Intense electrical fields acting for a long time on an insulating material eventually cause its deterioration, due to the interaction of Partial Discharges (PD) with the polymeric surface. This phenomenon leads to the formation of gas-filled fractures where charged particles aree free to move and produce a higher electrical field. The propagation of this defect in the dielectric, giving rise to the Electrical Treeing, is one of the main causes of ageing of insulating pieces of electric cables and can be modeled by a system of PDEs \cite{villa}. In particular one has to model i) the movement of charges in the gas-filled fracture and ii) the evolution of the electric field and potential in both materials. 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 an 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. The derivation of the model follows a reasoning similar to \cite{inge}, \cite{zunino}, %\cite{scialo}, but presents some differences due to the specific features of the problem. 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. For a more accurate representation of the solution around the fracture, where steep gradients and discontinuities may arise, we are moreover considering XFEM. Finally, this model will be coupled with the 1D reduced equations for the movement of charges in the gas-filled fracture, approximated by a one-dimensional graph.