Electric field calculation and the influence of water trees on insulation breakdown in needle–plane geometry

This paper presents analytical and numerical methods for the calculation of the electrical field distribution in the absence and in the presence of water trees in needle–plane geometry. The needle electrode is considered hyperboloidal and conical. A study of different analytical expressions used in literature for hyperboloidal needle–plane configuration reveals that the same values for the electric field are obtained. In order to determine the electric field in conical needle–plane configuration, a numerical method is proposed. The accuracy of this method is proven for the hyperboloidal needle–plane configuration. Using the same method, the electrical field distribution is determinated in conical plane configuration with and without water trees. Water trees generate a very important modification of the electric field distribution. Basically, the electric field decreases inside the polymer zones degraded by water trees and increases outside these zones. Finally, some results of experiments performed on needle–plane specimens with and without water trees are given. A very good correlation is remarked between experimental results and numerical calculations. These results can serve to understand the pre-breakdown behavior of a cable insulation containing needle–plane type defects in the presence of water trees.