As the load on the power system grows and new transmission facilities become increasingly difficult to build, the utilities must look to ways to make the most of the current transmission system. Adaptive relaying is one way to enhance the ability of the power system. On the Florida - Georgia interface an adaptive out-of-step relay is being installed. This relay determines if swings on the power system will remain stable by performing a better then real-time transient stability study. Because of the computing capacity required for a transient stability study, the study cannot be performed on the full power system. A reduced model must be used. In this thesis, various methods of obtaining reduced models for use in the relay will be explored. The models will be verified with a full system model using Electric Power Research Institute's (EPRI) Extended Transient-Midterm Stability Package (ETMSP).