High Temperature Superconducting (HTS) devices are taking an important role in electrical power systems. The Finite Element Method (FEM) often simulates the device in itself, and some simplified models are applied to represent the equipment in electric grid studies, sometimes neglecting its physics. In this scenario, the development of models that can simulate the equipment integrated with the grid may be useful. Due to it, this paper presents a coupling method to link the superconducting devices modelled by 3D FEM to the power electrical system. This model enables an electromagnetic transient analysis. Moreover, by the FEM model, the critical current density of the tape can be examined in the transient period. A saturated iron-core superconducting fault current limiter (SIC-SFCL) will be modeled and connected to the power electrical grid as a study case. The simulation results are compared with experimental data to validate the model.