Lightning Induced Voltages on Power Lines: Theory

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Abstract
Theory is presented which shows that nearby lightning return strokes can induce voltage surges of either positive or negative polarity on an overhead line depending on the location of the lightning relative to the line. The Telegraphers' Equations are solved with the return stroke vertical and horizontal electric fields as forcing functions. The hori zontal electric fields are calculated from measured or assumed vertical fields and assuned earth conductivities. For a typical return stroke, voltage waveforms are presented for a line of 500 m length and one of 5 km length for the following conditions: earth conductivities between 10-2 mhos/m and 10-5 mhos/m, earth permittivities between εϒ= 15 and εϒ= 3, and lightning ground strike points between 0.2 km and 5.0 km of the line at a variety of positions around the line. Measured voltages on a 460 m test line described in a companion paper are compared with calculated voltage waveforms derived from measured vertical electric fields, in accordance with the developed theory. Calculated waveshapes are found to be in moderately good agreement with the measurements, but calculated magnitudes are about a factor of 4 lower than measured. Possible errors in both theory and measurement are discussed. Voltage measurements reported by other investigators are, in general, consistent with the present theory