Milica Rancic

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.

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.

Analysis of wire antenna structures above lossy homogeneous soil

Characteristics and performance of antennas positioned in the air above lossy half-space are more or less influenced by its electrical parameters. This influence is mathematically expressed by so-called Sommerfelds integrals that are not solvable in a closed form. In this paper, a number of simple approximations will be used for their evaluation. In order to illustrate the range of validity of those approximations, a few practically important antenna structures will be analysed solving the Halléns integral equation and applying the point-matching method. Obtained results will be then discussed and compared to available ones of other authors. Based on presented results, corresponding conclusions will be made.

Simple approximation for accurate analysis of horizontal dipole antenna above a lossy half-space

Horizontal dipole antenna above a lossy ground will be analysed in the paper. Sommerfeld type integrals that express the influence of the ground on antenna characteristics will be solved applying simple approximations. Results for the HDA input impedance/admittance will be graphically illustrated and compared to corresponding ones of other authors.

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.

Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic Volatility

After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes m ...

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

A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate its non-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents’ modelling is illustrated through an essential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape.

Engineering Mathematics II : Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most releva ...

Engineering Mathematics II

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most releva ...