# Field analysis in power supply lines by integral equation method

liField analysis in power supply lines by integraJ. equation methodll

subm1 tted by FOe, PIK YlJE for the degree of Ph.D

at the University of Hong Kong in December, 1974.

Abstract

In this thesis, the integral equation (I.E.) method has been employed successfully to solve field problems in power supply lines. Though the I.E. method is mathematically quite involved, it is shown that it is possible to treat the integral equation as a system of linear equations. Hence the transformed simultaneous linear equations can be considered as the starting point for solving problems either in overhead

lines or \Ulderground power cables.

In overhead lines, especially in Extra-High-Voltage and Ultra-

High-Voltage systems, an evaluation of the electric field near each conductor, especially the maximum electric field, is essential as corona and radio interference become important considerations in the design of such lines. The I.E. method has many advantages over the other existing methods in calculating the potential gradient at the surface of the overhead lines in that it yieldS reasonably accurate results with comparatively simple numerical computations. The difference between the present method and the existing methods is the basic assumption.

In the I.E. method, subconductor surfaces are treated as equipotential lines whereas in other existing methods, the subconductor surfaces usually do not coincide with the simulated equipotential lines. The method can also be applied equally well to symmetrical or asymmetrical bundle conductors with or without ground wires. Other parameters such as capacitances, potential gradients at the earth surface etc. are also

included in the computer program.

In underground cable systems, the I. E. method proves to be very

effective in tackling the thermal field problem, especially when the cables are buried shallow and thus the earth i s surface can no longer be

treated as isothermal. .It has been found that the thermal resistance (external) obtained wi::;h a non-isothermal earth surface is considerably higher than that obtained under the assuumption of an isothermal earth surface. With non.-isothermal earth surface, the temperature difference on the earth surface between the spot vertically above the cable and the spot at a distance eClual to twice the depth of burial of the cable away could be as high as lOoe. The finite-difference or fini te-?lement method could likewise be used to solve the problem of a non-isothermal ea>:>th surface, but the computer storage re'luired and the execution time would be much more than that using the I.E. method.

Advisor:

School:The University of Hong Kong

School Location:China - Hong Kong SAR

Source Type:Master's Thesis

Keywords:electric lines overhead underground power distribution mathematical models integral equations

ISBN:

Date of Publication:01/01/1975