Calculating a simple earth system

Calculating the cross-section of the ground wire for power stations

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Earthing (grounding) system according to IEC, BS-EN and IEEE standards

Step 1
Good earthing (grounding) system according to IEC/BS EN 62305-3:2011 standard

E.5.4 Earth-termination system
E.5.4.1 General
(…) The LPS designer and the LPS installer should select suitable types of earth electrodes and should locate them at safe distances from entrances and exits of a structure and from the external conductive parts in the soil, such as cables, metal ducts, etc. Hence the LPS designer and the LPS installer should make special provisions for protection against dangerous step voltages in the vicinity of the earth-termination networks if they are installed in areas accessible to the public (see Clause 8).
The recommended value of the overall earth resistance of 10 Ω is fairly conservative in the case of structures in which direct equipotential bonding is applied. The resistance value should be as low as possible in every case but especially in the case of structures endangered by explosive material. Still the most important measure is equipotential bonding.

E.5.4.2.2 Type B arrangement
(…) The type B earth-termination system is preferred for meshed air-termination systems and for LPS with several down-conductors.
This type of arrangement comprises either a ring earth electrode external to the structure, in contact with the soil for at least 80% of its total length, or a foundation earth electrode.

E.5.4.3.2 Foundation earth electrodes
(…) A further problem arises from electrochemical corrosion due to galvanic currents. Steel in concrete has approximately the same galvanic potential in the electrochemical series as copper in soil. Therefore, when steel in concrete is connected to steel in soil, a driving galvanic voltage of approximately 1 V causes a corrosion current to flow through the soil and the wet concrete and dissolve steel in soil.
Earth electrodes in soil should use copper, copper coated steel or stainless steel conductors where these are connected to steel in concrete.

Step 2

Resistivity of soil
Resistivity measurements for good earthing (grounding) system according to IEEE Std 80-2000
(…) A number of measuring techniques are described in detail in IEEE Std 81-1983. The Wenner four-pin method, as shown in Figure below, is the most commonly used technique. In brief, four probes are driven into the earth along a straight line, at equal distances a apart, driven to a depth b. The voltage between the two inner (potential) electrodes is then measured and divided by the current between the two outer (current) electrodes to give a value of resistance R.

Wenner four-pin method
then for b « a:

where

ρa– is the apparent resistivity of the soil in Ωm
– is the measured resistance (R=U/l) in Ω
– is the distance between adjacent electrodes in m
– is the depth of the electrodes in m

Resistivity for types of soil according to IEC 60364-5-54:2011

Nature of ground Resistivity [Ωm]
Marshy ground
Alluvium
Humus
Damp peat
From some units to 30
20 to 100
10 to 150
5 to 100
Malleable clay
Marl and compact clay
Jurassic marl
50
100 to 200
30 to 40
Clayey sand
Siliceous sand
Bare stony soil
Stony soil covered with lawn
50 to 500
200 to 3 000
1 500 to 3 000
300 to 500
Soft limestone
Compact limestone
Cracked limestone
Schist
Mica-schist
100 to 300
1 000 to 5 000
500 to 1 000
50 to 300
800
Granite and sandstone according to weathering
Granite and very altered sandstone
1 500 to 10 000
100 to 600

Step 3
Good conductors and rods for earthing (grounding) system according to IEC/BS EN 62561-2:2012

Material, configuration and cross sectional area of earth electrodes

Material Configuration Cross sectional area a) Recommended dimensions
Copper
coated
steel c)
Solid round ≥ 150 h) 14 mm diameter, if 250 µm minimum radial copper coating, with 99.9% copper content
Solid round ≥ 50 8 mm diameter, if 250 µm minimum radial copper coating, with 99.9% copper content
Solid round ≥ 78 10 mm diameter, if 70 µm minimum radial copper coating, with 99.9% copper content
Solid tape ≥ 90 3 mm thickness, if 70 µm minimum radial copper coating, with 99.9% copper content

a) Manufacturing tolerance – 3%
c) The copper shall be intrinsically bonded to the steel. The coating can be measured using an electronic coating measuring thickness instrument
h) In some countries, the cross sectional area may be reduced to 125 mm²

Step 4

Good cross section of earthing conductors according to IEEE Std 80-2000

11.2.2 Copper-clad steel
(…) Copper-clad steel is usually used for underground rods and occasionally for grounding grids, especially where theft is a problem. Use of copper, or to a lesser degree copper-clad steel, therefore assures that the integrity of an underground network will be maintained for years, so long as the conductors are of an adequate size and not damaged and the soil conditions are not corrosive to the material used.

Calculation of the cross section of earthing conductors based on IEEE standards 80-2000

A – earthing conductor cross section in mm²
I – rms current in kA
TCAP – thermal capacity per unit volume in J/(cm³ °C)
tc – duration of current in s
αr – thermal coefficient of resistivity in 1/°C
ρr – resistivity of the ground conductor in mΩ-cm
Ko – 1/α o or (1/α r) – Tr in °C
Tm – maximum allowable temperature in °C
Ta – ambient temperature in °C

Samples cross section for copper clad conductors with different rms current in kA (I) and duration of current in s (tc)

A)  Φ 8 mm – 50 mm²
B)  Φ 10 mm – 78 mm²
C)  20 x 3 mm – 60 mm²
D)  25 x 3 mm – 75 mm²
E)  30 x 3 mm – 90 mm²
F)  30.5 x 3 mm – 105 mm²
G)  30 x 4 mm – 120 mm²
H)  40 x 4 mm – 160 mm²
I)  40 x 5 mm – 200 mm²

Step 5

In the points from 4A to 4D there are the guidelines to design earthing (grounding) systems to the particular building facilities and structures according to the standards for these facilities.

GROUNDING SYSTEM OF TRANSMISSION LINE TOWER (HV AND MV)
BS EN 50522:2010

Resistance of the tower ground ring:

D = L/π– iameter of the ring in m
L – length of the ring tape in m
– half the width of the tape in m
ρE – soil resistivity in Ωm

Resistance of the grounding rod with depth h:

– length of the grounding rod in m
– diameter of the grounding rod in m
ρE – soil resistivity in Ωm

Resistance of the grounding system:

As the tapes and vertical rods of the external rods’ system are connected with the steel immersed in the stop footing concrete of the antenna tower, they have to made of precious metals, such as copper-bonded steel, stainless steel or solid copper. Copper-bonded steel materials were applied in the presented installation. This allowed to decrease the grounding (earthing) costs by 45% comparing to the stainless steel or solid copper.

POWER STATION (HV and MV)
IEEE Std 80-2000

14.3 Schwarz’s equations
(…) Schwarz developed the following set of equations to determine the total resistance of a grounding system in a homogeneous soil consisting of horizontal (grid) and vertical (rods) electrodes. Schwarz’s 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.
Schwarz used the following equation introduced by Sunde and Rüdenberg to combine the resistance of the grid, rods, and mutual ground resistance to calculate the total system resistance, Rg.

R1 – ground resistance of grid conductors in Ω
R2 – ground resistance of all ground rods in Ω
Rm – mutual ground resistance between the group of grid conductors, R1, and group of ground rods, R2 in Ω

Ground resistance of the grid

ρE – is the soil resistivity in Ωm
Lc – is the total length of all connected grid conductors in m
α ‘- is for conductors buried at depth h in m
2α – is the diameter of conductor in m
– is the area covered by conductors in m2
k1, k2 – are the coefficients [see Figure 1 and 2]

Lr – is the length of each rod in m
2b – is the diameter of rod in m
nR – number of rods placed in area S

A – is the length of the grid, B – is the width of the grid,
A/B – is the length-to-width ratio, h – is the depth of the grounding grid

curve 1 for depth h = 0
y1 = – 0.04x + 1.41
curve 2 for depth 
y2 = – 0.05x + 1.20
curve 3 for depth 
y3 = – 0.05x + 1.13

curve 1 for depth h = 0
y1 = 0.15x + 5.50

curve 2 for depth 
y2 = 0.10x + 4.68

curve 3 for depth 
y3 = – 0.05x + 4.40

As the tapes and vertical rods of the external rods’ system are connected with the steel immersed in the stop footing concrete of the antenna tower, they have to made of precious metals, such as copper-bonded steel, stainless steel or solid copper. Copper-bonded steel materials were applied in the presented installation. This allowed to decrease the grounding (earthing) costs by 45% comparing to the stainless steel or solid copper.

GROUNDING SYSTEM OF LV TRANSMISSION LINE TELECOMMUNICATION TOWERS
HD 60364-5-54

Resistance of the tower ground ring

L – length of the ring tape in m
ρE – soil resistivity in Ωm

Resistance of the grounding rod:

L – length of the grounding rod in m
ρE – soil resistivity in Ωm

Resistance of the grounding system:

As the tapes and vertical rods of the external rods’ system are connected with the steel immersed in the stop footing concrete of the antenna tower, they have to made of precious metals, such as copper-bonded steel, stainless steel or solid copper. Copper-bonded steel materials were applied in the presented installation. This allowed to decrease the grounding (earthing) costs by 45% comparing to the stainless steel or solid copper.

GROUNDING SYSTEM OF HIGH-VOLTAGE LINES WIND TURBINE FACILITIES CONSTRUCTION
(IEC) BS EN 62305-3

E.5.4 Earth termination system
E.5.4.1 General
(…) the LPS designer and the LPS installer should make special provisions for protection against dangerous step voltages in the vicinity of the earth-termination networks if they are installed in areas accessible to the public (see Clause 8).
The recommended value of the overall earth resistance of 10 Ω is fairly conservative in the case of structures in which direct equipotential bonding is applied. The resistance value should be as low as possible in every case but especially in the case of structures endangered by explosive material. Still the most important measure is equipotential bonding.

E.5.4.2 Types of earth electrode arrangements
E.5.4.2.1 Type A arrangement
(…) This type of arrangement comprises horizontal or vertical electrodes connected to each down-conductor.
Where there is a ring conductor, which interconnects the down-conductors, in contact with the soil the earth electrode arrangement is still classified as the type A if the ring conductor is in contact with the soil for less than 80% of its length.

E.5.2.2 Type B arrangement
(…) This type of arrangement comprises either a ring earth electrode external to the structure, in contact with the soil for at least 80% of its total length, or a foundation earth electrode.

For bare soild rock, only the type B earthing arrangement is recommended.

As the tapes and vertical rods of the external rods’ system are connected with the steel immersed in the stop footing concrete of the antenna tower, they have to made of precious metals, such as copper-bonded steel, stainless steel or solid copper. Copper-bonded steel materials were applied in the presented installation. This allowed to decrease the grounding (earthing) costs by 45% comparing to the stainless steel or solid copper.