General Formulas for Lightning Impulse Impedance of Horizontal and Vertical Grounding Electrodes

Voltage drop developed between the grounding electrode under lightning current and distant neutral ground determines the protection efficiency. The peak value of such voltage can be computed from known impulse impedance and current peak value. For the first time, in this letter, general formulas are derived for impulse impedance of horizontal and vertical electrodes valid for any length up to 100 m, soil's resistivity of 30 to 1000 Ωm, and current impulse front time of 0.2 to 10 μs. Waveforms of typical lightning impulses given in IEC standards are used, but it is shown that results are also relevant for other impulse waveforms. Soil ionization effects are taken into account, and the accuracy of the formulas is investigated. New formulas enable an estimate of lightning protection grounding's surge efficiency in a wide range of practical situations.