Inductan: a simple, robust and fast numerical tool to evaluate self-inductance of arbitrarily shaped coil with few windings

We built a numerical tool allowing the evaluation of self-inductance of arbitrarily shaped coils with few windings. This tool named Inductan aims to be relevant, reliable and reasonably fast in order to be integrated in a more complex model. It is based on a formulation involving the vector potential and the Biot & Savart equation. The general equation giving the self-inductance coefficient is simplified according to the hypothesis of the envisaged geometry allowing to transform a 3d integral in a curvilinear integral operating on just one dimension of space. The numerical implementation is presented as exhaustively as possible, with its particular issues linked to the discrete representation of the coil. The tool is validated first on canonical geometry for which it exists an analytical formulation and second with direct experimental measurements obtained on laboratory coils with controlled and known, but not canonical, shapes.