Measurement of Earth Resistence and Resistivity

MEASUREMENT OF EARTH RESISTANCE AND RESISTIVITY

Name Index No Field Group Date of practical Date of submission

: J.A.T. Jayaweera : 090231N : Electrical Engineering : G 06 : -10-2011 : -10-2011

EXPERIMENT: Measurement of earth resistance and resistivity. AIM: a) To determine the earth resistance of an earth electrode b) To determine the resistivity variation of the earth

THEORY

(a) Determination of earth resistance i. earth resistance of an earth electrode(small depth of insertion) Consider an earth electrode of radius r driven vertically into the earth. Assume the depth of insertion is small and that only a hemispherical portion is in contact with the earth as shown below.

r0 x dx

Consider an elemental hemisphere of soil of radius x and thickness dx. Its resistance dR can be expressed as

𝑑𝑅 =

𝜌 × 𝑑𝑥 2 × 𝜋 × 𝑥2

𝑤ℎ𝑒𝑟𝑒 𝜌 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑖𝑙

If the earth is assumed homogeneous the total resistance is given by ∞

𝑅=

∞

𝑑𝑅 = 𝑟0

𝑟0

𝜌𝑑𝑥 𝜌 = 2. 𝜋. 𝑥 2 2𝜋𝑟0

ii. earth resistance of an earth electrode (rod or pipe) Consider an earth electrode of radius r0 driven vertically into the ground to a depth of l. consider a concentric layer of soil of thickness dx at a distance x as shown below. This layer is a thin cylinder above the tip end and is a hemisphere below the tip of the electrode.

l

x

dx

r0

The resistance of this is given by 𝑑𝑅 =

𝜌𝑑𝑥 + 2πxl

2𝜋x 2

From which, the total resistance of the earth electrode is given by ∞

𝑅= 𝑟0

∞

𝜌𝑑𝑥 𝜌 = 2𝜋𝑥(𝑥 + 𝑙) 2𝜋𝑙

𝑟0

1 1 𝜌 𝑟0 + 𝑙 − 𝑑𝑥 = ln⁡ ( ) 𝑥 𝑥+𝑙 2𝜋𝑙 𝑟0

In both cases considered, if the current passes to the earth through the electrode the voltage variation along the surface of the earth is of the form shown below.

Vx

0

iii.

𝑟0

X

Measurement of earth resistance

E0

Vx E

P

C

d

Consider the earth electrode E and current electrode C to be supplied by a source E0 as shown. The voltage difference Vx between the electrode E and the potential electrode P will vary in manner similar to that of the graph shown above near the earth electrode and near the current electrode. Also in the current region, there will be negligible voltage variation. The total variation of voltage along the earth surface is shown in graph (1). From this figure the maximum voltage drop along the earth surface due to electrode E may be assumed equal to E1

Vx

Vx E2

E2

E1

E1

graph (1)

graph (2)

Under these conditions the current driven into the earth through this electrode is I1 and the earth resistance of the electrode is given as R = E1/I1 . Note: The distance between two current carrying electrodes should be sufficiently large in order to obtain full voltage E without any significant error. Otherwise the voltage measured will be less than E1 as shown in graph (2). The resistance areas of the two electrodes should not overlap.

(b) Determination of earth resistivity

I

I r2 r1

A

D B

C r4

X dx

r3

A and D are current electrodes though which the current I is supplied. B and C are potential electrodes across which the potential is measured.

Consider the voltage drop across the thin layer of radius x and thickness dx as shown in figure with voltage across is dV and resistance dR. 𝜌𝑑𝑥 𝑑𝑅 = 2𝜋𝑥 2 The components of the voltage measured are due to the current in A, 𝑟2

𝑉 ′ 𝑏𝑐 =

𝑟2

𝐼𝑑𝑅 = 𝑟1

𝑟1

𝜌𝐼𝑑𝑥 𝜌𝐼 1 1 = ( − ) 2 2𝜋𝑥 2𝜋 𝑟1 𝑟2

Due to the current in D, 𝑟3 ′′

𝑉 𝑏𝑐 =

𝑟3

𝐼𝑑𝑅 = 𝑟4

𝑟4

𝜌𝐼𝑑𝑥 𝜌𝐼 1 1 = ( − ) 2𝜋𝑥 2 2𝜋 𝑟4 𝑟3

So that 𝑉𝑏𝑐 = 𝑉 ′ 𝑏𝑐 + 𝑉 ′′ 𝑏𝑐 =

𝜌𝐼 1 1 1 1 ( − − + ) 2𝜋 𝑟1 𝑟2 𝑟3 𝑟4

Wenner method This particular case of the above analysis where the distance between the electrodes are chosen equal. AB = BC =CD = A, then 𝜌 = 2𝜋. 𝐴. 𝑉𝑏𝑐 /𝐼

Calculations a) Variation of Earth Electrode with Depth of Electrode

Depth of Electrode (m)

Earth Resistance (Ω)

0.2

375

0.4

170

0.6

117

0.8

80

1.0

74

1.2

70

1.4

57

1.6

47

1.8

34

2.0

30

Variation of Earth Resistance with Depth of Electrode 450

400

350

Earth Resistance (Ω)

300

250

200

150

100

50

0 0

0.2

0.4

0.6

0.8

1

1.2

Depth (m)

1.4

1.6

1.8

2

2.2

b) Determination of earth resistivity

Electrode Span A (m)

Potential Electrode Voltage V

Earth Current I (mA)

Resistivity (𝜌) ( Ωm)

10.0

0.4

370

67.926

7.5

0.3

210

67.320

5.0

0.5

200

78.540

3.0

1.5

230

122.932

2.0

5.7

530

135.148

1.5

3.7

300

116.239

Sample calculation Using Wenner method 𝜌 = 2𝜋. 𝐴. 𝑉𝑏𝑐 /𝐼

When A=10 m,

𝜌=

2𝜋 𝑋 10 𝑋 0.4 0.37

= 67.9263 Ωm

Variation of Earth Resistance of Earth Electrode E with position of Potential Electrode P 250

200

Earth Resistance(Ω)

150

100

50

0 0

5

10

15

Distance between earth electrode(m)

20

25

Discussion  What is the importance of studying earth resistance and resistivity? We can basically identify three wiring systems widely used in distribution networks and household applications. Those are TT, TN and IT configurations. Those three required proper grounding method or in other words Earthing system. In order to designing good grounding system it is essential to know the earth resistance and resistivity in the particular area. Furthermore having good understanding about the earth resistance and resistivity improved the reliability of the wiring system, reduce the power factor issues and improve the protection for humans and live stocks. Also it helps to design the most appropriate earth electrode for the particular application.  Why it is important to bring the earth resistance to a desirable value? It is very important to maintain the earth resistance in desirable value due to the following factors  In order to ensure the protection against the faulty situation maintaining the earth resistance in a desirable range is very essential because the grounding systems and fault detection devises are deigned to the particular value range which should cope with the earth resistance.  To reduced the heat dissipated due to fault current and take required precautions( i.e. Selecting the cables)  Limit the voltage due to lightning

In order to cope with the different resistivity levels there are four standard method of grounding the earth electrode. (i.e Single rod method, Multiple rod method, copper plat method and Conductor mesh method ) So it is vital to select most suitable method of grounding the earth electrode.  What is the range that the earth resistance normally lies? Many different factors have a direct effect on the resistivity of the soil. So it is very difficult to define exact range for the earth resistance. Normally it will vary from 1.5 Ωm to the upwards of over 1,000 Ωm. Furthermore we can identify several major factors which affect the soil resistivity.  Moisture content - Moisture content can be a large factor in determining the resistivity of the soil. The soil resistivity remains relatively low (or constant) if the moisture content of the soil is greater than 15%. If lower the moisture contents resistivity of the soil will be higher.  Mineral content - Another large factor in the determination of soil resistivity is the content of minerals, such as salts or other chemicals. For values of 1% (by weight) salt content, the soil resistivity remains low (or constant). If lower the salt contents resistivity of the soil will be higher.  Compactness and temperature - With temperature, the colder the soil is, the higher the resistivity. Due to seasonal changes where the temperature can change drastically for a particular area, the resistivity of the local soil can also change drastically. Also if the compactness of the soil is increased the resistivity of the soil will also increase.

In the university premises where the practical has been conduct the resistivity is vary from 68 Ωm to 135 Ωm.

 Suggestions for reduce the earth resistance In order to reduce the resistivity of soil following methodologies can be followed.    

Lengthen the electrode which enables them to go deeper and if possible reaches the water table. Use copper plate electrode instead of pipe electrode. Use more than one earth electrodes. Treat the soil with some type of ground enhancing material (i.e. Earth gel, GEMTM, salt, chemical rod, etc.)  Terminating radial conductors with vertical electrodes. This measure is more effective in low to medium soil resistivity.