Karl Lundengård

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.

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.

Measured electrostatic discharge currents modeling and simulation

Analytically extended function (AEF) for modeling measured electrostatic discharge (ESD) currents is presented in this paper. This function is used for the IEC 61000-4-2 Standard current and AEF parameters are calculated using least-squares method. Procedure of obtaining function parameters is simple for experimentally measured multi-peaked functions, such as lightning and other ESD currents. Simulation of ESD currents is done by simple electric circuits and using MATLAB.

Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations

Genetic algorithm (GA) is applied for the estimation of two-peaked analytically extended function (2P-AEF) parameters in this paper. 2P-AEF is used for approximation of measured and typical lightning discharge currents. Lightning discharge channel is often modeled as thin-wire vertical antenna at perfectly conducting ground. Engineering lightning stroke models assume that the current along that channel is related to the channel-base current which may be measured at the instrumented tall towers and in triggered lightning experiments. Mathematical modeling of lightning currents is important in verification of lightning strokes models based on simultaneously measured electromagnetic fields at various distances, so as in lightning protection studies, computation of lightning induced effects and simulation of overvoltages in power systems. Typical lightning discharge currents of the first positive, first negative, and subsequent negative strokes are defined by IEC 62305 Standard based on comprehensive measurements. Parameters of 2P-AEF’s approximation of the typical negative first stroke current are determined by GA and compared to approximations obtained by other functions. Measured currents at Monte San Salvatore in Switzerland, at Morro de Cachimbo Station in Brazil, and in rocket-triggered lightning experiments at Camp Blanding in Florida are approximated by 2P-AEFs, and good agreement with experimentally measured waveshapes is obtained.

Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras

Abstract The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of ( p , q )

Modelling of measured lightning discharge currents to tall towers

{(p,q)}

NOVEL APPROACH TO MODELLING OF LIGHTNING CURRENT DERIVATIVE

-deformations of Witt and Virasoro algebras as well as 𝔰 ⁢ 𝔩

Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases

\mathfrak{sl}

Multi-peaked analytically extended function representing electrostatic discharge (ESD) currents

(2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.

On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents

Lightning discharge currents and their derivatives have been measured at instrumented tall towers for a few decades already. Results of those measurements are used for lightning research purposes, modelling of lightning discharges and making improvements in lightning protection. Some of the measured lightning currents are represented in this paper by the multi-peaked analytically extended function (MP-AEF). The same function may be used for lightning current derivatives, thus providing their analytical integration.