Predrag D. Rancic

A Channel-Base Current Function for Lightning Return-Stroke Modeling

A mathematical function for the approximation of various lightning channel-base current waveshapes, which can be included in different lightning return-stroke models is presented in this paper. Its derivative, integral, and Fourier transform are determined analytically. The parameters of this function are also calculated according to the waveshapes of the first positive, the first and subsequent negative stroke channel-base currents as given in the International Standard IEC 62305-1.

Vertical dipole antenna above a lossy half-space: Efficient and accurate two-image approximation for the Sommerfeld's integral

A new, simple and general model for near field numerical calculation of the Sommerfelds integral kernel (SIK) that corresponds to introduction of two fictitious images is proposed in this paper. Applying this model, the unknown current distribution (UCD) and input impedance of the vertical dipole antenna (VDA) placed above linear, isotropic and homogenous lossy half-space are determined. For this purpose, the system of integral equations of Hallens type (SIE-H) is used, which was numerically solved using the point-matching method and assuming the UCD in a polynomial form.

Electromagnetic Field in the Vicinity of Lightning Protection Rods at a Lossy Ground

In this paper, the lightning discharge channel in the vicinity of vertical lightning protection rods is modeled in the frequency domain by a vertical mast antenna coupled with vertical parasitic elements. The ground is treated as linear, isotropic, and homogeneous lossy half-space. The vertical mast antenna and the rods are treated as a unique system as for boundary conditions that results in the electric field integral equation (EFIE) for the unknown current distributions along their axes. EFIE is numerically solved by using the method of moments and a polynomial approximation of the current distributions. The influence of the ground is taken into account through a Sommerfeld integral kernel modeled in a simple and very efficient way using one new approximation that can be classified as a two-image approximation. This approximation gives good results in the frequency domain for modeling in both near and far electromagnetic fields.

Model for Analyzing a Pillar Grounding System with Cylindrically-Shaped Concrete Foundation

Abstract Unknown currents along the pillar grounding systems wire conductors are determined in this article. The system consists of a vertical wire electrode inside the cylindrical concrete foundation and a ring electrode fed by two earthing conductors. The article includes one simple procedure for modeling the influence of a concrete cylinder surrounding a vertical ground electrode on a grounding system, which reduces this problem to analysis of an equivalent single wire in the homogeneous ground. Unknown currents of polynomial form are determined, solving the integral equation system using the Method of Moments. Afterward, self-, mutual, and total impedances of the system are determined.

Influence of foundation on pillar grounding system's characteristics

Purpose – The purpose of this paper is to estimate influence of the pillar concrete foundation approximated by a semiconducting semi‐sphere on the pillar grounding system.Design/methodology/approach – Unknown current distributions and impedance of pillar grounding system, which consists of a ferro armature modelled as a single electrode inside concrete foundation, ring electrode and two earthing conductors, are determined in this paper. Concrete foundation is approximated by a semi‐spherical semiconducting inhomogeneity. The expressions for electric scalar potential are formed using the quasi‐stationary image theory, including a recently proposed Greens function for the point source in the presence of a semiconducting sphere. Based on the quasi‐stationary antenna model, unknown currents are determined solving the system of integral equations using the moment method and polynomial approximation for current distributions.Findings – The influence of inhomogeneity is not negligible for real values of specifi...

Square-shaped electrode as pillar grounding system

The pillar grounding system formed of a basic horizontal linear ground square-shaped electrode and an iron armature connected to the main grounding connector is analyzed in the paper. During analysis, a recently proposed procedure for modelling the influence of a concrete cylinder on a grounding system is used. Afterwards, the system of integral equations having leakage currents¿ distributions as unknowns is solved.

Current Distribution and Impedance of Ring Electrode Pillar Grounding System: Quasistationary Antenna Model

Unknown current distributions (UCDs) and grounding impedance of horizontal linear ground ring electrode fed by two earthing conductors are determined in this paper. The position and shape of earthing conductors corresponds to practical realization of such system. In order to solve this problem, quasistationary antenna model of linear grounding system (LGS) is formed. Based on this model UCDs are determined by numerical solving of the system of integral equations using method of moments (MoM) and entire domain polynomial approximation for UCDs. Afterwards, the LGS impedance and electric scalar-potential (ESP) distribution at the ground surface in the pillar surrounding are determined.

One Model of Lightning Discharge Electromagnetic Field in the Vicinity of Single Protection Rod in Frequency Domain

In this paper unknown current distribution (UCD) is determined along vertical mast antenna (VMA) which models lightning discharge channel (LDC) in the vicinity of vertical lightning protection rod (LPR) in frequency domain. Counterpoises of VMA and LPR are modeled by small semi-spherical ground electrodes, while real ground is modeled as homogeneous lossy half-space (LHS). VMA and LPR are treated as unique system as for boundary conditions which results in the System of integral equations of two potentials (SIE-TP) for UCD-s along VMA and LPR. SIE-TP is numerically solved by using point matching method (PMM) and polynomial approximation for the UCD-s. The influence of the real ground, expressed through Sommerfelds integral kernel (SIK), is modeled using new so- called two-image approximation (TIA). This approximation gives good results for modeling in both near and far field. The lightning impulse problem can thus be solved using IFT (inverse Fourier transform) applied to the results in frequency domain obtained for each frequency in the presented way.

Two shifted coupled asymmetrical vertical dipole antennas above a lossy half-space

The unknown current distributions (UCDs) along a system of two coupled asymmetrical vertical dipole antennas arbitrarily placed above a lossy half-space, are determined in this paper. Antennas are fed by two ideal voltage generators of voltages U/sub 1/ and U/sub 2/. The UCDs are determined by numerical solving of system of integral equations of Hallens type (SIE-H) using the point-matching method and the polynomial current approximation. The SIE-H was solved in the so-called symmetrical and asymmetrical working regimes, and afterwards, self- and mutual- admittances/impedances were determined. The influence of the semi-conducting medium, expressed by the Sommerfelds integral kernel (SIK), was modelled in a very simple, general and accurate way.