Lightning Induced Voltages on Power Lines: Theory

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 ¿¿= 15 and ¿¿= 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

[1]  A. Sommerfeld.  Über die Ausbreitung der Wellen in der drahtlosen Telegraphie , 1909 .

[2]  C. F. Wagner,et al.  Induced voltages on Transmission Lines , 1942, Transactions of the American Institute of Electrical Engineers.

[3]  Hiroaki Koga,et al.  Lightning Surge Waves Induced on Overhead Lines , 1979 .

[4]  Ashok K. Agrawal,et al.  Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field , 1980 .

[5]  R. D. Hill.  Electromagnetic radiation from erratic paths of lightning strokes , 1969 .

[6]  A. R. Hileman,et al.  The Influence of the Prestrike on Transmission-Line Lightning Performance , 1958, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[7]  R. H. Golde.  Lightning Surges on Overhead Distribution Lines Caused by Indirect and Direct Lightning Strokes [includes discussion] , 1954, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[8]  A. Eriksson,et al.  Lightning-Induced Overvoltages on Overhead Distribution Lines , 1982 .

[9]  E. Philip Krider,et al.  The electric fields produced by lightning stepped leaders , 1977 .

[10]  P. Chowdhuri,et al.  Voltages induced on overhead multiconductor lines by lightning strokes , 1969 .

[11]  Martin A. Uman,et al.  Calculations of lightning return stroke electric and magnetic fields above ground , 1981 .

[12]  Y. T. Lin,et al.  Lighting return-stroke models , 1980 .

[13]  W. S. Price,et al.  Calculation of Transmission Line Lightning Voltages by Field Concepts , 1957, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[14]  J. R. Grant,et al.  Characterization of Lightning Return Stroke Electric and Magnetic Fields From Simultaneous Two- Station Measurements (Paper 9C0949) , 1979 .

[15]  Pritindra Chowdhuri,et al.  Voltage surges induced on overhead lines by lightning strokes , 1967 .

[16]  S. B. Griscom,et al.  The Prestrike Theory and Other Effects in the Lightning Stroke , 1958, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[17]  W. Evans,et al.  High‐speed photographs of lightning at close range , 1963 .

[18]  C. E. R. BRUCE,et al.  The Lightning and Spark Discharges , 1941, Nature.

[19]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[20]  R. H. Golde,et al.  The lightning discharge , 1941 .

[21]  E. Philip Krider,et al.  Radiation field wave forms produced by lightning stepped leaders , 1975 .

[22]  J. R. Carson.  Wave propagation in overhead wires with ground return , 1926 .

[23]  Martin A. Uman,et al.  Transient electric and magnetic fields associated with establishing a finite electrostatic dipole , 1983 .

[24]  S. Rusck,et al.  Induced-lightning overvoltages on power transmission lines with special reference to the overvoltage protection of low voltage networks , 1958 .

[25]  K. Norton.  The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere , 1936, Proceedings of the Institute of Radio Engineers.

[26]  K. Norton,et al.  Propagation of Radio Waves over a Plane Earth , 1935, Nature.

[27]  Martin A. Uman,et al.  The RF spectra of first and subsequent lightning return strokes in the 1‐ to 200‐km range , 1980 .