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A fast algorithm is proposed to calculate the lightning electromagnetic field over a perfectly conducting earth surface.

The channel base current is approximated by a number of sub‐domain quadratic functions using the proposed adaptive sampling technique, and the derivative and integral of the channel base current with respect to time can be analytically expressed. With the help of these approximations, the ideal electromagnetic field of the lightning channel can be evaluated along the lightning channel with respect to the height.

The computational time can be greatly reduced using the proposed approach to evaluate the electromagnetic field of a lightning channel in the time domain.

The adaptive sampling technique is a general‐purposed approach, which can be potentially used in other applications to fit a function with the minimal number of intervals.

The electromagnetic field radiated from a lightning channel is the excitation for analyzing the field-to-transmission line coupling problem. The purpose of this paper is to propose a novel efficient approach to evaluate the horizontal electric field of the lightning channel expressed by the generalized Sommerfeld integral.

The asymptotic integral is extracted from the original one, which actually makes the Sommerfeld integral tail reach its convergence very quickly. To handle the sharp variance around k0, a closed-form integral, which is obtained by replacing the original kernel with an approximated function, is presented in detail. The numerical examples validated the proposed approach in the both frequency and time domain.

The approach proposed in this paper has been validated by the comparison with results in other papers. The agreement among these results reaches very well, and the approach proposed in this paper is more efficient and easy to implement, especially for the calculation of the tail integral part.

In accordance with the numerical experiments, the proposed approach can be served as a qualified candidate in terms of computational efficiency to evaluate the electromagnetic field generated by the lightning channel.

The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils.

The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands.

The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors.

The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

The purpose of this paper is to present an original iterative nodal approach to calculate the fault current distribution on overhead lines.

By changing the mutual couplings among different conductors into the equivalent voltage sources, node voltages are updated iteratively by using conventional nodal analysis with those additional sources until the convergence is achieved.

The proposed algorithm can handle the complicated topology of a power transmission line and has no difficulties in taking all physical couplings into account. The fault current distribution calculated by this method is in good agreement with those published in the literature. Although the proposed approach is iterative, the CPU time needed is still reasonable compared to the direct solution approach. The memory requirement is low because the coefficient matrix is highly sparse for the nodal analysis of each iteration loop.

The proposed approach can serve as an alternative in calculating the fault current because of its efficiency and ease of implementation.