In traditional power systems, the large mechanical inertia of the synchronous generators maintains the system frequency close to 60 Hz. Traditional transient stability programs solve the electrical network at 60 Hz and also use this frequency to convert between power and torque. Currently, however, with the large proliferation of alternative energy sources, larger frequency deviations are often encountered. This paper applies the Shifted Frequency Analysis (SFA) method to transient stability studies. SFA is based on an EMTP discretization of time-varying phasors, which results in the correct electrical frequency for the network admittances. Also, the correct machine velocity is used for the electromechanical equations. Test cases are presented using a classical 3-Bus system and the larger IEEE 39-Bus test system. The results with SFA are very close to the detailed EMTP solution compared to the traditional solution, while using integration steps similar to those of traditional transient stability software.