The EMTP software (Electromagnetic Transient Program) for modeling the behavior of electric power systems is commonly used to obtain the transient response of system disturbances, for example caused by fault currents. We have developed specific modules describing practical HTS materials that can be used to describe new architectures involving superconducting power devices, for example fault current limiters. These modules include flux-pinning scaling models that vary smoothly in their parameterization of the J-T-B-E (current density, temperature, magnetic field and electric field) surfaces. In addition, the non-linear low temperature materials properties, such as specific heat, are included for a more accurate description of device behavior. The advantage of this approach is that the complex and non-linear flux-pinning and thermal characteristics of HTS devices can be integrated into power network models. The modeling is presented, with an emphasis on fault current limiters where three domains of operating characteristics are identified.