A mixed-dimensional multiscale model of partial discharges and electrical treeing

Beatrice Crippa
MOX - Dipartimento di Matematica - Politecnico di Milano
Monday 10th June 2024
Aula Saleri
Electric power is a key component of the energetic system, and one of the main causes of ageing and deterioration of solid insulating components in the electric cables consists in Partial Discharges (PD). They are caused by the effect of high electrical fields acting on dielectric domains for a long time, leading to the formation of gas-filled fractures, in which charged particles are free to move and generate an internal electric field. This process gives rise to the Electrical Treeing, a self-propagating internal defect whose development can be fully described by a coupled system of Partial Differential Equations (PDEs). One of the main challenges consists in the geometry of the crack produced by the Electrical Treeing: a ramification with very small diameter that would require an extremely fine 3D mesh. For this reason we derive a hybrid dimensional 3D-1D system of equations for the electrostatic problem in the gas and dielectric domains, to compute with an affordable cost the electric field responsible for te movement of charges in the gas. In this work we consider a mixed FEM discretization for the 3D and 1D problems and propose some test cases with simple geometry to validate the proposed approach with analytical solution, and perform comparisons with the fully resolved 3D problem. The result of this work will be coupled with the 1D reduced model describing the movement of charges in the gas-filled fracture, consisting in pure transport and diffusion-transport equations solved with a Finite Volume scheme on a one-dimensional graph. Contatti: anna.scotti@polimi.it carlo.defalco@polimi.it