Thanks to recent scientific achievements, second generation high-temperature superconductor coated conductors (HTS-CCs) can carry enormous current densities with reduced losses. In addition, they are able to switch from a negligible resistivity state to a high resistivity state (quench) in a very fast time. The most promising application for this technology is represented by resistive superconducting fault current limiters (SFCLs). These devices enable us to operate the grid at larger power flows without the need of expensive upgrading interventions. One of the crucial challenge for the design of SFCLs is to deal with the inhomogeneous properties the superconducting materials present. The inhomogeneity of the material properties causes a non uniform transition to the high resistivity state. The consequence is a local heat generation. As HTS-CCs are characterized by low thermal conductivity, the heat does not diffuse longitudinally and the conductors are exposed to local thermal runaway. This Ph.D. thesis focuses on the numerical modelling of (RE)BaCuO-based HTS-CCs for resistive fault current limiter applications. The purpose of numerical modelling is to improve the HTS-CCs thermal stability and to optimize the design of resistive SFCLs. First, we develop a thermal-electrical coupled model that describes the transient response of long length (hundreds of meters) inhomogeneous HTS-CC candidates. The implementation of the inhomogeneous properties is based on Gaussian distributions derived from commercial wires. The electrical part of the model has been tuned to fit experimental measurements made on commercial coated conductors. The thermal part of the model has been validated with the support of finite element methods (FEMs). Then, we extended the modelling of HTS-CCs to SFCL modules. The model of a resistive SFCL has been interfaced with the characteristic parameters of two real medium voltage grids. The effect of the tape inhomogeneity has been analyzed under real fault scenarios. Afterwards, we used FEM calculations to investigate the possibility of improving the thermal stability of commercial HTS-CCs. In this respect, we analyzed the effects of a medium inserted between a HTS-CC and the cooling bath. The benefits of the concept idea has been demonstrated through a simplified 2D electro-thermal model (2D ET). In its turn, the assumptions used to develop the 2D ET model have been validated with a 2D magneto-thermal model (2D MT) and a 3D electro-thermal model (3D ET). The 2D MT model has been used to compare the magnetic and the thermal dynamics of a HTS-CC, whereas the 3D ET model has been used to study the quench propagation across the width and along the length of a HTS-CC.