## Theses

Spring 1994

Thesis

#### Degree Name

Master of Science in Electrical Engineering - (M.S.)

#### Department

Electrical and Computer Engineering

Cohen, Edwin

Wu, Shih-Chang

Clements, Wayne I.

#### Abstract

The transient voltage surge caused by lightning is the major source contributed to the disturbance on power systems. The calculation of induced voltages, which is the propagated voltage surge on overhead power lines due to indirect lightning strokes, has been the subject of theoretical and experimental studies. The objective of this research is to develop a comprehensive numerical method to study the induced voltages on an overhead power line caused by a lightning return stroke with arbitrary shapes, for examples inclined lightning, zigzag lightning, etc.

A finite-length lightning channel of any direction in 3-D space has been modelled and closed-form expressions of the inducing potentials have been derived from image theory. The total inducing scalar potential and inducing vector potential caused by an arbitrarily shaped lightning stroke are evaluated by superposition. Because that the presented numerical model simulates the realistic state and takes into account the retarded-height difference between the original sources and the image sources, the bipolar characteristic of the inducing scalar potential as well as the bipolar induced voltage waves are observed.

The final induced voltage is completely composed of two components, one is the traveling voltage wave created by the inducing scalar potential, and the other is the standing voltage wave created by the vertical component of the inducing vector potential. The induced voltage on the power line is calculated by solving the partial differential equations in which the horizontal component of the inducing vector potential is taken into consideration. A computer program has been developed to perform the comprehensive calculations with the use of the finite-difference time-domain method in which the differential equations are converted into difference equations. Through this numerical program, the induced voltage is evaluated as functions of time and space on the power line. The numerical algorithm has been validated by a simulation test on a Gaussian pulse propagation.

With the use of the program, parametric effects on the induced voltage caused by a vertical lightning stroke are inspected systematically. The comparisons of the induced voltage caused by inclined lightning strokes are made under various conditions. The effect of the horizontal component of the inducing vector potential has been illustrated. The results show that the severity of the inclined return stroke on the overhead power line is considerably harmful, especially when the return-stroke velocity gets faster or the inclined angle increases. This high voltage surge should be taken into account in the lightning protection design of transmission lines as well as distribution lines.

COinS