Analytical formulation of lightning-induced voltages on multiconductor overhead lines above lossy ground

This paper presents analytical expressions for calculation of lightning-induced voltages (LIV) on multiconductor overhead lines above lossy ground. The transmission-line return-stroke model is used and the propagation effect on the electromagnetic field is approximated by the surface impedance method. Assuming a linear return-stroke current, the standard numerical integrations along the lightning channel and the overhead line are avoided, and the result is a fast and stable formulation that contains only a single convolution integral. The described method applies for distances between 100 m and 10 km and is valid the first few microseconds where the maximum LIV usually occurs. A simplified approach to how to include overhead line losses is also outlined. A model is proposed that can be included in the electromagnetic transients program ATP-EMTP for calculation of LIV in larger and practical systems.