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Estimation of Parameters for the Multi-peaked AEF Current Functions
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
(English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713Article in journal (Refereed) Epub ahead of print
Abstract [en]

An examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is presented in the paper. 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 is presented. This framework is used to find parameters for some common waveforms with a single peak, such as Standard IEC 62305 lightning currents. Illustration of fitting a p-peak AEF to recorded lightning current data is also presented.

Keyword [en]
Analytically extended function, Electromagnetic compatibility, Lightning discharge, Marquardt least-squares method
National Category
Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33096DOI: 10.1007/s11009-016-9501-zScopus ID: 2-s2.0-84973100963OAI: oai:DiVA.org:mdh-33096DiVA: diva2:963133
Available from: 2016-09-08 Created: 2016-09-08 Last updated: 2017-02-14Bibliographically 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 textScopushttp://link.springer.com/article/10.1007/s11009-016-9501-z

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