University of Ljubljana

Faculty of Electrical Engineering

Earth Resistance and Calculation of Earthing

Seminar paper at subject

Distribution and Industrial Systems

Student: Rajne Ilievska

Mentor: Prof. dr. Grega Bizjak

Study year 2017/ 2018

Ljubljana

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Contents

1. Introduction ........................................................................................................................................ 4

1.1 Basic concepts of earthing ............................................................................................................ 4

2. Specific resistance of the soil .............................................................................................................. 6

2.1 Moisture content in the earth soil ................................................................................................ 7

2.2 Temperature of the ground .......................................................................................................... 7

2.3 Salinity of soil ................................................................................................................................ 8

2.4 Compaction of the ground ............................................................................................................ 8

3. Measuring the specific soil resistance ................................................................................................ 9

3.1 Wenner method .......................................................................................................................... 10

3.1.1 Calculation of soil resistivity ................................................................................................ 11

3.2 Schlumberger method ................................................................................................................ 13

3.3 Implementation of the measurement ........................................................................................ 13

4. Interpretation of the results ............................................................................................................. 14

5. Types of earthing .............................................................................................................................. 16

5.1 Materials of the earthing electrodes and application ................................................................ 17

6. Measurement and calculation of earthing ....................................................................................... 17

6.1 Measurement .............................................................................................................................. 17

6.2 Calculation .................................................................................................................................. 21

7. Impulse resistance ............................................................................................................................ 22

8. Conclusion ......................................................................................................................................... 25

9. Questions .......................................................................................................................................... 25

10. Calculation example ........................................................................................................................ 26

References ............................................................................................................................................ 27

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ABSTRACT

In power systems one of the most important aspect is the earthing in order to protect

the people and the equipment in case of an electrical fault. This seminar paper aims to present

a general overview of the main parameters and calculations in an earthing system. In order

to calculate the required parameters, a measurement of the soil resistivity is necessary. In the

first part of the seminar paper is described what is soil resistivity, what affects on it, which

are the characteristic values of the resistivity of different soils, how it is calculated or

measured. The second part of the seminar paper gives information for the types of earthing

electrodes that are used in an earthing system and how the resistance of the earthing

electrode is measured or calculated.

Key words: earthing, soil resistivity, earthing electrodes, measurement, calculation

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1. Introduction

1.1 Basic concepts of earthing

The term earthing in power system refers to a conductive connection between metal

parts of an installation in a building, or power plant, which can under any circumstances be

under voltage, and the earth through an earthing electrode. The main part of an earthing

system is the earthing electrode set in the ground, and its primary task is to conduct the so

called ''current of error'', or current from atmospheric discharge, in such a way that the earth

will not be exposed to voltages that would put people in danger in the immediate

surrounding. In case of large faults in a transformer substation or overhead steel supports,

at the place of error the potential rises, sometimes reaching values of several kilovolts. By

flowing the current through an earthing electrode into the ground the potential of the ground

rises. The ‘earth potential rise’ is highest at the point where current enters the ground and

declines with distance from the source. The shape and spacing of the equipotential lines

around the earthing electrode depends of the shape of earthing electrode, the size of the

current and the specific soil resistivity [3].

When designing an earthing system, two voltages characterise the criteria for safety

around the installation: touch voltage and step voltage. The ‘touch voltage’ is the potential

difference between the earth potential rise on a structure and the surface potential at a point

where a person is standing (normally 1m), whilst at the same time having one or both hands

in contact with the structure. The ‘step voltage’ is the difference in surface potential

experienced by a person bridging a distance of 1m with their feet [4]. The allowed values for

touch voltage and step voltage depending on the duration of the current flow through the

earthing system are defined with technical regulation in each country according to different

standards. Also, there are different values for touch and step voltages depending on the place

where the fault occurs, in or out of the plant [3]. For providing safe operation touch voltage

and step voltage should be lower that the allowed values.

Picture 1 Step voltage and touch voltage

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All the parameters that are important in an earthing system, touch voltage, step

voltage, distribution of the potential, the resistance of the earthing electrode, depend on the

dimension and configuration of the electrode and the specific resistance of the soil where it

is set. The resistance of the earthing is the transient resistance between the earth electrode

and the soil, the resistance of the electrode, the resistance of the conductor that bonds the

objects and the earth electrode, in dependence of the resistance of the soil. It is defined as a

ratio between the potential of the earthing electrode and the current that flows through:

𝑅𝑒 =𝜑

𝐼=

𝑈

𝐼

This resistance is known as resistance to propagation. In addition to this parameter, there is

also impedance Z of an earthing system, that is defined as a parallel impedance of all the

earthing resistances connected in the earthing system including overhead lines, cables, as

well as pipelines and water supply lines that are also connected in the earthing system [1].

In order to calculate the required earthing parameters, it is necessary to measure the soil

resistivity. After the measurements and the calculation of the parameters, the results are

compared to the tolerable voltage limits that should be met.

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2. Specific resistance of the soil

The earth’s soil has an electric property – earth resistance to the flow of electric

current. This property shows how much the soil resists the flow of electricity. It is important

parameter when designing an earthing system. In most of the cases very strict requirements

are set for the characteristics of the earthing parameters: soil resistance, touch voltage, step

voltage when taking the current of the error, so it is necessary that they are calculated as

accurately as possible. The earthing resistance depends from the specific earth resistance of

the soil where the earth electrode is placed. The earth’s soil resistance varies in wide range

of values, depending on the composition of the ground. However, the soil resistance is not a

constant value, it varies depending on the conditions or with depth. The temperature, the

quantity of the water in the pores of the earth, the amount of salts dissolved in the water,

they all have an impact of the values of earth’s soil resistance [1]. In fact, the saline solution

is an electrolyte that fills the space between particles of the earth and conducts the electric

current in the ground. According to this, the soils that have many pores, for example marl and

some types of clays, have small values for the specific earth resistance. On the other hand,

the soils with small amount of pores, such as limestone or dolomites, have high values for the

specific earth resistance. In the table below are given the approximate values of the specific

earth resistance for different types of earth soil.

Table 1 Specific soil resistance for different composition of the soil

Type of environment, composition of the soil

Specific earth resistance – ρ [Ωm]

Sea water 1

Distilled water 10000

Water from river 20 – 40

Wetland 30

Cracked limestone 200 – 2000

Sand 100 – 800

Marl 20 – 300

Clay 100

Humus soil 100

Dolomit 200 – 10000

Concrete 1000000

Granite 600 – 10000

Moist sand 200

Gravel 2000 – 6000

Rocky ground 3000

Sandy clay 50 – 60

Marble >5000

Bentonite 2 – 8

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From the values given in the table it is shown that different composition of the earth affects

its resistance. Among the best conductivity have wetlands, clay and soil with metal content.

Most unfavourable is stone-based soil. However, the soil is usually composed of several layers

with different composition and in rare cases there is homogenous composition.

2.1 Moisture content in the earth soil

Soil moisture changes seasonally and has different content according to the depth. In

the periods when the months are rainy the specific resistance has lower values and in periods

with no rain the values are higher. When the earth is dry it is a weak conductor, or in other

words by reducing moisture content the resistance increases [2]. The states when the earth

is dry or frozen are dangerous because then the specific resistance has the greatest values.

On the figure below is shown the dependence of the specific resistance of the earth from

humidity. As shown, the specific resistance is significantly greater if the relative humidty is

below 15%. For humidity over 15% the specific resistance is much lower and changes in

resistance with change of humidity are milder.

Picture 2 Dependence of the soil resistivity from the moisture content in the soil

2.2 Temperature of the ground

The temperature of the ground is a significant factor affecting the value of the specific

resistance of the earth. At the same level of humidity of the earth with increasing the

temperature the resistance decreases. By freezing the water in earth the resistance increases

significantly. In order to avoid this undesirable occurrence the earthing should be set at depth

at which the earth doesn’t freeze. Picture 3 shows the dependence between the specific

resistance and the temperature with different percentage of water in the earth.

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Picture 3 Dependence of the soil resistivity from temperature and different moisture content

2.3 Salinity of soil

The salinity of soil is another factor that has an impact on the value of the specific

resistance of earth. If the percentage of salt is below 0.5% it doesn’t affect the specific

resistance. If the percentage of salt is between 0.5% and 1% then there is sudden increase of

the conductivity of earth, i.e the specific resistance of earth decreases. For concentrations of

salt above 1% the resistance decreases but slowly and this case is not recommended because

at concentrations of salt above 1% causes corrosion to the metal of the earthing [1].

2.4 Compaction of the ground

The ground changes its charachteristics depending on the pressure on it. The external

pressure reduces the space between particles of the ground and capillary forces rise which

leads to larger amounts of water kept by the soil and thus decreasing of the resistance.

Picture 4 Dependence of the soil resistivity from compaction of the ground

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3. Measuring the specific soil resistance

As it was shown in the previous section, the composition of the ground is not homogenous,

even if the material is the type of environment is the same, there are differences in the value

of the specific soil resistance of different locations, due to for example moisture content or

compaction of the ground. When measuring the specific resistance, not only the resistance

of the soil is measured, but also the thickness of the indivdual layers can be determined. The

specific soil resistance is measured with geoelectrical probing. Geoelectrical probing is a

measurement recording the electrical potential arising when current is input into the ground.

When a single electric current source is used the current flows radially out from the source

and the equipotential surfaces are perpendicular. In case when a set of electrodes is used the

shapes become more complex. In a real situation they will become even more complex since

the resistivity of the ground changes.

Picture 5 Simplified current flow lines and equipotential lines arising from single source

On Picture 5 is shown a single source through which the current flows in the ground. Тhe

equipotential lines have half-spherical shape symmetric in all directions. We consider the

source as a point source and use the mirroring method, analysing a sphere with radius r and

area S=4πr2. In that way the current that is injected in the ground is 2I. The density of the

current is:

𝐽 =2𝐼

4𝜋𝑟2=

𝐼

2𝜋𝑟2

The relation between the density of the current and the electric field strength E is the

conductivity σ of the environment where the source is set, or the resistivity ρ:

𝐽 = 𝜎𝐸 =𝐸

𝜌

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The electric field strength is then:

𝐸 =𝜌 ∙ 𝐼

2𝜋𝑟2

If 𝜑∞ is the potential of the reference earth in infinity and we assume that 𝜑∞ = 0, then the

potential on distance r is:

𝜑𝑟 = 𝜑∞ + ∫ 𝐸(𝑟) ∙ 𝑑𝑟∞

𝑟

= 0 + ∫𝜌𝐼

2𝜋𝑟2𝑑𝑟 =

𝜌𝐼

2𝜋𝑟

∞

𝑟

This equation is later used in calculation of the soil resistivity.

The number of electrodes can be different and electrodes can be placed differently. According

to this there are few possible methods of measuring. Most commonly the methods for

measuring soil resistivity are methods with 3 probes and methods with 4 probes. The most

commonly used methods are the methods with 4 probes such as Wenner method and

Schlumberger method.

Picture 6 Most commonly used configurations of the method with 4 probes. A and B denote current probes, M and N denote potential probes

3.1 Wenner method

The Wenner method (Frank Wenner, USA, 1915) is a method that uses 4 probes: two inner

probes are potential and two outer probes are current probes. They are placed on equal distances a

as it is shown on Picture 7.

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Picture 7 Wenner method

The outer probes are connected to a current source and the inner probes are connected to a

voltmeter for measuring the potential difference between the points of the ground where the

probes are placed. The current source and the measuring devices are usually placed in one

single instrument. This instrument shows the current which flows between current probes

and the voltage between potential probes [2].

3.1.1 Calculation of soil resistivity

If the dimensions of the probes are negligible compared to the distance between them, we

can treat them as points. The potentials of the probes M and N are:

𝜑𝑀 =𝐼 ∙ 𝜌

2𝜋𝑎−

𝐼 ∙ 𝜌

2𝜋2𝑎=

𝐼 ∙ 𝜌

4𝜋𝑎

𝜑𝑁 =𝐼 ∙ 𝜌

2𝜋2𝑎−

𝐼 ∙ 𝜌

2𝜋𝑎= −

𝐼 ∙ 𝜌

4𝜋𝑎

where

ρ is soil resistivity

I is the current which flows through the current probes

a is the distance (spacing) between the probes

The voltage between probes M and N is:

𝑈𝑀𝑁 = 𝜑𝑀 − 𝜑𝑁 =𝐼 ∙ 𝜌

2𝜋𝑎

The soil resistance is then:

𝜌 =𝑈𝑀𝑁

𝐼∙ 2𝜋𝑎

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𝜌 = 𝑅 ∙ 2𝜋𝑎

where

R is the measured value of the resistance with an instrument

This equation is valid when a≥10·b , where b is depth of digging of the probes. If a<10·b , this

means that the probes are placed close to each other on distances less than 3 m, since the

depth is usually 20 to 30 cm [2].

Picture 8 Wenner method for small distances of the probes

In this case, when calculating the soil resistivity, it should be taken into account the depth of

digging b. Here, the probes are also treated as points and the mirroring method is used. Points

A and B are mirrored in A’ and B’ in terms to the boundary ground-air. The boundary is

eliminated and we consider an area with specific soil resistance ρ.

Therefore, the potential in point M is:

𝜑𝑀 =𝐼 ∙ 𝜌

4𝜋(1

𝑎−

1

2𝑎+

1

√𝑎2 + 4𝑏2−

1

√4𝑎2 + 4𝑏2)

and the potential in point N is:

𝜑𝑁 =𝐼 ∙ 𝜌

4𝜋(

1

2𝑎−

1

𝑎+

1

√4𝑎2 + 4𝑏2−

1

√𝑎2 + 4𝑏2)

After arranging of the equations, the equation for calculating soil resistivity for small

measuring distances is obtained:

𝜌 =4𝜋𝑎 ∙ 𝑅

1 +2𝑎

√𝑎2 + 4𝑏2−

2𝑎

√4𝑎2 + 4𝑏2

The measuring is repeated many times for different values of the distance a (1m, 2m, 3m, 5m,

8m, 10m…). Distances larger than 10 m are used when the results from the previous measures

indicate that the soil has extremely non-homogenous structure, or the purpose of measuring

is not only earthing, but also some other calculations [1].

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Disadvantage of the Wenner method is that voltage between the potential probes drops

rapidly over long distances, reaching a value of only a few mV that cannot be registered with

some instruments [2].

3.2 Schlumberger method

With Schlumberger method the potential probes are placed generally in a fixed

position, at the centre of the measurement alignment, while the current probes are placed

symmetrically on the outer sides [5]. Throughout the measurements, only the current probes

are moved further away on a new position allowing the current to flow deeper in the ground.

The potential probes are moved from time to time in case when the signal becomes weak.

Typically, the distance at which current probes are placed is determined on a logarithmic scale

with at least 10 positions per decade [5]. This is an advantage over the Wenner method in

terms of saving both labour and time.

Picture 9 Schlumberger method

If c>>b and d>>b the specific soil resistivity is calculated as:

𝜌 =𝜋 ∙ 𝑐 ∙ (𝑐 + 𝑑)

𝑑𝑅

where

c is distance between potential probes

d is distance between a current and a potential probe

3.3 Implementation of the measurement

When measuring the specific resistivity of the soil it is important how many

measurements will be made and at which places. This depends on the system for which the

earthing design is made. When earthing a transformer station with mesh earthing, the

meaurements are implemented in the nodes of the mesh. In case of earthing a transmission

tower the question is whether to measure at all places where towers are placed along the

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line, or to perform measurements just on a selected number of places. The initial approach is

to perform measurements at two adjacent places. If it is estimated that the resistivity of soil

does not change significantly, then the measurements are performed at specific places, for

example at every third or fifth tower. However, if the environment is extremely changing in

geological structure, measurements have to be performed at each tower place.

4. Interpretation of the results

Probably, the most difficult part of the measurement is the interpretation of the

results. The objective is to find an analytical procedure for the number, the thickness and the

specific resistivity of each layer of the soil. In other words, a soil model has to be defined in

that way that it is approximately a good match of the actual soil, since a perfect match is

unlikely to be derived. Usually the models that are used are the uniform model and the two-

layered model of the ground. Multi-layered models may be used if the conditions are more

complex.

A uniform model is used if there is not a significant variation in the specific resistivity

for various probe spacings. The soil resistivity is calculated as an average value of the

measured data:

𝜌 =𝜌1 + 𝜌2 + ⋯ + 𝜌𝑛

𝑛

However, in most of the cases the soil will not meet the criteria for using this equation.

In general, the soil is never homogenous, most often it has many layers that may be

horizontal, or in some cases vertical. The depth and the specific resistivity of the layers can be

determined with an analytical procedure. It is assumed that the ground is horizontally layered,

usually approximated with a two-layered model. The assumption for a horizontally layered

model is quite ideal, however it is the most acceptable approximation. This model consists of

an upper layer with finite depth h and a lower layer with infinite depth.

Picture 10 Two-layered model of the ground

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In most cases this representation is sufficiently accurate for designing an earthing system. The

specific resistivity of the soil defined with a two-layered model with depth h of the upper layer

and distance a between the probes, is:

𝜌 = 𝜌1[1 + 4 ∙ ∑(

𝑁

𝑛=1

𝑘𝑛

√1 + (2𝑛ℎ𝑎)

2−

𝑘𝑛

√4 + (2𝑛ℎ𝑎)

2)]

where

k is a reflection factor defined as 𝑘 =𝜌2−𝜌1

𝜌2+𝜌1

ρ1 is the soil resistivity of the upper layer

h is depth of the upper layer

In order to determine the parameters ρ1, ρ2, h, the method of smallest squares is used. A new

function F(ρ1, ρ2, h) is defined:

F(𝜌1, 𝜌2, h) = ∑(𝜌𝑎𝑖 − 𝜌𝑖 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)2

𝑁

𝑖=1

Where

ρai is the specific resistivity for different distances a between the probes

ρi measured is the measured specific resistivity for the same distances with Wenner

method.

The function should be minimized by the parameters ρ1, ρ2, h, which means to find the partial

derivatives 𝜕𝐹

𝜕𝜌1= 0

𝜕𝐹

𝜕𝜌2= 0

𝜕𝐹

𝜕ℎ= 0. [2]

Nowadays the calculations are made with numerical methods using a software.

Another property of the ground which is important when designing an earthing

system, specifically for choosing a material for the earthing electrode, is the corrosive

aggressiveness of the soil. It depends on many factors such as structure of the ground,

moisture content, pH values, presence of certain chemicals, aeration, etc. Estimation of the

corrosive aggressiveness of the ground can be given on the basis of the value of specific

resistivity. In general, soil with specific resistivity less than 20 Ωm is highly aggressive whereas

soil with specific resistivity above 60 Ωm is less aggressive [1]. According to analysis it is found

out that in soil such as clay corrosion appears sooner than in soil such as sand and gravel.

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5. Types of earthing

According to the purpose of earthing it can be:

- Protective earthing

- Functional earthing

- Earthing for atmospheric discharge

Protective earthing refers to earthing of all the metal parts of a building that do not belong to

an electric circuit, nor are they found directly in electrical contact with them, and yet, in case

of fault they can come under voltage [1]. The protective earth electrode reduces the voltage

and thus prevents the possibility of occurrence on conditions that are dangerous to the lives

of people who operate with the appliances or equipment affected with the defect, or moving

in their vicinity. Functional earthing refers to earthing of a part of an electric circuit that

provides certain function or performance characteristic of that circuit, such as neutral point

of generators and transformers, neutral conductor, etc [1]. It can be direct or indirect

earthing. Direct earthing is performed by directly connecting to the earthing system, whereas

indirect earthing through some impedance. Earthing for atmospheric discharge refers to

earthing of a lightning installation and serves to drain the current of atmospheric discharge in

the ground.

According to the position in the ground earthing electrodes are divided into:

- Horizontal

- Vertical

Horizontal earthing device is composed of horizontally laid elements (electrodes), which are

in the ground at relatively low depth. The shape of the horizontal earthing device can be

mesh, ring, triangle, rectangular or complex as a combination of some of the mentioned

forms. Vertical earthing device consists of one or more vertical rods in the ground that are

galvanically connected. The length of the rod is usually 2m to 5m, although sometimes when

the lower layers of the soil have small specific resistance, the length can be greater [1]. To

eliminate the danger of too high potential of the vertical electrode it is necessary to perform

the so-called '''shaping of the potential''. This is achieved with additional placement of one or

two rings around the rod.

Picture 11 Example of different types of configurations of earthing electrodes

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5.1 Materials of the earthing electrodes and application

Materials which are most commonly used for the earthing electrodes are galvanized

iron, copper, iron or steel coated with lead or copper and other materials. Earthing electrodes

made of iron are common in practice but they are affected by corrosion, that depends on the

structure of the soil where the electrodes are set. Copper has significantly better

characteristics than iron, but it is an expensive material. In some cases it is given preference

over other materials.

Depending on the configuration, horizontal and vertical earthing electrodes have

different application. When earthing a transmission tower for overhead line most commonly

used is horizontal configuration. Vertical configuration is not common for earthing system of

transmission towers, except in cases when the soil has many layers and deeper layers have

lower value of the resistivity, or the surrounding of the tower is limited and a horizontal

configuration is not feasible. Vertical configuration is mostly used with a mesh earthing of a

transformer substations. Usually they are in shape of a rod with length 2-5m or a specific

shapes like letters “L”, “U” or “T”. [1]

6. Measurement and calculation of earthing

To determine the resistance of the earthing, the distribution of potentials along the

surface and the frequency histograms of touch voltage and step voltage in order to get their

maximum, minimum and average values, there are few approaches:

- Direct measurements

- Model experiments in laboratory

- Calculations

Nowadays, with the development of technology, computer calculations are mostly applied,

while experimental methods are practically out of use. Using mathematical models and

numerical methods results are obtained with very high accuracy.

6.1 Measurement

Direct measurements of the earthing are based on U-I method, using potential and

current probe and autonomous measuring instrument, known as earthing tester. Current is

injected through the earthing that returns to the current probe through the ground, closing

the electric circuit. The current is rising the potential and by shifting of the potential probe on

equal distances, the potential of the earthing is recorded. According to the Ohm’s law the

tester automatically calculates the resistance of the earth electrode. With such an instrument

it is possible to measure also the soil resistivity.

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Picture 12 U-I method for measuring earthing resistance

On Picture 12 is shown the U-I method for measuring the resistance of earthing electrode

Re. The voltage between the earthing electrode and the potential probe is:

𝑈𝐸−𝑃 = 𝜑𝐸 − 𝜑𝑃 = 𝜑𝐸𝐸 − 𝜑𝐸

𝐶 − 𝜑𝑃𝐸 + 𝜑𝑃

𝐶

where

𝜑𝐸𝐸 is the potential of the earthing electrode caused by the current flowing in the

earthing electrode

𝜑𝐸𝐶 is the potential of the earthing electrode caused by the current flowing out of the

current probe

𝜑𝑃𝐸 is the potential of the potential probe caused by the current flowing in the earthing

electrode

𝜑𝑃𝐶 is the potential of the potential probe caused by the current flowing out of the

current probe

The exact value of the resistance of the earthing electrode s measured when:

−𝜑𝐸𝐶 − 𝜑𝑃

𝐸 + 𝜑𝑃𝐶 = 0

−𝜌𝐼

2𝜋𝐿𝑐−

𝜌𝐼

2𝜋𝐿𝑝+

𝜌𝐼

2𝜋(𝐿𝑐 − 𝐿𝑝)= 0

The solution in terms of Lp gives the location of the potential probe which is Lp=0.618·Lc ,

which is known as “61,8%” rule. [2]

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Picture 13 Measured earthing resistance

A common case in practice is an earthing system with many earthing electrodes connected

parallel. In this case it is necessary to measure the total resistance of the system, but also for

every earhing electrode separately, especially if the earthing system is for atmospheric

discharge. The earth electrodes do not have to be disconnected from the system. The

measuring method used in this case is with autonomous measuring instrument and current

clamp, as well as current and potential probes. The clamp is placed around an individual

earthing electrode, in that part of the installation where it is necessary to measure the

resistance. This method is known as a selective method for measuring earth resistance.

Picture 14 Selective method using one clamp

Another possibility of a selective method is with two current clamps and the difference from

the previous method is that here there are no probes used. A known voltage is induce by one

clamp and the other clamp measures the current [6]. This measurement is applied urban

environments where it is not possible to set a potential and current probe.

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Picture 15 Selective method using two clamps

As a specific case it should be mentioned the measurement of the resistance of transmission

towers for overhead lines. Transmission towers are earthed with individual earthing

electrodes under the tower or in the immediate vicinity. There is a shield wire above the

overhead line that is connected with each transmission tower and has galvanic connection

with the individual earthing electrodes. The role of the shield wire is protection of overhead

lines from direct lightning strike. Since all the earthng electrodes are connected through the

shield wire, the measuring of individual resistances becomes difficult. Disconnection of the

shield wire is not taken into account. There are special autonomous measuring instruments

for transmission towers, which measure the resistance of the individual earthing electrodes

without having to disconnect the shield wire. This instrument has source of alternating

current with high frequency up to 150 Hz. The primary task of the earthing of transmission

towers and overhead lines is protection against direct lightning strike. Therefore, to measure

the performance of the earthing relevant parameter is the so-called impulse resistance Ri of

the earthing electrode. The impulse resistance should be also measured with the high

frequency measuring instrument.

Picture 16 Earthing of transmission towers for overhead lines

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6.2 Calculation

When calculating the parameters of the earthing, some empirical formulas are often

used. Depending on the configuration of the earthing there are different equations for

calculating the resistance of earthing.

If the earthing electrode is vertical rod, set in soil with resistvity ρ, then the earth resistance

of propagation is calculated as:

𝑅𝑒 =𝜌

2𝜋𝑙∙ 𝑙𝑛

4𝑙

𝑑

where

l is the length of the rod

d is the diameter of the rod

If the earthing electrode is set horizontally in the ground, the earth resistance of propagation

is calculated as:

𝑅𝑒 =𝜌

𝜋𝑙∙ 𝑙𝑛

𝑙

√ℎ ∙ 𝑑

where

l is the length of the electrode

d is the diameter of the electrode

h is the depth at which the electrode is set

The earthing can be also half-spherical. In this case the earth resistance of propagation is

calculated with the following equation:

𝑅 =𝜌

𝜋 ∙ 𝐷

where

D is the diameter of the sphere

Picture 17 Half-spherical earthing

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These empirical relations are simple, yet sufficiently accurate for simple and quick calculations

of the performance of the earthing system. However, in practice the earthing system is often

more complex in terms of configuration and shape of the earthing electrodes. It can be in a

shape of a ring, triangle, rectangular, star connection of the electrodes etc. All the elements

that the earthng system contains, also the different configuration of the system, affect the

parameters of earthing. For achieving results with greater accuracy it is necessary to use some

numerical method. With a numerical method we assume that the earthing consists of n linear

conductors that are galvanic connected, set in a homogenous soil with known resistivity.

According to this, with using the method of superposition, a system of Maxwell equations is

set, that describes the relation between individual elements of the system. Calculation is

reduced to solving a system of linear equations. By solving them, the parameters of the

earthing are determined. This is also applied for situations when two or more earthing

systems that do not have a galvanic bond are located close enough and affect one to another.

This refers to conductively coupled earthng.

7. Impulse resistance

As it was mentioned previously, under high impulse currents, like the current from

lightning strike, the resistance of the earthing electrode changes. Not only the resistance of

the electrode is changed, but also the resistance of the soil changes.

The impulse resistance of the earthing electrode is defined as:

𝑅𝑖 = 𝛼 ∙ 𝑅𝑒

where

α is factor of impulsiveness

Factor α has higher values for long horizontal earthing electrodes [1].

When lightning strikes, the impulse current that passes through the electrode creates

magnetic flux around the electrode. At the beginning when the change of the current is large,

the inductivity of the earthing electrode prevents the current flowing through the total length

of the earthing electrode. As a result, the current finds ways of flowing through the ground

at the beginnng, not passing the total length. Therefore, the resistance of the earthing

electrode is increased, i.e. the impulse resistance of the earthing electrode is higher than the

resistance in case of low frequency current.

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Picture 18 Variation of earthing resistance of the electrode under impulse discharge

The previous equation can be used for calculating the impulse resistance if the factor α is

known and the standard value of resistance in case of low frequency current. Factor of

impulse is different for different types of earthing electrodes and various empirical equations

exist. Another way of calculating the impulse resistance is with calculation of the active length

of the electrode:

𝑙𝑎 = √𝑇𝑐

𝐿1 ∙ 𝐺1

where

L1 is longitudinal inductance

G1 is longitudinal conductivity

Tc is time constant of change of impulse current

𝐿1 =𝜇0

2𝜋𝑙𝑛

2𝑙

𝑑

𝐺1 =1

𝑅𝑒 ∙ 𝑙

Depending on the time constant, impulse resistance can be calculated as:

𝑅𝑖 =1

𝐺1∙𝑙 if Tc > 1.49·G1·l2

𝑅𝑖 =1.21

√𝐺1∙𝑇𝑐 if Tc ≤ 1.49·G1·l2

where

l is the length of the electrode

In the first case the active length is approximately equal to the total length of the earthing

electrode, which means that the earthing electrode has total share in conducting the current,

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i.e. Ri=Re. In the second case the impulse resistance is larger, which means that in the period

of the impulse the earthng electrode is conducting only with the active length.

On the other hand, under high impulse currents the earth resistance of the soil is

reduced. The high impulsive current establishes a strong electric field in the ground that

causes ionisation of the soil. The reduction of the resistance of the soil is a result of the

ionisation.

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8. Conclusion

This seminar paper shows the basic measurements and calculations that have to be

done when designing an earthing system. Methods for measuring the specific soil resistance

and the resistance of the earthing electrodes were reviewed. One of the most commonly used

methods for measuring the soil resistivity is the Wenner method. Simple formulas were

presented for determination of the resistance. However, for more accurate calculations

nowadays are used numerical methods and computer calculations.

9. Questions

1. What is soil resistance and from which factors depends its value?

Soil resistance is an electric property of earth’s soil that shows how much the soil resists the

flow of electricity. The earth’s soil resistance varies in wide range of values depending on the

composition of the ground. Factors which have an impact on the value of the soil resistance

are: moisture content in the soil, the temperature, the amount of salts dissolved in the water,

the compaction of the ground.

2. Which methods are used for measuring the specific soil resistivity?

The specific soil resistance is measured with geoelectrical probing which is a measurement

recording the electrical potential arising when current is injected into the ground. According

to the number of probes and their placement there are few possible methods of measuring:

method with 2 probes, method with 3 probes, method with 4 probes. Wenner method and

Schlumberger method which are commonly used, are methods with 4 probes, the difference

is in the placement of the probes.

3. Which types of earthing electrodes are used in earthing systems?

Earthing electrodes which are used in earthing systems can be horizontal and vertical.

Horizontal earthing electrodes are laid horizontally in the ground at relatively low depth. The

shape of the horizontal earthing device can be mesh, ring or complex such as half-sphere or

combination of some of the mentioned forms. Vertical earthing electrode is a rod placed in

the ground usually on depth 2 m to 5 m, or sometimes deeper. It can be in shape of letters

''L'', ''U'', ''T'' or similar.

4. How is measured the earthing resistance?

Direct measurements of the earthing are based on U-I method, using potential and current

probe and autonomous measuring instrument, known as earthing tester. The current injected

through the earthing electrode and the current probe, is rising the potential and by shifting

the potential probe on equal distances, the potential of the earthing is recorded. The tester

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automatically calculates the resistance of the earth electrode. In case when the system has

many earthing electrodes for measuring the resistance of the individual electrodes, clamps

are used.

5. How does a high impulsive current affects on the resistance of the earthing electrode and

on the soil resistance?

High impulsive current increases the resistance of the earthing electrode, while the resistance

of the soil is reduced due to ionisation.

10. Calculation example

The specific resistance of the soil is measured with the Wenner method. For distances of the

probes a1=1 m, a2=3 m, a3=5 m and a4=7 m the measured resistances are R1=39 Ω, R2=41 Ω,

R3=78.3 Ω R4=69 Ω respectively. If the probes were set on depth 0.3 m calculate the specific

resistance of the soil for each measurement. What can we conclude for the structure of the

soil based on the results?

a1=1 m R1=39 Ω ρ1=?

a2=3 m R2=41 Ω ρ2=?

a3=5 m R3=78.3 Ω ρ3=?

a4=7 m R4=69 Ω ρ4=?

b=0.3 m

Solution:

In the first measurement the distance between the probes is less than 3 m, i.e a<10·b, the

specific resistance of the soil is calculated as:

𝜌1 =4𝜋𝑎1 ∙ 𝑅1

1 +2𝑎1

√𝑎12 + 4𝑏2

−2𝑎1

√4𝑎12 + 4𝑏2

=4𝜋 ∙ 1 ∙ 39

1 +2 ∙ 1

√12 + 4 ∙ 0.32−

2 ∙ 1

√4 ∙ 12 + 4 ∙ 0.32

= 278.9 Ω𝑚

In all the other measurements the distance between the probes is a≥10·b. The soil resistivity

is then calculated as:

𝜌2 = 𝑅2 ∙ 2𝜋𝑎2 = 41 ∙ 2𝜋 ∙ 3 = 772.8 Ω𝑚

𝜌3 = 𝑅3 ∙ 2𝜋𝑎3 = 78.3 ∙ 2𝜋 ∙ 5 = 2459.9 Ω𝑚

𝜌4 = 𝑅4 ∙ 2𝜋𝑎4 = 69 ∙ 2𝜋 ∙ 7 = 3034.8 Ω𝑚

The results show that the resistance of the soil varies greatly, so we can say that the structure

of the soil is not homogenous.

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References

[1] R. Achkovski, Zazemjuvanje i zazemjuvachki sistemi vo elektroenergetskite mrezi, Skopje, 2008.

[2] V. Dimchev, Merenje vo elektroenergetikata, Skopje, 2014.

[3] H. Požar, Visokonaponska rasklopna postrojenja, Zagreb, 1973.

[4] C.Bayliss, B.Hardy, Transmission and Distribution Electrical Engineering.

[5] Moller, Sorensen & Auken, Geoelectrical methods.

[6] “Earth ground testers,” FLUKE, [Online]. Available: www.fluke.com.