Search

The Cooray–Rubinstein formula is most widely used to evaluate the horizontal electric field generated by a lightning return stroke over a lossy ground. In this paper, a new method for fast evaluation of the Cooray–Rubinstein formula in time domain is proposed, by means of approximating the integral form of the modified Bessel function of the first kind using Gauss numerical integral. In the proposed method, the integral form of the modified Bessel function of the first kind is expressed by a summation of exponential functions, and a recursive convolution is achieved, which makes the calculation of the Cooray–Rubinstein formula in time domain much more efficient. Besides, the residues and poles due to the expression of the kernel function K( s) can be obtained directly for any ground conductivity and permittivity which makes the method proposed very simple and easy to program. The numerical examples demonstrate the validity and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

Cooray–Rubinstein formula has been extensively used for the evaluation of the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. Considering the good characteristics of the formulation in terms of “step response” kernel $K_{\varepsilon }(t)$ corresponding to the ground surface impedance, proposed by Andreotti et al. recently, a new method for evaluating the Cooray–Rubinstein formula in the time domain is proposed in this paper. In this method, $K_{\varepsilon }(t)$ is first expressed by an integral of exponential function based on the integral formula of the modified Bessel function of the first kind, and then approximated by a piecewise exponential function using the Gauss numerical integration. Finally, taking advantage of the piecewise recursive convolution, the time-domain Cooray–Rubinstein formula for evaluating the lightning horizontal electric field can be calculated accurately and efficiently. The validity and efficiency of the proposed method are demonstrated by the comparisons with the methods in other literature. [ABSTRACT FROM AUTHOR]