**An investigation into the effect of varying the installation angle of the earth rod between 0° and 90° for a small substation earth grid.**

Earth rods connected to earth systems are used widely to reduce the resistance of earth electrodes for substations [1], as well as other applications. It appears, however, that earth rods are rarely installed at any angle besides vertically downward. There is little reference in scientific literature to installing earth rods at an angle [2]. Besides soil profile and resistivity, there are other factors that influence the efficacy of the earth rod. The combination of these factors may determine an optimum installation angle for each particular case.

**Background**

The optimum earth rod installation angle would depend primarily on the soil model, i.e. where the favourable soil is located. The soil model is an approximation of the soil structure, given in terms of various horizontal layers and their resistivities.

There are two main aspects that determine how effective an earth rod is:

- The soil profile in terms of the resistivity of the soil in which the earth rod is installed.
- The coupling between the rod and other earthing conductors in proximity.

In this article, we explore the influence of these two factors on the resistance of the electrode to determine if any general practical guidelines can be established for an optimum installation angle.

*Soil resistivity*

The effect of the earth rod in reducing electrode resistance depends on the resistivity and thickness of the soil layers through which the rod passes.

If low resistivity soil resides on the top of the soil structure, the contact with favourable soil can be maintained by applying the earth rod at a shallow angle without penetrating the higher resistivity soil underneath. When the favourable layer is superficial, the application angle will be small, tending towards horizontal.

It has been shown that, for soil models where deeper layers have higher resistivity, installing earth rods at an angle to maintain increased contact with low resistivity soil (rather than vertically downward) is between two and eight times more effective at reducing the electrode resistance [2].

When the high resistivity soil is superficial, the earth rod must be applied vertically down, to have as much contact with good soil underneath as possible.

*The proximity effect*

The coupling between the earth rod and the rest of the earthing system reduces the earth rod efficacy. This coupling is specifically conductive through the soil due to the voltage gradient established by the current density in the soil. Horizontally buried earth rods have the lowest coupling effect with the main earth electrode.

**Methodology**

A simple substation electrode was modelled in the SES Tech CDEGS software package. CDEGS is popular in industry design and research environments to simulate and design earthing systems.

Various parameters such as different soil models and the angle and length of the earth rod were simulated. The model was a symmetrical 40 x 40 m square horizontal earth grid with a 2,5 m square mesh size, buried at 0,5 m, with one earth rod applied at each corner of the grid, as shown in Fig. 1.

The main grid conductors and the earth rods were 10 mm diameter copper round bar (the results are not sensitive to the conductor parameters within typical ranges of dimension and material). The software was used to simulate the injection of a fixed 50 Hz AC current. The software then computed the electrode resistance. The normalised resistance of the overall electrode obtained from the simulations was used to determine the characteristic of varying installation angle for various soil models.

*Earth rod parameters*

The default earth rods were 12 m long. This length was selected as it is towards the upper end of practical earth rod installation using conventional techniques. This length of rod also has an appreciable effect on the resistance of the 40 x 40 m electrode.

The installation angle was modelled at an angle increasing from 0° (horizontal) to 90°(vertical), with an increment of 15°.

*Soil models*

Several simple, two-layer soil models were developed. These models were either high upon low resistivity, or conversely, low upon high resistivity. The top layer of the soil models was simulated at various thicknesses of 1; 2,7 and 5,5 m. The bottom layer is taken to be infinite.

**Proximity effect**

The installation angle was varied in a homogeneous soil structure to isolate the proximity effect. Note that the burial depth of the entire electrode system must be very deep in relation to the electrode dimensions for the proximity effect to dominate the characteristic.

For shallow depths, the results are distorted by the influence of the air above the soil surface, which is assumed to have infinite resistivity. That is, the sectional area of soil surrounding the electrode which is available for conduction increases with increasing depth. The resistance is therefore related to the average burial depth of the electrode.

Fig. 2 demonstrates the combination of proximity effect and the influence of depth. The graph appears counterintuitive as it would seem that the resistance should increase with increasing angle. The characteristic is the combination of two competing factors.

The following comments can be made:

- The minimum resistance is at around 30° but is favourable over a wide range from about 15° to 50°. This is slightly shifted from the range in [2] of 30° to 60°, probably due to the very shallow burial depth of 0,5 m used in this study, as opposed to 0,8 m used in [2].
- For shallow angles, the average burial depth of the rod dominates the characteristic, and the resistance decreases with depth.
- For larger angles, the proximity effect dominates and results in an increase in resistance with depth.

The burial depth was investigated to determine a theoretical depth where the pure proximity effect was demonstrated.

The resistance for the model electrode reduced with increasing depth until stabilising at 200 m below the surface. Below this depth, the proximity effect would be evident without the influence of burial depth. This stabilisation is shown in Fig. 3 for depths approaching 200 m.

At this depth, the resistance followed the expected exponential curve with a maximum at 90°, as depicted in Fig. 4, demonstrating a reduction in electrode resistance as the coupling between the rods and the main grid is reduced.

From Fig. 4, it can be seen that, due to the proximity effect alone, the optimum angle will be shallow (say, 0° – 10°), horizontally away from the earthing system.

**Effect of soil structure**

*Soil model 1 m top layer thickness – high-upon-low*

The first soil structure simulated was a superficial soil layer of about 1000 Ωm approximately 1 m thick, below which the soil resistivity was an average of about 400 Ωm. The following can be noted from the results shown in Fig 5:

- The minimum resistance is between about 15° and 30°.
- The resistance increases for angles less than 15° despite the benefit of a reduction in proximity effect, as most of the rod is in the soil layer of higher resistivity.
- Past 30°, the majority of the earth rod is in soil of higher resistivity, and the proximity effect dominates, producing a near exponential increase in resistance as the angle increases.

*Soil model 1 m top layer thickness – low-upon-high*

The second soil structure simulated was a 1 m thick top layer of about 400 Ωm with a bottom layer of 1000 Ωm (see Fig. 6).

The following comments can be made:

- The minimum electrode resistance is at 0°, which increases rapidly as the rod approaches and then enters the soil with higher resistivity.
- After about 20°, an increase due to the proximity effect results in a gradual exponential increase which is dampened by a reduction due to increasing depth and therefore increasing soil volume surrounding the rod.

*Soil model 2,7 m top layer thickness – high-upon-low*

The simulations were repeated with a top layer soil thickness of 2,7 m (see Fig. 7). The following salient comments can be made about the results:

- The electrode resistance has a minimum at about 45°. The resistance is insensitive to the installation angle between about 30° and 70°.
- The resistance increases rapidly for angles shallower than about 30° as most of the rod is in the top layer of higher resistivity.
- For angles past 45°, there is a slow exponential increase due to the proximity effect which is offset by increasing burial depth affecting the volume of the soil surrounding the rod.

*Soil model 2,7 m top layer thickness – low-upon-high*

This soil model was a 2,7 m thick top layer with resistivity of 400 Ωm, with a bottom layer of 1000 Ωm (see Fig. 8).

The following remarks are applicable:

- The minimum resistance is at 45°.
- It increases for angles shallower than 15° as most of the rod is in the layer of higher resistivity.

*Soil model 5,5 m top layer thickness – high-upon-low*

This soil model was a 5,5 m thick top layer with resistivity of 1000 Ωm, with a bottom layer of 400 Ωm (see Fig. 9).

- The minimum resistance is for steep angles between 60° and 80°.
- The resistance falls off rapidly for angles larger than about 15° as the rod approaches and then enters the layer of lower soil resistivity. The effect of the soil profile dominates the characteristic as the layer is fairly thick compared to the length of the rod.
- The proximity effect is evident for angles larger than 70°.

*Soil model 5,5 m top layer thickness – low-upon-high*

This soil model was a 5,5 m thick top layer with resistivity of 400 Ωm, and a bottom layer of 1000 Ωm (see Fig. 10).

- The minimum resistance is between 0° and 15°.
- The resistance increases rapidly for angles greater than 15° due to the effect of proximity and due to the fact that that most of the rod is in the layer of higher resistivity.

In this model, the lower resistivity top layer of the soil model, combined with its substantial thickness compared to the other models, strongly favours shallow earth rod angles. The effect of the soil model is potentiated by the reduced proximity effect associated with small angles, resulting in an exaggerated result.

**Conclusion**

The optimum installation angle for an earth rod must be determined for each particular case individually from the soil model. Simulations will determine the best case but, in most situations, the electrode resistance is not sensitive to the angle and the rod is effective over a fairly wide range.

The incorrect angle can produce very poor results. For small electrodes, the effect of earth rods can be significant and the correct application can be worthwhile.

There are several factors that determine the optimum angle:

- Average burial depth of the earth rods (increasing sectional area of soil with depth, for conduction of current).
- The installation angle determines the percentage of the rod that is exposed to layers of lower resistivity.
- The steeper angles increase the proximity effect caused by coupling with the main electrode.

The installation angle affects the proportion of the earth rod that contacts favourable soil. For lower resistivity superficial layers, the proximity effect potentiates the reduction in resistance for shallow installation angles. For lower resistivity at deeper layers, the proximity negates the benefit of steeply driven rods.

The following guidelines may be used with caution:

- In most cases, good results are obtained at angles between 30° and 60° except for specific cases where one effect is dominant. An example are soil profiles with a relatively superficial low-resistivity top layer where, for shallow angles, the contact with better soil dominates the result. For steep angles, the proximity effect dominates.
- The efficacy of the earth rod is not sensitive to the installation angle which is an advantage for practical construction.
- Very small angles of less than 10° or large angles of more than about 80° generally do not produce favourable results for most soil models, except for specific cases where one effect dominates the profile.

This investigation produced interesting results showing how, in different situations, the factors affecting the resistance vary resulting in very different characteristics.

**Acknowledgements**

This article is based on a paper presented at the Earthing Africa symposium and is published here with permission.

**References**

[1] Institute of Electrical and Electronics Engineers: “IEEE guide for safety in AC substation grounding”, IEEE Std 80-2000.

[2] F Yang, S Wang, Z Li, B Zhang and R Zeng: “The new three-dimensional structure of long grounding rods for large-scale substations”, Seventh Asia-Pacific International Conference on Lightning, November 2011.

Contact Gavin Strelec, Eskom, Tel 011 629-5570, gavin.strelec@eskom.co.za