Numerical calculation of earthing electrical field in rocky ground
Abstract
This paper solves the complex picture of the electric potential created by a mesh earth electrode of a high-voltage plant built on karst soil. The finite element method, one of the most important modern methods of numerical analysis, is used in the solution. Due to the specificity of the problem, an extension of the finite element method has been introduced. Known analytical expressions for the contribution of sources included in the function of approximation of the potential by a finite element have been used. This extension has unified the numerical and analytical approaches to the calculation, while retaining the advantages of each of them. The idea was realized by combining the finite element method and the mean potential method. This type of calculation is abbreviated as: numerical-analytical calculation. It solves the field of an earth electrode in soil with an arbitrary surface configuration and an arbitrary degree of heterogeneity. The obtained results have confirmed the correctness of the solution method. The errors in the calculation of the earth electrode potential and the touch voltage are acceptable from the point of view of the design of the earth electrode. Chapter 2 presents the theoretical foundations of the finite element method. The open boundary problem is solved by using a mapped infinite element, and the global system of equations is formed and efficiently solved by the frontal method. Isoparametric mapping is used, so the division of the calculation area into elements is significantly simplified. The performed calculation examples show how the variation of the element mesh affects the accuracy of the calculation. Chapter 3 presents the theoretical foundations of the mean potential method. Calculation examples examine how the method of dividing the earthing conductor into parts (rods) affects the accuracy of the calculation. The conclusions drawn are also valid in the case of numerical-analytical calculation. Chapter 4 presents the theoretical foundations of numerical-analytical calculation. Calculation examples examine the accuracy of the calculation and how it is affected by the variation of the element mesh. It is shown that the numerical-analytical calculation is significantly more stable to the variation of the element mesh than the calculation using the finite element method. In addition, it provides more accurate results and has wider application possibilities. Chapter 5 presents a numerical-analytical calculation of a short rod field located on the surface of layered soil. In the calculation examples made, the deviations are very small, so in this way the so-called theoretical curves of apparent specific resistance for non-layered heterogeneous soil can be calculated. Chapter 6 provides guidelines for further development of numerical-analytical calculation of mesh earthing in karst soil, i.e. in soil of arbitrary configuration.
Slavko Vujević
Professor Emeritus
An expert in electrical engineering, particularly known for his contributions to numerical modeling of electromagnetic phenomena, lightning protection, and grounding. Throughout his career, he was a key member of the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split, where he taught, mentored students, and actively participated in scientific research and international professional organizations.