Please cite this article in press as: K. Kajita, et al., Computation of lightning electromagnetic pulses using the constrained interpolation profile method, Electr. Power Syst. Res. (2014), http://dx.doi.org/10.1016/j.epsr.2014.02.017 ARTICLE IN PRESS G Model EPSR-3937; No. of Pages 8 Electric Power Systems Research xxx (2014) xxx–xxx Contents lists available at ScienceDirect Electric Power Systems Research j o ur na l ho mepage: www.elsevier.com/locate/epsr Computation of lightning electromagnetic pulses using the constrained interpolation profile method Kenta Kajita, Yoshihiro Baba ∗ , Naoto Nagaoka, Akihiro Ametani Doshisha University, Department of Electrical Engineering, Kyoto 610-0321, Japan a r t i c l e i n f o Article history: Received 7 November 2013 Received in revised form 13 February 2014 Accepted 17 February 2014 Available online xxx Keywords: Constrained interpolation profile method Electromagnetic field Finite-difference time-domain method Lightning channel model Lightning Maxwell’s equations a b s t r a c t In this paper, a numerical procedure for computing electric and magnetic fields in a three-dimensional space using the constrained interpolation profile (CIP) method is presented. Then, this method is applied to computing electric and magnetic fields, which are generated by a current wave propagating upward along a vertical lightning return-stroke channel. The lightning return-stroke channel is modeled by a phased-current-source array. The spatial and temporal distribution of the lightning return-stroke channel or phase-current-source array is represented by a new simple mathematical function of height, time and channel-base current. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Recently, electromagnetic computation methods have been used frequently in analyzing lightning electromagnetic pulses and surges [1]. Among electromagnetic computation methods, the finite-difference time-domain (FDTD) method [2] and the method of moments (MoM) [3] have been most frequently used. There- fore, their fundamental theories, advantages and disadvantages are familiar to researchers related. On the other hand, methods other than these two are little known. In this paper, a numerical procedure for computing elec- tromagnetic fields in a three-dimensional (3D) space using the constrained interpolation profile (CIP) method [4] is presented. Although the CIP method has been employed in numerical compu- tations in Hydromechanics, it is a sort of new methods in lightning electromagnetic-pulse and surge computations. Then, this method is applied to computing electromagnetic fields, which are gen- erated by a current wave propagating upward along a vertical lightning return-stroke channel located on a flat perfectly conduct- ing ground, and the CIP-computed waveforms are compared with the corresponding waveforms computed using the FDTD method. The lightning return-stroke channel is modeled by a phased- ∗ Corresponding author. Tel.: +81 774 65 6352; fax: +81 774 65 6801. E-mail addresses: dum0316@mail4.doshisha.ac.jp (K. Kajita), ybaba@mail.doshisha.ac.jp (Y. Baba), nnagaoka@mail.doshisha.ac.jp (N. Nagaoka), aametani@mail.doshisha.ac.jp (A. Ametani). current-source array [5]. The spatial and temporal distribution of the lightning channel is represented by a new simple mathematical function of height, time and channel-base current. 2. The theory of the CIP method 2.1. Fundamental The CIP method is one of the finite-difference methods, which was proposed by Yabe et al. [4]. The advection equation for one- dimensional spatial-variable function f(x, t) is given by ∂f ∂t + u ∂f ∂x = 0 (1) where u is the propagation velocity of a wave of interest. As one of the schemes for numerically solving Eq. (1), the upwind finite-difference scheme is known. However, the use of this scheme causes numerical dispersion as shown in Fig. 1, when a relatively coarse grid is used. Differently from the upwind finite-difference method, the CIP method considers not only electric- and magnetic- field values on grid points but also their spatial derivative values there. In principle, therefore, it can suppress numerical dispersions even when a relatively coarse grid is used. The CIP method employs an additional advection equation for spatial derivative given below. ∂g ∂t + u ∂g ∂x = 0 (2) where g = ∂f/∂x. http://dx.doi.org/10.1016/j.epsr.2014.02.017 0378-7796/© 2014 Elsevier B.V. All rights reserved.