The analytic expressions of lightning electromagnetic fields generated by tortuous channel with an inclined lower section are obtained by decomposing the current infinitesimal and solving Maxwell's equations. By using the transmission line model and pulse function to express the channel-base current, the influence of length and tilt angle of the oblique part on lightning electromagnetic fields as well as the distribution laws of electromagnetic fields for different azimuth angles are analyzed. The results show that the electromagnetic fields in near area are mainly determined by the lower section of the tortuous discharge channel, and the peak values of electromagnetic fields in different field regions will increase with the increasing of the length of the lower section when L1 is shorter than the distance that return-stroke speed multiplied by peak time. Whereas the length of the lower section is longer than the distance that return-stroke speed multiplied by peak time, the waveforms of electromagnetic fields will overlap each other and won't be influenced by oblique part length of the discharge channel before the return-stroke current arrives at the inflection point. Moreover, the peak values of electromagnetic fields will decrease with the increase of tilt angle (the azimuth angle φ = 2π/3) and azimuth angle, and the impact of channel geometry on the electromagnetic field strengthens with the distance.

In this paper, the effect of the tilt angle of return stroke channel and the stratified lossy ground on the lightning-induced voltages on the overhead lines are studied using the modified transmission-line model with linear current decay with height (MTLL). The results show that the lightning-induced voltages from oblique discharge channel are larger than those from the vertical discharge channel, and the peak values of the induced voltages will increase with increasing the tilt angle. When the ground is horizontally stratified, the peak of the induced voltages will increase with increasing the conductivity of the lower layer at different distances. When the upper ground conductivity increases, the voltage peak values will decrease if the overhead line is nearby the lightning strike point and increase if the overhead line is far from the lightning strike point. Moreover, the induced voltages are mainly affected by the conductivity of the lower layer soil when the conductivity of the upper layer ground is smaller than that of the lower layer ground at far distances. When the ground is vertically stratified, the induced voltages are mainly affected by the conductivity of the ground near the strike point when the overhead line and the strike point are located above the same medium; if the overhead line and the strike point are located above different mediums, both of the conductivities of the vertically stratified ground will influence the peak of the induced voltages and the conductivity of the ground which is far from the strike point has much more impact on induced voltages.