Аннотация:
modeling and analyzing the characteristics of grounding electrode can help to achieve better system performance and reduce the risks associated with lightning strikes. Although a simple electrode is most often used in grounding systems, in soils with high resistivity, such as rocky and sandy soils, classical grounding is difficult to implement. This paper presents the modeling of simple and electrolytic grounding electrodes and compares their performance when subjected to lightning strikes. To overcome the mathematical models of proposed system, the current paper used finite element method
Ключевые слова:
grounding system, lightning, grounding electrode, soil resistivity, electromagnetic fields
DOI 10.24412/27128849202457411011120
УДК 620.9
Shahwali Amani
Peter the Great St. Petersburg Polytechnic University
(St. Petersburg, Russia)
MODELING OF SIMPLE
AND ELECTROLYTIC GROUNDING
ELECTRODES UNDER LIGHTNING IMPACT
Keywords: grounding system, lightning, grounding electrode, soil resistivity, electromagnetic fields.
The purpose of grounding systems is to protect electrical equipment, devices, networks, and people from any fault occurring in the electrical power network[1]. It provides a path between parts of the electric circuit and the ground. Therefore, electrical grounding plays a fundamental role in the protection and reliable operation of any electrical equipment or device and in the safety of personnel under fault conditions. The grounding system is mainly composed of subsystems such as strike termination, conductors, horizontal or vertical electrodes, as well as fittings and connectors,[1],[2]. These subsystems are made of materials including copper, aluminum, and galvanized steel[3]. However, in highvoltage substations and power stations, it can be designed as a grid that consists of a combination of conductors and electrodes and is buried in soil [3].
The behavior of the grounding electrode against lightening that is a highfrequency fault is completely different from steadystate faults. Most lightning strikes cause severe faults in electrical networks. This type of stroke has a large amount of current that changes the performance of the grounding and causes ionization of the soil that surrounds the electrode [4], [5].
The focus of this study is on the modeling of vertical simple and electrolytic grounding electrodes and their response to lightning strikes. These ground electrodes are most commonly used due to their ability to provide lowresistance paths to the ground and dissipate the huge amount of energy associated with lightning surges. By effectively channeling the electrical current into the ground, these electrodes minimize the risk of electrical damage, fires, and electric shocks[6].
Recently, numerical models based on the finite element method have given better results in modeling lightning impacts on the ground electrode. Consequently, it is essential to model the electric and magnetic fields and potentials to analyze the characteristics of the behavior of the ground electrodes[7].
In highvoltage applications, the published results of the numerical simulation of electric and magnetic field distribution, as well as the potential distribution for studies, are all for simple geometries. Although numerical simulation is a useful approach that gives the possibility to analyze the behavior of several phenomena, because of its complexity, COMSOL Multiphysics is used as a powerful way to solve the complex problems of the finite element method[7],[8]. In this study, a twodimension finite element method has been developed using real geometrical dimensions and is used to calculate the electromagnetic field distributions on the ground electrode.
The study consists of the following parts: section 2, illustrates a comprehensive literature review, and section 3 presents modeling, analysis, mathematical models, section 4 carried results and discussion. Conclusion and recommendations were drawn in section 5.
The electricity in the system contains the flow of electrons via conductors or metal circuit wires, always looking for the shortest possible routes to lower potential zones on the ground. In case of faults in power system, grounding will provide a direct pathway to the earth, preventing power surges that lead to equipment damages and electrical hazards[1].
There are many different approaches and techniques of grounding that are used for connecting electrical systems to the ground. The two common types are explained in the below section.
A vertical electrode is the most commonly used means for grounding electrical systems. It is a metallic device that is buried into the ground to create a lowimpedance path to earth for electric currents that are generated during a lightning stroke[4], [5]. Most commonly, the ground electrode is made of copperbonded and galvanized steel. However, in certain situations, stainless steel or solid copper ground electrodes are also used, considering the unique conditions of that specific environment. The vertical grounding electrode is simple, economical, and provides protection for the electrical system. However, it cannot provide that level of protection as more complex grounding systems do[9],[10].
Fig.1: A typical Grounding Rod [11]
The material, size, and depth of the grounding rod are determined by the specific requirements of the electrical system as well as the local standards. NEC table 250.66 is used for sizing grounding electrode conductors. It is important to make sure the grounding system is installed correctly and to maintain its effectiveness to provide safety in electrical systems[12].
Electrolytic grounding devices are used in soils with high resistivity, such as rock and sandy soils, where the use of classical grounding is difficult or fundamentally impossible. Grounding devices based on electrolytic grounding electrodes can be more functional and operational. This type of grounding uses an electrolytic process to improve the conductivity of the grounding connection to the earth[13].
An electrolytic grounding device[3] contains a hollow perforated metal electrode, made in a vertical design, filled with a mixture of mineral salts. A mixture of bentonite and graphite powder is poured into a dug channel, which, due to their properties when in contact with water, turns into an electrically conductive nonfreezing gel and prevents the rapid leaching of the mixture of mineral salts from the electrode cavity[9],[10].
Next, the electrode is placed in a dug channel, and, after connecting to the grounding conductor, it is covered with soil. The connection unit can be a threaded clamp into which the grounding conductor is inserted and clamped, a welded currentcarrying wire connected to the grounding conductor separately, or any other known connecting device that provides highquality electrical and mechanical contact. The joints are waterproofed to reduce corrosion[14], [15]
To ensure periodic inspection and control of the operation of the entire structure, as well as to measure the resistance of the grounding device, a well with a removable hatch is installed on the surface of the earth. After installation, it is necessary to pour water into the neck of the vertical part of the electrode. The mixture of mineral salts turns into an electrolyte (leaching). This electrolyte penetrates the soil, increasing its electrical conductivity (lowering its electrical resistivity) and reducing its freezing temperature (lowering the freezing temperature), as a result of which the effectiveness of grounding is significantly increased [10]. The conductivity of the soil remains high. In addition, all materials used to implement the technical solution are highly resistant to aggressive environments, nontoxic, and environmentally friendly[10], [13].
Fig.2: A typical electrolytic ground electrode[15]
While designing the grounding system, care should be taken that the system is appropriate both for clearing the faults and for generated lightning energy. The system must have longterm performance, be capable of meeting new standards and codes for safety, and have enough body points to facilitate the addition of new equipment [10], [15].
The purpose of this research is to carry out an analysis of the design features of simple and electrolytic types of grounding conductors and select the optimal design for further research.
The simulation of the ground electrode has been carried out using COMSOL Multiphysics. It is a powerful platform for modeling of and solving of scientific problems based on partial differential equations. With this software, we can build conventional models for one type of physics model into Multiphysics models that solve coupled physics phenomena. In this article, the model has been built by defining physical quantities such as material properties for each type of material (cupper and soil, fig. 2) by their permittivity and electrical conductivity (tables 2 and 3) for the defined boundary conditions[14],[16]. Subsequently, COMSOL internally compiles a set of partial differential equations representing the entire model. We can access the results through a flexible graphical interface.
We examined the electric and magnetic fields as well as the potential distribution on the surface of the ground electrode for different values of electric permittivity and soil resistivity, the results are shown in section 4.
In below the geometry of the vertical ground electrode is built in COMSOL software.
Table 1: Geometrical Parameters of Ground Electrode
Name 
Expression 
Value 
Description 
d 
25[mm] 
0.025 m 
Diameter of grounder 
l 
5000[mm] 
5 m 
Length of grounder 
V 
{200000*(EXP(t/0.0000005)EXP(t/0.000067))} 
1.78E+05 
Lightning Pulse 
t 
1.2e6[s] 
1.2E6 s 
time 
The following physical properties for soil and the grounder (Copper) is used when for further studies and simulation of the model.
Table 2: Material Property of the Soil 

Electrical conductivity 
σ 
1/15000 
S/m 
Relative permittivity 
εr 
12 
1 
Relative permeability 
μr 
1 
1 




Table 3: Material Property of the Grounder “Copper" 

Electrical conductivity 
σ 
58500 
S/m 
Relative permittivity 
εr 
1 
1 
Relative permeability 
μr 
1 
1 
The behavior of electric field intensity [E] and electric flux density [D] is considered in electrostatic problems. The first condition that these quantities are obeying is differential from Gauss law. This law illustrates that the flux out of any closed volume is equal to the charge contained within that volume. The Maxwell equations are the basic equations used to calculate the electric field. The below equations are used for the electrostatic model of the present simulation[17]:
curl(H) = J ………. (1)
Equation (1) describes the relation between the changing magnetic field and current density, and it is known as MaxwellAmpere’s law as it well describes the behavior of electric field and magnetic field[18], [19].
We further proceed with taking the divergence from both sides of the above equation as follows:
……..(2)
The left side of the above equation (1) is equal to zero, as the divergence of any curl is equal to zero. The uppercase Q represents the external source of current, while J is the current density. As in the current simulation, there is no external source or flow of charges into or out of the system, therefore, the total charge represented by Q is equal to zero[20].
………. (3)
In the formula (3) above, the relation of current density [J] is described to the electric field (E), the conductivity [σ], and the time rate of change of electrical flux density..
The above relation between the electric field and electric potential is a fundamental law of electromagnetism[17], [21]. It describes that the electric field at a given point in space is equal to minus the rate of change of electric potential with respect to position.
In the magnetic field equation, the first formula is the Ampere’s Law:
……………….(5)
The next equation in magnetic field part is BiotSavart law:
………….(6)
Equation (6) is used to calculate the amount of magnetic field produced by a currentcarrying wire. The right side of equation, the curl of vector potential [∇×A], is a vector potential that represents the circulation of vector potential at a given point in space.
If we apply divergence to both sides of equation (6), the Gauss law for magnetic fields can be obtained. As div(B) =0, or the net magnetic flux through any surface is zero, “∮ B · dA = 0" [22].Any closed surface encloses a net magnetic charge of zero, due to the fact that lines in a magnetic field always form closed loops. It denotes that there can be no net flux because each magnetic field line that enters a closed surface must likewise exit it.
The next equation of magnetic field describes the relationship of current density with electric field, velocity of material, magnetic field, and external current density, as shown below:
…………………..(7)
Maxwell Faraday Equation
(8)
For the purpose of coupling a magnetic field and an electric field, the external current density is applied to the system. Using the COMSOL Multiphysics, in the electric field part of the model, the equation of the magnetic field is written as shown below:
Subsequently, in the magnetic part of the model, the equations from the
electric part are added in blue:
In the above, [Jd] is the displacement current, and [Ji] is the induced current.
The program solves the above equations for potential distribution over a userdefined domain with userdefined sources and boundary conditions. Finally, the simulation results are displayed for potential, electric, and magnetic field distributions.
The first part of this section represents the results of the simple electrode and the second section for the electrolytic electrode along with comparison the performance of both electrodes:
Based on the above criteria the model has been simulated and the results are shown as below:
Fig.5: Distribution of Electric Potential along the grounding electrode.
Fig.5 illustrates the distribution of electric potential surrounding the electrode. As shown, there is a high level of potential in the vicinity of the electrode, and it decreases gradually as move away from the electrode to the soil surrounding it. This information can be used for the calculation of some parameters, e.g., electric field strength, current density, and so on.
Fig.6: Magnetic flux density propagation along the grounder for different time slots.
The graph in Figure 6 shows the propagation of electromagnetic waves along the length of the ground for different times [0, 0.01, 3] microseconds. At a certain time, point, the wave would reach 5m and cover the whole length of the ground.
To calculate the wave length, we take the first time point of 0.01 and multiply it by the wave speed, which is approximately 60 m/sec, this results in 0.6m. In the same way, the wave length for different time points can be calculated, as shown in the table below:
Table 4: Propagation of magnetic flux density along the simple ground electrode 

Time (µsec) 
Wave Speed(m/µsec) 
Wave Length(m) 
Plot color in Fig.9 
0.01 
60 
0.6 
Dark Blue Line 
0.02 
60 
1.2 
Green Line 
0.03 
60 
1.8 
Red Line 
0.04 
60 
2.4 
Violet Line 
0.05 
60 
3 
Purple Line 
0.06 
60 
3.6 
Yellow Line 
Fig.7: Propagation of electric field along the grounder for different time slots.
Fig. 7 shows the propagation of the electric field along the ground. The field lines are similar to those of the magnetic field strength distribution. Only the values for the electric field and magnetic field are different. It is important to note that the electric field is composed of two components. The first component is the negative gradient of potential, which is electric field intensity according to Ohm’s law in derivative form. The second component is the time derivative of magnetic vector potential or induced electric field intensity.
Fig.8: Variation of current in the grounding electrode
for different permittivity of surrounding soil
If the permittivity of the soil that surrounds the ground electrode is increased and its conductivity is decreased, then there is a wave effect as can be seen in the above current line graphs. The above plots, with different colors in Fig.9, show the results of changes in the current in the simple ground electrode while changing the permittivity of the surrounding medium(soil).
From graphs in Figure 11, it can be concluded that, when the soil permittivity is higher, there is a wave effect in the current plot. By decreasing the permittivity of soil around the ground, the wave effect is decreasing.
Fig.9: Dependence of current in the grounder
by changing of the surrounding soil resistivity.
Fig.9 shows the results: when the resistivity of the surrounding medium is changed, there is a significant change in the current. By increasing the value of the resistivity of the soil, the current in the electrode is noticeably decreasing.
So, from the above considerations, we can conclude that, when the soil resistivity is higher, we can observe the wave effect in the current shape. The wave effect cannot be observed in soils with low resistivity. In this case, the current shape is more similar to the lightning pulse shape.
For the purpose of studying the performance of the electrolytic electrode, the geometry of the simple ground electrode is used with necessary modifications, including the electrical conductivity of the soil, as shown in Fig. 13.
Fig.10: Dependence of electric conductivity on distance.
As can be seen in Fig. 10, the electrical conductivity of soil is influenced by the distance. By moving far away from the electrode, the electrical conductivity decreases and the resistivity increases accordingly. The further the current travels, the more resistance it encounters. Additionally, the conductivity of the medium varies depending on the composition, presence of chemicals, and moisture contents. If the distance from the ground involves a transition from the moist region to the dry region, the conductivity decreases. Therefore, specific environmental and soil conditions, as well as specific grounding in place, can impact the relationship between electrical conductivity and distance from the ground.
Fig.11: Dependence of Magnetic Induction along the length
of electrode at different time points
Fig. 11 shows propagation of magnetic field along the length of the electrode. the colored lines in this figure shows the wave propagation first three time points. At a certain time, the wave covers the whole length of the electrode [5 m].
Fig.12: Dependence of electric field strength
on electrode length at different time points.
Fig. 12 illustrates the propagation of an electric field along the length of the electrode. If we compare figs. 11 and 12, there is a similarity between these two plots: the distribution of magnetic field and electric field along the length of the electrode. Only the values between these two sets of plots are different.
Fig.13: Current in the grounder for different dielectric
permittivity values(simple [ε] electrolytic [ εe])
In Fig. 13, the changes in the electrical current are shown for both simple and electrolytic electrodes. These currents are the results of various values of relative dielectric permittivity in the surrounding medium, considering the constant value of resistivity. This comparison shows a significantly higher value of current flowing through the electrolytic electrode compared to the simple one.
Similarly, we change the resistivity value in the range of 500 to 5000 Ω·m while keeping a constant value of 25 for the relative permittivity. The results of currents flowing through each type of electrode are shown in fig.14:
Fig.14: Comparison of the Current through simple and electrolytic
electrodes for different values of resistivity of the soil.
In fig.14, the electrical current in simple and electrolytic electrodes under the influence of resistivity is displayed. By comparing the flow of current in each electrode, we can observe a significantly higher value in the electrolytic electrode compared to the simple electrode.
A welldesigned grounding system is very important for the protection of people, equipment, and overall electrical supply networks. Therefore, each electrical system must be earthed in order to dissipate the fault current into the ground and prevent damage to equipment and people nearby. The value of earthing resistance is directly proportional to the type of earthing electrode and soil resistivity. By selecting earthing electrode with good conductivity and placing it in good soil, the resistivity of the earth will be reduced, and the grounding system will function more effectively.
In this paper, the modeling and performance of simple and electrolytic ground electrodes under lightning effects have been analyzed. The simulation and evaluation of the performance these electrodes have been carried out in COMSOL Multiphysics. This paper commenced with a literature review that gives a comprehensive overview of lightning and the characteristics of simple and electrolytic ground electrodes. This review provides the foundations for further simulations and analysis in the next sections of the paper.
The subsequent sections focused on studying the functionality of a simple vertical electrode. The performance of the electrode under lightning impact for different values of dielectric permittivity and soil resistivity has been analyzed. The values of current under each condition have been found and compared in following tables:
Table 5: Maximum electrical current in ground electrode for different [εr] 

Eps 
Rho (Ω*m) 
Electrode Length[m] 
Peak current in a simple electrode(A) 
Peak current in the electrolytic electrode(A) 
25 
5,000 
5 
659.69 
2782.2 
18 
5,000 
5 
489.37 
2257.4 
14 
5,000 
5 
390.41 
1895.8 
9 
5,000 
5 
258.72 
1435.4 
4 
5,000 
5 
217.5 
1335.3 
1 
5,000 
5 
216.84 
1329.7 
Table 6: Maximum electrical current in ground electrode for different [εr] 

Eps 
Rho (Ω*m) 
Electrode Length[m] 
Peak current insimple electrode(A) 
Peak current in electrolytic electrode(A) 
25 
5,000 
5 
289.01 
2403.3 
25 
4,000 
5 
293.62 
2474.5 
25 
2,500 
5 
435.45 
2825.5 
As a result of comparison in table 5 and 6, the electrolytic electrode allows more current to flow to ground, creating a path with lower resistivity. Therefore, it is recommended to implement electrolytic behavior of the electrodes, especially in high resistance areas.
The findings of this paper can help researchers optimize the design of grounding, enhance the reliability and safety of electrical systems under lightning impact, and provide more effective lightning protection strategies for various applications.
Ссылка для цитирования:
Shahwali Amani MODELING OF SIMPLE AND ELECTROLYTIC GROUNDING ELECTRODES UNDER LIGHTNING IMPACT // Вестник науки №5 (74) том 2. С. 1101  1120. 2024 г. ISSN 27128849 // Электронный ресурс: https://www.вестникнауки.рф/article/14504 (дата обращения: 05.11.2024 г.)
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