*Article* **An E** ffi**cient Method for Calculating the Lightning Electromagnetic Field Over Perfectly Conducting Ground**

### **Xin Liu \* and Tianping Ge**

Department of Electrical Engineering, North China Electric Power University, Baoding 071003, China; gtp970321@163.com

**\*** Correspondence: liuxinncepu@ncepu.edu.cn

Received: 29 May 2020; Accepted: 18 June 2020; Published: 22 June 2020

**Abstract:** In the implementation of the Cooray–Rubinstein formula, the calculation of a lightning electromagnetic field over perfectly conducting ground accounted for most of the computation time. Commonly, evaluating the ideal lightning electromagnetic field is based on the numerical integration method. In practice, only a su fficiently small discretization step is essential to ge<sup>t</sup> an accurate result, which leads to a relatively large number of calculations and results in a lengthy computation time. Besides, the programming is relatively complicated because the propagation of the lightning current along the channel must be considered. In order to increase the e fficiency and simplify the programming, an improved method is proposed in this paper. In this method, the evaluation of the ideal lightning electromagnetic field is equated with a summation of analytical formulae and a simple integral operation, so it would be more e fficient and easily programmed. The validation of the proposed method is demonstrated by some simulation examples.

**Keywords:** lightning; electromagnetic field; analytical formula
