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On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge CurrentsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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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, p. 151-172Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Heidelberg: Springer, 2016. p. 151-172
##### 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, id: diva2:963136
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt504",{id:"formSmash:j_idt504",widgetVar:"widget_formSmash_j_idt504",multiple:true}); Available from: 2016-09-08 Created: 2016-09-08 Last updated: 2019-06-24Bibliographically approved
##### In thesis

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.

1. Generalized Vandermonde matrices and determinants in electromagnetic compatibility$(function(){PrimeFaces.cw("OverlayPanel","overlay1073960",{id:"formSmash:j_idt786:0:j_idt790",widgetVar:"overlay1073960",target:"formSmash:j_idt786:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design$(function(){PrimeFaces.cw("OverlayPanel","overlay1329412",{id:"formSmash:j_idt786:1:j_idt790",widgetVar:"overlay1329412",target:"formSmash:j_idt786:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions$(function(){PrimeFaces.cw("OverlayPanel","overlay1329454",{id:"formSmash:j_idt786:2:j_idt790",widgetVar:"overlay1329454",target:"formSmash:j_idt786:2:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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