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  • 1.
    Javor, Vesna
    et al.
    Faculty of Electronic Engineering, Department of Power Engineering, University of Niš, Niš 18000, Serbia.
    Lundengård, Karl
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation2017In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, ISSN 0018-9375, Vol. 60, no 5, p. 1415-1426Article in journal (Refereed)
    Abstract [en]

    Lightning discharge currents waveshapes and their derivatives with multiple peaks are measured in artificially triggered lightning experiments and at instrumented tall towers. Such waveshapes are represented in this paper by the N-peaked analytically extended function (NP-AEF) and Marquardt least-squares method is applied for the estimation of its nonlinear parameters. Typical channel-base currents of the first negative, subsequent negative strokes, and positive strokes, based on comprehensive measurements by Berger et al. at Monte San Salvatore in Switzerland, are approximated by NP-AEFs and used in the computation of lightning electromagnetic fields. A new attenuation factor introducing nonlinear current attenuation along the channel is applied within the modified transmission line model (MTLSIN). A lightning return stroke is assumed to have a vertical discharge channel at the perfectly conducting ground. In order to validate this model, calculated lightning electromagnetic fields are compared with the typical, as measured by Lin et al. at various distances from the discharges. Lightning currents and their derivatives measured at the tall towers are also approximated by NP-AEFs. For the measured artificially triggered lightning currents, MTLSIN is applied for the calculation of their electromagnetic fields. These are compared with the measured fields of specific lightning strokes, so as to results of other models.

  • 2.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Niš, Faculty of Electronic Engineering, Niš, Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Application of the multi-peaked analytically extended function to representation of some measured lightning currents2016In: Serbian Journal of Electrical Engineering, ISSN 1451-4869, Vol. 13, no 2, p. 145-155Article in journal (Refereed)
    Abstract [en]

    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.

  • 3.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia..
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal DesignManuscript (preprint) (Other academic)
    Abstract [en]

    Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents' modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current.

  • 4.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Estimation of Parameters for the Multi-peaked AEF Current Functions2017In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1107-1121Article in journal (Refereed)
    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.

  • 5.
    Lundengård, Karl
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Javor, Vesna
    University of Nis, Faculty of Electronic Eng., Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents2016In: 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]

    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 - 5 of 5
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