Electric Field Enhancement from Semiconductive Protrusions in Extruded Power Cables

The paper deals with calculation of the field enhancement from semiconductive protrusions in high voltage polymeric cables. The scientific community has traditionally used two different equations: The Larmor formula assuming spheroidal shape of the protrusion and the Mason formula assuming hyperboloidal shape. The Larmor equation can only be used for sharp protrusions (small tip radius) that are not representative for the majority of the protrusions found in power cables. On the other hand, the Mason equation has not this restriction, but can give values very much different from those obtained by the Larmor formula. It will be emphasized in the paper that the Mason formula was derived for needle-plane geometries and is therefore not valid for estimation of the field enhancement of protrusions extending into the insulation from a conductive plane. On the other hand, the Larmor formula follows from the analytical solution of the Laplace equation for the electric field outside a spheroidal-shaped protrusion in a plane-plane geometry. It is thus the best available formula for calculating field enhancement from semiconductive protrusions in high voltage cables. The paper will also introduce a new solution to the Laplace equation making it possible to extend the Larmor equation to spheroidal protrusions of all shapes, including those typical for modern cables.