On the use of lumped sources in a nonlinear lightning return stroke model and extension for evaluating strikes to tall objects

The use of lumped current and voltage sources is investigated in a nonlinear return stroke model that includes the dependence of the channel per‐unit‐length resistance on the lightning current and the variation of the channel impedance with height. First, considering the case of lightning strikes to flat ground, it is shown that equivalent channel currents can be obtained regardless of the lumped source type (current or voltage) connected at the channel base. This equivalency is obtained provided the effect of current reflections coming from the upper part of the channel is taken into account in the derivation of the voltage source waveform, which is made according to a procedure proposed by the authors. The nonlinear return stroke model is then extended for evaluating lightning strikes to tall grounded objects. Two different possibilities are considered for selecting the channel impedances in this case. In one approach, the impedance of each channel segment is calculated by considering its total height to ground whereas in the other approach the distance from each channel segment to the excitation point at the tower top is considered. It is shown that currents calculated along a lossy channel are nearly independent of the considered approach, whereas differences of about 10% are expected in the peak values of currents calculated along a 102‐m‐high object. Also, regardless of the selected approach, relatively small errors are observed in the evaluation of the total charge transferred to ground, which is convenient for allowing a consistent comparison between lightning strikes to flat ground and lightning strikes to grounded objects of different heights. Finally, comparisons with results obtained with the transmission line return stroke model show that the nonlinear interaction between the channel resistance and the lightning current has a moderate effect on the predicted tower currents, as opposed to the channel currents, which are greatly affected by such interaction.