.

# Introduction

The short-time large ground fault currents will make the power systems unstable and meantime be danger to persons and network equipment. Hence, the grounding grid design should consider the constraints of the step voltage, touch voltage, ground potential rise (GPR), and ground resistance for the sake of safety. In modern substations, the grounding system is an essential part of the overall electrical system; its design has very much importance [1,2].

According to IEEE 80 standard [2], the grounding grid resistance must be low enough to assure that faults currents dissipate through the grounding grid into the earth, while the ground potential rise on the earth’s surface must be kept under certain tolerances. [2].

As it is known the person’s safety which is one of the main goals of the grounding systems is usually affecting by the ground potential rise (GPR) and step and touch voltages of grounding grid structure during grounding faults of electrical networks [3-9]. In order to limit the GPR to safe values, it is necessary to design a right grounding grid that effectively connects with the metallic structure of the substation to ensure the safety criteria [10-12]. Some of the investigators and designers suggested unequally spaced grids as a method to save about 34% of grounding grid material [13-15].

Some parameters of grounding grids such as grounding resistance and step and touch voltages can be calculated using simplified assumptions and some of these parameters are difficult to be calculated by simplified method but they are determined by using experimental techniques [16-17]. Some investigators have proposed formulas to calculate the earth surface potential, touch voltage, step voltage and grounding resistance. Others used the charge simulation method to carry out the same calculations [18- 19]. Experimental models are used to obtain the same parameters by other investigators [20-22].

The optimal design of grounding systems for the substations is to suitably arrange the conductors of grounding systems to equalize the leakage current distribution and the potential gradient of ground surface; while keeping the step and maximum touch voltages within the safe limits; this would ensure making all grounding conductors sufficiently utilized so certified as a safe and economic design method. IEEE 80-2000 standard is used in the design of safe grounding grid. Based on this standard software, programs are designed and used in choosing the economical design and installation of substations grounding system through a lot of alternatives [23-25]. Optimum design of grounding system in uniform and non-uniform soils using ANN is presented by Gouda et al. [26]. Optimized design of substation grounding system using newly developed IEEE compliant software is reported by Vyas et al. [27]. Optimal design of the grounding grid by FEM considering different layered soil models is reported by Anton [28].

Recently, new techniques are used in the design of the most economical grounding system [29-36]. Designing of the grounding grid system having safety and grounding resistance requirements with the lowest cost is a nonlinear problem with relative minimum points. Some techniques have been proposed to achieve this goal. One of these techniques is the optimum compression ratio (OCR). Many studies of grounding grid design have been planned on the trial-and-error approaches. These approaches make the mesh dimension of the grounding grid satisfy with constraints of the touch voltage, step voltage, GPR and grounding resistance from standards. In this paper design of unequally spaced grounding grid by hybridization of Optimum Compression Ratio (OCR) and Particle Swarm Optimization (PSO) Techniques, is suggested. As it is known PSO is a powerful scheme for the solution of similar problems. The proposed technique proved that it is suitable for determining the best design of a substation grounding system. It offers almost 20% of copper savings comparing with the unequally spaced traditional methods.

# Methods used in the Design

# Optimum Compression Ratio (OCR)

The conductor compression ratio “C” is related to the grid
dimensions and the maximum conductor separation d_{max}
which occurs toward the center of the grid and is given by:

$${d}_{max}=\frac{L(1-CR)}{1+CR-2C{R}^{(\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$2$}\right.+1)}}Niseven\text{\hspace{1em}}\left(1\right)$$

$${d}_{max}=\frac{L(1-CR)}{2(1-C{R}^{(N-1)/2})}Nisodd\text{\hspace{1em}}\left(2\right)$$

Where N is the desired number of conductors
perpendicular to a given grid axis of length L. When the
grounding conductors are arranged according to an exponent
regularity, the conductors span decreases gradually from
the center to the side of the grounding grid. The i^{th} conductor
span from the center is

$${d}_{i}={d}_{max}.C{R}^{i}\text{\hspace{1em}}\left(3\right)$$

For the optimal design of grounding grids, the optimum compression ratio can be used, in which the touch voltage reaches its minimum value if the grounding grid is designed under this compression ratio [37]. Grid conductors of unequally spaced grid having denser conductors at the edges proved the most safe and efficient design [38-40]. However, one merit of the use of unequally spaced grid produces more uniform current density in the grid conductors and therefore remarkable decrease in the voltage gradients of the earth’s surface is reported [41-44]. Then, the touch voltage for such grid reaches its lowest values and thus the conditions of safety for human above the earth surface of the substation will be ensured. It is concluded by [42] that the use of unequally spaced grid using OCR technique saves about 34% of grounding grid material. Sequentially the cost of the installation of the grid will be reduced. An empirical expression is obtained to calculate OCR as follows [23].

Where

$$b=-0.3503-9.6311{e}^{(-0.3666L)}\text{\hspace{1em}}\left(5\right)$$

$${a}_{0}={a}_{01}+{a}_{02}k+{a}_{03}{k}^{2}\text{\hspace{1em}}\left(6\right)$$

$${a}_{1}={a}_{11}+{a}_{12}k+{a}_{13}{k}^{2}\text{\hspace{1em}}\left(7\right)$$

$${a}_{2}={a}_{21}+{a}_{22}k\text{\hspace{1em}}\left(8\right)$$

Where k is the segments number of the conductor in any
direction; h is the laying depth of the grid. The relationship
between a_{0}, a_{1}... and L is given in Table 1 [23].

**Table 1: **Relationships between a_{0}, a_{1}, a_{2} and L.

Coefficients | L ≤ 100 m | 100 m ≤ L ≤ 175 m | 175 m ≤ L ≤ 250 m | L>250 m |
---|---|---|---|---|

a_{01} |
0.44 | 0.38 | -0.51 | 0.32 |

a_{02} |
-77.43 | -50.65 | -33.18 | -15.44 |

a_{03} |
15.63 | 13.88 | 18.49 | 13.42 |

a_{11} |
0.033 | 0.19 | 1.15 | 0.38 |

a_{12} |
76.9 | 50.21 | 32.82 | 15.16 |

a_{13} |
-15.56 | -13.83 | -18.44 | -13.38 |

a_{21} |
-0.067 | -0.037 | -0.029 | -0.022 |

a_{22} |
0.5 | 0.41 | 0.34 | 0.26 |

# Particle Swarm Optimization (PSO) algorithms

The (PSO) Particle Swarm Optimization is defined as a multi-agent search technique that ensures a swarm of particles and each particle performs a prospect solution in the swarm. All the particles fly meanwhile multidimensional the search space. Each particle is regulating its position with respect to its own practice and the experience of neighbors [45]. Therefore, in a PSO technique, all particles are beginning randomly and estimated to compute fitness together with finding the personal best and global best. After that, a loop starts to find an optimum solution. In the loop, first the particles’ velocity is updated by the personal and global bests, and then each particle’s position is updated by the current velocity. The loop is ended with a stopping criterion predetermined in advance. Basically, two PSO algorithms, namely the Global Best (Gbest) and Local Best (Lbest) PSO, have been developed which differ in the size of their neighborhoods [45].

# Voltage profile computation by using image method

By using the Infinite Series Potential Method (I.S.M) [8,9], the potential difference in volts can be calculated in three dimensions (x, y, z) using the following equation.

$$v\left(x,y,z\right)=\frac{I\rho [lnf\left(x,y,z\right)]}{4\pi l}\text{\hspace{1em}}\left(9\right)$$

Where

$$f\left(x,y,z\right)=\frac{\sqrt{{(x+0.5l)}^{2}+{y}^{2}+{z}^{2}}+x+0.5l}{\sqrt{{(x-0.5l)}^{2}+{y}^{2}+{z}^{2}}+x-0.5l}\text{\hspace{1em}}\left(10\right)$$

Where I is the short circuit current in ampere, l is grid
side length in meter and ρ is the soil resistivity in Ωm [20,
21]. If there is a grid of total conductor length (L_{C}) buried
in uniform soil, the total potential differences (V_{Total}) caused
by this grid; means interference between any point and all
conductors of the grid and its images, it will be the sum of
the potential caused at this point by this grid conductors and
all its images [44].

$${V}_{Total}=\frac{I\rho {{\displaystyle \sum}}_{x,y}\left[\mathrm{ln}f\left(x,y,z\right)+\mathrm{ln}f\left(x,y,z+2h\right)\right]}{4\pi {L}_{C}}\text{\hspace{1em}}\left(11\right)$$

# Design of Unequally Spaced Grounding Grid using Optimal Compression Ratio (OCR)

The safe design of the unequally spaced grounding grid
system should limit the ground potential rise (GPR), step and
touch potentials of grounded structures during electric power
faults to safe values, besides reaching to the predetermined
value of the grounding resistance. In this paper, the ground
potential rise, step voltage and touch voltage are calculated
along the center conductor for unequally spaced grid area
A=105 × 105 m^{2} having 64 meshes. Figures 1(a) and (b)
give the unequally spaced grid ground potential rise (GPR)
and step potential of grounding grid structure along the
center conductor in case of unequally spaced grid having
denser conductors at the edges under different values of
compression ratios (CR) when the short circuit current is 10
kA and the soil resistivity is 100 Ωm.

**Figure 1:** The ground grid potential rise and step potential versus the compression ratios (a) The ground grid potential rise (GPR) and (b) step potential along
the center of the square grounding grids.

**Figure 2:** The relation between the meshes number, GPR and the value of
OCR.

Summary of the relations between the grid ground potential rise (GPR), step and touch potentials and grid resistance from one side and the compression ratios on the other side is given in Table 2. By the analysis of the obtained results given in Figure 1 and Table 2, it is concluded that the ground potential rise along the grid center conductor, the touch and step voltages along the center conductor and grid resistance reach their lowest value when the compression ratio for this grid reaches 0.493 and the grid number of meshes is 64. These results are in agreement with that obtained by Gouda [46].

**Table 2: **Summary of the relation between the GPR, step and touch potentials
and grid resistance from one side and the compressed ratios from the other side,
N=64.

Compression Ratio (CR) | GPR (Volt) | Emesh (Volt) | Estep (Volt) | Ground Resistance (Ω) |
---|---|---|---|---|

CR=0 | 2480.5 | 601.49 | 245.7 | 0.4134 |

CR=0.1 | 2295.3 | 559.26 | 238.45 | 0.3825 |

CR=0.2 | 2178.6 | 486.98 | 213.08 | 0.3631 |

CR=0.3 | 2116.6 | 417.96 | 188.28 | 0.3528 |

CR=0.4 | 2106 | 313.57 | 145.4 | 0.351 |

CR=0.493 | 2097.6 | 218.66 | 102.38 | 0.3496 |

CR=0.6 | 2203.2 | 266.56 | 149.34 | 0.3672 |

CR=0.7 | 2305.9 | 326.45 | 215.82 | 0.3843 |

CR=0.8 | 2411.5 | 401.7 | 267.5 | 0.4019 |

CR=0.9 | 2518.8 | 499.5 | 13.115 | 0.4198 |

CR=1 | 2626.4 | 593.7 | 353.2 | 0.4377 |

To obtain the relation between the number of meshes and optimum compressed ratios, calculations are done when the short circuit current is 10 kA and the soil resistivity is 100 Ω.m. Figure 2 gives the relation between the ground grid potential rises (GPR) along the center of the square grounding grids for different values of compression ratios (CR).

Summary of the relations between the grid ground potential rise (GPR), step and touch potentials and grid resistance from one side and the compression ratios on the other side is given in Table 2.

Unfortunately, it is found that the OCR value is not constant for all the grounding grids. Each grid with different number of meshes has its own OCR. Figure 2 illustrates the relationship between the grounding potential rise over the center conductor and the relation between OCR for the unequally spaced grid as a function of conductor compression ratio. Remarkable, these relationships usually have an obvious ‘’U’’ shape. It is noticed also from Figure 2 that increasing in the grid meshes number increases it’s OCR. As example OCR for 36 grid meshes is 0.31, it is 0.493 for N=64, 0.58 for N=100 and 0.65 for N=256. The voltage profile distribution samples in 3D for optimum compressed ratio value given in Figure 3. It is observed that at CR=0.493 the ground potential is more uniformly distributed.

**Figure 3:** The voltage profile along all grid conductors in case of unequally
spaced grid having denser conductors at the edges of (A=105 × 105 m^{2},
N=64) (Eq 12) in case of OCR=0.493.

# Design of the Grounding Grid using Particle Swarm Optimization (PSO)

In this part of the paper, the step voltage, touch voltage, ground potential rise (GPR), and grounding resistance, based on ANSI/IEEE Std 80 and applying the particle swarm optimization (PSO) to obtain the optimal grounding grid design, which includes number of meshes, and is laying at known depth. Grid design has to consider factors of safety and minimum used copper. The design grid parameters of the grounding grid and used copper volume are estimated based on ANSI/IEEE Std 80 [2].

# Total volume of the grounding grid conductors

Attention has to be considered for the copper grid volume. To have the optimal design of grounding grid with minimum cost, the objective volume function has to be optimized while satisfying the safety considerations and predetermined value of grounding resistance.

The copper volume of the grid conductors is evaluated as given in equation (13).

$$\text{ObjectiveVolume}=minimise\left\{(\pi \times {\left(\frac{d}{2}\right)}^{2}\times \left(N{L}_{c}+N{w}_{c}\right)\times {L}_{c})+(\pi \times {\left(\frac{{d}_{r}}{2}\right)}^{2}\times {N}_{r}\times {L}_{r})\right\}\text{\hspace{1em}}\left(13\right)$$

Where

d is grounding grid diameter of the conductor (m)

NL_{c} is conductors number in the length direction

Nw_{c} is conductors number in the width direction

d_{r} is the ground rod diameter (m)

# Safety criteria constraints and grounding resistance

The safety standard includes that the actual grid mesh and step potentials must be less than or even equal the values of the corresponding acceptable potentials which are borne by humans without being subjected to electric shocks.

$${E}_{mesh-Actual}\le {E}_{mesh-acceptable}$$

$${E}_{step-Actual}\le {E}_{step-acceptable}\text{\hspace{1em}}\left(14\right)$$

The recommended limits of the grounding potential rise, GPR value is usually 5000V for the substations grounding grids [2].

$$GP{R}_{-acceptaple}\le GP{R}_{max}\text{\hspace{1em}}\left(15\right)$$

The grounding resistance of the designed grid has to be equal or less than the target grid resistance.

$${R}_{g}\le {R}_{target}\text{\hspace{1em}}\left(16\right)$$

For the most high-voltage and large substations, the grounding resistance is usually less than 0.5 Ω. In smaller substations, the acceptable value usually depends on the local conditions [2]. The conductors’ separation in x and y directions is proportional to the grounding grid dimensions as follows [2]. In case of unequally spaced grid, the space between the conductors depends on the designed compressed ratio.

$${D}_{x,min}\le {D}_{x}\le {D}_{x,max}$$

$${D}_{y,min}\le {D}_{y}\le {D}_{y,max}\text{\hspace{1em}}\left(17\right)$$

The burial depth of the grid influences the ground potential rise and the grid resistance. According to standards, the grid burial depth is recommended to be between 0.25- 2.5 m.

$${h}_{min}\le h\le {h}_{max}\text{\hspace{1em}}\left(18\right)$$

Finally, a mathematical model is formulated in general constrained optimized problem.

$$minimise\left\{f\left(x,v\right)=Volume\right\}$$

$$S.t\{\begin{array}{c}g\left(x,v\right)=0\\ h(x,v)\le 0\end{array}\text{\hspace{1em}}\left(19\right)$$

f(x,v) is defined as the objective function, g(x,v) and h(x,v) are defined as the set of equality and inequality constraints, respectively, x is known as state variables and v is the vector of variables. The control variables depend on the designer vision.

# Applications of the PSO algorithm in grounding grid design

The field data that are given in Table 3 is used for the designing of grounding grid by using PSO algorithm. The control variables considered in the design using PSO algorithm are the spacing between the grid adjacent conductors (continuous variable), the grid burial depth (continuous variable), rods number (integer number and continuous variable), and the grounding conductor crosssectional area (discrete variable). The PSO algorithm and the grounding grid optimization flowchart is given in [36].

**Table 3: **The field data of the grounding system.

Grid parameter | Field data |
---|---|

A (Grid area, m^{2}) |
105 × 105 m^{2} |

ρ (Soil resistivity, Ωm) |
100 Ωm |

I ( Fault current, A)_{f} |
10000 Amp |

D ( Decrement factor)_{f} |
1 |

S (Current division factor)_{f} |
0.6 |

t (Duration of fault current)_{f} |
1 sec |

t ( Duration of shock)_{s} |
1 sec |

ρ (Crushed Rock Resistivity)_{s} |
2500 Ω.m |

h_{s} (Thickness of Crushed Rock) |
0.102 m |

Diameter of the conductors | 0.01 m |

E-_{touch}tolerable |
572.72 v |

E-_{step}tolerable |
1819.9 v |

The obtained designed parameters are given in Table 4 and it is compared with the parameters of grounding grid equally spaced between each conductor that is designed by using IEEE Std 80-2000. It is noticed that the design of the grounding grid using PSO algorithm gives saving in copper volume and mass of the grounding grid by about 24.9% and decreases the step potential by 12.3%, but unfortunately, an increase in GPR and the mesh voltage by 5.5% and 4.9% respectively is noticed. It should be noted that nevertheless these values give a safe design for the grounding grid and meets the requirements of the design (Table 5).

**Table 4: **Grounding grid parameters using IEEE std 80-2000 and PSO without
using rods.

Ground grid design without using rods | Using IEEE Std 80-2000 | Using PSO |
---|---|---|

h (laying depth, m) | 1 | 0.9 |

D (Spacing between each conductor and the other, m) | 15 | 21 |

NLc (Number of conductors in each side) | 8 | 6 |

Volume (m^{3}) |
0.1319 | 0.0990 |

Mass (kg) | 1179.18 | 885.06 |

GPR (v) | 2553.9 | 2695.2 |

Estep (v) | 303.35 | 266.01 |

Emesh (v) | 538.92 | 565.51 |

Ground Resistance (Ω) | 0.4257 | 0.4492 |

**Table 5: **Grounding grid parameters using IEEE std 80-2000 and PSO with
using rods, equal space between conductors.

Ground grid design with rods | Using IEEE Std 80-2000 | Using PSO |
---|---|---|

h (laying depth, m) | 1.5 | 1.1 |

D (Spacing between each conductor and the other, m) | 26.25 | 35 |

NLc(Number of conductors in each side) | 5 | 4 |

Nr (Number of rods) | 17 | 16 |

Lr (Rod length, m) | 3 | 3 |

Dr (Rod diameter, m) | 0.03 | 0.03 |

Volume (m^{3}) |
0.1185 | 0.0999 |

Mass (kg) | 1059.39 | 893.106 |

GPR (v) | 2566 | 2755.5 |

Estep (v) | 215.53 | 185.03 |

Emesh (v) | 476.87 | 559.11 |

Ground Resistance (Ω) | 0.4277 | 0.4593 |

The voltage profile of the grounding grid design using IEEE Std 80-2000 and using PSO in the 3-D and also the GPR in 2-D are given in Figure 4.

**Figure 4:** Voltage profile of the ground system design, (a) using IEEE Std 80-2000 (b) using PSO in 3-D and (c) GPR of grounding grid using IEEE Std 80-2000
and PSO in 2-D.

# Design of the Grounding Grid using Hybridization Between CR and PSO Algorithm Uniform soil

Hybridization of the CR method and PSO algorithm is done to obtain the most economical and safe grounding grid. It can be considered as an evolutionary technique for the unequally spaced grounding grid design. In this technique, the compressed ratio CR is taken as one of the variables that are optimized by PSO. One advantage of the suggested method is to obtain unequally space, economical and safe grounding grid design.

The control variables considered are the spacing between
conductors, the required copper volume and the number of
conductors in each side. It is found that the optimized value
of CR is 0.23 in the case under study (A square grounding
grids of 105 × 105 m^{2} area, buried in 100 ohm m uniform
soil resistivity and the current emanating from this grid into
the soil is 10 kA). Figure 4 (a) shows the voltage profile in
3-D of the grounding grid designed by using IEEE Std 80-
2000. Figure 4 (b) gives the voltage profile by using PSO in
3-D. GPR of grounding grid by using IEEE Std 80-2000 and
PSO in 2-D is given in Figure 4(c). Table 6 gives the design
parameters of the grounding grid system by using OCR and
PSO, the grid conductors are unequally spaced.

**Table 6: **Design of the grounding grid using OCR and PSO, the grid conductors are unequally spaced.

Ground grid design | Using CR | Using OCR | New technique |
---|---|---|---|

CR | 0.9 | 0.119 | 0.23 |

h | 1.5 | 1.5 | 1.5 |

D (Conductor spacing m), N_{Lc} |
[17.5-35-35-17.5], 5 | [17.5-35- 35-17.5], 5 | [26.25- 52.5-26.25], 4 |

Volume (m^{3}) |
0.0825 | 0.0825 | 0.0660 |

Mass (kg) | 737.55 | 737.55 | 590 |

GPR (v) | 2656.6 | 2252.4 | 2327.2 |

Estep (v) | 204.55 | 109.08 | 128.14 |

Emesh (v) | 472.56 | 295.43 | 429.15 |

Resistance (Ω) | 0.4428 | 0.3754 | 0.3879 |

The comparison is done between grid designed by using the new technique, using OCR method and also by using compressed ratio equals 0.9 as given in Table 6. Figure 5 (a) shows the ground potential rise of the three grids, Figure 5 (b) shows the mesh voltage and Figure 5 (c) gives the step voltage of the designed grids. Using the new technique in the grounding grid design indicates that 4 conductors only in each side of the grid gave economical and safe grounding grid. From Table 6 it is noticed that 19.27% saving in copper volume of the grounding grid is done by using the new technique and slight increase is observed in the grid resistance, ground potential rise and mesh voltage comparing with using OCR and CR=0.9 methods in the design of the grounding grid, with acceptable safe design.

**Figure 5:** Voltages of grounding grid design, (a) GPR, (b) Mesh voltage and (c) Step voltage of the designed grids given in Table 6.

# Non-uniform soil

The apparent soil resistivity of two-layer soil can be evaluated using the following formulas that are developed by Sunde [47]:

The apparent soil resistivity of three layers’ soil can be evaluated using the following method:

$${\rho}_{a0}=2\left({\rho}_{2}-\left({\rho}_{2}-{\rho}_{1}\right).{e}^{-js}\right)-\left({\rho}_{2}-\left({\rho}_{2}-{\rho}_{1}\right).{e}^{-2js}\right)\text{\hspace{1em}}\left(20\right)$$

Where

ρ_{ao}: Apparent soil resistivity between first and second
layer

ρ_{1}: First layer soil resistivity

ρ_{2}: Second layer soil resistivity

S: the spacing between probe electrodes of measuring
soil resistivity.

d_{1}: First layer soil thickness

δ : Scaling factor

$$j=\delta /2({d}_{1})\text{\hspace{0.17em}},\text{\hspace{0.17em}}=\frac{\mathrm{ln}\left(\frac{{\rho}_{1}}{{\rho}_{2}}\right)-ln(0.0176)}{3.5}$$

The apparent soil resistivity of three layers’ soil can be evaluated using the following method:

The apparent soil resistivity of three soil layers is obtained
by evaluating initial apparent soil resistivity between the
first and second layer that is represented by (ρ_{ao}) by using
ED. Sunde equation (20) [47]. Then considering the initial
apparent soil resistivity which evaluated between t first and
second layers (ρ_{ao}) as a first layer and then, considering the third layer resistivity as a second one. Thus the apparent soil
resistivity of the three layers can be calculated as follows:

$${\rho}_{a}=2\left({\rho}_{3}-\left({\rho}_{3}-{\rho}_{ao}\right).{e}^{-qs}\right)-\left({\rho}_{3}-\left({\rho}_{3}-{\rho}_{ao}\right).{e}^{-2qs}\right)\text{\hspace{1em}}\left(21\right)$$

Where

ρ_{ao}: Apparent soil resistivity between first and second
layer

ρ_{a}: The apparent soil resistivity, ρ_{3} Third layer soil
resistivity

d_{2}: Second layer soil thickness, d_{1} First layer soil thickness

$$q=\lambda /2({d}_{1}+{d}_{2}),\text{}\lambda =\frac{\mathrm{ln}\left(\frac{{\rho}_{ao}}{{\rho}_{3}}\right)-ln(0.0176)}{3.5}$$

For the design of grounding grid using hybridization
between CR method and PSO Algorithm (New technique) in
case of two or three layers soil, first of all the apparent soil
resistivity has to be calculated by using the above explained
method or measured by using four electrodes method
(Winner method). Then the peak value of the calculated or
measured apparent soil resistivity with respect the space
between the electrodes will be used in the grounding system
design. The apparent soil resistivity in the above example is
taken 80 Ωm. The designed grid parameters using the new
technique are given in Table 7. It is found that the optimized
value of CR is 0.23 in the case under study, square grounding
grids of 105 × 105 m^{2} area, buried in the first layer of the three layers and 80 Ω.m apparent soil resistivity of the three
layers. The current emanating from this grid into the soil is
10 kA. Figure 6 (a) shows the voltage profile in 3-D of the
grounding grid designed by the suggested technique and
Figure 6 (b) shows the ground potential rise.

**Table 7: **Grounding grid parameters of three layers by using the suggested
technique.

Ground grid design | Using suggested technique |
---|---|

Soil resistivity | 80 Ω.m |

CR | 0.23 |

H | 1.5 |

D | [26.25 52.5 26.25] , 4 |

NLc | 4 |

Volume (m^{3}) |
0.0660 |

Mass (kg) | 590 |

GPR (v) | 1861.7 |

Estep (v) | 102.51 |

Emesh (v) | 343.32 |

Ground Resistance (Ω) | 0.3103 |

**Figure 6:** Voltages of grounding grid design using the new technique of three layers example (apparent soil resistivity is 80 Ω.m) (a) Voltage profile (b) Ground
potential rise.

# Conclusion

In this paper, the design methods of grounding grid using optimum compression ratio method and particle swarm optimization technique are presented. It has been found that each grid has its own OCR depending on the grid meshes number. Hybridization of compression ratio and PSO techniques is suggested. This approach is purposed to control the grounding copper volume of the grounding grid with the aid of controlling the grid conductors’ length under the safety limitations. The proposed technique offers almost 20% of copper savings while respecting all design requirements and safety measures. Hence it is obvious that the suggested method is quite satisfactory for the design of grounding system in uniform as well as multi-layered soils and meets IEEE safety criteria. Hence this technique proves to be an effective method and copper savings for preliminary design at least of the optimum grounding grid, rather than using the experience rules.

Khodr HM, Salloum GA, Miranda V (2006) Grounding system design in electrical substation: An Optimization Approach. IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela. [ Ref ]

IEEE 80-2000 (2000) Guide for safety in AC substation grounding. IEEE. [ Ref ]

Sverak JG (1999) Progress in step and touch voltage equations of NSI/IEEE Std 80. IEEE Trans power Delivery 13: 762-767. [ Ref ]

Sverak JG (1984) Simplified analysis of electrical gradient above a ground grid. IEEE Trans power Delivery 103: 1-25. [ Ref ]

Nahman JM and Djordjevic VB (1995) Nonuniformity correction factors for maximum mesh and step voltages of ground grids and combined ground electrodes. IEEE Trans Power Delivery 10: 1263-1269. [ Ref ]

Nahman JM, Djordjevic VB (1998) Maximum step voltages of combined grid-multiple rods ground electrodes. IEEE Trans Power Delivery 13: 757-761. [ Ref ]

Thapar B, Gerez V, Balakrishnan K, Blank DA (1991) Simplified equations for mesh and step voltages in AC substation. IEEE Trans on Power Delivery 6: 601-607. [ Ref ]

Zaini HG, Ghoneim SS (2012) Earth surface potential and grounding resistance for grounding grid in two-layer model soil. IEEE International Conference on Power System Technology (POWERCON) pp: 1-5. [ Ref ]

Dessouki SS, Ghoneim S, Awad S (2011) Earth surface potential for scaled vertical rod into two layer soil model. 17th ISH2011, Hanover- Germany, August. [ Ref ]

Choi CS, Kim HK, Gil HJ, Han WK, Lee KY (2005) The potential gradient of ground surface according to shapes of mesh grid grounding electrode using reduced scale model. IEEJ Trans on Power and Energy 125: 1170-1176. [ Ref ]

He J, Zeng R, Gao Y, Tu Y, Sun W, et al. (2005) Optimal design of grounding system considering the influence of seasonal frozen soil layer. IEEE Trans Power Del 20: 107-115. [ Ref ]

Sun W, He J, Gao Y, Zeng R, Wu W, Su Q (2000) Optimal design analysis of grounding grids for substations built in non-uniform soil. IEEE Trans Power apparatus and system 2000: 1455-1460. [ Ref ]

Phithakwong B, Kraisnachinda N, Banjongjit S, Chompoo-Inwai C, Kando M (2000) New techniques the computer-aided design for substation grounding. Power Engineering Society Winter Meeting, IEEE 3: 2011-2015. [ Ref ]

El-Sayed M, El-Refaie S, Elmasry E, Abd –Elrahman, Abdo MH (2015) Achievement of the best design for unequally spaced grounding grids. Ain Shams Engineering Journal 6: 171-179. [ Ref ]

Puttarach A, Chakpitak N, Kasirawat T, Pongsriwat C (2007) Ground layer depth and the effect of GPR. IEEE PES Power Africa 2007 Conference and Exposition. [ Ref ]

Rajotte Y, De Steve J, Fortin J, Lehoux R, Simard G (2005) Earth potential rise influence near HV substations in rural areas. CIRED (Turin). [ Ref ]

Bharat Sanchar Nigam Limited, A Govt of India Enterprise (2005) Measurement earth potential rise (EPR) zone. No EPR/A-002, CGM and Technical and Development Circle. [ Ref ]

Malik NH (1989) A review of the charge simulation method and its applications. IEEE Trans Elect Insul 24: 3-20. [ Ref ]

Navarrina F, Moreno L, Bendito E, Encinas AM, Ledesma A, et al. (1991) Computer aided design of grounding grids: A boundary element approach. Proc 5th Eur Conf Math Ind M Heiliö pp: 307-314. [ Ref ]

Gouda OE, Amer GM, EL-Saied T (2006) Computation of potential profile at a surface above energized unequally spaced grounding grid. The eleventh international Middle East power systems conference, MEPCON 2: 517-522. [ Ref ]

Takahashi T, Kawase T (1991) Calculation of earth resistance for a deep driven rod in a multi-layer earth structure. IEEE Trans 6: 608-614. [ Ref ]

Heppe J (1979) Computation of potential at surface above an energized grid for other electrode, allowing for non-uniform current distribution. IEEE Trans 98: 1978-1989. [ Ref ]

He J, Zeng R, Gao Y, Tu Y, Sun W, et al. (2005) Optimal Design of Grounding System Considering the Influence of Seasonal Frozen Soil Layer. IEEE Trans Power Del. [ Ref ]

Sun W, He J, Gao Y, Zeng R, Wu W, et al. (2000) Optimal design analysis of grounding grids for substations built in non-uniform soil. IEEE Trans Power Apparatus and System 2000: 1455-1460. [ Ref ]

Thabet A (2002) Grounding systems of electric substations in non-uniform earth structure with new analysis. High Institute of Energy, Aswan. [ Ref ]

Gouda OE, Amer GM, EL-Saied TM (2006) Optimum design of grounding system in uniform and non-uniform soils using ANN. Int J Soft Compute 1: 175-180. [ Ref ]

Vyas KA and Jamnani JG (2014) Optimized design of substation grounding system using newly developed IEEE Compliant Software. International Journal of Engineering Development and Research, IJEDR pp: 88-93. [ Ref ]

Habjanic A and Trlep M (2007) Optimal design of the grounding grid by FEM considering different layered soil models. Przegląd Elektrotechniczny 83: 112-114. [ Ref ]

Gabr AZ, Helal AA, Said HE (2016) Optimal design of substation grounding grid based on genetic algorithm technique (World Academy of Science, Engineering and Technology). International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering. [ Ref ]

Otero AF, Cidras J, Garrido C (1998) Genetic algorithm based method for grounding grid design. IEEE International Conference on Evolutionary Computation Proceedings pp: 120-123. [ Ref ]

Neri F (2004) A new evolutionary method for designing grounding grids by touch voltage control. IEEE International Symposium on Industrial Electronics pp: 1501-1505. [ Ref ]

Yi-min, Min-Fang P, Hai-tao H, Yue-hua Y (2009) Optimal design of grounding grids based on genetic algorithm. Third International Conference on Genetic and Evolutionary Computing. [ Ref ]

Yang Wei, Wen X, Lan L, Wu C, Yang Y, et al. (2009) The analysis on soil structure for the grounding projects. Power and Energy Engineering Conference, Wuhan, China. [ Ref ]

Gursu B and Ince M (2009) Limiting GPR in a two layer soil model via Genetic algorithm. Journal of the franklin institute 346: 768-783. [ Ref ]

Zhiqiang H and Bin Z (2011) Soil model’s inversion calculation based on genetic algorithm. 7th Asia-Pacific International Conference on Lightning. [ Ref ]

Fergany AE (2013) Accelerated particle swarm optimization based approach to the optimal design of substation grounding grid. Przeglad Elektrotechniczny 89: 30-34. [ Ref ]

Gouda OE and El Dein AZ (2017) Ground potential rise of faulty substations having equal and unequal spacing grounding grids conductors. IET Generation, Transmission & Distribution, Volume: 11: 18-26. [ Ref ]

Costa MC, Filho MLP, Marechal Y, Coulomb JL, Cardoso JR (2003) Optimization of grounding grids by response surfaces and genetic algorithms. IEEE Transactions on Magnetics 39: 1301-1304. [ Ref ]

Gouda OE, Amer GM, Ibrahim H (2011) Surface potentials and GPR of substation grounding. Cired, 21st International Conference on Electricity Distribution, Frankfurt. [ Ref ]

Gouda OE, Amer GM, EL-Saied T (2005) Computation of potential profile at a surface above energized unequally spaced grounding grid. The eleventh international Middle East power systems conference, MEPCON 2: 517–522. [ Ref ]

Vyas KA and Jamnani JG (2012) Optimal design of grounding system for HV/ EHV substations in two layered soil. International Journal of Emerging Technology and Advanced Engineering 2: 383-392. [ Ref ]

Zhongdong D, Zhenyu Y, Xishan W, Hun X (2005) The optimum design of grounding grid of large substation. Proceedings of the XIVth International Symposium on High Voltage Engineering, Tsinghua University, Beijing, China. [ Ref ]

Huang L, Chen X, Yan H (1995) Study of unequally spaced grounding grids. IEEE Trans Power Del 10: 716-722. [ Ref ]

Gouda OE (2011) Optimum design of grounding system of high voltage substations. Lambert Academic Publishing. [ Ref ]

Bai Q (2010) Analysis of particle swarm optimization algorithm. Computer and Information Science. [ Ref ]

Gouda OE (2017) Design Parameters of Electrical Network Grounding Systems. Advances in Computer and Electrical Engineering, IGI Global. [ Ref ]

Sunde ED (1968) Earth conduction effects in transmission systems. D Van Nostrand Company Inc. [ Ref ]