Journal of Electrostatics 43 (1998) 127—143 Conformal mapping comparison of resistive and capacitive grading materials J.P. Rivenc*, A. Loubie`re, T. Lebey Laboratoire de Ge & nie Electrique, de Toulouse, 118 route de Narbonne, F-31062 Toulouse Cedex, France Received 4 July 1997; received in revised form 4 November 1997; accepted 4 November 1997 Abstract Field concentration is a phenomenon observed in many equipments of electrical engineering. It is very difficult to avoid, however, that it has a very bad influence on insulating materials. In order to reduce the stress which these materials have to withstand, nonlinear “varnishes” have been used as grading materials in many applications such as in stator bars, high-voltage cable connectors, etc. Despite their intensive use, very little is known about the properties required for a grading behaviour. Hence, the scope of this paper is to:  provide an analytical tool based on conformal mapping to predict the potential and field distribution in the case of both linear and nonlinear grading materials  consider some cases for which numerical methods cannot always give a solution  eventually, understand the grading mechanism involved in capacitive and resistive varnishes through an analysis of electromagnetic equations combined to lumped element circuits.  1998 Elsevier Science B.V. All rights reserved. Keywords: High electrical field; Stress grading varnishes; Capacitive and resistive materials; Conformal mapping; Electromagnetic equations 1. Introduction In high-voltage engineering, electrical stresses may become locally so strong that the field enhancement points are considered as the weakest of the insulation. Indeed, in large rotating machines, a phenomenon, known as the needle effect, occurs when conductors, surrounded by an endwinding material, fit into a slot in the stator steel core, as shown in Fig. 1. There, the stress may be locally greater than the air electrical breakdown field. From one part, superficial discharges occur, from another part species such as ozone or gases belonging to the NO  group, are created and react with * Corresponding author. Tel.: 33 5 61 55 67 97; fax: #33 5 61 55 64 52; e-mail: rivenc or lebey@lget. ups-tlse.fr. 0304-3886/98/$19.00  1998 Elsevier Science B.V. All rights reserved. PII S0304-3886(97)00168-X