| 1. |
- Javor, Vesna, et al.
(författare)
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Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations
- 2017
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Ingår i: International Journal of Antennas and Propagation. - : Hindawi Limited. - 1687-5869 .- 1687-5877. ; 2017
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Javor, V., et al.
(författare)
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Modelling of measured lightning discharge currents to tall towers
- 2017
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Ingår i: Conference Proceedings - 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2017. - : Institute of Electrical and Electronics Engineers Inc.. - 9781538639160
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 3. |
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| 4. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases
- 2017
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Ingår i: AIP Conference Proceedings. - : American Institute of Physics (AIP). - 0094-243X. - 9780735414648 ; , s. 020094-1-020094-7
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Konferensbidrag (refereegranskat)abstract
- In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process.
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| 5. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Electrostatic discharge current modelling using multi-peaked analytically extended function
- 2017
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Ingår i: Proceedings of 2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech). - : IEEE conference proceedings. - 9789532900712 ; , s. 272-277
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Konferensbidrag (refereegranskat)abstract
- In order to establish realistic requirements for ESD generators used in equipment and device testing, as well as to ensure and improve the repeatability of tests, an analytical expression of real electrostatic discharge (ESD) currents is sought for. It should be adoptable to various test levels, test set-ups and procedures, and also various ESD conditions (approach speeds, types of electrodes, relative arc length, humidity, etc). A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition.
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| 6. |
- Lundengård, Karl, 1987-
(författare)
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Generalized Vandermonde matrices and determinants in electromagnetic compatibility
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 7. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Modelling mortality rates using the powerexponential function
- 2017
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Ingår i: Booklet of abstracts of SPAS2017 - International Conference on Stochastic Processes and Algebraic Structures– From Theory Towards Applications.
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Konferensbidrag (refereegranskat)abstract
- There are many models for the mortality rates of humans and other organisms. A phenomenon that complicates the modelling of human mortality rates is a rapid increase in mortality rate for young adults (in western Europe this is especially pronounced at the age of 25). We will examine models for mortality rates based on power-exponential functions, compare them to empirical data for mortality rates and other models.
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| 8. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents
- 2017
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Ingår i: AIP Conference Proceedings, Volume 1798. - : American Institute of Physics (AIP). - 9780735414648 ; , s. 020093-1-020093-10
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Konferensbidrag (refereegranskat)abstract
- A multi-peaked analytically extended function (AEF), previously applied by the authors to modeling of lightning dischargecurrents, is used in this paper for representation of the electrostatic discharge (ESD) currents. In order to estimate itsnon-linear parameters, the Marquardt least-squares method (MLSM) is used. ESD currents’ modelling is illustrated through anessential example corresponding to approximation of the IEC Standard 61000-4-2 waveshape.
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| 9. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Novel Approach to Modelling of Lightning Current Derivative
- 2017
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Ingår i: Facta Universitatis Series. - Nis, Serbia. - 0353-3670 .- 2217-5997. ; 30:2, s. 245-256
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Tidskriftsartikel (refereegranskat)abstract
- A new approach to mathematical modelling of lightning current derivative is proposed in this paper. It builds on the methodology, previously developed by the authors, for representing lightning currents and electrostatic discharge (ESD) currents waveshapes. It considers usage of a multi-peaked form of the analytically extended function (AEF) for approximation of current derivative waveshapes. The AEF function parameters are estimated using the Marquardt least-squares method (MLSM) and the framework for fitting the multi-peaked AEF to a waveshape with an arbitrary number of peaks is briefly described. This procedure is validated performing a few numerical experiments, including fitting the AEF to single- and multi-peaked waveshapes corresponding to measured current derivatives.
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