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On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-3204-617X
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-9635-0301
University of Nis, Faculty of Electronic Eng., Serbia.ORCID iD: 0000-0002-2356-8710
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2016 (English)In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering, Series: Springer Proceedings in Mathematics & Statistics / [ed] Sergei Silvestrov, Milica Rančić, Heidelberg: Springer, 2016, 151-172 p.Chapter in book (Refereed)
Abstract [en]

According to experimental results for lightning discharge currents, they are classified in the IEC 62305 Standard into waveshapes representing the first positive, first and subsequent negative strokes, and long-strokes. These waveshapes, especially shot-term pulses, are approximated with a few mathematical functions in literature, in order to be used in lightning discharge models for calculations of electromagnetic field and lightning induced effects. An analytically extended function (AEF) is presented in this paper and used for lightning currents modeling. The basic properties of this function with a finite number of peaks are examined. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as for the given charge transfer and specific energy is described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach are also discussed.

Place, publisher, year, edition, pages
Heidelberg: Springer, 2016. 151-172 p.
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 178
National Category
Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33097DOI: 10.1007/978-3-319-42082-0_10Scopus ID: 2-s2.0-85015267484ISBN: 978-3-319-42082-0 (print)ISBN: 978-3-319-42081-3 (print)OAI: oai:DiVA.org:mdh-33097DiVA: diva2:963136
Available from: 2016-09-08 Created: 2016-09-08 Last updated: 2017-09-04Bibliographically approved
In thesis
1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Open this publication in new window or tab >>Generalized Vandermonde matrices and determinants in electromagnetic compatibility
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.

In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.

The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.

The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2017
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 253
National Category
Mathematics Mathematical Analysis Computational Mathematics Probability Theory and Statistics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-34864 (URN)978-91-7485-312-4 (ISBN)
Presentation
2017-03-23, Kappa, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2017-02-14 Created: 2017-02-14 Last updated: 2017-03-14Bibliographically approved

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Publisher's full textScopushttps://link.springer.com/chapter/10.1007/978-3-319-42082-0_10

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