Modeling of the Lightning Return Stroke Current at a Tall Structure Using the Derivative of the Heidler Function

Kristofer Bitner

doi:10.32920/ryerson.14653575.v1

Abstract

Traditionally tall structures have been modeled as simple lossless transmission lines. This model is inadequate for the CN Tower, which may be modeled as a series of transmission lines with different characteristic impedances resulting in a reflection coefficient at each discontinuity. Analysis shows that these vary significantly and are related to the ratio of the current derivative peak to the current derivative 10%-90% risetime, suggesting that they are frequency dependent. The magnitude of the reflection from the return stroke front, if it does exist, is much smaller that was previously proposed. An alternative approach to modeling, based on modeling the current derivative, is proposed and it is found to provide a better match with the measured waveforms. The CN Tower is modeled as a series of uniform lossless transmission lines and the channel is represented by the MTLL model. The features of the measured magnetic field waveform are well reproduced.

Highlights

IntroductionMuch has been learned about lightning since Benjamin Franklin’s supposition that it was an electric current and his famous experiment with the kite and key
The measured current derivative and current wave forms were very well reproduced and a reasonable agreement was found between the waveshapes of measured and calculated magnetic field waveforms
The use of the modified transmission line (MTL) model for the tall structure including the structural discontinuities along with the use of the modified transmission line with linear current decay (MTLL) model for the return stroke channel should be used in the modeling of the return stroke current at other tall structures

Summary

Introduction

Much has been learned about lightning since Benjamin Franklin’s supposition that it was an electric current and his famous experiment with the kite and key. The tools of modern science provide us with much better means to study and understand this powerful and dangerous phenomenon. The practical purpose for the study of lightning is the same as it was over 250 years ago, for protection. Lightning has caused untold amounts of damage to life and property, from the hundreds of annual world-wide lightning deaths to the destruction of homes and land due to lightning-caused fires. Lightning backfiashover on power transmission lines can produce currents strong enough to destroy high voltage transformers and deprive populations of electricity. Lightning has been found to cause damage to both the power and electronic systems of wind power plants, most often resulting in power outages [1]

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Conclusion