introduction on grounding design

8/12/2019 Introduction on Grounding Design

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Grounding Grid Design

Introduction

Since the early days of the electric power industry, the safety of personnel in and around electric power

installations has been a primary concern. With ever increasing short-circuit powers and, thus, fault current

levels in today typically interconnected power systems; there is a suitable renewed emphasis on safety.

The safety of people may be compromised by the rise in the ground potential of grounded structures

during unbalanced electric power faults. In such conditions, humans touching grounded structures can be

subjected to high voltages. Safe operation of electrical instalments calls for a properly designed and

installed earthing and grounding system, in order to ensure that the magnitude and duration of the electric

current conducted through body are not sufficient to cause ventricular fibrillation.

In general terms, and for substations in particular, a proper grounding path of low impedance ensures low

potential rise and also a fast clearing time for faults (a fault remaining for long within a system may cause

several critical issues, including those related with power system stability. Thus, faster clearing improves

overall reliability, more than ensures better safety, because any person coming into contact with available

metallic parts and/or metallic enclosures is exposed to higher risk increasing potentials and fault durations).

In the following we will try to summarize grounding system design procedures for safety start with a very

simplified coverage of the basic principles in grounding design, followed by some focus on main aspect of

the design procedure which cant be treated comprehensively.

The main points in grounding system design are:

The characteristics of a grounding system

A well-designed grounding system, shall ensure reliable performance of installations over their whole

service life.

The electrical installation grounding system is an essential part of the overall electrical system. By the

proper grounding calculation and design for electrical installations the following results can be achieved:

-

Determine the minimum size of the grounding conductors required for the primary (and secondary)grounding system, which provide a way for conducting electric current towards the earth without

exceeding the operating limits of equipment

- Guarantee that human and animal beings in the vicinity of grounded facilities are surrounded by asafe environment, ensuring that the design is appropriate to prevent dangerous potentials

A grounding system includes all of the interconnected grounding facilities in the electrical installations area,

including the ground grid, overhead ground wires, neutral conductors, underground cables and their

shields if present, equipment cabinets and enclosures, foundations and structural steel, etc.

The ground grid consists of horizontal interconnected bare conductors (mat) and ground rods. The design

of the ground grid to control voltage levels to safe values should consider the total grounding system toprovide a safe system at an economical cost.


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Safe grounding requires the interaction of two grounding systems:

- The intentional ground, consisting of grounding systems buried at some depth below the earth'ssurface;

- The accidental ground, temporarily established by a person exposed to a potential gradient in thevicinity of a grounded facility

A low substation ground resistance is not, in itself, a safety guarantee. There is no automatic relation

between the resistance of the grounding system as a whole and the maximum shock current to which a

person might be exposed. An electrical installation with relatively low ground resistance might be

dangerous, while, another substation, with very high ground resistance, might be safe or could be made

safe by a careful design and the right precautions.

During typical unbalanced ground fault conditions the maximum potential gradients along the earth surface

may be of sufficient magnitude to endanger a person within the area. Moreover, hazardous voltages may

develop between grounded structures or equipment frames and the nearby earth.

To provide a safe condition for personnel within and around the substation area, the grounding system

design limits the potential difference a person can come in contact with to safe levels.

Potential can be essentially reduced by an equipotential wire mesh safety mat installed below ground level.

This mesh will have to be installed in particular in the nearness of any equipment people might touch, and

connected to the ground grid. Such an equipotential mesh will equalize the voltage along peoples path and

between equipment and their feet. To ensure continuity across the mesh, interconnections between

sections of mesh and between the mesh and the main grounding grid should be made so as to provide a

permanent low-resistance reliable high-integrity connection.

The ground grid design has to limit the voltages, which produce the body current, to a safe level in order to

ensure the current circulating in the human body is lower than the tolerable value, to ensure the grounding

system is reliable and durable, it can resist melting and mechanical deterioration under the most adverse

fault conditions, and it is able to maintain its function during the whole installation service life.

The main reference for determining the safe conditions is IEEE Std. 80, IEEE Guide for Safety in AC

Substation Grounding, which provides general information about substation grounding, the main

definitions and the simplified design equations necessary to calculate a substation grounding system.

While the calculation formulae described in IEEE std 80 for the grounding system, in particular aboutground resistance, can be substituted by computer based complex algorithm (which will be the main object

of the next pages), which can be able to consider very special conditions for soil model, grid geometry and

size, rods distribution, spacing and orientation; the permissible and safe value, as explained and obtained

by the IEEE std 80 methodology, are a wide-spreading reference.

In particular, the guide's calculation of safe values is based on the permissible body current which can

interest the human body when a person becomes part of an accidental ground circuit.

Only for the sake of clearness and without entering in deep detail, at least, the following points shall be

matched to ensure a reliable, safe and trouble-free grounding system:


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Needed information: input data

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

- Layout of the electrical installation-

Maximum fault current flowing into the grounding system- Maximum fault clearing time- Ambient (and/or soil) temperature at the site- Soil characterization (i.e. including soil testing methods, measurements on site and data

interpretation for soil model implementation)

- Resistivity of any surface layers intended to be laid- data concerning existing earthing systems- data concerning nearby existing infrastructures (pipes, fences, buildings, etc.)- critical points of exposure

Typical results: output data

- grounding system design- grounding system list of materials- if needed, individuation of possible options for controlling ground resistance and touch, and step

voltages

- if needed, evaluation of the influence of new grounding systems on existing infrastructures andprecautions and measures to limit transfered voltages to safe levels.

Main definitions

Ground potential rise (GPR): The maximum electrical potential that a substation grounding grid may attain

relative to a distant grounding point assumed to be at the potential of remote earth. GPR is the product of

the magnitude of the grid current, the portion of the fault current conducted to earth by the grounding

system, and the ground grid resistance.

Step voltage: The difference in surface potential experienced by a person bridging a distance of 1 m with

the feet without contacting any other grounded object.

Touch voltage: The potential difference between the ground potential rise (GPR) and the surface potential

at the point where a person is standing while at the same time having a hand in contact with a grounded

structure.

Mesh voltage: The maximum touch voltage within a mesh of a ground grid.

Metal-to-metal touch voltage: The difference in potential between metallic objects or structures within the

substation site that can be bridged by direct hand-to-hand or hand-to-feet contact. Note: The metal-to-

metal touch voltage between metallic objects or structures bonded to the ground grid is assumed to be

negligible in conventional substations. However, the metal-to-metal touch voltage between metallicobjects or structures bonded to the ground grid and metallic objects inside the substation site but not

bonded to the ground grid, such as an isolated fence, may be substantial. In the case of gas-insulated


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substations, the metal-to-metal touch voltage between metallic objects or structures bonded to the ground

grid may be substantial because of internal faults or induced currents in the enclosures.

Transferred voltage: this is a particular case of the touch voltage. A voltage is transferred into or out of the

substation, from or to a remote point external to the substation site. The maximum voltage of any

accidental circuit must not exceed the limit that would produce a current flow through the body that couldcause fibrillation.

Permissible body current limits

The duration, magnitude, and frequency of the current affect the human body as the current passes

through it. The most dangerous impact on the body is a heart condition known as ventricular fibrillation, a

stoppage of the heart resulting in immediate loss of blood circulation. Humans are very susceptible to the

effects of electric currents at 50 and 60 Hz. The most common physiological effects as the current increases

are perception, muscular contraction, unconsciousness, fibrillation, respiratory nerve blockage, and

burning. The threshold of perception, the detection of a slight tingling sensation, is generally recognized as

1 mA. The let-go current, the ability to control the muscles and release the source of current, is recognized

as between 1 mA and 6 mA. The loss of muscular control may be caused by 9 mA to 25 mA, making it

impossible to release the source of current. At slightly higher currents, breathing may become very difficult,

caused by the muscular contractions of the chest muscles. Although very painful, these levels of current do

not cause permanent damage to the body. The magnitude of ac electric current (at 50Hz or 60Hz) that a

human body can withstand is typically in the range of 60 to 100mA, when ventricular fibrillation and heart

stoppage can occur. The only way to restore the normal heartbeat in case of heart fibrillation is through

another controlled electric shock, called defibrillation. Considering such risk, permissible body currentdetermination according IEEE Guides emphasizes the importance of fibrillation threshold and the Guide

itself adopts as a reference the shock energy that can be statistically survived by 99.5% of persons weighing

approximately 50 kg. Where females are expected to be on site, the suitable option is to choose 50kg as the

reference body weight. On the contrary, users of IEEE guide can adopt the permissible values tolerable by a

body weighing 70 kg, which is a more common value for male adults. The choice of body weight (50kg or

70kg) depends on the expected weight of the personnel at the site and the accessibility by the public.

The substation grounding system design should limit the electric current flow through the body to a

standard value, assumed below the fibrillation current.

Soil Resistivity

The resistivity properties of the soil where the earthing grid will be laid is an important factor in

determining the earthing grid's resistance with respect to remote earth. The soil resistivity and the

structure of the soil have significant effects on the GPR Soils with lower resistivity lead to lower overall grid

resistances and potentially smaller earthing grid configurations can be designed (i.e. that comply with safe

step and touch potentials).

It is good practice to perform soil resistivity tests on the site. There are a few standard methods formeasuring soil resistivity (e.g. Wenner four-pin method). A good discussion on the interpretation of soil

resistivity test measurements is found in IEEE Std 80 Section 13.4. Particular care when performing soil
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resistivity tests has to be taken about interference caused by possible in-ground metallic services and

objects such as underground cables, water supply pipes, drainage pipes, sewerage pipes, and building and

machinery foundation piles. Buried services may also provide an unintended conductive path for transfer

potentials.At any rate, geotechnical data identifying soil/rock types and depths also provides a useful cross

check when interpreting test results.

Yet, sometimes, to conduct soil resistivity tests isn't possible and an estimation must be adopted. When

estimating soil resistivity, one should choose on the side of caution and select a higher resistivity. IEEE Std

80 Table 8 gives some guidance on range of soil resistivities based on the general characteristics of the soil.

Measured soil resistivity data may need to be adjusted for seasonal variation or test limitations, based

upon additional data gathered and engineering experience, when deciding upon a resistivity model to use

in each part of the earthing system design analysis. Computer software or other calculation methods

should be used to convert the test data or bibliography data to a model which represents the actual soil

structure.

Highly non-uniform soil conditions may be encountered. Such soil conditions may require the use of

multilayer modeling techniques if an equivalent two-layer soil model is not feasible. A multilayer soil model

may include several horizontal or vertical layers. Again, specific computer software can be adopted to

interpret highly non-uniform soil resistivity. In fact, the equations that govern the performance of a

grounding system buried in multilayer soil can be obtained by solving Laplaces equations for a point

current source, or by the method of images, which gives identical results. The use of either method in

determining the earth potential caused by a point current source results in an infinite series of terms

representing the contributions of each consequent image of the point current source, which today can be

normally handled by consumer level computing machines provided with the right software.

Areas characterized by very high soil resistivity need special consideration (even considering the cases in

which ground resistivity may significantly vary during the annual weather cycle. Common approaches to

take care of this problem are:

o to use deep driven ground rods so that they are in contact with the soil zone deep enoughto remain unaffected by surface climate conditions;

o to treat the soil around ground rods with chemical substances which may absorb/vary soilmoisture;

o Use of chemical rods


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The importance of High Speed Fault Clearing

The duration of an electric shock also contributes to the risk of mortality, so the speed at which faults are

cleared is also vital. Given this, we need to prescribe maximum tolerable limits for touch and step voltagesthat do not lead to lethal shocks.

Allowable body current ; where: is the rms magnitude of the current through the body, in Ampere; is the duration of the current exposure, in seconds

, where

is the empirical constant related to the electric shock energy tolerated by a certain

percent (99.5 %) of a given population.

for persons weighting approximately 50 kg while

for a body weight of 70 kg.Assuming precautionary a body weight of 50 kg, the tolerable body current, for time in the range from0.03 s to 3.0 s is

Considering the significance of fault duration both in terms of equations and implicitly as an accident-

exposure factor, high-speed clearing of ground faults is advantageous for two reasons:

- The probability of exposure to electric shock is greatly reduced by fast fault clearing time, incontrast to situations in which fault currents could persist for several minutes or possibly hours.

- Both tests and experience show that the chance of severe injury or death is greatly reduced if theduration of a current How through the body is very brief.

The allowed current value may therefore be based on the clearing time of primary protective devices, or

that of the backup protection. A good case could be made for using the primary clearing time because of

the low combined probability that relay malfunctions will coincide with all other adverse factors necessary

for an accident. An additional incentive to use switching times less than 0.5 s results from scientific

researches providing evidence that a human heart becomes increasingly susceptible to ventricular

fibrillation when the time of exposure to current is approaching the heartbeat period, but that the danger

is much smaller if the time of exposure to current is in the region of 0.06 to 0.3 sec. In reality, high ground

gradients from faults are usually infrequent, and shocks from this cause are even more uncommon.

Furthermore, both events are often of very short duration. Thus, it would not be practical to design against

shocks that are merely painful and cause no serious injury, i.e., for currents below the fibrillation threshold.

Accidental Ground Circuit conditions and step and touch voltage criteria

When electricity is remotely generated and there are no return paths for earth faults other than the earthitself, then, there is a risk that earth faults can cause voltage gradients (called ground potential rises) near

the site of the fault which can be dangerous. There are two conditions that a person within or around the


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substation can experience that can cause them to become part of the ground circuit. Step voltage (the

voltage difference between a persons feet and is caused by the voltage gradient in the soil at the point

where a fault current enters the earth) and touch voltage (the fault current being discharged to the earth

by the substation grounding system and a person touching a grounded metallic structure). Touch potential

represents the same basic hazard than step voltage, except the potential exists between the persons hand

and feet. This happens when a person standing on the ground touches a structure, an enclosure or a

metallic mass which is involved in conducting the fault current to the ground. Since the current likely path

within the human body runs through the arm and heart region instead of through the lower extremities,

the danger of serious injury or death is far greater in the case of hand-feet potential. For this reason, the

safe limit of touch potential is usually lower than that of step potential.

The grounding system can be used to dissipate fault currents to remote earth and reduce the voltage

gradients in the earth. The touch and step potential calculations are performed in order to assess whether

the earthing grid can dissipate the fault currents so that dangerous touch and step voltages cannot exist.

The Thevenin voltage is the voltage between terminals H and F when the person is not present. TheThevenin impedance is the impedance of the system as seen from points H and F with voltage sourcesof the system short circuited. The current through the body of a person coming in contact with H and Fis given by:

The human body resistance is, by convention, assumed equal to 1000 (Eq. (10) IEEE Std. 80-20007.1). Hand and foot contact resistances are equal to zero. Gloves and shoes resistances are assumed

equal to zero during design calculations.

Moreover, according IEEE Guide, assuming the ground resistance of one foot (with presence of thesubstation grounding system ignored) expressed in , the following conservative formulas for the Thevenin

equivalent impedance , are used.For touch voltage accidental circuit: And for the step voltage accidental circuit: Traditionally, for the purpose of circuit analysis, the human foot is usually represented as a conducting

metallic disc and, the contact resistance of shoes, socks, etc., is neglected. Moreover the metallic discrepresenting the foot traditionally is taken as a circular plate with a radius of 0.08 m. And, assuming ahomogeneous earth of resistivity equal to and adopting the formula for expressing the ground resistanceof one foot in terms of the following formula are available: And, thus, with only slight approximation, for touch voltage accidental circuit

And for step voltage accidental circuit


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Assuming or applying the presence of a thin layer (0.08m - 0.15m) of high resistivity material (such as

gravel, blue metal, crushed rock, etc) over the surface of the ground is commonly used to help protect

against dangerous touch and step voltages. This is because the surface layer material increases the contactresistance between the soil (i.e. earth) and the feet of a person standing on it, thereby lowering the current

flowing through the person in the event of a fault.

IEEE Std 80 Table 7 gives typical values for surface layer material resistivity in dry and wet conditions.

Effect of surface Layer Materials

Applying a thin layer (0.08m - 0.15m) of high resistivity material (such as gravel or crushed rock) over the

site surface of ground, where applicable, is commonly used, because the surface layer material increases

the contact resistance between the soil (i.e. earth) and the feet of the person standing on it, thereby

lowering the current flowing through the person in the event of fault. IEEE Std 80 Table 7 gives typical

values for surface layer material resistivity in dry and wet conditions.


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The actual ground resistance of a foot standing on a thin surface layer is not the same as the surface layer

resistance, because the layer is not thick enough to have uniform resistivity in all directions. Thus, a surface

layer derating factor needs to be applied in order to compute the foot ground resistance in the presence of

a finite thickness of surface layer material. This derating factor can be exactly calculated adopting complex

algorithm or computer based tools or even approximated by an empirical formula as per IEEE Std 80

Equation 27:

Where is the surface layer derating factor, is the soil resistivity (m), is the resistivity of thesurface layer material (m) and is the thickness of the surface layer (m).Maximum allowable touch and step voltages

Adopting the derating factor when calculating the maximum allowable touch and step voltages, allowscalculating the maximum tolerable voltages for step and touch scenarios, with IEEE Std Section 8.3 for body

weights of 50kg and 70kg:

Touch voltage limit - the maximum potential difference between the surface potential and the potential of

an earthed conducting structure during a fault (due to ground potential rise):

Step voltage limit - is the maximum difference in surface potential experience by a person bridging a

distance of 1m with the feet without contact to any earthed object:

Where: is the touch voltage limit (V); is the step voltage limit (V); is the derating factor,resistivity of the surface material (m) and is the duration of shock current (s)

If no protective surface layer is used, then Cs =1 and s = .

Maximum Grid Current

The maximum grid current is the worst case earth fault current that would flow via the earthing grid back

to remote earth. In most cases, the largest value of grid current will result in the most hazardous condition.


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For these cases, the following steps are involved in determining the correct design value of maximum grid

current for use in grounding calculations:a) Assess the type and location of those ground faults that are likely to produce the greatest flow of current

between the grounding grid and surrounding earth, and hence the greatest GPR and largest local surface

potential gradients in the substation area.

b) Determine, by computation, the fault current division factor Sf for the faults selected, and establish the

corresponding values of symmetrical grid current Ig.

c) For each fault, based on its duration time, tf, determine the value of decrement factor Df to allow for the

effects of asymmetry of the fault current wave.

d) Select the largest product Df Ig, and hence the worst fault condition.

Current Division Factor

Not all of the earth fault current will flow back through remote earth. A portion of the earth fault current

may have local return paths (e.g. local generation) or there could be alternative return paths other than

remote earth (e.g. overhead earth return cables, buried pipes and cables, etc). is the zero-sequence faultcurrent, expressed in Amperes. A current division factor must be applied to account for the proportionof the fault current flowing back through remote earth. Computing the current division factor is a task that

is specific to each project and the fault location and it may incorporate some subjectivity (i.e. "engineeing

judgement"). In the most conservative case, a current division factor of

can be applied, meaning

that 100% of earth fault current flows back through remote earth. The symmetrical grid current iscalculated by: Decrement Factor

The symmetrical grid current is not the maximum grid current because of asymmetry in short circuits,

namely a DC current offset. This is captured by the decrement factor, which can be calculated adopting

IEEE Std 80 Equation 79, the decrement factor is : Where is the duration of the fault (s) and is the DC time offset constant, which is derived from IEEEStd 80 Equation 74:

Where: is the reactance/resistance ratio at the fault location andis the system frequency (Hz).


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The maximum grid current is lastly calculated by: Correct grounding conductors sizing and dimensioning with respect to thermal strength,

Each element of the grounding system, including grid conductors, connections, connecting leads, and all

primary electrodes, should be so designed that for the expected design life of the installation, each

element:

a) will have sufficient conductivity, so that it will not contribute substantially to local voltage differences;

b) will resist fusing and mechanical deterioration under the most adverse combination of a fault

magnitude and duration;

c) will be mechanically reliable and rugged to a high degree;

d) will be able to maintain its function even when exposed to corrosion or physical abuse;

Both in MV and HV electrical subsystems, especially where source and load are far from each other and

connected through overhead lines, it often happens that ground fault current may not have a metallic path

for returning to the source and it has to flow through the earth. Thus grounding sysstem have to carry this

current to or from the groundmass. The fault current values and the fault duration (which is assumed

according with the setting of the protective relays/circuit-breaking devices, which will operate to clear the

fault) are the main aspect which govern the conductor selection. Determining the minimum allowable size

of the earthing grid conductors is necessary to ensure that the earthing grid will be able to correctly

withstand the maximum earth fault current. Like a normal conductor under fault, the earthing grid

conductors experience an adiabatic short circuit temperature rise. However, unlike a fault on a normal

cable, where the limiting temperature is that which would cause permanent damage to the cable's

insulation, the temperature limit for bare grounding grid conductors is the melting point of the conductor

it-self. The minimum conductor size capable of withstanding the adiabatic temperature rise associated with

an earth fault is given by re-arranging IEEE Std 80 Equation 37:

Where is the minimum cross-sectional area of the grounding grid conductor (mm), is themaximum energy related to the earth fault (As), is the maximum allowable (fusing) temperature (C),is the ambient temperature (C), is the thermal coefficient of resistivity at ) and isthe resistivity of the earthing conductor at ( ). While is obtained with the formula:

is the thermal capacity of the conductor per unit volume . The material constants Tm,r, r and TCAP for common conductor materials can be found in IEEE Std 80 Table 1.


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As described in IEEE Std 80 Section 11.3.1.1, there are alternative methods to formulate the equation for

determining the minimum cross sectional area of grounding conductors, all of which can also be derivedfromfirst principles.There are also additional factors that should be considered (e.g. taking into account

future growth in fault levels), as discussed in IEEE Std 80 Section 11.3.3.

It is very obvious that connections between conductors and the main grid and between the grid and ground

rods are as important as the ground conductors themselves in maintaining a permanent low-resistance

path to ground. Thus, two main aspects have to be matched: the type of bond used for the connection of

the conductor in its run, with the ground grid and with the ground rod and temperature limits, which joints

can withstand, even considering that most frequently used grounding connections are mechanical pressure

type. Temperature limits are stated in IEEE Guide 837 for different types of joints based on the joint

resistance normally obtainable with each type. Exceeding temperature limits during the flow of the faultcurrents may result in permanent damage to the joint and cause the increasing of joint resistance, which

will result in further overheating. The joint will ultimately fail and result in grounding system degradation or
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total loss of ground reference with critical results.

Particular attention has to be dedicated to grounding of fences, in the proximity of switched and surge

arrestors (which have to be grounded properly), along cable trays if metallic, and for any possible live part.

There are other elements of substation grounding system design that have not been discussed in the

present paper. These elements include the refinement of the design, the effects of directly buried pipesand cables, special areas of concern including control and power-cable grounding, surge arrester

grounding, transferred potentials, and installation considerations.

Several variables influencing design

There are many parameters that may have an effect on the voltages in and around electrical installations

area. Since voltages are site-dependent, it is impossible to design one grounding system that is surely safe

and acceptable for any location. The grid current, fault duration, soil resistivity and soil structure, surface

material, and, moreover, the size and the shape of the grid all have a substantial effect on the voltages

profiles in and around the substation area. If the geometry, location of ground electrodes, local soil

characteristics, and other factors contribute to an excessive potential gradient at the earth surface, the

grounding system may be inadequate from a safety aspect despite its capacity to carry the fault current in

magnitudes and durations permitted by protective relays.

Ground Grid Resistance

Normally, the potential difference between the local earth around the site andremote earth is consideredto be zero (i.e. they are at the same potential). However, during unbalanced earth fault (when the fault

current flows back through remote earth), the flow of current through the earth itself causes local potential

gradients in and around the site. The maximum potential difference between the site and the remote earth

is known as Ground Potential Rise (GPR). A good earthing grid has a low resistance (with respect to remote

earth) to minimize the ground potential rise (GPR) and consequently avoid dangerous touch and step

voltages. Calculating the earthing grid resistance usually goes in parallel with earthing grid design.

The maximum GPR is calculated by:

Where is the maximum ground potential rise (V), is the maximum grid current (A) and is the earthing grid resistance (). It is important to note that this is a maximum potential differenceand that earth potentials around the site will vary as regard as to the point of fault.

The earthing grid resistance mainly depends on the area taken up by the earthing grid and its perimeter,

the total length of buried earthing conductors and the number of earthing rods / electrodes. IEEE Std 80

offers two alternative options for calculating the earthing grid resistance:

1) simplified method (Section 14.2)

2) Schwarz equations (Section 14.3)
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IEEE Std. 80 also includes methods for reducing soil resistivity (in Section 14.5) and a treatment for

concrete-encased earthing electrodes (in Section 14.6).

As a first approximation of the grounding system resistance value in uniform soil can be obtained by means

of the generalization of the formula for a circular metal plate at zero depth:

[ ] is the substation ground resistance in , is the soil resistivity in m, A is the area occupied by theground grid in m, LT is the total buried length of conductors in m, H is the depth of the grid in m

Schwarz in Analytical expression for resistance of grounding systems, AIEE Transactions on Power

Apparatus and Systems, vol. 73, no. 13, part III-B, pp. 10111016, issued in August 1954 developed the

following set of equations to determine the total resistance of a grounding system in a homogeneous soil

consisting of horizontal electrodes (grid) and vertical electrodes (ground rods). Schwarzs equations

extended accepted equations for a straight horizontal wire to represent the ground resistance, R1, of a grid

consisting of crisscrossing conductors, and a sphere embedded in the earth to represent ground rods, R2.

He also introduced an equation for the mutual ground resistance Rm between the grid and rod bed.

is the substation ground resistance in ,

is the ground resistance of the only horizontal conductors

(grid), is the ground resistance of all and only vertical conductors (rods) and is the mutual groundresistance between the horizontal conductors and the vertical ones. ( )

Where, as in the previous formulas is the soil resistivity (assumed uniform) expressed in , isthe total length of connected grid (horizontal) conductors (m), is the length of each vertical rod, is thetotal area covered by conductors , is the number of rods placed within the area, is thediameter of grid conductors , is the diameter of rods , are coefficients depending on the length to width ratio of the involved area , the area itselfand the depth of laying with the respect

.


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When the calculated GPR is lower than both the permissible touch and step voltages, then, the mesh and

step voltage are surely lower than the tolerable limits and the planned earthing grid certainly fulfills its

purpose. When GPR is greater than the tolerable touch voltage further analyses (namely the calculation of

the maximum expected mesh voltage ( ) and step voltage ( ) within the mesh of a earthinggrid as per IEEE Guide Section 16.5) and possible design refining are necessary.

The calculation of mesh voltage is possible by approximated formulation available in the Guide, or can be

obtained by adoption of computer based tool, which allow to consider with less approximation the

geometric characteristics of the grounding grid. Tools exist which simply apply the formulation available in

Guide up to more complex tools which, after the introduction of all the needed inputs, are able to able to

analyze the performance of grounding systems of any shape with a high detail level and provide more than

the values of the earthing grid resistance and GPR, also surface potential, touch and step voltage analysis

over the area of the grid and 2D and 3D perspective potentials views.

Once, in any correct way, the actual expected values of mesh voltage ( ) and step voltage ( )according grid geometry and other hypotheses have been obtained, they have to be compared with the

tolerable maximum touch and step voltages. If both

and

are verified, then the

grid design is safe. On the contrary, design refining is necessary to attain a safe earthing grid.

Possible choice for refining may be:

Redesign the earthing grid to lower the grid resistance (e.g. more grid conductors, more earthingrods, longest earthing rods, greater area, etc. ) and re-compute earthing grid resistance mesh and

step potential calculations.

Limit the total earth fault current or create alternative earth fault return paths Consider soil treatments to lower the resistivity of the soil Greater use of high resistivity surface layer materialsThe length, number and placement of ground rods affect the resistance of the path to earth. One veryeffective way of lowering ground resistance is to drive ground electrodes deeper. Under uniform soil

assumptions, doubling of ground rod length reduces resistance about of 4045% (as the number or length

of rods is increased, the reduction of ground resistance is not in inverse proportion); yet, usually, soil

conditions are not uniform and it is critical to have accurate data available by measuring ground rod

resistance with appropriate instruments. While, increasing the diameter of the ground electrode has

negligible effect in lowering the earth resistance.

For maximum efficiency, grounding rods should be placed no closer together than the length of the rod

itself (each rod forms an electromagnetic shell around it, and when the rods are too close, the ground

currents of the shells interfere with the nearest ones). Yet, for economic reasons, there is a limit to themaximum distance between rods, in fact, greater distances mean greater surfaces needed and greater cost

for additional conductor needed to connect the rods.


16/16

Computer Based Tools

As can be seen from above, touch and step potential calculations can be quite a tedious and laborious task,

and one that could conceivably be done much quicker and safer by computer based tools which areavailable. Even the IEEE Guide Std 80 recommends the use of computer software to calculate grid

resistances, and mesh and step voltages, and also to create potential gradient visualisations of the site.

Several computer software packages can be used to assist in earthing grid design by modeling and

simulation of different earthing grid configurations. The tools either come as standalone packages (CDEGS

or AutoGrid by SES, SafeGrid by Electrotechnik, CYMGRD by CYME Inc. of COOPER Power Systems, ) or plug-

in modules to power system analysis software (such as PTW's GroundMat, ETAP's Ground Grid Design

Assessment, NEPLANs GSA).

Common input data needed:

Electrical data (unbalanced fault current values, data for calculation of earthing current, faultmaximum duration, etc.)

Geometrical data(grounding system layout, grid conductors path and depth, ground rods position,length and orientation, materials adopted, conductor cross-sectional areas, etc. )

Site physical data(soil resistivity, superficial thin layer thickness and resistivity)

Typical output results for software package:

Maximum permissible touch and step voltages Minimum cross-sectional area of grounding conductors Ground grid resistance and Ground Potential Rise (Rg, GPR and also Cs and Df factors)

Typical refinements as regard as the results which could be obtained by analytical simplified approach:

finite element analysisin order to be able to consider grids of any shape (with or without the optionto choice the number of elementary sources to be implemented during calculation, starting from the

input geometry)

Ground potentials and and touch and step voltages distribution within area or along path characterization of soilstarting from measures, and implementation by uniform soil representation

or by double layer model (more than the optional thin surface layer)

simply buried, encased or buried in treated soil electrodes (many software packages give thechance to consider the electrodes simply buried in the soil or also encased in concrete and even

buried in treated soil)

All the above said generalization and refinements for the solution of the problem of safety assessment for

grounding grid would not be possible without the adoption of suitable computer based tools. Moreoversuch software packages give the chance to export tabular and graphical outputs which ease the matter of

calculation description and results interpretation and comprehension.
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introduction on grounding design

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