Influence of arbitrary resistivity distribution of ground on the surface potential of earthing systems

Research output: ThesisMaster's Thesis


The aim of this thesis is to give an overview of how the measured soil resistivity of a test area can be used to get a good approximation of the real distribution of soil resistivity in a model. This approximation is the reference model to compare different, simplified models in their behaviour of the surface potential distribution. The effect of this simplification on the error is shown to avoid dimensioning errors of earthing systems.
This work contributes to the question either detailed ground investigation is needed or not.
The following questions and goals are defined:
•How can one derive the "real" resistivity from the apparent resistivity?
•How can the soil model be implemented for a numerical simulation process?
•How does the arbitrary resistivity distribution influence the surface potential?
•What is the influence if the soil model will be simplified (e.g. homogeneous, layered)?
For the measurement a soil measurement unit with an automatic measuring routine is used. The electrodes were in Wenner-alpha configuration. The measurement is a Pseudo-3D measurement, meaning the area is investigated line by line.
The reference model is find by solving the inverse problem with an inversion software.
This found model is then imported into a finite element method software, where the surface potential distribution of a simple earthing system, consisting of two half spherical shaped electrodes, is evaluated. The model is placed in vacuum, so the excitation current can only flow through the model.
In the whole thesis the static current field is used for calculation.
A homogenised model where only the apparent resistivity values are used, shows the biggest error. Using a layered model with the average apparent resistivities shows a better approximation. The best approximation is achieved by using a layered model with the average inversion model resistivities (reference model).
Due to the change of the resistivity in the inversion model along the investigated line, it can be seen that the zero crossing of the surface potential is not in the middle of the electrodes, but slightly before. Therefore the step and touch voltages would be affected due to this horizontal distribution of the resistivity.
For good dimensioning of the earthing system, a detailed ground investigation and inversion process to find a good approximation of the real soil resistivity distribution is necessary. The better the soil measurement, the better is the inversion process, the better is the final soil model. A quick estimation can be easily made with the apparent resistivity.
Due to different soils at different places, no general statement can be achieved by this thesis. To be able to analyse the influence more precisely, several different models would have to be established.
To get better data for the inversion process, the measurement should be made, using a true 3D measurement.
Maybe this type of measurement can be used to find and evaluate the condition of an earthing system.
This thesis shows only the influence on the surface potential. More interesting will be the step voltage. The calculation of the step voltage along a line can be easily made, but maybe there is a way to plot the step voltage somehow in a Difference Plot for the whole surface.
The investigated earthing system consists only of two half spherical shaped electrodes, more complex earthing systems shall be investigated.
The next steps would be taking the soil ionization effect into account, because this effect show a significant reduction of the occuring surface potential, as in [1] shown.
Use the quasi-static magentic field to find the influence of the soil impedances, where also magnetic couplings occur, because power systems normally do not work with static currents.
Translated title of the contributionEinfluss der beliebigen Widerstandsverteilung des Bodens auf das Oberflächenpotential von Erdungssystemen
Original languageEnglish
QualificationMaster of Science
Awarding Institution
  • Graz University of Technology (90000)
  • Friedl, Katrin, Supervisor
Publication statusPublished - Feb 2020

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