Vesna Javor

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.

New Functions for Representing IEC 62305 Standard and Other Typical Lightning Stroke Currents

New functions for approximating various lightning currents, either measured, assumed or generalized in the standard IEC 62305, are presented in this paper. The channel-base current function and its parameters, as well as analytical expressions of this function derivatives, integrals, and integral transformations are given. Parameters of new functions for representing first stroke currents, subsequent stroke currents, and long stroke currents from the standard IEC 62305 are calculated, so as of two-rise front function typical for experimentally measured first negative stroke currents. Results for lightning electric and magnetic field at different distances from the channel-base obtained by using the proposed function and the Modified transmission line model with exponential decay with height are in good agreement with the results from literature, but any other lightning stroke model can be used as well.

Multi-peaked functions for representation of lightning channel-base currents

A new function is presented in this paper for representation of multi-peaked currents of lightning strokes. Experimentally measured lightning channel-base currents often have a few emphasized peaks. If such currents are approximated with a suitable analytical function, having analytical integral and derivative, lightning electromagnetic field is calculated based on some engineering, electromagnetic or other model of lightning strokes. For the function presented in this paper and two engineering models with new attenuation factors, calculated field results at different distances from the channel base are in better agreement with measurements. Analytically obtained Fourier transform of this function is useful for calculations of lightning electromagnetic field at a lossy ground.

Approximation of a double‐peaked lightning channel‐base current

Purpose – The purpose of this paper is to present a new function for approximating lightning channel‐base currents which is useful in return stroke modelling and for calculating lightning electromagnetic fields and induced effects in conductive structures, installations and systems.Design/methodology/approach – The derivative and integral of the function are obtained analytically. Function parameters are calculated to approximate theoretically assumed or experimentally measured first stroke channel‐base currents using least‐squares method. The proposed expressions are useful for calculating lightning electromagnetic field using thin wire antenna approximation and lightning stroke models. Analytically obtained Fourier transform of the function is needed in the case of a lossy ground.Findings – The function can approximate both double and one‐rise front waveshapes, so as faster and slower decaying tails. Some important function characteristics can be chosen prior to the approximation procedure, such as the ...

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.

Application of the Marquardt least-squares method to the estimation of pulse function parameters

Application of the Marquardt least-squares method (MLSM) to the estimation of non-linear parameters of functions used for representing various lightning current waveshapes is presented in this paper. Parameters are determined for the Pulse, Heidler’s and DEXP function representing the first positive, first and subsequent negative stroke currents as given in IEC 62305-1 Standard Ed.2, and also for some other fast- and slow-decaying lightning current waveshapes. The results prove the ability of the MLSM to be used for the estimation of parameters of the functions important in lightning discharge modeling.

Modeling of Lightning Strokes Using Two-Peaked Channel-Base Currents

Lightning electromagnetic field is obtained by using “engineering” models of lightning return strokes and new channel-base current functions and the results are presented in this paper. Experimentally measured channel-base currents are approximated not only with functions having two-peaked waveshapes but also with the one-peaked function so as usually used in the literature. These functions are simple to be applied in any “engineering” or electromagnetic model as well. For the three “engineering” models: transmission line model (without the peak current decay), transmission line model with linear decay, and transmission line model with exponential decay with height, the comparison of electric and magnetic field components at different distances from the lightning channel-base is presented in the case of a perfectly conducting ground. Different heights of lightning channels are also considered. These results enable analysis of advantages/shortages of the used return stroke models according to the electromagnetic field features to be achieved, as obtained by measurements.

Application of the Multi-Peaked Analytically Extended Function to Representation of Some Measured Lightning Currents

A multi-peaked form of the analytically extended function (AEF) is used for approximation of lightning current waveforms in this paper. The AEF function’s parameters are estimated using the Marquardt least-squares method (MLSM), and the general procedure for fitting the p-peaked AEF function to a waveform with an arbitrary (finite) number of peaks is briefly described. This framework is used for obtaining parameters of 2-peaked waveforms typically present when measuring first negative stroke currents. Advantages, disadvantages and possible improvements of the approach are also discussed.

Parameters of lightning stroke currents defining their mechanical and thermal effects

Mechanical and thermal effects of lightning strokes depend on values of the impulse charge and specific energy of a lightning discharge current. For typical lightning currents and different lightning protection levels (LPL) as defined in IEC Std. 62305 these values can be calculated as the integral of channelbase current function and integral of the square of that function. The results presented in this paper for the new channel-base current function (NCBC) are in good agreement with experimentally measured values of these quantities. This function is used for approximating lightning channel-base currents and it provides a very simple calculation procedure. Values of the impulse charge and specific energy are useful for estimating reliability of some lightning protection structure and its parts for the defined LPL.

Fourier transform of the pulse function for application in high voltage technique

One function for approximating pulse quantities in high voltage technique is presented in this paper. Function derivative, its integral, as well as its Laplace and Fourier transform are obtained analytically. Numerical results for the Fourier transform of the pulse function are also presented. The pulse function having adequately chosen parameters is applied in lightning discharge modeling for lightning electromagnetic field calculation and the results are compared to the results from literature.