The calculation methods on the internal self-inductance and equivalent resistance of conductive cylindrical pipes are explained in consideration of skin effect stems from “Maxwell’s equations related to Faraday’s law, Ampere’s law and Gaussian law” and “electric characteristic within conductors”. The calculation results in the internal selfinductance and the equivalent resistance are shown on the conductive cylindrical pipes made from steel with high relative permeability. The potential difference per meter φ/l along the activated conductive cylindrical pipes stems from the effects on the external self-inductance, the internal self-inductance and the equivalent resistance is compared each other. In the cases 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 the equivalent resistance taken into account the skin effect can be neglected compared to the effect in the external self-inductance on the potential rise. In the cases of the thin conductive cylindrical pipes with small radius 5×10-3 m and the lightning return strokes conductive current characterized by low rising frequency 10/350 μs and small peak 1 kA, the effects in the internal self-inductance and the equivalent resistance are 20 % and 8 % for the effect in the external self-inductance on peak value of the rising potential, respectively. Single Models (conductive cylindrical pipes 600m in length) are proposed for the evaluation.
The Models of high rise towers 600m in height struck by lightning return strokes are proposed to estimate provisional potential along the Models φ. The 15 conductive cylindrical pipes 5×10-1 m in radius made from steel are used for down-conductors of the Models. Grounding resistance is given as 1, 2 and 5 Ω.
The transfer theorem between conductive current Ic and displacement current Id is explained based on the Maxwell’s equation related to Ampere’s law. The Group Models which can calculate the tendencies on the diverging in the displacement current Id and the displacement current density d along the Models of high rise towers struck by lightning return strokes are proposed. A Group Model consists of a cylindrical conductors group and a metallic cylindrical outer coaxial pipe. The provisional potential along Models of high rise towers on each height φ is given to the cylindrical conductors groups. The metallic cylindrical outer coaxial pipes are grounded. Radius of the metallic cylindrical outer coaxial pipe is varying. The tendencies on the displacement current Id and the displacement current density d between the cylindrical conductors groups and the metallic cylindrical outer coaxial pipes are analyzed. The displacement current Id and the displacement current density d are stems from the surface electric field on the outer side in the cylindrical conductors groups evaluated with the Maxwell’s equations related to Gaussian law. The electric field is owing to “provisional potential along Models of high rise towers evaluated on each height φ” and “capacitive coupling on Group Models between cylindrical conductors groups and metallic cylindrical outer coaxial pipes which simulates capacitive coupling between the Models of high rise towers on each height and the flat ground”.
The experimental tendencies on the deformation in the conductive current waveforms of lightning return strokes along high rise towers Ic which have been already measured are introduced. The current peaks Ip and rising frequencies fr on the conductive current Ic drastically decrease corresponding with rise of evaluation height along the towers. Causes of the experimental results are broadly explained stems from the tendencies on the diverging in the displacement current Id and the displacement current density d along the Models of high rise towers analyzed with the Group Models.
The typical waveforms on conductive current of lightning return strokes 10/350 µs and 1/200 µs are selected for the evaluation.