Closed-Form Spectral-Domain Green's Functions for Infinitesimal Current Source in Multilayer Soil

Abstract

This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium that consists of air and multilayer soil. Closed-form kernel functions of the spectral-domain Green’s function for scalar electric and vector magnetic potentials (Lorentz potentials) were obtained for every layer of the multilayered medium as analytic solutions of the systems of linear equations. Validation of the proposed closed-form expressions is performed by numerical solving of the system of linear equations and by numerical comparison with expressions derived from existing closed-form expressions developed for the source layer of the multilayer dielectric medium. For an arbitrary-oriented ICS, scalar electric potential of its horizontal component is chosen as a unique scalar electric potential. Accordingly, dyadic Green’s function of vector magnetic potential is corrected.

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.

Ivan Krolo

Assistant Professor | Department of Theoretical Electrical Engineering and Modelling

Researcher and assistant professor at the Faculty of Electrical Engineering, Mechanical Engineering, and Naval Architecture in Split, with research focus on the development of numerical models for grounding systems and issues related to electrical safety in low-voltage and high-voltage systems.

Dino Lovrić

Associate Professor | Department of Theoretical Electrical Engineering and Modelling

Associate professor at the Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture in Split, with reserch focused on the development of numerical models of grounding systems in various types of soil, particularly in scenarios involving the dissipation of alternating current and transient currents caused by lightning strikes or switching overvoltages, also involved in developing models of dynamic and transient processes in power systems using modern numerical methods.