Cooray–Rubinstein Formula for the Evaluation of Lightning Radial Electric Fields: Derivation and Implementation in the Time Domain

Caligaris, Carlo; Delfino, Federico; Procopio, Renato

doi:10.1109/temc.2007.913226

Cited by 72 publications

(34 citation statements)

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“…The limits of validity of the CR formula have been studied by Cooray [2002Cooray [ , 2008Cooray [ , 2010 and by Shoory et al [2005] (and will be discussed later in this section). The time domain counterparts of the CR formula were derived by Caligaris et al [2008] and Andreotti et al [2015]. [2007] have proposed an approximate time domain formula for horizontal electric field and tested its validity within a distance from 100 to 1500 m several meters above ground of conductivity 0.1, 1, and 10 mS/m.…”

Section: 1002/2015jd023245mentioning

confidence: 99%

FDTD simulation of LEMP propagation over lossy ground: Influence of distance, ground conductivity, and source parameters

2015

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We have computed lightning electromagnetic pulses (LEMPs), including the azimuthal magnetic field H φ , vertical electric field E z , and horizontal (radial) electric field E h that propagated over 5 to 200 km of flat lossy ground, using the finite difference time domain (FDTD) method in the 2-D cylindrical coordinate system. This is the first systematic full-wave study of LEMP propagation effects based on a realistic return-stroke model and including the complete return-stroke frequency range. Influences of the return-stroke wavefront speed (ranging from c/2 to c, where c is the speed of light), current risetime (ranging from 0.5 to 5 μs), and ground conductivity (ranging from 0.1 mS/m to ∞) on H φ , E z , and E h have been investigated. Also, the FDTD-computed waveforms of E h have been compared with the corresponding ones computed using the Cooray-Rubinstein formula. Peaks of H φ , E z , and E h are nearly proportional to the return-stroke wavefront speed. The peak of E h decreases with increasing current risetime, while those of H φ and E z are only slightly influenced by it. The peaks of H φ and E z are essentially independent of the ground conductivity at a distance of 5 km. Beyond this distance, they appreciably decrease relative to the perfectly conducting ground case, and the decrease is stronger for lower ground conductivity values. The peak of E h increases with decreasing ground conductivity. The computed E h /E z is consistent with measurements of Thomson et al. (1988). The observed decrease of E z peak and increase of E z risetime due to propagation over 200 km of Florida soil are reasonably well reproduced by the FDTD simulation with ground conductivity of 1 mS/m.

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Section: 1002/2015jd023245mentioning

confidence: 99%

FDTD simulation of LEMP propagation over lossy ground: Influence of distance, ground conductivity, and source parameters

2015

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“…Barbosa and Paulino [114] proposed an approximate time-domain formula for the horizontal electric field whose range of validity was stated to be equivalent to that of the Cooray-Rubinstein formula (which is in the frequency domain). Caligaris et al [115] mathematically derived the timedomain counterpart of the Cooray-Rubinstein formula.…”

Section: ) Use Of Dedicated Algorithmsmentioning

confidence: 99%

Overview of Recent Progress in Lightning Research and Lightning Protection

Rakov

Rachidi

2009

IEEE Trans. Electromagn. Compat.

201

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Abstract-This review paper, prepared for this second special issue on lightning of the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, summarizes major publications on lightning and lightning protection since the first special issue published in November 1998, i.e., during the last decade. The review is organized in the following five sections: lightning discharge-observations, lightning discharge-modeling, lightning occurrence characteristics/lightning locating systems, lightning electromagnetic pulse and lightning-induced effects, and protection against lightning-induced effects.

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“…The CR expression has been originally obtained in the frequency domain, but its counterpart in the time-domain is important when dealing with codes for the analysis of electromagnetic transients in power networks. For this reason, an effort has been made in that respect [18], [19]. In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved.…”

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confidence: 99%

“…For this reason, an effort has been made in that respect [18], [19]. In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved. An in-depth analysis of the formulation presented in [18] and [19] reveals that the kernel of the convolution integral is characterized by a class of functions describing a Dirac delta function.…”

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confidence: 99%

“…In particular, in [18], a timedomain expression has been derived; in [19], the numerical algorithms presented in [18] have been improved. An in-depth analysis of the formulation presented in [18] and [19] reveals that the kernel of the convolution integral is characterized by a class of functions describing a Dirac delta function. It is well known, e.g., [20], that, in this case, any numerical algorithm for the solution of the convolution integral requires a preliminary extraction of the Dirac pulse (irregular term) in order for the algorithms to work on a regular function, and hence to converge according to a desired accuracy.…”

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confidence: 99%

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