FINITE-ELEMENT SOLUTION FOR ELECTRIC-FIELDS OF CORONATING DC TRANSMISSION-LINES

Analytical computation of steady-state corona losses on HVDC transmission lines presupposes knowledge of two quantities: of the electric field vector and of the space charge. Both quantities could be sought in the entire interelectrode space, but it is mandatory to know them at least at electrode surfaces. Magnitude and direction of the field vector may be in general determined by superpositions in which effects of the electrode geometry (with defined applied potentials) are combined with those of resultant distribution of space charge (caused by corona activity). This paper approaches determination of ionized electric fields as a proper Boundary Value Problem and concentrates on the numerical solution for the case of the DC field in air when a unipolar space charge is present. Relevant differential equations are suitably formulated and are solved with the aid of the Finite Element Method. On that basis two iterative schemes are defined which render the solution of the ionized field. A simple example of coaxial cylinders, reducible to a one-dimensional problem, is presented to explain the procedure and to obtain valuable insight into such questions as formulation of the problem, details of the computational algorithm, convergence, preferred location of nodes, etc. Experience gained paves the way for extension of the proposed approach to two-dimensional cases that represent closely geometries of actual HVDC transmission lines. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.