Numerical Investigation of the Use of Electrically Conductive Concrete-Encased Electrodes as Potential Replacement for Substation Grounding Systems

Abstract

This paper presents a numerical investigation regarding the possibility of using electrically conductive concrete (ECON) combined with concrete-encased electrode (CEE) technology to develop new substation grounding systems (SGSs) called ECON-EE as a replacement for conventional copper or galvanized steel grounding grids. In the first step, the validation of the commercial FEM software used to perform grounding system analysis was performed in terms of the grid resistance (R_G), ground potential rise (GPR), and step and touch voltages, using a symmetrical 70 m × 70 m conventional copper SGS. Next, several numerical simulations of an ECON-EE grounding system with the same dimensions as the conventional copper grid used for FEM software validation were performed. Thus, several parameters of the ECON-EE grounding system were studied, such as the geometry, dimensions, and resistivity of ECON and the diameter of the rebar. The numerical results obtained permit us to demonstrate that ECON-EE grounding systems can perform better than conventional SGSs equipped with vertical rods, particularly in the case of high ground resistivity. Moreover, it was demonstrated that the two main ECON-EE parameters affecting the grounding resistance and the touch and step voltages are the section area and the resistivity of the ECON. As discussed in detail in this paper, the proposed ECON-EE grounding system can offer several advantages compared to conventional SGSs in terms of efficiency and durability, as well as in terms of simplicity of conception and implementation.

1. Introduction

Grounding systems are some of the most important components in all electrical networks and particularly in substations. Correctly designed grounding systems ensure the protection of the equipment and the safety of the personnel from the dangers of electrical faults, as well as providing the continuity of the power supply [1,2,3]. In general, a substation grounding system (SGS) is constituted of copper-based wire or galvanized steel tape arranged as a horizontal mesh of varying size, buried in the ground, and connected to all the electrical equipment and towers present in the substation. In case of high earth resistivity, vertical rods can be added to the horizontal mesh to reach layers of lower resistivity at a greater depth [3]. SGS provides low grounding resistance in order to meet electrical safety standards in terms of the resulting ground potential rise (GPR) and the ensuing touch and step voltages [4,5].

Over the last few decades, a huge amount of research has been conducted on improving conventional SGSs. One of the solutions commonly considered in the case of high ground resistivity is to employ a ground enhancing material (GEM), as presented in a detailed review in [6,7], which can be found in natural or chemical form. As GEM is effective in reducing grounding resistance, one of the main concerns in using GEM lies in the possibility of it being leached away by heavy rainwater or, for some chemical products, the risk of increasing the corrosion of the grounding electrodes, as well as environmental contamination [6,7]. To address this issue, electrically conductive cement (ECC), another chemical GEM, has also been proposed since the mid-1970s [8,9]. Once hardened, ECC becomes an electrically conductive solid encapsulating the electrode, resulting in a durable decrease in ground resistance even in dry soil conditions, and excellent performance under transient current faults [9,10,11]. Moreover, ECC is environmentally safe and maintenance-free as it is significantly more durable than soft GEM and contributes to protecting the copper electrode against corrosion and theft [8,9].

Another alternative to GEM techniques is the use of concrete-encased electrodes (CEEs), also called Ufer grounding [12]. CEE grounding exploits the advantages of the chemical properties of ordinary concrete coupled with the presence of steel reinforcing rods (commonly called rebars) [13]. In CEE grounding, the dissipation of the fault current in the ground is ensured by the steel rebars acting as electrodes and the concrete, which, as with ECC, significantly increases the electrical contact surface area of electrodes with the surrounding ground. Studies have demonstrated that CEE grounding is equal or even superior to conventional grounding, with a significant reduction in the value of the grounding impulsive impedance both in low and high soil resistivity [13,14]. This technology has been used for a long time in building footers and concrete floors, as well as in communication towers and steel transmission towers [6,12,13]. However, to the best of our knowledge, very few studies have been conducted on the possibility of using CEE as a replacement for the entire substation grounding. This partly explains the current lack of consensus and standards (IEC or IEEE) for the use of CEE in large substations, although there are a few CEE requirements in the National Electrical Code (NEC) [15]. Another important aspect regarding the use of CEE in building grounding versus substations is that in large buildings, foundations buried deep in the ground provide a large contact surface with generally moist ground. This situation permits us to compensate for the poor electrical conductivity of ordinary concrete used in CEE grounding [13]. This is not the case for substations where the grounding grid is generally buried at a lower level, between 0.5 m and 1.5 m, where the moisture content can be low [6]. In this context, it is necessary to take into account the limitation of the size of each section constituting the grounding grid, which provides a small surface of contact with the surrounding ground compared to the foundations of a building. From these observations, it becomes evident that ordinary concrete used in CEE is not suitable for SGSs.

To address this issue, one solution can be found by combining the advantages of ECC with those of CEE. ECC can provide low resistivity compared to ordinary concrete but, being a cement, it cannot achieve the mechanical properties of concrete made with aggregates of larger size and reinforced with rebars [9,13]. Such a solution can be found in the use of electrically conductive concrete (ECON) as a replacement for ordinary concrete in CEE. Over the last three decades, a huge number of studies have been performed to develop ECON dedicated mainly to heating and de-icing functions [16,17] As reported in a recent comprehensive review [18], ECON is obtained by incorporating steel or carbon fibers, steel shavings, graphite powder, graphene, and carbon nano-tubes [18]. ECON can achieve durable electrical resistivity of 500 Ω-cm [17,18,19], which is up to 10 times lower than concrete buried deeply in the ground [13]. Several practical applications have been conducted over the last two decades, which have permitted us to evaluate the efficiency, durability, and mechanical properties, as well as the cost of such ECON heating and de-icing systems for bridge decks, airport runways, and highways [18,19,20].

Although ECON can now be considered a mature technology in the field of heating and de-icing systems, a small number of applications have been proposed for its use in grounding systems and particularly in substations as a copper grid replacement [21,22,23]. In one study [21], ECON with a resistivity of 500 Ω-cm was simply used as a GEM, forming a slab of 1.25 m thickness in which the entire substation grounding grid area of 120 m × 85 m was embedded. Although the results obtained under a switching surge current are very promising, such a solution is not cost-effective and is difficult to implement in a large substation. Another study has proposed the use of ECON for rod grounding electrodes, which were laid in parallel on the bottom and side walls of the foundation ditch of a transmission tower to build a new type of stereo grounding grid for transmission towers [22]. This study proposed both an ECON mix as well as experimental on-site resistance to achieve ground measurement. The results obtained demonstrated that the resistivity of the ECON mix becomes stable after 42 days of aging with a value of 530 Ω-cm, and its fluctuation between −40 °C and 50 °C was less than 5%. In another study [23], the electric heating effect of a classical model of transmission tower foundation using ECC with rebars (Ufer grounding) was numerically investigated in order to compare its behavior under a lightning strike when ordinary concrete or ECON is used. The results obtained demonstrated that the use of ECON in the ECC grounding permits obtaining better grounding current dispersion, resulting in a drastic decrease in the internal temperature inside the foundation, which remains uniform compared to ordinary concrete.

Using ECON combined with CEE technology seems to be an interesting alternative as a replacement for conventional copper or galvanized steel grounding grids used in SGSs. However, as demonstrated in the above literature review, very little research has focused on this specific subject despite technological progress made in ECON development. With the aim of demonstrating the feasibility of using ECON-EE technology in a large SGS, this paper presents some preliminary results obtained from a numerical investigation of a substation grounding system of 70 m × 70 m buried at a depth of 0.5 m. Comparisons between the same grid made with a regular copper conductor mesh with and without vertical rods and a grid made with the proposed ECON-encased electrode (ECON-EE) mesh were performed in terms of grid resistance, GPR, and step and touch voltages. These important parameters in grounding design were also investigated as a function of ECON electrical conductivity and geometry, as well as the diameter of the steel electrodes encased in the ECON. The numerical investigation was performed using the commercial finite element analysis software package Comsol Multiphysics^®, version 5.5. Although Comsol Multiphysics^® has been used to successfully calculate the grounding resistance of simple vertical rods in different configurations [24,25,26,27], it was decided to validate, as a first step, its capacity to model more complex conventional grounding systems by comparison with results available in the literature and obtained from different commercial grounding design software packages [28]. Particular attention has been paid to the dimensions used for the soil model, as it has a direct influence on the calculation of the ground resistance, as demonstrated in this paper.

The results obtained represent an initial step toward demonstrating the feasibility of using ECON-EE technology as a replacement for conventional copper grid substation grounding. Indeed, the different results obtained permitted us to demonstrate that the proposed ECON-EE grounding system can perform as well as or even better than a conventional copper grid system equipped with vertical rods, particularly in areas of high ground resistivity. It was also demonstrated that designing such a new grounding system is quite simple and depends on two main ECON parameters: its section area and its resistivity. The ECON-EE system can also provide an interesting solution to copper theft, which has become a growing problem for electricity infrastructure around the world. Moreover, as ECON-EE technology meets all the requirements in terms of mechanical constraints, such technology could be extended to the foundations of the power equipment and towers present in the substation in order to develop a complete interconnected grounding system.

2. Validation of Conventional SGS Modeling Using General FEM Software

2.1. Geometry and Parameters of an SGS

Before using the general FEM software Comsol Multiphysics^® to model the proposed ECON-EE grounding system, it was decided to validate its capacity to model a conventional SGS. For this, an SGS model extracted from an earthing benchmark study proposed by [28] was used. The grounding grid presents square dimensions of 70 m × 70 m (Figure 1a), buried at 0.5 m in the ground, constructed with a copper conductor of 9.27 mm diameter (2/0 Cu) and symmetrically spaced at 14 m in each direction. The use of vertical rods 7.5 m in length and 15.9 mm in diameter, located at each conductor intersection around the grid perimeter (for a total of 20 rods), was also studied (Figure 1b).

The simulations were performed for uniform soil with a resistivity ρ of 140 Ω-m (without vertical rods) and for a two-layer soil model with the first layer of 6.096 m depth with a resistivity ρ₁ of 300 Ω-m and the second layer (infinite) with a resistivity ρ₂ of 100 Ω-m (with only vertical rods).

2.2. Construction of the FEM Model of the Grounding Grid

Figure 2 presents the FEM model of the grounding grid without rods and with a uniform soil model, whereas Figure 3 presents the FEM model with vertical rods and a two-layer soil model. As described in Figure 2, the soil is divided into three semi-hemispherical regions with the same electrical properties but with different finite element sizes and properties. The inner region, with a fixed radius of 60 m surrounding the grid, uses the finer mesh size to match the mesh size used for the grid, as illustrated in Figure 4. The intermediate region of radius r_i also uses finite elements but with a larger size than the inner region. Finally, the outer region of 10 m width contains infinite elements available in Comsol Multiphysics^® [29]. All the simulations in this paper were performed under stationary conditions.

The principal problem with the FEM model is defining the size of the intermediate region as this can directly affect the results of the grounding resistance [24]. Moreover, such information seems difficult to find in the literature, given the lack of consensus on the required minimum size for r_i. Thus, it was decided to perform a parametric study in order to determine the influence of its size on the grounding resistance R_G. As demonstrated in [25], R_G (Ω) can be simply calculated from the dissipated power P_d in the volume occupied by the ground, as follows:

$$R_G=\frac{U^2}{P_d}$$

(1)

where U (V) is the voltage applied to the grid and P_d (W) is the dissipated power in the ground, which can be determined with the following expression [25]:

$$P_d={{\displaystyle \iiint }}_V^{}E·JdV$$

(2)

where E (V/m) and J (A/m²) are, respectively, the electric field and the current density flowing in the ground (modeled by the finite and infinite region) produced by the potential U applied to the entire grounding grid.

For R_G calculation, a potential U of 1 V is applied as a boundary condition at all the surfaces of the conductors forming the grid, and a ground condition (0 V) is applied at the exterior surfaces of the infinite region.

Table 1. Influence of the dimension of the intermediate region on the grounding resistance.

k	RG (Ω)	Difference (%)
1	1.284	-
2	1.108	22.47
3	1.054	6.09
4	1.021	3.40
5	1.001	2.09
6	0.999	0.20
7	0.998	0.10

presents the value obtained for R_G as a function of the parameter k defined as a multiple of the diagonal size d_G of the grid where

$$r_i=k·d_G$$

(3)

As can be observed in Table 1, the value of the grounding resistance R_G decreases when k (or r_i) increases until a certain value where the decrease in R_G becomes non-significant. Indeed, when k changes from 5 to 6, the change in the R_G value is less than 0.20% and it decreases to 0.10% for k equal to 7. In this way, the change in R_G becomes negligible and, considering that increasing the size of the finite region increases the number of finite elements as well as the calculation time, a k value equal to 5 for all the simulations seems to be the best compromise.

2.3. Validation of the Proposed FEM Model

This section presents the comparison of the results obtained with the proposed FEM model and the results extracted from the benchmark study [28]. Figure 4 presents the FEM model used for a two-layer soil system using the same k value of 5 obtained in the previous section.

Once the RG value is calculated using Equation (1), another simulation is performed to determine the GRP and the step and touch voltages with a current I of 744.8 A injected in the grid at the point P₄ defined in Figure 1a and used in [28]. The step voltage (V_step) is computed as the potential difference between the ground surface potential 1 m apart, with one point directly over the corner of the grid and the other on a diagonal and 1 m outside the grid (points P₂ and P₃ in Figure 1a). The touch voltage (V_touch) was calculated at the center of the corner mesh (point P₁ in Figure 1a), and its determination requires the implementation of an equation in Comsol Multiphysics^®, which is expressed as follows:

$$V_{touch}=GPR-V_{surface}=I \times R_G-V_{surface}$$

(4)

where V_surface represents the potential distribution obtained at the ground surface and GPR is the ground potential rise defined as the product of the injected current I by the grounding resistance R_G calculated at the first step.

Table 2. Comparison of the FEM results with a benchmark study performed for a copper grid without vertical rods and a uniform soil model.

	FEM	Grounding Software [28]
RG (Ω)	1.00	1–1.01
GPR (V)	745.54	743.9–749
Vtouch (V)	195.62	194.9–200.34
Vstep (V)	86.97	70.92–89.3

presents a comparison of the results obtained for the FEM grid model without vertical rods (Figure 1a) and with uniform soil, with the results obtained with four grounding design software packages, as presented in [28]. The results are presented as an interval of the lower and higher values obtained by the grounding software packages. In the same way,

Table 3. Comparison of the FEM results with a benchmark study performed for a copper grid with vertical rods and a two-layer soil model.

	FEM	Grounding Software [28]
RG (Ω)	0.980	0.97–0.974
GPR (V)	729.90	719.5–725.75
Vtouch (V)	271.09	261–268.81
Vstep (V)	100.52	101.3–117

presents the comparison results obtained for the FEM grid model with vertical rods (Figure 1b) and with a two-layer soil model (Figure 3). As can be observed in Table 2 and Table 3, very good concordance is obtained with the proposed FEM simulations. In the case of a uniform soil model (Table 2), all the FEM results fall within the range of values obtained with the grounding software packages. For the two-layer soil model (Table 3), the FEM results are higher by less than 1% than the values obtained with the grounding software packages, except for the step voltage, which is lower by 1%.

Figure 4 presents an example of the distribution of the equipotential lines of the touch voltage obtained from Equation (4) for the grid without vertical rods and using a uniform soil model; Figure 5 presents the corresponding distribution of the touch voltage along the diagonal of the grid. As can be observed, the distribution of the touch voltage is quite symmetrical at the surface of the grid. The maximum values of the touch voltage distribution are obtained close to the center of each grid mesh and the minimum values are above the electrode intersections.

The different results presented in this section permit us to demonstrate the capability of a general FEM software package to design a grounding system, as the results provided by it are significantly close to the results obtained from specific grounding design packages.

3. Numerical Investigation of the ECON-EE Grounding

3.1. ECON-EE Grounding Modeling

The proposed ECON-EE grounding principle consists of a steel electrode encased in an ECON section to form a grounding grid. For comparison purposes, the geometry and the dimensions of the electrode grid formed by encased electrodes are the same as the 70 m × 70 m grid without vertical rods (Figure 1a) used for the FEM model validation. However, for this study, the two-layer soil model (Figure 3) was used to simulate the worst case in terms of soil resistivity, rather than the uniform soil model of 140 Ω-m.

For all the simulations, the electrical resistivity ρ_E of the ECON was fixed at 5 Ω-m, in accordance with the average values found in the literature [16,17,18,19,20,21,22]. The first series of simulations was performed with a conventional steel rebar of ½ inch diameter (12.7 mm) used as an electrode, which represents the minimum size specified in the National Electrical Code (NEC) as a reference for Ufer grounding [15]. With this rebar electrode used to form the heart of the grounding grid of 70 m × 70 m area, a parametric study was performed to evaluate the influence of the ECON section dimensions on the grounding resistance R_G. For this, the electrical resistivity of the ECON was kept constant, and the electrical conductivity of the rebar was fixed at 6.7 × 10⁶ S/m, as recommended in [30].

Figure 6a presents an overview of the ECON-EE grounding model and Figure 6b a view of the ECON-EE section parameters. As can be observed, the rebar grid (in blue) is centered in the ECON square section (in grey) with side length a. A square section was chosen for this study as this geometry can be easily obtained onsite by directly pouring the ECON into the trenches, compared to a circular shape requiring specific molds. As specified in the NEC concerning requirements for Ufer grounding [15], the minimum concrete thickness between the rebar and the soil is equal to 50.8 mm (2 inches), as illustrated in Figure 6b. Considering this, the minimum value for the square section side a must be equal to 114.3 mm (4.5 inches). For all the simulations, the distance between the ground surface and the top of the ECON-EE system was fixed at 0.5 m and kept constant.

3.2. Influence of the ECON-EE Square Section Area

Table 4. Parametric study results of the ECON-EE square section with side length a with the two-layer soil model.

a (mm)	RG (Ω)	GPR (V)	Vtouch (V)	Vstep (V)
114.3	1.059	789.01	295.38	142.20
139.7	1.047	779.73	285.33	141.68
165.1	1.036	771.34	276.76	140.91
190.5	1.026	764.08	269.08	139.42
215.9	1.017	757.33	262.12	138.41
241.3	1.009	751.23	255.94	137.26
266.7	1.001	745.55	249.83	135.86
292.1	0.994	740.28	244.42	134.60
317.5	0.987	735.31	239.03	133.11
342.9	0.981	730.70	234.46	131.64
368.3	0.975	726.35	229.85	130.12
419.1	0.964	718.09	221.49	127.01
520.7	0.945	703.70	206.97	117.51

presents the results obtained from the parametric study in terms of ground resistance, GPR, and step and touch voltages. The different voltages were determined at the same points as defined in Figure 1a, for the same injected current of 744.8 (A) as used in Section 2.3. For all the simulations, the distance between the soil surface and the ECON-EE grounding system was constant and equal to 0.5 m. For comparison,

Table 5. Comparison of the results obtained for a copper and rebar grid without ECON, with the two-layer soil model, and without vertical rods.

	Copper Grid	Rebar Grid
Conductor diameter (mm)	9.27	12.7
RG (Ω)	1.188	1.176
GPR (V)	884.96	886.31
Vtouch (V)	394.88	386.22
Vstep (V)	117.16	118.71

presents the results obtained for the copper and the rebar grid without ECON under the same conditions.

At first observation, a comparison of the results of Table 3 and Table 5 shows that the addition of vertical rods to the copper grid significantly improves the grounding resistance as well as the GPR and the touch and step voltages. This demonstrates the efficiency of vertical rods in the case of soil having low resistivity. In addition, the results of Table 5 demonstrate that the use of rebars as grid electrodes is quite equivalent to the use of copper with regard to the value of R_G and the touch and step voltages. The low electrical conductivity of the rebar (88.82% lower than copper) seems to be compensated for by its larger diameter (37% larger than copper).

The analysis of the parametric study presented in Table 4 shows that the increase in the ECON-EE section leads to a slow decrease in the ground resistance R_G and the corresponding touch and step voltages. As illustrated in Figure 7, the variation in R_G and the touch voltage decrease follow a power curve, whereas the step voltage decreases linearly with the increase in a. As the ground resistance recommended by the IEEE standard for substations must be equal to or less than 1 Ω [4], this critical value is reached from the ECON-EE section side equal to 266.7 mm. With these values, it is interesting to note that the touch voltage is reduced by 7.84 % compared to the results in Table 3 obtained with the copper grid with vertical rods. However, as can be observed from the results in Table 3 and Figure 7, the value of the step voltage obtained with the different ECON-EE surface area remains higher than the value obtained in Table 3 for the copper grid with vertical rods, with a difference between 41.46% for the smaller side a, and 18.10% for the longer side a.

The efficiency of the ECON-EE grounding is also illustrated in Figure 8, presenting the evolution of the distribution of the touch voltage along the grid diagonal (Figure 1a) as a function of the square geometry with side length a, which is compared with the distribution obtained for the copper grid with vertical rods. The results obtained show that the maximum values of the touch voltage decrease with the increase in the ECON-EE area (or side a).

3.3. Influence of the Electrical Conductivity of the ECON-EE Square Section

In this section, the influence of the electrical resistivity ρ_E of the ECON is investigated for an ECON-EE square section with a side length a of 266.7 mm leading to a grounding resistance value of 1.001 Ω, as presented in Table 4.

Table 6. Influence of the ECON resistivity ρ_E on the ECON-EE grounding system parameter for a square section side length a equal to 266.7 mm and ρ₁ = 300 Ω-m.

ρE (Ω-m)	ρ1/ρE	RG (Ω)	GPR (V)	Vtouch (V)	Vstep (V)
300	1	1.176	886.31	386.22	118.71
150	2	1.090	811.80	319.07	125.21
50	6	1.030	766.93	272.4	131.75
10	30	1.004	748.02	252.11	135.38
5	60	1.001	745.62	249.83	135.86
1	300	0.998	743.61	247.40	136.37
0.25	1 200	0.998	743.61	247.40	136.37
0.01	30 000	0.998	743.61	247.40	136.37

presents the results obtained for different values of ρ_E and its influence on the grounding system parameters. Figure 9 presents the evolution of R_G and the touch and step voltages plotted as a function of the ratio ρ₁/ρ_E, where ρ₁ = 300 Ω-m is the resistivity of the first soil layer and ρ_E the resistivity of the ECON-EE. From the results obtained, it can be observed that the grounding resistance and the touch voltage decrease by 14.88% and 35.31%, respectively, when the ECON resistivity ρ_E decreases from 300 to 5 Ω-m, corresponding to a ρ₁/ρ_E ratio increase from 1 to 60. After this, both the grounding resistance and the touch voltage remain constant as the ECON resistivity decreases or the ratio of ρ₁/ρ_E increases. Such behavior of the grounding resistance is consistent with the results reported in [13,31] in the case of a simple vertical rod embedded in a cylinder of ordinary concrete [13] or GEM [31]. It is also interesting to note that the step voltage follows the opposite trend to the touch voltage, with an increase until a ρ₁/ρ_E value of 60, followed by a constant value for higher ECON resistivities.

3.4. Influence of the Geometry of the ECON-EE Section

In this section, the influence of the ECON section geometry is investigated. For this, two section geometries were studied, a circular section (Figure 10a) and a rectangular section (Figure 10b), with the same encased rebar electrode of 12.7 mm diameter used in the previous section and centered in the middle. The simulation parameters were the same as used in the previous section, and the distance between the ground surface and the top of the ECON-EE system was maintained at 0.5 m. In addition, as for the square section, the height of the rectangular section was fixed at 114.3 mm, which is the minimum side dimension of the square section in order to maintain the minimum required ECON thickness between the rebar and the ground at 50.8 mm (see Figure 10a), as required by [15].

In order to study the influence of the ECON section geometry, it was decided to compare the results with those obtained for the square section with side length a = 266.7 mm, which permits us to obtain a grounding resistance R_G of 1.001 Ω (see Table 4), equivalent to the minimum value required for large substation grounding [4]. However, for comparison purposes, two different studies were performed: a study where the areas of the circular and rectangular ECON sections were the same as that of the square one, and another where the perimeters of the circular and rectangular ECON sections were identical to that of the square section. The results are presented in the subsections that follow.

3.4.1. Circular and Rectangular Sections of the Same Area

Keeping the same area for the circular and rectangular ECON sections as for the square one permits us to keep constant the electrical resistance of the ECON-EE per unit length [32], as well as allowing the same quantity of material required for the construction of the grounding system. With this assumption, the radius r of the circular section can be defined as follows:

$$r\left(mm\right)=\frac{a}{\sqrt{\pi }}=150.5$$

(5)

and the width w can be expressed as follows:

$$w\left(mm\right)=\frac{a^2}{114.3}=622.3$$

(6)

Table 7. Influence of the ECON section geometry on the ECON-EE grounding system parameters with the same section area equal to a² with a = 266.7 mm.

ECON Geometry	Section Area (m2)	Perimeter (m)	RG (Ω)	GPR (V)	Vtouch (V)	Vstep (V)
Square	0.071	1.067	1.001	745.55	249.83	135.86
Rectangular	0.071	1.473	1.000	744.80	248.05	143.56
Circular	0.071	0.946	1.002	746.29	250.85	132.84

presents the results obtained for the circular and rectangular sections of the same surface area and compared with the results obtained previously for the square section under the same modeling parameters. As can be observed, the values of the grounding resistance R_G and the touch voltage obtained for the rectangular and circular sections are identical to the values obtained for the square section, with a difference lower than 0.1%, which can be attributed to calculation error. However, for the step voltage, the section geometry seems to have a certain influence, with a difference of 2.22% lower and 5.67% higher for the circular and rectangular sections, respectively, compared to the square one. The evolution of the touch voltage along the grid diagonal presented in Figure 11 confirms that the influence of the different sections is not significant.

3.4.2. Circular and Rectangular Sections with the Same Perimeter

In general, the analytical formulation used to calculate the grounding resistance of a grid depends principally on the geometry of the electrodes, which influences the contact surface area with the surrounding soil [13,32]. From this observation, it was decided to study the influence of circular and rectangular ECON sections with the same section perimeter as the square one in order to validate this assumption. Hence, the radius r of the circular section can be defined as follows:

$$r\left(\mathrm{mm}\right)=\frac{2a}{\pi }=169.8$$

(7)

and the width w can be expressed as follows:

$$w\left(\mathrm{mm}\right)=2a-114.3=419.1$$

(8)

Table 8. Influence of the ECON section geometry on the ECON-EE grounding system parameters with the same equivalent perimeter equal to 4a with a = 266.7 mm.

ECON Geometry	Section Area (m2)	Perimeter (m)	RG (Ω)	GPR (V)	Vtouch (V)	Vstep (V)
Square	0.071	1.067	1.001	745.55	249.83	135.86
Rectangular	0.048	1.067	1.011	752.99	257.18	145.59
Circular	0.091	1.067	0.993	739.59	243.92	130.57

presents the results obtained for the circular and rectangular sections with the same perimeter and compared with the results obtained previously for the square section. As can be observed, the influence of the ECON geometry with the same perimeter seems to be higher than those obtained for the sections with the same area. For the rectangular section with a small area surface (0.048 m²), the grounding resistance and the touch voltage are 1.00% and 2.94% higher than for the square section, respectively. For the circular section with a larger area (0.091 m²), the grounding resistance and the touch voltage are 0.80% and 2.73% lower than for the square section, respectively. Moreover, the rectangular and circular sections present a step voltage 7.17% higher and 3.89% lower, respectively, than that of the square section.

Figure 12 presents the evolution of the touch voltage along the grid diagonal obtained for the three sections. As can be observed, the larger difference between the touch voltage of the rectangular section and the square one is obtained for the maximum value of the touch voltage distribution obtained close to the center of each grid mesh.

3.5. Influence of the Rebar Diameter

In this section, the last parameter studied was the size of the rebar acting as the electrode embedded in the ECON. Different simulations were performed for the ECON-EE square section of the 266.7 mm side with the same two-layer soil model as used in previous sections. The results are presented in

Table 9. Influence of the rebar diameter on the ECON-EE grounding system parameters for a square section with a 266.7 mm side, with the two-layer soil model.

Rebar Diameter (mm)	Imperial Bar Size	RG (Ω)	GPR (V)	Vtouch (V)	Vstep (V)
12.7	#4	1.001	745.55	249.83	135.86
19.05	#6	1.000	744.80	249.27	136.01
25.4	#8	1.000	744.80	249.27	136.01
32.26	#10	1.000	744.80	249.27	136.01
43.00	#14	0.999	744.06	248.53	136.06
57.33	#18	0.998	743.31	247.77	136.24

with the different grid parameters determined at the same points as used previously and presented in Figure 1a.

The results presented in Table 9 seem to demonstrate that, for the same square section of ECON, the influence of the rebar diameter is not significant. Another means to prove this assumption is to use the analytical formulation proposed in [32] to determine the equivalent radius of a single conductor modeling the rebar embedded in the ECON square section. The proposed formulation, initially developed for an electrode embedded in GEM, can easily be applied to the ECON-EE in the same manner. Hence, the equivalent radius r_eq of the single conductor model can be expressed as follows [32]:

$$r_{eq}=r_b{\left(\frac{r_0}{r_b}\right)}^{1-\frac{{\rho }_E}{{\rho }_1}}$$

(9)

where r_b is the radius of the rebar, ρ_E is the resistivity of the ECON-EE, ρ₁ is the resistivity of the first layer of the soil model, and r₀ is the radius of the ECON circular section with the same area as the square section and given by Equation (5).

With the simulation parameters used for the results of Table 9, ρ_E = 5 Ω-m, ρ₁ = 300 Ω-m, a = 266.7 mm, and r₀ = 150.5 mm, and Equation (9), r_eq can then be determined for the different rebar diameters, as presented in

Table 10. Calculation of the equivalent radius r_eq as a function of the rebar diameter for a square ECON-EE section of the 266.7 mm side.

Rebar Diameter (mm)	Imperial Bar Size	req (mm)
12.7	#4	142.74
19.05	#6	143.70
25.4	#8	144.40
32.26	#10	144.97
43.00	#14	145.67
57.33	#18	146.37

.

The results presented in Table 10 demonstrate that the influence of the rebar diameter on the equivalent radius is not very significant, with an increase of only 2.54% in r_eq when the rebar diameter increases from 12.7 mm to 57.33 mm. These results demonstrate the fact that increasing the rebar diameter seems not to affect the grid parameters, as confirmed by the simulation results in Table 9.

4. Discussion

In this paper, many simulation results have been presented in order to demonstrate the feasibility of using a new grounding system based on the use of simple rebars encased in an electrically conductive concrete section in order to replace conventional copper grids for substation grounding. The analysis of these different results permits us to highlight several advantages of using such new types of grounding systems, as well as the main parameters of the ECON-EE system influencing the grounding resistance and the touch and step voltages, as discussed in the following sections.

4.1. Most Influential ECON-EE Parameters

4.1.1. ECON-EE Section Area

As demonstrated by the different results obtained, for the same ECON resistivity, the main parameter influencing the grounding system parameters is the surface area of the ECON, and this occurs independently of the geometry of the section. Indeed, the results of Table 4 and Figure 7 show that increasing the section area of the ECON-EE leads to a significant decrease in the grounding resistance R_G and the touch voltage, which both follow a power curve decrease with the increase in section area. As can be observed, the decrease in the touch voltage is more significant than R_G when the side section varies from 114.3 mm to 520.7 mm, with a decrease of 10.76% and 29.93% for R_G and the touch voltage, respectively. For the step voltage, its decrease is equal to 17.36% for the same side length increase, and its decrease seems to follow a linear curve instead of a power one.

In the same way, the results in Table 7 and Table 8 have demonstrated that the geometry of the ECON section has no real influence on the grounding system parameters as long as the section area is the same. When the section area is kept constant for different section geometries, the R_G and the touch voltages are similar. The only difference observed was in the step voltage, with a difference of 2.22% lower and 5.67% higher for the circular and rectangular sections, respectively, compared to the square one. Although not very significant, this difference can be explained by the apparent surface of the ECON-EE section, which is greater and lower for the rectangular and circular sections, respectively, than that of the square section. The apparent section seems to have a small influence on the distribution of the potential at the surface of the ground in the vicinity of P₂, where the step voltage is determined (see Figure 1a). This influence can be observed in Figure 11 and particularly in the magnified section of the end of the touch potential distribution. As can be observed, the touch voltage at P₂ is lower and higher for the rectangular and circular sections, respectively, compared to the square section. In this condition, the potential difference calculated between points P₂ and P₃ becomes higher for the rectangular section and lower for the circular one, and this explains the difference obtained in the step voltage for each section.

Finally, the influence of the ECON-EE section can also be seen in the results of Table 8, for which the perimeter of the section is maintained constant. Indeed, the lower and higher values of R_G and the touch and step voltages were obtained for the circular and rectangular sections with a larger and smaller surface area, respectively. These results provide another confirmation that the ECON-EE surface area is one of the main parameters influencing the SGS parameters.

4.1.2. ECON-EE Resistivity

From the results presented in Table 6 and Figure 9, it can be concluded that ECON resistivity is another parameter directly influencing the SGS parameters. Moreover, the results of Figure 9 are interesting in the sense that the influence of the ECON resistivity also depends on the resistivity of the surrounding ground and particularly on the ratio of the ground resistivity to the ECON resistivity (ρ₁/ρ_E). As demonstrated in a study performed on GEM’s influence [31], decreasing the ECON resistivity seems to have a significant effect on the grounding resistance diminution until a ρ₁/ρ_E ratio equal to around 60. From this value, increased ECON resistivity seems not to affect the grounding resistance. These results are very interesting as they demonstrate that, for higher ground resistivity, where grounding can be difficult, the resistivity of the ECON must be higher in order, which is easy to obtain. By contrast, for lower ground resistivity, the ECON resistivity must be lower, which is more difficult to achieve. At present, the ECON resistivity obtained with specific conductive fillers can be as low as 0.25 Ω-m, corresponding to a minimum ground resistivity of 15 Ω-m [17]. These results also demonstrate that ECON-EE seems to be better adapted to soil with higher soil resistivity but can also be effective in other types of soil.

4.2. Efficiency of the ECON-EE Grounding System Compared to Copper Grid

Table 3 presents the results used as a reference obtained for a copper grid with vertical rods for a two-layer soil model with ρ₁ = 300 Ω-m and ρ₂ = 100 Ω-m. A comparison of the results with the results presented in Table 5 demonstrates the necessity and the efficiency of vertical rod addition in decreasing the grounding resistance. Now, by comparing the results of Table 3 with the results of Table 4 and Table 6, it can be observed that the best result can be achieved with an ECON-EE square section with a 266.7 mm side and a resistivity of 5 Ω-m. Indeed, with these ECON-EE parameters, the grounding resistance is equal to 1 Ω, as recommended by IEEE Std 80 [4]. However, for the touch and step voltages recommended by the standard, it may be necessary to determine the recommended values for a ground resistance ρ₁ of 300 Ω-m. For this, the Equations (10) and (11) provided by the IEEE Std 80 to calculate the allowable touch and step voltages were used, respectively [4].

$$V_{touch}\left(V\right)=I_b.\left(1000+6C_s.{\rho }_s\right)$$

(10)

$$V_{step}\left(V\right)=I_b.\left(1000+1.5C_s.{\rho }_s\right)$$

(11)

where t_f (s) represents the duration of the current fault event; ρ_s is the resistivity of the soil; C_s represents the surface layer derating factor, which accounts for the effect of the presence of a high-resistivity surface layer in the substation, and I_b (A) is the allowable body current, which can be survived by 99.5% of persons and can be expressed as follows:

$$I_b=\frac{0.116}{\sqrt{t_f}} \mathrm{for} \mathrm{a} \mathrm{body} \mathrm{weight} \mathrm{of} 50 \mathrm{kg}$$

(12)

$$I_b=\frac{0.157}{\sqrt{t_f}} \mathrm{for} \mathrm{a} \mathrm{body} \mathrm{weight} \mathrm{of} 70 \mathrm{kg}$$

(13)

Figure 13 and Figure 14 present the distribution of allowable touch and step voltages as a function of t_f obtained for body weights of 50 kg and 70 kg with ρ_s = ρ₁ = 300 Ω-m and Cs = 1, meaning that no high-resistivity surface layer is present in the substation (worst case). In these figures, the touch and step voltages obtained for ECON-EE square sections with 266.7 mm and 520.7 mm sides and for the copper grid with vertical rods are also represented for comparison.

As can be observed in Figure 13, the comparison of the different touch voltage values shows that the copper grid with vertical rods performs the worst, with maximum current fault durations of 0.38 s and 0.70 s for body weights of 50 kg and 70 kg, respectively. For the square ECON-EE section with a 266.7 mm side, the values obtained are 0.45 s and 0.83 s for body weights of 50 kg and 70 kg, respectively, and they increase to 0.66 s and 1.21 s for the ECON-EE square section with a 520.7 mm side. These values remain significantly higher than a typical fault clearing time of 40 to 90 ms, considering a breaker opening time of 2 to 5 cycles and a relay operating time of half a cycle, as mentioned in [33], and significantly higher than the duration of a lightning strike. Finally, for the step voltage (Figure 14), although the values of the step voltage obtained with the ECON-EE square sections are higher than the values obtained for the copper grid with vertical rods, the ECON-EE values remain lower than the values recommended by the IEEE Std 80 for a current fault duration of up to 3 s.

4.3. Advantages and Disadvantages of Using an ECON-EE Grounding System for a Substation

4.3.1. Advantages of the ECON-EE Grounding System

As presented in the previous sections, the different results obtained tend to confirm the fact that the proposed ECON-EE grounding system can perform as well as or even better than a conventional copper grid system, which requires, in the case presented in this paper, the addition of vertical rods in order to meet the standard requirement for substation grounding. In this case, the ECON-EE grounding system presents a certain advantage over the copper grid in terms of the cost of installation, because it is no longer necessary to dig supplementary holes for vertical rod installation. Moreover, the installation of the ECON-EE grounding system should not require supplementary operation compared to copper grid installation as, for each solution, trenches must be dug approximatively to the same depth.

Moreover, as presented and demonstrated in this paper, the design and dimensioning of the ECON-EE grounding system is not complicated, since the grounding resistance and the touch and step voltages are principally governed by the section area of the ECON-EE and its resistivity, whose value depends on the resistivity of the ground in a ratio of 60.

As demonstrated in Section 3.5, the diameter of the rebar encased in the ECON section has no real influence on the grounding system parameters. The rebar diameter will only have a direct influence on the permissible ground current fault, whose value will increase with the increase in the rebar diameter, as demonstrated in [13]. Hence, with the same ECON-EE section area and resistivity, it becomes easy to adapt the grounding system at different substation ratings by only modifying the diameter of the rebar and without changing the parameters of the ECON-EE grounding system obtained for the substation ground resistivity. Moreover, as presented in the literature review, ECON-EE, which can be considered an improved Ufer grounding system, performs very well under lightning strikes in terms of the diminution of the impulse ground resistance compared to that of the power frequency, and also permits us to improve the heat dissipation to the ground during the current fault.

Another advantage of the ECON-EE grounding system is the protection against vandalism and copper theft.

4.3.2. Disadvantages of the ECON-EE Grounding System

The first disadvantage of the ECON-EE grounding system can be attributed to its cost. As mentioned in [20], ECON can be produced with an estimated cost of around USD 400 per m³. The average cost of a ½-inch diameter steel rebar can be estimated at around USD 3.7 per meter [34]. Hence, in the case of the ECON-EE square section with a 266.7 mm side, the cost of material (ECON plus rebar) can be estimated at around USD 32 per meter. This cost can be compared to the cost of a stranded bare wire 2/0 Cu, the average price of which calculated from several suppliers can be estimated at around USD 17.4 per meter. Thus, ECON-EE’s cost can be 1.84 times the cost of a simple copper wire grid. However, this cost does not take into account the need for vertical rods in the case of high-resistivity soil and the cost of digging and installing the rods.

Another disadvantage could be attributed to the possible corrosion of rebars, as mentioned in [6] in reference to Ufer grounding used in soil of high acidity. However, rebar or electrode corrosion in ECON or ECC seems to be lower than in ordinary concrete, as observed in different studies [9,20,35]. The use of carbon-based material and silicate fumes or fly ash in ECON or ECC seems to delay the corrosion of the encased electrodes [20,35]. Moreover, rebar corrosion can also be managed using corrosion inhibitors in ECON or by replacing steel rebars with galvanized rebars, or even stainless steel rebars, which are less affected by corrosion but are more costly. The cost of galvanized rebars is approximately 15% higher than that of steel rebars, but they are 40 times more resistant to corrosion than steel rebars [36]. The cost of stainless steel rebars is around 6 times the cost of steel rebars, but their corrosion resistance is 1500 times higher than that of carbon steel rebars [36].

Finally, another disadvantage of using ECON-EE in SGSs is the lack of experimental studies conducted on real sites in order to follow the evolution of the grounding resistance of a large ECON-EE grounding system over time, and the influence of environmental parameters, such as ground composition, rain, cold weather, etc. Nevertheless, some data obtained on natural sites over several years are available from studies performed on ECC [9,10], as well as on ECON in pavement heating applications [18,19]. The results obtained demonstrate the stability of ECC or ECON resistivity over time, which is an important parameter for maintaining stable grounding resistance. The stability of the resistivity is also a good indication that electrode corrosion is not a concern when electrodes are encased in ECC or ECON because, in the presence of electrode corrosion, the resistivity should increase significantly, as demonstrated in [35].

5. Conclusions

As a general conclusion, the results presented in this paper have permitted us to evaluate the possibility of using a new concept of substation grounding systems using electrically conductive concrete with rebars used as electrodes. The results obtained and the comparisons performed with conventional copper grid electrodes have demonstrated that the proposed ECON-EE grounding system can perform better than a copper grid equipped with vertical rods, especially in high-resistivity soil, where the cost of ECON-EE grounding seems to be equivalent to the cost of a copper grid with vertical rods. Moreover, ECON has become a mature technology in the field of pavement de-icing, and its use in the development of substation grounding systems with rebars as electrodes must be considered a serious candidate for a conventional SGS replacement. Indeed, as demonstrated in this paper, the design and dimensioning of an ECON-EE grounding system is quite simple and is principally governed by two parameters: the section area and the resistivity of the ECON.

However, in order to be accepted and integrated into international standards as an alternative solution to conventional SGSs, ECON-EE grounding technology has to demonstrate its long-term durability and efficiency under different environmental conditions as well as during different types of faults. To this end, several numerical and experimental studies are currently underway to characterize the electrical behavior of the ECON-EE system under different current faults and to study the evolution of the grid resistance of a small-scale ECON-EE system as a function of seasonal influences. The results obtained from these studies will be presented in future papers.