A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray–Rubinstein Formula Fitted by Orthogonal Polynomials

The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray–Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray–Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray–Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray–Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray–Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.