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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]

In this study, a method is proposed for expressing the transient ground resistance of the overhead transmission lines (TLs) by the exponential polynomial. The relation of the poles due to the rational approximation of the ground resistance between the ground conductivity, permittivity and the line geometry is fully discussed. A concept of 'normalise poles' is introduced, which makes it very easy to evaluate the poles according to any ground conductivity, permittivity and line geometrical geometry. A new and easily programmed method is achieved which can overcome the uncertain error caused by the conventional vector fitting method when approximating the ground resistance. Based on this method, a recursive convolution can be achieved for analysing the multi‐conductor TLs system, so good efficiency can be obtained. Several examples are provided to demonstrate the validation of the proposed method for evaluating the transient ground resistance with different ground parameters and line geometry, and an application on calculating the lightning induced voltages of the overhead TLs system is also provided. [ABSTRACT FROM AUTHOR]

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]