Contents

**What is Electrical Earthing**

Electrical Earthing can be defined as the process of transferring the immediate discharge of the electrical energy directly to the Earth with the help of the low-resistance wire. In previous two post** “Electrical Earthing | Importance of Electrical Earthing | Methods and Types of Earthing“** and **“Measurement of Earth Resistance | Earth Tester“** we have discussed importance, Methods and Measurement of earthing. Now we will learn how to calculate number of earthing electrodes required. Number of earthing electrode and earthing resistance depends on the resistivity of soil and time for fault current to pass through ( 1 sec or 3 sec)

## Permissible values for Earth Resistance

- Major Substation/ Power stations = 0.5 ohm
- Major Substaion / EHT stations = 1 ohm
- Minor Substations / 33 KV Substations = 2 ohm
- Distribution Transformer Structures = 5 ohm
- Tower foot Resistance = 10 ohm
- Neutral Bushing = 2 ohm
- L. T Poles = 5 ohm
- H.T pole = 10 ohm
- Service connection = 4 ohm

**Calculate Earth Resistance of Single Rod, Pipe, Strip or Plate**

- Earth resistance of single Rod as per BS7430 \\\;\\\;\;\;R=\frac{\rho }{2\pi L}\times \left [ log_{e} \left ( \frac{8L}{d} \right )-1\right ]\\\;\\

where \\\rho= Resistivity of soil (ohm meter)\\ L = length of electrode (meter) \\d = Diameter of electrode (meter)

**Example:** Calculate the earth resistance of rod having length of 4 meter and diameter 12.3mm. The resistivity of soil is 500Ωm\\\;\\R = \frac{\rho }{2\pi L}\left [ log_{e}\left ( \frac{8L}{d} \right )-1 \right ]\\\;\\R = \frac{500 }{2\pi \times 4}\left [ log_{e}\left ( \frac{8\times 4}{12.2\times 10^{-3}} \right )-1 \right ] = 136.75 \Omega

- Earth Resistance of single rod or pipe electrode as per IS 3040 \\\;\\R=\frac{100\rho }{2\pi L}\left [ log_{e}\left ( \frac{4L}{d} \right ) \right ]

Where\\ ρ = Resistivity of soil (Ωmeter)\\L = length of Electrode(cm)\\d=diameter of Electrode(cm)

- Resistance of earth strip as per IS 3043 ( in this strip should be buried in the soil)\\\;\\R = \frac{\rho }{2\pi L}\left [ log_{e}\left ( \frac{2L^{2} }{w \times t}\right ) \right ]

Where\\ ρ = resistivity of soil(Ωmeter)\\L = length of strip (m)\\w = width of strip(m)\\t= depth of strip(m)

4. Resistance of single plate electrode as Per IS 3040\\\;\\\;\;\frac{\rho}{A} \times \left(\sqrt{\frac{3.14}{A}}\right)\\\;\\Where \\\rho= Resistivity of soil (Ωmeter) \\A= Area of plate on both side (meter^{2})

**Example:** Calaculate the resistance of Earthing plate of 600 x 600mm, having soil resistivity 100 Ω-meter\Area of Plate (both Side) = 2 x L x B = 2 x 0.600 x 0.600 = 0.72 m^{2}

Resistance of Plate = \frac{\rho}{A} \times \left(\sqrt{\frac{3.14}{A}}\right)\\\;\\Resistance of Plate = \frac{100}{0.72} \times \left(\sqrt{\frac{3.14}{0.72}}\right)=290.045 \Omega

## Calculation of Fault current

The Short circuit fault current “I_{f} ” is calculate by the formula given below \\\;\\ I_{f} = \frac{P \times 100}{ \sqrt[3]{3} \times V_{s} \times Z\%}\\\;\\The short circuit amps obtained from this method ignores the source impedance. If you do have this impedance then use the following equation.\\\;\\ I_{f}=\frac{P\times 100}{\sqrt[3]{3}\times V_{s}\times (Z\%+Z_{s}\%)}\\\;\\

This equation gives more accurate with the result now. However, source impedance is not easily available. This piece of information is typically obtained from the utility serving you. Z_{s}% (source impedance) encompasses the impedance of the entire power system, calculated upto the primary side of the indicated transformer.

Where \\P = rating of Transformer in KVA\\V_{S} = secondary Voltage (V) \\Z% = percentage Impedance of Transformer \\Z_{s} % = percentage Source impedance.

**Example:** A transformer’s nameplate details are 25 kVA, 440V secondary voltage, 5% of percentage impedance, calculate the short circuit fault current.

we know short curcuit fault current is given by\\\;\\ I_{f} = \frac{P \times 100}{ \sqrt[3]{3} \times V_{s} \times Z\%}\\\;\\ \\\;\\ I_{f} = \frac{25 \times 100}{ \sqrt[3]{3} \times 440 \times 5} = 0.787kA\\\;\\

## Calculate Number of earthing elctrodes (pipes/rods/plate) Required

Calculate number of Gi earthing pipes required. The earthing pipe has 100 mm diameter, 3 meter length. system has fault current 50KA for 1 sec (t) and soil resistivity{ρ} is 72.44Ωm.

The various step to calculate number of earthing pipes are

- Maximum allowable current density at the surface of earthing electrode \\\;\\ I = \frac{7.57 \times 1000}{\sqrt{\rho} \times t} A/m^{2}\\\;\\ I = \frac{7.57 \times 1000}{\sqrt{72.44} \times 1} = 889.419\;A/m^{2}\;\;(as Per IS 3043)\\\;\\
- Surface area of earthing electrode having 100 mm diameter and 3 meter length = 2πrl = 2 x 3.14 x 0.05 x 3 = 0.942 m
^{2}. - Maximum current dissipated by one earthing electrode = current density x surface area = 889.419 x 0.942 = 837.833 A
- Number of Earthing pipes required = fault current / maximum current dissipated by one Earthing electrode ( Earthing Pipe) = 50000 / 837.833 = 60
- Thus the Total Number of Earthing pipes required = 60 No’s

## Total Resistance of Group of Earthing Electrodes (Pipes/rods/plates)

From The above Example we need 60 number of earthing pipes. now we will calculate the total resistance of 60 pipes.

Resistance of single earthing pipe = \frac{100\rho }{2\pi L}\left [ log_{e}\left ( \frac{4L}{d} \right ) \right ]\\\;\\ Resistance of single earthing pipe = \frac{100 \times 72.44 }{2\times \pi \times 300 }\left [ log_{e}\left ( \frac{1200}{10} \right ) \right ]= 18. 408

Overall Resistance of 60 pipes = 18.408 / 60 = 0.307 Ω\\If the pipes are connected by a GI Strip having width 12mm, length 2200 meter buried in ground at depth of 200 mm

Resistance of Earth strip (R_{e} ) = \frac{\rho }{2\pi L}\left [ log_{e}\left ( \frac{2L^{2} }{wt}\right ) \right ]\\\;\\. Resistance of Earth Strip (R_{e} ) = \frac{72.44 }{2\pi 2200}\left [ log_{e}\left ( \frac{2\times 2200^{2} }{.012}\right ) \right ] = 0.107 \Omega

Net Earthing Resistance of 60 pipes and earth strip = \frac{0.307 \times 0.107}{0.307 + 0.107}\\\;\\ Net Earthing Resistance of 60 pipes and earth strip = 0.079 Ω

*Note: if GI Plates/rods is used as Earthing Electrode then overall resistance = (Resistance of Single Plate/rod)/(Number of Plates/rods required)*

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