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The calculation methods on the internal self-inductance and equivalent resistance of conductive cylindrical pipes are explained in consideration of skin effect based on “Maxwell's equations related to Faraday's law, Ampere's law and Gaussian law” and “electrical characteristic within conductors”. The calculation results on the internal self-inductance and equivalent resistance are shown on the conductive cylindrical pipes made of steel with high relative permeability. The potential difference per meter ϕ/l along the activated conductive cylindrical pipes stems from the effects on external self-inductance, internal self-inductance and equivalent resistance is compared each other. In the case of the thick conductive cylindrical pipes installed for the main down-conductors of high rise towers for example 5×10−1 m in radius, the effects in the internal self-inductance and equivalent resistance taken into account skin effect can be neglected compared to the effect in external self-inductance on the potential rise. In the cases of the thin conductive cylindrical pipes with small radius 5×10−3 m on the lightning return strokes characterized by low rising frequency 10/350 µs and small conductive current peak 1 kA, the effects in internal self-inductance and equivalent resistance are 20 % and 8 % for the effect in external self-inductance on peak value of rising potential respectively. Single Models (conductive cylindrical pipes 600m in length) are proposed for those evaluations.

journal of lightning research

Evaluation on Conductive and Displacement Current Along Towers Struck by Lightning Return Strokes Based on Exact Estimation in Self- Inductance, Resistance and Capacitance of Down-Conductors with High Relative Permeability