A New Approach in Calculation of Step Voltages for Complex Grounding Systems by Analytical Considerations Only

Lightning strikes can have devastating effects to human beings. Not only direct strikes, connecting leaders, induced or touch voltages are dangerous, but also step voltages are an issue. Although touch voltages are more critical in terms of mortality rate, in case of step voltages the involved area on ground can be quite large. This is the reason why in half of all cases, where lightning injures human beings, step voltages are responsible. To overcome this threat, the grounding system plays a major roll, when the lightning current should be diverted into ground. An inadequate grounding system may not only lead to a high ground potential rise, it may also lead to high step voltages in direct vicinity to the structure to be protected. However, when a grounding system is planned, step voltages are not considered in detail, because calculation of step voltages is quite time consuming. Some regulations are given for placing down conductors, because the largest ground potential rise exists at the point where the lightning current enters ground. Standards also give information on grounding rod arrangements or grounding rings as well as some simple equations, from which an assembled low frequency grounding resistance can be derived. Nowadays step voltages are calculated using complex simulation tools. Hereby different effects can be taken into account, like soil ionization, travelling waves, dispersion or even complex soil layers. However, most of the time these effects are neglected, because when considering a worst case, soil ionization for instance leads to smaller grounding resistances and in consequence to a lower step- or touch voltage. In this work a new approach is presented, in which an analytical consideration is used to describe a complex grounding system that consists of electric conductors of certain radii. This method has been implemented in a MATLAB algorithm and is able to calculate step voltages on ground level very fast, in a couple of milliseconds. This enables the user to plan a grounding system more efficiently, because the user has a direct response on the step voltage, when a grounding element is adjusted. Because the solution is based on analytical expressions, the method can also give reference information to stationary simulation tools. In this work an overview on the methodology is given, as well as a verification and some examples showing the full potential of this new methodology.