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

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 (Psi/ 1 along the activated conductive cylindrical pipes sterns 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 5x10-(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 5x10(-3) 3 m on the lightning return strokes characterized by low rising frequency 10/350 mu S 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. The Models of high rise towers 600m in height struck by lightning return strokes are proposed to estimate provisional potential along the Models (phi. The 15 conductive cylindrical pipes 5x10(-1) m in radius made of steel are used for down-conductors on the Models. Grounding resistance is given as 1,2 and 5 Omega. The transfer theorem between conductive current I-c and displacement current Id is explained based on the Maxwell's equation related to Ampere's law. The Group Models which can calculate the tendency on the diverging in the displacement current Id and displacement current density j (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 tendency on the displacemnt current Id and displacement current density j(d) between the cylindrical conductors groups and the metallic cylindrical outer coaxial pipes is analyzed. The dislplacement current Id and displacement current density j(d) are sterns from the surface electric field E on outer side in the cylindrical conductors groups evaluated with the Maxwell's equatlons related to Gaussian law. The electric field E is owing to "provisional potential along Models of high rise towers evaluated on each height (phi" and "capacitive coupling on Group Models between cylindrical conductors groups and cylindrical coaxial pipes which simulates capacitive coupling between the Models of high rise towers on each height and the flat ground". The experimental tendency on the deformation in the conductive current waveforms of lightning return strokes along high rise towers I-c which has been already measured is introduced. The current peak I-p and rising frequency f(r) on the conductive current I-c drastically decrease according to rise of evaluation height along the towers. Causes on the experimental results are broadly explained based on the tendency on the diverging in the displacment current Id and displacement current density j(d) along the Models of high rise towers analyzed with the Group Models. The typical waveforms on conductive current of lighting return strokes 10/350 mu s and 11200 mu s are selected for those evaluations.