Lambert W Function Applications in Electrical Insulation Engineering

Mathematical modelling is a fundamental instrument in the development of theoretical validation for experimental results and in their interpretation. The gist of this paper is the application of a special multi-valued function, called Lambert W function, to several aspects of electrical engineering. This multi-valued function serves the purpose of inverting a vast gamut of expressions involving exponential functions, and can be used in many models concerning electrical insulation issues, yielding lower computational times as opposed to other methods solving nonlinear problems. In particular, this paper presents the analytical calculation of parameters for capacitor field and equipotential lines, Paschen’s law inversion, a model for electric field distribution in power cables, the inversion of Schottky and Dissado, Montanari, Mazzanti model for cable life estimation.