# Earth Electrode Resistance

By on

Earthing of electrical systems is essential for the correct functioning and the protecting of life and equipment in the event of faults. The earth electrode (connection of the earthing system to the ground) is an essential part of any system.

The estimation of electrode resistance and functioning during the design stage ensures workable solutions are proposed, enhances the operation and potentially reduces the cost of any installation.

## General Calculation of Electrode Resistance

Theoretical Example

Sphere of radius r, fully surrounded:

Method  - assume a current I, is injected into an electrode then at some point distant from the electrode, the current density is:

If the resistivity of the ground is r, the electric field is:

By integrating the electric field from the surface of the electrode to infinity, the voltage of the electrode is:

Apparent resistance Rg, can now be found from:

## Resistance and Distance from an Electrode

Resistance Contribution v's Distance
Around an earth electrode the resistance of the soil is the sum of series resistances of virtual shells of earth propagating outward from the electrode. Shells nearest to the electrode have the smallest surface area and hence the largest resistance.

The figure illustrates the contribution of the earth to the total resistance of the electrode at increasing distances from the surface of the electrode. As can be seen from the figure, 67% of the total resistance is accounted for at a distance of 0.3 M from the electrode.

In high resistivity locations, decreasing the resistivity in the area close to the electrode by use of ground enhancing materials  (chemical treatment or the use of concrete) will improve the effectiveness of the earth system.

## Resistance to Ground (Earth)

The following formula (source: IEEE Std.142:1991) enable the resistance to ground to be calculated.

 Hemisphere, radius a One ground rod, length L, radius a Two ground rods, s > L, spacing s Two ground rods, S < L, spacing s Buried horizontal wire, length 2L, depth s/2 Right angle turn of wire, length of arm L, depth s/2 Three point star, length of arm K, depth s/2 Four point star, length of arm L, depth s/2 Six point star, length of arm L, depth s/2 Eight point star, length of arm L, depth s/2 Ring of wire, diameter of ring D, diameter of wire d, depth s/2 Buried horizontal strip, length 2L, section a by b, depth s/2, B < a/8 Buried horizontal round plate, radius a, depth s/2 Buried vertical round plate, radius a, depth s/2

Where:
R - resistance in Ω
ρ - resistivity in Ω.cm
d - distances - in cm

## Multiple Ground Rods

Spacing Factor
No.Rods F
2 1.16
3 1.29
4 1.36
8 1.68
12 1.80
16 1.92
20 2.00
24 2.16

Spaced several rod lengths apart:

Spaced one rod length apart:

## Ground Enhancing Materials

Ground enhancing materials (GEM) is a technique where the ground immediately surrounding an earth electrode is replaced with a low resistance material. The intent is to reduce the earth electrode resistivity. Use of GEM would be in areas where the ground resistivity is very high and problems arise in trying to achieve the required electrode resistance.

## Calculation of Resistance

The resistance, R, expressed in ohms , of a vertical electrode surrounded by an infill of material
is given approximately by the following equation[2]:

Given:
ρ       - resistivity of soil (Ω.m)
ρc     - resistivity of infill material (Ω·m)
d       - diameter of electrode (m)
D       - diameter of infill (m)
L       - length of electrode (m)

### Issues and Concerns

GEM treatment may not be permanent and should be check regularly. This is particularly true of chemical treatment which may leach away into the surrounding soil over time resulting in the earth electrode resistance increasing to unacceptable levels. Some GEM treatments may also have corrosive effects on the earth electrode or other negative environmental consequences.

## References

• [1] IEE Std. 142-1991, Grounding of Industrial and Commercial Power Systems, Institute of Electrical and Electronic Engineers
• [2] BS 7430:1998, Code of Practice for Earthing, British Standards Institute

More interesting Notes:

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

myElectrical Engineering

#### View 1 Comments (old system)

1. Joe says:
7/11/2012 10:13 PM

How would you approximate resistance if you had a four point star but, two ends of the star had ground rods connected?

Comments are closed for this post:
• have a question or need help, please use our Questions Section
• spotted an error or have additional info that you think should be in this post, feel free to Contact Us

Tech Topics/Application Notes - Siemens

There are a lot of interesting two page type notes on various medium voltage topics – switchgear, circuit breakers, bus systems etc. It is on the Siemens...

Reading is a bit of a hobby of mine and I"ve done a few off-topic posts in the past on this. Rather than continue doing the occasional post I thought ...

Getting Started with Patents

If you have a great idea or invent something the last thing you want is someone to steal the idea. One of the things you can do is protect the intellectual...

Capacitor Theory

Capacitors are widely used in electrical engineering for functions such as energy storage, power factor correction, voltage compensation and many others...

IEC 61439 Verification Methods

The (relatively new) switchgear and control gear standard, IEC 61439 'Low-voltage switchgear and controlgear assemblies' has three methods which can be...

Harmonised Cable Codes and Colours

Within Europe the European Committee for Electrotechnical Standardization (CENELEC) has standardised the both the designation and colour of cables.   ...

Induction Motor Calculator

Just added a page to the tools, which will allow you to calculate the synchronous speed, slip and rated torque for an induction motor. Not a particularly...

Introduction to Cathodic Protection

If two dissimilar metals are touching and an external conducting path exists, corrosion of one the metals can take place.  Moisture or other materials...

Cable Trumps

Bored at work and would rather be playing trump card game with you son. The next best thing (or not) maybe the online cable trump card game from AEI Cables...

Voltage Drop in Installations - Concepts

Problems on achieving maximum voltage drop within an installation come up often. Depending where you live, local regulations will have different limits...

## Have some knowledge to share

If you have some expert knowledge or experience, why not consider sharing this with our community.

By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.

To get started and understand our policy, you can read our How to Write an Electrical Note